E\ 
 
 Libris 
 
 K. 
 
 OGDEN 

 
 THE 
 
 METAPHYSICS OF ARISTOTLE.
 
 THE 
 
 METAPHYSICS OF ARISTOTLE, 
 
 TRANSLATED FROM THE GREEK ; 
 
 WITH 
 
 COPIOUS NOTES, 
 
 IN WHICH 
 
 THE PYTHAGORIC AND PLATONIC DOGMAS RESPECTING NUMBERS AND 
 IDEAS ARE UNFOLDED FROM ANTIENT SOURCES. 
 
 iSS^^ 
 
 TO WHICH IS ADDED, 
 
 A DISSERTATION 
 
 ON 
 
 NULLITIES AND DIFERGING SERIES; 
 
 IN WHICH 
 
 THE CONCLUSIONS OF THE GREATEST MODERN MATHEMATICIANS ON THIS SUBJECT ARE 
 
 SHOWN TO BE ERRONEOUS, THE NATURE OF INFINITELY SMALL QL'ANTITIES IS 
 
 EXPLAINED, AND THE TO 'EN, OR THE ONE OF THE PYTHAGOR.^ANS 
 
 AND PLATONISTS, SO OFTEN ALLUDED TO BY ARISTOTLE 
 
 IN THIS WORK, IS ELUCIDATED. 
 
 BY THOMAS TAYLOR. 
 
 SIS ^otvov o(piKos VJ y^ajJiiJ.aa-t Kona'ii^ivog, 
 
 LONDON: 
 PRINTED FOR THE AUTHOR, 
 
 BY DAVIS, WILK3, AND TAYLOR, CHANCERY-LANE, 
 
 AND SOLD B.T J. WHITE, FLEET-STREET; J. JOHNSON, ST. PAUL's CHURCH-YABDJ 
 
 J. CUTHELL, HOLBORN; AND E. JEFFREY, PALL-MALL, 
 
 1801.
 
 \%0\ 
 
 INTRODUCTION. 
 
 A MONG the prodigies of genius who have largely benefited 
 mankind by diflfeminating philofophy, Ariftotle maintains a very 
 diftinguiflied rank. When we confider that he was not only well 
 acquainted with every fcience, as his works abundantly evince, but 
 that he wrote on almoft every fubjedt which is comprehended in the 
 circle of human knowledge, and this with matchlefs accuracy and 
 fkill, we know not which to admire moll, the penetration or extent of 
 his mind. For capacious indeed mull that mind have been which 
 embraced the vaft orb of exiftence, and left nothing unexplored in 
 the heavens or the earth, and penetrating that genius which arrived 
 at the luminous boundaries of human knowledge, and rendered 
 them acceffible to others. With a bold, yet not impious hand, he 
 appears to have withdrawn the awful veil of Nature herfelf, to have 
 dete6led her moll fecret myileries, and ranged through every part 
 of her variegated dominions. In fliort, he feems to have pofTefled 
 and to have exercifed the power of reafoning in the greatell perfec- 
 tion poffible to man ; and fuch of his works as have efcaped the 
 ravages of time will ever be confidered by the genuine lovers of 
 foience, as treafures which from their lingular excellence are def- 
 tined to perifli in no lefs a cataflrophe than that of a deluge or 
 general conflagration. 
 
 * But
 
 11 
 
 INTRODUCTION. 
 
 But of all his works, the following, which is evidently from the 
 nature of it the moft fublime, perhaps no kfs excels in that accu- 
 racy of didtion, fl^ilfulnefs of arrangement, and fecundity of con- 
 ception, for which the Stagirite is every where fo remarkable ; but, 
 at the fame time, it is equally diftinguilhed from the reft by the pro- 
 found obfcurlty in which the meaning of the greater part of it is 
 
 involved. 
 
 Previous, however, to any farther remarks on this work, it will 
 perhaps be better fnft to prefent the reader with a divifion of the 
 books of Ariftotle, that it may appear where his Metaphyfics fhould 
 be placed ; 2dly, to fliow w^hat the end is of his philofophy, and 
 which of his writings lead us to this end ; sdly, what kind of dic- 
 tion he employs ; 4thly, why he defignedly wrote with fuch ob- 
 fcurity ; and, 5thl)% what qualifications are required in an auditor 
 of thf following work. 
 
 Of his remaining works, therefore, fome are theoretic, others 
 pradical, and others inftrumental. Likewife, of thofe books which 
 are entirely theoretic or contemplative, fome are theological, as his 
 Metaphylics ; others phyfical, as his eight books infcribed Phyfical 
 Aufcultation, and the books confequent to this, fuch as thofe On 
 the Heavens, On Generation and Corruption, 8cc. ; and others aga'n 
 are mathematical, fuch as thofe on Mechanics and Indivifible IJnes. 
 In hke manner with refpedt to his pradical writings, fome are 
 moral, as his Nicomachean and Eudemian Ethics, and thofe which 
 are infcribed the Great Morals ; or they are economic and politic, as 
 the books which are thus infcribed. LaftJy, of the books wbicli 
 are called iiiftrumental, fome are on the art of demonftration, as his 
 Laft Analytics, others refpe(5ling things which precede a knowledge 
 of the demonftrative fyllogifm, as his Firft Analytics, his book Oi^ 
 Interpretation, and his Categories ; and others again are refpedting 
 things which often become the fubjed: of demonftration, or ai'e 
 
 fubfervicnt
 
 INTRODUCTION. 
 
 Ill 
 
 fubfervient to it, fuch as his Topics, his books On Sophillical (i. e. 
 apparent) Arguments, and On the Art of Rhetoric. And fuch is the 
 fummary and univerfal divifion of the writings of Ariftotle. 
 
 adly. The end of Ariltotle's moral philofophy is perfedlion 
 through the virtues, and the end of his contemplative philofophy 
 an union with the one principle of all things : for he fcientifically 
 knew and imfolded this principle, as is evident from the twelfth 
 book of the following work, in which he clearly pronounces that 
 the domination of many is not good. The common end, however, 
 both of his moral and contemplative philofophy, which man 
 ought to purfue, is the laft and moft perfed: felicity of which our 
 nature is capable ; and at the end of his Nichomachean Ethics he 
 tertifies that he who arrives at this felicity ought not to be called a 
 man but a god. All the works of the philofopher lead us to the 
 attainment of this end: for fome of them unfold tons the art of 
 demonftration ; others, that we may become virtuous, inftrua; us 
 in morals •, and lallly, others lead us to the knowledge of natural 
 things, and afterwards to thofe luminous beings which are placed 
 above nature. 
 
 With refpeft to his diction, it is of that kind that the words may 
 adhere to the fenfe and the fenfe to the words ; a mode of writing 
 both intelledhial and admirably adapted to the profimdity of his 
 conceptions : for he either immediately gives a folution to a doubt, 
 or, connecting many doubts, he briefly folves all of them by one 
 and the fame folution. He is likewife never willing to deviate: 
 from evidence, which being produced either by intellecfl or fenfe,. 
 he efpecially adduces and celebrates the latter when he difputes 
 with thofe who in every thing confider fenfe as the ftandard of 
 truth. Hence, there is fuch an irrefiltible ftrength in his demon- 
 ftcations, that, when he cannot perfuade by affumptions not rafhly 
 introduced, he at lealt procures aflent by the force of neceflity. 
 
 a 2. Thi5j.
 
 iv INTRODUCTION. 
 
 This, too, is peculiar to Ariftotlc, that he was never willing to 
 depart from nature, but even contemplated things which tranfcend 
 nature through a natural habit and knowledge; juft as, on the con- 
 trary, the divin€ Plato, after the manner of the Pythagoroeans, con- 
 templated whatever is natural fo far as it partakes of that which is 
 divine and above nature : fo that the former confidered theology 
 phyfically, and the latter phyfics theologically. He likewife never 
 employs fables and enigmas, and never afceilds into the marvellous 
 and the myftic, but adopts obfcurity as a fubllitute for every other 
 veil, and involved mode of writing ; the reafon of which we pro- 
 pofecl to inveftigate, as the fourth object of inquiry. 
 
 Thofe more antient than Ariftotle, thinking that it was not fit to 
 expofe their wifdom to the multitude, inftead of clear and explicit 
 diction, adopted fables and enigmas, metaphors and fimilitudes ; 
 and under thefe, as veils, concealed it from the profane and vulgar 
 eye. But the Stagirite praifes and employs obfcurity, and perhaps 
 accufes and avoids philofophical fables and enigmas, becaufe fome 
 interpretation may be given o'f them by any one, though their real 
 meaning is obvious but to a few. Perhaps, too, he was of opinion 
 that fuch obfcurity of di(5tion is better calculated to exercife the 
 mind of the reader, to excite fagacity, and produce accurate atten- 
 tion. Certain, indeed, it is, that the prefent fafliionable mode of 
 writing, in which every author endeavours to adapt e\'ery fubjedl 
 to the apprehenfion of the meanefl. capacit)^, has debilitated the un- 
 derftanding of readers in general, has fubjecSted works of profound 
 erudition to contempt merely becaufe they are not immediately ob- 
 vious, and, as if the highell; truths were on a lc\el with the fidlions 
 of romance, has rendered inveitigation difguil:ing whenever it is 
 abilrufe. That this obfcurity, however, in the writings of Arillotle 
 does not arife from imbecility, will be obvious to thofe w^ho are but 
 inodcrately fl^iilled in rhetoric : for fuch is the wonderful compref- 
 
 lion,
 
 INTRODUCTION. v- 
 
 lion, fuch the pregnant brevity of his di6lion, that entire fentences 
 are frequently comprifed in a few words ; and he condenfes in a hne 
 what Cicero would dilate into a page. His books On Meteors, his 
 Topics, and his Politics likewife evince that he was capable of 
 writing with perfpicuity as well as precifion ; and among his loft 
 works, Simplicius informs us that his Epiftles and Dialogues were 
 moft elegantly written. Indeed, fays he, none even of the moft 
 illuftrious writers is equal to Ariftotle in epiftolary compoHtion. 
 
 And lallly, the qualifications which are peculiarly requilite in an 
 auditor of the following work are a naturally good difpofition, a 
 penetrating fagacity, and an ardent love of truth. For, as he is here 
 led to the contemplation of eternal and immoveable natures, and 
 the firft caufe of all things, a naturally good difpofition is neceflary, 
 that he may pofTefs the moral as preparatory to the reception of 
 the theoretic virtues. Penetrating fagacity is likewife neceflary, 
 from the unavoidable obfcurity of the fubje(5t, and from its being 
 laft in the progrefhons of human tmderflanding, though firft in the 
 nature of things. To which we may add, that to fee diftin6tly that 
 there are other objects more real than thofe of fenfe, to elevate the 
 mental eye to the principles of things, and gaze on their dazzling 
 fpiendor, requires no common acutenefs, no fmall degree of pe- 
 netration. And both a good difpofition and fagacity will be un- 
 equal to the tafk, unlefs attended with an ardent love of truth : for 
 this is the wing by which the mind rifes above fenfe, and fbars to 
 the fummit of philofophy, 
 
 1 he defign of Arirtotle in this work is to lead us from forms 
 merged in, or infeparable from, matter, to thofe forms which are 
 entirely immaterial, and which, in his own words, are the moil 
 luminous of all things. But he conflders thefe forms fo far only as 
 they are beings ; or, in other ^A'ords, fo far as they are the progeny 
 of one firft being, and are chara6terifcd by cfTence. Nothing, 
 
 therefcivc,
 
 ■vi INTRODUCTION. 
 
 therefore, is difciiffed in this work pertaining to will or appetite, or 
 any tiling of this kind, becaufe thefe are vital powers ; nor to fen- 
 fation, the dianoetic - energy ancl intelligence, becaufe thefe are the 
 properties of gnoflic natures. Hence, we fhall find that the Meta- 
 phyfics of Ariftotle unfold all that is comprehended in the great orb 
 of being, fo far as every thing which this orb contains is llamped 
 as it were with the idiom of its fource. The fame thing is like- 
 wife efFedted by Plato in his Farmenides ; but, as we have before 
 obferved,. more theologically, conformably to the genius of his phi- 
 lofophy, which always confiders nature fo far as fhe is fufpended 
 from divinity. The Metaphy fics of Ariftotle are, therefore, the fame 
 with the mod fcientific dialectic of Plato, of which the Parmenides- 
 of that philofopher is a moft beautiful fpecimen, with this differ- 
 ence only, that in the former the phylical, and in the latter the 
 theological, character predominates. 
 
 That the reader, however, may be convinced of this, it will be 
 requilite to be more explicit, and to lliow in what the employment 
 of fcientific dialectic confifts. The bufmefs, then, of this firft of 
 fciences is ta employ definitions, divifions, analyfations,. and de- 
 monllrations, as primary fciences in the inveftigation of caufes ; 
 imitating the progreffions of beings from the firft principle of 
 things, and their continual converfion to it as the ultimate objedb 
 of defire. '* But there are three energies," lays Proclus -}-, " of this- 
 moft fcientific method r the firft of which is adapted to youth, 
 and is ufefui for the purpofe of roufing their intelle<5b, which is, 
 as it were, in a dormant ftate ; for it is a true exercife of the eye of 
 the foul in the fpeculation of things, leading forth, through oppo- 
 fite pofitions, the efiTential impreflion of ideas which it contains, 
 
 * For an explanation of this word fee the end of this IntrodudioHi 
 t In Parmenid. lib. L 
 
 an4
 
 INTRODUCTION. vii 
 
 Snd confidering, not only the divine path as it were, which con- 
 ■dudls to truth, but exploring whether the deviations from it con- 
 tain any thing worthy of belief; and laftly, ftimulating the all- 
 various conceptions of the foul. But the fecond energy takes 
 place when intelledl refts from its former invelligations, as becom- 
 ing moft familiar with the fpeculation of beings, and beholds 
 truth itfelf firmly eifabliflied upon a pure and holy foundation. 
 And this energy, according to Socrates, by a progreffion through 
 ideas, evolves the whole of an intelligible nature, till it arrives at 
 that which is firft ; and this by analyfing, defining, demonflrating, 
 and dividing, proceeding upwards and downwards, till, having 
 entirely inveftigated the nature of intelligibles, it raifes itfelf to a 
 nature fuperior to beings. But the foul, being perfedtly ellabliflied 
 in this nature, as in her paternal port, no longer tends to a more 
 excellent obje6l of defire, as fhe has now arrived at the end of her 
 fearch : and you may fay that what is delivered in the Phaedrus 
 and Sophifta is the employment of this energy, giving a twofold 
 divifion to fome, and a fourfold to other operations of the dialectic 
 art; and, on this account, it is affigned to fuch as philofophize 
 purely, and no longer require preparatory exercife, but nourifli 
 the intellect of their foul in pure intelle<5tion. But the third energy, 
 which is exhibitive according to truth, purifies from twofold igno- 
 rance *, W' hen its reafons are employed upon men full of opinion ; 
 
 and this is fpoken of in the Sophifta f," 
 
 hi 
 
 * That i?, when n man is ignorant that he is ignorant : and this is the dlfcafe 
 of tlie iiuiltitude. 
 
 •j- The fame incomparable man likewifc in the fame iiivahiablc work fusilier 
 obferves concerning this mafier fcience as follows : 
 
 " The di.iledic method is irreprehenfible and moft expeditions ; for it is con- 
 nate with things themfelves, and employs a multitude of powers in order to the 
 attainment of truth. It likewifc imitates intelle<5l, from which it receives its ])rin- 
 
 ciplcs,
 
 viii INTRODUCTION. 
 
 In this laft mentioned dialogue, Plato thus unfolds the employ- 
 ment of his dialedlic. " Guejl. Do we not fay, that to divide 
 according to genera, and neither to think that the fame fpecies is 
 different, nor a different fpecies the fame, is the bufinefs of the 
 dialed:ic fcience? 'Tbea. We do fay fo. GueJl. He, therefore, 
 who is able to do this, fufficiently perceives one idea every way 
 
 ciples, and afcends through well-ordered gradations to being itfclf. It alfo termi- 
 nates the wandering of the foul about fenfiblcs ; and explores every thing by 
 methods which cannot be confuted, till it arrives at the ineffable principle of things. 
 
 " The multitude, however, are unacquainted with the power of dialectic, and are 
 ignorant that the end of this fcientific wandering is truth and intellect : for it is 
 not poffiblc for us to recur from things laft to fuch as are firft, except by a progrcf- 
 fion through the middle forms of life. For, as our defcent into the realms of mor- 
 tality was effected through many mediums, the foul always proceeding into that 
 which is more compofite,, in like manner our afcent muft be accomplished through 
 various mediums, the foul refolving her compofite order of life. In the firft place, 
 therefore, it is rcquifitc to defpife the fenfcs, as able to know nothing accurate, 
 nothing fane, but poflcfling much of the confufed, the material, and the paflive, 
 in confequence of employing certain inftruments of this kind. After this, it 
 follows that we fliould difmifs imaginations, thofe winged Stymphalidas of the foul, 
 as alone pofteffing a figured intelle<ftion of things, but by no means able to appre- 
 hend unfigurcd and impartible form, and as impeding the pure and immaterial in- 
 telledtion of the foul, by intervening, and difturbing it in its inveftigations. \x\ 
 the third place, w-e muft entirely extirpate multiform opinions, and the wandering 
 of the foul about thefc ; for they are not converfant with the caufcs of things, nor 
 do they procure for us fcience, nor the participation of a fcparate intellcd. In 
 the fourth place, therefore, we muft haftily return to the great lea of the fciences, 
 and there, by the affifiance of dialccftic, furvey the divlfions and compofitions of 
 ihefc, and, in ftiort, the variety of forms in the foul, and, through this furvey un- 
 weaving our vital order, behold our dianoetic part. After this, in the fifth place, it 
 is rcquilite to- fcparate ourfelves from compofition,. and coiitemplate by intclle6tual 
 energy true beings : for intclledl; is more excellent than fcience ; and a life accord- 
 ing to-intclIe<3 is preferable to that whiclris according to fcience. Many, therefore, 
 arc the wanderings of the foul : for one of thcic is in imaginations, another ia 
 opinions, and a third in the dianoetic power. But a life according to intclledt is 
 alone incrratic. And this is the myftic port of the foul, into which Homer con- 
 diwils Ulyilcs,, after an abundant wandering of lite." 
 
 extended
 
 INTRODUCTION. ix 
 
 extended through many things, the individuals of whtch are placed 
 apart from each other, and many ideas different from each other 
 externally comprehended under one, and one idea through many- 
 wholes conjoined in one ; and laftly, many ideas every way divided 
 apart from each other. This is to know fcientifically how to di- 
 ftinguifli, according to genus, in what refpedl particulars communi- 
 cate, and how far they do not communicate, with each other." 
 Here genus is fignified by one idea extended through many : for genus 
 is not an aggregate of fpecies, as a whole of parts, but it is prefent 
 to every fpecies, to which it is at the fame time prior. 
 
 But every fpecies fubfifling feparate from other fpecies, and from 
 ^enus itfelf, participates of genus. By many ideas^ different from 
 £ach other ^ but externally comprehended imder one idea, which is ge- 
 nus, fpecies are fignified ; externally comi^rehended indeed, as 
 being exempt from fpecies, but comprehending the caufes of fpe- 
 cies : for genera, truly fo called, are both more antient and more 
 efiential than the fpecies which are ranked under them. Of 
 genera, alfo, fome have a fubfiftence prior to fpecies, but others 
 fubfift in them according to participation. To perceive thefe two, 
 therefore, viz. one idea extended through many, the individuals 
 of which fubfiic apart from each other, is the province of the 
 divijive power of dialc61ic ; but the other two pertain to the dcjiniti'js 
 power of this art : for definition perceives one idea through many 
 wholes conjoined in one, and coliefls into one definite conception 
 many ideas, each fubfifting as a Vviiole. It alfo connedtg them vatU 
 ipach other, and perfeds one idea from the alTumption of all wholes ; 
 conjoining the many in one. Befides this, it confiders the many 
 y.'hich it has collcdled in one, lying apart, and the whole which is 
 produced from them. 
 
 . PJatQ has given molt happy fpeclmcns of that pa^t o£thc dialeaic 
 
 b art
 
 % INTRODUCTION, 
 
 ait which proceeds through oppofite arguments, and alfo of thaC 
 ■which is alone converfant with the confutation of the falfe. Hence, 
 Socrates exercifes young men hke a god, conildering (as in the 
 Theeetetus) whether that which appears to everyone is true or not, 
 and whether fcience is fenfe or not. In the Lyfis, alfo, where he- 
 inveftigates what a friend is, at one time lie evinces that the fimilar 
 is a friend to the fimilar, and at another time, that the contrary is a 
 friend to the contrary. And, at one time, that the lover is a friend, 
 and at another the beloved. An exercife of this kind, therefore, is 
 adapted to }'oung men who are lovers of learning, and who poffefs 
 a manly ftrength of mind, that they may not be wearied in their 
 inveftigations. But, when he contends with the Sophifls, who 
 pretend to be fkilled in all fciences and arts, he employs the elendic 
 modes of diale<5lic, evincing, that in their affertions they contradid; 
 themfelvcs, till, being vanquiflied on all fides by this artifice, 
 {7roc^ax^ovc[/.svoi , they are made fenfible of their own falfe wifdom,. 
 and become purified from erroneous opinion. The Gorgias, too, 
 and Protagoras are full of this kind of dialedic, and fuch other 
 dialogues as are intended as a defence againft the attacks of the 
 Sophifts, fuch as the contefts in the Republic with Thrafymachus.. 
 But when the perfons of the dialogue neither require reproof, nor 
 exercife, he extends the firlf energy, and genuinely unfolds the 
 •truth of dialectic ; as when Socrates in the Phasdo, eftablifiiing 
 certain hypothcfes, and invelligating things confequent to thefe, 
 fhows that the foul is not the recipient of that which is contrary to 
 itfelf, viz. death ; and, having demonfirated this to thofe who are 
 prefent, he again refers them to the firfi: hypothefes, and defires 
 them to confider whether they are true. 
 
 The dialectic energy therefore is triple, either fubfifting through 
 oppofite arguments, or alone unfolding truth, or alone confuting 
 
 falfehood i
 
 INTRODUCTION. xi 
 
 falfehood : and the reader will find the firft of thefe energies em- 
 ployed by the Stagiritc in his fcientific enumeration of doubts, and 
 the other two in the remaining parts of this work. 
 
 In the courfe of this work, Ariftotle denominates this metaphy- 
 seal fcience at one time zv/fdom^ at another time ibe Jirjl philofophyy 
 and at another theology ; fignifying, by each of thefe appellations, 
 that it does not rank among thofe arts and faiences which are con- 
 verfant with the knowledge of things necelTary, or which inquire 
 into things fubfervient to the advantages and conveniencies of the 
 mortal life, but that it is a knowledge and fcience to be purfued 
 for its own fake, and which fpeculates the firft principles and 
 caufes of things ; for thefe are beings in the moft eminent degree. 
 Hence, in the fixth book, of his Nicomachean Ethics, he defines 
 wifdom to be the moft accurate of fciences, the fcience of things 
 moft honorable, that is, principles, and the fummit of all difciplines. 
 With the multitude, indeed, merged in fenfe, whatever does not 
 contribute to the good of the merely animal life, is confidered as a 
 thing of no value ; and hence, by the better part of them it is 
 regarded with indifference, and by the greater number with con- 
 tempt. It is vain to talk to fuch as thefe of a good purely in- 
 telledtual, which is independent of chance and fortune, which is 
 defirable for its own fake, and which confers the moft pure and 
 permanent felicity on its pofTeffor : for, what pafTion can it gratify ? 
 Avhat fenfe can it charm ? Ignorant of the mighty difference be- 
 tween things neceflary and fuch as are eminently good, they 
 miftake means for ends, purfue the flying mockeries of being, for 
 fuch are all fenfible natures, and idly attempt to gralp the phan- 
 toms of felicity. 
 
 The conceptions of the experimental philofopher who expecfts 
 to find Truth in the labyrinths of matter, are, in this refpecSl, not 
 tfcuch more elevated tlian thofe of the vulgar : for he is ignorant 
 
 b 2 that
 
 lii INTRODUCTION'. 
 
 that Truth is tlie moll fplemlicl of all things, that fhc is the conftanS 
 companion of Divinity, and proceeds together with him through 
 the u'livcrfe ;- that the fliining traces of her feet are only confpi- 
 ciious in form ; and that in the dark windings of matter llie left 
 nothing hut a moft otfcure and fleeting refemblance of hcrfelL 
 This delufive phantom, however, the man of modern fcience ar- 
 dently explores, unconfcious that he is running in profound dark- 
 nefs and infinite perplexity, and that he is hallening after aiT 
 object which eludes all detedlion, and mocks all purfuit. 
 
 It is well faid indeed by Ariftotle, that wifdom is the fcience of 
 principles and caufes, fince he w'ho knows thefe, knows alfo the 
 effecfls of which they are the fource. Such a one knows particulars 
 fo far as they are comprehended in univerfals, and this knowledge 
 is fuperior to that which is partial, and co-ordinated to a partial 
 objecSt : for, does not every thing energife in a becoming manner^ 
 Avhen it energifes according to its own power and nature ? As, for 
 inftance, does not nature, in conformity to the order of its eflence, 
 energife naturally, and intellecft intelledtually ? for, this being: 
 admitted, it follows that knowledge fubfifts according to the na- 
 ture of that which knaws, and not according to the nature of that 
 which is known. Particulars, therefore, when they arc beheld 
 invelopcd in their caufes, are then known in the moft excellent 
 manner ; and this is the peculiarity of intelleftual perception, and 
 refembles, if it be lawful fo to fpcak, the knowledge of Divinity 
 himfelf. For, the moft exalted conception we can form of his 
 knowledge is this, that he knows all things in fuch a manner as is 
 accommodated to his nature, viz. divifible things indivifibly, things 
 multiplied uniformly, things generated according to an eternal 
 intelligence, and totally whatever is partial. Hence, he knows fen- 
 fiLles v.ithout poftefting fenfe, and, without being prefent to things 
 in place, knows them., prior to all local prefence, and imparts to 
 
 every
 
 INTRODUCTION. >ii» 
 
 every thing that which every thing is capable of receiving. The 
 nnftable elTence, therefore, of apparent natures is not known by 
 him in an unftable, but in a definite manner ; nor does he know 
 that which is fubje<fl to all- various mutations dubioufly, but in a 
 manner perpetually the fame ; for, by knowing himfelf, he knows 
 every thing of which he is the caufe, pofleffing a knowledge 
 tranfcendently more accurate than that which is co-ordinate to the 
 objects of knowledge. Hence, in order to know fenfible natures, 
 he is not indigent of fenfe, or opinion, or fcience ; for it is himfelf 
 that produces all thefe, and that, in the unfathomable depths of 
 the intelle6lion of himfelf, comprehends an united knowledge of 
 them, according to caufe, and in one llmplicity of perception. 
 
 Wifdom, therefore, confidered as a caufal knowledge of particu- 
 lars, refembles the knowledge of Divinity, and is confequently molt 
 honorable and moif excellent. And hence the wife man, from 
 refembling, muft be the friend of Divinity. Beautifully, therefore, 
 is it obferved by Ariil:otle, " That the man who can live in the 
 pure enjoyment of his intelledt, and who properly cultivates that 
 divine principle, is happieil in himfelf, and moft beloved by the 
 gods : for, if the gods have any regard to what paffes among men 
 (as it appears they have), it is probable that they will rejoice in 
 that which is moft excellent, and by nature the moft nearly allied 
 to themfelves ; and, as this is intelleil, that they will requite the 
 man who moft loves and honors this, both from his regard to 
 that which is dear to themfelves, and from his adiing a part which 
 is laudable and right *J' 
 
 The 
 
 * The above tranflation is from the Hermes of Mr. Harris, p. 302. This moft 
 elegant fcholar had the happy art of uniting, in his occafional tranflations from 
 anticnt writers, perfpicuity with precifion, the exd£i manner with the accurate 
 meaning of his author. And it is much to be regretted that he fo foon abandoned 
 
 the
 
 xiv INTRODUCTION. 
 
 The contemplative or intelle6lual energy indeed, when it is pof- 
 feffed in the higheft perfedtion of which our nature is capable, 
 railes its poffeflbr above the condition of humanity. " For a life 
 according to intelled;,'* fays the Stagirite, " is more excellent than 
 that which falls to the lot of man : for he does not thus live, fo 
 far as he is man, but fo far as he contains fomething divine. And 
 as much as this divine part of him differs from the compofite, fo 
 much alfo does this energy differ from that of the other virtues. If, 
 therefore, intelle6t compared with man is divine, the life alfo which 
 . is according to intelle<5t will be divine with refpeft to human life. 
 It is however requifite, that we fliould not follow^ the exhortations 
 of thofe who fay that man fliould be wife in human, and a mortal 
 in mortal concerns, but we lho\ild endeavour as much as poUible 
 to immortalize ourfelves, and to do every thing which may con- 
 tribute to a life according to our moft excellent part. For this, 
 though it is fmall in bulk, yet far tranfcends all the other parts 
 in power and dignity." After this, he fliows that intellect is the 
 true man, from its being that which is moft powerful, principal, 
 and excellent in our nature ; " fo that," fays he, " it would be abfurd 
 not to choofe that which is our proper life, but that which belongs 
 to fomething different from ourfelves." 
 
 Ridiculous, therefore, as well as grovelling are thofe conceptions 
 which lead men to value knowledge fo far only as it contributes to 
 
 Ihe philofophy of Plato and Aiifiotlc, after he had fo fucccfsfully fludicd the cate- 
 gories of the latter, and formed fuch jufl: conceptions of the fublime do61rines of 
 the former. He appears indeed to have furveycd that philofophy as a building 
 whole foundations cannot be Ihakcn, and vvhofe lummit reaches the heavens. He 
 may be faid to have even afccnded the rock on which this mighty building flands, 
 and to hine opened its everlafiing gates ; but, dazzled by the excefTive fplendour 
 which biirft upon him from its moll interior reccflcs, he timidly withdrew to the 
 neighlxanng valley of Philology, and, having entered the temple of that goddefs, 
 immediately became one of her moft illuftrious votaries. 
 
 the
 
 INTRODUCTION, tv 
 
 the neceffities, the comforts, and rhe refinements of the merely 
 human hfe; and partial and unfcientific is that definition of virtue, 
 which makes its higheft energies to be thofe of morality : for 
 moral virtue is more human, but intelleiftual more divine. 7 he 
 former is preparatory to felicity ; but the latter, when perfect, is 
 accompanied with perfect beatitude. Virtuous, therefore, is the 
 man who relieves the corporeal wants of others, who wipes away 
 the tear of forrow, and gives agony repofe ; but more virtuous he, 
 who, by dilTeminating wifdom, expels ignorance from the foul, 
 and thus benefits the immortal part of man i for it may indeed 
 be truly faid, that he who has not even a knowledge of common 
 things is a brute among men ; that he who has an accurate know- 
 ledge of human concerns alone, is a man among brutes ; but, that 
 he who knows all that can be known by intelle6tual energy, is a 
 god among men. 
 
 Wifely, therefore, does Plato aflert that the philofbpher ought 
 not to defcend below fpecies, and that he fliould be folely employed 
 in the contemplation of wholes and unwerjals. For he who de- 
 fcends below thefe, defcends into Cimmerian realms, and Hades 
 itfelf, wanders among fpeftres devoid of mind, and expofes himfelf 
 to the danger of beholding the real Gorgon, or the dire face of 
 Matter, and of thus becoming petrified by a fatiety of flupid 
 paflions. 
 
 The life of the man who, pofTefling true wifdom, energifes 
 according to theoretic virtue, is admirably defcribed by Plato in his- 
 Thextetus as follows : 
 
 " Socrates. Let us fpeak, lince it is agreeable to you, about the 
 coryphaei. For why fliould any one fpeak of thofe who are 
 converfant with philofophy in a depraved manner ? In the firft 
 place, then, the coryph;£i from their youth neither know the way 
 to the forum, nor where the court of juftice or fenate-houfe is 
 
 fitxiated
 
 xvl INTRODUCTION. 
 
 fituatecl, or any 'other common place of affembly belonging to 
 
 the city. They neither hear nor fee the laws or decrees, whether 
 
 promulgated or written. And, as to the ardent endeavours of their 
 
 companions to obtain magilb^acies, the aflbciations of thefe, their 
 
 banquets and wanton fcaiUngs accompanied with pipers, — thefe 
 
 they do not even dream of accomplifliing. But whether any thing 
 
 in the city has happened well or ill, or what evil has befallen any 
 
 one from his progenitors, whether male or female, of thefe they are 
 
 more ignorant than, as it is faid, of how many meafures called choes 
 
 the fea contains. And befides this, fuch a one is even ignorant that he 
 
 is ignorant * of all thefe particulars : for he does not abftain from 
 
 them for the fake of renown, but, in reality his body only dwells and 
 
 is converfant in the city; but his dianol'tic part confidering all thefe 
 
 as trilling and of no value, he is borne away, according to Pindar, en 
 
 all fides, geometrizing about things beneath and upon the eaith, 
 
 artronomizing above the heavens, and perfecTtly inveftigating all the 
 
 nature of the beings which every whole contains, but by no means 
 
 applj'ing himfelf to any thing which is near. 
 
 " Tbeodorus. How is this, Socrates ? 
 
 " Socrates. Jul!:, O Theodorus, as a certain elegant and graceful 
 Thracian maid-fervant is reported to have faid to Thales, when 
 while aftronomizing he fell into a well, that he was very dcf.rous 
 of knowing what the heavens contained, but that he was ignorant of 
 what was before him, and clofe to his feet. In the fame manner 
 all fuch as are convex fant in i:)hilofophy may be derided. For, in 
 reality, a charailer of this kind is not only ignorant of what his 
 
 * The multitude are ignorant tliat tlicy arc igncrniit with rcfpctfl (o objects of 
 all others the moll; rpleiidid and real; Lnit the corypha-an philofophcr is ignorant 
 that he is ignorant with rcfpccSl to objeds mofl iinfiibfianlial and oblcure. The 
 former ignorance is the confeqnencc of a dcfcft, but the latter of a tianfccndcncy 
 of gnoilic energy. 
 
 neighbour
 
 INTRODUCTION. xvii 
 
 neighbour does, but he fcarcely knows whether he is a man, or 
 feme other animal. But what man is, and what a nature of this kind 
 ought principally to do or fuffer, this he makes the obje& of hi/ inquiry, 
 and earnejlly inveJligates'^K Do you underftand, Theodorus, or not ? 
 
 " theodorus. I do : and you are certainly right. 
 
 " Socrates. For, in reaHty, my friend, when a man of th3:s kind is 
 compelled to fpeak (as I faid before) either privately with any one, or 
 publicly in a court of jultice, or any where elfe, about things before 
 his feet, and in his "view, he excites laughter, not only in Thracian 
 maid fervants, but in the other vulgar, fince through his unfkilful- 
 nefs he falls into wells, and every kind of ambiguity. Dire de- 
 formity too caufes him to be confidered as a rultic : for, when he is 
 in the company of llanderers, he has nothing to fay reproachful, as 
 he knows no evil of any one, becaufe he has not 7nade individuals the 
 objetls of his attention. Hence, not having any thing to fay, he ap- 
 pears to be ridiculous. But, when he is in company with thofe 
 that praife and boaft of others, as he is not only filent, but openly 
 laughs, he is confidered as delirious : for, when he hears enco- 
 miums given to a tyrant or a king, he thinks he hears fome fwine- 
 herd, or fliepherd, or herdfman proclaimed happy, becaufe he milks 
 abundantly ; at the fame time he thinks that they feed and milk 
 the animal under their command, in a more morofe and infidious 
 manner ; and that it is necelfary that a characSter of this kind fliould 
 be no lefs ruftic and undifciplined through his occupation than 
 fliepherds, the one being inclofed in walls, and the other by a flieep- 
 cot on a mountain. But when he hears any one proclaiming that 
 
 * When intclle(5lual men, therefore, are compared with fuch as are folely buficd 
 in the invefligation of fenfible particulars, who are alone delighted with objects of 
 fcnfe, and who do not even dream that thefe objects rather refenibic the delufions of 
 ilcep than the realities of vigilant perception, we may exclaim in Homeric lan- 
 guage, 
 
 The race of tliefe fuperior far to thofe, 
 
 Ae he that thunders to the (Ircam that flowi. 
 
 he
 
 ,»m INTPvODUCTION. 
 
 he poflefTes ten thoufand acres of land, or a iHll greater number, as> 
 if he poiieiTed things wonderful in multitude, it appears to hini 
 that he hears of a very trifling thing, in ccnfequence of being ac- 
 cuftomed to furvey the whole earth. As often, too, as any one cele- 
 brates the nobility of his family, evincing that he has feven wealthy 
 grandfathers, he thinks that this is entirely the praife of a dull, 
 mind, and which looks to a thing of a trifling nature ; through 
 want of difciphne being incapable of always furvey ing the univerfe, 
 and of inferring by a reafoning procefs, that every man has had 
 innumerable myriads of grandfathers and progenitors, among which 
 there has often been an innumerable multitude of rich and poor, 
 kings and flaves, Barharians and Grecians. But when any one, cele- 
 brating his progenitors, enumerates five-and-twenty of them, and 
 refers their origin to Hercules, the fon of Amphitryon, it appears to 
 him a thing unworthy to be mentioned. For, as it is entirely owing 
 to fortune that any one is able to enumerate five-and-twenty proge- 
 nitors from Hercules, he would laugh, even if any one could enu- 
 merate fifty from the fame origin ; confidering fuch as unable to 
 reafon, and liberate themfelves from the arrogance of an infane 
 foul. But, in every thing of this kind, the coryphaeus we are de- 
 fcribing will be ridiculed by the vulgar, partly becaufe he will be 
 confidcred by them as arrogant, and partly becaufe he is ignorant 
 of, and dubious about, things before his feet. 
 
 " 'fheodorus. You ipeak, Socrates, of things which certainly take 
 place. 
 
 '■'■Socrates. But when any one, my friend, draws him on high, and is. 
 willing that he fliould abandon the confideration of whether I injure 
 you, or you me, for the fpeculation of juftice and injuftice, what 
 each of them is, and in what they differ from all other things, or from 
 each other ; or that, difmifling the inquiry whether a king is happy 
 who pofleffes abundance of gold, he flrould afcend to the contem- 
 plation of a kingdom, and umyerfally of human felicity and mifery, 
 
 of
 
 INTRODUCTION. xis 
 
 of what kind they are to any one, and after what manner it is 
 proper for human nature to acquire this thing and fly from that; — 
 about all thefe particulars when that little fliarp foul, fo converfant 
 with law, is required to give a reafon, then he in his turn is affected 
 worfe than the coryphaeus : for he becomes giddy, through being 
 fufpended from a lofty place of furvey, and being unaccullomed to 
 look fo high. He is alfo terrified, is filled with uncertainty, and 
 fpeaks in a barbaric manner; fo that he does not indeed excite 
 laughter in the Thracian vulgar, nor in any other undifciplined 
 perfon (for they do not perceive his condition), but in all thofe whofe 
 education has been contrary to that of flaves. And fuch, Theo- 
 dorus, is the condition of each ; the one, whom we call a philofo- 
 pher, being in reality nourifhed in truth and leifure; and who, 
 though he ought not to be blamed, yet appears to be ftupid and of 
 no value, when he engages in fervile offices ; fince he neither 
 knows how to bind together bundles of coverlids, nor to make 
 lauce for banquets, nor compofe flattering fpeeches. But the other 
 of thefe chara<flers is able to accomplifli all thefe fervile offices with 
 celerity and eafe, but knows not how to clothe himfelf jn a liberal 
 manner^ nor how in harmonious language properly to celebrate the 
 true life of the gods and bleffed men.'* 
 
 With refpeit to the arrangement of thefe books, I have retained 
 the order in which they were difpofed by antiquity, and publifhed 
 by Aldus and Befl'arion. This order, however, though fcientifically 
 accurate, certain philologifts have prefumed to cenfure, and Petit 
 and Dr. Gillies, in giving to the public an arrangement totally dif- 
 ferent from that which was adopted by the earlieil: and heft of 
 Ariilotle's Greek interpreters, have fufficiently proved that they 
 attempted to redify what they did not underftand. The arrange- 
 ment of Dr. Gillies in particular is no lefs remarkable for the pre- 
 
 c 2 fumptioa
 
 %x INTRODUCTION. 
 
 fumption, than the ignorance,\vhich it difplays : for, either he ne'^er 
 read thefe books, or he read them without attention ; he read them 
 not with the eye of a philofopher, but with that ambitious fpirit 
 ■which feeks for fame in innovation, and applaufe in iingularity. 
 That this cenfure is no lefs jull than fevere, will be at once obvious- 
 by the following obfervations. 
 
 According to Dr. Gillies, that book of the Metaphyfics which 
 was confidcred by the antients as the 5th fliould Hand as the ill. 
 The loth book is with him the 2d ; the 2d and 4th, the 3d ; the 
 ifr and 3d, the 4th ; the 6th, 7th, and nth, the 5th ; the 8th is the 
 6th ; the Qtli, the 7th ; the 13th, the 8th ; the 14th, the 9th ; and 
 the 1 2th, the loth.. A reader moderately Ikiiled in the philofophy 
 of Arirtotle, on feeing the metaphyfical writings of the Stagirite 
 thus difpofed, would be led to imagine that Dr. Gillies, Avhen he 
 thus dillurbed the order of thefe books, had juft emerged from the 
 Chaos of Milton, attended by Confufion and Uproar, Rumor and 
 Chance, Havoc and Ruin. For, in the lirft place, in the fecond 
 chapter of the loth book, Ariftotle quotes what he has faid in the 
 7th hook. " If (fays he) nothing of univerfals can be effence, as 
 we have afTerted in our difcourfes refpecfling effence and being *, 
 &c." The reader will find that this is afferted by Ariftotle in the 
 7th book, and that he there difcourfes concerning being and effence. 
 So that, according to Dr. Gillies, lince this loth book fliould ftand 
 as the 2d, and the 7th as the 5th in order, Ariftotle either quotes a 
 book which he had not yet written, or was ignorant that when one 
 book depends on another, the dependant book fliould be placed, 
 prior to that on which it depends ! Again : according to Dr. Gillies,, 
 that book which was conlidered as the 4th by the antients, ought 
 
 * E; di yx-<i5;v tcaiv xa^oXov ^vvxtov cxxtikv zivoii, ku^xtt!^ sv joig 't^'s^i ovu'ictcj xixi ret tts^l 
 Tcw evTCf ci^rjat Xoyotiy k.t-A^ 
 
 to
 
 INTRODUCTION. 
 
 xxt 
 
 to be placed before that which they arranged as the third ; and this 
 third book he fays treats of principles. This book, however, wholly 
 confifts in an enumeration of thofe doubts which are folved in the 
 4th and following books. So that Ariltotle is made by Dr. Gillies 
 to enumerate doubts to be folved, after he has folved them. 
 
 Further Hill : " We are not inclined (fays Dr. Gillies* to enter into 
 the 6th, 7th; and nth books of Arirtotle s Metaphyfics, where he ex- 
 amines with a degree of attention, of which the fubjedl would now 
 appear totally unworthy, the numbers of Pythagoras, and the ideas 
 of Plato. Thefe three books properly conftitute one, which ought 
 to ftand as the fifth, and be entitled, Concerning Ideas or Univerlals 
 conndered as the Caufes of the Univerfe." So far, however, are the 
 numbers of Pythagoras and the ideas of Plato from being difcuifed in 
 thefe books, that, as the reader will eafily difcover, the 6th and yth, 
 are employed in the confideration of definitions, and in the nth he 
 recapitulates what he had before demonftrated ; but numbers and 
 ideas are alone difculTed in the ift, 13th and 14th books. Laftly : 
 " the 13th, 14th and nth books (fays he) treat of a being totally 
 diftindt from matter ; necefiary, eternal, infinite in perfedtion ; one 
 fubftantially and numerically, the primary caufe of motion, himfelf 
 immoveable." This alfo is perfecflly falfe : for the 12th book only 
 treats of. this being; the 13th and 14th books, as wx have already 
 obferved, being entirely employed in the difcuffion of mmibers and 
 ideas. 
 
 And thus much concerning Dr. Gillies at prefent, as I fhall again, 
 in this Introdu(5lion, have occafion to notice what he has given to 
 the world under the name of Ariftotle, when I fear the accufation 
 will be ftill more weighty, and the cenilire unavoidably more 
 fevere. But it is now time to conlider thefe books in the order in- 
 which they have been tranliiiitted to us by the antients. 
 
 * Vol. I. of his Ariltotle, p. loi, 
 
 Since^.
 
 •xxU INTRODUCTION. 
 
 Since, then, this fcience fpeculates being fo far as it is being, and 
 therefore confiders the principles of heing, and whatever is confe- 
 quent to it, hence, in the lirft place, it receives a twofold divifion. 
 And becaufe different opinions were entertained by the antients 
 refpe6ling the principles of being, which it is neceffary to examine, 
 this is the bnfinefs of the third part of this fcience. So that the 
 metaphyfical fcience confifts of three parts. Firft, of the fpecula- 
 tion of being fo far as it is being : fecondly, of things confequent 
 to being fo far as it is being : and thirdly, of the different opinions 
 which have been entertained rcfpedting its principles. 
 
 But, iince the fpeculation of caufes requires a previous know- 
 ledge of their firlT: genera, and of the opinions which the antients 
 entertained refpedling them, hence, in the firft book, Ariftotle 
 relates what the antients knew of the firft genera of caufes ; fliows 
 that thefe genera are four, and informs us that this number ap- 
 pears to have been adopted by the antients. After this, he relates 
 the different opinions of the antients concerning the caufes of things, 
 but efpecialh^ thofe of the theologifts, becaufe the opinions of 
 natural philofophers on this fubje6t have been confidered by him 
 in his Phyfics. Thefe theologifts, therefore, who contended that 
 the principles of things were mathematical entities and numbers, 
 he apparently oppofes in this book, and defers .the completion of 
 this controverfy to the thirteenth and fourteenth books. 
 
 In the fecond book, he notices the difficulty, and yet facility, 
 with which the fpeculation of truth is attended, and obferves, that 
 though each of thole Avho have philofophized has added nothing, 
 or but a little to this fpeculation, yet fomething of magnitude is 
 produced from th^ir affertions wlien colledcd. This book, as 
 Alexander Aphrodifienfis well obferves, appears to be mutilated, 
 if the beginning and end of it are confidered. Yet it may be faid, 
 as he juftly adds, to be a preface to the whole of contemplative 
 
 philofophy.
 
 INTRODUCTION. xxiii 
 
 philofophy. In this book, alfo, he proves that caufes are finite in 
 number ; and conckides with enumerating the fources of error in 
 fpeculative inveitigations. 
 
 Again : fince, without previous doubting, it is not poffible to ob- 
 tain an. accurate knowledge of any thing, hence, in the third book.. 
 he enumerates the doubts which pertain to this fcience. This 
 book is evidently preceded by the firll and fecond, becaufe they are 
 entirely of a prefatory nature ; and it precedes all the others, becaufe 
 they either contain a folution of the doubts enumerated in this 
 book, or a knowledge of fuch things as are neceffary to a folution 
 of thefe doubts. 
 
 In the fourth book, he fliows that the firft philofophy confiders 
 being univerfally, and therefore, that it may not omit things which 
 are p.refent with being in common fo far as being, contemplates 
 axioms, or the fyllogiftic principles of fcientific knowledge. He 
 likewife fhows that the principle which precedes all others is this, 
 that it is impoffible for affirmation and negation to be at the fame 
 time verified of the fame thing. Hence, he infers, that from him 
 who denies this principle no reafoning can be admitted, nor any 
 affirmative or negative propofition. 
 
 In the next place, fince it is the bufinefs of the firfl: philofophcr 
 to confider being univerfally, and whatever pertains to being in 
 commouj and things cornmon to being are thofe which all dilci^ 
 plines employ, hence, the fpeculation of thefe is the proper bufinefs 
 of the metaphyfician, becaufe thefe alone belong to being fo far as 
 it is being. Befides, what the logician collects probably, the firll 
 philofopher concludes fcientifically ; but the logician confiders and 
 difcourfes about things which are either univerfally common, or 
 common in a very extended degree, and which are multifarioufiy 
 predicated. Hence vulgar diale6lic, or logic, is fimilar to the firft 
 philofophy, becaufe it is converfant with the fame things, though 
 
 with.
 
 . xxiv INTPvODUCTION. 
 
 with probability onh', and not fcientifically. Hence, likewife, thofe 
 tilings vvliich are the attendants of being in common, and which all 
 fcienccs employ, are confidered by Ariilotle in the fifth book : for 
 in the third book he had informed us that the difcuffion of thefe be- 
 longs to the firfl i)hilofopher. This book therefore properly ranks 
 as the fifth : for, as Alexander Aphrodifienlis Jullily obferves, it. is 
 proper that, after having fhown what are the objects with which 
 the firll: philofophy is converfant, which is unfolded in the fourth 
 book, a difcuflion fhould immediately follow of thofe things which 
 are neceflary to the fpeculation and demonflration of all that is 
 required to be demonflrated. 
 
 Again : Ariilotle fliows in many places that the firft philofophy 
 confiders being fo far as beiiig : for other fciences diftribute being 
 among themfelves, and each confiders its own part, not by in- 
 quiring into its nature, and contemplating it as being, but by ex- 
 jjloring its accidents. Thus, for jnftance, ailronomy does not con- 
 iider the nature, bat the different motions of the ftars. This then, 
 is obfcurely fliown by Ariilotle in the fixth book, in which alfo he 
 evinces that the firft philofophy confiders the definition of every 
 thing, unfolds how every thing is to be defined, whether intelligible 
 or fenfible, and indicates what are the proper fubjedts of definition. 
 The whole of the feventh book is employed in the difcuffion of 
 xlefinitions ; but, fince definitions properly pertain to efTence, and 
 not to the accidents of being, hence, in this book he again fpeaks of 
 being, and fays that it is multifarioully predicated, as he had before 
 informed us in the third book. 
 
 In the eighth book he continues to difcufs definitions, and fum- 
 marily repeats what he had before delivered on this fubje(5l. 
 
 Having therefore, in the feventh and eighth books, difcourfed 
 concerning being confidered by itfelf, he very properly makes the 
 Speculation of that which is in energy and that which is in capa- 
 city
 
 INTRODUCTION. xxv 
 
 city the fubjefl of the ninth book : for being is predicated of both 
 thefe. 
 
 hi the tenth book he confxders whether ibe one of the Pythago- 
 raeans and Platonifts has any fvibfiftence, and for this purpofe, by a 
 divifion of ibe one, fliows how it ought to be conceived, and how 
 it is fometimes underftood in fenfibles. 
 
 In the eleventh book he repeats what he had before demon- 
 fl-rated, and fuggefts to us that a dodtrine of this kind is different 
 both from Phyfics and Mathematics, and alone deferves to be called 
 wifdom. Since he alfo difcuffcs, as far as to this book, the queftions 
 which he propofed in the third book, he relates certain queftions in 
 this book, which either had not been folved, or were not fufficiently 
 explained. 
 
 'in the twelfth book he difcourfes of the firft principle of things, 
 and of the multitude of principles confubfiftent with him, for the 
 fake of which the whole of his Metaphyfics was compofed. 
 
 And laftly, in the thirteenth and fourteenth books, he fully dif- 
 cuffes all the doubts pertaining to the. Pythagoric and Platonic 
 doctrine of numbers and ideas. Ariftotle, indeed, appears to be a 
 great enemy to this dodtrine ; but, in the copious notes which we 
 have given to thefe books, it is I prefume clearly fliown that his 
 obje(5lions are every where pretended, and not ferious. Perhaps 
 his defign in this oppofition was to lead the reader into all the 
 myfleries of this dodlrine, in the fame manner as Parmenides, in 
 the dialogue of Plato which bears that name, under the pretext of 
 doubts unfolds to Socrates all the orders of ideas, as is beautifully 
 lliown by Proclus in his MS. Commentary on that abftrufe dia- 
 logue. 
 
 And here perhaps it may not be improper to notice what appears^ 
 to be the peculiaiity of his philofophy, and fliow more fully wl^f^ 
 iie thus with fuch apparent violence oj)pofes Plato's dodrine of 
 
 d ideas.
 
 sxvi INTRODUCTION. 
 
 ideas. That Ariftotle then was not an enemy to the dogma, that 
 in the intellect of the fabricator of all things there are forms or 
 ideas, which prefubiift as paradigms, and as the produdlive princi- 
 ples of whatever has a perpetual fubfiftence in the univerfe, is 
 exident from hence, tliat in the twelfth book, of the following 
 work, he aflerts that there is a twofold order, one in the world, and 
 another in the caufe of the world, juft as we fay that there is one 
 order in an army, and another in the commander of the army. 
 Bnt, where there is order, there mnfl: neceflarily be reparation, 
 and things which are orderly difpofed. If any one however de- 
 fines the order which is in the univerfe, this order cannot certainly 
 accord with that which is in the intelledt of the Demiurgus, and 
 confequently, the appellation of the one muft be difcordant with 
 that of the other. Ariitotle, therefore, not enduring thofe con- 
 ceptions of ideas, which together with fenfible appellations intro- 
 duce definitions which comprehend in themfelves a phyfical and 
 material nature, refufes to call the caufes of man and horfe, man 
 itfclf, and horfe itfelf, biit is not averfe to the firft caufe being 
 called by purer names, fuch as good, efience, life, intelleft, and 
 energy. If, then, it fliould be faid that thefe fubfift in the divine 
 intellect, but that they are not fuch as thofe which the fenfible 
 region contains, it may reafonably be contended that the fame 
 affertion may be made refpedling man and horfe, and every thing 
 elfe of a fimilar kind. Ariftotle, therefore, was in general averfe 
 to caufes receiving the fame appellations with their fenfible efte<5ts ; 
 and this was the peculiarity of his philofophy, and the rcafon why 
 he oppofes with fuch apparent hoftility the friends of ideas. 
 
 When the jargon of the fchoolmen was firft exploded, and the 
 new philofophy, or the inveftigation of truth in the infinity of 
 particulars was fubftituted in its ftead, one among the many cen- 
 fures which were then pafled on the philofophy of Ariftotle, was 
 
 this,
 
 INTRODUCTION. xxvii 
 
 this, that it was dogmatic in the extreme, and that its author no lefs 
 endeavoured to tyrannize over the minds of his readers, than his 
 ilhiftrious pupil Alexander to obtain univerfal dominion. There 
 never perhaps was an inftance of cenfure more unjuft than this ; 
 Cnce Aiiftotle every where recommends inveiligation and doubt- 
 ing, and difplays no lefs modefty in propofing doubts, than fagacity 
 in diiTolving them : for, having exercifed himfelf like Plato, in that 
 part of dialecftic, which, as we have already obferved, proceeds 
 through oppoilte arguments, when, in philofophifing, a queftion is 
 propofed, before he folves it he ufually introduces another queftion, 
 and, from the folution of the latter, folves the former. He often 
 likewifc brings many doubts together, which he diffolves by one 
 and the fame, or by continual, anfwers. But, that the reader may 
 be fully convinced that the philofophy of Ariftotle is of all others 
 moft foreign to dogmatic aflertion, and moft friendly to doubting, 
 I fhall, in the firft place, prefent him with an accoimt of the words 
 and the modes of expreflion by which he lignifies doubting. 
 Aporein (aTO^f/vj then, is properly to doubt, and this is the word 
 which Ariftotle moft frequently ufes ; but the formulae by which 
 he exprefles that word in the inveftigation of truth, as well in the 
 theoretical as in the pratftical parts of his philofophy, are various. 
 And thefe are fometimes fvibfervient to the doubts propofed from 
 the beginning of the chapter, and to what has been adduced in 
 former chapters, and fometimes they promote a more diligent invef- 
 tigation in the middle or end of a chapter f. Sometimes the word 
 
 f ThuP, among others, lib. iii. Metaphyf. c. i, ct lib. xi. c. i , a-Koy^^asnv mv rt;, 
 foiiie one may doubt. Likewife, lib. vii. c. i ct c. 9. lib. iii. c. 4 et 6. lib. ii. de 
 Animac. 11, ct lib. i. c. 8. lib. i. Mag. Mor. c. 35. lib. ii. Mag. Mor. c. 3, 6, et 11. 
 lib. vii. de Moribus, c. 2. lib. i. Meteor, c. 3 et 14. lib. i. de Anima, c. i et 7. lib. v. 
 dc Moribus, c. 11, ct lib. ii. c. 3. lib. v. Eiidcm. c. 12. lib. ix. c. 2. lib. v. Nat. 
 
 d 2 Aufc.
 
 xxviii INTRODUCTION. 
 
 aro^iot, doubt, alone in the fmgular or plural number comprehends 
 the matter of the whole, or the better part of the chapter, by which 
 the propofition of things dubious is exhibited ••• : and fometimes 
 other words joined with this denote the fame doubt t ; to all which 
 the words zxj'ko^zi)) and zv-KO^iGH. fignifying abundance correfpond as 
 
 the end \. 
 
 Aufc. c. 9. lib. vii. c. 5. lib. i. dc Gen. et Corr. c. j. lib. de Senru ef Senfili, c. 5 ct 6.. 
 et de Inceiru Aniraalium, c. 1 1 . lib. ii. de Gen. Animal, c. 2. lib. ii. de CceIo, c. 14. 
 hi lib. ii. de Generat. Animalium c. iii. we have other formulas, lovioov S' ix'^^^svov 10-71 
 v-OiicnTto-J/iTai, ScC., Tcy. mavToc ocTro^-nxi, ttcts^ov, &c., (Xtto^hv caiayn.(xm. lib. iii. Met. C. 6. 
 li-b. iv. Nat. Aufc. c. 4. lib. ii. de Sophift. Elenchis c. 33. S5; «7rof,;croi/, lib. iii. Met. 
 c. I. Likevviic to airoi^iiv is joined with tm /SoyAjWi)/, lib. vi. de Moribus c. 1 1. The 
 philofopher, alfo, by the word cc-ko^i% differently exprefles doubt : for he either ex- 
 preffes it through this, i<Tii 5c onroua, lib. dc Animalium Motione, c. 4. et ktto'ao. h 
 £(rT( o/TT)7, lib. ii. de Sophift. Elench. c, 33. lib iii. Met. c. i. or by kito^mv lyjiv,. 
 lib. i. de Anima, c. i. et lib. ii. c. 5. et c. 11. lib. iii. Nat. Aufc. c. 5. lib. vii. 
 Metaphyf. c. 5. lib. i. Nat. Aufc, c. 3. lib. iv. Metaphyf. c. 3. lib. i. dc Gen, ct Corr. 
 c. 3. or by aTTp^tcnv Tnx^xa-xsiv, as lib, iii. Met. c. 1. et lib. ii. Mag;. Mor. c. 6. Or by 
 TTOisiv aTTO!>iocv, as lib. iii. Nat. Aufc. c. 5. or by dTfc^im ocucf-iv, as lib. viii. Met. c. 3. 
 
 * This may be fcen in lib. iii. Metaphyf. c. 1. lib. iii. de Rep. c. 3. lib viii. 
 Met. c. 6. lib. xii. Met. c. 6. lib. xiii. Met. c, i et 2. lib-, iv. Nat. Aufc. c. 3. 
 lib. ii. de Coelo, c. 12. lib. i. de Gen. et Corr. c. 1 1. lib. i. de Moribus c. 10. lib. ii.. 
 de Moribus, c. 3. lib. v. de Moribus, c. 2. ct lib, ix. c. 2. et 3. ct 8, et 9, ct 11. 
 lib, i. Mag, Moral, c, 35. lib. vi. Eudemior c. 2. et lib. vii. c. 8. lib. iii. de Anima, 
 c. 10. lib. dc Animalium Inceflu, c. 10. 
 
 •\- Viz. Either STria-KSTmo-Qoit, as in lib. de Animalium Motione, c. iv. and cry.5i|//f, as 
 lib. ii. Mag. Mor. c. 4. lib. i. Meteor, c. 13. ct lib. viii. Nat. Aufc. c. 3. lib. i, de 
 Moribus, c. 10. He alfa ufes the word es7ro^);/x« as well elfewhere as lib. iv. Nat. 
 Aufc. c. 6. lib, xi. Met, c. 2. and huTro^uv, lib, iii. Met. c. i. lib. \v. c. 5. ct lib. i. 
 de Moribus, c. 1 1. ct 2. lib. vii. c. 7. Categ. de Relatis, c. 7. lib, xi. Met. c, 1 1. 
 ^b, i, de Gen. et Corr. c. 5. ct lo. lib, i. Meteor, c. j, lib, iv. Nat. Aufc. c. 5, et 
 lib. i. Eudem.c 4. 
 
 \ As may be fcen lib. iii. Met c. i. et lib. i. dc Anima, c. 2. And the words 
 »jj.(pi<rQ}iretv and u^<pi<j^riTri(yii denote the fame doubting. See lib. i. Eudcm. c. 3, 
 et 4. lib. vi. c. a. lib. i.. de Coelo, c. ii. lib. ^. Met. c. i. 
 
 In.
 
 INTRODUCTION. xxix 
 
 In the next place, it will be proper to obferve that metaphylicat 
 doubting, according to Ariftotle, begins from an ignorance of the 
 caufes of being, from whence admiration of the greateft efFe6ls 
 arifes, and then receives its confummation when the caufes and 
 principles of the univerfe are known. But the philofopher in the 
 third book of his Metaphyfics, which, as we have obferved, is 
 wholly employed in the enumeration of doubts, affigns four 
 reafons why in the inveftigation of truth we fliould begin from 
 doubting. The firft is, " becaufe the power of acquiring pofterior 
 knowledge is derived from the folution of prior doubts." Hence, 
 in his Nicomachean Ethics, he fays that the folution of doubt is in- 
 vention *. The fecond reafon is, " becaufe thofe that inveftigate 
 ■without having previoufly doubted, refemble thofe who are igno- 
 rant whither they ought to go t^" For he iliows that doubting is a 
 road through which we mull: necelTarily pafs in the inveftigation- 
 of truth- Not that we are to be continually employed in doubting, 
 but only till w^e arrive at truth, the obje6l of our fearch. The third 
 reafon which Ariftotle affigns is, '* becaufe without doubting thofe 
 that inveftigate cannot know whether they have found what they 
 explore. For, the end to thefe is not manifeft ; but is manifeft to 
 thofe who previoufly doubt in a proper manner." Hence, thofe 
 only who have previoufly doubted, know truth when they have 
 found it ; but thofe who without doubting happen to meet with 
 truth, are ignorant that they have found it. And the fourth reafoa 
 
 * H yap Xvo-ig T7}g ccvrcpixg svasa-ig sent- Lib. vii. C. T. 
 
 •j- The words uTropyjToci, S/aTropi^cra/ and ivTroprja-ai, vvhicli tiie philofopher ufes in this 
 place, accord with each other ; for they refer to thofe that aie travelling ; vroaog: 
 fignifying a iz-aji. But by the verb ocTroprjo-ai in the beginning of this padage and 
 elfewhcre he fignities a previous doubting of particulars; but by ha7ropr,(rjei a more; 
 profound inveftigation, and a folicitude of penetrating through all doubts, and in- 
 creafing. the doubt itfcif by various rcfleilions and arguments. 
 
 which
 
 XXX INTRODUCTION. 
 
 which the philofopher afTigns why we fliould begin from doubting 
 is, " becaufe he is neccflarily better fitted to judge, who has heard 
 all the oppolite reafons, which may be compared to the adverfaries 
 in a law-fuit." Conformably to this, he clfe where obferves, " that 
 the demonftrations of contraries are doubts concerning contrai'ies ;, 
 and, at the fame time, affertions will be niore credible, if, previous 
 to their being delivered, all that can be urgetl in defence of the 
 contending arguments is heard *." In fliort, the whole of his Meta- 
 phyfics confirts either in the enumeration and folution of doubts, 
 or in the difcuffion of fuch things as are fubfervient to theii" folution. 
 And we have largely fliovvn that every j>art of his works abounds 
 with doubting, and that he every where exhorts the reader to doubt,, 
 as above all things necelTary to the perception of truth. It may, 
 therefore, from all this be fairly and fafely concluded that thofe 
 who have reprefented his philolofophy as tyrannical, have either 
 ignorantly confounded it with the baibax-ous reveries of the 
 fchoolmen, or, defirous of becoming didators in philofophy them- 
 felves, like Lord Bacon and Malebranche, have moil unjuilly 
 afcribed to the Stagirite that unbounded ambition with which they 
 were fo eminently infpired ; an ambition which is fatisfied with 
 nothing fliort of unrivalled renown, and which 
 
 " Bears, like the Turk, no brother near the throne." 
 
 It has aHb been faid, though unjuifly,that, according to Ariftotle, 
 the firft mover, whom he calls intelka, eternity, and God, is only 
 the final, but not the effedive caufe of the world. That the firft 
 
 At yap Tuv cyaVTiuv ur-ohi^iic, cc7:o^iat 7!.yi rujv ivoivitcov sta-iv, ijx.a. h Kxi ^kXKov 
 ^aTu. Lib, i. dc Coelo, c, :o. 
 
 * 
 cxy it 
 
 mover
 
 INTRODUCTION. xxxi 
 
 mover is, however, according to Ariftotle, an efFe<5live caufe, is evi- 
 dent from what he fays in the fecond book of his PhyficaJ Aiifcul- 
 tations, in the divifion of caufes ; for he there denominates an 
 effective caufe to be that whence the principle of motion is derived ; 
 and again, that whence the firft principle of mutation or reft origi- 
 nates. Thus, for inftance, fays he, he who confults is a caufe, and a 
 father of his fon, and, in fliort, that which makes of that which is 
 made *. In the firft alfo of his books De Ccelo, he fays, " that 
 neither God nor Nature produces any thing in vain f ;" and in an- 
 other part of the fame book he aflerts, " that eternity from always 
 fubfifting receives the appellation of immortal and divine, whence 
 alfo being and life are imparted to other things, to fome more accu- 
 rately, and to others more obfcurely J." In th€ firft book, like wife, 
 of his Metaphyfics, praifing Anaxagoras, and prior to him Hermo- 
 timus, as not only admitting material caufes of the univerfe, but 
 contemplating intelledt as the effective and final caufe, he obferves 
 as follows : " He, therefore, who aflerted that as in animals, fo alfo 
 in nature, there is a certain intellect, which is the caufe both of the 
 world and of all order, will appear like one fober, when comj^ared 
 with thofe antients that fpoke raflily §." And fliortly after he adds, 
 ** Tliofe, therefore, who entertained this opinion, together with, 
 eftablilhing a principle of things, which is the caufe of their fub- 
 
 * OSsv ■>} ot^yji "TYig ^!Tct'Zo?<.YiS -^ vrpcTnj ri T>}g y!^;[j.rj'rscijg' oiov o f2ouXiV(rocg ccnioy, kxi o 
 vrcnr,^ tov tskvov, koh oAwj to vrotovv tcd 'Ttoiov^-vov. 
 
 ■)■ Ovo2v fMXTYjv TTOiii cvT= Bioc, ovTS Tj (pu(ng. 
 
 ;}; Oil uiMV avro rov ccsi sivoci t'/jv iirc^ivj^ioiv iiKyipsv ccSxvcctcs koci Bsiog, oSiv kxi loig 
 tiKXotg s^-/;pT'/jTai, Totg jj-sv a/cp/bicTTSpov totg h aj^cev^oTcpcy, to nvect ts Ksct ^^v. 
 
 § 'Sow 5s Tig r-iTTMv sivxi, Kcc9x7ri^ iv Toig ^CAiotg Kat m t;; (pv(r;i, tov cxitiov kxi tov mxt- 
 p,ou K(xi Trig Toc^icng TraCDjj, otov vri^uy i'puvn irxf (intj Xeyovjug -xovg tt^qtz^ov. Metaph. 
 lib. i. cap. J. 
 
 lifting
 
 ^xjcii INTRODUCTION. 
 
 fifting in a beautiful manner, eftabliflied aLb a principle which is 
 the caufe of motion to things *." 
 
 Should it be afked why Ariliotle does not fo openly call God an 
 effective as he does a final caufe, we rej^ly w' ith Simplicius f, that 
 lince that which makes, makes that which is generated, and that 
 which is generated at the fame time introduces a temporal begin- 
 ning of generation, hence he refufes to call the celeilial bodies, 
 which he demonftrates to be perpetual, generated, though he often 
 and clearly denominates the caufe of them an efFedlive caufe. And, 
 perhaps, if fome one fliould affert that the terms generator and 
 maker are properly adapted to things in generation and corruption, 
 becaufe they introduce a partial time, he will employ different ap- 
 pellations when fpeaking of things perpetual. Ariftotle indeed, 
 does not refufe to call motion perpetual, though its very being 
 confifts [cV Tw •ymsa^oii) in generation, or becoming to be ; but he is 
 unwilling to fay that it has a perpetual generation, becaufe that 
 which is generated appears not to have had a prior fubliilence, and 
 will afterwards be corrupted. 
 
 That the reader may clearly comprehend the latter part of the 
 twelfth book of the following work, fee the beautiful fimplicity of 
 Ariltotle's theory of the mundane fyftem, and at the fame time un- 
 derhand how grofsly it has been mifreprefented by modern wit, the 
 following extradls from his Phyfical Aufcultations and books On 
 the Heavens are added :|;. It is not my intention in this place to 
 make a comparifon between the antient and modern fyftems of 
 
 O/ jx.:-v ow ovTcog vrtoKa^ZxwjTC-g, ccimcc tov KaXug zti-j cutixv ctpxV' ^'''^' '^^^ ovtoov 
 i^aruv, nxt tyj-^ toiuvv/jv o^Jiy -,; Kiy/jcns VTra^yji roig ova-iv. Metaph. lib. i. cap- 3. 
 ■[ In I'hyf. p. 321. 
 
 + Thcfc cxtradls arc taken from the two hooks ot' Pioclus On Motion; but 
 Prqclus collcflcd them from the above-mentioned writings of Ariftotle, and digefted 
 them fo as to form an elementary work on Phyfics. 
 
 altronomy,
 
 INTRODlJCTION. XKxiii 
 
 aftroiiomy, or to difcufs the merits of either ; but I wifli to fuggeft 
 to aftronomers of the prefent day, that it is not fafe to conchide that 
 hypothefes are true, merely becaufe they folv^e the phcenomena ; 
 fince it is poffible from falfe premifes to educe true conclulions. 
 Thus we may fyllogife in the firll figure : Every ftone is an animal ; 
 every man is a ftone : Ergo, every man is an animal. And the in-r. 
 ference is indeed true, but not fcientific : for the premifes are not 
 the proper caufes of the conclufions. I Ihall, therefore, only obferve 
 further on this fubje6t at prefent, that he by whom the following 
 hypothefes and definitions are admitted, muft alfo unavoidably 
 affent to the propofitions which are deduced from them, and to 
 Ariftotle's fyftem of aftronomy, which is the fame with that adopted 
 by Plato. 
 
 HYPOTHESES. 
 
 Every natural body is moveable according to place. 
 
 Every local motion is either in a circle, or in a right line, or 
 mixed from thefe. 
 
 Every natural body is moved according to one of thefe motions. 
 
 Every natural body is either fimple or compounded. 
 
 Every fimple motion is the motion of a fimple * body. 
 
 Every fimple body is moved with one motion according to na- 
 ture. 
 
 DEFINITIONS. 
 
 That is hea"'/y which is moved towards the middle. 
 That is light which is moved from the middle. 
 That is faid to be moved in a circle which is continually borne 
 from the fame to the fame. 
 
 * Simple bodies., according to Arillotle, are thofe which naturally pofiefs an in- 
 herent principle of motion. For animals and plants pofiels a principle of motion ; 
 but in thefe it proceeds from foul and not from nature. 
 
 e Contrary
 
 xxxir iKTRODUCTIONr 
 
 Contrary motions are from contraries to contraries. 
 One motion is contrary to one. 
 
 Time is the number of the motion of the celeftial bodies. 
 The motion is one which is without difference according ta^ 
 fpecies, and belongs to one fubjedl, and is produced in a continued". 
 
 time. 
 
 Theorem i. 
 
 Things which are naturally moved in a circle are fimple. 
 
 Dcmonjlration. 
 
 Let AB be that which is naturally moved in a circle. I fay that 
 AB is fimple : for, fmce the motion in a circle is a fimple motion ;. 
 but every fimple motion is the motion of a fimple body ; hence AB 
 is a fimple body. Things, therefore, which are naturally moved 
 in a circle are fimple. 
 
 Theore?^'2. 
 
 Things naturally moved in a circle, are neither the fame witlr, 
 thofe moved in a right line, nor with thofe which are compofecjj 
 from things moved in a right line.- 
 
 BemonJIration: 
 
 Let AB be that which is naturally moved in a circle. I fay that 
 it is not the fame with thofe things which are moved in a right line. 
 For, if it is the fame with any one of thefe, it muft either be naturally 
 moved upwards or downwards. But every fimple body is moved 
 with one fimple motion according to nature. Hence, that which 
 is naturally moved in a circle, is not the fame with any thing moved 
 in a right line. But neither is it the fame with any thing com- 
 pounded. For it has been fhown that every thing which naturally 
 moves in a circle is fimple; but that which conlifts from things 
 
 moved
 
 INTRODUCTION. xxxv 
 
 moved in a right line is a compofite. AB, therefore, which is natu- 
 rally moved in a circle, is neither the fame with things moved in a 
 right line, nor with thofe compofed from thefe. 
 
 Theorem 3. 
 
 Things which are naturally moved in a circle, neither participate 
 of gravity nor levity. 
 
 Demonjlration. 
 
 For if AB is either heavy or light, it is either naturally moved to 
 the middle, or from the middle : for, from the definitions, that is heavy 
 which is moved to the middle, and that is light which is moved 
 from the middle. But that which is moved either from or to the 
 middle, is the fame with fome one of the things moved in a right 
 line. AB, therefore, is the fame with fomething moved in a right 
 liiie, though naturally moved in a circle, which is impolTible. 
 
 Theorem 4. 
 Kothing is contrary to a circular motion. 
 
 Demonjlration. 
 For if this be poffible, let the motion from A to B be a circular 
 inotion, and let the motion contrary to this be either fome one of 
 the motions in a right line, or fome one of thofe in a circle. If, 
 then, the motion upwards is contrary to that in a circle, the motion 
 downwards and that in a circle will be one. But if the motion 
 downwards is contrary to that in a circle, the motion upwards and 
 that in a circle will be the fame with each other : for one motion is 
 contrary to one into oppofite places. But if the motion from A is 
 contrary to the motion from B, there will be infinite Tpaces between 
 two contraries; for between the points A, B infinite circumferences 
 may be defcribed. But let AB be a femicircle, and let the motion 
 
 e 2 from
 
 xxxvt INTRODUCTI ON. 
 
 from A to B be contrary to the motion from B to A. If, therefore, 
 that which moves in the femicircle from A to B Hops at B, it is by- 
 no means a motion in a circle : for a circular motion is continually 
 from the fame to the fame point. But, if it does not liop at B, but 
 continually moves in the other femicircle, A is not contrary to B. 
 And if this be the cafe, neither is the motion from A to B contrary 
 to the motion fi-om B to A : for contrary motions are from contra- 
 ries to contraries. But let ABCD be a circle, and let the motion from 
 A to C be contrary to the motion from C to A. If, therefore, that 
 ■which is moved from A pafles through all the places fimilarly, and 
 there is one motion from A to D, C is not contrary to A. But if 
 thefe are not contrary, neither are the motions from them contrary. 
 And in a fimilar manner with refpedt to that which is moved from 
 C, if it is moved with one motion to B, A is not contrary to C, fc^ 
 that neither will the motions from thefe be contrary. 
 
 Theorem $^ 
 
 Things which are naturally moved in a circle, neither receive ge- 
 neration nor corruption.. 
 
 DemonJTration. 
 
 For let AB be that which is naturally moved in a circle, I {ay that 
 AB is without generation and corruption : for, if it is generable and 
 corruptible, it is generated from a contrary, and is corrupted into a 
 contrary. But that which is moved in a circle has not any contrary- 
 It is therefore without generation and corruption. But that there 
 is nothing contrary to things naturally moving in a circle, is evi- 
 dent from what has been previoufly demonftrated : for the motions 
 of things contrary according to nature are contrary. But, as we 
 have dcmonftrated, there is nothing contrary to the motion in a 
 circle. Neither, therefore, has that which is moved in a circle any 
 
 contrary. 
 
 Theorem
 
 INTRODUCTION. ixxvii 
 
 Theorem 6. 
 
 The powers of bodies terminated according to magnitude are not 
 
 infinite. 
 
 lyemonjlration. 
 
 For, if poffible, let B be the infinite power of the finite body A *, 
 and let the half of A be taken, which let be C, and let the power of 
 this be D. But it is neceffary that the power D lliould be lefs than 
 the power B : for a part has a power lefs than that of the whole. 
 Let the ratio, therefore, of C to A be taken, and D will meafure B. 
 The power B therefore is finite, and it is as C to A, fo D to B ; and 
 alternately as C to D, fo A to B. But the power D is the power of 
 the magnitude C, and therefore B will be the power of the mag- 
 nitude A. The magnitude A, therefore, has a finite power B ; but 
 it was infinite, which is impoflible : for, that a power of the fame 
 fpecies Ihould be both finite and infinite in the fame thing, is im-- 
 
 poffible. 
 
 Theorem 7.. 
 
 Simple bodies are terminated according to fpecies.. 
 
 Dejnonjiration.- 
 For let the magnitude A be a fimple body. Since, therefore, ^ 
 iimple body is moved with a fimple motion, A will be moved with 
 a fimple motion. And if it is moved in a circle, it will have one 
 nature and one form. But if it is moved according to any one of 
 the motions in a right line, if it is moved from the middle only, it 
 will be fire, but if only to the middle, earth. But, if it is light with 
 refpe(Sl to one thing, and heavy with refpecSl to another, it will be 
 fome one of the middle elements. The fpecies therefore of fimple 
 bodies are terminated. 
 
 Theorem 8. 
 Time is continued and perpetual. 
 
 Demort"-
 
 xx%\Yi\ INTRODUCTION. 
 
 D£monJlration, 
 For, if it is neither continued nor eternal, it will have a certain 
 beginning. Let, therefore, A B be time, and let its beginning be A. 
 But if A is time, it is divifible, and we fliall not yet have the be- 
 ginning of time, bvit there will be another beginning of the be- 
 ginning. But, if A is a moment or the now, it will be indivifible, 
 and the boundary of another time : for the now is not only a be- 
 ginning, but an entl There will therefore be time before A, 
 Again : if B is the boundary of time, if B is time, it may be divided 
 to infinity, and into the many boundaries which it contains. But if 
 B is the now, the fame wdll alfo be a beginning : for the now is not 
 only a boundary, but a beginning. 
 
 Theorem 9. 
 
 A circular motion is perpetual. 
 
 D.emoylration. 
 IvCt the circular motion be that of the circle A B, I fay that it is 
 perpetual : for, fince time is perpetual, it is alfo neceffary that mo- 
 tion fliould be perpetual. And fince time is continued, (for there 
 is the fame now in the paft and prefent time) it is neceffary that 
 there fliould be fome one continued motion : for time is the num- 
 ber of motion. However, all other motions are not perpetual: 
 for they are generated from contraries into contraries. A circular 
 motion, therefore, is alone perpetual : for to this, as we have de - 
 monftrated, nothing is -contrary. But that all the motions which 
 fabfift between contraries, are bounded, and are not perpetual, we 
 thus demonftrate. Let A B be a motion between the two contraries 
 A and B. The motion, therefore, of A B is bounded by A and B, 
 and is not infinite. But the motion from A is not continued with 
 tliat from B. But, when that which is moved returns, it will Itand 
 
 flill
 
 INTRODUCTION. xxxix 
 
 ftill in B : for, if the motion from A is one continued motion, and 
 alfo that from B, that which is moved from D will be moved into 
 the fame. It will therefore be moved in vain, being now in A. 
 But nature does nothing in vain : and hence, there is not one mo- 
 tion. The motions, therefore, between contraries are not per- 
 petual. Nor is it poflible for a thing to be moved to infinity in a 
 right line : for contraries are the boimdaries. Nor when it returns 
 will it make one motion* 
 
 Theorem la^ 
 
 That which moves a perpetual motion is perpetual- 
 
 'Demonjlration.- 
 For let A be that which moves a perpetual motion. I fay that 
 A alfo is perpetual : for, if it is not, it will not then move when iti 
 is not. But this not moving, neither "does the motion fubfift, 
 which it moved before. It is however fuppofcd to be perpetual. 
 But, nothing elfe moving, that will be immoveable which is perpe- 
 tually moved. And if any thing elfe moves when A is no more,, 
 the motion is not continual; which is impoffible. Hence, that 
 which moves a perpetual motion is itfelf perpetual. 
 
 Theorem it. 
 
 That which is immoveable is the leader of things moving aiKl 
 
 moved. 
 
 Demonjlration. 
 
 For let A be moved by B, and B by C, I fay that this will fome 
 time or other ftop, and that not every thing which moves will be 
 itfelf moved : for, if poflible, let this take place. Motions, there- 
 fore, are either in a circle, or ad infinitum. But, if things moving 
 and moved are infinite, there will be infinite multitude and mag- 
 nitude ; for every thing which is moved is divifible, and moves- 
 
 froni
 
 ^1 INTRODUCTION. 
 
 from contaa:. Hence, that which confifls from things moving 
 and moved infinite in multitude, will be infinite in magnitude. 
 But it is impoffible that any body, whether compofite or fimple, 
 can be infinite. But, if motions are in a circle, feme one of things 
 moved at a certain time, will be the caufe of perpetual motion, if 
 all things move and are moved by each other in a circle. This, 
 however, is impoHible : for that which moves a perpetual motion 
 is perpetual. Neither, therefore, is the motion of things moved, 
 in a circle, nor ad infinitum. There is, therefore, that which 
 moves immoveably, and which is per pet vial. 
 
 But from hence it is evident, that all things are not moved ; for 
 there is alfo fomething which is immoveable. Nor are all things 
 at reft ; for there are alfo things which are moved. Nor are fome 
 things always at reft, but others always moved ; for there are alfo 
 things which are fometimes at reft, and fometimes moved, fuch as 
 are things which are moved from contraries into contraries. Nor 
 are all things fometimes at reft, and fometimes moved ; for there 
 is that which is perpetually moved, and alfo that which is per- 
 petually immoveable. 
 
 Theorem 12. 
 
 Every thing which is moved, is moved by fomething. 
 
 Demonjlration. 
 Let A be that which is moved, I lay that A is moved by fome- 
 thing : for it is either moved according or contrary to nature. 
 If, therefore, it is moved according to nature, that which moves is 
 nature ; but, if contrary to nature, that which employs violence 
 moves : for every motion contrary to nature is violent. 
 
 Theorem 13. 
 That which firft moves a circular motion is impartible, or with- 
 out parts. 
 
 Demon-
 
 I N T R O D U C T I O N\ xii 
 
 DemonJIratton. 
 
 For let A be that which moves the firft motion : for it is neceflaiy 
 that there fliould be fomcthing of this kind, becaufc every thing 
 which is moved is moved by fomcthing. But A, if it is that which 
 iirft moves, will be immoveable : for that which is immoveable is 
 the leader of all things which are moved. And, fince it moves a 
 jTerpetual motion, it will polTefs an infinite power of moving ; for 
 finite powers have alfo finite energies : for energy proceeds from 
 power. So that if its energy is infinite, its power alfo will be in- 
 finite. Hence, that which firft moves a circular motion, muft ne- 
 ceflarily either be body, or incorporeal. But if body, it is either 
 finite or infinite. There is not however an infinite body. And if it 
 is a finite body, it will not pofTefs an infinite power. But the powers 
 of things bounded according to magnitude are finite, as has been 
 demonftrated. Hence, that which firft moves a circular motion, is 
 not a body. It is therefore incorporeal, and pofiTcfiTes infinite 
 power. 
 
 hi tranflating the Metaphyfics of Ariftotle (for it is now time to 
 fpeak of the following tranfiation) I have endeavoured as much as 
 poflible to give the literal meaning of every fentence, wdthout 
 paraphrafing what I conceived to be the fenfe of my author, or 
 expanding what might appear to be too concife. The ftudied ob- 
 fcurity indeed of Ariftotle's dicStion in this work is perhaps without 
 a- parallel in any antient or modern writer. Not daring, therefore, 
 IC' impofe on the reader by prefenting him witli my conceptions 
 as thofe of the Stagirite, nor prefuming to meafure that mighty 
 genius by my own, I have in general, after giving the moft faithful 
 tranfiation in my pov/er of dubious pafiages, either explained thent 
 by notes, or left them to the decifion of the reader : for as I write, 
 not v.ith any defign of procuring the fleeting and contemptible 
 
 f applaufe
 
 xlii INTRODUCTION, 
 
 applaufe of the day, but with an e}x to the approbation of more 
 equitable pofterity, I have endeavoured by acling the'part of a faith- 
 ful tranflator to procure for the follow ing copy a duration co-ex- 
 tended with that of the original. It is furely not arrogant to hope- 
 that, while the genius of Ariftotle like fome mighty vefTel fails tri- 
 umphantly through the vaft fea of ages, followed by other veffels 
 of confiderable magnitude, and with ail its fails fwelling with the 
 ftrongeft breath of fame, 
 
 My bark altcndant ma}' aufpicious faiP, 
 PuiTuc tlie triumph, and partake tlic galc» 
 
 How much I have been indebted to two of thofe great attendant 
 veiTels, or, in other words, two of the Greek interpreters of Ariftotle, 
 Alexander Aphrodifienfis and Syrianus, and particularly of the 
 latter, will be evident to every one who reads the following notes,. 
 and wdio has in his poireffion the Commentaries which have been 
 publillied of the former, and thofe in manufcript of the latter. 
 
 And here I cannot refrain from noticing, and with an indignation 
 ■which I truft Plato himfelf would allow to be generous*, the 
 arrogance of Dr. Gillies, in the Preface to what he calls a tranflation 
 of the Ethics and Politics of Ariftotle., " My time, fays he, was 
 miferably misfpenr in examining Ariftotle's numerous commenta- 
 tors ; Greek, Arabic, and Latin." That his time might have been 
 miferably misfpent in perufing the Arabic and Latin commentators 
 of Ariftotle, may perhaps be admitted, though even here an ex- 
 ception is to be made to fuch a writer as Averroes, becaufe his com- 
 mentaries contain extracts from antient authors, whofe works are 
 now no more ; but his time could only have been miferably mif- 
 fpcnt in examining the Greek interpreters of Ariftotle, becaufe he 
 
 * r^u^cc y.-ncwS' 
 
 did
 
 INTRODUCTION. - :!;ii,i 
 
 did not underftand them. What ! after a period of more tiian two 
 thoufand years,— after the abolition of the Academic and Peripatetic 
 fchcols, — when Philofophy has retired into deep fohtiide, and even 
 Echo no longer anfwers to her lyre, fliall one, who is i\o native of 
 Greece, and who is totally unfkilled, as we have feen, and fhall ftill 
 farther fee, in the fublimer part of Arirtotle's w^orks, prefame to 
 vilify the writings of men of exalted genius, who devoted their 
 lives to the ftudy of the Peripatetic and Platonic philofophy, of 
 which they had a traditional knowledge, who had the felicity of 
 having the Greek for their native tongue, and of being able to confult 
 books written by the immediate difciples of Ariftotle and Plato, 
 and w^hich are now irrecoverably loft ? I am fure I have no perfonal 
 enmity to Dr. Gillies, nor is what I have, and fhall fay of him dic- 
 tated either by malevolence or envy. May his reputation in v/hat he 
 has deferved well of the public be lafting, and his laurels among 
 his countrymen ever bloom ! But it was furely fome evil genius 
 that in an evil hour tempted him to abandon Hiftory for Philo- 
 fophy, and Herodotus for Ariftotle. 
 
 '•' Touch not HctSior, Hedor is my due," 
 
 was the exhortation of Achilles to Patroclus. And how much is it 
 to be wiflied that fome one deeply fkilled in the Peripatetic philo- 
 fophy, had with like friendly zeal faid to Dr. Gillies, " touch not 
 the obfcurity of Ariftotle, it is not to be \'anquiflied by you, the 
 attempt will be fruitlefs, and the iffue fatal to your fame." Fatal 
 indeed, it muft be : for his tranflation of Ariftotle has neither the 
 manner, nor frequently the matter*, of the original. His ftyle, 
 
 inftead 
 
 * Tnftanccs of the truth of this afll-rtion are lb numerous in this tranflation of 
 Dr. Gillies, that it would be ehdlefs to adduce them. I Ihall therefore only pre- 
 fent the reader with the following, which calually prcfcnted themfelves. The 
 
 f % beginning
 
 xliv INTRODUCTION. 
 
 inftead of conveying to the reader an idea of the unadorned purity 
 
 and wonderful compreffion of that of the Stagirite, is pompous and 
 
 diffufe ; and he frequently ventures to introduce entire fentences of 
 
 his own, which are wholly unauthorifed by the text. 
 
 Had 
 
 beginning of the fixth chapter of the fixth book of the NIcoinachean EthicF, is as 
 follows. JLtt-i V rj STrKTzyjUij Tnpi rocv ku9oXov uttiv v'rroXyi'tJjig, r.Oii tc'J'j s^ UVA'/Kijc ovtvov' 
 iiO'i 3' &■&%«/ TMV a7rodiix.TCov x.ai -Traa-yjg STricrTrjixyig' u.:-tu Koyov yy.^ y) i7ricm;jj.ri' rrig apyjig 
 10V i7ti<rri'jov ovr ocv STfurryi^ri itrj, ovts rsyjr,, ovts (pLiOvr,crig' to jj.sv yoc^ iTrta-rYjTov, 
 aTTohiKTC'^. di Si TvyxxvovTiv ovo'xi %;(it ta evo'zyjo^ivx aKKcxjg iyjiv. 1 hat is, " Since 
 fcience is a definite perception (for fuch is the meaning of the word vTroXyf^ig in 
 Ariftotle's philofophy) of things univerfal, and of things which have a ncceffary 
 fubfiftence ; and fince there are principles of the objcdts of demonfiration, and of 
 every fcience (for fcience fubfifts in conjuncSlion with rcafon), there will neither be; 
 fcience, nor art, nor prudence of the principle of that which may be fcientifically 
 known ; for the objed of fcientific knowledge is demonflrablc ; and art and pru- 
 dence are converfant with things which have a various fubfillence." This paflage 
 js tranflatcd by Dr. Gillies as follows : " Since the objed of fcience as above ob- 
 ferved is univerfal and demonftrable truth, and whatever is demonltrable muft be 
 founded on principles, it is manifeft that there muft be primary principles, which are 
 not fcience, any more than they are art or prudence. They are not fcience, becaujer 
 all fcience is demonJiraUe ; they are not art or prudence, bccaule thefe have for their 
 fubje6t things contingent and variable." Here, in the tirft place, no notice whatever 
 is taken of the word \}7toXy\'\>^i\ ii"fU '" ^'^^ "^^^ place, fcience is confounded with 
 the object of fcience. For the words lo jj.;v yap STTta-TYiTov, uitohint-xoy \. c. for the 
 ohjed of fcientifjc knoivleclge is clemonfirahle, arc rendered by Dr. Gillies, becaufe all 
 fcience is denionflrable." 
 
 Again : the latter part of the eighth chapter of the fixth book of the fame work, 
 is as follows : oii 3' >; £ppov)jcr/f ovv. S7ricrTrjiJ,yj ipavs^ov' rev yocp sa-yjXTCv sa-jiv, cca-Trip n-y^rui' 
 TO yxp TTpxy.TiKoy tciovtov. xvrnisnxi jUif dj; tm vu' o uiv yap i/ovg, Tctii/ opoov, uiv ovk ta-ri 
 ?.oyog' ti 01 rov c<r%XTOv, cv ovx. cO-tiv iTTKrryijxy], ctAA' uia-9riTig' ot% '^ ruiv I'Stcvv, aAA' htx 
 utv^xic^'zdcn OTi TO sv Totg iMx^rjy.XTi'KOig icrypcTOv, Tpr/Mvoy' crrriosTxi ya^ kxksi' «AA' avTtj 
 jj.xK?.o)/ uia^YiO-ig ■// Cp^ovrio-ig' iKuvrig ^5, aAAo iilog. i. e. " That prudence is not leience 
 is evident : for, as we have faid, it is converlant with that which fubfifts as an cx- 
 trcn.e : for that which is pradlical is a thing of this kind. But it is oppofed to 
 jnteileft : for intellcdt is converfant with terms or limits, (i. c. axioms,) of which 
 there is no definition : but prudence is converfant with that extreme, the percep- 
 tion
 
 INTRODUCTION. xlv 
 
 Had Dr. Gillies ftuclied merely as a philologift tliofe invaluable 
 treafiires of antient wifdom, the Greek interpreters of Ariftotle, his 
 time would have been at lealf fo far well fpent, that he would have 
 been prevented from making fuch an erroneous arrangement of 
 
 Ariflotle's 
 
 fion of wliicli is not tlic province of fcicnce, but of fcnfc. Not indeed that it is 
 a fentiblc perception of things which arc the proper ohjcds of fenfe, but it is of 
 thnt kind, as when we perceive that in mathematical figures a triangle is the iaft : 
 for figures tlop there *. This perceplion, however, rather belongs to fenfe; but 
 that which pertains to prudence is fpecificallv different." Dr. Gillies tranflatcs this 
 paflage as follows : " Prudence is manifeftly different from fcicnce ; being the 
 perception of thofe particular and praiflieal truths which admit not of demonftration ; 
 whereas intelledt is employed about thofe general and primary principles which 
 require not anv proof. In the chain of mental faculties, intellei5t and prudence then 
 form the two extreme links ; prudence holding the extreme of individuality ; and 
 . intelle6t, that of generalization. Prudence, then, may be called common fenfe^ 
 llnee it is converfant about objcdls of fenfo ; but in a manner fpecifically different 
 from that in which the other fcnfes are refpe6tively converfant about their particular 
 objcfls." Here, what Ariftotle fays relpecfting a triangle is entirely omitted ; and 
 I truft that the reader does not require to be told that no part of this paflage can 
 with propriety be called a tranflation. 
 
 Not only tingle palfages are continually tranflated in this manner, but entire chap- 
 ters. I fliall give the reader, as an infiance, the third chapter of this book. Ao^«- 
 y.iyoi ow xvM^sj, 'TTspi uuTuiv "TTxKiv Afyw/A-'v. STTU oYj oig c(X;9ivsi ■/] \l>v)(^yj toe KX7Ci(pccmi ij 
 a7ro(pxvat, ttsvt; tcv x^i9jj.ov' ravrx o sctti, Tcyj/ri, i7ri<Trri^j.-/i, (p-^ovrjcrig, croCpix, yovg. VTio- 
 A'/yiJ/i/ yxp xxi ^o^:^i i-J^sy^rxt J/ai^^uSccr^ai. cTT/ctt^^); |a» ovv Ti sa-Tiv, ivrivSiv (pavepov, st 
 0:1 aix.piQoXoyciiT9xi, kxi jj/,] xKoXovSiiv laig ojJ.oioT',icri' 7Txv'c=g yx^ viroKxjjt.Sxvou.sv, o S7ri<rrx- 
 y,s9x ^v\ iv^iyj<r9xt xhXug sy,itv. rx ^; sv^iyo^svx xKKc<jg, otxv c^m tov B^Moeiy yiv/jiai, 
 Kx'j9xvit it i'jiiv, '/? jU,);. s^ avxyxyjg x^x sctti to stt/ctt/Jtov* xt^toi/ xpx. tu yap s^ xvxyK-i]g 
 cnx, xTrKuig xi dix Trxi/Tx. rx o xi oix, xysv/jTX kxi x^9xiiTX- sti, ^i^xKTi] vi'xcra iTrtcrTyjuy; ^oKU 
 sivxi, KXI TO cTrta-TYiTov, yxaS'/jTOv* SKTr^oyivwa-Ko^jisvuv S; "nxcrx oi^xa-y.xKnx' oo<r7rsp kxi 3v Toig. 
 K'/xXvTtKOtg sKsyoiMSV. Yj ^;v yxp, oi nrxyuiy-iig' t; §j <Tv7J.oyi(yy.tc' -J ^yj S;j STTxyuy/i xpy^/j 
 scrri y.Ki tov kx9oXov' o o; (rv70^oyt(T^og, ix. tcu]/ kx9oKov. ti<nv txpx xpy^xi, s^ ciiv 6 crvKKoyto-- 
 fMcg, cov OVK sa-Ti (rvKXoy kt i^og' izxyuyvj xpx. )j j^iv xpx i7ri<nifiy.yi sa-Tiv i^tg xttc^ikti ?(.;■!, 
 ■/ixi oiTu a?'.Xx Ti'QOCi^liopi^o^cSx sv Toig amhvTiKOig. orxv yxp iioog %i<rTevr,; kxi yvupiuoi 
 
 * i. e. All figures are ultimately refolved into triangles. 
 
 aVTM
 
 Nivi INTRODUCTION. 
 
 Ariftotle's Mctaphyfical writings as we have already noticed, and 
 from committing thofe grofs errors which we have detecfted in the 
 notes to the following work. One of thefe, indeed, it will be ne- . 
 ccllary to difcufs more largely at prefent. " The real fiibje6l (fays 
 he*) of Ariflotle's Metaphyfics, (which has been grofsly miftakeu 
 through a prepofterous arrangement of the treatifcs which they 
 comprife) is the vindication of the exiftence and nature of truth,, 
 againll: the cavils of Sophiil:s, and thofe now called Metaphyficians ; 
 
 and 
 
 avTM toTiv at Oi^yjxi, iiri<Tiurc/A' zt yap [jLyj jjL:cKXoy tcv <ri^:7:£^y.!Tij.y.T0c, kxtcc o-vu.Sik,7iKC^ 
 i^,--i Ty\v s7ria-T/ju.r]v. Trijt jj.;y ovv i7ri<nrj^-^g ^iujpi(r9i<} rov t^iottgv tovto'j- i. c. " Afiliining", 
 therefore, a more elevated exordium, let us again fpeak concerning thcfij. I_et, 
 then, the habits by which the foul enunciates truth by affirming or denying, be five, 
 in number. And thefe are, art, fcience, prudence, vvifdom, intcllcft. For by hy- 
 polepfis (or a definite conception of a tiling) and opinion, it is poffiblc to be 
 deceived. What fcience therefore is, will be from hence evident, if it is j)ropcr to 
 invefligate with accuracy, and not to follow fimilitudes : for wc all of us appre- 
 hend that a thing of which we have a fcientific knowledge cannot have a various 
 fubfiftcncc. But of things which have a various fubfifiencc, we are igno- 
 rant whether they cxill or not, when they are removed from our perception. 
 The objc(5l of fcience therefore is from nccefuty, and confequcntly is perpetual : 
 for, in fhort, all fuch things as have a neccfiary fubfiftencc are perpetual. 
 But tilings perpetual arc without generation, and arc incorruptible. Again : all 
 fcience appears to be didactic, or capable of being tanght, and the objedl of fcience 
 may be learnt. But all do^ririne is from things previoufly known, as wc have tliid 
 in our Analytics : for it is eidier through indu(?tion, or through fyllogilm. But 
 induction indeed is a principle, and is the princi])lc of that which is univcrfid ; and 
 fyllogifm confifts from things univerfal. There are, therefore, principles from which 
 f)llogifm confifts, and thefe principles are not colledied by a fyllogiflic procefs. 
 Hence they fubfift from induction. Science then is a dcmonftrativc habit, and fuch 
 other things as we have ai<::ribcd to it in our Analytics. For, when a man believes 
 .that a thing fubfifts after a certain manner, and the principles of it are knojvn to 
 him, then he has of that thing a fcientific knowledge. For if he has not a greater 
 knowledge of the principles than of the conclufion, his poileflion of fcience will be 
 
 * Vol. i. p. 86. 
 
 4iccidental
 
 INTRODUCTION. xlvii 
 
 and this dodlrine concerning truth ilkiftrated in the demonflration 
 of the being of one god. in oppofition to Atheifts on one hand, and 
 Polytheifts on the other." If by Polytheifts Dr. GilHes means men 
 who beheved in a multitude of felf-exiftent beings independent of 
 each other, and of one firft caufe, there were no fuch men among 
 the Greeks and Romans, as muft be obvious to every one who is 
 Gonverfant with the writings of the heathens, and as is fully evinced 
 by Dr. Cudworth, in his IntelletSlual Syftem ; nor am 1 acquainted 
 with any antient nation who entertained an opinion fo monftrous 
 and dire. But, if by Polytheiils he intends to fignify men who 
 
 accidental. And let thus much fufficc concerning fcicnce." The following is the 
 tranflation of .this chapter by Dr. Gillies. " Let thefe habits be the five following : 
 art, feience, prudence, wifdom, intellect. In matters of opinion we arc liable to be 
 deceived ; not fo in matters of feience. The former relates to things variable in 
 their nature, of whofe very cxiilence we may doubt, unlefs \Vhen they arc adually 
 perceived ; the latter is converfant about things unalterable, neccflary, and eternal, 
 incapable of being generated, exempt from corruption ; the knowledge of which 
 admits not of degrees between total ignorance and abfolutc certainty. All fcicnce 
 may be taught, and all teaching implies principles, namely thofe truths which arc 
 prcvioufly known by experience or reafon. The firft principles are acquired 
 by indudlion, that is, by intelleift operating on experience. Science, then, may 
 be defined a demondrativc habit, dillinguithcd by thofe properties which we 
 have afcribed to it in our Analytics. The principles of feience mull be perceived 
 with the cleareft evidence; for unlefs they be more evident than the conclufions 
 drawn from them, thofe conclutions will not form feience ftridly lb called ; becaufe 
 liicir truth does not neceflarily proceed from the truth of their premifcs; with 
 which they arc conne6tcd not cfTentially, but only by way of acccfTion or appcn- 
 dage." 
 
 The reader will eaiily perceive in this tranflation that Dr. Gillies was not content 
 with omitting fome parts of the original, and inferting fomc things unauthorifcd by 
 the text, but that he has not even preferved that fcientific mode of writing, fo uni- 
 verfally adopted by Ariftotle, and which difplays fuch an invincible force of rcafon- 
 ing. And in this arrogant and inaccurate manner he has tranflatcd the whole of 
 what he calls Ariflotle's Ethics : for the Eudemian Ethics and Great Morals of that 
 philofopher, yet remain to be tranflatcd. 
 
 6 . believed
 
 xlviii INTRODUCTION. 
 
 believed in the exiftence of divine natures, the immediate progeny 
 of one firft caufe, with which they are profoundly united, Ariftotle 
 is fo far from oppofing this dodrine in his Metaphyfics, that, in the 
 eighth chapter of the tw^elfth book *, he demonftrates their exii>- 
 ence. hi this chapter he exprefsly-fays, " It is neceffary that each of 
 the revolutions of the celeflial orbs ^fljould he moved by an effentially im- 
 moveable and eternal ejfence ;" and^ that thefe ejfenccs ^^PjouUI be as 
 many in nwnber as the revolving fpheres : and the conclufion of it is 
 remarkably ftrong in fupport of this opinion. "Our akcestohs, 
 lays he, and men of great ANTiQj.irrY, have left us a tradition 
 
 INVOLVED IN FABLE, THAT THESE FIRST ESSENCFS ARE GODS, AND 
 THAT THE DIVINITY COMPREHENDS THE WHOLE OF NATURE. TTiS 
 
 reft indeed is fabuloufly introduced for the purpoje of perfuacUng the mul- 
 titude^ enforcing the laws, and benefiting human life. For they afcribe 
 to THE FIRST ESSENCES a hu7nan farm, and [peak of them as refembling 
 other animals, and offert other things confequent and Jimilar to thefe. 
 But if among tiikse assertions any one separating the rest 
 retains only the first, viz. that they considered the first 
 essences to be cods, he will think it to be divinely said: and 
 it may be probably inferred, that as eviiry art and philo- 
 sophy has been invented a5 often as possible, and has again 
 p£r.ished, these opinions also of the antients have been pre- 
 SERVED AS RULics TO THE PRESENT TIME. Of the oplnions of our 
 fathers., therefore, and men of the highejl antiquity, thus much only is 
 manifcfl to us f." To thefe firft effences alfo, he alludes in the fol- 
 lowing 
 
 * See ihc note to that Ijeok, in wliicb tills fubjcdt is largely difcuflcd. 
 
 "j" nocpali^cTKi S; vvro txv a-^yjiciMV itai ttuXocuc-j, sv ^j-v^ov <yyjri^jicc:i ■Kxry.T'.yKuy.jj.^voc' 
 70ig VTrs^cv, on ■■^iot rs iitiv ovtci, y.o-.i TiiPiiyji to B^iov jyiv oX'/jv (pvriv. -xu oi Koi-ttoc y.v9iKcii; 
 .jj y/j 'TV'^CTr^yfr^ Tjioj T/jv TTSt^cc twv 7:c7J\ui-j, kai ttpo; T,y sig rovg voi/.ovg %ai to <rvjJ-(piMv 
 ^p>;(r/;'. avd^cijTroui-is ts yap tovtcv;, zed tMV (xK7:x/ toJMv oiJ.oiovg tkti XsycviTi, kxi Tovroig
 
 INTRODUCTION. xlix 
 
 lowing beautiful paflage in the fecondbook, " -/Is are the eyes of bats 
 to the light of day\fo is the intelle5i of our foul to fucb things as are natu- 
 rally the mojifplendid of all:'' So prevalent, indeed, was this do6trine 
 among the antients, that even fo late as the time of the Emperor 
 Commodus, the elegant Maximus Tyrius obferves, " That there is 
 in all the earth one according law and opinion, that there is one 
 God, the kmg and father of all things, and many gods, fons of God, 
 ruling in conjunition with him. This is aflerted by the Greek 
 and the Barbarian, by the inhabitant of tlie continent, and by him 
 who dwells near the fea, by the wile, and by the unwdfe. And if 
 you proceed even as far as to the utmoft fliores of the Ocean, there 
 alfo there are gods, riling very near to fome, and fetting very near 
 to others*." And this lliows how little Dr. Gillies was acquainted 
 
 with 
 
 i'S^'x ay.o'Kcv^cc kxi 7rxjtx7rKri<Tic< Tct; sizvijx-votg' liv si rig '/jM^i<rxg ocvto Xa&oi jj,oiw zo Trpw- 
 ■rov, OTi Biovg coovto Tocg TT^Mxag ovcrixg Sr^xi, 3=i:og ccv sip'tja-^xi, vajj-iTsis' xai koctx to smog 
 •TtoXXxKig iUpyj^svYig etg to 'Svvjctov S){,y.crr-/jg kxi TS-x^v^g x,xt (piKocro(piocg, k.xi ttxXiv (p^ujoi^ivocy, 
 Ttxi TXVTXS txg ^o^xg cx^ivuiv, oiov "Ku^ixvx Trs^tcnirMa-^xi U-^XPi Tov vvv' -4 ^-v ovv Trxr^iog 
 ^o^x, ■n.x.i >} TTx^x ruj'j TT-iccTujv, sTTi ro(rovTov vj^juiv (pxv;gx jmovov. Di'. Gillies's tranflation 
 or aiialyfis, or by whatever other name he may think fit to call it, of this pallage is 
 Its follows : " This do<flrine (viz. concerning a firft incorporeal mover) was delivered 
 down from the antients, and remains with their pofierily, in the form of a fable ; 
 which, with many additions to it, has been employed for the fervice of legidation, 
 and for bridling the paflions of the multitude. The gods have thence been repre- 
 fcntcd as endowed with human forms, and agitated by human paifions; from which 
 flrange fuppofitions, many confequences not lefs ftrange have very naturally been 
 derived. Yet, from the motley mafs of fiftion, if we feparate this finglc propofition 
 thai deity is the firjt offuhjlances, it will a[)pear to be divinely faid ; and to have been 
 faved as a precious remnant, in the wreck of arts and philofophy, which it is probable 
 have often flourillicd, and often fallen to decay." Analyfis of Ariilotlc's works, 
 p. 136. The grofs ignorance, or wilful perverfion of Ariftotle's meaning, dif- 
 playcd in this tranflation by Dr. Gillies, mull be obvious to every one. 
 
 * 'Kvoi itoig XV iv TTxiTX y/j o^o(p!.K)vov vo^ov Kxt Xoyov, on Ssog ng tckviuv (3«criX;vg Kxi 
 TrxTtip, Kxi ^iot .TToKKoi, B^ov Tra/S.-fj (rvvxp-x^ovTsg Biu' rxvtx h 'EhhrjU hsysi, kxi 
 
 g ^eip<Zx'^QS
 
 1 INTRODUCTION. 
 
 with the Metaphyfics of Arillotlc, of which he has prefunicl ro 
 give an aiialylis, and with the general opinion of all antiquity, on a 
 fubje6l which of all others is the moil interelting and the molt 
 fublime. I fliall therefore conclude thefe IlricStures on Dr. Gillies 
 with obfei-ving, that if all the philofophical writings of the antients 
 were to be tranilated into modern languages, in the fame manner 
 in which he has tranflatcd the Ethics and Politics of Ariltotle, and 
 the fame analyfis were given of their doctrines which he has given 
 of thofe of the Stagirite, fuppoling the originals to be at the fame 
 time deftroyed, a period more dreadful would be realized than 
 
 when 
 
 The NORTH by myriads pour'd her barb'rous fons. 
 Dire nurfe of Goths, of Alans and of Huns. 
 
 From a fincere love of truth, which I firmly believe is, as Plato fays, 
 the fource of every good both to gods and men, and from my great 
 veneration for the works of Ariflotle, of which in conjundlion 
 with thofe of Plato I have been a fludent nearly twenty years, and 
 not from any perfonal enmity whatever to Dr. Gillies, I have been 
 unavoidably induced to be thus fevere. 
 
 Whatever may be the fate of the following work, whatever the 
 opinion which may be formed of it by the critics, this I can fay 
 with juflice and without vanity, that the reader will find the ge- 
 nuine dodlrines of Pythagoras and Plato on the moft fublime fub- 
 jedls more fully and faithfully unfolded, and this from antient 
 
 iSccfiQupcg Xsyn, xui o ijTre/pwTJjf j kcci o Bx>.octtio^, xxt o <to^o:, y-oci o ocTopos" KOiv sirt tcu 
 ccy^-xvcv iX9ijg rctg riicvas, kuku 9:Ct, TOtg jj.;v uviTymTzq ayxov jj.ccKu, roig oi, koiju^vc^-^oi. 
 Diflert. i. Such, however, has been the ignorance of the greater part of modern 
 writers on this moft interefling fubjedl, that Socrates has been celebrated by thcin as 
 ftiperior to moft of the heathens^ for believing in one firft caufe ; though the exift- 
 e-.icc of one fupreme Ruler and Tabricator of all things was never denied by any but 
 Aiheift>. 
 - . fourccs.
 
 INTRODUCTION. li 
 
 foiirces, in the notes to this tranilation, than in any other modem 
 pubUcation. To accompHfli this, 1 have devoted myfelf to the 
 liudy of antient wildom, amidlt the prelTure of want, the languor 
 and weakncfs occafioned by continual difeafe, and fevere toil in 
 fituations not only uncongenial with my difjiofition, and highly 
 unfavourable to fuch a purfuit, but opprefled by tyranny, and ag- 
 gravated by infult. Amidit all this, and yet this is but a rude de- 
 lineation of endurance, what has been my recom^jenfe from the 
 critics, for having brought to light truths, which have been con- 
 cealed for ages in oblivion, for having tranflated and iilullrated 
 writings, which, from their intrinfic merit, have been preferved 
 amidft the ravages and revolutions of time, fanatic fury, and bar- 
 baric de vacation? Not the praife due to well-meant endeavours 
 and generous exertion ; not the equitable decilion of candid criti- 
 cifm ; not even the cool, difpaffionate and benevolent cenfure which 
 Pity fuggefts while Humanity w^rites ; — but the favage inventive of 
 mercilefs Malevolence, the Itupid fiander of Ignorance, and the 
 imbecil fcorn of dull Impertinence. Thefe have been my rewards 
 from the critics» Through the combined efforts of thefe foes to 
 grea.t and virtuous emulation, my WTitings have been explored for 
 the purpofe of detecting and magnifying faults w^hich in other 
 authors have been configned to oblivion, and not w^ith any inten- 
 tion (for to this indeed they were inadequate) of combating the 
 dodfrines which 1 have fo zealoully endeavoured to propagate. Yet 
 it is from a faithful reprefentation of thefe doiStrines, that I look 
 forward with ardent, and I truft unprefuming hope, to the appro- 
 bation of a better age, in w^hich the page of criticifm will not be 
 ifained by malignant defamation, and in which the labours of the 
 now opprefled champion of Truth and Wifdom fhall be appre- 
 ciated by Equity herfelf, and be at lead honorably^ if not lai'gelv 
 recorded in the archives of Immortality. 
 
 g 2 Yet,
 
 lii INTRODUCTION, 
 
 Yet while the hand of Misfortune has thus heavily oppreirecl^ 
 though not fubdued me, and gigantic hijuftice has endeavoured to 
 crulli my literary exertions, the eye of Providence, from which 
 nothing can be concealed, appears to have more than glanced at my 
 endurance. It fent me friends, it even procured me patronage, in 
 two gentlemen, whofe merits are as uncommon as the purfuits 
 which they have patronifed are fublime. Of thefe gentlemen, 
 William and George Meredith, were I to fay all that fiicnd- 
 fliip prompts, or gratitude demands, I Ihould only wound their 
 feniibility, and perhaps weary the reader, without either fatisfying 
 juftice on the one hand, or adequately expreffing all that I feel on 
 the other. Let lilence therefore indicate what cannot be told. 
 
 Thus much, however, may and muil be faid, that the prefent 
 work is given to the public under the aufpices of thefe gentlemen, 
 the elder of whom difplays a fingularly line tail:e and folid judg- 
 ment on all the fubjedls of polite literature, and the younger pof- 
 feffes exquifite talents in his profeffion as an architedt, and a know- 
 ledge of the Gothic architecfture, at once accurate, extenlive, and 
 uncommon. Thefe talents and this knowledge, unnoticed as they 
 are, and almoft unknown, he has acquired under very difcourag- 
 mg circumftances ; but it is the chara6leriftic of true genius to 
 poffefs an ardor which neither difficulties can terrify, nor obllacles 
 retard. 
 
 The author, therefore, of the prefent work glories in being able 
 thus publicly to teftify, that for the completion of fuch an arduous 
 undertaking, he has not been obliged to ftoop to any of thofe humi- 
 liating methods, by which works of coniiderable magnitude and 
 imr>ortance are unfortunately too often forced into light, — and that 
 vinder the aufpices of thefe gentlemen he has been enabled to 
 inifold the wifdom of Ariftotle and Plato, without any other view 
 than that of benefiting mankind, and receiving that approbation 
 5 from
 
 INTRODUCTION. Im 
 
 from the liberal and difcerning Avhich his labours may deferve. 
 While he has the good fortune to enjoy their friendfliip, and expe- 
 rience their fupport, as he has hitherto dared the attacks of male- 
 volent critics*, by whom, like UlyfTcs, he has been 
 
 Spiirn'd, but not inov'd 
 
 he is confident that he iliall ilill be able to defy the united efforts of 
 the whole tribe of verbalifts, fciolirts, and pedants, 
 
 " thougli numerous in our iflc, 
 
 As 1:alf-formil infects on the banks of Nile." 
 
 Laftly, it is my intention, if the prcfent ^^•ork is fufficiently fuc- 
 cefsful, and if I am bleffed with health and leifure adequate to fo 
 great an undertaking, to give the public, under the fame liberal 
 patronage, and in an Englifli drefs, all that remains of the mighty 
 leader of the peripatetic philofophy. 
 
 As the reader will find that frequent mention is made in the 
 courfe of this work of the dianoetic part or power of the foul, it 
 will be necefiary to obferve, that both according to Ariftotle and 
 Plato, this part of the foul fubfiils immediately after intellecSl, which 
 is the fummit of our effence, and the energy of which confifts in 
 immediate intuition without the labor of reafoning. The dia- 
 noetic power, therefore, when it energifes according to its proper 
 nature, is that power which reafons fcientifically, or, in other words, 
 
 * I do not dcfpife verbal criticirm, but I confidcr it ns ranking In one of the 
 lowcft departments of literature ; nor do I defpile verbid crities when they a6t like 
 men confcious of their literary inferiority. But when, infiead of behaving with 
 that modefiy which beconnes thofc whofc proper ftation is the veftibule of knowledge, 
 they afllvme an authority which is alone the prerogative of tho high prieib of wifdom, 
 wc may pertinently apply to them what Ulyfles faid to the female flaves of Penelope, 
 
 " The fcourge, the fcourge flwll lafli you into fenfe." 
 
 which
 
 Jiv INTRODUCTION. 
 
 which by affuming the principles of its reafoning from intellc6l, 
 which principles we denominate axioms, produces demonitrative 
 conclufions. Subordinate to this is the doxaftic* energy, or the 
 energy of opinion, which fimply knows that a thing is, but does 
 not know why it is. Thus it knows the conclulion of dianoctic 
 reafoning, as, for inftancc, that every rational foul is immortal, and 
 the univerfal in particulars, as, that every man is a biped ; but, 
 having no knowledge of the caufe of exiitence, it is inferior to in- 
 tellectual and dianoetic energy. 
 
 It may likewife be neceilary to obferve that, as fkill in verbal cri- 
 ticifm is confidered at prefent, though very falfely, to be the tell of 
 erudition, 1 have given numerous emendations of the text in the 
 following work, partly from my own conjedture, but principally 
 from comparing the text of the printed editions of Ariftotle's Meta- 
 phyiics with the Commentary of Alexander Aphrodifienlis. It 
 is much to be regretted that a Latin tranflation only of this Com- 
 mentary is extant ; and that it extends no furtlier than to the 
 twelfth book of the Metaphyfics. However, I have been fortunate 
 in obta,ining an excellent edition of this tranflation, which appears 
 to be faitiiful, is by no means void of elegance, and is very intelli- 
 gible to one converfant with the perij^atetic philofophy.. 
 
 With refpcft to the Differtation on Nullities and Diverging Series 
 at the end of this work, the mathematical reader will I truft be 
 pleafed with a difcovery, w^hich unfolds the nature of infinitely 
 fmall quantities, and may probably lead to the complete fummation 
 of all kinds of infinite feries ; and the reader of Plato will no doubt 
 
 * As there are no words in ihc EngliHi langnngc correfponding to the words dox- 
 qftic ?LX\d dtano'e'tic,\\. is nccetiary to employ thcCc terms, in ilkiftrating the philofophy 
 of Ariflotlc and Plato. The Greek is the genuine language of genuine philofophy, 
 and modern languages, which, compared with it, are barbarous, can only be enriched 
 .nnd refined, by adopting as much as poflibic Grecian terms, 
 
 be-
 
 INTRODUCTION. Iv 
 
 be gratified to find a Pytbagoric and Platonic dogma elucidated, 
 which is of all others the moil abftiufe, the moll important, and the 
 moft fublime. 
 
 I fliall conclude this Introdud;ion with acquainting the reader 
 that as the propagation of the philofbi^liy of Plato, to which that 
 of Arillotle may be confidered as introduiSlory, has been for many 
 years the great objeil to Avhich all my exertions have tended, that 
 objedt will now probably be obtained ; a Nobleman of high rank 
 having generoufly offered to give that aid to my tranflation into 
 Englifli of Plato's works, without which it might not have been 
 prefented to the public in that handfome manner in which it will 
 now appear.
 
 ARISTOTLE'S METAPHYSICS. 
 
 BOOK I. 
 
 C H A p. I. 
 
 XIlLI' nien naturally defire to know*; a token of which Is the love of the 
 fenfes ; for, feparate from utility, they are loved for themfelves, and this is 
 efpecially the cafe with the fenfe of feeing. For, as I may fay, we choofe 
 to fee, in preference to every thing elfe, not only that we may ad, but like- 
 wife when we have no intention of ading. But the caufe is, that this fenfe 
 in a moft eminent degree makes us to know fomething, arid renders many 
 differences manifeft. Animals therefore are produced naturally pofTeffing 
 fenfe. But from fenfe, in fome of them memory is not ingenerated, and in 
 others it is. And on this account, fome animals are prudent, but others are 
 more capable of difcipline than thofe who are not able to exercife the power 
 
 * That knowledge is more excellent than aftion is evident from this, that every siSlion is folely 
 referred to fome end diftind from itfelf. For the exercife of the moral virtues themfelves, which 
 mofl of all things appears to be defirabic for its own fake, is referred to fomething elfe, viz. a pu- 
 rification from vice. But this is not the cafe with any contemplation or fcieuce : for here indeed 
 the inferior fciencesare referred to the higher to which they are preparatory, as for inftance the 
 Phyfical to the ^letaphyfical fcience, but at the fame time they are defirable for their own fakes, as 
 well as for the fake of the higher contemplations to which they lead. But no aflion is fimply 
 defirable for its own fake, but for the end alone to which it is direfted. Plotinus, in his book 
 On Nature, C'.ntemplaiion, and The One (to my tranflation of which I refer the reader), beautifully 
 proves that all things defire contemplation, and verge to this as their end; not only rational, but 
 alfo irrational animals, plants, and whatever participates of life however debile and obfcure. 
 
 B cf
 
 2 A R 1 S T O T L E ' S M E T A P H Y S I C S, Boose I. 
 
 of memory. Thofe indeed arc prudent without difcipline, who are unai)Iar 
 to hear loutids, luch as bees, and other animnls oi this kind, if any fuch are 
 to be found. But thofc learn, vvlio tt'gether with memory poffefs the fenfe of 
 hearing. Other animals thereiore live from phantafy, and memory, and parti- 
 cipate but a Uttle of experience ; but the human race Uvcs from art alfo, and 
 veafoning. But men derive experience* from memory. For memory being 
 often exercifed aliout the fame thing, gives perfection to the power of one 
 experience. Hence .experience appears to be nearly hmilar to fcience and art. 
 But fcience and art proceed to men through experience. For experience, as 
 Pokis f rightly obferves, produces art, but u ifkilfulnefs chance. But art is 
 then effcded, when, {rom many conceptions of experience, one univerfal opi- 
 nion about things fimilar is produced. For to have an opinion that to Callias, 
 Socrates, and to many otheis levtrally confidered, laboring under a cenain 
 difeafe, this particular thing is expedient, is the province of experience ; but 
 thit it is expedient to al! of this kind who are denned according to one fpe ie?, 
 and who are afflided with this dileafe, fuch as 'he phlegmatic, or the choleric, 
 or thnfe who are in a 'ever from heat, is the prr^viuce of art. 
 
 With refped therefore to adling. expe-ience feems in no refped to differ 
 from art ; but we fte that the fkiliul more readily accomplifh what they mtcnd, 
 than thofe who poffefs the reafon of a thing with' ut experience. But the caufe 
 of this is, that experience is a knowledge of particulars, but art of tning^ uni- 
 verlal. But all adions and generations are about that which is particular. 
 For he who cures does not give health to man, unlefs by accident, ^^ut to 
 Callias or Socrates, or fome one of others who are thus denomina'ed, and who 
 happens to be a man. If any one therefore poffeffes the reafon of a thing 
 without experience, and know\s indeed that which is univerfal, but is ignorant 
 of the individual it contains, he will often err in his attempts to cure. For 
 that which is particular polleflls a greater capability of being cured ; but at the 
 fame time we are of opinion that to know, and to underftand, btlong rather to 
 art than to experience, and we think that artifts are wiler than the experienced, 
 becaufe in all men wifdom is rather the confequence of knowledge thanof any 
 
 * Experience appears to be a certain univerfal knowledge of any particular often repeated in 
 the memory; but art is not only a knowledge of this, but of every thing fimilar to this com- 
 prehended as it were in one. 
 
 f An Agrigenti'ie Sophift, the difciple of Ciorgias the Rhetorician. He is one of the perfons 
 in the dialogue of Plato called the Gorgias : and, according to Suidas, he wrote the genealogy 
 and alfo a catalogue of the fliips, of thofe who went to the ficge of Troy. 
 
 thing
 
 Eooiil. ARISTOTLE'S METAPHYSICS. 3 
 
 thing tlfe. But this takc^ place, becaufe fome know, and others do not know 
 the caufe of a thing. For the fl-iilful indeed know that a thing is, but they 
 do not know ivhy it is ; but the fcientific know the lahy and the caufe ( f a 
 thing. On this account we confider thofe who in any thing are mafter artifts, 
 as more honrrable, as thofe who know more than manual operate rs, and 
 likewife as more wife, becaufe they know the caufes of things which are 
 ma<le. But others, like certain inanimate beings, make indeed, but make 
 deftitute of knowledge, jufl in the fame manner as tire burns. Inanimate 
 beings, therefore, make each of thefc things by a certain nature; but manual 
 artificers through cuftom ; as being wifer, not from their engaging in adive 
 purfuits, but from their pofTeffing reafon, and knowing the caufes of things. 
 And, in ihorr, it is a lign that a man pcffefTes knowledge, when he is able to 
 teach ; and on this account we think that art is more fcience than experience : 
 for the former are able, but the latter are not able, to teach. 
 
 Further flill, we do not think that any one of the fenfes iswifdom, although 
 each is the moft: principal knowledge of particulars ; but the fenfes do not aflert 
 the why refpeding anv thing, as for inftance, -dohy fire is hot, but only that it is 
 hot. It is probable, therefore, that the firfi: inventor of any art, befides the 
 common fenfes, was admired by men, not only becaufe fomething of things 
 invented was ufeful, but as being wife and differing from other men. But 
 ■when many arts were difcovered, fome of which pertain to things neceffiry, 
 but others to the conduft of life, from that time we have always confidered 
 thofe who know the caufes of things as wifer than manual artificers, becaufe 
 their fciences do not regard utility. Hence all fuch things as contribute to 
 the common purpofes of life being procured, thofe fciences were invented, 
 wl'.ieh neither refpedt pleafure * nor things neceffarv, and they were firft dif- 
 covered in thole places in which men abounded in leifiire. On which account 
 the mathematical arts firft originated about Kgypt ; for there the tribe of 
 priefts was permitted to be at leiliiie. In our moral treatifes f, therefore, we 
 
 have 
 
 * Ariftofie very" properly reduces tliofe arts which adminifter to pleafure into the order of 
 things which are invcfligaicd fcr the fake of utility, and the end of which is a certain jflion : 
 but pleafure is the iiifcparable attendant and companion, and not the end, of contemplation. 
 
 t Ariftotlehere refers to his rtthbook of Nicomachacan bthics, in which he fays there are five 
 things by which the foul enunciates truth, cither by nffiriration or negation, viz: art, prudiiicc,. 
 fcience, ivifikm, and nitcluH Of thcle, he fays, art is a habit effeclive of things, in coMJun£tion 
 with reafon ; fcietuc, a demonllrative habit, by which we acquire ti.e knowledge of things necef-- 
 fary and eternal ; jn/dtiice, a habit of ading in conjundion w ith true reafon, in things which are; 
 
 B 2 good
 
 4 A R I S T O T L E • S M E T A P H Y 3 I C S. Boor I. 
 
 liave declared what the difference is between art and fcience, and other things 
 of a kindred nature. But that for the fake of which we engage in the prefent 
 difcourfe, is the belief of all mankind, that what is called wifdom, is con- 
 verfant with firft caufes and principles. So that, as we before ohferved, the 
 ikilful man appears to be wifer than thofe who merely energize from any one 
 of the fenfes ; the artifl: than the fkilful ; the architect than manual artificers; 
 and the theoretic than fabricators. That wifdom, therefore, is a fcience about 
 certain caufes and principles, is evident. 
 
 CHAP. 11. 
 
 But, fmce we inveftigate this fcience, we fliould confider from the fpecu- 
 lation of what caufes and principles fcience is wifdom. If any one therefore 
 fhall apprehend the opinions which we entertain refpeding a wife man, perhaps 
 from this the thing propofed will become more evident. In the firft place 
 then, we are of opinion, that a wife man in the moft eminent degree knows 
 fcientifically all that can be known ; not poffeffing a fcience of things according 
 to that which is particular, but according to that which is univerfal. In the 
 next place, we confider him as a wife man, who is able to know things diffi- 
 cult, and which it is not eafy for man to know. For, to perceive according to 
 fenfe is common to all men ; on which account this is eafy, and he who thus 
 energizes is by no means wife. In the third place, we are of opinion, that he 
 who is more accurate, and more capable of teaching the caufes of things, is 
 more wife refpeding every fcience. Further ftill, that of fciences, that which 
 is eligible for its own fake, and for the fake of knowing, partakes more of 
 wifdom than that which is eligible for the fake of things which are contingent ; 
 and that the more principal fcience partakes more of wifdom than that which 
 is fubfervient. For it is not proper that the wife man Ihould be commanded, 
 but that he fhould command ; nor ought he to be perfuaded by another, but one 
 lefs wife ought to be perfuaded by him. And fuch and fo many are the 
 opinions which we entertain refpeding wifdom and wife men. 
 
 good or evil to man ; intellcfl, that power of the foul by which we knoMr the imlemonftrable 
 principles of tlemonflration ; and ivijcloin^ the fcience and intellect of tilings mod honorable by 
 nature, and the intcllcft of principles : in other words, it is the intelleiSlual vifion of thofe 
 eternal, immoveable, and intelligible natures the exiftence of which is proved by Ariflotle in the 
 12th book of this work. For thefc arc things moft honorable by nature, and the principles of 
 the univerfc. 
 
 But,
 
 Book I, A R I S T T L E 'S M E T A P H Y S I C S. § 
 
 But, among thefe, to know all things neceflarlly belongs to him who in 
 the mofl: eminent degree poflefTes univerfal fcience *. For fuch a one in*a 
 certain refpe£t knows all fubjeils. But things moft eminently univerfal are 
 nearly mofl: difEcuk too for man to know. For they are mofl remote from the 
 fenfes. But the moft accurate of the fciences are thofe which efpecially re- 
 late to things firft. For thofe fciences which confift from fewer thinrrs, are 
 more accurate than thofe which are denominated from addition ; as arithme- 
 tic than geometry. But indeed that fcience is more do£lrinal which fpccu- 
 lates the caufes of things. For thofe teach others, who about every thing 
 relate the caufes. But to know, and to know fcientifically for the fake of 
 fuch knowledge, efpecially belongs to the fcience of that which is moft emi- 
 nently the objeiSl of fcientific knowledge. For he who choofes to know 
 fcientifically for the fake of fuch knowledge, efpecially choofes that which is 
 moft eminently fcience. But fuch is the fcience of that which is moft emi- 
 nently the objedl of fcientific knowledge. And objects of this kind are things 
 flrft and caufes. For, through and from thefe, other things are known, but 
 thefe are not known through things ih fubjedtion to them. But the moft 
 principal of fciences, and which is more a principle than the fcience which 
 is in fubje<5lion, is that which knows on what account every thing is to be 
 done. But this is the good of every thing ; and univerfally that which is 
 beft in every nature. From all therefore that has been faid, that name which 
 is the obje(5l of our inveftigation falls into the fame fcience. For it is necef- 
 fary that this ftiould be fpeculative of firft principles and caufes. For the 
 good alfo, and that for the fake of which a thing fubfifts, is one among the 
 number of caufes. 
 
 But that this fcience is not employed in making, is evident from thofe who 
 firft philofophifed. For, both now and at firft, men began to philofophife 
 through wonder f : at firft indeed admiring fuch dubious particulars, as were 
 of a more eafy folution ; but afterwards proceeding in this manner gradually, 
 they began to doubt about things of greater importance, fuch as concerning 
 
 * The fcience of beings, fo far as they are beings, is the moft univerfal fcience ; and he who 
 poflefles this fcience, in a certain refpe£t knows all things : for he fees particulars compre- 
 hended in univerfals, and eileiTls in their caufes. 
 
 t As the defign therefore of modern philofophy, /• e. the purfuit of matter througli her dark 
 and infinite labyrinths, feems rather calculated to excite than to remove wonder, it may be 
 truly faid, that philofophy now ends where it formerly began. 
 
 the
 
 6 ARISTOTLE'S M E T A T H Y S 1 C S. Book!. 
 
 the properties participated by the moon, the fun, and the ftars, and the gene- 
 ration of the univerfe. But he who doubts and wonders, is of opinion that 
 he is ignorant ; and, on this account, a philofopher in a certain refpedl is a 
 lover of fables*. For a fable is cornpofed from things wonderful. So that 
 if now and at firft men philofophifed, in order to fly from ignorance, it is 
 evident that they purfued fcientific knowledge for the fake of knowing, 
 and not for the fake of any life. But the truth of this is alfo teftified by 
 that which has happened. For nearly all fuch things as are neceiTary being 
 prefent, and which contribute both to eafe and the conduft of life, prudence 
 of this kind began to be inveftigated. It is evident therefore, that we feek 
 after fcientific knowledge for the fake of no other utility than that which 
 ariles from itfelf ; and that as we call him a free man who exills for his own 
 fake, and not for the fake of another, fo this alone among the fciences is libe- 
 ral : for tliis alone fubfifts for its own fake. On this account, too, the pof- 
 feffion of it may juftly be confidered as not human. For in many refpeds 
 human nature is fei vile ; fo that, according to Simonides, divinity alone pof- 
 lefTes this honor ; but it is unbecoming that man fliould only invefligate- 
 the fcience which pertains to himfelf :j". But, if the poets fay any thing to 
 the purpofe, and a divine nature is naturally envious, it is likely that it would 
 efpecially happen in this particular, and that all thofe would be unhappy who 
 furpafs the reft of mankind. But neither does a divine nature admit of envy ; 
 and poets (according to the proverb) fpeak falfely in many things. 
 
 Nor is it proper to think that any other fcience is more honorable than 
 a fcience of this kind. For that which is divine is alfo moft honorable. 
 But a thing of this kind will alone fubfift twofold. For the fcience which 
 divinity poffcffcs is efpecially divine ; and this will likewife be the cafe with 
 the fcience of things divine + , if there be fuch a fcience. But the fcience of 
 
 * A philofopher may be faid to be a lover of fables, becaufe he fludies to learn things which, 
 from being unknown, are admirable } for fables are cornpofed from things admirable and incre- 
 dible. 
 
 ^ The word fiov.ov is evidently wanting in the original in this place. Inflead, therefore, of 
 flvsfa ^'ovx aiicv /J.n fiiTtiv rr.v xa6' auTOv mirntiw, wc fliould read avi^a $'oux a^iov i/.ri fiovoi, &C. 
 
 X /^riftotle has already informed us that the fcience which is the fubjett of this woik, fpecu- 
 lates firft principles and cauffs, and he now further intimates that it is the fcience of tilings 
 divine. There are therefore, according to Ariftotle, div'aie priiidpla atul caiifes; and tliefe are 
 the intelligiblcs which in the twelfth book he places over the ftarry fphcres, and which in rea- 
 lity arc no other than thofe incorporeal caufes denominated by Plato idias. 
 
 which
 
 Booxl. ARISTOTLE'S. METAPHYSICS. 7 
 
 which we are ipcaking alone poffelfes both thefe prerogatives. For divinity 
 appears to be a caufe and a certain principle to all things ; and either alone, 
 or in the mod eminent degree, divinity pofTefles fuch a fclence as this. All 
 other fciences therefore are more ntceffiry, but no one is better than this. 
 But it is requifite in a certain refpecl to eftabllQi this fclence in an order con- 
 trary to that of the inquiries which men made from the beginning. For all 
 men, as we have faid, begin from wonder to invefligate the manner in wlilch 
 a thing fubfifts ; juft as it happens to thofe, who have not yet contemplated 
 the caufe of thole wonderful llgures that move fpontaneoufly, or the caufe of 
 the revolutions of the fun, or the reufon of the incommenfurabiiity of the dia- 
 meter of a fquare to the fide. For it feems admirable to all men, that a 
 thing which is not the leaft of things, fliould not be meafured. But it is re- 
 quifite they fhould end in the contrary, and in that which is better, accord- 
 ing to the proverb, as is the cafe in thefe things when they learn them. 
 For there is not any thing which would appear more wonderful to a geome- 
 trician, than if the diameter fhould become commenfurable to the fide. And 
 thus we have declared what the nature is of that fclence which is the objeft 
 of our inveftigation, and what the mark to which the inquiry and the whole 
 method ought to be direded. 
 
 CHAP. III. 
 
 But, fince it is evident that it is requifite to confider the fclence of caufes 
 from its principle (for we then fay that each particular is known when we 
 know the firfl: caufe of it), and caufes are faid to iubfift in a fourfold refpc£t, 
 one of which we affert to be efeiicc'-'^, and the fubfilHng as a certain particu- 
 lar thing (for the inquiry. On what account a thing exlfts, is referred to the 
 laft reafon f) and caufe and principle form the firft ivby : but a fecond 
 caufe is ;»i^//fr ; and th:it v/hich fubfiRs as a fubject: a third is that ivhence 
 the beginning of motion is derived : but the fourth is the caufe oppolite to 
 this, thai for the fake of which a thing fubffs, and the good (for this is the 
 end of all gtnerationj. This being the cafe, though we have fpeculated 
 
 * By f^wcf here -Ariftotle mczn^ form ; for every thing is that which it is througli form. 
 Hence things defined are deliued tlirough this. 
 
 t Tiiat is, to definition ; but this is the formal caufe. 
 
 fufTiciently
 
 8 ARISTOTLE'S METAPHYSICS. Book I. 
 
 fufficiently concerning thefe caufes In our Phyfics, yet, at the fame time, we 
 Ihall take along with us In our inquiry thofe who prior to us have engaged 
 in the fpeculation of beings, and have philofophifed about truth. For it is 
 evident that they alfo affert that there are certain principles and caufes. A 
 repetition, therefore, of what they have faid will be of advantage to the pre- 
 fent difcuffion. For, either we fhall find another genus of caufc, or we fhall 
 more firmly believe thofe we have juft now enumerated. 
 
 The greater part then of thofe that firft philofophifed were of opinion 
 that the principles of all things alone fubfifted in the fpecles of matter. For 
 that from which all things fubfift, from which they are firft generated, and 
 into which they are finally corrupted, the eflence indeed remaining but be- 
 coming changed by participations, this, fay they, is the element, and this is the 
 principle, of things. Hence they were of opinion that neither is any thing 
 generated nor corrupted, becaufe this nature Is always preferved. Juft as we 
 fay that Socrates Is neither fimply generated, when he becomes beautiful, or 
 a mufician, nor is corrupted when he lofes thefe habits, becaufe the fubjedt, 
 Socrates himfelf, remains ; in like manner, neither is any one of other things, 
 either generated, or corrupted. For It Is requlfite there fliould be a certain 
 nature, either one, or more than one, from which other things are generated 
 while it Is Itfelf preferved. 
 
 But with refped to the multitude and form of this principle, all philofo- 
 phers do not all'ert the fame. For Thales indeed, who was the leader of this 
 philofophy, faid that this principle is water. On this account he afferted that 
 the earth is placed upon water, entertaining perhaps this opinion from 
 feeing that the nutriment of all things was moift, that the hot itfelf was ge- 
 nerated from this, and that from this animals lived. But that from which 
 any thing is generated Is the principle of that thing. On this account, there- 
 fore, he formed this opinion, and becaufe the feeds of all things have a moift 
 nature. But water is the principle of nature to things moift. But there are 
 fomc who think that men of the greateft antiquity, who flourlfhed long be- 
 fore the prefent generation, and who firft theologized *, entertained the very 
 fame opinion refpedllng nature. For they made Ocean f and Tethys the 
 parents of generation, and the folemn oath of the gods water, which Is called 
 
 * Ariftotle here doubtlcfs means Orpheus, Ilomcr, and Hefiod. 
 
 t Hy Ocean the antient theologifts fignified the divine caufe of all motion, and by Tethys 
 iht caufe which feparates all the different kinds of motion from each other. 
 
 9 Styx
 
 Book I. ARISTOTLE'S METAPHYSICS, 9 
 
 Styx* by the poets. For that which is the mofl: antient is the moft honorable : 
 but a ft)lcmn oath is the mofl. honorable. That this opinion, therefore, re- 
 fpeding nature is very antient, is perhaps not immanifefl:. Thales indeed 
 is faid to have difcourfed in this manner refpeding the firfl; caufe. For no 
 one v\'ill think that Hippo deferves to be ranked with theie, on account of the 
 meannefs of his cogitative part "f. Anaximenes and Diogenes placed air prior 
 to water, and confidered it as in the moft eminent degree the piinJple of 
 fimple bodies. Hippafus the Mctapontine, and Heraclitus the Fphefian, 
 confidered lire as the principle of all tilings. But F.mpedocles, who intro- 
 duced four princip'es, befides thofe already mentioned added earth for the 
 fourth. For according to him thefe always remain, and are not generated, 
 but are mingled and feparated in multitude and paucity, into one, and from 
 one. But Anaxagoras the Clazomenian, who was prior in age to Empe- 
 docles, but pofterior in his works, afferts that there are infinite principles. 
 For he fays, that nearly all things which confift of fimilar parts, fuch as water 
 or fire, are thus generated and corrupted by concretion and feparation alone ; 
 but that otherwife they are neither generated nor corrupted, but remain as 
 things eternal. From thefe men, therefore, any one might be led to think 
 that caufe alone belongs to that which is called the fpecies of matter. But 
 in confequence of their proceeding in this manner, the thing itfelf afforded 
 them a paflage, and compelled them to inveftigate. For though every cor- 
 ruption and generation is in the moft eminent degree, from fomething, as 
 fubfifting from one, or from many things ; yet, why does this happen, and what 
 is the caufe of it ? for the fubjedl itfelf does not make itfelf change. I fay, for 
 inftance, that neither wood nor brafs is the caufe that either of thefe is 
 changed. Nor does wood make the bed, nor brafs the ftatue, but fomething 
 elfe, which is the caufe of mutation. But to inveftigate this is to inveftigate 
 another principle, which we fhould call that from whence motion derives its 
 beginning. Thofe, therefore, who have entirely touched upon this method 
 from the beginning, and who affert that the fubje£t is one, have not rendered 
 any thing in this inquiry difficult to themfelves ; but fome of thofe who 
 aflert that all things are one, as if vanquiftied by this Inquiry, aflert that the 
 one is immoveable, and likewlfe the whole of nature, not according to gene- 
 
 * S/J.V may be confidered as the caufe by which divine natures retain an immutable famenefs 
 of eflence. 
 
 t Ariftotle doubtlefs fays this of Hippo becaufe he was an atheift. 
 
 C ration
 
 IS ARISTOTLE'S METAPHYSICS. Book I. 
 
 ration and corrugation (for this is an antient opinion, and acknowledged by all 
 men), but alio according to every other mutation. And this is the pecii- 
 li;iritv of trieir dodrine. 
 
 Of thofe, therefore, who aflert that the univerfe Is alone one, it has fo 
 happened that no one has perceived a caufe of this kind, except Purmenides* j 
 and this has h:mpened to him fo far as he admits that there is not only one, 
 but, in a certain refped:, two caufes. But to thofe who admit that there are more 
 than two caufes, it belongs in a ftill greater degree to affert a caufe of this kind ; 
 fuch as thofe who confider as caufes the hot and the cold, or fire ar.d earth. 
 For they ule fire as poifefrmg a motive natuie ; but water and earth, and 
 things of this kind, as endued with a nature contrary to the motive. But after 
 thefe and fuch 1 ke principles, as not being luflicient to generate the nature 
 of things, again, being compelled, as we have faid, by trutli, they invelli- 
 gated th;it principle whieh is confequent to this. For perhaps neither earth, 
 nor any other llmilar nature, is the caufe that feme things fubfift, and that 
 others are generated in a good and beautiful manner, nor is it probable that 
 they entertained fuch an opinion. Nor, again, is it proper to afcribe a 
 ihlnr' of fuch great importance to chance and fortune. He f therefore who 
 
 alTerted 
 
 * It n-.ufL be obferved of Parmenkles, that lie wrof-c fome things according to truth, and 
 ■otliers according to opinion. Plato admires the profundity of his conceptions. See my Intro- 
 duiSiion to, and Tranflation of, Plato's Parmenide?. See alfo that trcafury of antient erudition, 
 the Commentaries of Simplicius on the Phyfics of Aiillotle. 
 
 4 The following remark.; b!e extract from the loft works of Anaxagoras, of whom Ariflotle 
 is now fpeaking, will doubtlcfs be acceptable to the philofophic reader, as I believe he will not 
 find the whole of it in Englilh., in any other place. The paiTage is preferved by Simplicius in 
 Arift. Phyf p. 7- 
 
 Noi/5 06 £<r-iv aTTfijov, X2( ay-oxfaTE;, xai ixz/juktm ci>J<)'i xf»:/xa;Tr aM.x fiovo; auTo; a.p' iaulov sjTty. 
 El un yap a(p' ixuTOV nv, a\>ct teoj ZfjiciAimo a^^w, .ueteijcev av a.7ra\i^v xf)i/^aTuv, ei i/x^ixiKTo tew- tv 
 fravTi yap TravToj ftoi^a Evsriv, iiffTt!^ £v toi{ ^focrSiv £iaci ^£^£XTal• km aiXKu^-uiv auTov Ta j-i-.u/zE/xr/^fVis, ufc 
 ^l.rJ^'.vo; xfiy«^"S xpaTjiv o/ioiw;, i)j Kai /icvov tonx ccp' iauiou. En yzf f^cn-Torarovre ctjivtuv xfiMariuv, 
 KM Kae^ifaiTOTOV. Kai yvu/J.w yc ■xt^i ifano; 'nxuav lax^'t «^' "^X^f MfVirov. 'O^ayE y),ux-iv £X-', "ai /ac^a 
 xai Oar-Til, TTxvriov vcu; xpTEi. Kai thj TTFfixtJflS'ios thj cuj/.'^ajrti vcui iK^xT-nav/ u; W£f(x«f»io-ai t»v 
 «tpyttv. Kai TTPiiTO'J avo Tou a-iM'.K^ou nflaro TTE^ixufW^ai' fnnh ttXcIOV ?r£fi%a)f£i, xai ■nipixa^mTU iiri 
 7l^£0v. Kai T£» aufi/xcii-yjj-iva, T£ nai azoxpivo/xiva, km 3iaKjii»o,a£va, Ttavia syTiaje vov;, Kai OTTcia £^£^^J 
 taiviif xai OTTO a »v, xai o<ja. \uv Eriv, *-' oTOio. iTai. Oavra iiVio:^iJiTi\'7i voui' km Tur Tt^i^apniriv -rauir.v, 
 viv n\i TTEfiXWPEEi, TJiTE aT^ui- KM «>.i(J{, Kut » ffE^Jiv-i, Kctt awp, Kai aifinf, SI a7!OK^i]/o/^[\oi. 'H Jf Tre^ixa- 
 cM^i; ai/Xn ettoivwev ecTrcxfinaSM' km aTTCii^ntTM utto te a^jciou to ttuhvov, km airo tou -^vx^ou to 5e^/x,cv, km 
 alt!) TOU ^ofipou TO Xa^sTfov, KM ant) TOW fliEfoi/ TO |>;fov. Moifai Je ■foM«i lti»~w UffiV TtavTO, Tta^i Se ouhv 
 
 aVOK^iHTM
 
 BookT. ARISTOTLE'S metaphysics. h 
 
 aflerted that as in animals, fo alfo in namre, there is a certain lntelle<fl, which 
 is the caufe both of the world, and of all order, will appear like one fober, 
 when compared with thofe antients that fpoke rafhly. We evidently know, 
 therefore, that Anaxagoras touched upon thefe reafons ; though Hermotimus 
 the Clazomenian is faid prior to him to have mentioned a caufe of this kind. 
 Thofe, therefore, who entertained this opinion, together with eftablifhing a 
 principle of things, which is the caufe of their fubfifting in a beautiful manner 
 eftabliihed alfo a principle which is the caufe of motion to things. 
 
 CHAP. IV. 
 
 But fome one may' fufpecSt that Hefiod firft invefllgated a thing of this 
 kind ; and llkewife that this is the cafe with any other who may have confi- 
 dered love or defire as a principle in beings, fuch, for inflance, as Parmenides. 
 For he alfo, devifmg the generation of the univerfe, fays : " He produced 
 
 •avBH^iverai Iri^ov awo rou Its^ou, 7r^^^v vou. Nowj h ttx; hfjLOiOi en, xai o fiu^av nai o fhaacm' trtfov 3t 
 
 ;. e. " Intellect is infinite, poflefles abfolutc power, and is not mingled with any thing • 
 but is alone itfelf by itfelf. P"or if it were not by itfelf, but were mingled with fomething elfe, 
 it would participate of all things (for in every thing there is a portion of every thing, as I 
 have before obferved) ; ar-d things mingled together would prevent it from having a fimilar do- 
 minion over things, as when alone by itfelf. For it is the moft attenuated and the moft pure 
 of all things It liicewire poflelfes an univerfal knowledge of every thing, and is in the higheft 
 degree powerful. Whatever foul poflefles, greater or lefler, — over all thefe intelled has domi- 
 nion. Every thing too that comprehends or contains, is fubje£l: to its power ; fo that it even 
 comprehends the principle itfelf. And firft of all, indeed, it began from that which is fmall 
 to exercife its comprehending power; but afterwards it comprehended more and more abund- 
 antly. Intelleft alfo knew all that was mingled together, and feparated, and divided, together 
 with what they would in future be, what they had been, and what they now are. All thefe in- 
 telledl adorned in an orderly manner, together with this circular enclofure which is now com- 
 prehended by the ftars, the fun and the moon, the air and the nether, which are feparated from 
 each other. But this comprcliending iiitelle6l made things to be feparated; and feparated the 
 denfe from the rare, the hot from the cold, the lucid from the dark, and the dry from the nioift. 
 There are many parts indeed of many things ; but, in fliort, no one thing is feparated from an- 
 other except intelled. Every intelle£t too is fimilar, both the greater and the lefler; but no 
 other thing is fimilar to another." Anaxagoras, from this pafTage, which Simplicius informs us 
 is from the firft book of his Phyfics, appears to have been well acquainted with the twofold 
 order of things, the intdUgibU and the Jeiiftble, as wcli as the Pythagorjeans and PJato. 
 
 C 2 Love
 
 12 ARISTOTLE'S METAPHYSICS. Book I. 
 
 Love the firft of all the gods." But Hefiod *, " Chaos was generated the 
 firil of all things; but afterwards wide-bofomed Earth, and Love who excels 
 among all the Immorrals:" as if it were fit that there fiiould be a certain 
 caufe in beings whiv:h moves and comprehends things, and binds them toge- 
 ther. With refoeiTt to thefe, therefore, we may be permitted afterwards to 
 judge, which of them ought to rank as the hrft. But fmce the contraries to 
 things good appear alio to be inherent in nature, and not only order .ind 
 the beautitul, but diforder and the bafe ; and, fmce things evil are more in 
 number than fuch as are good, hence a certain other philofopher has intro- 
 d\ic&<\ frietidjijip andjiri/e, each, according to him, being the caufe of evil and 
 good. For, if any one fhould follow and receive this dodrine in that part of 
 his nature which reafons fcientihcally, and not according to what Empe- 
 docles f has flammering!y aiferted, he will find that friendfhip is the caufe 
 of things good, but ftrife of things evil. So that, if any one fhould fay that 
 Empedocles in a manner aflerts, and is the firft who alTerts, that good and 
 evil are principles, he will perhaps fpeak well ; fmce good is the caufe of all 
 things that are good, and evil of fuch as are evil. Thefe, therefore, as we 
 have faid, thus far touched upon thofe two caufes which we have defined in 
 our Phyfics ; I mean the material caufe, and that whence motion is derived: 
 but yet they have touched upon thefe caufes obfcurely, and in no refpe£t 
 cleaily, but juft in the fame miniier as thofe do, who are unexerciied in bat- 
 tles. For thefe advancing tow:!rds their opponents often ftrike excellent 
 blows; but neither do thefe ftrike from fcience, nor do thofe feem to know 
 
 * In my Introduflion to the Parmenidjs of Plato, I have proved that tiroi /xev v^ulira Xao; yevcT* 
 in the Theogony of Hefiod, was confiiiered by all antiiiuity as fignifyitig that Chaos luas gme- 
 ruted the firft of all things, and not that it was the firft of things ; though Cudvi-orth, from 
 being ignorant of this circumftance, accufes Hefiod as leaning to the atheiftical fyftem (Vide 
 Arid, de Ccclo, lib. iii. & Sex. Empiric, adverfus Math. p. 383, edit. Steph.). Simplicius, 
 therefore, very properly obfcrves, " that Hefiod, wlien he fays that Chaos luas frji generated-, in- 
 finuates that there was fomething prior to Chaos from which Chaos was produced. For it is al- 
 ways neceflary that every thing which is generated (hould be generated from fomething. But 
 this is alfo infinuated by Hefiod, that the firft caufe is above all knowledge and every appella- 
 tion." Simplic. de Ctelo, p. I47, Perhaps by Chaos Hefiod intended to fignify a certain infinite 
 and unknown origin of things ; or perhaps, according to Damafcius, the incomprehenfible and 
 perfectly united nature of that which is intelligible. I only add, that Chaos is the fecond of 
 thofe principles after the firft caufe of all, which was called by Pythagoras tlie indtfiniie duad, 
 and by Plato the infinite. See more on this fubjedt in the following notes to the third book. 
 
 I Concerning this doftrine of Empedocles, fee the following notes to the third book. 
 
 what
 
 Book I. A R I S T O T L E'S M E T A P H Y S I C S. 18 
 
 what they aflert. For they do not fcarcely in any refpciS: appear to ufe thefe 
 principles, except in a Tmall degree. For Anaxagoras ufes intelledl as a rr,a- 
 chine to the fabrication of the world, [ jufl as the gods are introduced in tra- 
 gedies, when very difficult circumftances take place * ;] and, when he doubts 
 on what account it neceflarily is, he introduces it by force. But, in other 
 things, he confiders every thing elfe rather than intelled as the caufe of ge- 
 nerated natures f. And Empedocles indeed ufes caufes more than Anaxa- 
 goras ; but yet neither fufficiently, nor in thefe does he find that which is 
 confentaneous. For in many places, according to him, frieiiJ/hlp feparates, 
 and Jirife rningles things together. For when the univerfe through Jlrife 
 is feparated into the elements, then fire, and each of the other elements, is 
 mingled into one. But when all things through fr'tendfiip accord in one, 
 it is neceflary that the parts from each fhould be again feparated. Empe- 
 docles therefore, in this refpecft, differing from thofe who were prior to hirp, 
 was the firfl: that, by making a divifion, introduced this caufe ; not making 
 one principle of motion, but fuch principles as are different and con'rary. 
 Further flill, he was the firfi: who alTerted that the elements which are confi- 
 dered as belonging to the fpecies of matter, are four; yet he dnes not ufe 
 them as four, but as if they were alone two. For he ufes fire indeed by it- 
 felf, but its oppofites, earth, air and water, as if they were one nature. But 
 of this any one may be convinced, by confidering his verfes. He, therefore, 
 as we have faid, fpeaks in this manner, and alTerts that there are fo many- 
 principles. 
 
 But Leucippus, and his afTociate Democritus, aiTert that the elements of 
 things are ih.e full and the void; affirming that the former is being, and the latter 
 non-being. And again of thefe, they call the full and the folid being, but the 
 void and the rare non-being. On this account they fay that being has not 
 any more fubfiflence than non-being, becaufe neither has void lefs fubfiftence 
 than body. But thefe are the caufes of beings as matter. And, jufl as thofe 
 who make the fubj:<St effence of things to be one, generate other things from 
 
 * In the original the words within the brackets are not to be found ; but it appears from the 
 text of Alexander Aphrodifienfis, that they ought to be inferted, though this has not been no- 
 ticed by any of the editors of Ariftotle. Hence, therefore, we fee the origin of that famous 
 line of Horace : 
 
 Nee deus intcrfit, nifi dignus vindice nodus. 
 
 f Plato fays nearly the fame of Anaxagoras in his'Phsedo. 
 
 the
 
 14 ARISTOTLE'S METAPHYSICS. Book I. 
 
 the participations of this fubjedl, and eftablifh the rare and the denfe as the 
 principles of participations ; in the fame manner thefe alfo affert, that diver- 
 fities are the caufes of other things. But they fay that thefe are three : figure, 
 order, and pofition. For they affert that being differs by ryfmox, diathege, 
 and trope : but of thefe ryfmos is figure, diathege order, and trope pofition : for 
 the letter a differs from the letter n in figure, but the fyllable an from na in 
 order, and Z from N in pofition. But thefe men, in a manner fimilar to 
 others, negligently omit to confider with refpeit to motion, whence it is de- 
 rived, and how it lubfifts in beings. And thus far, as we have faid, thofe 
 prior to us appear to have inveftigated the two caufes of things. 
 
 CHAP. V. 
 
 But among thefe, and prior to thefe *, thofe who are called Pythagora^ans, 
 and who were the firft that applied themfelves to mathematics, gave the 
 precedency to thefe difciplines ; and, in confequence of being nouriflied in 
 them, were of opinion that thefe are the principles of all beings. But fince 
 among thefe difciplines numbers are firft by nature, and it appeared to them 
 that in numbers more fimilitudes both to things which are, and to things in 
 generation, are feen, than in fire, earth, and water (for this particular pro- 
 perty f of numbers is juftice, that foul and intelledl:, and again another oppor- 
 tunity, and in a fimilar manner, as I may fay, with refpeft to each of the 
 reft); and further ftill, fince they perceived the participated properties and 
 reafons ij: of harmonies in numbers, and fince other things appeared in every 
 refpe£t to be naturally affimilateu to numbers, but numbers are the firft ele- 
 ments of every nature ; hence they conceived the elements of numbers § to 
 
 • Ariftotle, fays Alexander Aphrodlfienfis, fpeaks in this manner becaufe Pythagoras him- 
 felf was a little prior to Democritus and Leucippus, and many of his auditors flourifhed at the 
 fame time with thefe two philofophers. 
 
 f The word here ufed by Ariftotle for property, as alfo in many other parts of this work, is 
 5ra9o{, which is literally pnjjlon. It may therefore fuffice, once for all, to obferve that wherever 
 •naSaf and ?ra9» occur, they t\gn\i-^ participated property or properties. Plato alfo ufes waffos in this 
 fenfe. 
 
 X Acyoc, renforit wherever it occurs in Ariftotle, either Tpnifies computatioti, in calculations and 
 
 reckoning, or that inward inttlle£lual difcurfus commonly called reafouing^ or a certain produc' 
 
 iive and fsminil principle, or thot nihich is indicative atid definitive of a thing : in the prefent paf- 
 
 fage it fignlfies a prodiiflive principle. 
 
 i Concerning the numbers of the Pythagorxans, fee the notes on the thirteenth book of this 
 work. j^g
 
 Book!. ARISTOTLE'S METAPHYSICS. is 
 
 be the elements of all things, and that all heaven is harmony and number; 
 and fiich things as are acknowledged to be evinced both in numbers and har- 
 monies, thefe they colleded together and ad;ipted to the participated proper- 
 ties and parts of the heavens, and to the whole order of things. Likewife, if 
 any thing was found any where to be much deficient, they fiipplied the de- 
 fedt, tliat the whole of their treatife might properly accord with itfclf. I fay 
 for inflauce, fince the decad appears to be perfeiV, and to comprehend all the 
 nature of numbers, hence they fay that the bodies \^hich revolve in tlie hea- 
 vens are ten ; but as nine only are apparent, they make the tenth to be anti- 
 chthon, or the oppcfite earth. But thefe things are confidered by us more 
 accurately in other places *. 
 
 However, we have related thefe th'ngs that we may underfland from thefe 
 men what the principles are which they eftablifh, and how they fall into the 
 above-mentioned caufes. For it appears that they alfo confidered number as a 
 principle, as matter to beings, and as participated properties and habits. But 
 they affert that the elements of number are the even and the odd ; and that 
 of thefe, the one is bounded, but the other infinite ; and that the one is coni- 
 pofed from both thefe, becaufe it is both even and odd. They likewife aflert 
 that number confirts from the one, and that numbers, as we have faid, com- 
 pofe the whole of heaven. But others of thefe aflert that there are ten prin- 
 ciples, which are denominated according to co-ordination, viz. 
 
 BOUND, THE INFINITE: 
 
 THE ODD, THE EVEN: 
 
 THE ONE, multitude; 
 
 RIGHT HAND, LEFT HAND: 
 
 THE MASCULINE, THE FEMININE: 
 
 THE QUIESCENT, THAT WHICH IS IN MOTION: 
 
 THE STRAIGHT, THE CURVED: 
 
 LIGHT, DARKNESS : 
 
 GOOD, evil: 
 
 THE SQUARE, THE OBLONG. 
 
 Alcmascn the Crotonian appears to have entertained this opinion: and 
 either he derived this dogma from them, or they from him. For Alcmxon 
 flouriflied when Pythagoras was an old man. But his dodrine was fimilar 
 to that of thefe men. For he fays that the multitude of human affairs re- 
 
 * ('. e, in his books dc Ccelo. 
 
 celvcs
 
 Ig ARISTOTLE'S METAPHYSICS. Book I. 
 
 ceives a twofold divlfion (meaning into contrarieties), yet not diftinguiflied 
 as they dirtinguiHi tliem, but defined in a caiual manner : fuch as white, 
 black ; fweet, bitter ; good, evil ; the fmall, the great. He therefore fpokc 
 indefinitely concerning the reft : but the Pythagoreans declare how many, 
 and what are the contrarieties. Hence thus much may be underftood from 
 both, that contraries are the principles of beings ; but from the Pythagoreans 
 we learn the niunber and quality of thefe principles: yet it is not clearly de- 
 termined by them how they may be applied to the above-mentioned caufes. 
 But they appear to difpofe the elements as in the fpecies of matter. For from 
 thefe, as things inherent, they fay that efiTence is compofed and fafliioned. 
 From thefe things, therefore, the conceptions of the antients, who afTerted that 
 the elements of nature were many, may be fufficiently feen. 
 
 But there are fome who have difcourfed about the univerfe as if it were one 
 nature : yet all of them have not difcourfed after the fame manner, neither of 
 that which fubfilb beautifully, nor of that which fubfifts according to nature. 
 By no means, therefore, does the difcourfe concerning thefe men harmonife 
 with the prefent fpeculation of caufes. For they do not fpeak like certain 
 phyfiologifi:s, who, fuppofing be'ng to be one, at the fame time generate from 
 the one, as from matter ; but their affertions are of a difi'erent nature. For 
 the phyfiologifls who contend that being is one, when they generate the uni- 
 verfe, at the fame time add motion : but thefe men aflert that the univerfe is 
 immoveable. Tiius far, however, a difcourfe about thefe men is adapted to 
 the prefent inquiry. For Parmenidcs appears to have touched upon the one 
 according to reafon, but IVlelifliis according to matter. Hence the former 
 afllrts that the univerfe is finite *, but the latter that it is infinite. But Xeno- 
 
 phanes, 
 
 * The following remarkable pailage from Simplicius in Phyf. p. 7, on the concord of thefe 
 anticrit philofcphcrs refpecling the principles of things, will, I doubt not, be highly acceptable 
 to the liberal reader: 
 
 " Pe' haps it will not here be improper to digrefs a little, and point out to the more Rudious how, 
 though the antients appear to differ from each other in their opinions concerning the principles of 
 things, yet at the iame time they harmonioufly agree. For fome of them difcourfed concerning 
 the intelligible atui firfl principle of things, as Xenophanes, Parmenides, and MtlifTus ; Xcno- 
 phanes and Parmenides, indeed, calling it one and finite : for it is neceffary that tbe one fliould 
 have a fubfidencc prior to multitude, and that the caufe of bound and limitation to all things, 
 fliould be rather defined according to bound than according to infinity; and that the every-way 
 perfect, and which has received its proper end, fliould be definite, or rather fliould be the end, 
 as it is the beginning of all things. For the imperfefl being indigent, has not yet received the 
 
 limitation
 
 DookL ar [stotle's metappiy si CS, 17 
 
 phaiies, wlio was the firft that iiltrcduced this dodtnne (fur Parmenldes is faid 
 to have been his difciple), did not affcrt any thing clearly ; nor does he appear 
 to liave apprehended the nature of either of thefe, but, looking to the whole 
 of heaven, he fays that (be one is God. Thefe men, therefore, as we have faid, 
 are to be difmiifed in the prefcnt inquiry ; two of them, iftdeed, entirely, as 
 being a little too ruRic, viz. Xenophanes and Meliflus. But Parmenides ap- 
 pears to have fecn more than thefe where to fpeak. For, befules being itfelf, 
 he thought fit to confider non-being as nothing, and hence was neceflarily of 
 opinion that being is one, and nothing elfe ; concerning which dodrine we 
 have fpoken more clearly in our Phyfics. But being compelled to follow the 
 phenomena, and conceiving that, according to reafon, the one had a fubfifl- 
 ence, but, according to fenfe, the many, he again eftabliflies two caufes and 
 two principles, viz. the hot and the cold, or, in other words, fire and earth. 
 But of thefe he difpofes the one, viz. the hot, according to being, but the 
 other according to non- being. 
 
 From what has been faid, therefore, and from thofe wife men who adhered 
 to reafon, we now i^eceive thefe particulars. From the firft indeed *, that 
 
 the 
 
 limitation of bound. Tliis exception, however, muR be made, that Xenoplianes places it beyond 
 motion and reft, and every anti-ordination, as being the caufe of, and tranfcending, all things, 
 in the fame manner as Plato in the firft 1-ypothefis of his Parmenides. But Parmenides beholding 
 it as fubfifling according to/ntne ^ndjinii/ar (/. e. as having an eflcnce perpetually the fame with, 
 and fimilar to, itfelf), and as above all mutation, and perhaps energy alfo and power, celebrates 
 it as immoveable, and alone as being exempt from all things. Meliillis too, in a fimilar manner, 
 appears to have contemplated the immutability of this caufe, and to have evinced that he is /'«- 
 finile, as alfo utihegotten, from the never-failing nature of his eflence and th.c infinity of his 
 power." 
 
 The oppofition, therefore, of Ariftotle to the doclrine of thefe philofophers, is, as ufual, di- 
 refted to the literal and not to the true meaning of their aflertions. 
 
 * Arlllotle here means thofe philofophers who fpeculated the fenfible order of things and in- 
 veftigated the elements of bodies, viz. Thales and Heraclitus, Anaximenes and Diogenes, Anax- 
 imander, Leucippus and Democritus. Of thefe, Thales aflerted that the element of bodies was 
 water, in confequencc of furveying its prolific, nutritive, connedlive, vivific, and yielding nature ; 
 but Heraclitus, that it was fire, from regarding, the vivific and demiurgic nature of this element. 
 Anaximenes affirmed that it was air, from beholding the plaftic power of this element, and the 
 facility with which it pervades fire and water; and Anaximandcr, that it was of a middle nature, 
 between fire and air, from the facility with which it receives mutation. And, laftly, Leucippus 
 and Democritus called the elements of bodies atoms, in confequence of regarding the diflcrcnce 
 of their figures, pofition, and,order. So that, as SimpHcius juftly obferves of the antlent philo- 
 fophers, fome contemplated the intelligible, and others the fenfible, order of things. Some in- 
 
 D vcftigated
 
 13 ARISTOTLE'S MET A PHYS I CS. Book I. 
 
 the principle cf tilings is corporeal (for water, and ftre, and the like, arc 
 bodies) ; and of thcfe fome aflert that there is one, but others that there are 
 many corporeal principles ; but both agree in placing thefe principles as in 
 the Ipecies of matter. But from certain others who eftablifli this caufe, we 
 receive befides this the principle whence motion is derived ; and according to 
 fome there is one principle, but according to others there are two principles 
 of this kind. As far, therefore, as to the Italic philofophers, and feparate 
 from them, others have fpoken in a more becoming manner about thefe things, 
 except, as we have faid, that they ufed two caufes ; and of thefe fome made 
 the other caufe, or that whence motion is derived, to be one, but others to be 
 two. The Pythagora:ans, after the f.ime manner, faid that there are two 
 principles. But thus much they added, which is peculiar to them, that they 
 did not think the finite, and the infinite, and the one^ were certain other na- 
 tures, fuch as fire, or earth, or any other fimilar thing ; but they were of opi- 
 nion, that the infinite itfelf, and the one itfelf, are the elTence of thefe things 
 of which they are predicated : and hence they aflerted that number is the 
 eflence of all things. After this manner, therefore, they unfolded their opinion, 
 refpcdling thefe things, and began to fpeak about what a thing is, and to 
 define ; but they treated this affair in a very fimple manner. For they defined 
 fiiperficially, and confidcred that in which a given definition is firft inherent, 
 as the eirence of the thing ; juft as if any one lliould think that the double 
 and the duad are the fame, becaufe the double firft fubfifts in two. But per- 
 haps the double is not the fame with the duad : and if it be not, one thing vrill 
 be many*; which confequence happens alfo to them. From thole, there- 
 fore, who firft philofophifed, and from others, thus much may be received. 
 
 veftigated the proximate, and others the more primary, elements of bodies. Some, again, fur- 
 veyed the more partial, but others the more total, prerogative of an elementary nature. And 
 latlly others, exploring all the caufes and concaufes of things, fpeak diiVerently from each other 
 in phyfiologifing, at the fame time that their aflertions are not contrary to each other. 
 
 * That is to fay, if things of which a definition is firfV truly predicated be the fame as the 
 definitions which are predicated of them : but many definitions firft accord with one thing 
 (for the Pythagoreans, for inftance, called the number 7, both opportunity and Minerva); hence 
 one and the fame number will be many things, fince many different definitions accord with if. 
 There is, however, no abfurdity in admitting that one thing may be many : for evevv cflentially 
 producing caufe comprehends in itfelf, unitedly, all the multitude of which it is the caufe, in 
 the fame manner as the centre comprehends tlic fummits of all the radii of a circle. 
 
 CHAP.
 
 Book. I. AIIISTOTLE'S METAPHYSICS. 19 
 
 CHAP. vr. 
 
 After the above-mentioned plulofophers, the bufinefs with Plato next fiic- 
 cceds, who in many things followed thefe Pythagorasans, but who alfo had 
 fome peculiar dodrines different from the philoCophy of the Italics. For, 
 when he was a young man, affociating firfl of all with Cratylus, and being 
 familiar with the opinions of Heraclitus, that all fenfible things are perpetu- 
 ally flowing, and that there is no fcience refpedting th.m, he afterwards 
 adopted thefe opinions. But as Socrates employed himfelf about ethics, iind 
 entirely neglcded the fpeculation refpeding the whole of nature ; in morals, 
 indeed, invefligating the univerfal, and being the firfl who applied himfeh to 
 definitions; hence Plato, approving this his inveftigation of univerfals, ad.'pted 
 thus much of his dodrine, that thefe definitions refped other things, and are 
 not converfant with any thing fenfiblc. For he was of opinion, that it is im- 
 poffible there fhould be a common definition of any fenfible nature, as fenfi- 
 bles are always changing. Things of this kind, therefore, he denominated 
 ideas *, but afferted that all fenfible things were denominated as different 
 from, and as fubfifling according to, thefe. For, according to him, the multi- 
 tude of things fynonymous is homonymous to forms according to participa- 
 tion ; but he only changed the name participation. For the P) thagorseans fay 
 that beings are imitations of numbers ; but Plato, changing the name, calls 
 \\\tm participations of numbers. They omit, however, to invelligate in com- 
 mon what the participation or imitation of forms is. Further Rill, befides 
 things fenfible, and forms, they fay that the mathematics are things of a mid- 
 dle nature, differing indeed from fenfibles in that they are eternal and im- 
 moveable, but from forms in that they are certain fimilar multitudes, every 
 form itfelf being only one thing. But, fince forms are caufes to other things, 
 he was of opinion that the elements of thefe are the elements of beings. He 
 thought, therefore, that the great and the fmall were principles as matter, but 
 the one \ as effence. For from thefe, through the participation of the oncy 
 forms are numbers. He afferted, indeed, that the one is effence, and that 
 
 * Of the Platonic doctrine of ideas we (hall fpeak largely in our notes to the thirteenth 
 book of this work. 
 
 f All this, as likewife all that follows refpe£ling ideas and numbers, will be largely difcufTed, 
 and the dodlrine of Plato and the Pythagorecans on thefe fubjetts folidly defended, in the notes 
 to the thirteenth and fourteenth books of this work. 
 
 D 2 nothing
 
 £0 AR I STOTLE'S METAPH YSIC S. Boox I. 
 
 nothing elfe is called the one^ in this refpedt fpeaking in a manner fimilar to 
 the PythagoriEans ; and, like them, he alfo confidered numbers as the caufes 
 of effcnce to other things. But this is pecuhar to him, to make the diiad in- 
 ftead of the iri/in'ite confidered as one, and to compofe the mjinlte from the 
 great and the fmall. 
 
 Further ftill : Plato afferts that numbers are different from things fenfible ; 
 but the Pythagorseans fay that they arc things themfelves, and do not place 
 mathematics between thefe. The one, therefore, and numbers, were confi- 
 dered as different from things themfelves, and not as the Pythagoreans con- 
 fider them ; and, as well as forms, were introduced in confequence of dialedlic 
 invefligation. For the more antient philofophers were not flsiilled in dialeclic. 
 Through the fame inveftigation, alio, Plato made the duad to be a different 
 nature from the one, becaufe numbers, except thofe that rank as firft, are 
 aptly generated from it, as from a certain exprefs refemblancc of a thing ; 
 though, indeed, the contrary to this happens to be the cafe. For it is not 
 reafonable it fhould be fo. For now they make many things from matter, 
 but form generates once only. But one table appears to be produced from 
 one matter. However, he who introduces form makes many tables. The 
 male, too, is in a fimilar manner related to the female. For the female is 
 filled from one copulation, but tlie male fills many. And yet thefe are imi- 
 tations of thofe principles. Plato, therefore, has thus defined refpedling the 
 objecfls of inveftigation. 
 
 But it is evident, from what has been faid, that he ufes only two caufes ; 
 that which relates to what a thing is, and that which fubfifts according to 
 matter. For forms, accordi-^g to liiai, are the caufes to other things of 
 effence ; but the o?ie is the caufe of this to forms. And what is this caufe 
 which lubfifts according to matter? It is that iubje£t matter through which 
 forms are faid to belong to things fenfible ; and the one is faid to be in forms, 
 becaufe this is the duad, or the great and the fmall. Further ftill : he attri- 
 butes lo the elements the caufe of fubfifting well and ill, each to its proper ele- 
 ment; and this, we fav, fome of the more antient philofophers, viz. Empedo- 
 cles and Anaxagoras, have inveftigated. In a brief and fummary manner, 
 therefore, we have difcuffed who thofe were that have fpoken, and how they 
 have fpok 'H, refpcding principles and truth*. 
 
 * It is well obferved here, by Alexander Aphrodifienfis, that Arlflotlc, conformably to his 
 ufual manner of fpeaking, calls corilcwplative philofophy truth; and this, as it appears to me, with 
 the greateft propriety, for the end of this philofophy is the perception of the liighcfl truth. 
 
 But.
 
 BooK.r. ARISTOTLE'S METAPHYSICS. 2i 
 
 But, at the fame time, we obtain thus much from them, that of thofc-who 
 have fpoken concerning a principle and caufe, no one has faid any thing in 
 addition to what we have delivered in our Phyfics ; but ail of them have 
 fpoken obfcurely, though in a certain refpedl they appear to have touched 
 upon thefe two. For fome fpeak of principle as matter, whether they fup- 
 pofe there is one or many principles, and whether they confider principle as 
 body, or as incorporeal: as Plato, when he fpeaks oi the great and the f mall -, 
 Empedocles, oi fire and earth, "water and air ; and Anaxagoras, of the infinity 
 offimilar parts. But all thefe touched upon a caufe of this kind ; and, be- 
 fides thefe, thofe who have eflablilhed as a principle eirher lire or water or 
 that which is more denfe than fire, but more attenuated than air ; for fome 
 aflert that the firft element is a thing of this kind. Thefe, therefore, had only 
 an obicure conception of this caule ; but certain others had fome cnnceptioa 
 whence the principle of motion is derived,, viz. thofe who make friendlhip 
 and ftrife, or intellect, or love, a principle. But no one has clearly affigned 
 the nature and effence of this principle. However, they efpecially fpeak re- 
 fpeding it who adopt the hypothefis of forms, and the things which fubfift in 
 forms. For neither do they confider forms and the things which forms con- 
 tain as ma'ter to fenfibles, nor as if the principle of motion was derived from 
 thence. For they fay that they are rather the caufe of immobility, and of 
 things being at reft. But, according to them, forms impart the particular 
 being which each individual of other things pofleffes ; and the one imparts the 
 fame to forms. But that, for the fake of which adions, mutations and mo- 
 tions fubfift after a certain manner, they denominate a caufe; yet they do not 
 affert that it is a caufe, nor do they fpeak of it conformably to what it natu- 
 rally is. For thofe who fpeak of intellect, or friendftiip, place thefe caufes as a 
 certain good, but do not fpeak of them as if for the fake of thefe either being 
 or any generated nature f ibfifts, but as if from them the motions of things 
 were derived. In a fimilar manner, thofe who fay that the one ^ or beings is a 
 nature of this kind, aflert indeed that it is the caufe of effence ; yet do not 
 fay that any thing eiiher is, or is generated, for the fake of this. So that in 
 a certain refpedt it happens that they afl^ert, and yet do not afl^ert, that the good 
 is a caufe of this kind; for they fpeak not fimply, but cafually. That we 
 have therefore rightly determined concerning caufes, and refpedlng their 
 number and qiafry, all thefe philofophers appear to teftify, fince they were 
 not able to touch upon any other caufe. And, befides this, that principles 
 
 fhould
 
 22 ARISTOTLE'S METAPHYSICS. Book. I. 
 
 fhould be inveftigated, either all of them in this manner, or feme one of the 
 four, is evident. But after this it is requifue that we fliould confider in what 
 manner each of thefe fpeaks, and what are the doubts which arife refpecling 
 principles themfelves. 
 
 CHAP. VII. 
 
 It is evident, therefore, that thofe err manifoldly, who confider the unl- 
 verfe as one, and as being one certain nature, as matter ; and this corporeal, 
 and pofleffing magnitude. For they only admit the elements of bodies, but 
 not of things incorporeal, though at the fame time things incorporeal have a 
 fubfiilence. And befides this, endeavouring to affign the caufes of genera- 
 tion and corruption, and phyfiologifmg about all things, they take away the 
 caufe of motion. Further ftill, by placing effence as the caufe of no one 
 thing, and not confidering the isohat \ and befides this, thinking that there 
 might eafily be any principle of fmiple bodies (except earth , they did not 
 attend to the manner in which, according to them, the generation of thefe from 
 each other is accomplilhed ; I mean fire and water, earth and air. For fome 
 ■things are generated from each other by concretion, and others by feparatlon. 
 But this, with refpeitto the being prior and pofterior, differs much. For that 
 may appear to be the moft elementary of all things, from which the elements 
 are generated by a firfl: concretion : but a thing of this kind will, among bo- 
 dies, confift of the fmalleft parts, and be the moft attenuated ; on which ac- 
 count, fuch as place fire as a principle fpeak in the higheft degree conform- 
 ably to this do£trine. But every one acknowledges that a thing of this kind 
 is alfo the element of other bodievs. No one, therefore, of thofe later philofo- 
 phers who fpeak oi the one, has thought fit to confider earth as an element, on 
 account of the magnitude of its parts. But each of the three elements has 
 had a certain arbitrator ; for fome fay that this is fire, others water, and others 
 air. Though why, like the multitude, do they not fay that earth alfo is an 
 element ? f^r they fay that earth is all things. Hefiod alfo afferts, that earth 
 was the firft thing generated among bodies ; fo that this opinion happens to 
 be both aotient and popular. According to this reafoning, therefore, if any 
 one fhould fay that any thing belonging to thefe, except fire, is more denfe 
 than air, but more attenuated than water, he will not fpeak rightly. But if 
 
 that
 
 Book I. ARISTOTLE'S METAPHYSICS. 23 
 
 that which is pofterior in generation is prior by nature*, and that which is 
 digefted and ming'ed together is pofterior in generation, the contrary of thefe 
 will take place ; tor water will be prior to air, and earth to water. And 
 thus much may fuflice rei'petfling thole who eftablifh one caufe fuch as we 
 have mentioned. 
 
 But the fixme things may be faid, if any one fliould think that there are 
 many corporeal principles, as Empedocles, who fays that the four elementary 
 bodies are matter : for it is neceflary that partly the fame things, and partly 
 fuch as are peculiar, fliould happen to him. For we fee that the elements are 
 generated from each other, as the fire and earth of the fame body do not 
 always remain. But we have fpoken refpedling thefe in our Phyfics f, and 
 alfo refpeding the caufe of things moving, whether it is to be confidered as 
 one or two ; nor is it to be thought that this has been aflerted in a manner 
 altogether irrational. But, in fine, thofe whofpeak in this manner mufl: necef- 
 farily take away internal mutation. For the cold is not from the hot, nor 
 the hot from the cold. And what contraries tliemfelves will fuffer, and what 
 that one nature will be, which becomes fire and water, Empedocles does not 
 fay. 
 
 But if any one fhould think that Anaxagoras afferts there are two elements,. 
 he v/ill, in the higheft degree, think according to reafon ; for though he does 
 not clearly aflert this, yet it follows from neceflity, if any one fpeaks con- 
 formably to his dodtrine. It is indeed abfurd to fay, that at firft all things 
 were mingled together ; both becaufe it muft happen that all things prior to. 
 this ought to have fubfifted unmingled, and becaufe every thing is not natu- 
 rally adapted to be mingled with every thing. To which it may be added, 
 that from this dodrine, parucipated properties and accidents muft be ieparated 
 from fubftances (for mixture and feparation belong to the fame things) ; yet 
 if any one follows, and at the fame time accurately confiders his aflei tions, he 
 will perhaps appear to have advanced Ibmething new. For, at the time 
 when nothing was feparated, it is evident nothing could be faid refpeding that 
 eflence. I fay, for inftance, that it was neither white nor black, nor of any 
 colour between thefe ; but that it was from neceffity culourlefs : for other- 
 
 * That is to fay, that which is perfe£l is prior by nature to the more imperfect, ahhough It 
 is rendered pofterior by generation. But that which pre-exifts in time, is more imperfeil.. 
 Thus the foundation is more imperfeft than the houfe, and the boy than the man. 
 
 f Viz. in lib. iii, de Coelo. 
 
 wife
 
 24 ARISTOTLE'S METATHysICS. Book!. 
 
 ■wife It would poflefs fome one of thefe colours. In like manner, it muft 
 have been taftelefs : and, from the fame reaibning, it could not have been 
 any thing elfe of the like land. For it is not poihble that it co\ild poffefs any- 
 quality or quantity, or be any adual thing, fmce fomething of thofe things 
 which are called partial forms would be inherent in it. Eut this is impoffi- 
 ble, in conftquence of all things (according to him) being mingled together; 
 for they would now be feparated. But he fays tiiat all things were mingled 
 except intelled ; and that this alone was unmingled and pin-e. Hence it 
 comes t'l pafs, that he proclaims, as principles, the one (for this is fimple and 
 unmingled), and another thing, as if it were being, fuch as we confider the 
 indefinite to be, before it is bounded and participates of a certain form. So 
 that this is afTcited, indeed, neither wiih redtitude nor perfpicuity ; yet he 
 wufhes to fay iomething fimilar to what more modern philofophers have faid, 
 and more agreeable to the prelent phenomena. But the'e philofophers only 
 fpeak in a manner accommodated to the aflertions refpeding generation, cor- 
 ruption, and motion. For they nearly alone invefligale an eilence, principles 
 and caufes of this kind. 
 
 But with refped to fuch. Indeed, as make all beings the fubjed of their fpe- 
 culatlon, and confider fome beings as fenfible and others as not fenfible, it is 
 evident that they inquire concerning both genera ; and on this account any one 
 may be induced to dwell longer on the confideration of what they have faid, 
 well or ill, with refped to our prefent invefligation. Thrfe, therefore, who ..xt 
 called Pythagora^ans, ufe principles and elements in a more incredible manner 
 than phyfiologifts. But the reafon Is, becaufe they do net receive thefe from 
 fenfibles. For mathematical entities are without motion, except thofe things 
 which pertain to aftronomy. Yet notwithfianding this, they difcourfe about 
 and difcufs all things refpedHng nature. For they generate the heaven, and 
 obferve what happens refpeiling Its parts, partici; ated properties, 'and opera- 
 tions ; and into thefe they refolve principles and caufes, as agreeing with 
 other phyfiologifts, that whatever Is fenfille is being, and is comprehended by 
 that which is called heaven. But, as we have faid, and as they alfo affert, they 
 fpeak fufficiently refpedlng caufes and principles, and even afcend to a higher 
 order of beings'^ ^z.w^ this more than is adapttd to difcourfes concerning nature; 
 but they arc filent as to the mode In which motion, bound, and infinity, 
 the even and the odd, thefe being alone the fubjeds of hypothefis, fubfill ; or 
 
 * That is, to incorporeal and immoveable natures. 
 
 how
 
 Took I. ARISTOTLE'S METAPHYSICS. 25 
 
 hew it is poflihle that generation and corruption can exlfl: without motion and 
 mutation ; or how the operations of the bodies which revolve in the heavens 
 can be accomplifhed. 
 
 Further flill, whether any one grants them that magnitude is from thefe, 
 or whether this is ihown to be the calc ; yet, at the fame time, after what 
 jmanner will fome bodies poflefs levity, and others gravity, relpedling which 
 their hypothefes and axTertions do not lefs accord with mathematical bodies 
 than with fenfibles ? Hence they do not fay any thing refpeding fire, or 
 earth, or other bodies of this kind; and this, I think, becaufe they do not 
 aflert any tiling which is their own concerning fenfible natures. Again, 
 how ought we to receive the alT^rtion, that the participated properties of num- 
 ber, and number icfelf, are the caufes of things which exift, and are produced 
 in the heavens, both from the beginning, and at prefent, at the fame time that 
 thtre is no other number bcfides this number, from which the world is com- 
 pofed ? For fince, according to them, opinion and opportunity are in this part 
 of the worlJ, but a little higher or a little lower, injuftice*, and feparation, or 
 mixture, and they adduce demoaftration that each of thefe is number, and it 
 happens from this mode of reafoning, that there is now a multitude of confli- 
 tuted magnitudes, becaufe thefe properties follow the refpedive places; — fince 
 this is the cafe, whether is it owing to that number which is in the heavens 
 ihat each of thefe exiRs, or to another number befides this ? For Plato fays it 
 is owing to another number; though he alfo thought that numbers are thefe 
 things, and are the caufes of thefe ; but that they are indeed intelligible 
 caufes, while thefe are nothing more than fenfibles. Refpcding the Pytha- 
 gora^ans, therefore, we ihall fpeak no further at pr£ient ; for it is fufficient to 
 have thus much touched upon them. 
 
 But thofe who conlider ideas as caufes, in the firft place exploring the 
 caufes of thefe things, introduce other things equal to thefe in number: juft 
 as if fome one, wifliing to numerate, fliould think that he cannot accom- 
 pliih this if there are but a few things, but that he can numerate if he increafes 
 
 *■ Alexander Aphrodifieiifis informs us tliat in fome copies to avinyiTov, the unconquered, is 
 found inftead of aJwia, injujlke. But, fays he, the ttncoiiqiiered was called by the Tythagorsans 
 the number five, becaufe, in a right-angled triangle, of thofe fides containing the right angle, one 
 is as three, and the other as four; and the bafe is as five. Since, therefore, the bafe is in power 
 equal to both together, it is called the vicfor, and the other fides are faid to be fanquifie-d. 
 Hence the number five was denominated by them unconquered, being as it were not fitrl>nJJfJ, 
 but unconquered ■inA fuperior. 
 
 E their
 
 26 ARISTOTLE'S METAPHYSICS. Book I. 
 
 their number. For nearly forms are equal, or not lefs th«n thofe things, of 
 which, inveftigating the caufes, they proceed from thefe to thofe ; for, ac- 
 cording to each individual thing, there is a certain homonymous form, and be- 
 fides the eflences of other things, there is the one in many, both in ihefe, and 
 in eternal entities. Further ftill, forms do not appear to have a Ibbfiftence, 
 according to any one of thofe modes by 'which we * bave Jlioion them to fub" 
 fijl. For, from fome, the reafoning does not neceffarily follow ; and from 
 others forms are produced of thofe things, of which we do not think there 
 are forms ; for, according to the reafons arifmg from the fciences, there are 
 forms of all fuch things as there are fciences ; and from that argument for 
 ideas, which is founded in confidering the 07ie in the many, it follows, that 
 there are alfo forms or ideas of negations. Likewife, in confequence of the 
 ability to underftand fomething of things corruptible, there will alfo be forms 
 of corruptible natures ; for there is a certain phantafm of thefe. 
 
 Further ftill, with refpedt to the moft accurate of reafons, fome make ideas 
 of things relative, of which we do not fay there is an eflential genu% and fome 
 aflfert that there is a third man ; and, in Ihort, the reafons refpeding forms 
 fubvert thofe things which, the aflerters of forms are of opinion, have a fubfift- 
 ence prior to ideas themfelves. For it happens that the duad is not firft,but 
 number, and that which has a relative is prior to that which has an eflential 
 fubfiftence. All fuch particulars likewife happen, as, being confequent to the 
 opinions refpe<!ling forms, are adverfe to principles. Again, from the notion 
 according to which we fay there are ideas, there will not only be forms of 
 eflences, but alfo of many other things : for there is one conception not only 
 refp-ding eflences, but alfo refpe£ling other things ; and fciences are not only 
 fciences of eflence, but alfo of other things; and ten thoufand fuch like parti- 
 culars happen. But, from necefllity, and the opinions refpeding forms, it fol- 
 
 * It appears from the commentary of Alexander, that in this place we fliould r^ad JijEi^aAiw, 
 and not Jtixvurai ; for the authority of Alexander's copy is certainly to be preferred to that of any 
 now cxifting. I have accordingly adopted SiSiixa/^Ei' in rny verfion. 
 
 It is remarkable too, that Alexander, who was no friend to the Platonic docElrine of ideas, and 
 who, though on the whole an excellent interpreter of Aiiftotle, did not fee his true meaning on 
 that fubjecV, fliould in this place obfevve " that Ariftotle fays ive have fiown, as if he profefled, 
 while relating the opinion of Plato refpe£ling ideas, to relate it alfo as his own, and as if he 
 did not oppofe it as a foreign dogma, but difcufled and examined it as his own." Indeed it 
 appears lo me that this very paflage is fufiicient to prove that the objc(Slions of Ariftotle to 
 Plato's theory of ideas are rather pretended than real. 
 
 lows.
 
 Boojtl. ARISTOTLE'S METAPHYSICS, 27 
 
 lows, th?''. If forms are pariicipable, there are only ideas of eflences : for they 
 are not parcicijateJ" according to accident; but it is requifite that things 
 fhouki participate each idea, fo far as each idea is not predicated of a fubjed. 
 I mean, juft as if any thing participates of the double, this aho partici[ates of 
 the perpet- al, but according to accident. For it happens to the double to 
 be eternal; fo 'hat forms will be eflences; and thefe both ha:e and there 
 will fignify eflenoe. Or what will be the meaning of that.aficrtion, that the 
 one in many is foinething different from fenfible things ? And if there is the 
 fame form, both of ideas and their participants, there will be fomething 
 common. F:>r whv, in duads, which are corruptible, and in many but 
 eternal duads, is the duaJ faid. to be more one and the fame than in this, and 
 in fome particular thing? But if tliere is not the fame form, the name only 
 will be common ; and it will be juft as if fome one fliould call both Clinias 
 and a piece of wood a man, at the fame time that he perceives no communion 
 whatever between them. 
 
 But fome one may, in the moft eminent degree, doubt what it is that forms 
 contribute to fuch things as are eternal among fenfible% or to things which 
 are generated and corrupted : for neither are tiiey the caufes of any mo- 
 tion, nor of any mutation whatever to thefe. Nor yet do they afford any 
 affidance to the fcience of other things (for they ^re not the effence of thefe, 
 fince in this cafe they would refide in them) ; nor do they contribute to the 
 being of other things, fmce they are not inherent in their panicipants. For 
 thus, perhaps, they might be confidered as caufes, as a white colour mixed with 
 a body may be faid to be the caufe that the body is white. But that affer- 
 tion, which was lirft made by Anaxagoras, and afterwards by Eudoxus and 
 others, refpeding the temperament of things from fimilar natures, may be 
 eafily confuted ; for it is eal'y to co11e£l many and impoffible confcquences in 
 oppolition to this opinion. Eut, indeed, neither do other things fubfill from, 
 forms, according to any of thofe modes which are generally adduced. And 
 to fay that forms are paradigms, and that they are participated by other things, 
 is to fpeak vainly, and to utter poetical metaphors. For, v.-hat is that which 
 operates looking to ideas ? for it is poffible that any thing may both be, Jfnd be 
 generated fimllar, without being affnnilated to that to which it is fimilar; fo that, 
 Socrates both fubfifting and not fubfifting, fome other may be generated fuch 
 as Socrates is : and, in like manner, it is evident that this will follow, although 
 Socrates fhould be eternal. Befides, there will alfo be many paradigms of the 
 
 E 2 fame
 
 28 ARISTOTLE'S METAPHYSICS. Book L 
 
 fame thing ; and confequ-Titly forins, as man, animal, biped ; and at the fame 
 time, man himlelf, or the ideal ihan, will have a fubfiftence. 
 
 Furtlier ftill, forms will not only be paradigms of fenfibles, but alfo of forms 
 themfelves ; as, for inftance, genus, fo far as genus, will be the paradigm of 
 fpecies : fo that the fame thing will be both paradigm and image. Again, 
 it may feem to be impoffible that eflence Ihould be feparated from that of 
 which it is the effence. So that how will ideas, fince they are the effences of 
 things, be feparated from them ? But, in the Phiedo, forms are faid to be 
 the (.aufes, both that things are, and that they are generated ; though, at the 
 fame time, participants will not be generated, even admitting the fubfiftence of 
 forms, unlefs that which is motive fubfifts. And befides this, many other 
 things .".re made, fuch as a houfe and a ring, of which we do not fay there 
 are forms : fo that it is evident that other things may be, and may be gene- 
 rated, through fuch caufes as we have juft now mentioned. 
 
 Again, if forms are numbers, how will they be caufes ? Whether becaufe 
 beings are different numbers ? as, for inftance, man is this number, Socrates an- 
 other, and Callias a number different from both. Why, therefore, are thofe 
 the caufes of thefe ? For it is of no confequence, if thofe are eternal, but 
 thefe not. But if it is becaufe fenfible natures are the reafons of numbers, 
 as a fymphony, it is evident that there will be one certain thing, of which 
 they are reafons or ratios. If, therefore, this one thing is matter, it is 
 evident that numbers themfelves alfo will be certain ratios of another thing 
 *o another thing. I fay, for inftance, if Callias is a ratio in numbers of 
 fire and earth, water and air, and of certain other fubjeds, man himfelf alfa, 
 whether this idea is a certain number or not, will be a ratio of certain things 
 in numbers, without being himfelf number, and will not through thefe things 
 be fome particular number. 
 
 Further ftill : from many numbers one number is produced ; but how is 
 one form produced from forms ? But if form is not produced from forms, 
 but from the unities which are in number, after what manner will the unities 
 fubfift ? For, if they are of the fame fpecies, many abfurd confequences * 
 will cnfue ; and if they are not of the fame fpecies, nor the fame with each 
 
 * Thefe confequences he enumerates in the thirteenth book, to the notes on which we refer 
 the reader. In thefe too (as we have already obfcrved) the reader will find a folation of the 
 preceding and fubfequent objections. 
 
 Other,
 
 Booitl. A R ISTOTLE'S METAPH Y SICS. 29 
 
 other, nor all the reft the fame with all, in what do they differ, fince they are 
 impaffive ? For thefe things are neither reasonable, nor conformable to intel- 
 lectual conceptions. Befides, it will likevvife be necelfary to eftabliih another 
 ctitain genus of number with which arithmetic muft neceflarily be conver- 
 fant ; and all fuch things as by feme are denominated media. How then do 
 thefe things fubfift, or from what principles do they derive their fubfiftence ? 
 Or why will they be media between things here and thofe ? Befides, each 
 of the unities which is in the duad will fubfift from a certain fomething 
 prior to them, viz. the duad itfelf. This, however, is impoffible. 
 
 Further ftill ; fince every idea is number, why is it one ? And befides 
 this, if the unities are not • different, it will be requifite to fpeak in the fame 
 manner as thofe who fay that there are four or two elements : for each of 
 thefe does not call that which is common an element ; as, for inftance, body, 
 but Hre and earth, whether body is fomething common or not. But now 
 the aflertion is juft as if the one confifted of fimllar parts, like fire or water j 
 but if this be the cafe, numbers will not be effences. It is, however, evident, 
 that if the one is any thing, and this is a principle, the o?ie is predicated in a 
 manifold refpe£t ; for it is impoffible it fhould be otherwife. But we, who 
 wifti to reduce effences into principles, affert f that length conlifts from the 
 long and the fhort, and from the fmall and the large : that fuperficies is 
 compofed from the broad and the narrow ; and body from the deep and the 
 low. But how can a plane poffefs a line, or a folid a line and plane ? For 
 the broad and the narrow are a genus different from that of the deep and 
 the low. As, therefore, number is not inherent in thefe, becaufe the much 
 and the few are different from thefe, fo it is evident that neither will any 
 one of the fuperior fubfift in any of the inferior natures. But neither 
 is the broad the genus of the deep ; for thus body would be a certain fu- 
 perficies. 
 
 Again : from what principles will points be compofed ? This genus, 
 therefore, Plato oppofes, as being a geometrical dogma ; but he calls it the 
 principle of a line; and often afferts that there are indivifible lines, though 
 it is neceffary there fhould be a certain bound of thefe. So that, for the 
 
 * Inftead of Siapofoi here, as in the printed text, the fenfe requires that we fliould read aSia- 
 
 t Here, again, it appears from the commentary of Alexander that we muft read nflf^fv inftead 
 of Tiflfvrai. The words of Alexander are, " Ponimus dixit, ut conftet oratio fupraJidis. Naui 
 de idearum opinionc, velut de propria, dlflerit." 
 
 fame
 
 so ARISTOTLE'S METAPHYSICS. Book I. 
 
 fame reafon that there is fuch a thing as a line, a point alfo has a fub^iRence. 
 And, in fhorr, fince Wiidom inveftigates the cauie of things appa ent, this 
 indeed we omit'''' : for we fay nothing refpefting the caufe whence the bedn- 
 ning cf mutaiit^n is derived. But, thinking to affign the elTence of things 
 apparent, ive foy that there are other eflences ; and we in vain defcribe the 
 manner in which thofe are the eflences of thefe : for, as we have before ob- 
 ferveJ, it is to no purpofe to affert, that this is effeded by participation. Nor, 
 again, are id as fuch caufes as we perceive in fciencts, and through which 
 every inicliecl: and every nature produces; nor do t'ey touch upon any caufe 
 ■which we lav is one of the principles. But, with thc^fe of the prefent day, 
 the inattieinatical fciences generated philofophy, though they fay it is requi- 
 fite t ) be converfant with thefe difciplines for the lake of other things. 
 
 Further ftiH, the fuhjtft matter itfelf f may be confidered as being rather 
 mathematical matter, and as that which ought rather to be predicated and to 
 be confidered as the difference "f eff^nce and matter, fuch as the great and the 
 fmall ; juft as phyfiolog'.rts aflert that the rare and the denfe are the firfl: 
 ■differences of the fubj^d: matter. For thele are certain excefles and defeds. 
 But refpedling motion what ought we to thii'k? For if thefe (viz. excefs 
 and defedl) are motions it is evident that foru s will be moved : hut if they 
 are not motions, whence is motion derived ? For the whole fpeculation 
 refj edbing nature will be taken a'^ ay. And befuies this, that which feems to 
 be eafy u ili not be accompliflied, viz. to demonftrate that all things are one X' 
 
 For 
 
 * Here in the nrinted text Ariftotle fays tixa/jitv, and fliortly after ^eyc/nv; both which confirm 
 the reading, Ictoie mtntiontii, from Alexander. 
 
 -j- ;'. e. the indefinite duad. 
 
 j The following rena-kiible paflage refpe£ling the Pythagorxans is from the Commentary 
 of Alexander on this part : " I he Pythagorseans believed that t/:e one is the formal principle and 
 caufe of all things, in conftquence of perceiving that the nature of unity is the caufe of being 
 and prefervation to every thing for every thing, fo far as it is, is one thing) ; but, on the con- 
 trary, that thi- iliffol'.ition of tie one into the many, is the caufe of deftru£lion. For every 
 thing in its own nature is, fo far as it is preferved in that alone. But, ■when it is dilTolved, it is 
 immediately aboliflied. Their belief of this vias partly derived from animals, which, while they 
 continue in one and ihe fame fpecies, are preferved, but perifli if they are didblved ; and partly 
 from the feveral fpecies of things inanimate. 
 
 " 'Chey wire likewife rf opinion, that the world itfelf is on that account preferved, becaufe it 
 endures in one and the fame flate, and that it would be dtflroyed if it fliould depart, as I may 
 fay, hom that ideniiiy ind unity. On this account, thinking that the nature oi ihe one is the 
 
 caufe
 
 Book I. A RI S T O T L E'S M E T A P H Y S I C S, 31 
 
 I"or all things do not become one by expofition, but a certain one Itft If, if any 
 one allows all things. Nor yet this, unlefs he admits that there is an univerfal 
 genus. But this in certain things is impoffible. Nor is there any reafon in 
 thofe things which are pofterior to nunbers, viz. lengths, fuperficie? and folids, 
 with refpefl to the mode in v/hich they are or will be ; nor do they poITefs any 
 power. For thefe can neither be forms (for they are not numbers) nor things 
 ■which have a middle fubfiftence (for thofe are mathematical), nor can they 
 be things corrupiible : but again thefe appear to be a fourth genus, different 
 
 caufe that every thing is, and fubfifts in a becoming manner, they eflabliflied the one as the prin- 
 cipal caufe of all things ; and confidered ideas as the caufes of being to other things, becaufe 
 they are monads, and on this account are the formal caufes of fubfillence, and of fubfifting in 
 a proper manner to tliofe things which are referred and fubje£led to them. 
 
 " In the next place, they endeavoured to reduce all things to one proper eflence in the follow- 
 ing manner. The feveral individuals of the human fpecies being propofed, they confidered 
 the fimilltude in all of them ; which finding to be one and the fame in all men, fo far as they 
 are men, and referring all men to this monad," they aflerted that they were men through the 
 communion of this one, which they denominated, in all men, man it/elf. They reafoned too in 
 the fame manner, with refpecb to horfes, dogs, and other animals. 
 
 " Again, comparing men with dogs and other animals, tliey were of opinion that thefe were 
 animals through a certain monad, which is the caufe of their fubfiftence as animals, and this 
 monad and idea they called ariimal it/elf, and to it referred all animals. Then confidering ani- 
 mals, plants, and other bodies, and finding that thefe are eflences through the communion of one 
 thing, they eftablllhed a certain idea and monatl of eflencCj that is, ejlriee Hfeif-, to which they 
 referred all effences. For the fame reafon, conceivirfg that fubftance and quality are beings 
 through the communion of being, they devifed being itfelf, to which all beings are referred." 
 
 It murt here be obferved that being itfelf, or the laft monad in this quotation, is no other than 
 the h ov, or one being, of Parmenides, and which, from being perfeflly abforbed in the nature of 
 the ineffable principle of th'ings-,^ the one itfelf, is the firft eflable one; and is the fame with the 
 atber of Orpheus, and the bound of Phijolaus and Plato, concerning which fee the following 
 notes to the third book. See alfo, concerning this firfl being, the fecond hypothefis of the Par- 
 menides of Plato. 
 
 But the following appears to be the reafon v,-hich induced the Pythagoraeans to call all things 
 one. Every monad has a certain multitude co-ordinated to itfelf, and every multitude is com- 
 prehended by a certain monad, with which it accords. But fince every where the monad binds 
 to itfelf the caufe of multitude, and it is not pofTible for multitude to fubfift without this caufe; 
 hence the Pythagora'ans, looking to the incomprehenfible caufe of the monad, which caufe is 
 profoundly one, venerated being as one, contemplating all multitude in tie one, and celebrating 
 the one being (to ev ov) prior to the many. Thus, the monad in numbers has a multitude. co-ordi- 
 nated to itfelf, viz. all the numbers as far as to ten, commonly called units, which multitude is 
 comprehended in the nature of the monad 5 for it is monadic, in the fame manner as all the 
 numbers pofterior to ten are decadic. Biit at the fame time the monad contains in itfelf the caufe 
 of all this multitude. See more on this molt intereftiiig fubjed in the notes to the thirteenth 
 and fourteenth books. frnm
 
 33 ARISTOTLE'S METAPHYSICS. Book I. 
 
 from thofe three. And, ia fhort, it is impoffible that any one can fiad hy 
 inveftigation the elements of beings, unlefs he divides them, lince they are 
 jnanifoldly predicated ; tfpecially, if he inveftigates from what eiementi thty 
 are compofed. For it is not poflible to admit thofe things from which 
 .adion or paflion, or the llraight, confift; but, if it were poffible, they could 
 only be admitted as belonging to beings : fo that either to invefligate, or to 
 think it pc flible to poficfs, the tlements of all beings is not true. For, how 
 can any one learn the elements of all things r fuice it is evident that he can- 
 not pofieis any antecedent knowledge. For, as he who learns geometry may 
 indeed previoufly know other things, but cannot ha^ve a prior knowledge of 
 any of the particulars with which the fcience of geometry is convcrfant, and 
 in which he is to be inftruded ; fo likewife in olliLr things. So that, if there 
 ■be a certain fcience of all tilings, as fome af.ert, he who pofrefles this fcience 
 cannot iiave any pre-exiftent knowled^je. But yet every diLipliiie fubfifts 
 through a prior knowledge, either of all things, or of certain particulars ; and 
 is accomplifhed, either through demonftration or through definitions. For it 
 is requifite that thofe things fhould be foreknown from which definition con- 
 fiRs. And the like takes place with refped to the knowledge which is ac- 
 quired by indudlon. But if we pofTefs an innate knowledge of things, it is 
 wonderful how we happen to be ignorant that we pollefs the mofl excel- 
 lent of fciences'*. Further fliil, how can any one know from what particu- 
 lars all things confift, and how will this be manileft ? For this is dubious: 
 for fome one may doubt juft as refpeding certain fyllables, fince fome aflert 
 that the fyllable za, is compofed from f, d, a f ; but others fay it has a differ- 
 ent found, and not any one of thofe founds that are known. Again, 
 how can any one, not pofleffing fenfe, know fenfibles ? yet it is requifite he 
 fhould, if thofe are elements of all things, from which things confift, juft as 
 compofite founds from their proper elements. From what has been faid, 
 therefore, it is evident that all philofophers feem to inveftigate, though ob- 
 fcurely, thofe caufes which we have fpoken of in our Phyfics, and that we 
 are not able to affign any other cauie different from fome one of thefe. For 
 
 * Wc pofTefs all knowledge In capacity \ but it requires the affiflance of the reafoning power 
 to call it forth into energy. And this arifes from our union with a corporeal nature, which in- 
 volves us in the darknefs of oblivion. 
 
 t Formerly, fays Alexander in his Commentary on this part, not only ^ was wiitten with 
 two letters (viz irJ , but alfo | and 4^ ; the former with kct, and the latter with ttv ; and hence 
 rfiefe are called double letters. 
 
 in
 
 Book I. ARISTOTLE'S METAPHYSICS. S3 
 
 in one refpeA, all thefe have been mentioned by philofophers prior to us ; 
 but in another refpe(ft they have been by no means mentioned. For the firfl: 
 philofophy, as being young, and at its firft commencement, appears to ftam- 
 mer about every thing. For Empedocles fays, that bone confifts from reafon 
 (viz. form). But this is the very nature and eflfence of a thing. However, 
 if this were admitted, in like manner flefli, and every thing elfe, muft either 
 be reafon or nothing ; for, through this, both flefh and bone, and every other 
 thing, fubfift, and not through matter, which he calls fire and earth, and 
 water and air. Thefe things he would neceffarily admit, if they were aflerted 
 by another perfon ; but he docs not fpeak clearly refpeding them. Things 
 of this kind, therefore, we have rendered manifeft before. But fuch doubts 
 as may arife refpeding them we fhall again relate ; for, from thefe, we may 
 perhaps be enabled to folve future doubts. 
 
 ARISTOTLE'S
 
 ARISTOTLE'S METAPHYSICS. 
 
 BOOK II. 
 
 C H A P. I.* 
 
 1 H E fpeculation of Truth Is partly difficult, and partly eafy ; a token of 
 which is this : that no one can fpeak of it according to its dignity, and that 
 all men are not difappointed in the purfuit of it, but every one afferts fome- 
 thlng refpeding Nature ; and though each of thofe who have philofophifed 
 has added nothing, or but a little, to this fpeculation, yet fomething of mag- 
 nitude is produced from the affertions of all of them colledted together. So 
 that, if this appears to be the cafe, who, as we are accuftomed to fay prover- 
 bially, will mifs the gate f ? In this refped:, therefore, the fpeculation of 
 truth will be eafy ; but that all thofe who philofophife fhould together pofTefs 
 a certain whole, while at the fame time each is deftitute of a part, evinces the 
 difficulty of this fpeculation. But perhaps, fmce the difficulty is twofold, the 
 caufe of it is not in things themfelves, but in us. For, as are the eyes of bats 
 
 * It may not be improper to remind the reader tliat this book is called by the Greeks the 
 lefler ^i, or the IciTcr firft, and is a kind of preface to the whole of contemplative pliilofophy ; but 
 unfortunarcly appears to be mutilated. See more concerning it in the Introdudlion. 
 
 f This proverb, fays Alexander, which is ufed in things eafily effefted, is taken from archers 
 aiming at a certain mark j which mark, if narrow, they hit with difficulty, but, if broad, with 
 facility. 
 
 it)
 
 BookIL ARISTOTLE'S metaphysics. ^ 
 
 to the light of day ^ fo is the hitelkn. of our foul to fuch things as arc naturally 
 ihe moji Jplendid of all* . But it is not only juft to return thanks to thofe 
 with whofe opinions fome one may accord, but llkewife to thofe who have 
 fpoken more fuperficially ; for they alfo contribute fomething, fince they 
 exercife our fpeculative habit : for, if Tiinotheus had not exlfted, we fhould 
 not ha.vje had much modulation; and without Phrynis there would not have 
 been fucTi a perfon as Timotheus. The fame thing may be faid of thofe who 
 have difcourfed concerning truth : for from fome of them we .receive certain 
 opinions; but others were the caufes of their entertaining fuch opinions. 
 
 But it is right to call philofophy a fcience fpeculative of truth : for the 
 end of fpeculative fcience is truth, but of pradtical fcience, a work : for prac- 
 tical men, if they confider how a thing fubfifts, yet do not fpeculate the 
 caufe of that thing by itfelf, but with relation to fomething elfe, and as con- 
 neded with the prefent time. But we do not know truth f without the 
 knowledge of caufes : and every thing is in the mofl: eminent degree that, 
 among other things, according to which the fynonymous is prefent with other 
 things : thus, fire is moft hot ; for this is to other things the caufe of heat. 
 Hence that is moft true, which is the caufe to pofterior natures of their being 
 
 * By the intelleft of our foul, is to be underftood the fummit of our dianoetic part, or that 
 part which reafons fcientiiically. By this fummit we perceive axioms, or felf-evident truths •, 
 and its energy is wholly intuitive. However, from its connection with fenfe, and the paffive 
 powers of the foul, which impede its proper energy, it has the fame relation to things naturally 
 the moll manifeft and fplendid (and thefe are moft fimple, and the principles of things), which 
 the eyes of bats have to the light of day. For the viGon of thefe is impeded by the diurnal 
 light through the imbecility of their eyes, though this light is in its own nature eminently 
 viCble, and the caufe of vifion. It mud, however, be remembered, that our intelle£l may, by 
 proper difcipline, become fo far fcparated from fenfe and phantafy, and fo ftrengthened, as, 
 even in the prefent ftate, to obtain the vifion of thefe moft luminous objeds in no contemptible 
 degree. 
 
 1 only add, xhzt ihtit 7wturany viojl fplendid of all things are evidently thofe intelligibles, the 
 cxiftence of which is demonftrated by Ariftotle in the twelfth book, and which correfpond to 
 the ideas of Plato. Either, therefore. Dr. Gilles never read this palTage, and the twelfth book, 
 or, which is more probable, he did not underftand them; for otherwife he never would have fo 
 laftily alTerted, that Ariftotle denied the exiftence of divine principles fubordinate to the caufe 
 of all things, and that one principal deCgn of his Metaphyfics was to explode this do£lrine ! 
 
 -j- That is to fay,. the truth of things of which there are caufes; for this without the know- 
 ledge of caufe cannot be known. But things firft and principles of which there are no caufes 
 are known without the knowledge of caufe, by xhc felf-vifi've energy zwA. projcHi-.n of intelle^ 
 
 F 2 true J 
 
 \
 
 as ARISTOTLE'S METAPHYSICS. Book 11. 
 
 true ; on which account it is neceflary that the principles of things eternal * 
 Ihould be always moft true : for they are noifometimes true, nor is any thing 
 the caufe of being to them, but they are the caufes of being to other things. 
 And hence, fuch as is the being of every thing, fuch alfo is its truth f. 
 
 C H A P. II. 
 
 But, indeed, that there Is a certain principle, and that the caufes of things 
 are not infinite, neither according to a proceffion in a right line, nor accord- 
 ing to fpecics, is evident. For, neither can this thing proceed from that to 
 infinity, as, for inftance, flefli from earth, earth from air, air from lire, and 
 (o on, w^ithout any end of the proceffion : nor can this be the cafe with that 
 caufe whence the principle of motion is derived', as, for inftance, that man is 
 moved by the air, this by the fun, and the fun by ftrife, and fo on without 
 end. In like manner, with refpe(ft to ihcfnal caufe, or that for the fake of 
 which a thing fubfifts, neither is it poffible in this to proceed to infinity ; as 
 that walking fhould be undertaken for the fake of health, health fhould be 
 acquired for the fake of felicity, and felicity for the fake of fomething elfe ; 
 and that thus always one thing (hould fubfift for the fake of another. In like 
 manner, a proceffion to infinity is impoflfible, with refped to iht formal caufe ; 
 for, in thofe things which have mediums, fo that fomething is laftj, and 
 fomething firft, that which is firft muft neceflarily be the caufe of that which 
 is pofterior to it. For, if it were requifite for us to affign the caufe of three 
 
 • That is, the firft principles, or intelligible caufes of the univerfe, of the ftarrjr fpheres, and 
 of the fpheres of the four elements (for thefe, according to Ariftotle, are perpetual, through the 
 incorporeal form with which they are conne£led). Ariftotle's ififel/igilrfes, therefore, are the fro- 
 diicing as well as the final caufes of things : for, a little further, he fays of thefe principles, that 
 " they are the caufes of being to other things." 
 
 + Hence it clearly follows, that mathematical genera and fpecies are more real beings than 
 fenfibles ; for mathematical is much greater than phyfical truth. According to Ariftotle, there- 
 fore, that umverfal which is the obje£t of mathematical fpeculation, does not fubfift in the 
 foul by an abfiradlion from fenfibles, for in this cafe it would not be more but lefs real than 
 fenfibles ; but, in confequence of poflefling more of being than fenfibles, from its truth being 
 more fplendid, it belongs to a fuperior order of things, or, in other words, is the eflential and 
 legitimate progeny of foul. 
 
 t That is, as Alexander well obferves, not firft and laft according to time, but according to 
 the formal difcrimination of caufes. 
 
 things,
 
 Book II. ARISTOTLE'S METAPHYSICS. 37 
 
 things, we (hould fay it is the firft of the three ; for it cannot be the laft^ 
 fince this is not the caufe of any thing: nor yet can it be the middle, for this 
 is the caufe only of one thing, viz. that wtiich follows it. But it is of no 
 confequence whether one, or many and infinite mediums are aflumed. But 
 with refpe<fl to things infinite in energy, and the infinite itfelf, all the parts 
 are fimilarly mediums as far as to the extremity; fo that, in fliort, if no- 
 thing is firft, th^re is no caufe. 
 
 But neither can a proceffion to infinity downwards take place, if in a pro- 
 ceffion upwards there is a principle of cau'es, viz. fo that from fire water (hall 
 be produced, from water earth, and fo always fomething elfe fliall be gene- 
 rated. For one thing is generated from another in a twofold refpedt, not as 
 this thing is faid to take place after that, as the Olympic from the Ifthmian 
 games ; but either as we fay a man is generated from a boy undergoing a 
 mutation, or air frotn water. We fay, therefore, that a man is generated 
 from a boy, as that which is generated from that which has already been ge- 
 nerated, or as that wh'ch is perfedl from that which is tending to perfedion. 
 For there is always a certain medium ; fo that, as generation is the medium 
 between being and non-being, in like manner, that which is making fubfifts 
 between that which is fimply being, and that which is fimply non-being. 
 But he who is learning is becoming to be fcientific : and this is the meaning 
 of the aflertion, that he who is fcientific is generated from him who learnsi 
 But water is generated fiom air, in confequence of air being corrupted. 
 Hence, in the former inftances, the things adduced do not revert into each 
 other, nor is a boy generated from a man. For, that which is making is not 
 produced from generation, but fubfifts after generation. Thus, day is gene- 
 rated from the dawn, becaufe it fubfifts after it; and, on this account, neither is 
 the dawn generated from the day. But the other inftances revert into each 
 other. 
 
 In both thefe cafes, however, it is impoflible that a proceffion to infi- 
 nity fhould take place. For, fince there are mediums, in the one cafe, it is 
 neceflary there fhould be an end ; and, in the other cafe, the things adduced 
 revert into each other ; for the corruption of one is the generation of the 
 other Bur, at the fame time, it is impoflible that the nature which is firft 
 ihould be corrupted, fince it is eternal : for, fince generation is not infinite in 
 an afcending progreffion, it is receflary that the nature fhould not be eternal, 
 from which being firft corrupted fomething is generated. Befides, that for 
 
 the
 
 88 ARISTOTLE'S METATHYSICS. Book 11, 
 
 the fake of which other things fubfifl is the endj but a thing of this kind 
 is that which does not fubiift for the fake of another, but other things fubfift 
 for the fiike of it ; fo that, if that which is laft is of this kind, there will not 
 be a procefijon to ^infinity. But, If there is not any thing of this kind (or 
 that which is laft), there will not be thai for the fake of which other things 
 fubfift. 
 
 Thofe, indeed, who introduce an infinite procefs are ignorant that they 
 take away the nature of the ^oo^;- though no one would attempt to do any 
 thing, if he were not to arrive at the end of his undertaking ; nor would 
 there be intelleft in things of this kind. For he who poffelfes intelleil 
 always ads for the fake of fomething. For this is a hmit ; but the end is a 
 Jimit. But neither can the formal caufe be referred to another more copious 
 definition ; for always the prior definition is more the definition of a thing, 
 but the pofterior is not the definition of a thing *. But where there is no 
 iirft, neither is there that which is confequent to the fiift. 
 
 Further ftill : thofe who fpeak in this manner take away fclentlfic know- 
 ledge. For it is not pofTible that any- thing can be known before we arrive 
 at things indivifiblef : for how can things be underftood, which are after this 
 manner infinite ? for the infinite here is not like that in a line, fince there is 
 tio end to the divifions of a line. But we do not underftand divifions unlefs 
 we limit them ; he, therefore, who paffes through the infinite will not num- 
 ber the fedions. Llkewife, with refped to matter, it is neceffary that it 
 Should be underftood fo far as it fubfifts in motion %. But nothing can be 
 infinite in energy ; and if this be the cafe, that by which infinite can be 
 IcnoWn is not itfelf infinite. But if likewife the fpecies of caufes were infi- 
 nite in multitude, neither thus could we obtain a knowledge of things ; for 
 -we then think that we kfiow when we know caufes. But we cannot in a 
 finite time pafs through that which is infinite according to addition. 
 
 ,.' •For tKc pofterior definition is not the definition of a thing, but of its definition. 
 
 t «'. t. Things which are known without a medium, fuch as definitions. 
 
 \ As matter is continually flowing, it can only be underftood as an infinite flux. But a thing 
 of this kind is not the obje£l of fclentlfic knowledge ; becaufe the objedls of fcience arc things 
 fahle and definite. Hence, according to Plato, matter is known by a fpur'tous reafinirtg ; and, 
 according to Ariftotlci by analogy. 
 
 CHAP.
 
 BooKir. ARESTOTLE'S METAPHYSICS. S$ 
 
 CHAP. III. 
 
 But aufcultatlons happen according to habits. For we think that we ought 
 to fpeak conformably to things to which weare accuftomed ; and things which 
 are aflerted contrary to thole to which we have been accuftomed appear 
 more unknown to us, becaufe they are ftrange and foreign. For that to 
 which we are accuftomed is more known. But the laws evince the great 
 power of cuftom, in which things fabulous and puerile poflefs, through 
 cuftom, greater power than the truth of knowledge. Some, therefore, will 
 not attend to thofe who fpeak, unlefs they fpeak mathematically ; and others 
 do not approve what is faid, unlefs it is fpoken paradigraatically. There are 
 alfo thofe who think that a poet fhould be adduced as a witnefs ; and others 
 expe£t that all things fliould be accurately delivered. To others, again, the 
 accurate is painful ; either becaufe they are unable to comprehend it, or be- 
 caufe they confider it as nothing more than micrology, or minute difcuffion. 
 For the accurate pofTeffes fomething of this kind ; and hence, as in contradls 
 minute attention, fo in difcourfe accurate difcuffion, appears to fome to be 
 illiberal. On this account, it is requifite to be inftru<3;ed how every thing is 
 to be admitted; becaufe it is abfurd at the fame time to inveftigate fcienpe, 
 and the manner in which fcience is to be obtained ; for it is not eafy to ac- 
 complifh either of thefe. Mathematical accuracy of difcuffion is not, how- 
 ever, to be required in all things, but in thofe only which have no connection 
 with matter: on this account fuch a mode of difcuffion is not phylical ; for 
 the whole of nature perhaps is connedted with matter. Hence, what nature 
 is ought firft to be confidered * ; for thus the object of the phyfical fcience, 
 and whether it is the province of one or of many fciences to fpeculate caufes 
 and principles, will be apparent. 
 
 ♦ Ariftotle's meaning here appears to me to be this : the order of fcipntlfic progreflion re- 
 quires that we fliould be exercifcd in phyfical prior to mctaphyfical fpeculations. What na- 
 ture is, therefore, ought to have been previoufly confidered by thofe who wifh to ftudy Meta- 
 phyfics with advantage. 
 
 \ 
 
 ARISTOTLE'S
 
 ARISTOTLE'S METAPHYSICS. 
 
 BOOK III. 
 
 CHAP. I. 
 
 JlN order to acquire that fcience which is the objed of our inveftlgation, it 
 is neceflary, in the firfl: place, to enumerate the particulars refpedtlng which it 
 is firft requifite to doubt. But thefe are the things of which there are differ- 
 ent opinions, and whatever befides thefe may have been negieded and 
 omitted. But, for thofe who wifh to doubt, it is advantageous to doubt in a 
 proper manner. For the power of acquiring pofterior knowledge is derived 
 from the folution of prior doubts. But it is not poffible for any one to 
 diffolve the bond of any thing, who is ignorant with what it is bound. The 
 doubting, however, of the dianoetic part of the foul, or that part which rea- 
 fons fcientlfically, manifefts the bond refpeding a thing. For, fo far as this 
 part of the foul doubts, fo far it is fimilar to thofe who are bound ; fince 
 neither he who is bound nor he who doubts is able to proceed any further. 
 On this account it is requifite, in the firft place, to contemplate all the diffi- 
 culties, both for the fake of thefe things, and becaufe thofe that inveftlgate 
 without having previoufly doubted refemble thofe who are ignorant whither 
 they ought to go : and, befides this, neither can they know whether they 
 have found, or not, the objed of their fearch. For the end to thefe is not 
 
 ma^iifeft ;
 
 Book III. ARISTOTLE'S METAPHYSICS. 41 
 
 manifeft ; but is manifeft to thofe who previoufly doubt in a proper manner. 
 Further ftill : it is neceffary that he fhould be better fitted to judge, who has 
 heard all the oppofite reafons*; which may be compared to the adverraries 
 in a law-fuit. 
 
 But the firft doubt is refpeding thofe things concerning which we have alfo 
 doubted in the preface f, viz. whether it is the province of one or of many 
 fciences to fpecuLue caufes :];; and whether it belongs to this fcience, alt ne to 
 confider the firft principles of efil-nce §, or likewife to fpeculate concerning thofe 
 
 * As it is the bufinefs of vulgar dialeflic (the fubjeft of Aridotle's Topics) to difpute from 
 probable arguments on Voth fules of a queftion ; in like manner, it is the province of fcientific 
 dialectic, to proceed through all oppofing reafons in its inveftigation of the truth. T he latter, 
 however, differs from the former in this, that its reafoning is always demonftratlve, and not 
 merely probable. 
 
 + That is, in the firft book ; for he there doubts concerning caufes. 
 
 ■ o 
 
 I What Ariflotle inquires is this : Becaufe there is an effective, alfo a formal and a final 
 caufe, and in fome things a material caufe, does he who knows a thing itfelf know all its 
 caufes, fo far as he has one fcience ? or, are many fciences converfant with many cauLs, fo that 
 one knows the effedive, another perhaps the material or the final, and another the formal 
 caufe ? 
 
 To this we reply, that one fcience confiders all thefe ; for, any one of them being unknown, 
 there will not be fcience of a thing. But, if his difcourfe refpedt wifdom, it would be very 
 ridiculous to think that it is ignorant of good or form, or the generative caufe of things. 
 
 § He inquires whether the firft philofopher, knowing the caufes of being, knows alfo that 
 truth which is contained in propofitions eminently the firft and immediate ; or, whether it is the 
 province of one perfon to know the principles of being, but of another to know the firft and 
 moft univerfal axioms. 
 
 But it is evident that it belongs to the fame perfon to know both thefe and thofe; for he 
 would not be perfe£t, if ignorant of either. Indeed, from the knowledge of both, he will 
 poflefs the fcience of fciences; from the fpeculation of axioms knowing demonftrative prin- 
 ciples which adminifter to other fciences. '1 hus, for inftance, he knows the axiom which is 
 fubfervient to diale£lic, and to all fciences which employ fyllogifm, viz. that it is impoffible that 
 the fame thing can be affirmed, and at the fame time denied, of the fame : alfo, that which is 
 employed by geometry, viz. that thofe things which are equal to the fame thing are equal to 
 each other; that which the natural philofopher ufes, that nothing can be generated from that 
 which is not ; and that which is common to all fciences, that good is the ultimate ohje£t of 
 defire. 
 
 As, therefore, it belongs to one and the fame perfon to poflefs fcience, and that which is 
 known by fcience ; and he who has not the one will be deftitute of the other : in like manner, 
 it is the province of one and the fame man to confider the caufes of beings, and demonftrative 
 principles, through which he will view beings themfelves, and the different kinds of knowledge 
 co-ordinated to different beings, a? from a lofty tower of intelleflual fpeculation. 
 
 G principles
 
 42 ARISTOTLE'S METAPHYSICS. Book IIL 
 
 principles from which all demonftrations are formed: fuch a?, whether it is 
 poffible that one and the fame thing can at the fame time be affirmed and denied; 
 and other things of this kind. And, if it is the bufinefs of this fcience to be 
 converfant with eflence *, whether there is one or many faiences about all 
 effences ; and, if there are many, whether all of them are allied to each 
 other t, or fome of them are to be called wifdom, and others fomething elfe. 
 This, alfo, it is ncceflary to inveftigate, whether we miift fay that fenfible 
 effences alone have a fubfiftence, or others befides thefe % ; and whether there 
 
 * He inquires whether, if it fliould be granted that wifdom is converfant with being, it will 
 be converfant with all beintj ; or, whether the knowledge of being will be diilributed among, 
 many fciences. 
 
 To this we anfwer, tliat it is the province indeed of wifdom to know all beings fo far as 
 they are beings ; yet this does not exclude the exiftence of other fciences, among which the 
 parts of being may be diilributed, though they may conuder fuch parts differently, and more 
 generally. Thefe fciences are arithmetic, aftronomy, phyGcs, medicine, and whatever others 
 there may be of this kind. 
 
 f This is M'hat remains of the former inquiry. To this it mny be replied, thr.t the fpecies of 
 the whole of philofophy, as, for inftance, the firft philofophy and phyfics, are allied to each 
 other and to the whole ; but that thofe fciences which are not principally converfant with 
 effences, as, for inftance, the mathematical fciences, as not being equal to wifdom in magni- 
 tude and dignity, can never be faid to be co-ordinated to it. Whence, neither are there many 
 wifdoms, but one which is moft true. However, thefe fciences, confidered as proceeding from 
 wifdom, and depending on the principles flowing from it, without being able to be removed 
 from it in the fmalleft degree, may be faid to be allied, both to each other, and to that moft ge- 
 neral fcience from which they are derived. And, as inttlleft is the tra«fcendent parent of all 
 fciences, (viz. is not diftributed among them, but has a fubfiftence feparate from the multitude 
 by which it is participated), though principally of wifdom, which it conftltutes as a monad 
 comprehending caufally in itfelf every fpecies of knowledge, and through it imparting the prin- 
 ciples of particulars : hence, neither are all fciences equally excellent, but that which is nearer 
 to is more venerable than that which is more diftant from wifdom ; but that which recurs to- 
 wifdom through rnany fciences is inferior to all the intermediate fciences. 
 
 But neither are they allied after the fame manner: for arithmetic is more allied to geometry^ 
 and to the other mathematical fciences, than to phyfics and medicine. But the divifive, the 
 analytic, the definitive, and the demon ftrative fcience more accord witli each other than with 
 certain ether fciences, becaufe they are proximately fufpended from wifdom itfelf, and through 
 it, together with a moft fplendid fire, the fire of intelleft, are imparted to fouls capable of being 
 led back to their paternal port. 
 
 X Ariftotle inquires, whether in conjun£lion with fenfible fubftances, as the heavens, the 
 earth, the middle elements, animals and plants, there are certain other eflences, viz. intelligible 
 effences. 
 
 To this we reply, that the apparent order of things, compared with true beings, or incorpo- 
 real nature?, may be more juftly called generation than cffeace. 
 
 is
 
 Book in. A U I S T O T L E' S M E T A P H Y S I C S. 4J 
 
 is one genus or many genera of effences *, according to the opinion of thofe 
 who introduce forms, and place things mathematical between thefe and fen- 
 ;fibles. Thefe things, therefore, as we have faid, muft be confidered f; and 
 
 likewife, 
 
 * This alfo is a part of the preceding problem ; for in what follows lie confiders that pro- 
 blem anil this as oiie^ But what he fays is to this cfFcdl : Though it fliould be granted that 
 there is a certain effence befides that which is the objecl of fenfe, will it be of one fpecies, or, 
 at leaft, of two fpecies ? For Plato, in the fixth book of his Republic, appears to confider the 
 dianoetic eflence as fubiifting between an intelleflual and fenfible nature ; or, in other words, 
 he places an eflence which is apprehended by fcientific reafoning, between that which is the 
 ■obje£t of the intuitive vifion of intelle£l and that which is the fubjett of the paflive percep- 
 tion of fjnfe. Under this dianoetic eflence he places the mathematical fciences, and not thofe 
 natures which are the obje£l:s of imagination and opinion ; for thefe are not elTences, But the 
 images of eflences. He alfo diflributes under this eflence whatever the foul eflentially con- 
 tains in herfelf, the geometric, arithmetic, and harmonic principles of which the intelleft of 
 the artificer of the univerfe eflabliflied in foul, as is fhown in the Timxus of Plato. 
 
 In anfwer, therefore, to Ariflotle's inquiry, we reply, that it may be faid that there is one 
 intelligible eflence of all things, when we alone feparate a fenfible eflence from it, accordintr to 
 a divifion of all things into two. It is alfo pofllble to fubdivide the unappareiu and dianoetic 
 eflence, into that which is properly intelligible and that which is properly dianoetic, according 
 to the divifion made by Plato in the Republic. We may alfo fubdivide each of thefe ; for 
 there are many intelligible and inteliedual orders, as is copioufly and beautifully fliown by 
 Proclus on Plato's Theology. And the order of fouls, to him who knows how to diftinguifli 
 ■beings according to fpecies, will be feen to poflefs much eflential diverfity. 
 
 t Ariflotle here inquires, whether wifdom confiders the eflences of things alone, or eflential 
 accidents. Tx) this we reply, that it confiders both eflences and things eflentially inherent; 
 by the analytic method receiving the principles of being ; by the divifive and definitive 
 method confidering the eflences of all things ; and, by the demonilrative method, concluding 
 ■fuch things as are eflTentially inherent in eflences. But, in the moft fimple and properly intelli- 
 gible eflences, there is no fuch thing as a difl:inftion into fubfl.ance and accident; and there- 
 fore they are neither capable of definition nor demonllration ; but are alone to be apprehended 
 by intelleftual projedion (vo£fa cTri^ohv), as Ariflotle himfelf aflerts in many places : " for in- 
 tellect (fays he) either comes into contaft, or does not, with its object." 
 
 But middle eflences are demonftrable accoiding to the things which they efienti.illy contain 4 
 eflential accidents fupervene univerfal reafoiis confidered by themfelves, and as adorning a fen- 
 fible nature, and therefore demonflration is alfo converfant with thefe ; and in material fpecies, 
 in individuals, and in fenfibles, fuch things as are properly accidents are perceived by imagina- 
 tion, and which are prefent and abfent without the corruption of their fubjeft. Thefe again, 
 being worfe than demonflirable accidents, are apprehended by afllmihtive reafonings (3i« thj 
 ciKoloXoyia;), not indeed by a wife man fo far as a wife man, but perhaps by phyficians, and 
 natural philofophers, and all of this kind. 
 
 I only add, that, of the fcientific methods above enumerated, the analytic proceeds in a retro- 
 grade order to that of the reft. For divifion proceeds from univerfals to particulars j defini- 
 
 G 2 tion^
 
 41 ARISTOTLE'S METAPHYSICS. Book III. 
 
 likewife, whether the fpeculatlon is alone refpecling efTenccs, or alfo refped- 
 ing the eflential accidents of efTences. And, befides this, whofe province it 
 is to fpeculate concerning y?/?,7(? and different'^ .,\\^t fnnilar and dljjim'ila}\ con^ 
 trariety, prior &nA pojicrior, and every thing elfe of this kind, about wliich 
 thofe who are (killed in dialedtic endeavour to fpeculate, making iheir inquiry 
 from things probable alone. 
 
 Further ftill, refpeding fuch things as are efientlal accidents to thefe ; and 
 not only what each of thefe is, but likewife if one is contrary to one. 
 
 tlon, from things fimple to fuch as are complex ; and demonitration, from caufes to things 
 caufed. But analyfis runs back from particulars to univerfals ; from the complex to tlie fimple, 
 and from things caufed to caufes. 
 
 • That it is the bufinefs of a wife man, according to Ariftotle, to confider efTences, and their 
 effential accidents, is evident, from what he fays in the beginning of the fourth book, viz. " that 
 there is a certain fcience which conGders being fo far as being, and its eflential properties." 
 
 But that the things which now prefent themfelves to our confideration are in the higheft 
 degree efientially inherent in being, is evident from hence, that tliey pervade through all beings. 
 For famenefs and difference, fimilitude and dilhmilitude, and fuch other things as he now pro- 
 pofes to confider, are not apparent in fome beings and abfent from others ; but, beginning on high 
 from intelligibles, and adorning every intelligible and divine nature, they proceed through the 
 effence of foul to the nature of the univerfe, to the heavens, and the realms of generation, and 
 impart to beings identity, equality, and fimilitude, from the all-beneficent nature of the one. 
 
 But diverfities, dinimilitudes, inequalities, contrarieties, prior and pofterior, and every thing 
 of this kind, proceed from a moft prolific and never-failing caufe of all things, viz. a duad of 
 infinite power (fymbolically called chaos by Orpheus and Hefiod), and are imparted to vifible 
 and fenfible natures ; fo that neither is there a nature fubfifting between impartible and par- 
 tible efl"ences, fuch as foul ; nor fo abftraded from all things by tranfcendency of efience ; nor 
 fo abjed, by fubfifting at the extremity of fenfible eftisfts, which is not diflingui(hed by thefe 
 fpecics. 
 
 Hence Plato, in the Sophifta, invefligating the genera of being, which pervade through all 
 things, enumerates famenefs and difference, effence, permanency and motion. The natural 
 philofopher and the mathematician ufe thefe genera as things credible [rmriuriKai) ; but the firfl: 
 philofopher employs them fcientifically and intelle£lually. Whence Ariftotle alfo, in the ninth 
 book of this work, difcourfes concerning all thefe, and latently (hows, that it is the province of 
 a wife man to have a fcientific knowledge of thefe. For, if one wlio is (killed in his dialeftic 
 difcourfes probably of thefe, as he afferts here, and in his Topics, who but the firft philofo- 
 pher, or the wife man, will confider them fcientifically ? 
 
 Should it be aiked, wjiy Plato among thefe genera enumerates motion and permanency, but 
 Ariftotle omits to mention them •, it may be replied, that Phtto, indeed, knowing that motion 
 and permanency were contained in the amplitude of divine and human affairs, neceffarily enu- 
 merates thefe in the genera of beings ; but Ariftotle, who thought that motion and permanency 
 alone pertained to natural bodies, was very confiftcntly of opinion, that the peculiarity of thefe 
 genera ftiould not be extended to all beings. 
 
 And
 
 Book III, ARISTOTLE'S METAPHYSICS. 45 
 
 And again, whether genera are princ'ples and elements *, or thofe things 
 which aie inherent in a thing, and into which it is divided. And if this is 
 
 * Two things are here propofed by Ariflotle : one, if the genera of things ought to be called 
 principles and elements ; principles, indeed, as caufes, but elements, as having a greater fimpli- 
 citv of fubfiftence, becaufe definition is at laft. refolved into thcfe : or, whether thofe things 
 which are inherent in any being, into which it is divided, and which are properly confidered 
 as belonging to it, ought to be thus denominated. 
 
 But the fecond obje£l of inquiry is, whether, though it fliould be granted that the genera of 
 things are principles, and not the things into which any being may be divided, — whether, I fay, 
 fuch as are more comprchenfive, and are extended to a greater multitude of things, ought to be 
 called principles and elements, or rather fuch things as are proximately predicated ; as, for in- 
 ftance, of Socrates, whether the principle is animal or man. 
 
 In anfwerto the firfl; queftion, it is nccelTary to alk, what principles are here the objctls of 
 inquiry ? For, if they are the material or the formal, fuch things as are inherent are principles ; 
 but, if they are the cffedive or the final, genera themfelves are principles; not, indeed, 
 thofe genera which are of poilerior origin, for thefe fubfift in cffeds themfelves. Thus, for 
 inftance, in Socrates, both man and animal are contained ; which can neither be the eftoftive 
 nor final principles of man, fince they are parts of his apparent etlence, and, in confe- 
 quence of being indigent .of a fubje£V, have not a feparate energy. But, if there are any 
 genera prior to particulars (as we (liall fully evince there are in the notes to the thirteenth 
 book), which are the caufes of fenfibles, which are beheld in the produftive principles of the 
 nature inherent in the mundane wholes, and which ftill prior to this fliine in the forms of the 
 mundane foul, and in the intelle£t of the artificer of the univerfe, thefe may be defervedly 
 called the caufes of fenfibles. But, in thefe, the final caufe is to be affigiied together with the 
 eifedlive, becaufe it appears more manifeftly in thefe, as being eftablilhed in the veflibule of 
 the good itfelf. 
 
 The anfwer to the fecond inquiry is more manifeft. For, if we confider genera and fpecies 
 as things of poilerior origin, ;. e. as merely fubfifting in the phantafy by an abftraclion from 
 fenfibles ; thofe genera which are more proximate to the fubftances called firft, or, in other 
 words, to corporeal fubflances, will be more eminently' fubftances, and on this account will 
 partake more of the nature of principles than thofe which are lefs fubftantial by being more 
 remote from fenfibles. But, if we confider genera and fpecies properly fo called, and which 
 are the efFeftive principles of particulars, both natural and demiurgic, it is manifeft that, among 
 thefe, that which is more comprehenfivc, and which extends itfelf to a greater multitude, is 
 a more divine caufe, fince without this nothing can poflefs either effence or energy. 
 
 Manifeft figns of thefe things are exhibited by logical genera and fpecies. For, of whatever 
 fpecies is predicated, of that alfo genus is predicated : but the converfe is not true. Genus, 
 therefore, is more comprchenfive than fpecies. Thus, of whatever the fpecies man is predi- 
 cated, of that alfo animal is predicated ; but man is not predicated of whatever animal is pre- 
 dicated. By transferring, therefore, predication of any particular to produftion, or, in other 
 words, confidering predication to be the image of caufal energy, we fhall pafs from images to 
 true genera and fpecies, and fpeculate their mutual connedion, their tranfcendency and fubjec>. 
 tion, and the dignity which they poflefs as the producing caufes of things, 
 
 the
 
 46 ARISTOTLE'S METAPHYSICS. Book m. 
 
 the cafe with genera, whether they are fuch things as are predicated the lafi; 
 of all of individuals, or fuch things as are firft ; as, for inftaiice, whether 
 animal or man is a principle, and is more a principle than that which is an 
 individual. But it is efpecially requifite to inquire, znA fcrioujiy co?ifider*\ 
 •whether there is any eflential caufe bebdes matter, or not, and whether this 
 is feparate, or not : likewife, whether it is one, or if there are many fuch 
 caufes ; and whether there is any thing befides a colleded whole f , or that 
 which is a compofite (but I mean by a colle£led whole, when any thing 
 is predicated of matter) ; or whether there is nothing befides : or whether this 
 is the cafe with Ibme things, and not with others j and, if this be the cafe, 
 what kind of beings thefe are. 
 
 Further flill, with refpedt to principles, whether they are bounded in num- 
 iber or fpecies J, viz. whether this is the cafe both with principles fubrifxlng 
 
 in. 
 
 * The antlent natural philofophers confined themfelves to tlie fpeculation of matter alone, 
 and called the prhicipleof things water, or air, or fire ; but others beheld indeed an efFeilivc 
 .caufe, but fuch a one ;i3 is infeparable from matter, as the Stoics, and others of greater antiquity. 
 /Others again admitted a caufe feparate from nature, as both Ariftotle and Plato ; the former of 
 whom openly admits that this caufe is the obje£i: of defire to all things ; and, latently, that it is 
 alfo the generative principle of the univerfe, as we have fliown in the Introduction to this work. 
 But Plato openly afcribes to it both thefe prerogatives. This being the cafe, Arillotle very pro- 
 perly inquires, which of tln;fe opinions is the more true : and it is evident that it mufb be the 
 latter, which was adopted by him and Plato. But, when he again inquires whether there is one 
 feparate caufe, or many 5 we reply, that there is both one and many, the many being co-ordi- 
 nated. to the one, and extended to it, as to the proper obje£i of defire, as Ariftotle alfo Ihows ia 
 the twelfth book of this work. 
 
 -]- Ariftotle here inquires whether, befides that which is compofite and fpccific, there are uni- 
 verfals, and eflential fpecies -, and if there are ideas of all things natural, artificial, beautiful, 
 b.ife, good, evil, pcrfedl, and imperfeft : or whether there are ideas of fome of thefe, but not 
 of others •, and, if this be the cafe, of which there are ideas, and of whicli not. 
 
 To this we fliall at prefent briefly reply, that there are no ideas of things bafe, imperfe£l-j 
 and evil ; for thefe fubfifl in the ultimate progreflions of nature, and this, becaufe partial 
 fouls, fuch as ours, are unable to vancjuifli the infinity of matter. Yet there are fabri- 
 catlve forms of eflences naturally permanent, in the fame manner as there are of things artip- 
 xial in art. That there are forms, indeed, of things artificial, Ariftotle openly admits, aflerting 
 in many places, that the material is perfeded from the-immaterial houfe, as in the fixth book of 
 this work : and that he alfo occultly admits that there are exemplars of tilings which perpe- 
 tually fubfift: according to nature, we have fliown in the Introduftion. 
 
 X Ariftotle admits, indeed, that principles are bounded; but he doubts whether they arc 
 bounded in number, in the fame manner, for inflance, as the four elements ; for thefe are four in 
 .nuniber ; and therefore body is not produced from air and fire fimply, but from mundane fire 
 
 .and
 
 Book III. ARISTOTLE'S METAPHYSICS. 47 
 
 in reafons (formal caufes), and thofe which fubfift in a fubje£l ; and whether 
 there are the fame or different principles of things corruptible and incorrup- 
 tible *. -Again, whether all principles are incorruptible, or whether the 
 principles of things corruptible are themfelves corruptiDle. Further flill, that 
 which is the inoft difficult of all, and polfelfes the greatefl: ambiguityf, is, 
 
 whether 
 
 and air, as fulsfiRing in the fubUinary region. Or whether the principles of things are 
 firft bounded in fpecies, in the fame manner as the twenty-four elements of fpeech ; for that 
 thefe are bounded in fpecies, and not in number, is manifefb from hence, that the whole of the 
 letter a is in many fyllables, and that one part of it is not in the fyllable b,7, and another part in 
 the fyllabley^f ; as air with one' part of itfclf conflitutes this body, and with anotlier part of 
 jtfelf a different body. He inquires, therefore, whether principles are bounded in number or 
 fpecies- To this we reply, that, if they are bounded in number, they are alfo bounded in 
 fpecies*; but it is evident that, if they are bounded in fpecies, it docs not -follow that they are 
 altogether bounded in number. For the twenty-four letters of the alphabet are bounded iii 
 fpecies, but are indefinite as to their number. 
 
 * Thefe things fecm to be propofed as two objetls of inquiry, viz. whether there are the 
 fame principles of things corruptible, and of things incorruptible. For, if there are the fame, 
 in what manner do they make thefe things to be incorruptible, but thofe corruptible ? But, 
 if different, whether are thefe incorruptible, but thofe corruptible ? 
 
 But, in whatever manner the divifion may be made, we reply, that the principles of things 
 incorruptible are entirely the principles of every kind of beings ; for the prolific and infinite 
 energy of fach principles can never be circumfcribed. But the principles of things corruptible 
 are not all of them the principles of incorruptibles. Hence, the proximate principles of corrup- 
 tibles are not the principles of any thing elfe. Yet neither are all thefe principles corruptible. 
 For the circulation of the heavens is attended, according to Ariftotle, with an effeftive caufe, . 
 yet it is not corruptible. 
 
 There are alfo other incorruptible as well as corruptible caufes of generated nqtures ; for, if, 
 as Ariflotle afferts, man and the fun generate man, it is manifeft that man has both a corrup- 
 tible and incorruptible caufe. The fame alfo takes place in horfe, dog, and every fublunary 
 fpecies ; for each of thefe has a partial and an univerfal caufe : but that principles which are 
 more univerfal fhould be corrupted^ is the mofl of all things impoffible ; for they can never be 
 generated from any thing, nor can other things be generated from them. 
 
 Thefe things are not only rightly afferted by the divine Plato, but alfo by Ariftotle : for, in 
 the twelfth book of this work, he introduces the principles of things eternal, as feparate and 
 immaterial forms, and as the objects of defire to all things, and fays, that there are certain 
 eternal principles of things corruptible. In the next place, he frequently, and in what follows, 
 generouQy (hows that generation would not be, unlefs there was fome eternal caufe of it. 
 
 f It is evident here, that Ariftotle did not confider the opinions of the antients refpefXhig 
 principles to be defpicable ; but, on the contrary, that he thought they deferved much attention. 
 . We fay, therefore, that all things would not defire the firlt being, unlefs they derived their 
 
 perfection
 
 48 AFxISTOTLE'S METAPHYSICS. Book III. 
 
 whether the one and being are, as the Pythagoreans and Plato fay, nothing elfe 
 than the effence of beings ; or this is not the cafe, but fomething elfe is the fub- 
 jed, as triendihip, according to Empedocles, but according to others fire, or 
 water, or air. And again, whether principles are things univerfal*, or have a 
 
 fubfiilence 
 
 pprfeclion from tlicnce ; and that, as they eternally depend on tl^s, they alfo eternally from 
 •tji's receive their bcinjr. Hence, if the iirft being is defirable to ail things, and is the caufe of 
 being to all, it produces from itfelf both true beings and intelligible fpecies. But as this firfl; 
 being, though the principle of all things, is after a manner co-ordinated with multitude, and 
 therefore has a certain alliance with it ; hence, prior to this f.rfl. bi;ing, it is requifite to confider 
 a fuper-effential one, ineflably abilracled from all beings in fimplicity and excellency, and which, 
 though it cannot be properly denominated, yet rray be more properly called the one than any 
 thing elfe, becpufe it is the fource of union to all beings, that is, of afiimilation to itfelf. The 
 Pythagoreans, therefore, 7iecf:(rarily placed ihe one and Icing at the fumniit of the whole of 
 things; this imparting the caufc of unity and of all good to beings themfelves, but the othev the 
 proper principle of being to other fpecies. 
 
 Empcdocks too, by friendlhip, appears to fignify nothing elfe than that one which is co-ordi- 
 nated with the indefinite duad ^ fo that friendfnp and Jlrife with him are the fame as ihe one 
 and the duad of the Pythagorseans, or the hound and infinity of Plato. From thefe two Empc- 
 docles produces the firft being, all intelligiMes, and the fenfible univerfe. For, if friendlhip, ac- 
 cording to this philofopher, is the caufe of union to the intclledlual fphere wliich fubfifts after 
 the one ; but ftrife is the caufe of multiplication, dlverfity, and prolific progrelTion ; is it not 
 evident that friendjhip is with him analogous to the above-mentioned co-ordinated one, but 
 firife to the indefinite duad >. For, as Empedocles w-as a Pythagorsean, how can it be fuppofcd 
 that he would adulterate tlie Orphic or the Pythagoric principles ? 
 
 But If Thales called water the one and being, but fome other dignified air or fire with thefe 
 appellations, fuch opinions have been reprobated by many of the antients, and efpecially by 
 the demoniacal Ariilotle. 
 
 * Principles, properly fo called, are to be confidcred as fubfifting above univerfal genera and 
 fpecies, and much more above particulars ; for thus they truly fubfift : 
 
 In matter particulars are confidered ; but in nature and foul the univerfal generated caufcs 
 of fenfibles pre-exift: nature, indeed, poirefiing the-moft fpecial fpecies, from which flie proxi- 
 mately generates things material and particulars; but foul previoufly afluming thefe, and, prior 
 to thefe, more univerfal reafons, through wliich dividing genera themfelves, and again uniting 
 the riiuhitude of her reafons, flic confiders all things by an afcending and defcending progreffion, 
 and operates according to a divifive, analytic, and definitive energy. But above thefe are 
 placed fabricative or demiurgic fpecies, and above thefe again the principles of thofe mighty 
 wholes, the mundane fpheres. And thus much in anfwer to the firrt inquiry. 
 
 To the fecond. queftion we reply, that a fubfiftence in capacity mufl be entirely excluded from 
 principles properly fo called. For fuch a fubfiftence is imperfefl, unprolific, and more adapted 
 to matter. But to thefe a fubfiftence in energy rather belongs, except that fome of them cau- 
 jiot be faid to be in energy, but arc rather energy itfelf. But the principle of all things (if it be 
 
 lawfu^
 
 Book III. A R I S T O T L E'S M E T A P H Y S I C S. 49 
 
 fubfiftencc like particulars; and whether they fubfift in capacity or energy. 
 Further Uill, whether they fubfift in any other manner than as things motive ; 
 for thefe thing , may afford matter for abundant doubt. And, befides all this, 
 whether numbers, lengths, figures, and points are certain eflences or not*: 
 and if they are eflences, whether they are feparated from fenfibles, or fubfift 
 in thetn. For, refpe5ling all thefe particulars^ it is not only difficult to dif cover 
 the truths but neither is it eafy to doubt well in a rational mantier. 
 
 CHAP. i:. 
 
 In the firft place, therefore, we mu(l inquire refpe(£ling thofe things which 
 we firft mentioned, whether it is the province of one or many fciences, to 
 fpeculate all the genera of caufes : for how can it be the bufinefs of one 
 fcience to know principles "f, fince they are not contrary to each other ? 
 
 Befides, 
 
 lawful fo to fpeak) is not only above a fubfiftence in capacity and a fubfiflence in energy, but is 
 even above energy itfelf ; for he is above being to which energy is fubordinate. 
 
 To the third queftion we reply, that thofe principles are immoveable, which are the caufes of 
 things eternal ; but that thofe are moved which fubfift among the caufes of things generated 
 and corrupted, as the fun and the ethereal circulation. 
 
 * To this w€ reply, that the eflence of thefe is manifold : for, in the works of nature, any one 
 may fee figure, number, phyfical fuperficies, and phyfical line and point. Thefe alfo fubfift in 
 our phantafy and opinion, viz. continued quantity in imagination, and number in opinion ; the 
 latter being more immaterial than the former ; and receive their perfetlion from the eflential 
 fpecies of the foul. 
 
 Thefe objects, therefore, of imagination and opinion, participate indeed of eflence, but 
 are not eflences. They may, therefore, rather be reduced under quantity, or quality, or fome 
 other predicament ; but the efTential reafons of the foul, of which thefe are images, may be de- 
 fervedly called eflTences. 
 
 But he who is able to fee the paradigms which fubfift in intelled and intelligibles will per- 
 ceive number, and figure, and magnitude itfelf, there enumerated. 
 
 t Ariftotle fyllogifes as follows: Caufes different in fpecies are not contrarie?. Of things 
 which diifcr in fpecies, and which are not contraries, there is not one fcience. There is. not, 
 therefore, one fcience of caufes. And in the fecond figure, caufes different in fpecies are not 
 contraries. Things which are under one fcience, if they differ in fpecies, are contraries : 
 caufe.s, therefore, are not under one fcience. 
 
 It is plain, however, that Ariftotle is not ferious in what he now fays; fince the major prc- 
 pofition is altogether faie. For it does not follow, that, if there is one fcience of contraries, 
 
 H there
 
 ^0 AR I STOTL E'S M ET APH Y SI C S. Book III, 
 
 Ecfides, with many beings all things are not prefent *. For, how is it 
 poflible that the principle of motion, or nature of the good, can fubfifl; 
 
 in 
 
 there is not one of things not contrary ; nor that, if contraries are under one fcience, things 
 v.hicli are under one fcience muft be immediately contraries. Nor perliaps do caufes always 
 differ in fpecies, as Ariftotle himfelf obferves in the fecond of his Phyfics. " For," fays he, 
 *• the end and the agent fomctimes concur in fpecies." 
 
 * He again fyllogifes as follows : The firR and moft beautiful fciences are converfant with 
 things immoveable. Sciences wliieh are converfant with things immoveable by no means have 
 a knowledge of all caufes, becaufe in things immoveable there is neither the efficient nor the 
 final caufe. The firff, therefore, and moft beautiful fciences have by no means a knowledge 
 of all caufes. 
 
 Here, again, Ariftotle affumes the mafk; fince the major propofition is again falfe. 'For, of 
 fciences, let the fpeculative be the firft and the moft beautiful: but of thefe, natural phllofophy, 
 which is converfant with things moveable, muft not be placed in the firft rank, fince mathema- 
 tics rather, and the firft philofophy, are better than this. But why do not all thefe fciences 
 confider the caufes of fenfibles .'' Becaufe, it may be faid, neither have immoveables an effec- 
 tive or final caufe. This, however, is far from being the cafe ; fince thefe alfo originate froni 
 a principle, and do not proceed to beings from chance. For every kind of being is either a 
 principle, or from a principle. But multitude cannot be a principle ; on this account, there- 
 fore, they will have both an effe<Slive and a final caufe. For things immoveable both knovif 
 and are known for the fake of good. 
 
 In the next place, that which was propofed from the firft is different from this inquiry : 
 for it was not propofed to confider, whether, the caufe failing, there can be fcience of a thing, 
 but whether, admitting the fubfiftence of different caufes, they are not confidered by one 
 fcience, but by many ; and that they are not, is not at prefent proved. The oppofite, indeed, to 
 this may be rather inferred : for, if ail fciences which are converfant with things immoveable, 
 know all the caufes which are inexlftent in the fubjefts of their fpeculation, and defpife 
 nothing which is inherent in them, wifdom alfo will know all the caufes of being fo far as it 
 is being. 
 
 In the third place, the reafoning of Ariftotle endeavours to prove, that the mathematical 
 fciences have not a finalcaufe. However, he falfely affumes, that a fubfiftence for the fake of 
 fomcthing is the end of aftion,but not of fpeculation; for there are not only ends of anions, 
 but, much more, of contemplations themfelves. Thus, we defire to contemplate for the fake of 
 good, of an aflimilation to divinity, and of our true prefervation. But the end of aflions is 
 partial, and is not properly an end, fince it muft always refer to contemplation ; for the fake of 
 which alone it fubfifts, as is beautifully ftiown by Plotinus in his book on Contemplation, Nature, 
 and The One, and to my tranflation of which I refer the reader. But, if geometricians do not 
 affign the end, when they demonftrate things effentially inherent in figures, it is by no means 
 •wonderful ; for neither do they confider the fubjedt, whether it is, or is not ; nor are they 
 bufily employed about the end; nor do they attend to any thing befides the cffential properties 
 of figures or magnitudes. Compared, therefore, with the firft philofopher, they are unfcien- 
 
 tific j,
 
 Book III. ARISTOTLE'S METAPHYSICS. SI 
 
 in things immoveable ? fince every thing which is eflentially and through its 
 own nature good is an end; and fo is a caufe, becaufe other things are 
 generated and fubfift fur its fake. But the end, and that for the fake of 
 which a thing fubiifts, are the end of a certain adlion. But all adions are 
 accompanied with motion : hence, it is not poflible that in things immoveable 
 there can be this principle, or a certain good itfelf. On this account alfo, in 
 the mathematical fciences, nothing is evinced through this caufe, nor is any 
 dcmonftration produced from it, becaufe it is better or worfe. But no one 
 makes any mention whatever of any thing of this kind ; fo that certain of the 
 fophlfts, fuch as Arifdppus, revile thefe fciences on this account. For in other 
 arts, fays he, and even fuch as are fordid, as in the tedonic art and that of the 
 currier, all things are aflerted on account of the better or the worfe ; but the 
 mathematical fciences do not pay any attention to things good and evil. 
 
 But again, if there are many fciences of caufes, and each is converf^nt 
 with a different caufe, which of thefe muft we aiTert to be that which we in- 
 veftigate ? or, who, among thofe that poflefs thefe fciences, will have a fcien- 
 tific knowledge of the thing inveftigated? For it happens, that all the modes 
 of caufes are prefent with the fame thing. Thus, for inftance, in a houfe, 
 tlie caufe ijohence motion is derived is art, and the builder ; but that for the 
 fake of which it fubfift s is the work; the matter is earth and ftones, and the 
 form is the definition. From thofe things, therefore, which v/ere formerly 
 decided by us, viz. which of the fciences ought to be called Wifdom, it feems 
 reafonable, that each fhould be thus denominated : for that fcience which is 
 ihe moft principal and the moft honourable, and which it is not juft other 
 fciences that rank as fervants fhould contradid, is the fcience of the end and 
 
 tific ; for, as tlie'ir principles are hypothetical, and therefore not properly known ; and as the 
 end and medium confifl alfo from things which are unknown, by what contrivance, fays Plato, 
 can a dedudion from thefe be called fcience ? That is, how can it be called fcience, according 
 to the highell. and moft true fubfiftence of fcience ? But the firfl philofopher beholds in 
 himfelf both luhy the circle is fuch a figure as it is defined to be, and what it imitates among 
 true beings. He likewifc fees what is the firft of figures, what their order, and whence they 
 are at the fame time conne£led with the caufe of good. Laflly, thofe are to be derided who 
 deny, that the mathematical fciences are the ofi^spring of intellect, though they are converfant 
 with the true conclufions of propofitions producing fcience. For, wJience is the truth derived 
 which they contain.'' Whence the order, which is at the fame time attended with an inde- 
 fcribable beauty ? Whence their power of opening and elevating the rational eye of the foul, 
 if, by a much greater priority, they did not largely participate of intelledtual good ? 
 
 H 2 th
 
 52 ARISTOTLE'S METAPHYSICS. Book III. 
 
 the good* [and, as it appears, ought to be called wifdomf ] ; for the reft 
 fubfift for the fake of this. 
 
 But, fo far as wifdom is defined to be the fcience of firfl: caufes, and of that 
 which is efpecially the objedl of knowledge^, the fcience of eflence may not 
 unjuftly vindicate to itfelf the name of wifdom. For, fince the fame thing 
 may be known in many ways, we fay, that he rather knows who knows a 
 thing from its inherent properties, than he who knows from particulars which 
 do not pertain to that thing. But, among thefe, one knows more than an- 
 other ; and this is efpecially the cafe with him who perceives what a thing is, 
 and not of him who apprehends the quantity or quality of a thing, or what 
 it is naturally adapted to do or fuffer. Further flill, in other things alfo §, 
 
 we 
 
 * For other diings are for the fake of this. For, fo far as wifdom poflefies this prerogative, 
 that it is the principal and miftrefs of otlier fciences, there will be no other fcience than that 
 which refpe£ts the end for the fake of wliich other things fubfift. For the end itfelf is digni- 
 fied with a power which leads to other caufes; fince thofe things for the fake of which all 
 things are produced preferve all things in the world, in a republic, in an army, and in each of 
 us. But all things are produced for the fake of good and the end. 
 
 f This part within the brackets is omitted in the printed Greek text ; but is in the text of 
 Alexander, and appears to be very properly inferted. 
 
 % So far, fays he, as wifdom is converfant with the firft caufes, and with that which is mofli 
 eminently the objeft of fcientific knowledge, that fcience which moft eminently knows form 
 itfelf is wifdom. And in the end he adds, that his knowleiige of things furpafPes that of all 
 others, who knows them through their proper mediums : for feme one may liave a certain 
 knowledge of a thing through privation or negation, as is the cafe with him who knows that a 
 point is impartible, and that a divine nature is immortal -, but he has a fuperior knowledge of 
 thefe, who knows them affirmatively, and through thofe things which they eflentially contain ; 
 as, for inftance, that a point is the extreme of a line, and a divine nature an eternal being, 
 faff.cient to itfelf, good, and the caufe of things eternal. But he has a flill fuperior knowledge 
 of thefe, who cannot indeed fpeak refpefling the quality or quantity of things, their energies or 
 participated properties (for all thefe are pofterior to eflence, and the fecond things from it), but 
 is able to point out the eflence of a fubje<£t Itfelf; for he who can efFeQ diis podefles the moft 
 perfe£l: of alt fciences. 
 
 § Effences indeed are known by definitions ; and hence the firfl fcience is the definitive.. 
 But things elTentially inherent are known by demonflration ; and hence the fecond fcience is 
 the demonflrative. But that fcience which confiders form itfelf, and at the fame time knows 
 all thefe, is both definitive and demonflrative; definitive, indeed, eflentially, becaufe this con- 
 fifls in knowing the effence of a thing ; but demonflrative, becaufe he who affigns the caufes of 
 things, does not ceafe demonflrating till he arrives at that which is efl^ential. Thus, it is not 
 fulhcient to fay, that fire has a power of feparating the parts of bodies, but it is requifite to 
 ihow why it poffefTes this power ; and, till we recur to definition, and evince that the very 
 
 eflence
 
 BooKirr. ARISTOTLE'S METAPHYSICS. S3P 
 
 we then think that we know each of thofe things of which there are demon- 
 ftrations, when we know what each is ; as, for inftance, we then know what 
 the fquaring of a right-hned figure is, when we know that it is the invention 
 of a mean proportional ; and in a fimilar manner, with refpe£t to other 
 things. But with refpe<3: to generations, adlions, and all mutation, we then 
 efpecially know, when we know the principle of motion. This, however, is 
 another principle, and is oppofite to that which ranks as the end ; fo that, to 
 contemplate each of thefe caufes may appear to be the province of another 
 fcience *. 
 
 With refpc^t, however, to the principles of demonflration, it is doubtful 
 whether the fpeculation of thefe is the province of one, or of many fciences : 
 but I call the principles of demonflration thofe common opinions from which 
 all men demonftrate f "• fuch as, it is neceflary that every thing fhould be 
 
 affirmed 
 
 efTence of fire confifts in this, we fliall not fpeak demonftratively. So that demonftration is- 
 alone the province of him who has a knowledge of form : and this caufe which is aflumed 
 from definition is the firft caufe ; not, indeed, according to afTignation [a!9ro5b5-iv], (for perhaps, 
 according to this, it is tiie laft), but it is naturally the firft, at which the demonftrator, when he 
 arrives, refls. Thus, why is a politician defirous that there fliould be mufic and gymnaftic in a 
 city ? That he may inftruft the citizens. Why does he inflrutt them ? That he may make 
 them fcientific. Why this ? Becaufe they are adapted to receive fcience. Why are they fo 
 adapted ? Becaufe they are rational beings. And why rational beings ? Becaufe in this the 
 very eflence of human nature confifts. Here then we fee a knowledge from firft caufes; and 
 the definition of a thing is the beft caufe of demonftration. Thus, for inftance, why is the 
 light eclipfed? Becaufe it is obftruifled by the earth: we have therefore a definition of a lunar 
 eclipfe; for a lunar eclipfe is a privation of the light of the moon, on account of the obftruc- 
 tion of the earth ; of which if you would form a demonftration, you have only to change the 
 pofition of the terms, as Ariftotle obferves in his laft Analytics. And again, to make a fquare 
 equal to a given reftangle, is nothing more than the invention of a middle line : for, let one, 
 fide of the reftangle be equal to 9, and the other to 4, the area will be 36, the mean propor- 
 tional between which is 6, the fide of the fquare required. 
 
 * That is, becaufe the fcience which knows the caufe of a thing is wifdom, it is not the 
 bufinefs of many fciences to confider caufe, but this is alone the province of one fcience. 
 
 ■f Ariftotle here aflerts, that demonftrative principles are common conceptions, confidered as 
 not difpofing or exciting us to adlion : for all things defire their proper end, from a common 
 conception, which when men are not able to obtain by their own exertions, they fly to a divine 
 nature for affiftance ; by which being moved, as Ariftotle alfo fays, they naturally defire to 
 know. Thefe, therefore, are only demonftrative principles, fo far as they are ufed by demon- 
 ftrations ; but they polTefs a knowledge more manifeft than the things which are demonftrated 
 by tliem. One of thefe axioms, viz. that it is impolTible for the fame thing to be and not to 
 
 be,.
 
 Si ARISTOTLE'S METAPHYSICS. Book III. 
 
 affirmed or denied; and, it Is impoffible for a thing at the fame time to be and 
 not to be ; and fuch other propolitions as are of a fimilar nature. Whether, 
 therefore, is there one or a different fcience of thefe and of eifence ? And if 
 there is one, whether or not mufl; we denominate it that fcience wliich we 
 DOW invefligate ? It is not, therefore, rational to fuppofe, that there is one 
 fcience of tiiefe * : for, wliy is it more the province of geometry than of any- 
 other fcience to fpeculate concerning thefe ? If, therefore, it is in a fimilar 
 manner the province of any fcience whatever, but it cannot be the province 
 ■of all the fciences, as neither is it the peculiarity of the reft, fo neither does it 
 belong to that fcience which Jcnows the elTences of things, to know the prin- 
 ciples of demonftration. And, at the fame time, how will it be the fcience of 
 thefe f ? For we now alfo knov/ what each of thefe is. Oihtr arts, therefore, 
 
 ufe 
 
 ^be, is defervedly placed by Ariftotle at the fummit of fcience ; but with refpe£l to that other 
 HO lefs important axiom, that every thing mud be either affirmatively or negatively fignified, it 
 mud be obferved, that in beings and things comprehenfible by fcience, it is neceffary tliat every- 
 thing fhould be affirmed or denied : but if there be a fupereflential nature, as the principle of 
 things is fliown to be by the Pathagorreans, and by Plato in the Parmenides and Republic ; and if 
 (as is the cafe) it has neither a name nor fcience, but is ineffable ; why is it neceffary that-this 
 fliould receive either affirmation or negation, about which all difcourfe is falfe ? 
 
 But fince Ariftotle fays, " and whatever other propofitions there may be of this kind," we 
 may add the axiom which aiTerts, that every thing defirable is good; alfo, that neither nature, nor, 
 by a much (tronger reafon, divinity, does any thing in vain ; that no fttbftance is produced from non- 
 entity, nor refolved into non-entity ; and befides thefe, the axioms of geometry, arithmetic, and the 
 ether fciences, all which are alone confidered by him who has a knowledge of caufes. 
 
 * Ariftotle now apparently endeavours to prove, that the fame fcience does not know 
 eflences and axioms ; but that his endeavours here are not real, but pretended, will be evident, 
 from examining his reafoning. 
 
 Wifdom, indeed, which proximately receives demonflrative principles from intelled, fpecu- 
 lates them from on high, in a manner fuperior to the difcurfive energy of demonftration, and 
 confiders their truth, order, and progrefficn from intelle£t. But it mud here be obferved, that 
 though axioms rank among things firft with refpe£l to demonftration, they are not fimply firfl: 
 according to nature ; for the firll philofopher who fpeculates and knows being itfelf, will de- 
 monftrate their truth, though they are indemonftrable by the particular fcience by which 
 they are employed. How then can the firft philufopher be faid to confider axioms in the fame 
 light as thofc who are ikilled in other fciences ? or how, if this be not admitted, will die para- 
 logifm ever take place, to which the conclufion tends ? 
 
 ■}• Ariftotle, in his reafoning in this place, is evidently not ferious ; for he infers, that, if 
 ^he principles of demonftration are knowable, they are alfo demonftrable ; and that, if demon- 
 ifl^able, .they have one fubjeft, as numbers, which, being the objecls of demonflration, Jiave one 
 
 fubjefl,
 
 Book III, ARISTOTLE'S METAPHYSICS. 55 
 
 life thefe as things known to them. But If there is a demonRratlve fcience 
 refpedllng them, it will be requifite there fhould be fome fubjed genus, and 
 that fome of them fl-iould be participated properties, and others axioms. For 
 it is impoflible that there can be demonftration of all things; ftnce it is ne- 
 ceffary that demonflration fhould confiil from certain things, be employed 
 about a certain thing, and be of certain things. Hence it happens, that there 
 is one particular genus of all things that are demonftrated ; for all demon- 
 flrative fciences ufe axioms. 
 
 But if the fcience of eflence Is different from the fcience refpedling thefe, 
 which of them is the more principal, and naturally prior *? for, univerfally,. 
 and in the mod eminent degree, axioms are the principles of all things. But, 
 if it is not the province of a philofopher, to whom does It belongs to con- 
 template the truth and falfehood about thefe ? And, In fhort, whether Is 
 
 fubjea, of which the odd and the even are paffions, together with the numbers formed by the 
 conjunaioii and multiplication of thefe. But it is falff, that axioms, if Icnowable, are alfo de- 
 monftrable ; and it is hkewife falfe, that, if demonftrable, they have a fubjctft : for things them- 
 felves are faid to be demonftrable in one way, and definitions and propofitions in another. But 
 if axioms have a fubje£l, participated properties alfo and axioms will be apparent about them t 
 hence there will be axioms of axioms. This abfurdity is not noticed by Ariftotle, but is entirely 
 confequent to what he fays. It alio follows, that axioms, if they depend on other axioms, are 
 not axioms ; for, in this cafe, we fliould not be hindered from an infinite progreflion ; axioms 
 being indigent of axioms to infinity. However, though axioms are not properly demonflrable, 
 yet they are knowable by the firft fcience, which is converfant with immediate propofitions, and 
 ■which, together with the on, or that a thing is, comprehends aWb the Siori, or luhy it is, as proxi- 
 mately proceeding from intelle£t, which it evolves, divides, and pervades. Nor, if axioms werc- 
 demonflrable, does it follow, that they would have one fubjed, fince they have an orderly fub- 
 fiflience, and an intelleftual elevation. 
 
 * If the fame perfon does not know the principles of things and of demonftrations, but this 
 Is the province of difl'erent pcrfons, each of them will be imperfedl ; the one not knowing 
 how to demonftrate, and the other embracing empty fyllogifms, as being ignorant of the nature 
 of tilings. Great indeed is the dignity of that fcience which confiders the moft comprehen- 
 five demonftrative principles of all things ; and what elfe but a wife man can the poflefTor of 
 this fcience be called ? This mafter fcience was denominated by Plato dialeclic, and by Ari- 
 ftotle the firjl philofophj. 
 
 I only add, that this firft philofophy, which is converfant with being fo far as being, imitates 
 intelle£t, in which intelleftion is not fcparated from intelligible. It is affimilated indeed to 
 intellcftion by a knowledge of axioms, but to intelHgible through the fpeculation of being 
 itfelf. But, if it were deficient in either, it would be an imitation of intellect, either pofleffing 
 intelle£lion without the intelligible, or intelligible without intellect j which is the fame thing 
 as to imitate inteliedl deditute of intellect. 
 
 there 
 
 /
 
 56 ARISTOTLE'S METAPHYSICS. Book III. 
 
 there one fciencG of all eflences, or many fciences * ? If, therefore, there is 
 not one fciencef, what kind of elfence mufl we eftablifli as the ohjedt of this 
 wifdoin ? But it is not rational to fuppofe, that there is one fcience of all 
 effences ; for there will alfo be one demonPiraiive fcience of all effential acci- 
 dents I ; fince every demo-nftrative fcience fpeculates, from common opinions, 
 effential accidents about a certain fubjedt. It is the bufinefs, therefore, of the 
 fame fcience, to fpeculate, from the iame cpinionn, eflVntial accidents about 
 the fame genus : for the confideiation of the oil, or, that a thing is, is the 
 province of one fcience ; and it is likewife the employment of one fcience to 
 fpeculate the particulars from which a thing confifts, whether it is the fame or 
 a different fcience ; fo that the like will take place with rcfpedt to accidents 
 whether thefe fciences contemplate them, or one of thefe. Further ftill, 
 whether the fpeculation is alone refpedling effences, or alfo refpedling things 
 accidental to thefe. But my meaning is : il, for inflance, a folid is a certain 
 effence, and lines and planes, whether it is the province of the fame or of 
 another fcience to know thefe, and things accidental about each genus ; for, 
 if it is the province of the fame fcience, it will be a certain demonftrative 
 fcience, and ihe fcience of effence. But demonftration does not appear to be 
 employed about the formal caufe : but if it is the province of another fcience, 
 what fcience will that be which fpeculates the accidents about effence ? for, 
 to affign this is very diiacult. 
 
 * Ariftotle here inquires, if there will be one fcience about every efTence, both intelligible 
 and fenfible ; and, if there is any middle nature, or more tlwn one, between thefe, whether 
 fciences alfo will be multiplied according to the diverfities of eiTences. In anfwer to this in- 
 quiry, it may be moll truly faid, that there is one fcience which is fupreme, and many proxi- 
 mate fciences; that there is one, indeed, which confuiers being fo far as being, and many 
 among which the parts of being are diilributed, and which are converfant with thefe parts in a 
 different manner from the mailer fcience, and do not confider them fo far as beings. 
 
 + One fcience, indeed, cfpecially fpeculates all beings. But if different fciences are conver- 
 fant with different orders of being, It is by no means obfcure, that the fcience which is em- 
 ployed about firfl and intelligible effences is the firft of fcierices. Whence, though it confiJers 
 every being fo far as being, it defires to energize principally about the intelligible. 
 
 X Why is tills abfurd ? For, if there are many demonftrative fciences, as geometry, aftro- 
 nomy, arithmetic, and many others ; yet, prior to all tliefe, there is one which confiders that 
 which is effentially accidental to beiug, fo far as being. This Ariftotle himfelf more clearly 
 affcrts in the fourth book of this work : for arithmetic demouflrates things eiTcntially inherent 
 in numbers; and geometry things effentially inherent in figures. But one demonftrative 
 fcience, i. e. the firft philofophy, demonftrates things effentially inherent in every being, not fo 
 far as it poffeffes equality or quantity, but fo far as it is being. 
 
 Further
 
 Book III. A 11 I S T O T L E'S M E T A P H Y S 1 C S. $f 
 
 Further (lill : whether muft we fay, that there are alone fenfible eflences, 
 or others befides thefe ? And whether is there one genus, or many genera 
 of eflences, according to the opinion of thofe who fay that there are forms 
 and natures fubfifting between forms and things fenfible, about which, ac- 
 coiding to them, the mathematical fciences are converfant ? In what manner, 
 therefore, we aflert that forms are caufes and eflences fubfifl;ing by them- 
 felves, has been related by us in our firfl; difcourfes refpeding them * : but as 
 the confideration of them is attended with abundant diificultyf, it is no lefs 
 abfurd to fay, that there are certain natures befides thofe which are in the 
 heavens, and that thefe arc the fame with fenfibles, except that the former 
 are eternal, but the latter corruptible. For they fay, that there are man itfelf, 
 and horfe itfelf, and health itfelf; but they do not afl^ert any thing elfe re- 
 fpeding thefe : and in this refped they ad fimilar to thofe who acknow- 
 ledge indeed that there are gods, but that they poflefs a human form ; for, 
 neither do the latter of thefe make any thing elfe than eternal men, nor do 
 the former make ideas to be at all different from eternal fenfible natures. 
 
 Again, if any one, befides forms and things fenfible, places things between 
 thefe, it will be attended with many doubts : for it is evident, that in a fimi- 
 lar manner there will be lines, and each of the other genera, befides thofe 
 
 * He here refers us to what is aflerted in the firft book, or greater a. Hence, fays Sy- 
 rianus, thofe are to be derided who confider that book as fpurious. 
 
 f To this we reply, tliat thofe divine men confidered ideas, of which they were fuch (Ire- 
 nuous aflertors, as differing in all things from fenfible forms : for they viewed the former as 
 divine eflences, impartible, felf-fubfiftent, as the fabricative caufes of mundane natures, and as 
 pofTeffing a perpetual uniformity of fubfiftence ; but the latter, as fuftaining every kind of mu- 
 tation, as perpetually flowing, and converfant with the circulations of time. But that Ariftotle 
 is not fcrious in what he here aflerts, is evident from hence : for it is by no means true, that 
 man in this terreftrial region differs only in the privation of eternity from man in the in- 
 telligible world, or, in other words, the regions of divine intellecSt : for mortal is inherent in 
 the definition of terreftrial man ; and Ariftotle, in this very work, manifeftly demonftrates, that 
 things in which the mortal and corruptible are inherent, pofTefs thefe, not from accident, but 
 cffentially -, fo that man, being eflentially mortal, is incapable of becoming the fame with man 
 in the intelligible world, by the acctfl'ion of eternity. 
 
 Syrianus here juftly obferves, that it is wonderful how readily Alexander approves this 
 aflertion of Ariftotle, without perceiving that what the philofoplier advances is erroneous. He 
 adds, that he cannot think that men who were fo well ikilled in the art of reafoning, ferioufly 
 oppofed the dodrine of ideas : becaufe, fays he, they do not injure the divine dogmas of Plato, 
 as neither do the arrows difcharged by the Thracians reach the ethereal gods. 
 
 I that
 
 «* ARISTOTLE'S METAPHYSICS. Book III. 
 
 that are fenfible * : fo that, fince aftronomy is one of thefe, there will alio be 
 another heaven befides the fenfible heaven, another fun and moon, and, in a 
 fimilar manner, the other natures which the heavens contain. Though, how 
 is it poflible to believe that there are fuch things as thefe j ? For, neither is 
 it rational to fuppofe, that this ideal heaven is immoveable, and it is entirely 
 irapofrible that it fliould be moveable. A fimilar confequence will enfue re- 
 fpeding thofe objeds about which the optic ^ fcience is employed, and like- 
 wife 
 
 * And where is the abfurdity that thefe fliould be intelligible, dianoetic, and fenfible ? Is it 
 not indeed neceflary, that there fliould be in the artificer of the univerfe a fabricative caufe of 
 the heavens and the fun ? and tliat in the divine fouls of the ftars there fliould be a truer heaven 
 and a truer fun than the apparent r or, in other words, that in thefe they fhould fubfift without 
 dimenfion in innmaterial perfeftion ? And are not the fenfible heaven and fun the receptacles of 
 thefe ? What alfo, is it to be fuppofed, can be the meaning of Plato, when in the Thesetetus 
 he fpeaks of the Coryphxan philofopher af^ronomizing above the heavens ? and again, when 
 in the Phtedrus, he fays that there are many blefled vifions and progrefiions within the heavensj 
 which are objeds of admiration to the genus of the blefled gods ? for it is evident, that he 
 cannot here mean the corporeal heavens ; fmcc body, however exalted, can never be the objeft 
 of felicitous contemplation to a divine nature. There are, therefore, flars above the heavens, or 
 rather intelligible lives of the fliars, whofe unconfufed union, never-failing communication, and. 
 conjundion with intelligible eflences, it is the bufinefs of Arillotle's wife man to contemplate. 
 There is alfo an intelligible heaven befides this, which is the objed of fenfe, the vifion of 
 whofe divinely-fplendid fpedacles gives beatitude to mundane divine natures ; fo that it is very 
 properly faid, that, befides intelligible and fenfible lines, there are certain lines which have a 
 middle fubfiftence, that is, which fubfifl; in foul according to a dianoetic chavaaeriftic. There 
 are alfo other heavens and other funs, intelligible, intelledual, and dianoetic : for, as the divine 
 Plato faySy the artificer of the univerfe, placing intelled in foul, and foul in body, caufed the 
 whole mundane animal to become intelligent and animated. Every thing, therefore, which is 
 beheld in the apparent heavens fenfibly and with dimenfion, fubfifts, in immaterial and produc- 
 tive powers, according to the nature of foul ; but, in forms in the highefl; degree impartible 
 and intelligible, according to intelled. 
 
 f Ariftotle admits, that there mufl: be an immoveable caufe of tilings which are moved, but is 
 adverfe to its being denominated after the fame manner with its efleds. But it is neceflary, as 
 Syrianus jufl,ly obferves, to advert to the method adopted by theologifls, among whom the pro- 
 grefiions are celebrated of many heavens, many funs, and many other particulars ; at the 
 fame time carefully remembering, that thefe heavens and funs have an incorporeal fubfiilence,. 
 and, that their progreflions Cgnify their becoming inefl'ably unfolded into light, from the 
 inefi"able principle of things. 
 
 But neither is it altogether impofllble, tliat there fliould be a moveable caufe of things which 
 are moved, unlefs we confine the term motion to corporeal natures. But who will not admit, 
 that true beings poflefs a fabricative and intelledual motion .? 
 
 t ihat Ariftotle is not ferious in what he here afii-rts mull be granted, unlefs we are willing 
 
 to
 
 BooKlir. ARISTOTLE'S MET A PHYSICS. 59 
 
 wife with refped: to harmonics in mathematics : for it is impolUble that thefe 
 flaould have a fubfiftence different from fenfibles, through the fame caufes: 
 for, if there are fenfibles and fenfes which have a middle fubfil'cence, it is evi- 
 dent that there will alfo be animals fubfifting betwesn them and things cor- 
 ruptible. But it may alfo be doubted, about what kind of beings it is requi- 
 fite to inveftigate thefe fciences *. For, if geod3:fia f differs in this only from 
 
 geometry, 
 
 to believe that he adopts confequences abfurd, and indeed impoffible. For, as he admits thaC 
 we have another eye befides that of fenfe, it mud have a power perceptive of thofe fpecies 
 which are the proper objeds of its vifion. For, if the univerfals which are beheld by the intel- 
 leclual eye are merely things abftradted from fenfible obje£ls, and therefore of an origin pofti- 
 rior to fenfibles themfelves, things which have no real fubfillence will be the fpeftacles of 
 intelled. Will not, therefore, that moft excellent part of us, intellect, be more unhappy than 
 the fenfible eye, fince this is co-ordinated to beings ; or, in other words, contemplates obje£ts 
 which have the fame reality of fubfiftence with itfelf ; while, on the contrary, intelleft will be 
 the fpetlator of delufion and non-entity? But if this is abfurd, and we have an intelleiSual 
 eye endued with a vifive power, there mufl be forms conjoined with this power, immoveable 
 indeed according to corporeal motion, but moved with intelledual energy. May we not alfo 
 alk, if there is no fpedlator of thofe harmonic reafons which divinity inferted in foul prior to 
 the apparent order of things ? According to Homer, all the mundane gods partake of the 
 mufes, and of the harmony proceeding from them : 
 
 ■ of the mufes full 
 
 , With beauteous voice alternately who fing. 
 
 There mufl:, therefore, be another Iiiirmony befides that which is fenfible. Since too, according 
 to Arillotle, there is one co-ordination of intelligible fpecies to the firft good (fee the end of 
 the twelfth book), muft there not in fuch an arrangement be the moft beautiful and divine 
 harmony ? The firft philofopher, conteinplating this harmony, is converfant with a melody 
 inefF.ibly more admirable than that which is produced by fenfible mufic. 
 
 * It is indeed truly dubious, what fciences are the greateft exemplars of fenfibles. Yet we 
 may reply in anfwer to the doubt, that thofe fciences which are employed about the immaterial 
 exemplars of fenfibles, are more immaterial than thofe which are converfant with natural fpe- 
 cies, or reafons, or natural numbers. 
 
 f But geodjefia does not alone difl^er in this from geometry. But the dilTerence confifts In 
 this, that the former regards the indigence of human nature, and the advantage of mortal life, 
 and is bufied with manual operation, without paying any attention to the fpeculation of real 
 being ; but the latter feparates the foul from fenfibles, purifies its intelleflual eye, and brings it 
 by a circular progrefllon as it were to intelleflual vifion, removing it from the more grofs and 
 figured compofition of material natures. What then follows from this .'' That there muft be 
 another medicinal art, befides that which is divine and that which is converfant with mortal 
 bodies. For, let there be a divine caufe of this art, or, in other words, an idea in the intelledb 
 of divinity, called by the antients Efculapius, which caufe or idea imparts to the firft beings an 
 
 I 2 eternally
 
 60 ARISTOTLE'S METAPHYSICS; Book IIL 
 
 geometry, that the former of thefe Is converfant with things which we per- 
 ceive, but the latter M'lth things which are not fenfible ; It is evident, that, be- 
 fides the medicinal fcience, there will be a certain fcience between medicine 
 Itfclf, and the medicine which iubfifts among us. But how is this pofilble ? 
 for there will alfo be certain falubrlous things, befides fuch as are fenfible, and 
 the falubrlous itfelf. And, at the fame time, neither is this true, that geo- 
 daefia * Is converfant with fenfible and corruptible magnitudes : for, thefe 
 being corrupted, k alfo will be corrupted. But neither will aftronomy be 
 converfant with fenfible magnitudes +, nor with this vifible heaven. For. 
 
 neither 
 
 eternally according meafure, but to middle and laft natures communicates this meafure when 
 they are capable of receiving i: ; let there be alfo a mortal phyfician who takes care of mortal 
 bodies ; — muft not, therefore, things which are fo diftant from each other be joined together by 
 fome common boundaries? And is it not neceffary to confidcr this art as having a middle 
 fubfiftence in the demoniacal and heroic orders, and in fouls liberated from a mortal life ? 
 And why may not philofophy, which purifies from the pafTions, be placed as a medium between 
 divine juflice, which is the medicine of all mundane depravity, and human medicine, which 
 is alone employed in taking care of generated and corruptible bodies ? We may therefore 
 fay, that thofe arts which contribute to the indigence of the mortal life proceed from the pro- 
 lific power of foul, on account of its fubfifleuce between lntelle£l and a corporeal nature. 
 Thefe arts, however, mufl be confidered as having an analogous fubfiftence in divine natures ; 
 and hence antient theoiugifts afcribe the fabrication of arms to the Cyclops and Vulcan^ and 
 the art of weaving to Minerva and Proferpine. 
 
 * What necelTity is there, that the arts of things corruptible fhould be corrupted with the 
 corruptible things themfelves ? For, this is jufh as if it fhould be faid that the definitions of 
 things corruptible are corrupted with the perifliable natures. But, as the fpecies are preferved, 
 though the individuals are mortal, it is neceiliiry that definition alfo (hould be preferved. 
 
 f The aftronomer confiders the fenfible heavens, but he does this as pofTefling certain uni- 
 verfal reafons which are the images of thofe forms by which the heavens were fabricated ; and,. 
 in confequence of conjoining thefe immaterial and univerfal reafons with the phenomena, he 
 exhibits things efTentially inherent in the celeflial orbs. But obferve, that the heavens them- 
 felves, though full of life and a divine power, yet, on account' o£ their bulk, and pofieffingdimen- 
 Cons, receive ii ':crporcal natures partially and attended with interval. For, fince we contain 
 one dianoetic principle, which bifefts all greatell ciixles in a fphere, and is the image of that 
 productive principle whicli caufes the univerfe to fubfifl; in conjunflion with its artificer, yet 
 the nature of body does not permit the heavens to receive collectively and in one all the power 
 of this principle. But it is by no means wonderful that it fliould be received by the heavens 
 feparatcly, and not colle^ively, nor fo accurately as that which is imparted by the maker, and 
 as that may be confidered which proximately proceeds from the Father of the univerfe ; for 
 that which imparts is perfedlly incorporeal, and that which receives is body ; and whatever is 
 jeceived is received according to the nature of the recipient. 
 
 But in anfwer to Protagoras, and all thofe who vilify geometry, it may fufTice at prefent to 
 
 obfervcj.
 
 BooKnr. ARISTOTLE'S METAPHYSICS. 
 
 «t 
 
 neither are fenfible lines fuch as the geometrician fpeaks of, fince nothing of 
 fenfibles is accurately ftraight or round : for a circle touches a rule not in a 
 point, but as Protagoras faid, confuting geometricians ; nor are the motions 
 and fpiral revolutions of the heavens fimilar to thofe about which aftrology 
 difcourfes ; nor have points the fame nature as the ftars. 
 
 But fome afTert *, that there are fuch things as are faid to fubfift between, 
 forms and fenfibles, which yet are not feparate from fenfibles, but in them. 
 To enumerate to thefe men the impoflibilities which attend this dodrine . 
 would require a long difcourfe : it is fufEcient, therefore, to have fpeculated 
 thus much refpeding them : for neither is it rational that this fhould alone 
 be the cafe with thefe, but it is evident that it would alfo happen that fpecies- 
 would fubfift in fenfibles j fince both thefe are the confequences of the fame 
 reafoning procefs. Further ftill : it would be neceflary that two folids fhould. 
 be in the fame place ; and mathematical entities would not be immoveable,. 
 
 obferve, that if tiie objetls of geometrical fpeculation furpafs in immateriality, purity, cer- 
 tainty, and truth, objedls of fenfe (and that they do fo the accuracy of the definitions and cou- 
 clufions of geometry fufficiently evinces), it is evident that geometry is converfant with a vene- 
 rable and illuflrious order of things, an order prior indeed to fenfibles, but pollerior to in— 
 telle£tual paradigms : for fuch is the dianoetic feries. 
 
 * Thofe who aflert, indeed, that there is a certain middle nature between intelligible and 
 fenfible fpecie?, and that this middle nature is contained in lafl and material forms, muft un- 
 doubtedly be allowed to err. But, fince unlverfal may bs confidered multifarioufly, as, fov, 
 inftance, man may be confidered as fubfifting in the nature of the univerfe^in our fouls, and 
 in any individual, as Plato; when the univerfal is of fuch a nature as to be common to many 
 things, then it haftens to matter, cannot abide in itfelf, and becomes the receptacle of peculiar 
 qualitie?, in conjunflion with which it fubfifts. 
 
 But Ariftotle a(ks. How can two folids be. in tha fame place i To which we reply, that the 
 advocates for ideas did not aflirm, that the univerfal which is co-ordinated with a folid is itfelf 
 a folid ; but that it alfo itfelf contributes to the one fubftance of a folid body. Every indivi- 
 dual, indeed, of the human fpecies contains man univerfal united with man particular ; and 
 yet there are not in him two animals, "31 two men, or two folids, but thefe converge to one 
 fubfidence. 
 
 Mathematical entities alfo, fays Arlflotle, would not be Immoveable in confeqnence of fub- 
 fifting in things moveable. But may we not fay, that they will remain unchanged as long as 
 the things which contain them fubfift ? For, neither are thofe things which are properly 
 common moved, while their recipients fubfift. And, laflly, he a(ks what neceflity there is of 
 introducing thefe, and placing them in fv;nfibles. To which we muft fay, that it is necelTary^ 
 fince fenfibles are imitations and images of intelligibles, that they alfo fhould poffefs certain 
 things which are more comprehenfive and common, prior to fuch as ar$ more fpecial and par- 
 ticular.. 
 
 its.
 
 62 ARISTOTLE'S METAPHYSICS. Book III. 
 
 in confequence cf fubfiftlng in things fenfible which are moved, /.nd, in 
 fhort, on what account can any one admit them to have a fubfiftence, and a 
 fubfiftcnce in fenfihles ? for there will be a certain heaven befides heaven, 
 except that it will not be feparate, but in the fame place j which is more 
 impofliblc. 
 
 CHAP. IIL 
 
 Respecting thefe things, therefore, there is great doubt*, viz. how they 
 may be admitted fo that we may obtain the truth ; and likewife refpeding 
 principles, whether it is requlfite to confider genera as elements and principles, 
 or rather thofe things from which being inherent every thing firfl; confifts : 
 as, for inftance, the elements and principles of voice appear to be thofe things 
 from which all voices are firft compofed, and not voice in common : and we 
 fay, that thofe things are the elements of diagrams, the demonftrations of 
 which are inherent ia the demonftrations either of all or the greater parr of 
 other things. Further ftill : both thofe who aflert that there is one element, 
 and thofe who fay that there are many, from which bodies are compofed, 
 and from which they confift, affert, that they are principles ; as, for inftance, 
 Empedocles fays, that fire and water, and the natures which fubfift together 
 with them, are elements, from which being inherent things exift ; but he 
 does not fpeak of thcfe as the genera of beings. Befides this too, if any one 
 is willing to confider the nature of other things, as, for inftance, a bed, from 
 what parts it confifts, and how thofe parts are compofed, he will then know 
 the nature of it. From thefe reafons, therefore, principles will not be the 
 f^enera of beings. But if we know every thing through definitions f, but 
 
 principles 
 
 * The doubt, fays Syrianus, whofe province it is to condiler fcientifically concerning like and 
 unlike, contrary and different, as it is the province of t\e Ikilled in dialeftic to confider thefe 
 according to probability, was in the order of the Problems tlie (ixth. But now, fays he, Arl- 
 ilode omits this, perhaps becaufe in the following book (the fourth) he was manifeRly to enun- 
 ciate thefe as belonging to the firft philofopher ; for this confideration does not require much 
 doubting, but rather enunciation and a brief reply ; or becaufe he delivers the moft perfeft 
 doarine concerning thefe in the tenth book. Hence, that which he had at firft ranked as the 
 feventh in order, he now affumes as the fixth. 
 
 t That we know every thing by definitions, is in a certain refpeft true : but how arc princi- 
 ples the genera of definitions ? No otherwife perhaps than as inherent in definitions. But if 
 we acbnit, that definitions and fpecies are alone derived from things of poftcrior origin, /. e. from 
 
 pniverfais
 
 BooKirr. ARISTOTLE'S METAPHYSICS. 63^ 
 
 principles are the genera of definitions, it is neceflary alfo that genera fhould 
 be the principles of things defined. And likewife, if to polTcfs the fcience of 
 beings * is to poflefs the fcience of forms, according to which beings are 
 predicated, in this cafe genera will be the principles of forms. 
 
 But fome alfo of thofe who afTert that the one, or being, or the great and 
 thefmall, are the elements of beings, ufe thefe as genera. However, it is not 
 poffible to call both thefe principles f : for there is one reafon of eflence ; but 
 the definition which is afhgned through genera, will be different from this, 
 and likewife that which affumes thofe particulars from which being inherent 
 a thing confifts : to which we may add %, if genera are in the mofl eminent 
 degree principles, whether is it requifue to think, that the firfl: of genera, 
 are the principles of things. Or the laft genera which are predicated of indi- 
 viduals ? for this is doubtful. For, if things univerfal are in a more eminent 
 degree principles, it is evident that the higheft genera will be the principles 
 ef things (for thefe are predicated of all things); and hence there will be as 
 many principles of beings as there are firft genera : fo that both being and the 
 one will be principles and effences ; for thefe are efpecially predicated of all 
 beings. But it is not poffible that there can be only one genus of beings,, 
 
 univerfals abftracled out of fenfibles, how can we call thefe the pnnciples of fpecies, or defini- 
 tions ? Bur, if we direct our mental eye to an order of things prior to fenfibles, perhaps we 
 may by this mean afcend to more true principles. 
 
 * Thofe who fay that the one, or being, or the indefinite duad, are the principles of things, and 
 the fourccs of perfection to beings, aflcrt, that from the one good proceeds to all things, from 
 being ellerice, from the indefinite dujd powers and energies, motions and progreflions, and al! 
 various augmentations ; and that there is no being which does not participate of thefe three, and 
 is not generated from them. There can be no impropriety, therefore, in calling thefe principles 
 the genera of all things. But, affigning the caufes on account of which things inherent are 
 more principles than genera, he employs the teftimony of Empedocles ; and, adducing the Pytha- 
 goreans and Plato as coadjutors of this opinion, he now fays, that either genera or principles 
 muft predominate. But we have already obferved, that, if different principles are differently 
 confidered, both may be true. 
 
 t Ariflotle, in his laft Analytics, demonftrates, that there is one moft proper definition of 
 the fpecies of every thing ; and that this is altogether effected by genera. According to his 
 opinion, therefore, principles fliould rather be called genera themfelves : for, if definition is from 
 genera, but the things from which definition confifts are principles, genera alfo will be prin- 
 ciples. 
 
 % This is the eighth queftion in the order of the Problems ; but now it is confidered as the 
 feventh, becaufe the fixth is omitted. 
 
 and- 
 
 /
 
 ,5,1 ARISTOTLE'S METAPHYSICS. Book III. 
 
 and that this Is cither the one or hehig : for it is neceffary that tiiere fliould 
 he. difierences of every genus, and that each fliould be one. But it is iin- 
 pofllblc either that fpecies fliould be predicated of the proper differences of 
 genus, or that genus fliould fubfift without its fpecies ; fo thaf, if either the 
 one or b^ing is genus, no difEerence will either be the one or being. But if 
 there are not genera, neither will there be principles ; fince genera are prin- 
 ciples. Further ftilh things fubfiftlng between thefe, comprehended together 
 with differences, will be genera as far as to individuals. But now this appears 
 to be the cafe with fonie, and not with others ; to which it may be added, 
 that differences are in a greater degree principles than genera. But if thefe 
 alio are principles, there will be, as I may fay, infinite principles, and efpe- 
 cially if any one eftabliflies the firfl genus as a principle. But if the one is 
 of a more primary nature *, and the one is indivlfible, but every thing indi- 
 vlfible is either fo according to quantity, or according to fpecies, and that 
 which is according to fpecies has a prior fubfiftence, but genera are more 
 divifible into fpecies, the one indeed will be predicated the lafl of all j for man 
 is not the genus of particular men. 
 
 Further ftill : in thofe things in which there is prior and pofterior f , it Is 
 
 not 
 
 * The reafoning of Arlftotle in this place is as follows : Indlvifible fpecies, fo far as iiidlvi- 
 fible, and more one than genus, fignifies principle more than genus -, for this is divifible, and 
 BOt more one than many. For, fince divifion takes place according to two modes, and fince the 
 prior is that which fubfifls according to fpecies (for this belongs to incorporeal eflences, and the 
 ten predicaments, but tlie other to quantities only) ; — in both thefe ways, that which is divided 
 is lefs one than that which divides : but this is efpecially the cafe with things which are divided 
 according to fpecies ; for they produce many wholes. Genera, therefore, divided into fpecies 
 contain fpecies in themfclves ; but the moft fpecial fpecies is not divided into particulars, but 
 as fpecies compofes individuals. The moft fpecial fpecies, therefore, Is more one than genus ; 
 and that which is more one is a principle. Hence the moft fpecial fpecies is more a principle. 
 But the reafoning is evidently falfe, fo far as pertains to the minor propofition ; for that which is 
 proximate to infinites cannot be more one than that which is eihblifhed more remote from 
 them. But neither is genus fo divided into fpecies as to be loft in the fubfiftence of thefe; 
 but, remaining true genus, it gives fubfiftence to fpecies. Genus, therefore, is more com- 
 prehenfive in power than fpecies, but not more Angular in number. But this is a property 
 which truly accords with principles. 
 
 t Since the differences according to which we diftinguifli the powers of fpecies are not 
 equally excellent with refpect to the fubfiftence of genera, and for the moft part have, among 
 themfelves, the order of form and privation, it is altogether necefl'ary that fpecies fhould differ 
 from each other according to better and worfe, prior and pofterior. Indeed, according to the 
 
 Pythagorseans,
 
 BoOKlir. ARISTOTLE'S METAPHYSICS. eS 
 
 not poffible that the thing which is predicated of thefe fhould be dIfFerent 
 from them. Thus, for inilance, if the duad is the firft of numbers, there 
 will not be any number befules the fpecies of numbers : and, in a fimilar 
 manner, neither will there be figures befides the fpecies of figures. Bur, 
 if this is the cafe with refpedl to thefe, fcarcely will there be genera of other 
 things befides fpecies : for genera appear efpecially to be of thefe. But, in 
 individuals, one thing is not prior and another pofterior. Further ftill :. 
 wherever one thing is better and another worfe, that which is better is 
 always prior ; fo that nothing of thefe will be genus. Hence, thofe things 
 which are predicated of individuals appear to be principles more than genera. 
 Again, it is not eafy to fay in what manner it is requifite to confider 
 thefe as principles. For it is necelfary that a principle and caufe fhould 
 exift exclufive of the things of which it is the principle, and that it fhould 
 be able to fubfift feparate from them. But why ftiould any one think, that' 
 any thing of this kind exifts befides that which is particular, except that it is 
 predicated univerfally and of all things ? But if on this acount, then things 
 more univerfal muft be confidered as principles in a more eminent degree i: 
 fo that firft genera will be principles. 
 
 CHAP. IV. 
 
 But there is a doubt * confequent to thefe things, which is the moft diffi- 
 cult and the moft necelfary of all things to contemplate, and which is the 
 
 fubjed; 
 
 Pythagorxans, the odd number is more excellent than the even, and the circle than right-lined 
 figures; and Hill further, the body which has naturally a circular than that which has a redli- 
 linear motion. Yet it does not follow from hence, that thefe fpecies are not placed under one 
 genus. For, though dift'erences are not in genus, but externally accede to fpecies, yet fpecies 
 may deri-ve from genus the fame and thejimllar, and, from differences, prior and pofierior, better 
 and ivorfe. Or, if we fay that genus contains in itfelf all the differences of fpecies, in this 
 cafe it places indeed about itfelf many fpecies, fome being more allied to its own nature, fome 
 having a middle order among things which proceed from it, and fome appearing at the ex- 
 tremity of thofe orders which it generates ; yet it confers on all an image, character, and in- 
 terior reprefentation, through which they may be referred to the one and moft general principle 
 from which they derive tiieir being. But, according to this one interior reprefentation, they are 
 alfo not picvs-'nted from being univocal ; though from other caufes they poffefs among theni- 
 felves a great variety and charadleriftic difference. 
 
 * Ariftotle here inquires, whether, befides fenfibles, there are fuch things as unlverfals. For, 
 if there are not, fays he, fcience will depart from beings, fince it will not be poflible for us to 
 
 K obtaiu
 
 6S AP. r ST OTLE'S METAPHYSICS. Book III. 
 
 fubjea of the prefent difcourfe. For, if there Is not any thing befides parti- 
 culars, but particulars are infinite, how is it poffible to poffefs the fcience of 
 infinites ? For, fo far as there is a certain one and the fame, and fo far as 
 there is fomeching univerfal, fo far we know all things. But if this is necef- 
 fary, and if it is requifite there fhould be foraething befides particulars, it 
 will alio be necelTary that there fhould either be laft or firft genera befides 
 particulars. That this, however, is impoffible, we have juft now doubted. 
 
 Further ftill: if there is efpecially fomethlng befides the whole, when any 
 thing is predicated of matter, whether, if there is a certain form, is it neceiTary 
 there fiiould be fomethlng (univerfal) befides all individuals ? or, that there 
 fliould be fomethlng univerfal befides fome and not befides others ? or, is there 
 no univerfal befides individuals ? If, therefore, there is nothing befides par- 
 ticulars, there will be nothing intelligible, but all things will be fenfibles, and 
 there will not be fcience of any thing, unlefs fome one aflerts that fenfe is 
 fcience. Again, neither will there be any thing eternal, nor any thing immove- 
 able*; for all fenfible things are corrupted, and are in motion. But if there 
 is nothing eternal, neither is it poffible there can be generation. For it is ne- 
 celTary that there fhould be fomethlng which is generated, and fomethlng 
 from which it is generated, and that the laft of thefe fhould be that which is 
 
 obtain a knowledge of things which are infinitely generated in an infinite time: for we now 
 think that we comprehend thefe through univerfals. But, if univerfals have no fubfiftence 
 (avv^orala), the whole of the firft philofophy, which confidis from the divifive, demonftrative, 
 and definitive method, will be vain, and nothing more than a delufive dream ; but, if there are 
 univerfals, there will again be genera and fpecies. To which we may add, that neither could 
 the infinite multitude of individuals exift without the fubfiftence of one caufe of infinite power ; 
 unlefs we fuppofe them to exift from chance. But, how can things be cafual which have a na- 
 tural fubfiftence ? If this, therefore, be the cafe, and an infinite number of men, horfes, and 
 many univocals, are generated in an infinite time, there muft be a unity of infinite power 
 prefiding over each of thefe fpecies, according to which the individuals of thefe fpecies are 
 infinitely generated in the univerfe in a definite manner. Further ftill : all animals in gene- 
 ration, or the fubluiiary region, are changed from that which is in Capacity, or feed, into that 
 which is in energy. But, if this be the cafe, it is requifite that there fliould be animal in energy 
 in the univerfe, which may lead into energy animals in capacity. After this manner, with re- 
 fpe(n: to man and every other animal, we muft confider true genera as endued with a generative 
 power according to nature, and true fpecies as giving form to the infinity of particulars. 
 
 * By taking away inteliigibles and the objefts of the dianoetic energy, not only intelle£l:, 
 intelligible, and fcience are taken away, but likewife every thing eternal. Ariftotle indeed 
 proves in his Phyfics, that every body is finite; and now alfo manifeftly fliows us, that, unlefs 
 there is fomethlng naturally eternal, generation could not fubfift. 
 
 unbcgotten,
 
 Book III. ARISTOTLE'S METAPHYSICS. (>i 
 
 unbegotten, if the progrefTion of things flops, and it is impoflible that any- 
 thing can be generated from non-entity. 
 
 Further ftill : there being fuch things as generation and motion*, it is ne- 
 ceffary alfo there fhould be a boundary or end : fur neither is any motion 
 infinite, but of every motion there is an end ; and it is not poffible a thing 
 Ihould be generated which cannot poflibly be generated. But that which is 
 made necelfarily is as foon as it is made. Again, if matter is, on account 
 of its being unbegotten, it is much more rational that there fhould be effence, 
 on which the being of matter depends : for, if neither efience is, nor mat- 
 ter, nothing whatever will have any fubfiftence. But, if this is impcflible. It 
 is necefl'ary that form and fpecies fliould be fomething befides the whole. 
 But again, if any one admits this, it is doubtful \ in what things he ihould 
 
 *It is neceflary that there fiiould be an end of every generation. For the motion of nature is 
 not a blind impulfe without defign, nor is the generation which is perfe£led by it deftitute of an 
 end. But if every generation has an end, but every uhimate end has alfo a beginning, (for this 
 muft be underftood,] there is a beginning and an end of all generation and motion. But that 
 every thing which is generated has an end, fince it alfo has a beginning, is manifeft, and is 
 thus proved by Ariflotle. That which is capable of being generated is generated, and confe- 
 qucntly arrives at the end of generation. Every generation, therefore, and motion, ranks 
 among things of which there is a beginning and an end. But of that which is eternal there is 
 neither beginning nor end. There is therefore no motion nor generation of an eternal nature. 
 If then tliere is any thing eternal, it is requifite that it {hould be ingenerable and felf-motive. 
 Hence it muft either be intelligible, or the obje£l of dianoetic energy. For thefe are without 
 generation, and immoveable. There are, therefore, intelligible and dianoetic objedts. But this 
 is what he propofed to fliow from the firft. By collefling, therefore, all that has been faid, it 
 follows, that if generation is, (and it is neceflary it fliould be,) there is fomething eternal. If 
 there is fomething eternal, there is fomething ingenerable and immoveable. If this be the cafe, 
 there is fomething intelligible And, if this be admitted, fenfibles are not the only things which 
 have a fubfiRence. 
 
 \ That which Ariflotle here inquires, viz. of what things there are ideas, and of what there 
 are not, the reader will find accurately difcufled by Plotinus in his book on IntelleE}, Ideas, and 
 Being -, and particularly by Proclus, in his MS. Commentary on the Parmenides of Plato. At 
 prefent, it may fuffice to fay, that there are no ideas (viz. incorporeal producing caufes) of 
 things artificial; and therefore Ariftotle now very properly denies the exigence of houfe fepa- 
 rate from the multitude of houfes : nor are there ideas of things contrary to nature, nor of 
 things evil, nor of things bafe, nor of particulars. But we fay that there are eternal, intel- 
 le£lual, generative, and providential exemplars of the wholes in the fublunary region and in the 
 heavens, and of the immaterial reafons of the foul. For an account of thefe wholes, which 
 Ariftotle in his Meteors calls colleclive Mies, and w-hich in the fublunary region are the fphere 
 of earth, the fphere of water, the fphere of air, and the fphere of fire, and, in the heavens, the 
 ftarry fpheres, fee my Introduction to tJie Tiniieus of Plato. 
 
 K 2 admit
 
 €€ ARISTOTLE'S MET A rHYS I CS. Book IIL 
 
 edmit it, and in what not. For it is evident that it cannot be admitted in all 
 things ; fince we do not admit that there is any houfe different from fenfible 
 houies. To which we may add, whether will there be one eflence* of all 
 things, as for inftance, of men ? But this is abfurd. For all things are not one 
 of which the elTence is one, but many and different. But this alfo is irra- 
 tional. At the fame time, too, how does matter receive each of thefc f? and 
 how is tlie whole (viz. fenfible p^ruculars) both thefe ? 
 
 Further 
 
 * This alfo may be doubted agalnft thofe who introduce Ideas, whether there is one idea of 
 all men-, v-hich idea they call man itfelf. But this, fays Ariftotle, is abfurd. For it would be 
 requifite that all men in this tcrrcftrial region fliould be one, as fubfifting with relation to one. 
 For all things are one, of which the elTence is one. But it will be proper to afk, What effence 
 is here alluded to ? Whether that which is according to infeparable, or that which is according 
 to feparable form ? If that which is according to infeparable form, the objedion made by 
 Ariftotle is indeed true. But if that which is according to feparable form, we may fiy that 
 there is no abfurdity in admitting that many and infinite particulars are generated from one 
 caufe ; and that, neverthclefs, they are of the fame fpecics among themfelves, if they are pro- 
 duced accordinir to that caufe. And, with rcfped to infeparable caufe, we may fay that it is 
 one in fpecies, but many and infinite in number. But to fuppofe that there are many feparable 
 and diiferent caufes, is partly irrational and partly neceflary. For, in the .intelleel of the Artificer 
 of the univerfe, one exemplar of men is fufficient ; and it is abfurd to fuppofe many, fince one is 
 fufficient for the purpofe of producing of all men. For, in what would thefe exemplars differ 
 ■ from each other, 'fince they would fubfift in the fame indivifible nature? It is alfo neceffary 
 that in the foul of the univerfe there fhould be a caufe of men that are here, and likewlfe in the 
 nature of the mundane wholes^ and, in lliort, that there fiiould be ideas according to every 
 order of beings. 
 
 ■f- The manner in which the fenfible receives its fubfiftcnce from the intelligible world ; or, in 
 other words, how the forms which are merged in matter fubfift ; whether, with reference to 
 ideas, they are like picT:ures, or images in a mirror, or imprefilons in wax, is a fubjed involved 
 in much obfcurity, and demands the moft profound inveftigation. For Plato fometimes calls 
 material forms icons, or refemblances, and aftimilates them to piclures ; but at other times he 
 aflimilates them to impreflions in wax, and at others again to images in water or mirrors. 
 
 For the fake of the liberal reader, therefore, the following obfervations on this intereftinj 
 fubje£l, derived from the very adytum of Platonic philofophy, are fubjoined. 
 
 The participations of intellcclual forms are aflTimilated to the reprefentacions in a mirror; 
 for as, in thefe, habitude and pofition caufe the image of the perfon to be feen in ihc mirror ; fo, 
 the nptitiide of matter extending itfelf as it were to the Artificer of the univerfe, and to the in- 
 cxhauftible abundance which he contains, is filled from him with forms. Tlie participations 
 are alfo aflimilated to the impreflions in wax. For ideas impart a certain veftige and impreffioH 
 of themfelves ; and neither is this imprclfion the fame with the feal by which it was produced, 
 ,a« neither is the form merged in matter the fame with the immaterial and divine form from 
 ^hich it originated. But this latter mode differs from the former fo far as it indicates a .cerr
 
 Book HI. A R I S T O T L E'S M E T A P H Y S I C S. 69 
 
 Further Rill : this alfo may be doubted refpeding principles. For, if they 
 are one in fpecies, there will be nothing which is one in number, nor will 
 
 there 
 
 tain pafTive property in the recipient ; for the mirror does not exiiibit paflivity fenfibly, as the wax 
 does in the latter inftancc. Hence fome of the Platonic philofophers, confidering matter as 
 impaflive in the participation of forms, afTimilate it to a mirror, but call forms images and repre- 
 fentations. Others again, confidering matter as pafTive, fay, that it is imprefled like the wax by 
 the feal, and call forms the paJTions of matter. 
 
 Forms alfo are faid to be like the fimilitudes of icons, whether efTeQed by the painter's, or the 
 plaftic, or any other art. For thefe forms, being fafliioned by a divine artificer, are faid to be 
 J'lnular to divine forms ; and hence the whole fcnfible order is called the icon of the intelligible. 
 But this affertion differs from the former, fo far as this feparates the maker from the exemplar; 
 but thofc produce the analogy from confidering both as one. And fuch are the modes accord- 
 ing to which material forms have been faid to fubfift with relation to fuch as are divine. 
 
 It mud, however, be obferved, that each of thefe is imperfect confidered by itfelf, and inca- 
 pable of reprefenting to our intelledtual conceptions the whole truth refpefting this participa- 
 tion.' For, in the firfl; place, confider as to the mirror, that the countenance beheld in it turns 
 Iifelf towards the mirror, while, on the contrary, an intelle£lual caufe beholds itfelf, and does 
 not direct its vifion to outward obje£l:s. If, too, the mirror appears to poflefs a communication 
 of fomething, but in reality does not, (for the rays are reflefted back to the countenance,) it is 
 evident that this alfo is foreign from the participation of divine forms -, for, as they are per- 
 feclly incorporeal, nothing can be feparated from them and diftributed into matter. 
 
 In the fecond place, if we confider the impreffions in wax, we fliall find, that both that which 
 impreffcs externally impreffes, and that which is paflivc to the impreffion is externally paflive ; 
 but form pervades through the whole of the fubjeft matter, and operates internally. For na- 
 ture fafliions body inwardly, and not externally like art. And above all, in this inftance, that 
 which is participated approximates to that which participates. But it is requifite that divine 
 forms fliould be exempt from all things, and not be mingled with any thing of a different 
 nature. 
 
 In the third place, let us confider the analogy from icons, and we fhall find this alfo deficient. 
 For, in the firft place, forms fafhion the whole of the fubjefl: matter by which they are received^ 
 and this by an internal energy : and; in the next place, the exemplar and the maker are here fepa- 
 rated from each other. Thus, the figure which is painted does not produce its Hkenefs on the 
 canvas, even though the painter ihould paint a refemblance of himfelf ; for it is the foul which 
 operates, and not the external fi.gure, which is the exemplar : nor does that which makes, ajft- 
 mllate that which is produced to itfelf; for it is foul which makes, and that which is produced 
 is the refemblance of external form. But divine forms are at the fame time paradigmatic and 
 demiurgic of their refemblances : for they have no fimilitude to the imprefllons in wax, but 
 polTefs an efHcacious efTence, and a power afhmilative of things fecondary to themfelves. 
 
 No one of thefe modes, therefore, is of itfelf fufhcient to reprefent the true manner in 
 which divine forms are participated. But, perhaps, if we can dlfcover the moft proper mode of 
 participation, we fhall fee how each of thefe touches on the trutli, at the fame time that it 
 .faljs fliort of the whole characteriftic.
 
 70 ARISTOTLE'S METAPHYSICS, . Sook IIL 
 
 there be the one Itfclf 2S\&. being itfelf. And how will it be poflible to know 
 fcientifically, if there is not in all things a certain one? But indeed, if they 
 are one in number *, each of the principles alfo is one in number, and there 
 
 It is requifite, therefore, in order to this participation, to confider as the caufes by which it 
 is efFe(fl:ed, the efTicacious power of primary and divine forms, and the defire and aptitude of 
 tlie natures which thence derive their formation. For neither is the fabricative and efficacious 
 power of forms alone fufRcicnt to produce participation ; for they are every where fimilarly 
 prefent, but are not fimilarly participated by all things. Nor is the defire and aptitude of the 
 participants fufl'icient without the produdive energy of forms; for defire and aptitude are of 
 themfelves imperfed. The prolific efTence, therefore, of the demiurgic intelle£l exerts an efli- 
 cacious energy, which the fubjed nature of fenfibles receives. But, in effefting this participa- 
 tion, it neither makes ufe of impulfions, for it is incorporeal; nor of any indefinite impetus, as 
 we do, for it is impafTive ; nor of any projeflile force, for it is perfedt ; but it operates by its 
 very efTence. Hence that which is generated is an image of its maker, intelledion there con- 
 curring with edence : fo that, according as he intellectually perceives, he fabricates ; and, ac- 
 cording as he fabricates, intelle£Vually perceives. Hence, too, that which is generated is always 
 generated by him ; for, in eflential produ6llons, that which is generated is every where confub- 
 fiftent with its maker. In confequence of this, in things fubfifting according to time, form, in 
 ihefuddt'ii, fupervenes its fubject matter, whatever has been effedled previous to its prefence, alone 
 removing the impediments to its reception. For, the fudden Imitates according to the n:iv, the 
 at-once-colle£led and eternal generation of all things through the aptitude of the recipient. 
 
 If, again, we defire to fee what it is which connedts demiurgic power with the aptitude of re- 
 cipients, we fhall find it is goodnefs itfelf, this being the caufe of all polfible union. For, parti- 
 cipations proceed to mundane caufes through a defire of good ; and demiurgic forms, through 
 goodnefs, make their progreffions into fecondary natures, imitating the inexhauflible and exu- 
 berant fountain of all good, which, through its own tranfcendent goodnefs, gives fubfiftence to 
 all the divine orders, if it be lawful fo to fpeak. We have therefore thefe three caufes of the 
 participation of forms, the one goodnefs of the Father of all things ; the demiurgic power of 
 forms, and the aptitude of the nacures which receive the illuminations of forms. But, partici- 
 pation fubfifl.ing according to thefe caufes, we may perceive how it is poffible to affimilate it to re- 
 prefentations in a mirror, and to refection. For aptitude and defire, which are imparted to fenfible 
 natures from on high, become the caufes of their being again converted to the fources whence 
 they vi-ere derived. This participation, too, may, after another manner, be affimilated to a feal.. 
 For the efHcacious power of divine caufes imparts a vejiige of ideas to fenfibles, and apparent 
 impreffions from unapparent forms. For we have faid that the demiurgic caufe unites both 
 thefe together. But he who produces an icon effe£ls fomething of this kind. For in a certain 
 refpedk he congregates the fubjedl and the paradigm ; fince, when this is accompliflied, he pro- 
 duces an impreflfion fimilar to the exemplar. So that thefe modes, in a certain refpeft, touch 
 upon the truth. But it is by no means wonderful if each is found to be deficient. For the re- 
 cipients of ideas are partible and fenfible ; and the chara£lerlftic peculiarity of thefe unapparent 
 and divine caufes cannot be circumfcribed by the nothingnefs of corporeal natures, 
 
 * We have before fliown how intelligibles are bounded both in fpecies and number. Let it, 
 however, be carefully remembered, that things emanating from principles, when they become 
 jningled with matter, are no longer fuch as the principles themfelves. 
 
 are
 
 Book III. A R I S T O T L E'S M E T A P H Y S I C S, 71 
 
 are not different principles of different things as in fenfibles ; as, for inftance, 
 . of this fyllable, which is the fame in fpecies, the principles alfo are the fame 
 in fpecies ; for thefe aUb are different in number. But if this is not the cafe, 
 and the principles of beings are cne in number, there will not be any thing 
 befides the elements. For, to call a thing one in number, or to call it a fen- 
 fible particular, differs in no refped : for, thus we call a fenfible particular one 
 in number ; but univerfal, that which is common in thefe. Juft, therefore, 
 as if the elements of fpcech were bounded in number, it would be neccffary 
 that all the letters fhould be as many as the elements, fince neither two nor 
 more than two of them would be the fame. 
 
 But a doubt in no refped: lefs than this is omitted, both by thofe of the 
 prefent day and the anlients, viz. whether there are the fame or different prin- 
 ciples of things corruptible and of things incorruptible. For, if there are the 
 fame principles, after what manner are fome things incorruptible, but others 
 corruptible ? and what is the caufe of this ? Hefiod *, indeed, and all fuch 
 theologifts alone paid attention to that which appeared probable to them- 
 
 felves, 
 
 *■■ In defence of Hefiod and the antient theologifts, it may be faid, What other principles 
 could they introduce than divine natures ? For neither is any thing more antient than a prin- 
 ciple, nor than divinity, or divine natures. The antient theologifts, therefore, neceflarily faid, 
 that all things were generated from the gods, viz. intellect, foul, the natures of bodies, and 
 things eternal and corruptible, Becaufe, therefore, fome things which proceed from divine 
 natures are immediately united to tliofe natures, being rooted as it were and concentred in 
 them j but fome are never naturally adapted to be immediately conjoined with them ; and others 
 again fometimes apoftatife, and fometimes are united with them, to which clafs of beings wc 
 belong ; — hence, thofe beings which are immediately or mediately perpetually united with 
 dK'ine natures are faid to be thence fed with ambrofia and ne£lar ; ambrofia affording them a 
 reparation from the realms of generation, in which mortality and impurity predominate ; but 
 tiecliir preventing them from being allured, through providentially prefiding over the extremity 
 of things, and caufing them to provide inflexibly and immutably over the mundane wholes. 
 Bi'.t thofe which are fometimes elevated to divine natures, but are naturally adapted to apofta- 
 tifj from thence, when they fpeak the truth, and obferve their oath, are faid to partake of nectar 
 and ambrofia ; that is, when they are extended to true being, and cuhivate a divine nature ; but 
 when they violate truth, and become perjured ; that is, when they decline to non-entity and 
 generation, and treat a divine nature with contempt ; then, as becoming mortal and frail, they / 
 
 are deprived of the aliment arifing from the vifion of an intelligible effence, and never partake 
 of it while they continue in this ftate of defection and revolt. Can any aflertion, therefore, be 
 more true than this ? 
 
 But if the aflertions of the antient theologifts are not obvious to every one, it is by no means 
 
 wonderful :
 
 72 ARISTOTLE'S METAPHYSICS. Eook im 
 
 felves, but negleded us. For, making principles to be gods*, and afierting 
 that all things originated from the gods, they fay that thofe natures are mor- 
 tal which have not tailed of nedtar and ambrofia. But it is evident that they 
 employ thefe names as expreffive of things known to themfelves, though, re- 
 fpeding the enunciation of thefe names, they fpeak beyond our conception. 
 For, if the immortals touch thefe for the fake of pleafure, nedar and ambrofia 
 are in no refped the caufes of their being f : but, if they are the caufes of 
 their being, how will the gods be eternal, fmce they require aliment? It is 
 not, however, worth while to fpeculate ferioufly ^ refpeding thofe things 
 which are fpoken fophiftically in a mythological manner. 
 
 But it is requifite to inquire of thofe who fpeak from demonftration, why, 
 If things are from the fame principles, fome are naturally eternal, but others 
 are corrupted. However, as they do not affign the caufe of this, and as it is 
 not rational that this fliould be the cafe, it is evident that there are neither the 
 fame principles nor caufes of thefe» For Empedocles §, who, it might be 
 
 thought, 
 
 wonderful : for perhaps thofe great men wrote with ftudied obfcurity, on account of the natural 
 inaptitude of the multitude to the comprehenfion of divine dogmas ; and perhaps alfo en-- 
 theaftic conceptions, or fuch as are the progeny of divine fury, are rather adapted to beobfcurely 
 fignified, than unfolded by the difcurfive energies of the rational power. 
 
 * Ariftotle, towards the end of the twelfth book, of this work, fays, that the antients, in 
 calling firft principles gods, fpoke divinely, 
 
 t In anfwer to this we may reply, that nutriment fignifies illumination from fupernal caules, 
 and a fupply of good. But this imparts (lill more abundant good to beings which are even 
 naturally good, and a more perfed eternity to beings effentially eternal ; fo that from fuch nu- 
 triment they become partakers of being, and of the caufe of ineffable delight. 
 
 J Ariftotle fays this in confequence of his great unwillingnefs, which we have noticed In the" 
 Introdudtion, to admit that caufes fhould be called by the fame names as their efFc£i:s. 
 
 § In defence of Empedocles we may fay, that, like other Pythagoraeans, he knew that therff 
 were two kinds of elTences, the intelligible and the fenfible ; that he did not fuppofe xhzt Jl rift 
 was a corruptive, and/ric'/iil/hip alone a produftive principle ; and that he v/as not filent with 
 refpe£t to the caufe of their alternate dominion ; — but that, being a follower of Orpheus and 
 Pythagoras, he eftabliflies, after the one great principle of all things, (of which neither he, nor 
 Parmenides, nor Pythagoras, ever intended to fpeak much,) thefe two principles, friend/l'ip and 
 Jirife, which the Pythagorneans denominated monad and duad^ and the latter of which they called 
 indefinite^ on account of its univerfally pervading power. From thefe two principles, according 
 to Empedocles, the intelligible and fenfible worlds emerged. In the intelligible world, there- 
 fore, which in his verfes he calls a fphcre ||, friendjbip predominates ou account of the union of 
 
 11 Vide Simplic, in Phyf. p. 25! et 165; 
 
 immaterial
 
 Book III. ARISTOTLE'S METAPHYSICS. 73 
 
 thought, would efpecially fpeak confiftently with himfelf, fufFers the very- 
 fame thuig: for he \)hcesjlrifc as a certain principle and caufe of corruption. 
 Yet it would feem that this no lefs than friendfliip is generated from ihe ofie-, 
 for all other things are produced from this (viz. flrife) except divinity. He 
 fays, therefore, " From which all things that were, that are, and that flsall 
 hereafter he, originated; from which trees alfo germinated, men and women, 
 wild beads and birds, fifhes nourished in the water, and the long-lived gods." 
 It is alfo evident, that all things fubf.fl: without thefe : for, if ftrife was not 
 inherent in things, all things (as he fays) would be one: fince, when they 
 come together, then ftrife ftands at the extremity of things. Hence it hap- 
 pens to him, that the moft bleffed divinity is lefs v.^ife than other beings : for 
 he does not know all the elements, becaufe he does not poffefs contention. 
 But knowledge is a conjundtion of fimilar with the fimilar. For he fays, 
 " By earth we behold earth, and by water, vpater ; by ^ther, divine asther, 
 and by fire, pernicious fire. By fdendlhip we perceive friendfhip, and by 
 flrife, baneful ftrife." 
 
 But, to return whence we digrefled : this is evident, that it happens to him 
 that ftrife is no lefs the caufe of corruption than of being ; and, in like man- 
 ner, that frlenddiip is not more the caufe of the being than of the corruption 
 of things ; for, coUefting them into one, it corrupts other things. And, at 
 the fame time, he does not mention any caufe of the tranfmutation, but that 
 it is naturally adapted to fubfift in this manner. " For, (fays he) when 
 mighty * contention was nourifhed in the members, it afcended to the ho- 
 nours of perfedl time f, which being viciflitudinary to them preceded the 
 
 ample 
 
 immaterial and divine eflences ; but in the fenfible \vox\AJinfe. And it is owing to the perfec- 
 tion proceeding to thefe principles from that caufe which is exempt from both, and which is 
 no other than the ineffable principle of things, that, though both are every where, yet one rules 
 over the intelligible, and the other over the fenfible world. 
 
 * Empedocles calls it mighty, in the fame manner as Orpheus in the following line, which is 
 only to be found in Syrianus, viz. ' 
 
 Xa^iAX Koii iMcya xcKiyLa 7r£>.a^iov Bv9a km sv6a. ./ 
 
 I. e. " A chafm and a mighty chafm every way immcnfe." 
 
 With Pythagoras it is the indefinite duad. Empedocles alfo affigns members to it and augmen- 
 tation, becaufe it is the fource of progrelTion, generation, multitude, multiplication, and all 
 augmentation, to the univerfe. 
 
 f Empedocles here, in conformity with Orpheus, fymbolically calls the firft principle of 
 
 L things
 
 74 ARISTOTLE'S MET APHYSICS, Book m, 
 
 ample oatli." As if It were neceflary, indeed, that a cliange fliould take 
 place. But at the fame time he evinces no caufe from neceffity, aflerting only 
 thus much conformably to his own doctrine, that he does not make fome 
 things corruptible and others incorruptible, but makes every thing corruptible 
 except the elements. But the doubt which is now mentioned is this : why^ 
 if all things are from the fame principles, have fome things a fubfiftence, and 
 others not? Thus much, however, may fuffice to fliow that they are not 
 from the fame principles. But, if the principles of things are different, one 
 doubt is, whether they alfo will be incorruptible or corruptible. For, if, they 
 are corruptible, it Is evident that they alfo muft neceffarlly originate from 
 certain other things : for all things are corrupted Into thofe things from 
 which they derive their being : fo that, on this hypothefis, it happens that 
 there are other principles prior to principles. But this is impoffible, whether 
 the progrefficn flops, or advances to Infinity. Further full : if principles are 
 taken away, how v^IU things corruptible fubfift ? But, if principles are in- 
 corruptible *, why, from thefe being incorruptible, do things corruptible fub„ 
 fift, but from others things incorruptible? For this is not rational; but Is 
 either impoffible, or requires a multitude of arguments. 
 
 Again : no one has endeavoured to fhow that thefe are different ; but they 
 fay that thefe are the fame principles of all things ; and they pafs by that 
 which vi^as firfl doubted by us, as if they apprehended this to be a thing of a 
 trifling nature. But this is of all things the moft dilTicult f to contemplate, 
 and, In order to know the truth, the moft neceiTary, whether bet7ig and the one 
 are the effences of things, and each of them is not any thing elfe, but this is 
 the one, and that is being? or, whether it is requifite to inquire what the one 
 is, and what being is, as if there was another nature fubjedt to thefe ? For 
 
 things Time : becnufe, wliere there is generation (fays Proclus) there alfo is time. Tlie fecond 
 of thefe principles, therefore, poffefles royal honours, from the perfedion which it derives from 
 t'nne: for, that which is moft eminently tlie firfl: meafures its infinite power. 
 
 * Wc have already faid, that the principles of things corruptible are incorruptible, but not 
 immoveable. But the principles of things incorruptible are both incorruptible and immove- 
 able. • 
 
 t This is properly the thirteenth Problem, but is here the twelfth, becaufe, as we have be- 
 fore obl'erve't, the llxth is altogether omitted. In the former part of thefe Notes we have 
 related what the Pythagorscans and Plato fay ; and fliown, that Empedocles is not difcordant 
 from th.m in thefe dogmas ; though this perhaps may be afferted of the philofophers of the 
 lomc fectj who thought that the one and being were water or fire, or fomething of this kind. 
 
 ferae.
 
 BookIII. AE.ISTO'1 LE'S met APH YSICS, 75 
 
 fome think that the nature of the one fubfifts ha that, and others in this 
 manner. For Plato, indeed, ard the Pythagoreans, do not think that being 
 differs from the onc^ but tliat this is the nature of them, as if the effence was the 
 fame, to be one, anJ to be a certain being. Bui thofe who are converfant 
 with Phyfics accord with Empedocles, who, as ifbringipg us back to that 
 which is more known,' ays that the o7ie\% being. For he may appear to affert 
 that this is fiiendfliip ; fince this is the caufe to all things of their being one. 
 But others fay that fire, and others rgain that air, is this o?!e and beings from 
 which beings fubfifl; and are generated. And, in like manner, thofe who efta- 
 bllfh more elements than thefe ; for it is neceffary for thefe alfo to aiTert, that 
 being and the one are as numerous as they fay principles are. But it happens, 
 if any one does not admit* that the one and being are a certain efience, that 
 
 * Even the apparent necefTity of this reafoning is very great: for, if there are univerfals, 
 much more are there things mofl. univerfal ; and, if there are things mofl: univerfal, there are 
 alfo the one and being abftracled from all things. For thefe are the mofl univerfal of things. 
 But, if thefe are not, things the mofl univerfal would be no more : or it would follow-, that 
 there is neither fcience, nor that things themfelves are naturally of the fame fpecies among 
 themfelves ; but that, through chance and inflability, thefe are of the fame fpecies with thofe, 
 but of a dillimilar fpecies from others. For, unlefs there was one pre fubfifting form, throu'T-li 
 the participitlon of which things are of a fimilar fpecies, but, through non-participation of 
 it, of a difTnnilar fpecies, what effeclive, preferving, and inevitable (ava^roofaros) caufe can there 
 be of thefe ? 
 
 But, if we more nearly examine what is here faid, we fliall find that both fpecies and uni- 
 verfals are at the fame time taken away with the hypothefis, and that fenfibles themfelves are 
 no lefs circumfcribed. For, unlefs there is a one abftra£led from all things, or, in other words, 
 which is neither fomething belonging to foul, nor to intellecl, nor even to being itfelf, there can 
 neither be any thing of univerfals nor of particulars. There cannot be the former, becaufe they 
 are naturally one and tnany, i. e. in thefe unity predominates over multitude ; nor the latter, be- 
 cajfc they are nniry and one, i. e. multitude predominates over unity. But it is neceflary that 
 a nature which is unity alone, without any conneclion v/ith multitude, fiiould have a fubfulenee 
 prior to thefe -, and, at the fame time, it m.ufl be obferved, that, unlefs an imparticipable one 
 prcfides over things which are participated, there will not be a caufe of union to beings ; in the 
 fame manner as the caufe of every pod'ible kind of eflence is taken away from things by thofe 
 who deny that being itfelf is the principle of all beings. For, as the one principle of good to 
 things is the good itfelf, which is neither the good of any particular thing, nor any thing elfe 
 befides good ; and as the caufe to all things of being moved is that which is felf-motive, and, of 
 that which is felf-motive, motion itfelf, which is neither the motion of this particular thins, 
 nor any thing elfe befides motion, br.r, as we have faid, is motion' itfelf: — in like manner, all 
 things which are knowable originate from knowledge itfelf, and all beings, fo far as beings, pro- 
 ceed from being itfelf: but things wliich arc united receive tlieh' union from the one, which is 
 .abftraded from all things. 
 
 L 2 neither 
 
 /
 
 76 ARISTOTLE'S METAPHYSICS. Book III. 
 
 neither can any one of other unlveifals have a fubfiftence ; for thefe are, of 
 all things, efpecially univerfal. But, if neither the one it/elf nor being it/elf is 
 fome particular thing, much lefs will any thing ell'e have a fubfiftence, except 
 fuch things as are called particulars. Further ftill : \{ the one is not eifence *, 
 it is evident that neither will number have a fubfiftence as a certain nature 
 feparate from beings: for number is monads; but the monad is a certain one. 
 But if the one itfelf is fome particular thing r, and likevvife be'mg itfelf, it is 
 necefl'ary that the effence of them fhould be being and the one ; for nothing 
 elfe is univerfally predicated of them \ but thefe very things. But, indeed, 
 if being itfelf and the one itfelf have a fubfiftence, a great doubt § will arife 
 how any thing befides thefe fubfifts. I mean, how there will be more beings 
 than one : for, that which is different from being is not || ; fo that, accordin 
 
 ■e 
 
 to 
 
 * It follows, indeed, from necefTity, that neither is there any efTential number, the one having 
 no fubfiftence, yet not for the reafon affigned by Ariftotle ; for it is merely logical, fince he 
 immediately falfely nflumes that fpecific and eflential numbers confift from unities. But, even 
 though it fhould be admitted that they do confift from unities, yet certainly the one, which is. 
 the fubjeft of the prefent fpeculation, does not confift from things which are of the fame 
 fpccies. The alTertion, therefore, of Ariftotle is in a certain refpccl true, fo far as unity in 
 numbers is an image of tl^e one itfelf. If, then, there is fomething abftra£led from the univer- 
 fality of things, there will alfo be fome number which is an intelleftual form, and an eflence 
 which is efpecially the firft and moft intelleiftual. But if the one itfelf is not, neither will the 
 principle be ; but, the principle not fubfifting, neither will that which is derived from the prin- 
 ciple fubfift. 
 
 f This alfo is rightly faid by Ariftotle : but he ufes effence in a more general way for the one i 
 becaufe, if there is fuch a thing as the one itfelf, or that which is the one only, and nothing elfe, 
 it is above eflence ; for effence is indigent of the one to its fubfiftence ; but the one is not indi»- 
 gent of eflence, left, inftcad of the one-, it ftiould become that which is united. 
 
 \ Here, again, that which is aflcrted is true ; but it is requifite to add, that though they are 
 not predicated of other things, yet they are to all things the caufes of being, and of being, 
 united. 
 
 § It is, indeed, a fubje£l; of profound fpeculation, how, from the one, which contains in itfelf 
 no appearand.' of multitude, and which has no diverfity, all things fubfift. Plotinus has confi- 
 dered this fubje£l with his ufual profundity ; and it appears, from Syrianus, that it was dif- 
 cufled by Porphyry and Jamblichus. It may fuffice at prefent to fay, that the Problem can 
 perhaps only be folved by afligning the exuberant fecundity of the one as the caufe of the fubfift- 
 ence of all things ; or, in other words, by conceiving that the one, at the fame time that it is tran- 
 fcendcntly fimple, is exuberantly prolific. 
 
 II Parmenides faid, that being was one, becaufe he confidered the whole of an intelligible 
 eflence as traiifcendently united. He alfo called that which is different from being, or a fen- 
 
 fible
 
 BookIIL ARISTOTLE'S metaphysics. 77 
 
 to the reafonlng of Parmenides, it necefllirlly happens that all beings are one, 
 and that this is being. But in both cafes a diiiiculty enfues * : for, whether 
 ^he one itfelf is not eflcnce, or whether it has a fubfiftence, it is impoffible 
 that number can be effence. But why it cannot, if the one is not, has been 
 fliown by us before. And if the one is, the fame doubt as that refpecfling 
 being remains : for, that fro^n which there will be another one, befides the 
 one itfelf, muft neceflarily be itfelf not one. But all beings are either one or 
 many, each of which many is one. . 
 
 Further ftill : if the one is indivifible, according to the axiom of Zeno, it 
 will be nothing : for that which neither when added nor when taken away 
 makes any thing to be greater, according to him, does not rank among beings y 
 becaufe being is magnitude, and, if magnitude, corporeal ; for this is in every 
 refpe£l being. But other things, when added, in a certain refpedl make that 
 which is greater, and in a certain refpeft nothing. Thus, a fuperficies and a 
 line make that which is greater ; but this is by no means true of a point and: 
 
 fible nature, non-being; and faid that non-being is nothing, becaufe it Is not in dignity equal to 
 being. Nor is it any thing with relation to being, nor does being derive any thing from its 
 fubfillence : for, as Socrates will remain one, though he fhould have many images; fo, the whole 
 of an intelligible eflence remains one, notwithftanding the fubfillence of the fenfible univerfe, 
 which, in reality, is nothing with relation to the intelligible world, except that it depends from 
 it, and thence derives its being and perfedlion. 
 
 * We have already faid, that, if the one has no fubfiftence, there will not be number ; for,, 
 the principle being abolilhed, it will neither itfelf ever be generated from another thing, nor 
 any other thing from it. But why does it follow, that number will not be, even if the one does 
 fubfift ? Is it through a hoflile attack (fis-foxi) of the firft hypothefis in the Parmenides of 
 Plato .'* But the multitude, which is there denied of the one, does not deftroy the multitude pro- 
 ceding from it, but deftroys the fubfiftence of any multitude in the one.. For, if it is truly cne^., 
 it will not be many. But Ariftotle here pretendedly afliimes, that whatever is befides the one 
 is nothing ; for all beings are either unity, or confift from unities. If, therefore, there is any 
 unity proceeding from the one, it will be different from the one ; but, fince it is difFerent from ths 
 me, it is nothing. And that which is nothing is a non-entity ; becaufe every being is either 
 one or many, each of which is one thing. In anfwer to this we may reply, that it does noC 
 follow that a thing proceeding from the otie is nothing. For, if it is not that one from which it 
 proceeds, muft it be concluded that it is not one, or nothing 1 We ought rather to fay, that it 
 is one in a fecond, and again in a third degree, and fo on. For, even the laft of things laft 
 the fleeting periftiable and material natures of fenfibles, participate of the one. And where 
 is there any thing intelligible and divine wliich is deprived of unity } The prolific nature of 
 the one, therefore, is a fufficient caufe, and it is not neceflary to inveftigate the fubjed from 
 which beings fubfift. 
 
 a monad. 
 
 3-
 
 78 ~ ARISTOTLE'S MET A PHYSICS. ^ Book III. 
 
 a monad. Buf, as he fpeaks thus importunately, and it happens that there is 
 fomething iadivifible, the foliowing arguments may be urged agalnft him : — 
 The addition of a thing of this kind does not make that which is greater, but 
 that which is more. But how will magnitude be compofed from one, or 
 more than one, of this kind? for it is ju(l as if it fliould be faid, that a line 
 confifts cf points*. But if any one fliould apprehend, according to the 
 aflcrtion of fome, that from the one itfelf\^ and another certain nature which 
 is not the one, number is compofed ; yet we muft, neverthelefs, invefligate on 
 what account, and how, that which is generated is at one time number, and at 
 another magnitude, if that which is not the one and inequality are of the fame 
 nature ? lor it does not appear how, from the one and this nature, nor how 
 from a certain one and this nature, magnitudes can be produced. 
 
 * Eflential mngnitiule is impartible, divine, and Intelligible, and fliines forth prcfoumlly 
 united with the firfl of beings. But fenfible magnitude, depending through nature as a medium 
 on the Artificer of the univerfe, who is the offspring of the good^ i. e. olthe oney becomes from 
 thence united: for, through imitation oi the one, all things impart union to natures pofrerior to 
 themfelves. What fimilitude, therefore, is there between faying that a line confifls from 
 points, which is proved to be impoiTible, and that the one itfelf produces various magnitudes ? 
 There is then nothing common in the two afi'ertions, except that, as all other things attraQ a 
 certain vefi:ige, and ultimate refemblance of the one ; fo, a point among indivifiblcs appears to 
 imitate //v ow. It is, however, imperfeft ; it is not feu'"-fubfi(lent ; and that which it is, is 
 fomething belonging to a thirg different from itfelf, that is, a line. It is alfo unproHhc and 
 deflitute of intellect ; but the one, being the caufe of every thing p,erfe£l, and of true being, and 
 abiding in itfelf, is eminently generative of the life of all things, and is the principle of in- 
 tclleiflion. But it is itfelf better than all thefe things of which it is the principle. 
 
 f Ariftotle here doubts, apparently agalnft Plato, how from the one and the indefinite diiad,vi;h\d\ 
 he calls non-one and inequality, he at one time produces number, and at another magnitude : for, 
 neither, fays he, if he conjoins number with the indefinite duad, inflcad of the one, will it be 
 manifeft how magnitude fubfilts from it. In anfwer to this we fay, that the intelligible monad 
 and duad generate the number which fubfifts in the intelligible world; and that thefe generate 
 fenfible analogous to intcliigible magnitude. But corporeal form is, as it were, the monad and 
 the one, and matter is the laft imitation of the indefinite duad, from w hicli two fenfible magni- 
 tude fubfifts. But, if Ariftotle wiCies to rank nature from its generative power according to 
 the one and the monad, we muft confider form itfelf acco.nilng to number. On which account 
 iTiagnitude muft be faid to fubfi.l in one WMy fronj the monad and the indefinite duad, wlicn tl-e 
 monad does not refign itfelf to the compofition of magnitude, and in another way from number 
 and the indefinite duad, when they are confidcrcd as the elements of magnitude. 
 
 CHAP.
 
 BooKlir, ARISTOTLE'S METAPHYSICS, ?? 
 
 CHAP. V, 
 
 But, confequent to tliefe things, It is dubious, whether numbers and bodies, 
 fuperlicies and points, are certain eflences or not. For, if they are not *, we 
 fhall not bo able ;o apprehend what being is, and what are the eflences of 
 things. For participated properties and motions, relatives, difpofitions, and 
 ratios, do not appear tO fignify the effence of any thing. For all thefe are 
 predicated of a certain fubjedl, and no one of them can be faid to be this or 
 that particular thing, but thofe things which efpecially appear to fignify 
 efience, are water, and earth, and fire, fro;n which compofite bodies confift :. 
 but the heat and cold of thefe, and things of this kind, are paflions, and not 
 eflences ; while body alone, which is paiRve to thefe things, fuflains them as 
 a certain being and efl'ence. But indeed body is lefs efl'ence than fuperficies, 
 and iliperficies than line, and line than unity and a point ; for by thefe body 
 is defined. And thefe indeed appear capable of fubfifting without body, but 
 it is impoflible thr.t bo;ly can fubfifl: without thefe. Hence the many think, 
 and the antients thought, that efl^ence and being are body, but that other 
 things are the participated properties of body ; fo that the principles of bodies 
 are alio the principles of beings : but the moderns, and thofe who are confi- 
 dered as wlfer than thefe, think that eflence and being are numbers. As we 
 have faid, therefore, if thefe things are not eflence, there will not, in fliort, be 
 
 * That which bounds has not always more of being than that which is bounded ; but this 
 h only true when the former is abllracled from the latter; as art with vefpe£l to artificial, and 
 nature with reference to natural bodies. The contrary, therefore, takes place, when that which 
 bounds gives itfelf up to the completion of the things bounded, and lofes its own proper nature 
 tlirougli profoundly mingling with that which it terminates. Nor does it always follow, that a 
 thing which takes awav, and at the fame time is not taken away, has more of eflence than that 
 which has an cppofite mode of fubfiftence, (fince, according to this, (tones would have more of 
 being than a houfe, timber than a fliip, and, in fhort, any kind of matter than that which is 
 formed from it ;) but this is only true when that which takes away is not any part of that which 
 is at the fame time taken away, nor an element, nor an extremity of it, nor in the order of 
 things which give themfelves up to its compofition. Thus, arithmetic has more of the eflential 
 than geometry ; for, when taken away, geometry is alfo taken away ; and it is neither any part, 
 nor element, nor extremity of geometry, nor that from which it is compofed, fo as to lofe its 
 own nature in the compofition. True genera, therefore, are prior to fpecies ; and fubilance, to 
 accidents. But fuperficies, as being more debile than body, is prior to body ; but it is not prior 
 as having more of eflence. It is however evident, that the rcafoning of Ariftotle is directed to 
 fuperficies as inherent in fubilance. 
 
 any
 
 80 ARISTOTLE'S METAPHYSICS, Book III. 
 
 any thing that is efience, nor any thing that is being. For It is not worth 
 while to call the accidents belonging tothefe, beings. But indeed, if this 
 fliould be granted, that lengths and points are more eflence than bodies *, yet 
 we do not fee the kind of bodies to which thefe muft belong ; (for it is im- 
 poITible that they can fubfift among fcnfibles.) 
 
 i\gain: all thefe appear to be the divifions j of body j one into breadth, 
 another into depth, and another into kngth. And befides this, in a fimilar 
 manner, every kind of figure is in a folid : fo that, if neither mercury is in a 
 ftone, nor the hrdf of a cube in a cube, fo as it is defined, neither therefore 
 is fuperficies in body X- Fcr, if this were the cafe with any one, it would 
 indeed be that which feparates the half. But there is the fame reafoning 
 refpe£ting a line, a point, and a monad. So that, if body is eminently 
 eflence, and thc!e are more eflence than body, but at the fame time thefe 
 neither are, nor are certain eflences; what being is, and what is the eflence 
 of things, will fly from our purfuit. For, in addition to what has been faid, 
 the irrational confequences reipeding generation § and corruption will take 
 place. For eflfence, when it formerly was not, but now is; or when it for- 
 
 * Thefe, liowcver, fubfifl: in fenfible bodies phyfically and materially ; and on this account 
 thev do not preferve the nature which they announce ; as neither does any other of material 
 forms. Yet they are nevcrthelefs in 7}iathematical body, which, though not fenfible, is at leafl 
 imaginable, or, in other words, has a fubfiftence in the phantafy ; and befides this, they fubfift in 
 the reafons or produftive principles belonging to opinion, and in intelligible fpecies. And yet, 
 though they fubfift in fo many ways, they do not prevent the fubfiftence of other efli;nces ac- 
 cording to each order of beings. 
 
 + Divifions, indeed, ine::iftent in bodies, are by no means the eflences of individuals ; but 
 muft not firji difference, by which all things are diftinguidied, introduce a divifion eftabliflied 
 according to fpecies and according to efTence .' 
 
 \ In anfwer to this it may be faid, that, in confequcnce of the fubfiftence of energy, it is not 
 necefTary that there fliould alfo be capacity, or i\\7it, capacity not yet exifting, there fliould likewlfe 
 not be energy ; but nothing hinders but that there may be one fuperficies in energy, as that 
 which bifedts the cube. For there are infinite divifions in capacity ; but, of things finite ia 
 energy, there is no reafon why divifions in energy may not alfo be confidcred. 
 
 § The reafoning of Ariftoile is as follows : Every eflence which fometimes is and fometimes 
 18 not, is circularly led to being through generation, but to non-being through corruption. But 
 tnefe extremes of magnitudes either are, or are not, without time; they are not, therefore, 
 eflences. And the reafoning is indeed true, fince every efltince which is generated and corrupted 
 requires a material caufe. But thefe extremes are not things of a material nature. I^ikewife, 
 when a line is divided, two points are produced : for, (iiyshe, a point, being one, is not divided 
 into two, fince it is indivifible. But thefe extremes, not having a prior exiftence, fubfift from 
 divifion without time and without generation. 
 
 merly
 
 Book III. ARISTOTLE'S METAPHYSICS. 81 
 
 merly was, but afterwards is not, appears to fuffer thefe things, viz. to be ge- 
 nerated and corrupted. But points, lines, and fuperficies, do not admit either 
 of generation or corruption, though they fometimes have a fubfiftence, and 
 fomeiimes not. For, when bodies mutually touch or divide each other, by 
 touching thefe become one ; but, when they are divided, they become two. 
 So that points, lines, and fuperficies, have no fubfiftence when bodies are 
 conjoined, but are then corrupted ; and when bodies are divided they have a 
 fubfiftence, though prior to this they had not a being. For a point which is 
 indlvifible is not divided into two; and if they are generated and corrupted, 
 they are made from fomething. The like takes place alfo refpedting tbc now 
 in time *. For neither does this admit of generation and corruption : but at 
 the fame time it always appears to be fomething elfe, though it is not a par- 
 ticular eflence. But it is evident that the like confequences alfo enfue re- 
 fpedling points, lines, and fuperficies ; for the fame reafcning takes place. 
 For all thefe, in a fimilar manner, are either bounds or divifions. 
 
 CHAP. VI. 
 
 In fl:iort, fome one may doubt why it is requifite to inveftigate certain 
 other natures befides fenfibles, and fuch as have a middle fubfiftence f , as, for 
 
 * That there are certain things, fays Arifl.otle, which, not having a prior exiftence, emerge 
 from generation and vanilh without corruption, and no one of which is a fubftance, the iionv, or 
 inftant, according to a temporal divifion, teflifies; to which alfo a point is aflimilated. In an- 
 fwcr to this, it may be faid that though thefe Are not eflences, yet they may poflcfs fome kind 
 of being ; for being is muhifarioufly predicated. 
 
 f The whole reafoning of Ariftotle here is as follows : — If, befides fenfible and mathematical 
 natures, we eftablifli ideas, fince fenfible individuals are many (as for inftance, many horfes, 
 many oxen, and many men), and alfo fince mathematical entities are many (for there are many 
 triangles, civclcs, fpheres, and pyramids); but it is requifite that we fliould not flop at the many, 
 but afcend to the monads which prefidc over the feveral individuals -, viz. one man, one triangle, 
 one circle, &c. ; — hence it is neceflary that each of the fpecies fhould be one in number; but, as 
 we have proved in the tenth problem, principles cannot be one in number. Species therefore, 
 that is, ideas, cannot fubfift. To this we reply, that though principles which fubfift in their 
 effects cannot, perhaps, have a numeral limit, yet it does not follow that this will be the cafe 
 with productive and fupreme caufes. For, if this were the cafe, neither would thefe feparate 
 intelligibles, the exiftence of which Ariftotle demonftrates in the twelfth book of this work, be 
 limited according to number, though he evinces that they are fo. It mud alfo be obferved, that 
 ihe antient fpeculative philofophers did not recur to Ideas for this caufe alone. 
 
 M inftance,
 
 «3 A R ISTOTLE'S MET A PH Y S ICS. Book III, 
 
 inftance, the forms which we eftablifli. For, if mathematical fpecies differ 
 from things which are here in fome other refpedt, yet they do not at all differ 
 in this, that many are of the fame fpecies ; fo that the principles of them will 
 not be bounded by number, as neither, of the lints which are here, are all the 
 principles bounded by number, but by fpecies ; unlefs fome one takes the prin- 
 ciple of this particular fyllable, or of this particular voice. For the principles 
 of thefe will alfo be bounded by number. And in a firailar manner with 
 refpedT: to the natures which have a middle fubfiflence : for there thofe things 
 which are of a fimilar fpecies are infinite. So that, if there are not certaia 
 other things befides fenfible and mathematical natures, fuch as fome affert 
 forms to be, there will not be an elfence one in number and fpecies ; nor will 
 certain principles of beings be fo many in number, but in fpecies. If, there- 
 fore, this is neceffary, it is alfo neceffary, on this account, that forms Ihould 
 have a fubfiflence : for, although thofe who affert thefe things do not exprefs 
 their meaning diflindly, yet this is what they wifh to fay ; and they mull 
 neceflarily affirm that every form is a certain effence, and that no one of 
 them fubfifta according to accident. Indeed, if we admit that forms are, and 
 that principles are one in number but not in fpecies, we Ihall aiTert thofe im- 
 poffibilities which muft neceffarily happen. 
 
 But a doubt which is near to this is, whether elements fubfift in capacity or 
 in fome other manner *. For, if in fome other manner, there will, in a certain 
 Tefpedl, be fomething elfe prior to principles f . For capacity Is prior to that 
 caufe. But it is not neceffary that every thing which is in capacity Ihould fubfift 
 in that manner. Bur, if elements are in capacity, it will happen that no one 
 being will have a fubfiflence :jl. For it is pollible for that to be which as yet 
 
 is 
 
 * He here inquires whether elements fubfift in capacity or energy. For by the words, or in 
 feme other mannery'is fignified hi energy; Ariftotle, perhaps, ftudioufly concealing this phrafe, left 
 he (hould take away the doubt belonging to the problem. For who will deny that the perfeft 
 is more principal than the imperfeiSt ? For the fame reafon, he does not fay caufes or principles,, 
 but elements. 
 
 f As if he had faid : If any one admits that elements are principles, fince capacity precede 
 every thing which is in energy, there will be fomething prior to principles. But now alfo, in 
 the fnme manner as before, he conceals the name of en^gy, together with this — that his argu- 
 ment is merely logical. For though, among generated natures, a fubfiflence in capacity is prior 
 to a fubfiflence in energy, yet this is not the cafe in -wholes, nor in divine natures, as Ariftotle 
 bimfelf demonftratcs in the ninth book of this work. 
 
 X His reafoning is now direiSiled to tlie opgofite ; viz. tliat the elements of things ought not 
 
 to
 
 Book III. ARISTOTLE'S METAPHYSICS. SS 
 
 is not ; for non-being is generated : but nothing of things impoffible is gene- 
 rated. It is neceflaiy, therefore, that thefe doubts fhould arife concerning 
 principles, and whether univerfals, or, as we fay, particulars, have a fubfifl- 
 ence *. For, if there are univerfals, they will not be effences : for nothing of 
 things common fignifies a certain fubjedt, but quality. But eflence is a fubjedl. 
 But if that which is predicated, and may be exhibited in common, is a fubjeiS, 
 
 to be fuppofed to fubfift in capacity. But the demonftratlon is as follows: — ^That vvliich is pof- 
 fible is alone generated ; for neither that which is impoffible, nor that which already is, can be 
 generated. That which is in generation, or in a progreiTion from that v/hich is not to that 
 which is, is not yet. That which is not yet, may happen not to be. So that, if principles are 
 in capacity, it may fo happen tiiat no being may originate from them. But he explains the 
 minor proof thus : Nothing of impoffibles is generated, to which that is equivalent, that what is 
 poiTible is alone generated. The medium, or middle, is as follows : That which is in generation, 
 or becoming to be, is non-being. It may therefore be faid. That neither is that which is in 
 energy that which is generated. But that it may happen that a thing which is not yet may not 
 be, Ariftotle confiders as manifeft in thefe propofitlons ■, becaufe it is poflible that it may be 
 naturally adapted to proceed into energy, and yet this may not altogether take place. All thefe 
 propofitions, indeed, have great power, if any one fliould aflert that all principles fubfift in 
 capacity, and that no one of them is in energy. 
 
 * This is the fourteenth in the order of the problems, but it Is nearly the fame with the 
 tenth. For Ariftotle here alfo inquires whether principles are things univerfal, or individuals ; 
 which is nearly the fame with the inquiry, whether they are bounded in fpecles or in number. 
 But he fays that, if we fuppofe them to be univerfals, we fliall deprive them of an eflentlal fub- 
 fiftence. For univerfals are not effences. Socrates himfelf is at leaft three effences ; individual, 
 fpecific, generic. But, if principles are not univerfals, they are either unknown, or they have 
 fomething prior to them ; each of which is irrational. For, if it be faid that principles arc un- 
 known, then nothing whatever will be known ; and if they are known, they are known through 
 univerfals. There will therefore be fomething prior to them of a more comprehenfive nature. 
 
 But we have often faid that principles properly fo called, i. e. the higheft principles, are above 
 the univerfal reafons of nature, and the produftive and gnoftic principles of the mundane foul. 
 But what Ariftotle now fays is not attended with any neccjfary confequence ; for neither is every 
 univerfal uneffential ; fince, if this were the cafe, nothing univerfal would be eternal, and fabri- 
 cative of particulars ; nor do we know particulars through univerfals of pofterior origin 
 (yj-Tffoym; ti3.^ayji), or, in other words, by an abftraiSlion of that which is common in fenfibles. 
 For either we know fcientifically, for inftance, that every man is a mortal rational animal, or 
 we do not. If we do, this knowledge could not be the refult of an abftraftion from the indi- 
 viduals of the human race ; becaufe, to effc£t this, fuch abftradion ftiould be made from all 
 the exifting individuals of our fpecies ; which is impoffible. And if we do not know this 
 fcientifically, fuch a concluGon is not indubitable and neceffary. And laftly, Ariftotle himfelf 
 will not fay that any univerfals tranfccnd immoveable genera. But even Alexander acknow- 
 ledges that the arguments of Ariftotle vsiih refpect to nearly all thefe particulars are merely 
 diakclicai. 
 
 IVI 2 Socrates
 
 84 ARISTOTLE'S METAPHYSICS. Book III. 
 
 Socrates himfelf will be many animals, and man and animal, If each fignifies a 
 fubjeft, and that which is one. If therefore principles are univerfals, thefe 
 things will happen ; but if they are not univerfals, but fuch as particulars, there 
 will not be objefls of fcientific knowledge. For all fcience refpedts things 
 univerfal : fo that there will be other principles unlverfally predicated, prior to 
 principles, in order that there may be a fcience of them. 
 
 ARISTOTLE'S
 
 ARISTOTLE'S METAPHYSICS. 
 
 BOOK IV. 
 
 C H A P. I. 
 
 X HERE Is a certain fclence which fpeculates being fo far as being and 
 the things which are cfl'entially inherent in it. But this fcience is not the 
 fame with any one of thofe which are called partial fciences. For no one 
 of the others confiders being univerfally fo far as being j but, cutting oiFa 
 certain part of it, they fpeculate that which is accidental to this part, as is the 
 cafe with the mathematical fciences. But, fince we inveftigate principles and 
 the higheft caufes, it is neceflary that they fhould be effentially principles and 
 caufes of a certain nature. If, therefore, thofe alfo who have inveftigated 
 the elements of beings, have inveftigated thefe very principles, it is alfo ne- 
 ceflary that the elements of being fhould not fubfift according to accident 
 but fhould fubfifl: fo far as they are beings. On which account, we alfo mufl. 
 take into confideration the firll caufes of being, fo far as being.. 
 
 C H A P. ir. 
 
 But being Is, Indeed, predicated varioufly, but with reference to one, and 
 to one certain nature j and not ec[uivocally, but in the fame manner as every 
 
 thing
 
 86 ARISTOTLE'S METAPHYSICS. Book IV. 
 
 thing nilubrlous is referred to health, partly from prcferving, partly from 
 producing, partly from indicating, and partly from being fufceptive of health. 
 This likewife takes place, in the fame manner as that which is medicinal is 
 referred to health : for one thing is called medicinal, becaiife it has a medi- 
 cinal power; but another, becaufe it is naturally adapted to procure health ; 
 and another, becaufe it is the work of the medicinal art. And, in a fimilar 
 manner, we admit the predication of other things. Thus, too, being is in- 
 deed predicated varioufly, but the whole of it with reference to one principle. 
 I'or fome things are called beings becaufe they are elTences ; others, becaufe 
 they are the pafTions of effence ; and others, becaufe they are the way to 
 cflence,, or are corruptions, or privations, or qualities, or effedive or genera- 
 tive of eflence, or of things predicated with reference to effence, or to the 
 -negations of fome one of thefe, or of effence. On this account alfo we fay that 
 non-being is non-being. As, therefore, there is one fcience of all things fane, 
 the like alfo takes place in other things. For it is the province of one fcience 
 to fpeculate, not only concerning things which are predicated according to 
 .one, but alfo concerning things which are predicated with reference to one 
 nature. For thefe, likewife, in a certain refpedl are predicated according to 
 ■one. It Is evident, therefore, that it is the province of one fcience to fpecu- 
 late beings fo far as they are beitigs. 
 
 But every where fcience is properly of that which is firft *, and from which 
 other things are fufpended, and through which they are predicated. If, 
 therefore, this is effence, it will be proper that a philofopher fliould poffefs 
 the principles and caufes of effences. For, of every genus f there is one 
 fenfe, and one fcience ; as, for Inftance, fince there is one grammatic fcience, 
 it fpeculates all vocal founds. On v/hich account alfo, to fpeculate fuch 
 things as are the fpecies of being, and fuch as are the fpecies of fpecies, is the 
 province of one fcience in kind. But, i^ being and the otic are the fame and 
 one nature, becaufe they follow each other, in the fame manner as principle 
 
 * Thus mcdiciiie, which is converfant with every thing that partakes of Iicalth, is properly 
 and principally the fcience of health, from which the reft derive their name. In like 
 manner, the difcipline refpedling things good is principally the difcipline of the firfl and 
 mod perfeQ good. The fcience of beings, therefore, will be principally the fcience of the 
 firil bciDg, or being itfelf. In like manner, the fcience of divine natures is properly the fcience 
 of God. 
 
 j- Alexander obferves, that Ariftotle ufes genus here in a more general way for nature. 
 
 -and
 
 Book IV'. A R I S T O T L E ' S M E T A P H Y S I C S. 97 
 
 and caufe, but not as being fignified by one definition, It is of no confequence, 
 if we confidcr them in a fimilar manner, but is indeed more conducive to our 
 purpofe : for, one man, and exifting man, and man are the fame. Nor does 
 it fignify any thing different, according to a repeated diiftion, to fay, man 
 is, and man, and one man. But it is evident that being is not feparated, 
 neither in generation nor corruption. And, in like manner with refpedl to 
 the one ; fo that it is evident that addition in thefe fignifies the fame thing, 
 and that the one Is nothing elfe befides being '*. Further ftill : the effence of 
 every thing is one, not according to accident. And in a fimilar manner that 
 which is fome particular being : fo that, as many as are the fpecies of the oney 
 fo many alfo are fpecies of beings concerning which to fpeculate the formal 
 caufe is the province of the fame fcience in kind : but, I fay, as for inftance, 
 concerning the fame^ and fimilar^ and other things of this kind, and things 
 oppofed to thefe. But nearly all contraries are referred to this principle. 
 Thefe things, however, are confidered by us in the elediion of contraries f ; 
 and fo many are the parts of philofophy as there are effences. So that it is 
 necefTary, that one kind of philofophy fliould be firft, and another fecondary,- 
 For, being and the one are things which immediately poffcfs genera \ ; on 
 which account fciences alfo are confequent to thefe. For, a philofopher is 
 fimilar to a mathematician ; fince mathematics alfo has parts, containing a. 
 firft and fecond fcience, and another confequent to thefe. 
 
 But, fince it is the province of one fcience to fpeculate oppofites, and mul- 
 titude is oppofed to the one, it is the bufinefs of one fcience to fpeculate nega- 
 tion and privation, becaufc the one is fpeculated both ways, of which there is 
 negation or privation. For we either fimply fay negation is not prefent, 
 or that it is not prefent to a certain genus. Hence, there, difference is pre- 
 fent to the one, except that which is in negation (for negation is the abfence 
 of it). But In privation there Is a certain fubje£l nature, of which privation is- 
 predicated : and multitude is oppofed to the one. So that it is the province of 
 the aforefaid fcience to know the oppofites to the things which we have men- 
 
 * This is true only of that one which is confubfiilent with the firft king, concerning which 
 •we have already fpoken in the notes to the third book, and fliall again fpeak in the notes to the- 
 fourteenth book. 
 
 f According to Laertius, Simplicius, and others, Ariftotle wrote a treatife wtfi rayaiov, con-^ 
 tertiing the Good, whic h is unfortunately loft, and to which Alexanda" fays he now refers. 
 
 X Viz. teitig and the one are predicated of certain genera, 
 
 tioned, 
 
 /
 
 «8 ARISTOTLE'S METAPHYSICS. Book;iV. 
 
 tioned, viz. the difierent, the diflimllar, the unequal, and fuch other thuigs as 
 are predicated, cuher according to the fame, or according to multitude and 
 the one ; among the number of which is contrariety. For contrariety is a 
 certain difierence ; but difference is diverfity. So that, fince the ofie is rnulti- 
 farioufly predicated, thefe alfo are predicated in various ways : but, at the 
 fame time, it is the bufinefs of one fcience to know all thefe. For it does 
 not follow that, if they are multifarioufly predicated, the fpeculatien of them 
 belongs to another fcience. But if the reafons ai^e referred, neither according 
 to one, nor to one, then it is the bufinefs of another fcience. But, fince all 
 things are referred to that which is firft, as, for inRance, fuch things as are 
 called one are referred to a firft one, we muft fay, that the like alfo happens 
 refpe£ling fame, and different, and contraries. So that by dividing, as often 
 as any particular is predicated, we muft refer it to that which is firft in each 
 category, that we may know how it is predicated \\\\.h refpedt to that firft. 
 For fome th'ngs are predicated from poffeffing that firfi: ; others, from 
 making; and others are predicated according to other fuch like modes. 
 
 It is evident, therefore, as we faid in the doubts * which we enumerated, 
 that it is the province of one fcience to fpeculate both concerning thefe and 
 effence.. But this was one of the things which we mentioned among the 
 doubts. And it is the bufinefs of a philofopher to be able to fpeculate about 
 all things. For, if not of the philofopher, who will he be who confiders whe- 
 ther Socrates, and Socrates fitting, are the fame, or if one is contrary to one, 
 or, what contrary is, or, in how many ways contrary and oppofite are pre- 
 dicated ? And in a fimilar manner refpe(3:ing other things of this kind. 
 Since, therefore, thefe things are the effential properties of the one fo far as 
 one, and of being fo far as being, but not fo far as the one and being are 
 numbers, or line?, or fire, it is evident that it is the bufinefs of that fcience 
 both to know what they are, and the things which arc accidental to them. 
 And thofe who confider thefe things, do not err in this refpe£l as not philo- 
 fophifi.ig, bur becaufe effence, of which they underftand nothing, has a prior 
 fubfiflence. For, as of number fo far as number there are peculiar properties; 
 fuch as imparity, parity, commenfurability, equality, cxcefs, and defed: ; and 
 thefe things fubfift in numbers both confidered by themfelves and with rela- 
 tion to each other ; and in a fimilar manner as there are other peculiar pro- 
 perties belonging to that which is folid and immoveable, to that which is 
 
 * Ari!lotle here refers to the thiid book. 
 
 moved,
 
 Book. IV. ARISTOTLE'S METAPHYSICS. :89 
 
 moved, to the light and the heavy ; fo alfo there are certain peculiar proper- 
 ties belonging to being fo far as being. And thefe are the things the truth 
 concerning which it is the bufinefs of the philofopher to confider j of which 
 this is a token, that thofe who are fkilled in dialectic, and fcphifts, affiime the 
 fame figure as the philofopher : (for the fophiftic art is only apparent wifdom, 
 and thofe who are fkilled in dialedic difcoiirfe concerning all things,) but being 
 is common to all things. They difcourfe, however, concerning thefe things, 
 becaufe they properly belong to philofophy. For the fophiftic and the dia- 
 lectic arts are employed about the fame genus with philofophy ; but philo- 
 fophy * diiTers from one in the mode of power, and from the other, in the 
 choice of life. For the dialectic art is piraftic refpe£ting thofe things of which 
 philofophy poffeffes the knowledge : but the fophiftic is apparently an art, 
 but is not really feu 
 
 Further ftill of contraries, the other co-ordination, is privation f : and all 
 things are referred to being and non-being, and to the one^ and multitude ; 
 as for inftance, rejl partakes of the one, but motion of multitude. But almoft 
 all men acknowledge that beings and efTence confift from contrarie?. For all 
 aflert that principles are contraries : according to feme, the principles of things 
 being the even and the odd ; according to others, the hot and the cold ; ac- 
 cording to feme, bound and infinity; and according to others, friendfhip and 
 .ftrife. All other things, too, appear to be referred to the one and multitude. 
 But redudlon is afllimed by us [in \ the fecondbook concerning the good]. 
 Principles however, both confidered abfolutely and as admitted by others, fall 
 into thefe as into genera. From hence therefore alfo it is evident that it is 
 the province of one fcience to fpeculate being fo far as being. For all thing? 
 are either contraries, or confift from contraries. But the principles of con- 
 traries themfelves are the one and multitude : and thefe belong to one fcience, 
 whether they are predicated according to one or not ; which perhaps is the 
 truth. But at the fame time, though the one is predicated in various ways, 
 
 * Both the firfl: philofophy and dialedic difcourfe concerning being and its accidents, and 
 each is fyllogiftic. But with the firft philofophy this fyllogiftic power is demonrtiative of true 
 and real beings ; but the diaIe£Vic art explores the truth indeed, but reafons only probably. 
 See more concerning the firft philofophy, or Ccientific dialedic, in the Introdudion. 
 
 t Cf all contraries, one order is privation, and the other yjrra. 
 
 X I have inferted thefe words from the Commentary of Alexander, as they are certainly ne- 
 ceflary to the fenfe : the words of Alexander are, " Rurfus ad ea qux in fecundo libro de bono 
 ^emonftrata funt relegat nos." 
 
 N yet
 
 50 ARISTOTLE'S METAPHYSICS. Book IV. 
 
 yet Other things are referred to the firft, and in a fimilar manner contraries. 
 On this account, though being and the one are not univerfal and the fame in 
 all things, or feparate, as perhaps they are not, yet fome things arc referred 
 to the one, and others are placed in a confequent order; and, on this account, 
 it is not the bufmefs of a geometrician to fpeculate what contrary, or the 
 perfeft, or the one, or being, or fame, or different, may be, unlefs from hy- 
 pochefis. That it is therefore the bufmefs of one faience to fpeculate being fo 
 far as being, together with the things which fubfift in it fo far as being, is 
 evident : and alfo, that the fame fcience is contemplative not only of eflTences,. 
 but of things fubfifting in effences, together with fuch particulars as have been 
 mentioned; and llkewife of prior and poflerior, of genus and fpecies, of whole 
 and parr, and other things of this kind. 
 
 CHAP. iir. 
 
 It muft be declared whether it is the bufmefs of one or of a different 
 fcience to fpeculate concerning thofe things which are called axioms* in the 
 mathematical difciplines, and concerning effence. But it is evident that it is 
 the province of one fcience, and that the fcience of the phllofopher, to con- 
 fider thefe things. For they are prefent with all beings, but not to any par- 
 ticular genus feparate from others. And all fciences indeed ufe thefe becaufe 
 they pertain to being fo far as being ; but every genus is being. They ufe 
 them, however, fo far as is fufficlent to their purpofe ; /. e. fo far as they con- 
 tain the genus refpedling which they bring demonftrations. So that, fince it 
 is evident that they are prefent to all things fo far as they are beings (for this 
 is common to them), the fpeculation of thefe alfo is the province of that fcience 
 which knows being fo far as being. On which account, no one of thofe who 
 confider things according to a part, endeavours to fay any thing concerning 
 them, wl'Cthcr they are true or not. For neither the geometrician nor the 
 arithmetician does this, but certain natural philofophers, who in fo doing adl 
 properly. For they alone think they fhould fpeculate concerning the whole 
 of nature, and concerning being. 
 
 But, fince there is yet fomething above that which is phyfical (for nature is 
 one particular genus of being), the confideration of thefe things alfo will per- 
 tain to that which is univerfal, and to him who contemplates the firfl effence. 
 
 * See the notes to the third book. 
 
 The
 
 BookIV. ARISTOTLE'S metaphysics, SI 
 
 The natural fclence, indeed, is a certain wifdom, but not the firfl. But thofe 
 who endeavour to fpeak concerning the truth of axioms, and to fliow how it 
 ought to be admitted, do this through their ignorance of analytics*. For it 
 is requifite to enter on thefe things with previous 'knovvledge, and not while 
 hearing tjiem mentioned begin to inveftigate. Hence, then, that it is the 
 bufmefs of the philofopher, and of him who fpeculates the whole of eflence, 
 lO far as it is naturally fuch, to confider likewife fyllogiftic principles, is evi- 
 dent. But it becomes him who efpecially knows what pertains to every 
 genus to declare the moft ftable principles of a thing. Wherefore it alfo 
 pertains to him to affign the moft firm principles of all things, who fpecu- 
 lates beings fo far as they are beings. And he who does this is the philo- 
 fopher. But that is the mofl: ftable principle of all things, concerning which 
 it is not poffible to be deceived. For it is neceflary that a principle of this 
 kind fhould be moft known (for all men are deceived refpedling things %vhich 
 they do not know); and, likewife, that it fhould be unhypothetic. For that 
 is not hypothefis vv'hich it is neceflary for him to pofTefs who underftands any 
 thing whatever which ranks among beings. But that which it is neceflary for 
 him to know who knows any thing, muft neceflarily be pcflefled by him who 
 knows any thing. That a principle, therefore, of this kind is the moft ftable 
 of all thing?, is evident. 
 
 What this principle, however, is, muft in the next place be declared. 
 Fcr it is impolTible that the fame thing can at the fame time be prefenc 
 and not be prefent with the fame thing, according to the famej and ail 
 fuch things as we have already difcufl^ed for the purpofe of removing the 
 difficulties which refult from logical inquiries. But this is the moft ftable of 
 all principles : for it has the above-mentioned condition. For it is impofllble 
 to apprehend that any thing can be the fame and yet not the fame, as fome 
 think Heraclitus aflcrted ; fince it is not necefliary to think that a thing is, be- 
 caufe it is aflerted by fome one to be. But if it dees not happen that contra- 
 ries are piefent with the fame thing (but the ufual additions have been made 
 by us to this propofition), and opinions are contrary, which are adverfe in a 
 contradiclory manner; it is evident that it is impofllble to conceive the fame 
 thing, at the fame time, to be and net to be. For he who is deceived about 
 
 * Aridotle, in his laft Analytics, fliows that there mud necelTariljr be principles of demonftra- 
 tion, and that thefe principles muft: be indemonfirable. See my paraphrafed tranflatiou of the 
 Tirll book ol this exceUiiit work, prefixed to any tranllation of Proclus on Euclid. 
 
 N 2 this 
 
 ./
 
 92 ARISTOTLE'S METAPHYSICS. Book IV. 
 
 this thing would at the fame time poflefs contrary opinions. Hence, all who 
 demonRrate reduce their demonftrations to this laft opinion; for this is na.- 
 turally the principle of all other axioms. 
 
 CHAP. IV. 
 
 There are, ho-vevcr, certain perfons who, as we have obferved, aflert that 
 the fame thing may be and may not be, and think conformably to what they 
 afTcrt. Many of thofe, too, who difcourfe concerning nature ufe the fame 
 affertion. But we now aflume that it is impofTible for the fame thing to be 
 and not to be ; and through this we have fhown that this is the raoft ftable 
 of all principles. Some, however, through want of erudition, have tliought 
 it worth while to demonftrate this axiom. For it is want of erudition not 
 to know what are the things of which it is proper to feek demonftration, and 
 what the particulars of which a demonftration is not requifite. For, in fhort, 
 it is impoffible that there fhould be a demonftrat'on of all things. For, if this 
 were admitted, there muft be an infinite progreftion : fo that neither thus 
 would there be any demonftration. But if it is not proper to feek demon- 
 ftration of certain things, yet ghefe men are not able to aflign what that is 
 which they confider as rather deferving to be called a principle of this kind. 
 It nnay, however, be demonftratcd elendlically that this is impoflible, if only he 
 who doubts fays any thing. But, if he fays nothing, it is ridiculous to in- 
 quire a reafon of him who does not fpeak, fo far as he does not fpeak. For 
 fuch a one, fo far as he is fuch, is fimilar to a plant. But I fay that to de- 
 monftrate elen(flically differs from demonftration, becaufe he who demon- 
 flrates feems to inquire that which is fought after in the beginning ; but when 
 there is another caufe of this kind, it will be confutation, and not demonftra- 
 tion. But the beginning of difcourfe to any one of thefe fliould be, not to 
 require him to affert that any thing is or is not (for perhaps fome one may 
 think that this is the thing which was required from the beginning), but to 
 defire him to fignify fomething both to himfelf and another. For this is ne- 
 ceflary, if he fays any thing : but if he does not, it is impoffible there fhould 
 be any difcourfe with fuch an one, either from himfelf, to himfelf, or to an- 
 other. But if any one admits this, there will be demonftration : for now 
 there will be fomething defined. Yet, not he who demonftrates, but he who 
 fuftains, is the caufe of this ; for, taking away difcourfe, he fuftains difcourfe. 
 
 In
 
 Book IV, A R I S TO T L E'S M E T A P H Y S I C S. $$ 
 
 In the firft place, therefore, it is evident that a name fignifies this particular 
 thing, either to be, or not to be : fo that not every thing wiil fubfift in this 
 particular manner, and yet not in this manner. Further ftill : if man fig- 
 nifies one thing, let it be this, a biptd animal. But I fay this fignifies one 
 thing, when if this thing is a man, whatever is a man is a biped animal. But 
 it is of no confequence, though fome one fhould fay tint it fignifies more 
 than one thing, if they are only definite ; for he may give to each definition 
 another name. I fay, for inRance, if he fliould affert that man does not 
 fignify one thing, but many things, one definition of one of which is a biped 
 animal. There are alfo many others, but the number of them is definite : 
 for the proper name may be placed in each of the definitions. However, if 
 fome one fhould not place it, but fhould fay that it fignifies infinite particu- 
 lars, it is evident there could be no definition of it, nor any difcourfe about 
 it. For, not to fignify one thing is to fignify nothing. But when names 
 have no fignification, then in reality the difcourfe of men with each other,, 
 and of a man with himfelf, can no longer fubfift. 
 
 For it is not poHible to underftand any thing when not underftanding one 
 thing; fince, if it were poffible, one name muft be impofed en this thing. 
 Be it therefore, as was faid at firft, that a name fignifies fomething, and that 
 it fignifies one thing. Hence, that man exifts, will not fignify the fame thing 
 as that man does not exift ; if man fignifies not only that which is afferted of 
 one thing, but one thing itfelf. For we do not think that to fignify one- 
 thing, is to predicate of one thing; fince, if this were admitted, a mufician, 
 that which is white, and a man, would fignify one thing : fo that all things 
 will be one, for they will be fynonymous : and it will not be pofFible for the 
 fame thing to be and yet not be, unlefs fo far as equivocally confidered. Jufl: as 
 if that which we call man, fhould be denominated by others not man. However, 
 that which is doubted is not this, whether it is poffible that the fame thing can 
 be a man and yet not a man in name, but whether this can take place in reality. 
 
 But if man and not man do not fignify that which is different, it is evident 
 that to be will be the fame as not to be a man ; for they wiil be one thing ; 
 fince this fignifies that they are one thing, as a tunic and a garment, if there 
 is one definition of each. But if they are one, to be and not to be a man 
 fignify one thing. It has been fhown, however, tha^^ they fignify that which 
 is different. It is neceffary therefore, if any thing is truly called a man, that 
 it muft be a biped animal : for this is that which man fignifies. But, if this is 
 
 necelfary, 
 
 /
 
 9t ARISTOTLE'S METAPHYSICS. Book IV. 
 
 neceflary, it is not poffible that this very thing fliould not be a biped animal. 
 For this is what is fignified by exifting neceflarlly, viz. that it is impoffible it 
 fhould not be a man.- It is not therefore poffible that it fnould be true to fay, 
 at the fame time, that the fame thing is both a man and not a man. The 
 fame reafoning, too, takes place with refpedl to the not being a man. For 
 the being of a man fignifies fom.ething different from the being of that which 
 is not a man; fince to be white, and to be a man, fignify things different. 
 For that is much more oppofed ; fo that it fignifies fomething different. 
 
 But, if any one fhould fay that white fignifies one and the fame thing with 
 man, again we fay that which was faid before, that all things, and not only 
 oppofites, will be one. But, if this is not pofTible, that which has been faid 
 will happen, if an anfwer is given to the interrogation. But, if he who is 
 :fimply interrogated adds alfo negations, he will not anfwer to the interroga- 
 tion : for, nothing hinders but that the fam.e thing may be man and white, 
 and other things infinite in multitude. Neverthelefs, when interrogated, if 
 it is true to fay that this is a man or not, he muft anfwer by that which 
 :fignifies one thing, and muft not add, that it is both white and large. For 
 it is impoffible to pafs through accidents, becaufe they are infinite. Either, 
 therefore, he muft pafs through all, or no one of them. In a fimilar manner, 
 therefore, if the fame man and non-man fubfifted infinitely, if we are inter- 
 rogated if man is, wc ought not to anfwer, that at the fame time non-man 
 alfo is ; unlefs in our anfwer we llkewife include fuch things as happen, if 
 .man is, or is not. But he who does not this will not difcourfe. 
 
 In fhort, thofe who make this affertion fubvert effence, and the formal 
 caufe : for it is neceffary they fliould fay that all things are accidental, and 
 that there is not any thing which is effeutially man or animal, and to which 
 the being of man or animal belongs. For, if there fhould be fuch a thing as 
 that which it is for a man to be, this will not be for a man not to be, or to 
 be not a man j although thefe are negations of this. For that which is figni- 
 fied was one, and this w^is the effence of a certain thing. But to fignify 
 effence is the fame as to affert that the being of a thing is nothing elfe. But, 
 if the being of a man belongs to a thing, it is impoffible that it fliould not 
 be man, or that it fliould be that which is not man ; for it would be fome- 
 thing elfe. So that they muft neceffarily fay that a formal and effential 
 definition of this kind, and which is always adapted to the fubjeifl:, is of a 
 non-entity, and that all things pertain to it accidentally} for ia this very 
 
 •thing
 
 Book IV. ARISTOTLE'S METAPHYSICS. 95 
 
 thing * eueiice and accident are feparated from each other. For, whitenefs 
 on that account happens to man, becaufe he is indeed whice, but not white- 
 nefs itfelf. Bur, if all things are predicated according to accident, there will 
 not be any firft univerfal. And if accident always fignifies a predication per- 
 taining to a certain fubjecft, a progreffion ad hifinituin muft neceffarily enfue. 
 But this is impoffible ; for they are not cnnnetfed with more than two. For 
 accident is not an accident to accident, unlefs becaufe both happen to the 
 fame thing. I fay, for inftance, as in that which is white, and a mufician ; 
 for here the mufician is white, becaufe both happen to a man : but Socrates 
 is not on that account a mufician, becaule both happen to a certain other 
 thing. Since, therefore, fome things are called accidents in this, and fome in 
 that way, thofe things which are called accidental, in the fame way as white 
 to Socrates, cannot be predicated infinitely, fo as, for inflance, that to So- 
 crates who is white fomething elfe fhould happen. For one thing is not 
 produced from all, nor is any thing elfe an accident to that which is white, 
 as, for inftance, a mufician : fince this does not more happen to that than that 
 to this. And at the fame time we have diftinguifhed with refpedl to acci- 
 dents, that fome things happen in this manner, but others as a mufician to 
 Socrates. Such things, however, as happen in this manner do not happen 
 as accident to accident; but this is the cafe with fuch as happen after the 
 other manner. So that all things are not affcrted according to accident. There 
 •will, therefore, be fomething which fignifies as effence : but if this be the cafe, 
 it is fhown that things contradictory cannot be predicated at the fame time. 
 
 Again : if all contradidions are at the fame time true of the fame thing, it 
 is evident that all things will be one. The fame thing, therefore, will be a 
 trireme, and a wall, and man, if it fo happens that fomething can be affirmed 
 or denied of every thing, as muft necefi^rily be the cafe with thofe who 
 fpeak according to the dodlrine of Protagoras. For, if to any one a man 
 appears not to be a trireme, it is evident that he will not be a trireme ; he is,, 
 however, if contradidlion be true, i^nd hence, that which Anaxagoras 
 aflerted, t kes place, viz. that all things fubfift together, fo that nothing is 
 truly one thing. They appear, therefore, to aflert that which is indefinite, 
 and, thinking to fpeak of being, they fpeak concerning non-being : for that 
 which is being in capacity, and not in energy, is the indefinite. Neverthe- 
 lefs, we muft fay to the authors of this hypoihefis that, of every thing, either 
 
 * For TowTo, in this place, read Toi/ry. 
 
 affirmation 
 
 /
 
 ?6 ARISTOTLE'S METAPHYSICS, Book IV. 
 
 affirmation or negation mufl; be predicated. For it is indeed abfurd that 
 the negation of a thing ftiould be true, but that the negations of other things 
 which are different from it fliould not alfo be true. I fay, for in fiance, if it 
 be true to affirm ,of a man, that he is not man, it is evident that he is alfo not 
 a trireme. If, therefore, affirmation is true refpediing him, negation is alfo 
 ^leceflarily true. But, if affirmation is not true, the negation of a trireme 
 ■will more pertnin to him than the negation of himfeif. If, therefore, that be 
 true, the negation of a trireme is alfo true; and if the negation, affirmation 
 likewife. Thefe things, therefore, happen to thcfe who. make this aflertion, 
 and alfo, that it is not neceffary to employ either affirmation or negation. 
 For, if it be true that the fame perfon is a man and not a man, it is evident 
 that he will neither be a man nor yet not a man : for of thofe two things 
 there are two negations. And, if that is one compoftd from both, the one 
 fo compofed will be oppofite. 
 
 Further ftill : either this will be the cafe refpe<5ling all thing?, and a thing 
 will be white and not white, being and not being, and in a fimilar manner 
 with refped to other affirmations and negations ; or this will not be the cafe, 
 but it will be true of fome things, and not of others. And, indeed, if it be 
 not true with refped to all things, thofe will be firm and definite. Bur, 
 if it be true with refpe<3: to all things, again, either of fuch things as there is 
 affirmation there will alfo be negation, and of fuch things as there is nega- 
 tion there will be affirmation ; or, of fuch things as there is affirmation there 
 will alfo be negation ; but of all fuch things as there is negation there will 
 ■not be affirmation. And if this be the cafe, there will be fomething which 
 is firmly non-being, and this will be a ftable opinion. However, if not to be 
 is fomething firm and known, the oppofite affirmation will be more firm. 
 But if it be neceffary to affirm in a fimilar manner whatever is denied, it is 
 either true to fay, by dividing, that a thing is white, and again that it is not 
 white, or it is not true. And, if it be not true to affert this by dividing, nei- 
 ther does he afftrt thefe things, nor has any thing a fubfiftence. But how 
 can any one fpeak of non- entities, or underftand any thing refpedling them ? 
 And, as we before obferved, all things will be one; and man, and gcd, and 
 trireme, and the contradidories of thefe, will be the fame. But if, in a fimilar 
 manner, every contradidion is true of particulars, one thing will in no refped 
 differ from another. For, if it Ihould differ, this will be true, and its pecu- 
 Jiarity. In like manner, that which we have afferted will take place, if it 
 
 fhould
 
 Book IV. A R I S T O T L E'S M E T A P H Y S I C S. 97 
 
 fhould happen that he who makes the divifion affirms that which Is true. 
 To which we may add that all men will fpeak the truth, and all men will 
 affcrt that which is falfe, and every one will acknowledge that hlmfeif fpeaks 
 falfely. At the fame time, too, It Is evident that fuch an one fpeculates a non- 
 entity : for he fays nothing. For he neither fpeaks in this manner, nor in 
 that ; but in this manner, and yet not In this manner. And, again, with re- 
 fpedl to thefe, he makes a negation of both, by afllrting that they are neither 
 in this manner, neither not in this manner, but in this manner, and not in this 
 manner: for, If this were not the cafe, there would now be fomething de- 
 finite. 
 
 Further ftill : if when affirmation Is true negation is falfe, and when this 
 is true affirmation is falfe, it will not be poffible at the fame time truly to 
 affirm and deny the fame thing. But fome one perhaps may fay, this is that 
 which was advanced In the beginning. Again, therefore, does he who ap- 
 prehends that a thing either Is, or Is not, in a certain refpcd, think falfely j. 
 but he who apprehends that a thing is both, conceive truly ? For, if his con- 
 ception be true, what elie is aiTcrted but this, that fuch is the nature of things ? 
 But if his conception be not true, but rather the conception of him who 
 rhinks after that manner, then things will be In a certain refpeft, and this will 
 be true, and not at the fame time not true. But if ail men in a fimilar 
 manner fpeak falfely and truly, It is not poffible for hiin who makes this 
 aflertion, either to fpeak or affcrt any thing: for, at the fame time, he muft 
 alTert the fame things, and not the fame. And if he apprehends nothing,, 
 but in a fimilar manner thinks and does not think, what difference will there 
 be between Inch an one and a plant ? Whence, alfo, it is fufficienily evident 
 tl'.at no one is thus affetted, neither of others, nor of thofe who make this 
 affetion. For, why does he walk to Megara, and not remain quiet, thinking 
 to walk ? nor immediately at break of day proceed to fome well, or to a pre- 
 cipice ? But he appears to adt cautioufly, as not fimilarly thinking it is not 
 good, and gc^od, to t;Ul. It is evident, therefore, that he apprehends that the one 
 is better, and the other not better. But, If this be the cafe, it is alfo neceffary 
 he fti(.uld tliink that this is a man, but that not a man j and that this thing ' 
 is fvvcet, but that not fweet. For he does not equally inveftigate and form an 
 oj'inion of all things, fince he thinks it is better to drink water, and to fee a 
 certain perfon, and afterwards fearches for thefe very things. Though it 
 would be requifite that he fhould equally inveftigate all things, if man and 
 
 O not.
 
 58 ARISTOTLE'S METAPHYSICS. Book IV- 
 
 not man, water and not water*, were fimilarly the fame. But, as we have 
 before obferved, there is no man who does not appear cautloufly to avoid the 
 one, and not the other. So that, as it feems, all men are perfuaded, that both 
 contraries are not expedient, if not with refpe<£t to all things, yet with refped: 
 to the better and the worfe. But if they thus think, not from fcientific know- 
 ledge, but opinion, much more ihould they be ftudious of truth, juft as the 
 iick fhould pay greater attention to health than thofe who are healthy. For 
 he who energifes according to opinion, when compared with him who ener- 
 gifes according to fcience, is not fanely difpofed with refped: to truth. 
 
 Further ftill : though all things fhould efpcciaHy fubfift in this manner, and 
 yet not in this manner, yet the more and the lefs are inherent in the nature 
 of things. For we do not fay that two things and three things are fimilarly 
 even ; nor does he fimilarly affert an untruth, who fays, that four things are 
 five, as he who affirms that a thoufand things are five. If, therefore, not fimi- 
 larly, it is evident that one violates the truth lefs than the other, and therefore 
 lays that which is more true. If, therefore that which is more true is nearer 
 to the truth, there will indeed be fomething true, to which that which is more 
 true is nearer. And, although nothing fhould be true, yet at leaft, as it ap- 
 pears, there is fomething which is more firm and more true : and thus we 
 ihall be liberated from that intemperate affertion, which prevents us from de- 
 fining any thing by our dianoecic part. 
 
 CHAP. V. 
 
 The do£lrine of Protagoras originates alfofrom the fame opinion ; and, in 
 a fimilar manner, it is neceflary that both thefe fliould either be, or fliould 
 not be. For, if all things of which we form an opinion, and which appear 
 to be, are true, it is neceflary that all things, at the fame time, fliould be both 
 true and falfe. For many apprehend things contrary to each other, and think 
 that thofe who do not entertain the fame opinions with themfelves are de- 
 ceived. So that it is neceflary that the fame thing fliould both be and not 
 be. And if this be the cafe, it is neceflary that every thing which is the 
 fubjedl of opinion fliould be true: for, both thofe who afliert that which 
 is falfe, and thofe who fpeak the truth, opine things oppofite to each 
 
 * 'TJiuf xai ovK i/Jiif is omitted in the printed text, but appears neceflary from the comment of 
 Alexander Aphrodifienfis. 
 
 otheto
 
 Book IV. ARISTOTLE'S METAPHYSICS. 99 
 
 Other. If, therefore, things fubfid; in this manner, the aflertlons of all men 
 will be true. That both thefe doftrines, therefore, originate from the fame 
 conceptions is evident. But the fame mode of reply muft not be adopted to 
 all fuch ; for fome require perluafion, but others force : for the ignorance of 
 thofe who think in this manner, in confequcnce of doubting, may be eafily 
 cured ; fince here the reply is not diredled to their difcourfe, but to their 
 dianoetic part. But the cure of fuch as fpeak in this manner for the fake of 
 difputation, is the confutation of that difcourfe which confifts In voice, and 
 of that which confifts in names. 
 
 This opinion, however, in thofe that doubt, originated from fenfibles ; 
 I mean, that contradidories and contraries fubfift together j and this, in 
 confequence of perceiving contraries generated from the fame thing. If, 
 therefore, it is impoflible for that whicli is not, to be generated, a thing ac- 
 cording to them will pre-exift as both contraries at once. Juft as Anaxagoras 
 and Deiuocritus fay that every thing was mingled in every thing. For De- 
 mocritus alio afff rts that there is a vacuum and a plenum in every part, and 
 that one of thefe is being and the other non-being. To thofe, therefore, who 
 from thefe things for n this opinion, we fay that in one refpedl they fpeak 
 rightly, and in another ignorantly. For being is pr^-dicated in a two-fold 
 refpedl ; fo that it is partly poflil)Ie for fomething to be generated from non- 
 being, and partly not ; and for the fame thing to be at the fame time being 
 and non-being, yet not according to the fame : for it is poffible that contra- 
 ries may at the fame time be the fame thing in capacity, but not in encgy. 
 
 Further flill : it is requifite they fhould confider that there is another ejfence 
 of things to which neither motion, nor corruption, nor, in Jloort, generation be- 
 longs. In a fimilar m inner too, the truth refpefting the phenomena was ob- 
 tained by fome from fenfibles. However, they ought not to think it fit that 
 truth fliould be judged either by multitude or paucity. But the fame t ling 
 to the tafte of fome appears to be fweet, but to that of others bitter. So that: 
 if all men were difeafed, or all men were infane, except two or three who 
 were well, and in pofTeffion of intelledl, thefe two or three might appear to 
 be difeafed and to be infane, but this would not be the cafe with the others. 
 
 Again : to many other animals, as well as to us, contrarief. appear to take 
 place refpedting the fame things ; and to each of us, with refpedl to himfelf, 
 things do not always appear the fame, according to fenfe. It is, therefore, 
 immanifeft which of thefe is true or falfe : for no one of thefe is more true 
 
 O 2 than • 
 
 /
 
 100 ARISTOTLE'S METAPHYSICS. Book lYc 
 
 than the other, but, with refpecfl to truth, they are fimilarly affeded. Hence 
 Democritus fays that either nothing is true, or that it is to us immanifeft. 
 In fhcrt, becaufe they are of opinion that prudence is fenfe, and that this is 
 alteration, they fay that whatever is fenfibly apparent is neceflarily true. 
 For, from hence, Enipedocles, Democritus, and, as I may fay, each of the 
 red, became obnoxious to fuch like opinions. For Empedocles fays, that ia 
 confequence of habit being changed, prudence alfo is changed. 
 
 " Man's counfel varies with the prtfcnt time." 
 
 And in another place he fays, 
 
 " Men, as their bodies change, in wifdom change *.'* 
 
 Parmenides alfo fpeaks after the fame manner: " As is the temperament oF 
 the flexible members in every one, fuch alfo is the intelle^l which is prefent 
 ■to men. For the nature of the members is entirely the fame with that which 
 energlfes prudeiit'udly f in all mankind. For that which is more than this is 
 an iiuellei2:ual conception." Anaxagoras alfo is reported by fome of his aflb- 
 ciates to have fald that things were fuch to men, as they apprehended them 
 to be. They fay, too, that Homer appears to have been of this opinion, who 
 affirms of Hedtor, when he was infane through a wound, " that he was wife 
 in an unufual manner J;''' as if thofe that are infane were prudent, but not 
 in the fame manner as thofe that poiTefs a found mind. It is evident, there- 
 fore, that if both the mentally fane and the infane are wife, things alfo fubfill 
 in this manner, and yet not in this manner. But that which refults from 
 this conclufion is moft grievous : for, if thofe who in the higheft degree per- 
 ceive that truth, which it is pofTible to perceive § (but thefe are they who in 
 
 * Empedocles d )ubtlefs meant to confine this aflertion to tlie multitude, who are in poflefTion 
 of no higher ivifckm tlian that of opinion. 
 
 t Parmenides too, I have no douhtj faid this with a view to the multitude whofe prudence 
 is not of an intellecluul nature, but is fokly converfant with the good of the mere animal life. 
 Hence he adds, Tliat which is more than this, /. e. wliith is beyond this, is an inttllcBual cou- 
 ctplion, 
 
 X KektSlJsi a^^of/;o^£C^Ta. 
 
 § If, therefore, according to Ariftotle, Parmenides, and Empedocles, and, in (hort, the Py- 
 thagor3eans and Plato, " perceived in the highrjl degree that truth which it is pofTible to per- 
 .ccive," it is plain that his objections to their doilrines are pretended, and not real. 
 
 the
 
 BvoKlV. ARISTOTLE'S MET APHYSICS. 101 
 
 t^3e blghejl degree Invejligate and love truth). If thefe entertain fuch opinions, 
 and aflerr fuch things refpedllng truth, mud not thofe defpond who endeavour 
 to philofophlfc ? For to invefligate truth will be to purfue things vohmt. 
 But this opinion was produced in them by fpeculatiug the truth of beings ; 
 and they apprehended that beings were alone things fenfible. In thefe, how- 
 ever, much of the nature of the indefinite is inherent, an I of that which 
 h indefinitely being, as we have ah^eady obferved. Htnce they fpeak pro- 
 bably, but do not aflert the truth ; for thus it is more becotning to fpeak, 
 than as Epicharmus fpeaks when writing againftXenophanes. 
 
 Further ftill : when they perceived that the whole of this vifible nature 
 v/as moved, and that nothing could be verified of that v/hlch Is changed, they 
 concluded that it was impofiible to affert any thing with tnuh of that which 
 13 in every refpe£l changed. For from this conception that opinion origl- 
 Eated, which ftands at the fummit of thofe we have mentioned, viz. the opinion 
 of thofe who profefs to Heraclitize, and which v/as adopted by Cratylus, who 
 at length thought that it was not proper to fpeak, but only moved his finger, 
 and reproved Heraclitus for afTerting that it was not poflible to enter twice 
 into the fame river. For he thought it was not poflible to do this once. But 
 to this aflertion we fay, that to be of opinion tliat a thing which is clianged 
 is not when it change?, poflefles fome truth, although it is attended with am- 
 biguity. For that which cafts away, polfefles fomething of that which it 
 calls away ; and of that which is in generation, or becoming to be, it is ne- 
 ceflary that fomething Ihould now be. In fhort, if it be corrupted, fome- 
 thing will fubfift ; and if it be generated, it is necefllu-y rliat the thing from 
 which it is made, and by which it was generated, fliould fubfift, and that 
 this fliould not be the cafe ad infinitum. Flowever, omitting thefe things, we 
 fay that it is not the fame thing to be tranfmuted according to quantity and 
 according to quality. Let it, therefore, be granted, that a thing docs not abide 
 according to quantity, yet we know that all things abide according to form. 
 
 Again : it is proper to reprove thofe who think in this manner, becaufe, 
 though they perceived this flux and mutation hut In the fmaller number of 
 feufibles, yet they entertained fimilar opinions refpeding all heaven. For 
 that with which we arefurrounded^ or the place of generation^ alone * fubffls 
 in continual generation and corruption ; but tins place, on account of its exi- 
 
 * According to Ariftotle, the heavens and heavenly bodies are divine and perpetual. See on 
 A\\& fubjecl his books De Ccelo. 
 
 lity.
 
 102 ARISTOTLE'S METAPHYSICS. Book IV, 
 
 lity, is, as I may fay, no part of the univerfe. So that it would have been 
 more equitable to have drawn a conclufion from the greater number refpedt- 
 ing the fewer, than to have condemned the former on account of the latter. 
 Further ftlll : it is evident that we may urge the fame things againft thefe 
 men, as were formerly urged by us. For we muft demonftrate, and perfuade 
 them, that there is a certain immoveable nature ; though it happens to thofe 
 who aflert that a thing is and is not at the fame time, that they muft rather 
 fay that all things are at reft than in motion. For, on this hypothefis, there 
 will not be any thing into which a thing may be changed ; for all things will 
 fubfift in all. 
 
 But, with refped to truth, we muft evince that not every thing which is 
 apparent is true. For, in the iirft place, it does not follow, that, if fenfe is 
 not deceived in the proper objeds of its perception, this is alfo true of the 
 phantafy ; for phantafy is not the fame with fenfe. In the next place, it is 
 worthy of admiration, if they doubt whether magnitudes are fo great and 
 colours fuch as they appear to thofe who are at a diftance, or fo great and 
 fuch as they appear to thofe who are near ; and whether they are fuch as 
 they appear to thofe in health, or fuch as they appear to the difeafed : and 
 with refpedt to weight, whether thofe things are heavier which are judged to 
 be fo by the weak, or thofe which appear to be fo to the ftrong ; and laftly, 
 with refpedt to truth, whether fuch things are true as appear to thofe who 
 are afleep, or fuch as appear to thofe who are awake : for it is evident they 
 do not think that things are fuch as they appear to the former of thefe. For 
 no one, if when in Libya he fhould dream that he was at Athens, would 
 when he awoke go to the Odeon *. Further ftill : with refpe£t to the future, 
 as Plato alfo obfervesf, the opinion of a phyfician and one unflcilled in 
 medicine is not fimilarly certain, as to one who hereafter will or will not be 
 well. 
 
 Again : with refpeil to the fenfes themfelves, the perception of a foreign 
 is not equally certain with that cidi proper objed, nor of that which is remote 
 wLth that which is near. But with refped to colour, the fight judges, and 
 not the tafte ; and of juices the tafte, and not the fight ; none of which fenfes 
 affirms that any circumftance fubfifts in a particular manner, and yet does not 
 
 • The Odeon, fays Alexander, is a certain part of the theatre at Athens, which is now called 
 ©v/UE^n, or the Scne. 
 
 i In his Protagoras. 
 
 fo
 
 Book IV. A R I S T O T L E'S M E T A P H Y S I C S. 103 
 
 fo fubfift, at ihcfiViie time, about the fame thing. But neither do the fenfes 
 doubt refpeding things to which they are paffive, at a different time, but re- 
 fpeding that to which the paffion happens. I fay, for inftance, the fame 
 wine may to the fame perfon at one time appear to be fweet, and at another 
 time not fweet, either becaufe the wine itfelf is chanfred, or the or^'-an of 
 tafte. But that which is fweet, when it is fo, Is never changed, but fweetnefs 
 is always truly affirmed of it: and that which will be fweet, neceffarily 
 fubfifts in this manner, though this conclufion is fubverted by all thefe ailer- 
 tions. For, as they affirm that there is no efience of any thing, they alfo 
 take away the neceffary fubfiftence of any thing. For that which is neceffary 
 does not admit of a various fubfiftence. So that, if any thing fubfifts from 
 neceflity, it will not fubfift thus, and yet not thus. And, in fhort, if that 
 which is fenfible alone fubfifts, nothing will be, if animated natures have no 
 exiftence ; for fenfe will not be. And if fenfe is not, it is perhaps true that 
 there are no fuch things as fenfible objedls, nor perceptions of fenfe ; for 
 fenfe is a paffion of a fentient nature. But that thcfubjeHs themfelves fhould 
 not fubfift which produce fenfe, even though fenfe were not, is impoffible. 
 For fenfe itfelf is not of itfelf ; but there is fomething elfe befides fenfe, which 
 neceffarily is prior to fenfe. For that which moves is by nature prior to that 
 which is moved ; nor will this be lefs the cafe, though thefe fame things are 
 referred to each other. 
 
 CHAP. VI. 
 
 There are fome, however, who doubt, both among thofe who are per- 
 fuaded of the truth of thefe affertions, and among thofe who are alone the 
 authors of fuch affertions. For they inquire who it is that judges of a maa 
 in health, and, in fhort, who it is that judges rightly refpeding every parti- 
 cular. Doubts of this kind are, however, fimilar to the doubt whether we 
 now fleep, or are awake: for all fuch doubts as thefe amount to the fame 
 thing. For the authors of them think fit to inveftigate the reafon and caufe 
 of all things ; fince they explore the principle, and exped to obtain it through 
 demonftration. However, that they are not perfuaded is evident from their 
 adions : but, as we have faid, this is the error of thefe men ; for they invefti- 
 gate the principle of things of which there is no principle. For the prin- 
 ciple of demonftration is not demonftration. Thefe men, therefore, may 
 
 eafily 
 
 /
 
 10-1 ARI STOTLE'S MET A FH YS 1 C S. Book IV. 
 
 eafily be perfLiacled of this ; for it is not difficult to apprehend. But thofe 
 who alone invefligate force in -words, inveftigate that which is impoffible : for, 
 at the fame time, they diredly aflert things contrary, deeming it fit to affirm the 
 contrary. However, if all things are not relatives, but feme fubfift themfelves 
 by themfelves, every thing which appears will not be true : for every thing 
 which appears is apparent to fome one. So that he who aflerts that all ap- 
 pearances are trae, makes all beings to be relatives. On which account it is 
 requifite to obferve to thofe who fearch for force in argument, and with this 
 view engage in difputation, that not that which appears is true *, but, it fhould 
 be added, that it is true to him to whom it appears to be fo, and when it ap- 
 pears, and fo far as it appears, and according to the manner in which it ap- 
 pears. But if they difpute, indeed, yet not in this way, it happens that they 
 rapidly aflert things contrary. For the fame thing may indeed to the fight 
 .nppear to be honey, but not to the tafte : and, as we have two eyes, if they 
 happen to be diffimilar, the fame things will not appear to be the fame to each 
 fight. As to thofe who, for the reafons formerly adduced, contend for the truth 
 of that which appears, and on this account affirm that all things are fimilarly 
 falfe and true, it is eafy to reply, that neither do the fame things appear to all 
 men, nor do the fame things always appear the fame to the fame perfon, but 
 frequently contraries appear at the fame time. For that which appears to the 
 fight to be one, to the touch appears to be many, when different fingers are 
 placed on it in fucceffion. Nor yet do the fame things appear to the fame fenfe, 
 and according to the fame, and. in a fimilar m.anner, and in the fame time. So 
 that this will be true. But, perhaps in confequence of this, it is neceffary to fay 
 to thofe who fpeak, not through doubting, but for ihe fake of difcourfe, that 
 this is not fimply true, but true to this or that perfon. And, as it was before 
 obferved, it is neceffary to make all things relatives, and refer them to opinion 
 and fenfe ; fo that neither was any thing, nor will there be any thing, if there 
 were no antecedent opinion of things. But if there was, or will be any thing, 
 it is evident that all things will not be referred to opinion. 
 
 Again : if a thing has a relative fubfiftence, it is either predicated as one to 
 one, or with relation to that which is definite ; and if the fame thing is both 
 half and equal, it is referred to thefe, but the equal is not referred to the double. 
 And with refpeit to opinion, if man is the fame with that which is the objedt 
 
 * A^TjSes is omitted in the text. 
 
 of
 
 Book IV. A R I S T O T L E ' S W E T A P H Y S I C S. 105 
 
 of opinion, tiiat which opines is not man, but that which is the obje£l of opi- 
 nion. But, if every tiling fubfifts with relation to that which opines, that 
 which opines will be infinite in fpecies. That the opinion, therefore, is the 
 moft firm of all things, viz. that oppofite aflertlons are not at the fame time 
 true, and what happens to thofe who contend that they are true, and why they 
 fpeak in this manner, has been fufficlently fhown by us. But, fince it is im- 
 poflible that contradidlion fliould at the fame time be true refpeding the fame 
 thing, it is evident that neither can contraries fubfift at the fdme time in the 
 fame thing. For the other of contraries is no lefs privation : but the priva- 
 tion of effence is a negation from a certain definite genus. If, therefore, that 
 it is impoffible at the fame time to affirm and deny is true, it is alfo impoffible 
 that contraries can at the fame time be inherent in a fubj^ft ; but either both 
 muft be inherent partially, or the one partially and the other fimply. 
 
 CHAP. vir. 
 
 Bltt neither is it poffible that any thing can fubfift between contradiilories ; 
 for it is neceffary either to affirm or deny one thing of every thing which is 
 one. This, however, will be manifeft, by firft of all defining what the true 
 is, and what tlie falfe. For to fay that being is not, or that that which is not 
 is, is falfe : but to affirm that being is, and that non-being is not, is true. So 
 that he who aflerts that this medium is or is not, afltrts that which is true, 
 or that which is falfe ; but he neither aflerts of being, nor of non-being, that 
 it is not or is. Again, if there is fomething between contradidlories, it will 
 either be, as is a dark colour between black and white, or as that which is 
 neither man nor horfe, between man and horfe. If, therefore, it fubfifts in 
 this manner, it will not be changed : for it will either be changed from that 
 which is not good into good, or from this into not good. But now it always 
 appears to take place : for there is no mutation except to things oppofite, and 
 thofe which fubfift between. But if there be a medium, thus alfo there will 
 be fome mutation or generation into white, not from that which is not white. 
 But this does not appear to be the cafe. 
 
 Further ftill : the dianoetic power of the foul either affirms or denies every 
 thing dianoetic and intelligible. But this is evident from definition, when it 
 afl'erts that which is true, or that which is falfe: for, when it compofes in t/jis 
 particular manner, affirming or denying, it aflerts the truth ; but when in (hat, 
 
 P it
 
 106 ARISTOTLE'S METAPHYSICS. Book TV. 
 
 it aflerts that which is falfe. Befides, this medium ought to be in all contra- 
 diflions, unlefs it is introduced for the fake of argument. So that neither will 
 any one aflert that which is true, nor yet that which is not true : and there 
 will be fomething * befides being and non-being. Hence there will be a 
 certain mutation befides generation and corruption. Further fllll : this me- 
 dium will alfo be in thofe genera, in which negation introduces its contrary. 
 As, for inftance, in numbers there will be that which is neither an even nor an 
 odd number ; but that this is impoflible, is evident from definition. Again : 
 there will be a progreffion to infinity, and beings will not only be fefquialter, 
 but even more than this : for, again, fomething will be found, of which it will 
 be poffible to deny the affirmation and negation of the medium of the former 
 contradidion : for the effence of it will be fomething elfe. 
 
 Further ftlU : when any one, being afked if a thing is white, fays it is not", 
 he denies nothing elfe than being ; but not to be is negation. But this origi- 
 nated trom the fame fource as the other paradoxical opinions : for fome, when 
 they are not able to folve the contentious arguments, yielding to reafon, they 
 fay that the fyllogiftic conclufion is true. Some, therefore, fpeak in this man- 
 ner throvigh this caufe ; but others, becaufe they inveftigate the reafon of all 
 things. But the principle to all thefe is to be affumed from definition ; and 
 definition is produced in confequence of its being neceflary that they fhould 
 fignify fomething : for a fentence, the name of which is a fign or fignifica- 
 tion, is the definition of a thing. The dodrine of Hcraclitus, indeed, when 
 he aOerts that all things both are and are not, feems to make all things true. 
 But Anaxagoras, when he afferts that there is a certain medium in contradic- 
 tions, makes all things to be falfe. For, when they are mingled, the mixture 
 is neither good, nor yet not good ; fo that it is not poffible to fpeak truly of 
 any thing. 
 
 CHAP. VIII. 
 
 These things being determined, it is evident that things which are pre- 
 dicated in one way only, and alfo that thofe which are predicated of all 
 things, cannot fubfift as fome fay they fubfift. For fome aflert that nothing is 
 true : for, fay they, nothing hinders but that all things may fubfift in fuch 
 a manner, as that the diameter of a fquare may be commenfurable with its 
 
 * Ti is omitted in the printed text, 
 
 fide.
 
 Book IV. A R I S T O T L E' S M E T A P H Y S I C S. 107 
 
 fide. But, according to others, all things are true. For their affertlons are 
 nearly the fame as thoie of Heraclitus ; fince he who fays that all things are 
 true, and that all things are falfe, feparately makes each of thofe aflertions : i'o 
 that if thofe are impoIFible, thefe alfo muft be impoffible. 
 
 Further ftill : it is evident that they are contradictions, which cannot pofli- 
 b'y be at the fame time true, or at the fame time falfe, though, from what 
 has been faid, it would rather appear that both are falfe *. But in all fuch 
 alRrtions it is neceffary to require, as we have before obferved, not that 
 a thing fhould be, or fiiould not be, but that it fliould fignify fomething; fo 
 that we muft difpute from definition, by affluning what the true or the falfe 
 fignines. But, if the true is nothing elfe than to fay that a thing which thus 
 fubfifts, does thus fubfift, and the falfe is nothing elfe than to deny that a 
 thing fubfifts in a certain manner, when it does thus fubfift, it is impoft"ib!e 
 that all things fhould be falfe : for it is neceffary that the other part of the 
 contradiflion fiiould be true. Further ftiil : if affirmation or nesation muft 
 ncceffarily take place refpefting every thing, it is impoffible that both fliould 
 be falfe : for the other part of the contradidion is falfe. But the common 
 faying applies to all fuch aflertions as thefe, viz. that they fubvert themfelves. 
 For he who fays that all things are true, makes alfo the contrary aflertion 
 true ; fo that he makes his own affertion not to be true. For the contrary 
 affertion fays that it is not true. But he who fays that all things are falfe, 
 fays alfo that his own afl'ertion is falfe. But, if they make an exception, the 
 one of the contrary affertion as alone not true, but the other of his own 
 as alone not falfe, neverthelefs it happens that they muft demand infinite 
 true and falfe affertlons. For he who fays that a true affertion is true, 
 affents to this, that it is true; but this will proceed to infinity y. It is, how- 
 ever, 
 
 * Aix^ori^a ^ijh eivM (hould be added in this place, as Is evident from the text of Alexander, 
 f What Ariftotle, with his ufual pregnant brevity, aflerts in tliis place, appears to be as 
 follows : — If the dogma of thofe be admitted who afiert that all things are true, not that afler- 
 tion alone will be falfe, that not all things are true, but that alfo which affinns it to be trm that 
 not all things are true, which is different from that which finiply fays that not all things are 
 true. Nor will this alone be falfe, but that alfo which aflirms it is true to aflert that the 
 aflertion is true which fays it is true that not all things are true, whicli, w verthtlefs, is differ- 
 ent from the former ; and fo, by the addition of the true, it may be demon (Irated, by him who 
 fays that one aflertion alone is falfe, that there are infinite falfe affert ons. 
 
 i3ut there may be a compofition of truths of this kind to infinity. Thus, on the hypothefis 
 
 Ta th.-it
 
 108 A RISTOTLE'S MET APHYSICS. Book IV. 
 
 ever, evident, that neither thofe who fay that all things are quiefcent afTert 
 the truth ; nor thofe who fay that all things are in motion *. For, if all 
 things are at reft, the fame things will always be true and falfe : but this ap- 
 pears to be changed. For he who fays this, once was not, and again will not 
 be. But if all things are moved, nothing will be true. All things, therefore, 
 will be falfe: but it has been demonftrate<l that this is impoffible. Again: 
 it is neceflary that being fliould be changed : for mutation is from fomething 
 into fomething. But neither are all things fometimes at reft: and fometimes 
 in motion ; fo that there is not that which is always moved, and that which 
 is always immoveable. For there is fomething which always moves things 
 that are moved ; and the firft; mover is itfelf immoveable. 
 
 that the afTertion is true that all things are true, it follows that the aflertion is falfe that not 
 every aflertion is true. Likewife, if all things are true, the aflertion is true that not all things 
 are true. Alfo this is falfe : it is true to fay that the aflertion is true, that it is true to fay that 
 not all things are true : and this will take place ad wjinituni. In like manner, on the hypothefis 
 that all aflertions are falfe, there will be infinite true aflertions, that, being excepted, ivhichjays 
 that all njprtions are falfe. For thus, not only that aflertion will be true that all aflertions are 
 falfe, but alfo that which aflirins it to be true to fay that all are falfe. For, unlcfs this is true, 
 that will not be true which preceded this ; but alfo that would be true, that the aflertion is true 
 which affirms it to be true that all things are falfe ; and this will be the cafe infinitely. 
 
 * According to Alexander, thefe words, "It is, however, evident, that neither thofe who fay 
 that all things are quiefcent aflert the truth, nor thofe who fay that all things are in motion," are 
 not found in fome copies, becaufe, fays he, they feem to belong to Phyfics. However, he adds, 
 they do not appear to be altogether foreign from the purpofe : for if it is admitted, that neither 
 all things are true, nor all things falfe, it follows, that neither thofe who fay that all things are 
 ijuiefcent aflert the truth, nor thofe who fay that all things are moved. 
 
 ARISTOTLE'S
 
 ARISTOTLE'S METAPHYSICS. 
 
 BOOK V*. 
 
 CHAP. I. 
 
 \'V I T H refped: to principle, one kind is faid to be that whence fome- 
 thing is firft moved ; as, for inftance, the principle of length, and of a way • 
 for the principle is from hence. On the contrary, another principle is that 
 whence any thing becomes the beft ; as, for inftance, with refpefl; to difci- 
 pline, we muft fometimes begin, not from the firft, and the principle of a 
 thing, but whence learning may he moft eafily acquired. Another principle 
 is that whence, from being inherent, a thing is firft produced ; as of a ihip 
 the keel, of a ho' fe the foundation ; and of animals, according to fome the 
 heart, according to others the brain, and according to others fomething elie of 
 this kind. But another principle is that whence, not being inherent, a thing 
 is firft produced, and whence motion and mutation are firft naturally adapted 
 to originate ; as an offspring from father and mother, and war from defama- 
 tion. 
 
 * Arlftotle has before infnrmed us that It is the bufinefs of the firft phllofopher to confider 
 being univerfally, and thole things which belong to beings in common. But things common to 
 being fo far as being, are fuch as all difciplines employ. Hence they are difcufled in the prefent 
 book. Let it be remembered too, that what vulgar dialedic infers by reafoning from probabi- 
 lities, the firft philofophy concludes fcientifically. 
 
 Another 
 
 /
 
 11§ ARISTOTLE'S METAPHYSICS. Book Y". 
 
 Another principle is that according to the free-will of which things ia 
 motion are moved, and mutable natures are changed, as princip^Jiiies, dynaf- 
 tles, kingdoms, and tyrannies in a city. Arts alfo are -called principles ; and 
 of thefe efpecially the mafter building arts. Further ftill : that uhence a 
 thing is firfl: known, is faid to be the principle of that thing ; as, for inftance, 
 hypothefes of demonllrations. Caufes too, are denominated, in as many ways 
 as principles; for all caufes are principles. It is common, therefore, to every 
 principle to be the firft w^hence a thing is either produced or known. But, of 
 thefe, fome have an internal, but others an external fubfiflence. Hence na- 
 ture is a principle, as is alfo an element, the dianoetic power, free-will, 
 elfence, and that for the fake of which a thing fubfifts. For good and the 
 ;bjeautiful ^ are to many things the principle both of knowledge and motion. 
 
 C HAP. IT, 
 
 Cause, in one refped. Is faid to be that from which, when Inherent, any 
 thing Is produced, as, for inftance, brafs of a ftatue, filver of a bowl, and the 
 kinds of thefe. In another refped, form and paradigm are caufes ; but in 
 this cafe they are formal caufes, and the kinds of thefe. Thus, for inftance, 
 the ratio of two to one, is the caufe of the diapafon : and, in fhort, number, 
 and the parts in a ratio, belong to this order of caufe. Further ftill : caufe is 
 that whence the firft principle of mutation or reft oinginates : thus, for in- 
 ftance, he who confuits is a caufe, and a father of his offspring ; and, in fhort, 
 he who makes of that which is made ; and that which has the power of 
 changing of that which is changed. 
 
 Again : caufe is as the end. But this ranks as that for the fake of which 
 other things fubfift ; as, for inftance, health of walking. For, on vv hat ac- 
 count does a man walk ? We fay, That he may obtain health ; and, thus fay- 
 ing, we think that we have afligned the caufe. Such things alfo are caufes, 
 as fubfift between another thing which moves, and the end. Thus, for in- 
 ftance, the caufe of health is either attenuation, or purgation, or medicine, or 
 inftruments. For all thefe are for the fake of the end. But they differ 
 
 * In the printed text it is to xtxkov, the evil; but it appears from the comment of Alexander, 
 ■that we (hould read to xa\ov, the beautiftil. Indeed, it appears that to xa*o; was found in fon-.e 
 copies in Alexander's time ; but I prefer to «*?,ov. 
 
 from
 
 EookV. ARISTOTLE'S METAPHYSICS. IH 
 
 from each otlier in this, that fome of them are as inftruments, hut others as 
 works. Caiifes, therefore, are nearly denominated in fo many ways. Bur, 
 fmce caufes are predicated multifarioufly, it happens that there are many 
 caufes of the fame thing, not according to accident ; as, of a ftatue, both the 
 ftatuary's art, and the brafs, and this, not from any thing elfe, but fo far as it 
 is a ftatue : yet tiiis does not take place after the fame manner, but the brafs is 
 as matter, and art as that whence motion originates. Some things abb are 
 mutually caufes with refpe£l to each other ; as labor is the caufe of a good 
 habit of body, and a good habit of body, of labor; not, however, after the 
 fame manner, but the one is as the end, and the other as the principle, of 
 motion. 
 
 Further ftill : the fame thing is fometimes the caufe of contraries : for that 
 which when prefent is the caufe of fome particular thing, the fame when ab- 
 fent, is, we fay, fometimes the caufe of the contrary. Thus, the abfence of 
 the pilot is the caufe of the deftru<5tion of the fhip, whofe prefence was the 
 caufe of its prefervation. But both the prefence and the abfence of the pilot 
 are as moving caufes. All the caufes, however, that we have now enume- 
 rated fall in o four moft manifeft modes. For the elements of fyllables, and 
 the matter of things fafhioned by art, alfo fire and earth, and every thing elfe 
 of this kind belonging to bodies, together with the parts of a whole, and the 
 hypotheles of a conclufion, are caufes, as things from which others are pro- 
 duced. But of thefe, fome are as a fubje£t, as, for inftance, parts ; but others, 
 as the formal caufe, fuch as the whole, compofition, and form. But feed, the 
 phyfician, he who confults, and,, in ihort, the maker of any thing, are all of 
 of them caufes, whence the principle of mutation or ftability originates; but 
 the reft: are as the end, and the good of other thiogs. For that for the fake 
 of which other things fubfift, wills to be the beft, and the end of others. But 
 there is no difference, whether it be called real or apparent good. There 
 are, therefore fo many fpecies of caufes. But the modes of caufes are many 
 in number. They may, however, be fummed up into a lefs numerous mul- 
 titude ; for caufes are predicated in a manifold refpedt ; and of thofe which 
 are of the fame fpecies, one is prior and another pofterlor ; as, for inftance, of 
 health, the phyfician, and the artificer ; and, of the diapafon, the double, and 
 number ; and always thofe things which comprehend any thing of particu- 
 lars. 
 
 Farther ftill : caufe is predicated as accident, and the genera of thefe ; as, 
 
 for
 
 112 ARISTOTLE'S METAPHYSICS. EookV, 
 
 for inftance, of a Ratue, Polycletus is in one refpe£l the caufe, and in another 
 refpeft the ftatuary, becaufe it happens to the ftatuary to be Polycletus: and 
 things wliich co iiprehend accident; as man is the caufe of a ftatue, or in 
 fhort animal, becaufe Polycletus is a man, and man is an animal. Of 
 accidents alfo, one h more remote and more proximate than another; as, for 
 inftance, if that wliich is white, and a mufician, fhould be faid to be the 
 caufe of a ftatue, and not only Polycletus, or a man. But, befides all thofe 
 which are propeily predicated, and thofe which are predicated according to 
 accident, fome caufes arc denominated as endued with capacity, but others 
 as energetic : thus the builder is the caufe of creeling the hcufe, or the 
 builder confidered as building. The like takes place alfo in efieds ; as, for 
 inftance, of this ftatue, or of a ftatue fimply, or in fhort (f an image; or of 
 this brafs, or brafs fimply, or univerfally of matter : and in a fimilar manner 
 with refpeft to accidents. Further ftill : both thefe and thofe are predicated 
 conjointly ; as, for inftance, not Polycletus, nor the ftatuary, but Polycletus 
 the ftatuary. At the fame time, all thefe with refpet£l to multitude are fix ; 
 but they are predicated in a twofold refpe6l : for they are predicated either 
 as that which is particular, or as genus, or as accident, or as the genus of 
 accidrn'', or as thefe conjoined, or according to capacity, or fimply confi- 
 dered, or, laftly, as energiling. But they fo far differ, that caufes in energy, 
 particulars, and thofe things of which they are the caufes, iiibfift together and 
 together ceafe to be ; as, for inftance, this phyfician with this convalefcent, and 
 this builder with this building. But this is not always the cafe with caufes 
 in capacity : for the houfe and the builder are not corrupted together. 
 
 CHAP. III. 
 
 Element is faid to be that from which, being primarily inherent and indi- 
 vifible in fpecies, fomething is compofcd. Thus, for inftance, the elements of 
 fpeech are thofe things from which fpeech is compofed, and into wliich it is 
 ultimately divided : but thefe elements are no longer divided into other words 
 diff"erent from themfelves in fpecies ; but, if it were poflible for them to be di- 
 vided, the parts would be of a fimilar fpecies. Thus the parts of water are 
 water, but the parts of a fyllable are not fyllables. In like manner the antients 
 called thofe the elements of bodies, into which bodies themfelves are ulti- 
 mately divided, but which are no longer divifiblc intoother bodies fpeclfically 
 
 different :
 
 3oo».V.. ARISTOTLE'S METATHYSICS. 11» 
 
 xliHerent : and whether there is one, or many of this kind, they call thefe ele- 
 ments. The elements of diagrams and demonftrations are denominated in a 
 fimilar manner. For fiift demonftrations, and thofe which are inherent in many 
 demonftrations, are fl»id to be the elements of demonftrations. But fuch as 
 thefe are fzrft fyllogifms compofed of three terms through one medium. 
 Hence alfo, metaphorically fpeaking, they call that an element, which, being 
 one and fmali, is ufeful for many purpofes. On which account, the fimple, 
 the fmall, and the indivilible, are liiid to be elements. Hence it comes to pafs 
 that things eminently univerfal are elements ; becaufc each of them being one 
 and fimple, it is inherent in rrlany things, or in all things, or in the greater 
 part of all things. 'The one alfo and a point to fome appear to be principles. 
 Since, therefore, thofe things ■which are called genera are univerfals and indi- 
 vifibles (for there is one definition of them), fome denominate genera them- 
 felves elements, and more fo than difference, becaufe genus is more univerfal. 
 For genus follows that to which difference is prefent ; but that to which genus 
 is prefent is not always attended with difference. But it is common to all 
 things, for that to be tlie element of any thing, which firft fubiifts in that 
 thing. 
 
 CHAP. IV. 
 
 Nature, in one refpefl, is faid to be the generation of things rifing Into 
 being ; as if any one, extending his voice, fhould pronounce the letter u. But, 
 in another refped;, that from which, when primarily inexiftent *, that which 
 is generated is generated. Further ftill : nature is that whence the firft 
 motion arifesf, in each of the things which fubfift naturally, fo far as a thing 
 is that which it is. But things are faid to be rifing into being, which receive 
 increafe through another thing by contadt, or being connafcent with it ; as 
 embryos. The being connafcent, hovirever, differs from contad: : for in the 
 latter nothing befides contact is neceffary ; but in things connafcent, there is a 
 certain one the fame in both, which makes them grow together, inftead of 
 merely touching each other, and caufes them to be one according to continu- 
 ity and quantity, but not according to quality. Again : Nature is faid to be 
 
 * i. e. The fubjeft and matter of a thing have the relation of nature. 
 t t> e. Natural form. 
 
 Q_ that
 
 T14 A R I S T O T L E • S M E T A P H Y S r C S: Book V. 
 
 that from the power of which, when It Is primarily inordinate * and immu- 
 table, fomerhing of natural productions either is, or is generated: as brafs is 
 faid to be the nature of a ftatue, and of brazen furniture ; wood, of fuch things 
 as are wooden ; and in a fimilar manner with refped to other things. For 
 each is from thefe, the firft matter remaining unchanged : for, after this man- 
 ner, they fay that the elements of things which fubfift naturally, are nature; 
 fome aflerting that this is fire, others that it is earth, others that it is air, 
 others again, that is water, and others that it is fomething elfe of this kind. 
 There are alfo thofe who aOcrt that nature is fome of thefe ; and there are 
 others who contend that it is all thefe. 
 
 Further ftlU : in another refpe£l:, nature Is faid to be the effence of things 
 which fubfifi; naturally ; and in this fenfe it is underflood by thofe who aflert 
 that nature is the firft compofition, and by Empedocles, when he fays that 
 there Is not any nature of beings, but that there is a mixture alone, and per- 
 mutation of things mingled, and that this mingling Is denominated nature 
 by men. So that fuch things, as either are, or are generated by nature (that 
 already fubfifting from which, they are naturally adapted to be generated, or 
 to be), are not yet faid by us to poflefs nature, unlefs th£y have fpecies and' 
 form. Hence that fubfifts from nature which is compofed from both thefe, 
 fuch as animals, and the parts of animals. But nature is the firft matter; and 
 tliis in a twofold refped : for it is either that which is firft with relation to a 
 thing, or tliat which is fimply the firfl. Thus, for Inftance, of brazen works, the 
 brafs Is firft with refped to thofe works ; but water perhaps is (imply the firft, 
 if every thing which is capable of being liquefied is water. Alfo form and 
 effence : but form Is the end of generation. Hence, by a metaphor, every 
 effence, in Ihort, is called nature, becaufe nature is a certain effence. From 
 what has been faid^ therefore, the firil nature, and that which is properly fo 
 denominated, is the eflence of thofe things which poffefs in themfelves the 
 principle of motion, fo far as they are fuch things. For matter, from being 
 the recipient of this, is called nature. Generations alfo, and to be born, are 
 called nature, becaufe motions are from thefe. Nature alfo is the principle of 
 the motion of things which have a natural fubfiflence, this principle being ia 
 a certain refpedl inherent either in capacity or energy. 
 
 * i..c. The proximate matter of a thing. 
 
 CHAP.
 
 BoorV, AllISTOTLE'S METAPHYSICS. 115 
 
 CHAP. V. 
 
 That is called necessary, without which as a concaufe it is not poffible 
 to live. » Thus, for inftance, refpiration and nutriment are neceflary to an ani- 
 mal : for it is impoffible that an animal can fubfift without thefe. Alfo that 
 is neceffary, without which good cannot either be, or be produced, or a ceitain 
 evil repelled and exterminated. Thus, to drink a medical potion is neceflary 
 To the prevention of difeafe ; and to fail to iEgina, to receive a fum of money. 
 To the neceffary alfo belong the violent and violence. But this is that which 
 oppofes and impedes contrary to impulfe and free-will. For the violent is 
 called neceffary ; on which account it is painful ; as Evenus alfo fays — " For 
 every thing neccjfary is grievous." And violence is a certain neceility, as 
 Sophocles alfo afferts — 
 
 " But thus I aft, by violence compelled." 
 
 Indeed, neceffity very properly feems to be fomething which cannot be per- 
 fuaded : for it is contrary to the motion of free-will, and to the motion of the 
 reafoning power. 
 
 Again : we fay that a thing is neceffarily fo, which cannot fubfift in any 
 other manner: and, according to this acceptation of the neceffary, every 
 thing elfe which is neceffiry,in a certain refpedt, derives its appellation. For 
 the violent is called neceffary, becaufe he who is under the influence of 
 violence cannot either a£t or fuffer from impulfe, on account of a compelling 
 power ; that being as it were neceffary, through which a thing cannot fubfift 
 in any other manner. The like alfo takes place in the concaufes of living 
 and good. For, when it is not poffible, either to obtain good, or to live with- 
 out certain things, then thofe things are neceffary, and this caufe is a certain 
 neceffity. Further ftlU : demonftration is of things neceffary, becaufe that 
 which is demonftrated, if it is fimply demonftrated, cannot have a different 
 fiihfiftence. But the caufes of this, are things firft, which cannot fubfift in 
 any other manner, and ftom which the dernonftrative fyllogifm is compofed. 
 Some things, therefore, are neceffary from a caufe different from themfelves ; 
 but others arc neceffary from no caufe, fince other things fubfift from ne- 
 ceffity through thefe : fo that the firft and proper neceffary is that which Is 
 fimple: for this cannot have a manifold fubfiftence ; and therefore cannot 
 fu')fift varioufly. For, if this were admitted, it would fubfift manifoldly. If, 
 therefore, there are certain eternal and immoveable natures, there is nothing in 
 them violent, nothing contrary to nature. 
 
 0^2 CHAP.
 
 lie ARISTOTLE'S MET A PHY SI CS;- Book V. 
 
 ^ CHAP. \''I. 
 
 One, is partly denominated according to accident, and partly eflentially. 
 According to accident, indeed, as Gorifcus and a mufician, and Corilcus the 
 mufician. For it is the fame thing to fay that Gorifcus and the mufiGian are 
 one, as to fay, Gorifcus the mufician : alfo to fay, the mufician and the juft, 
 and the juft mufician Gorifcus. For all thefe are 'Called one, according to 
 accident: the juft, indeed, and the mufician, becaufe they happen to belong 
 to one effence ; but the mufician and Gorifcus, becaufe the one happens to 
 the other. In like manner, too, in a certain refpeit, the mufician Gorifcus is 
 one with Gorifcus ; becaufe in this fentence, one part of the whole fentence 
 happens to the other ; as, for inftance, the mufician to Gorifcus, and the mu- 
 fician Gorifcus to the juft Gorifcus, becaufe no one part of each happens to- 
 the fame one. For there is no difference whether the mufician happens ro 
 Gorifcus, or Gorifcus the juft to the mufician Gorifcus. In a finiilar manner, . 
 one will be denominated according to accident, though it fhould be predicated 
 of genus, or fome one of univerfal appellations j as if, for inftance man, and 
 man the mufician ftiould be faid to be the fixme. For thefe are one, either 
 becaufe to man who is one effence, the being a mufician is accidental, or be- 
 caufe both happen to fome one among the number of particulars, as, for in- 
 ftance, to Gorifcus. Yet both are not inherent after the fame manner, but 
 the one perhaps as genus and as in effence, but the other as habit, or the 
 participated property of effence. Such things, therefore, as are called one 
 according to accident, are after this manner fo denominated. 
 
 But of tilings which are denominated one effentiallyj fome are fo called 
 from their continuity, as a faggot, which is held together by a bond, and 
 pieces of wood by glue. Aline alfo, though it be curved, if it poffefles con- 
 tinuity, is called one ; as likewife each of the parts of the body, fuch as a leg 
 and an arm. But of thefe, thofe things are more one, which are continuous 
 by nature, than thofe which are continuous by art. But that is called con- 
 tinuous, the motion of which is elfentially one*, and which cannot be 
 Gtherwife. And the motion is one which is indivifible, and indivifible accord- 
 ing to time. But thofe things are effentially continuous which are not one 
 
 * Viz. The whole of which is moved at once; one part not heing qulcfcent while anol'ier 
 gart is. moved..
 
 BookV.. ARISTOTLE'S M E T A P H Y S I C Si 117 
 
 by contad. For, if you place pieces of wood fo as to touch each other, you 
 will not lay that thefe are one piece of wood, nor one body, nor any thin^j 
 elfe continuous. In fhort, therefore, thofe things which are continuous are 
 called one, although they may be curved, and ftill more fuch things as do not 
 poflefs curvature. Thus the leg or the thigh is more one than the leg and 
 foot together, becaufc it is poffible that there may not be one motion of the 
 leg and foot. And a llraight is more one than a curved line. But we fay 
 that a line which is curved, and has an angle, is both one and not one, be- 
 oaufe it is poffible that a part of it may be moved, without the whole being at 
 the fame time moved. But of a right line, a part and the whole are always 
 moved together ; and it is not poffible that one part of fuch a magnitude 
 fhould be at reft, while another part is moved. 
 
 Further ftill : after another manner a thing is faid to be one, viz. from 
 having its fabje£k indifferent with refpedl to form. But the fubjecl of thofe 
 things is indifferent, tha form of which is indivifible * according to fenfe. 
 And the fubjedl is ehher the firft or the laft. For wine is called one, and 
 wattr one, fo far as each is indivifible according to form. And all liquors 
 are called one, as oil, wine, and fuch things as are fufible, becaufe the ultimate 
 fuhje£l of all thefe is the fame ; for all thefe are water and air. Thofe things 
 alfo are called one, the genus of which is one differing by oppofite differences. 
 And all thefe are called one, becaufe the genus is one which is the fubjedl of 
 the differences. Thus, for inftance, horfe, man, and dog, are one certain 
 thing, becaufe all of them are animals, and after a certain fimilar manner o;/ff, 
 as is the cafe with things of which the matter is one. But thefe things are at 
 one time thus called one, but another time they are called the fame, from the 
 fuperior genus, when they are not the proximate, but the laft fpecies of genus. 
 Thus the ilbfceles and equilateral triangle poflefs one and the fame figure, 
 becaufe both are triangles, but not the fame triangles. Again : thofe things 
 are called one, the definition of one of which is indivifible with refpe£t to the 
 definition of another: for every definition is itfelf effentially divifible. Thus, 
 that which is incre.ifed, zvA that which is diminifhed, are one, becaufe the de- 
 finition is one : juft as of fuperficies which have length and breadth, the 
 definition of the form is one. In fliort, thofe things are efpecially one, the 
 intellectual apprehenfion of the form of which is indivifible, and which caa . 
 
 * ;'. e. Which is not cut into different fcnfibles. 
 t En is omitted in the text. 
 
 neither
 
 118 ARISTOTLE'S METAPHYSICS. Book V. 
 
 neither be leparated by time, nor place, nor definition. For, unlverfally, fuch 
 thinqs as have not divifion, fo far as they have not, are called one. Thus, for 
 inftance, if man, fo fjr as man, is without divifion, man is one ; and if anisnal, 
 fo far as. animal, is indivifible, animal is one : but if magnitude, fo far as mag- 
 nitude, is indivifible, magnitude is one. Moft things, therefore, are called 
 •one, becaufe they either effedl, or poifefs, or fuffer feme ether one thing. 
 But thofe things are primarily called one, of which tlie effence is one, and 
 ■which are one either by continuity, or fpecies, or definition. For we numerate 
 as many, either thofe things which are without continuity, or thofe things of 
 ■which the form is not one. 
 
 Again : we fometimes fiy that a thing is one by continuity, if It poffefTes 
 quantity, and is continuous ; and we fometimes fay that a thing is not one, 
 -w-hen it Is not a certain whole, that Is, If it has not one form.. For we do 
 not fimilarly fay there is one, when we fee the parts of a fhoe placed any 
 how together, although there may be continuity ; but when it Is fo conti- 
 nuous, as to be a (hoe, and to poffefs a certain form, then it is one. Hence, 
 a circular line Is more than all other lines one, becaule it is a whole and per- 
 fect. But the very effence of the one confifts in this, that it is the principle 
 of number. For the firft meafure is the principle of every genus; and that 
 by which we firft know a thing Is the firft meafure of every genus. The 
 principle, therefore, of that which is knowable, Is in every genus the one. 
 But there is not the fame one in all genera. For here It Is diefis *, but there 
 a vowel, or a mute. Moreover, of gravity there Is one principle, and of 
 motion another. But every where the one is Indivifible, either in fpecies or 
 in quantity. Of thofe things, therefore, which are indivifible according to 
 ■quantity, nnd fo far as quantity, that which Is every way indivifible and with- 
 out pofition is called the monad : but that which is every way indivifible, 
 and has pofition, is a point. That which Is only divifible one way Is a line ; 
 that which is capable of a two-fold divifion is a fuperficies ; and that which 
 is every way and triply divifible according to quantity, is a body. And, con- 
 verfely, that which is divifible In a twofold refpedl is a fuperficies ; that which 
 is divifible only one way Is a line ; and that which Is every way divifible 
 is a body. But that which Is no way divifible according to quantity Is a 
 point and the monad ; without pofition, indeed, the monad j but with poll- 
 
 * /, e. The lead fenfible interval in muCc. 
 
 tlon,
 
 BookV. ARI STOTLE'S M ET APH YSI CS. 119 
 
 tion, the point. Again : fome things are one according to number, others 
 according to fptcies, others according to genus, and others according to ana- 
 logy. Thofe things, indeed, are one according to number, of wliicli the mat- 
 ter is one; but according to fpecies, of which the del'initiori is one ; and accord- 
 ing to genus, of which there is the fame figure of predication*; but things 
 are one according to analogy, which fubfiil as one thing with relation to 
 another. The pofterior, however, always follow the anterior. Thus, for 
 inftance, fuch things as are one in number, are alfo one in fpecies ; but fucli 
 things as are one in fpecies f, are not all of them one in number: but all? 
 things that are one in fpecies, are alfo one in genus. Such things, however, 
 as are one in genus, are not all of them one in fpecies, but are one according 
 to analogy. But fuch things as are one according to analogy, are not all of 
 them one according to genus. It is, however, evident, that the many is pre- 
 dicated in a manner contrary to the one. For foine things are called many 
 from not being continuous ; fome things from pofleffing matter, divifible ac- 
 cording to ipecies, fuch matter being either the firft or the laft ; and fome. 
 from poiftiring many of thofe reafons which declare the elfence of a thing. 
 
 CHAP. VIT. 
 
 Being is diftributed into the accidental and the eflential. Into the acci- 
 dental indeed, as when we fay that a juft man is a mufician, and, in a fimi- 
 lar manner, the mufician is a man. Thus too, we fay that the muficiart 
 builds, becaufe it happens that the builder is a mufician, or that the muficiare 
 is a builder. For, to affirm this thing to be that^ fignifies that th'is thing hap- 
 pens to that. Hence, with refpedt to what has been afferted, when we fay 
 that man is a mufician, and a mufician man, or that fomething white is a mu- 
 fician, or a mufician white, we fay this^ becaufe both happen to the fame 
 thing, but that becaufe it happens to being. But we fay that a mufician is a 
 man, becaufe the being a mufician is accidental to him. In like manner,, 
 foinething white is faid to be a man, becaufe that is a man to which the being 
 •white is accidental. Things, therefore, which are faid to be according to 
 accident, are faid to be after this manner, either becaufe both are inherent in 
 
 * /. e. Of which one fiipreme genus and one predicament are predicated, 
 
 j Thus the letter a is one in fpecies in the fyllablcsi(7, ai, ila, &c. but is not one in number. 
 
 the.
 
 120 ARISTOTLE'S METAPHYSICS. Book V. 
 
 the fame thing, or becaufe the predicate is prefent to the fubjed, or becaufe it 
 is the thing itfelf to which accident is prefent, of which the thing iifelf is 
 predicated. 
 
 But things are faid to fubfift effentially, which fignify the figures of predi- 
 cation "•'••. For, as often as they are predicated, fo often do they fignify being. 
 Since, therefore, of things predicated, fome fignify the eOence of a thing, 
 others the quality, others the quantity, fome the relation, others the adion 
 or pafficn, others the fituaiion, and others the time, being fignifies the fame 
 to each of thefe. For it is the fame thing, to fay the man is convalefcent, as 
 to fay the man convalefces, and the man is walking, or is cutting, as the man 
 •walks or cuts. And in a fimilar manner with refpe<3: to other things. 
 
 Again : the words lo be and it is, fignify that a thing is true ; but the v.ords 
 not to be, that it is not true, but falfe. In like manner with refpedl to affirma- 
 tion and negation. Thus, he who fays that Socrates is a mufician, fays that 
 he is, becaufe this is true ; or aflerts that Socrates is not white, afferts this be- 
 caufe it is true : but he who fays that the diameter of a fquare is not incom- 
 menfurable with its fide, fays this becaufe it is falfe. Further flill : to be and 
 .being partly fignify that which is in capacity, and partly that which is in 
 energy. Thus we fay that both he who is endued with fight in capacity 
 fees, and he who poflefles it in energy. And, in like manner with re- 
 fpedl to Icientific knowledge, we fay that both he is endued with fcience who 
 is able to ufe it, and he who does ufe it : and that, both a thing which is now 
 at reft, and a thing which is capable of being at reft, are quiefcent. We are 
 alfo accuftomed to fpeak in a fimilar manner with refped: to eflences. For 
 we fay that Mercury is in the ftone, and we fpeak of the half of the line in 
 capacity f, and call that corn which is not yet ripe. But when a thing is 
 poflible, and when it is not fo, muft be elfewhere determined. 
 
 CHAP. VIIL 
 
 With refpe6l to essence, fimple bodies, fuch as earth, fire, water, and 
 the like, are called eflences ; and, in fhort, bodies, together with animals and 
 dcemoniacal natures confifting from thefe, and the parts of thefe, are thus de- 
 
 * By the figures of predication, Ariftotle means the ten predicaments. 
 ■}• Ev 3W«/j£( is not in the text, but without doubt ought to have been. 
 
 7 nominated
 
 BooK^. ARISTOTLE'S METAPHYSICS. 121 
 
 nominated. But all thefe are called eflences, becaufe they are not predicated 
 of a fuhjed:, but other things are predicated of thefe. After another manner, 
 too, that is called efltnce which is the caufe of being, and which is inherent 
 in fuch things as are not predicated of a fubjeft, fuch as foul in an animal. 
 Further ftill : fuch parts as are inherent in things of this kind, defining and 
 fignifying a certain fenfible thing, and which being taken away, the whole is 
 alfo taken away. Thus, if fuperficies is taken away, body alfo, according to 
 fome, is deflroyed ; and fuperficies is deftroyed, by taking away line. And, in 
 fhort, to fome number appears to be a thing of this kind ; for, according to 
 them, nothing can fubfift if it is taken away, and it is that which bounds all 
 things. Again : the formal caufe, of which definition is the rcafon, is called 
 the effence of any thing. But it happens that eflence is predicated according 
 to two modes, viz. according to the ultimate fubjedi, which is no longer pre- 
 dicated of another thing, and according to that which is a certain definite par- 
 ticular, and is feparable : but of this latter kind are the form and fpecies of 
 every thing. 
 
 C H A P. IX. 
 
 Of things which are faid to be the same, fome are fo denominated accord- 
 ing to accident, but others eflentially *. Thus that which is white and the 
 mufician are the fame, becaufe they happen to the fame thing; and man and 
 mufician are the fame, becaufe the one happens to the other, viz. the being a 
 mufician happens to man. But this is the fame with either, and either of thefe 
 is the fame with this. For man and the mufician are the fame as man the mufi- 
 cian; and this is the fame with thofe. Hence all thefe are not predicated univer- 
 fally. For it is not true, to fay that every man and a mufician are the fame : for 
 univerfals fubfift eflentially, but accidents have not an eflential fubfiftence, but 
 are fimply predicated of particulars. Thus Socrates and Socrates the mufician 
 appear to be the fame. For Socrates is not predicated of many things. 
 Hence we do not fay every Socrates, as we fay every man. Some things, 
 therefore, are after this manner (aid to be the fame according to accident. 
 
 But fome things are faid to be the fame eflentially, in the fame manner as 
 tilings v.'hich are efl'entially one. For things of which the matter is one, 
 either in fpecies or number, are faid to be the fame : and alfo things of which 
 
 * Ta Je x«fl' ai/T« is omitted in the text, but doubtlefs ought to be inferted. 
 
 R the
 
 122 ARISTOTLE'S METAPHYSICS, Book V. 
 
 the efTence Is one. So that it is evident that famenefs is a certain unity of 
 eflence, either of many things, or when any thing is confidered as many, as 
 when anyone fays that a thing is the fame with itfelf; for then he confiders 
 that thing as two. 
 
 But things are called different, of which cither the fpecles, or the matter, 
 or definition of the effence is many: and, in (hort, differentia predicated in a 
 manner oppofite to fame. But things are faid to be different which are di- 
 verfe and yet in a certain refpedt the fame, with this exception alone, that they 
 are not the fame in number, but either in fpecies, or genus, or analogy. 
 Again : thofe things are different, of which the genus is different, alfo things 
 contrary, and fuch things as poffefs diverfjty in their effence. 
 
 Things are faid to be fimilar which are paffive to the fame thing*, and 
 which are paffive to a greater number of things fame than different ; and alfo 
 of which the quality is one. That alfo which poffeffes more, or the principal 
 of thofe contraries by which another thing may be altered, is fimilar to that 
 thing. But diflimilars are predicated in a manner oppofite to fimilars. 
 
 CHAP. X, 
 
 Opposites are contradi£lories, contraries, relatives, privation, and habir, 
 and thofe things from which fiich things as are lart originate, and into which 
 they are lefolved ; fuch, for inllance, as generations and corruptions : like- 
 wife things which cannot be at the fame time prefcnt to that which is the 
 receptacle of both ; — thefe things are ehher themfelves faid to be oppofed, or 
 the natures from which they confift. For a dark and a white colour cannot 
 be prefent at the fame time to the fame thing j and hence the things from 
 which thefe colours confift are oppofed to thefe. 
 
 Thofe things are called contraries which, differing in genus from each other, 
 cannot at the fame time be prefent to the fame thing ; alfo things which 
 among thofe in the fame genus have the greateft difference between them- 
 felves ; and things which being in the fame recipient differ very much from 
 each dther. Things, too, are called contraries, which differ the moft of all 
 
 • ». e. Says Alexander which are fimilar to each other according to fpecies and form, as the , 
 Dicfcurl called Zethus and Ampliion. 
 
 Others
 
 DooK V. A R t S T O T L E ' S M E T A P H Y S I C S", 123" 
 
 otliers under the fame power * ; and things of which the difference is the 
 greateft, either (imply, or according to genus, or according to fpecies. Bur, 
 of otlier things which are called contraries, fome are fo denominated becaufe 
 they poflefs, and fome becaufe they are recipients of, tilings of this kind. Some, 
 a2:ain, are fo called, becaufe they are effective, or paffive, agents, or patients, 
 rejedions or aflumptions, habits or privations of thefe and the like. But 
 fmce ibe one 2L'Ci beinj are manifoldly predicated, it is neceflary that other 
 things alfo fhould follow which are predicated according to thefe. So that 
 there will be a diftribution oi fame, different , and cojitrary through the feveral 
 predicaments. 
 
 But things are faid to be difilrent in fpecies, which, being of thefam.e genus 
 are not placed under each other, and alfo fueh things as being in the fame 
 genus poflefs difference, together with fuch as have contrariety in their efibnce. 
 
 Either all contraries too, or thofe which are primarily fo denominated, are 
 different in fpecies. Alfo thofe things are different in fpecies, the definitions 
 of which in the ullimate fpecies of genus are different, as man and horfe 
 which are individuals in genus, but their definitions are different. This is 
 Tikewife the cafe with fuch things which, being in the fame effence, poffefs 
 diverfity. But things are the fame in fpecies, which are predicated in a mcde 
 oppofite to thefe. 
 
 C H A P. XI. 
 
 "VViTii refped to pkior and posterior, fome things are fo called becaufe 
 there is a certain fii ft and a principle in every genus ; for that is prior which 
 is nearer to a certain principle, defined either imiply and by nature, or rela- 
 tively, or according to fitua'ion, or by certain things. Thus, for inftance, fome 
 •things are prior and poflerior according to place ; prior, indeed, becaufe they 
 a-e nearer to a certain place definite by nature, as to the middle, or the extre- 
 mity, or becaufe they are nearer to any thing Vv'hich is cafually definite. But 
 that which is more remote is poflerior. 
 
 Again : fome things are prior and pofteiior according to time. For fome 
 things are called prior, becaufe they are more remote from the prefent time, 
 as with rcfpedl to things which have been already tranfadted. Thus the 
 
 * By power here Ariftotle appears to me to fignify natural habit, which is the fubje(f\ of con- 
 traries ; as, for inftance, the vifive power is the fubjeft of acute and dull vifion. 
 
 R 2 Trojan
 
 Wi ARTSTOTLE'S METAPHYSICS. Book NT. 
 
 Trojan are prior to the Median tranfadlons, becaufe they are more diftant 
 from the prefent time. But other things are prior, becaule they are nearer to 
 the prefent time, as is the cafe with things future. Thus the Nem;£an are 
 prior to the Pythian games, becaufe they are nearer to the prefent time, which 
 prefent time we ufe as the beginning, and as that which is firft. Some things, 
 again, are prior and pofterior according to motion. For that which is nearer 
 to the firft mover of a thing, is prior ; and, in this fenfe, a boy is prior to a 
 man. But this is a certain principle fimply confidered. Some things, too, are 
 prior according to power ; for that which tranfcends in power and that which 
 is more powerful, are prior. But of this kind is that nature whofe free-will 
 fomething elfe which is pofterior neceflarily follows ; fo that, the former not 
 moving, the latter is not moved, and when the former moves the latter i^ 
 moved. But free-will is a principle. 
 
 Again : fome things are prior according to order : and thefe are fuch things 
 as are proportionally diftant from one certain definite thing. Thus, in a 
 dance, he who obtains the fecond place is prior to the third in rank ; and, in 
 a mufical inftrument, the paranete* is prior to the nete : for in the former 
 the Coryphaeus, but in the latter the middle, is the principle. After this man- 
 ner, therefore, thefe things, are faid to be prior. 
 
 But, according to another mode, that is faid to be prior which antecedes ia 
 knowledge, as being fimply prior. But, of thefe, fome are prior according to 
 reafon, and others according to fenfe. For, according to reafon, univerfals are 
 prior, but according to fenfe, particulars. And, according to reafon, accident is 
 prior to the whole ; as, for inftance, the mufician, to man the mufician. For the 
 whole reafon or definition will not be without the part ; though it is not poffible 
 that a mufician can be, unlefs there be a certain, or fome particular mufician. 
 
 Further ftill : the participated properties of things prior are called prior, as, 
 for inftance, reftitude is prior to fmoothnefs. For the former is an elTeutiai 
 property of a line, but the latter of a fuperficies. Some things, therefore, are 
 after this manner called prior and pofterior. But fome things are fo deno- 
 minated according to nature and eflence "j"; and thefe are fuch things as are 
 able to fubfift without others, but others cannot fubfift without them : which, 
 divifion is ufed by Plato, 
 
 * Paranete is the laft ftring but one, and neie is the laft firing. 
 
 f Kai ouruxy is omitted in the text, but belongs to it, as is evident both from the verfion of 
 Beflarion, and the Commentary of Alexander. 
 
 But
 
 BookV. ARISTOTLE'S metaphysics. 125 
 
 But fince to be is manifold, in the firfl: place, the fubje£l is prior, through 
 which effence is prior. In the next [lace, things in capacity are prior in a 
 different manner from thofe which are in energy. For fome things are prior 
 according to capacity, but others according to energy. Thus the half is in 
 capacity prior to the whole, and the part to the whole, and matter to eflence. 
 But thefe are pofterior in energy ; for the whole being diflblved, they will 
 be in energy. But after a certain manner all things which are called prior 
 and pofterior are fo called according to thefe. For fome things according to 
 generation * may be without others ; and after this manner the whole is prior 
 to its parts. But fome things may fubfift without others according to corrup- 
 tion ; and after this manner the part is prior to the whole. And the like 
 takes place in other things. 
 
 CHAP. XII. 
 
 Capacity is called, in the firft place, the principle of motion or mutatloa 
 in another thing, or fo far as it is another. Thus the architeQural art is a 
 capacity which docs not fubfift in the ftrudlure raifed by that art : but the 
 medical art being a capacity, will fubfift in him who is healed, but not fo far 
 as he is healed. In fhort, therefore, one thing which is the principle of muta- 
 tion Qr motion, is faid to be capacity in another thing, fo far as it is another. 
 But another thing is fo denominated from another, or fo far as it is another : 
 for fo far as it is paflive, it becomes paffive to fomething. Sometimes, there- 
 fore, when it is poflible for any thing to be paffive, we fay that it is capable of 
 being paffive ; but fometimes we aflert this, not according to every paffion, 
 but if a thing is capable of being paffive with reference to that which is better. 
 Again : benefiting another, or freely doing good, is called capacity. For 
 fometimes we fay that thofe who have alone walked or difcourfed, but not 
 well, or as they wifhed to do, are not capable of fpeaking or walking. And 
 in a fimilar manner with refpeil to being paffive. 
 
 Further ftill : all habits, through which the pofTeftbrs are altogether void of 
 paffim, or are immutable, or not eafily changed to a worfe condition, are 
 called capacities. For fome are broken, and bruifed, and bent, and in fliort 
 corrupted, not from being capable, but from not being capable, and from. 
 
 • Viz. Of that which is generated, when the whole is in energy, the parts cannot be in 
 energy. As the whole, therefore, is, and the parts are not, the whole is prior to the parts. 
 
 being
 
 126 
 
 ARISTOTLE'S METAPHYSICS. CookV. 
 
 being In fomething dericienr. But others are impaffive to things of this kind ; 
 and tliefe are fuch things as fcarcely and in a fmall degree are paffive, through 
 capacity, and the being capable, and from fubfifting in a certain manner. 
 
 But fince capacity is predicated in fu many ways, the capable or pojfible alfo, 
 after one manner is faid to be that which has the principle of motion or mu- 
 tation. For that from which a permanent condition or rePc may proceed, is 
 fomething capable in another, or fo far as it is another. In the fccond place, 
 that is capable whicli can be paffive to fomething tlfe. In the third place, 
 that which has a capacity of this kind of being changed to any thing, whe- 
 ther to that which is better, or to that which is woife. For that which is 
 corrupted appears to be capable of being corrupted, or it would not have been 
 corrupted, if this was impojible. But now it has a certain difpofitlon, caufe, 
 and principle of a paffion of this kind. For fometimes it appears to be fuch 
 becaufe it pcflefles fomething, and at other times becaufe it is deprived of 
 fomething. But if privation is in a certain refpe£t habit*, all poffibles from 
 pofleffing fomething will, indeed, be poffibles : and if privation is not a cer- 
 tain habit, poffibles will be denominated equivocally. So that a thing is 
 poffible, partly becaufe it pofTefles a certain ha' it and principle, and partly be- 
 caufe it pcfleffcs a privation of this, if it be poffible that privation can be pof- 
 felTed. 
 
 In tlie fourth place, a thing is capable or poffible becaufe it has not a ca- 
 pacity, or principle in another, fo far as another, by which It can be corrupted. 
 But further ftill : all thefe are called poffibles, becaufe they alone happen to 
 be generated, or not to be generated, or to be generated in a becoming man- 
 ner. For in inanimate natures a capacity of this kind is inherent, as in 
 inflruments. Thus they fay that one lyre is capable of founding and another 
 not, if it is not a well-founding lyre. 
 
 But incapacity is thg privation of capacity, and a certain ablation of fuch 
 a principle, as we have related, or an entire ablation of It ; or it is an ablation 
 of naturally poffeffing a thing, or of poffeffing when It is naturally adapted to 
 poffefs. For tiiey do not fiiy that a boy and an eunuch are fimllarly Inca- 
 pable of generating. Further ftiil : incapacity is oppofite as well to that ca- 
 pacity which Is alone motive, as to that which Is motive In a becoming man- 
 ner. And, with refpc£t to impoffibles, fome are fo denominated according to 
 
 * For privation is not the mere abfence of a thing ; but abfence accompanied wiih a difpo- 
 fition towards that which is abfeiit. 
 
 thefe
 
 BookV. ARISTOTLE'S metaphysics. 12? 
 
 thefc modes of lacapaclty, but others, after a different manner, as, for in- 
 ftance, the poffible and impoffible. That is impoiTible indeed, the contrary of 
 which is neceflarily true. Thus, it Is impoIFible for the diameter of a fquare 
 to be commenfurable with Its fide, becaufe a thing of this kind Is falfe. And 
 the contrary of this Is not only true, but neceOary, viz. that the diameter is 
 incommenfurable with the fide. That the diameter, therefore, is commen- 
 furable, is not only falfe, but is neceflarily falfe. But the contrary to this is the 
 poffible, when it is not neceifary tliat the contrary Is falfe. Thus, It Is 
 poffible for a man to fit ; for that he does not fit. Is not nccefiarlly falfe. The 
 poffible, therefore, after one manner, as we have faid, fignifies that which is 
 not neceffiirlly falfe. But after another manner, It fignifies that which is true j. 
 and according to another acceptation, that which may be true. But the ca- 
 pacity wliich is fpoken of In geometry, is metaphorically called capacity. 
 Thefe poffibles, however, are not fo called according to capacity. But all thofe 
 which aie denominated according to capacity, are all of tffem fo called with re- 
 ference to one firft capacity : and this is the principle of mutation In another fo 
 far as it is another. For, with refpecS to other things that are called poffibles,, 
 fome are fo called, becaufe fomething elfe pertaining to them poffeffiis a capacity 
 of this kind ; others, becaufe fomething belonging to them does not poffi^fs It j. 
 and others, becaufe they poflefs this capacity themfelves. And in a fimllar 
 manner with refpedl to impoffibles. So that the proper definition of the firft 
 capacity will be this, a principle effedive of mutation In another, fo far as k 
 is another. 
 
 CHAP. xiir. 
 
 Quantity Is called that which Is dlvlfible into things inherent, either or 
 each of which is one thing, and Is naturally adapted to be this definite parti- 
 cular. Multitude, therefore, Is a certain quantity, If it be numerable j but^ 
 magnitude, if it be meafurable. But multitude is called that which Is divifible 
 in capacity into parts non-continuous ; and magnitude that which Is dlvlfible 
 into parts continuous. Again : of magnitude, that which Is continuous one 
 way is length ; that which is continuous two ways, breadth ; and that which 
 is continuous three ways, depth. But of thefe, the multitude which is finite 
 is number; length Is a line ; breadth fuperficies; and depth body. 
 
 Further ftlU : fome things are called certain quantities effentially, but others 
 according to accident. Thus, for inftance, a line is a certain quantity effenr 
 
 tlally*
 
 iSe ARISTOTLE'S METAPHYSICS. BookV. 
 
 tially, but a muficlan accidentally. But, of quantities which have an eflen- 
 tial fubfiftence, feme are according to efience ; as, for inftance, a line is a 
 certain quantity. For, in the definition explaining what it is, a certain quan- 
 tity is inherent. But others are paffions and habits of an eflence of this kind ; 
 as, for inftance, the much and the few, the long and the fhort, the broad and 
 the narrow, the high and the low, the heavy and the light, and other things 
 of this kind. But the great and the fmall, the greater and the lefler, are the 
 ^fTential paffions of quantity, confidered as well elTentially, as whh reference 
 to each other. Thefe appellations alfo are transferred to other things. 
 
 But of thofe things which are called quantities according to accident, fome 
 are fo called in the way we have already mentioned ; for, becaufe that in 
 which a mufician and white are inherent is a certain quantity, thofe alfo are 
 called quantities. But others are fo called as motion and time. For thefe are 
 denominated certain continued quantities, becaufe thofe things are divifible, 
 of vhich thefe are paffions. And here I do not mean that which is moved, 
 but that in which motion is effefted. For, becaufe that is a quantity, motion 
 alfo is a quantity. Time alfo is quantity, becaufe motion is fuch. 
 
 CHAP. XIV. 
 
 Quality is called after one manner the difference of eiTence. Thus, 
 for inftance, when it is afked M^bat kind of an animal is man (or what is the 
 quality by which he is diftinguilhed from other animals), we anfwer that he 
 is a biped : when the fame queftion is afked of a horfe, the anfwer is that he 
 is a quadruped ; and when it is afked What kind of figure a circle is, we re- 
 ply, a figure without angles ; by which it appears that difference according to 
 effence is quality. After one manner, therefore, quality is called difference 
 of effence. But after another manner, as things immoveable, and mathema- 
 tical entities. Thus, for inftance, numbers are certain qualities, I mean fuch 
 as are compofite, and which are not alone referred to one, but of which 
 a fuperficies and a folid are imitations. But thefe are plane, fquare, and cube 
 numbers ; and, in fhort, whatever befides a certain quantity is contained in 
 the effence of number : for the effence of every number confifts in being 
 affumed once. 1 bus, for inftance, the effence of fix does not confift in twice 
 three *, or thrice two, but in being taken once : for once fix is fix. 
 
 • For twice thrw, or thrice two, is not Cmply fix, but fix in conjun<Sliom Mith a certain quality. 
 
 Again :
 
 BookV. ARISTOTLE'S metaphysics. 129 
 
 Again : fuch tilings are called qualities as are the paffions of efTences that 
 are moved ; as, for inftance, heat and cold, vvhitenefs and blacknefs, gravity 
 and levity, and things of this kind, according to which bodies are faid to be 
 internally changed. Further ftlll : virtue and vice ; and, in fhort, good and 
 evil, are qualities. Quality, therefore, may be nearly denominated according 
 to two modes ; and of thefe one is the principal. For the firft quality is 
 difference of effence : but of this the quality which is in numbers is a certcdn 
 part. For it is a certain difference of effence, but either not of thofe things 
 which are moved, or not fo far as they are moved. But thefe are the paffions 
 of things which are moved, fo far as they are moved, and the differences of 
 motions. But virtue and vice are certain parts of paffions : for they manifeft 
 the differences of motion and energy, according to which thofe beings that 
 are in motion, do or fuffer well or ill. For that which is able to be moved, 
 or to eneigife, in this particular manner, is good j but that which is moved, or 
 energifes, in that particular manner, is depraved. But efpecially good and evil 
 fignify quality in animated natures, and of thefe, particularly in fuch as poffefs 
 a free will. 
 
 CHAP. XV. 
 
 With refpedt to relatives, fome things are fo denom'mted, as the 
 double to the half, and the triple to the third, and, in Ihort, the multiple to 
 the fubmultiple, and the furpaffing to that which is furpaffed. But others 
 are fo called, as that which heats to that which is heated ; that which cuts to 
 that which may be cut ; and, in fliort, as that which is adlive to that which is 
 paffive. Others, again, are as that which is meafurable to meafure, that which 
 is the objeO: of fcience to fcience, and that which is fenfible to fenfe. 
 
 But the hrft among thefe are indeed denominated according to number, 
 either fimply, or definitely with refpedl to each other, or to one. Thus, the 
 double to one is a definite number : but multiple is the relation according to 
 number to one, but not definite ; as, for inftance, this or that. But fe{- 
 quialtcr * to fubfefquiaher is the relation according to number to a definite 
 number. Superpartient f to fubfuperpartient is according to the indefinite, 
 
 • Sefquialtcr ratio, is the ratio of 3 to a ; and fubfefquialter that of a to 3. 
 
 f Superpartient ratio is when one quantity contains another once, and a certain number 
 of aliquot parts befides ; and fubfuperpartient ratio is the ratio of the lefler of two fuch quan- 
 tities to the greater. 
 
 S In 
 
 \
 
 130 A RISTOTLE'S MET APH Y S IC S. Book V. 
 
 in the fame manner as multiple to one. But the exceeding to that which is 
 exceeded, is entirely indefinite according to number. For number is com- 
 menfurable ; but the exceeding and that which is exceeded are denominated 
 according to incommenfurable number. For the former is to the latter fo 
 much, and fomething ftill beyond. But this is indefinite : for whatfoever 
 takes place, it is either equal or not equal. All thefe relatives, therefore, are 
 denominated according to number, and are the properties of number : and 
 ftill further, the equal, the fimilar, and the fame, according to another mode. 
 For they are all denominated according to the one. Thus, things are fame of 
 which the eflence is one ; but fimilar of which the quality is one ; and equal 
 of which the quantity is one. But the one is the principle and meafure of 
 number. So that all thefe are called relatives according to number, but not- 
 after the fame manner 
 
 But things active and paflive are relatives according to an adive and pafTive 
 power, and the energies of powers ; as, for inftance, that which is capable 
 of healing to that which may be heated, becaufe they are endued with power ;: 
 and, again, that which heats to that which is heated, and that which cuts to 
 that which is cut, are relatives as things energifing. But of thofe things^ 
 which are relatives according to number, there are not energies, unlefs after 
 the manner we have elfewhere mentioned : for energies according to motion 
 do not belong to nutnbers. Befides, of thofe things which are called relatives 
 according; t power or capacity, fome are fo denominated according to time ;, 
 as, for inftance, that which makes to that which is made, and that which 
 will make to that which will be made. Thus, alfo, a father is calhd a 
 father of a fon; for the former makes, but the latter has been fomething 
 p.ilfive. 
 
 Again : fome things are called relatives according to a privation of power^ 
 as the impoffible, and fuch things as are fo denominated, as the invifible. 
 Things, therefore, which arc calLd relatives according to number and power, 
 are all of thein. fo called becaufe each derives that which it is from reference 
 to another, and not becaufe fomething elfe is denominated with reference to it. 
 But that which may be meafured, that which is the obje£t of fcience, and that 
 which is the objedl of the dianocitic power, are called relatives, becaufe fome- 
 thing elfe is denominated with reference to thefe. For that which is the obje£l 
 of the dianoetic power fignifies that the dianoetic power fubfifts with refer- 
 ence to it : but the dianoetic power does not fubfift with reference to him to 
 
 whom
 
 BookV, ARISTOTLE'S metaphysics, i3l 
 
 whom it belongs ; for the fame thing would be twice faid *. In like man- 
 ner, fight is the fight of fomething, and not of him to whom it belongs, al- 
 though to aflert this is true, but it is referred to colour, or fomething elfe of 
 this kind. But after that manner, the fame thing would be twice faid, I 
 mean, that fight is the fight of him of whom it is the fight. Of things, 
 therefore, which are eflentially relatives, fome are i'o called after this 
 manner, but others if their genera are things of this kind. Thus, for in- 
 ftance, the medicinal art ranks among relatives, becaufe the fcience which is 
 the genus of it appears to belong to relatives. Add, too, thofe things, by 
 which fuch as pofTefs them are called relatives. Thus, equality is a relative, 
 becaufe the equal is a relative ; and fimilitude, becaufe the fimilar is a rela- 
 tive. But fome things are called relatives according to accident. Thus, man 
 is a relative, becaufe it happens to him to be double ; and this belongs to re- 
 latives : white, too, is a relative according to accident, if it happens to the 
 fame thing to be double and to be white. 
 
 CHAP. XVI. 
 
 The perfect is denominated that of which no part can be CKternally 
 affumed. Thus, for inftance, the time of any thing is perfedt, beyond which 
 no time can be affumed which is a part of this time. The perfeft alio is that 
 which, according to virtue and well-being, has not a tranfcendency with re- 
 fpedt to a certain genus. Thus, a phyfician is a perfedl phyfician, and a piper 
 a perfedt piper, when they are in no refpe<rt deficient according to the fpecies 
 of their proper virtue. Thus, too, metaphorically fpeaking, in things evil, 
 we fay a perfedl fycophant, and a perfed thief; fince we alfo call thefe cha- 
 racters good ; as, for inftance, a good thief, and a good fycophant. Virtue 
 alfo is a certain perfedlion : for a thing is then pcrfeft, and every eflence is then 
 perfe(fl, when no part of iis natural magnitude, according to the fpecies of its 
 proper virtue, is wanting. 
 
 Further ftili : thofe things are called perfed to which a worthy end is pre- 
 
 * " For if any one (f.iys Alexsnder) ftould affirm that fcience is not referred to that vhich 
 
 is the objec): of fcience (to etti-jitov), but to him who poflelTes fcience, to the inquiry, What that 
 
 is of which it is the fciciice ? the anfwer v,-ill be, That of which it is the fcience ; /. e. he w'lio 
 
 poflefles fcience ; and thus the anfwer will be to r.o purpofe, and tlie fame thing will be twice 
 
 laid." 
 
 S 2 fent;
 
 132 ARISTOTLE'S METAPHYSICS. Ecok T. 
 
 fent: for they are perfed from poflefTing an end. So that, fince the end Is 
 fomething belonging to extremes, transferring it alfo to things depraved, we 
 fay that a thing is perfedly deftroyed, and is perfectly corrupted, when no- 
 thing of corruption or evil is deficient, but it has arrived at the very extre- 
 mity of thefe. Hence death, alfo, according to a metaphor, is called the end, 
 becaufe both are extremes. Things, therefore, effentially called perfed are in 
 fo many ways thus denominated ; fome, becaufe according to well-being, they 
 are in no refpedt deficient, nor have tranfcendency in each genus, nor any thing 
 belonging to them external. But other things are called perfed according to 
 thefe, becaufe they either efFed or poflefs fomething of this kind, or are 
 adapted to this, or in fome other way are denominated with reference to things 
 called primarily * perfed. 
 
 CHAP. xvir. 
 
 Bound is called that which is the laft of any thing beyond which no- 
 thing can be aflumed, as the firft thing which may be aflumed, and within 
 which primarily all things are placed; alfo, that which is the form of magni- 
 tude, or of that which poffcffes magnitude, and which is the end of every 
 thing. But that to which motion and adion tend, is a thing of this kind, 
 and not that from which they begin. Sometimes, however, it is both that 
 from which motion and adion proceed, and that to which they tend ; alfo 
 that for the fake of which other things operate, and the efllnce of every 
 thing, and the formal caufe to every thing. For this is the bound of know- 
 ledge ; and if of knowledge, alfo of a thing. So that it is evident, that in 
 as many ways as principle is predicated, in fo many ways bound alfo is predi- 
 cated, and ftill more multifarioufly. For principle is a certain bound j but it 
 is evident f that not every bound is a principle. 
 
 CHAP; xviir. 
 
 According to which is predicated multifarioufly. Confidered in one 
 way, it is the form and the eflence of every thing. Thus, for inftance, the 
 
 * IlfBTws is omitted in the original ; but according to the Commentary of Alexander Aphro- 
 dificnfis ought to be inferted. 
 
 f From the Latin verfion of Argyropylus, it appears that the manufcript he confulted ended 
 here «ith u( ?l^^!;^ -, for he concludes this chapter with ut patct. \ have therefore inferted thefe 
 words in my verGon, as they appear to me to be properly added. 
 
 good
 
 BookV. ARISTOTLE'S metaphysics, 133 
 
 good Itfelf is that according to which a thing is good. But confidered In an- 
 other way, it is that in which primarily a thing is naturally adapted to be 
 produced, as, for inftance, colour in fuperticies. Hence, that which is pri- 
 marily called according to •which is form ; but that which is fecondarily thus 
 denominated, is as the matter, and the firfl fubjedl of every thing. In ihort, 
 according to lahicb is predicated in as many ways as caufe. For to alk, ac- 
 cording to which did a man arrive ? is the fime thing as to alk, for the fake of 
 which did he arrive ? And to inquire according to which a man paralogifes, 
 or fyllogifes, is the fame thing as to inquire the caufe of his paralogifm, or 
 fyllogifra. 
 
 Again : according to which fignifies according to pofjtion ; as, for inftance, 
 accordi?ig to which does he fland ? or according to which does he walk ? For 
 all thefe fignify pofition and place. So that according to itfelf^ or the eflential, 
 is alfo neceflarily predicated multifarioufly. For, in the firft place, it fignifies- 
 the formal caufe of a thing, or the proper form and definition explaining its^ 
 eflence ; as, for inftance, Callias, and the proper form of Callias. In the 
 fecond place, it fignifies fuch things as are inherent in definition ; as, for in- 
 ftance, Callias is efentially an animal. For, in the definition of Callias, ani- 
 mal is contained : for Callias is a certain animal. In the third place, it figni- 
 fies that which primarily receives any thing in itfelf, or in a certain part of 
 itfelf. Thus, for inftance, fuperficies is eflentially white, and man is eflentially 
 an animal. For foul is a certain part of man, in which life is primarily in- 
 herent. In the fourth place, it fignifies that of which there is not any other 
 caufe. . For of man there are many caufes, fuch as animal, biped ; but, at the 
 fame time, man is man eflentially. And, in the fifth place, it fignifies fuch 
 things as are inherent in fome particular thing alone, and fo far as it is alone. 
 Hence, that which has a feparate, has alfo an effential^ fubfiftence. 
 
 CHAP. XIX. 
 
 Disposition is called the order of that which has parts, either according^ 
 to place, or according to capacity, or according to form For it is requifite 
 that it ihould be a certain pofition, as the name alfo, viz. difpoftion^ evinces. 
 
 CHAP
 
 134 ARISTOTLE'S METAPHYSICS. BookV. 
 
 CHAP. XX. 
 
 Habit is denominated, according to one mode, a certain energy, as it were, 
 of that which poflefles and that which is poffelTed ; being, as it were, a certain 
 aftion or motion. For, when any thing makes, and another thing is made, 
 the making fubfifts between. In like manner, habit * lubfifts between him 
 who poflefles a garment, and the garment which is pofl^efled. It is evident, 
 therefore, that there cannct be another habit of this habit. For there would 
 be a progrefllon to inflnity, if there was a habit of the habit which is pof- 
 fefl'ed. But, according to another mode, habit is called difpofition, conform- 
 ably to which that which is difpofed is well or ill difpofed, and this either 
 eifentially, or wiih relation to another. Thus, health is a certain habit ; for 
 it is a dlfpofltion of this kind. Further ft;ill : it is called habit, if it is a por- 
 tion of a difpofition of this kind. Hence alfo the virtue of parts is a certain 
 habit. 
 
 C H A P. XXT. 
 
 Passion is called in the firft place quality, according to which any thing 
 may be altered ; as, for inftance, white and black, fweet and bitter, gravity and 
 levity, and other things of this kind. But, in the fecond place, it fignihes the 
 energies and internal changes of thefe. And, ftill more than thefe, noxious 
 internal changes and motions, and efpecially fuch changes as are not only 
 noxious but painful. Laftly, calamities and forrows of great magnityde are 
 called pafllons, 
 
 CHAP. XXII. 
 
 Privation is faid to take place according to one mode, when a thing 
 does not poflefs fomething which is naturally adapted to be poficflld, although 
 it is itfclf not naturally adapted to poflefs it. Thus, for inrtance, a plant is 
 faid to be deprived of eyes. But according to another mode, when either a 
 thing iifelf, or the genus of it, does not poflefs a thing which it is naturally 
 adapted to poflefs. Thus, a blind man is deprived of fight in one way, and 
 a mole in another ; the latter according to genus, but the form,cr cflentially. 
 
 * For habit here is a certain having, which fubfifls between him who has, and tlie garment 
 which is had. 
 
 Further
 
 BookV, ARISTOTLE'S metaphysics, 135 
 
 Further ftill : privation takes place, if a thing is naturally adapted to poffefs, 
 yet does not poflefs when it is fo adapted. For blindnefs is a certain priva- 
 tion : but an animal is blu.d, not according to every age, but in that only in 
 which, when it is naturally adapted to fee, it doeS not fee. In like manner, 
 privation takes place when a th:ng does not polFels i?i ivbicb^ according to 
 which, to ivhich, 2,XiAfo far as it is fiaturally adapted to p^^/f^fs. Fuiti\er Hill : 
 a violent ablation of any thing is called privation. And, as often as nega- 
 tions are denominated from ^, fo often alfo are privations deno ninated. For 
 a thing is called aiiifon^ unec]ual, becaufe, though naturally adapted to poffefs 
 equalltv, it does not pofTefs it ; and aoratort, invinble, becaufe it is entirely with- 
 out colour, and becaufe it poflelfes it deledtively. In like manner, an animal 
 is called apous, without feet, when it is entirely deprived of feet, and when it 
 has them attended with fome dcfed. Attain : privation takes place when a 
 thing pofTefTes but a little, as any fruit with a fmall kernel, viz. In this cafe it 
 fubfifts in a certain refped defedively. Alfo, when a thing cannot be eiFedled 
 with facility, or in a proper manner. Thus, a thing is infecable, not only be- 
 caufe it is not cut, but becaufe it cannot be eafily or well cut. Further ftill ; 
 privation takes pbce when a thing is not in any refpe£l poffed'ed. For he 
 is not called blind who has only one eye, bur he who is deprived of fight in 
 both. Hence, not every man is good, or bad, or juft, or unjuft, but there \s> 
 alfo an intermediate character. 
 
 CHAP, xxiir. 
 
 To HAVE is predicated multifarioufly. After one manner it is denomi- 
 nated when any being ads accordinj. to its own nature, or according to its 
 own impulfe. Hence, a fever is faid to have a man, and tyrants cities, and 
 thofe who are clothed a garment. But after another manner, that m which 
 any thing fubfifts as a recipient. Thus, for inftance, the brafs has the form 
 cf the ftatue, and the body the difeife. In the third place, as that which 
 contains things contained. For a thing is faid to be had hy that in which it 
 is contained. 1 bus we fay, that the veft^. 1 has that wluch is humid, the city 
 men, and the fhip failors. Thus alfo the whole has the parts. Further 
 ftill : that which prevents any thing from being moved or ading accord- 
 ing to its own impulfe, is faid to have this very thing. Thus, pillars have 
 the iippofed weights, and poets make Atlas to have the heavens, in order to 
 
 prevent
 
 136 ARISTOTLE'S METAPHYSICS, Book V. 
 
 prevent them from falling on the earth, as certain phyfiologifts fay. After 
 this manner too, that which connects is faid to have that which it conneds, as 
 if every thing according to its own Impulfe would be feparated and difperfed. 
 And to be in any thing is predicated fimilarly, and in a manner confequent to 
 to have. 
 
 CHAP. XXIV. 
 
 To BE FROM A CERTAIN THING, IS after one manner predicated from 
 which, as from matter: and this in a two-fold refpedl, either according to the 
 firft genus, or according to the laft form. Thus, all liquids are from water, 
 and the flatue is from brafs. But after another manner, it is predicated as 
 from the firft moving principle. Thus, for inftance, from what did battle 
 arife ? From defamation, becaufe this is the princii'le of the battle. In the 
 third place, it is denominated from that which is a compofite from matter 
 and form, as the parts from the whole, the verfe from the Iliad, and the ftones 
 from the houfe. For form is the end ; and that which has the end is perfed. 
 In the fourth place, as fpecies from a part. Thus, man is from biped, and a 
 fyllable from a letter. For thefe are from thofe, in a manner different from 
 that in which the flatue is from brafs. For a compofite effence is from fen- 
 fible matter; but form alfo itfelf confifls from the matter of form *. Some 
 things, therefore, are predicated after this manner, and fome, if a thing fubfifls 
 according to a certain part of thefe modes. Thus, the offspring is from father 
 and mother, and plants from the earth, becaufe they are from a certain part of 
 thefe. In the fifth place, that which fubfifts after any thing according to time. 
 Thus, night is faid to be from the day, and a ftorm from fair weather, becaufe 
 the former are poflerior to the latter. But of thefe, fome are thus denomi- 
 nated from having a mutation into each other, as the particulars which have 
 been jufl mentioned; but others becaufe they are alone confequent according 
 to time. Thus, a navigation was made from the equinodial, becaufe it was 
 made after the equinodlial : and the Thargella -\ are from the myfleries of 
 Bacchus, becaufe they are poflerior to thefe myfteries. 
 
 * This matter is net fcnfible, fince tlie parts of definition, or, in fliort, of form, are not fen» 
 fible. For the matter of form and the very nature of a thing are the parts condituting defini- 
 tion, which, as well as form, are apprehended by the reafoning power. 
 
 r}^ Fcafts in honour of Apollo. 
 
 CHAP.
 
 « 
 UookV. ARIS_T0TLE'S metaphysics. 137 
 
 CHAP. XXV. 
 
 Part Is denominated according to one mode, that Into which quantity, To 
 far as quantity, can be divided. For, always that which is taken away from 
 quantity, fo far as quantity, is called a part of it. Thus, two is after a man- 
 ner faid to be a part of three. But, according to another mode, that alone is 
 called a part of quantity which meafures it. Hence in a certain refpeft two, 
 as we have faiJ, is a part of three, but in another refped is not. Again : 
 thofe things into which form can be divided without quantity are called the 
 parts of form. Hence they fay that fpccies are parrs of genus. Further 
 ftill : thofe things are called parts, into which.any thing is divided, or from 
 which the whole is compofed, or form, or that which poffeffes form. Thus, 
 the brafs is a part of a brazen fp'iere, or of a brazen cube. But this is the 
 matter in which form is received. An angle alfo is a part*. Again: thofe 
 things which are contained in the definirion of a thing are alfo parts of the 
 whole. Hence genus is called a part of fpecies j but fpecies is in a different 
 manner a part of genus. 
 
 CHAP. XXVI. 
 
 Whole is called that of which no part is wanting of thofe things from 
 which the whole is faid naturally to confift f. Alfo, it'bo/e is that which con- 
 tains things contained fo as to form one thing. But this in a twofold re- 
 fpeil : for either in fuch a manner that each may be one, or fo that one thing 
 may emerge from thefe. For univerfal, and, in fhort, that which is denominated 
 as being a certain whole, are univerfal and a whole becaufe they contain many 
 things, are predicated of particulars, and all are one according to the predicate. 
 Thus man, horfe, and god are all of them one, becaufe each of them is an animal. 
 But the continuous and the finite are a whole, when one thing is produced 
 from many things which are inherent, efpecially when this multitude is inhe- 
 rent in capacity, and not in energy. But of thefe, things which have a na- 
 tural fubfiftence are more wholes than things which are formed by art, as we 
 
 * For it fignifies form. 
 
 t For when no part is wanting to a thing which fubfifts naturally, fuch a thing is properly a 
 whole. 
 
 T have
 
 133 ARISTOTLE'S METAPHYSICS. Book Y. 
 
 have fald In the dlvifion of things denominated one. For totality is a certain 
 unity. Again : fince quantity has a beginning, middle, and end, of thofe 
 quantities in which pofition does not make a difference, the all is predicated ; 
 but of thofe in which it does make a difference, the whole is predicated. 
 And of thofe things which admit both, the ivhole and the all are predicated. 
 But thefe are things of which the fame nature remains in tranfpofition, but 
 not the fame form ; as, for inftance, wax and a garment. For they are called 
 ivhole and all, in confequence of poffefling both. But water, fuch things as 
 are moifl, and number, are denominated all. For we do not fay the whole 
 number, and the whole water, except metaphorically. But of thofe things of 
 which all is predicated as a certain one, all things is likewife predicated. 
 Thus, of things divided, we fay all the number, all thefe monads. 
 
 CHAP. XXVII. 
 
 The diminished or mutilated is predicated, not of every quantity 
 which may cafually occur, but it is requifite that it Ihould be divifible and a 
 whole. For two things are not mutilated, when one of them is taken away 
 (for a thing mutilated, and that by the ablation of which it was mutilated, can 
 never be equal) j nor, in fhort, is any number mutilated : for it is neccffary 
 that irs effence fhould remain. Thus, if a cup is mutilated, flill it is neceflary 
 that it fhould be a cup ; but a number is no longer the fame when a part is 
 taken away. Befides, neither can all thofe things be called mutilated, which 
 confift of diffimilar parts. For number is that which has diflimilar parts, as, 
 for inftance, the duad and triad : but, in fhort, none of thofe things are muti- 
 lated, of which the pofition makes no difference ; as water, or fire, and the 
 like. But it is neceffary that mutilated natures fhould be fuch things as have 
 an effential pofition. 
 
 Again : it is requifite that they fhould be continuous. For harmony con- 
 fifls from diflimilar parts, and has pofition, but it does not become mutilated. 
 Befides this, neither are fuch things as are wholes mutilated by the privation 
 of any part indifferently. For the principal parts of effence, or any parts in- 
 differently, being taken away, will not make that wiiich remains mutilated. 
 Thus, if a cup is perforated, it is not diminiflied or mutilated ; but this happens 
 when its handle, or fome one of its extremities, is taken away. A man alfo 
 is mutilated, not when his flefh or fpleen, but when feme extreme part, is taken 
 
 away.
 
 BookV. ARISTOTLE'S metaphysics. 139 
 
 away, and this not any part indifferently, but which, when wholly taken away, 
 cannot be again generated. Hence men that are bald are not mutilated. 
 
 CHAP, xxviir. 
 
 Genus is predicated, when the generation of things poflefling the fame 
 fpecies is continuous. Thus, for inftance, it is faid, as long as the genus 
 (i. c. race) of men may be, /. e. as long as the generation of them is continuous. 
 It is alfo predicated as that from which things derive their exiftence as the 
 firft mover. Thus, according to genus, fome are called Greeks, and others 
 lonians, becaufe the former defcended fiom Helenus and the latter from 
 Ion, as the firft generators. But genus is rather denominated from the gene- 
 rator than from the matter. For genus is alfo denominated from the female, 
 as, for inftance, from Pyrrha. Again : fuperficies is called the genus of fuper- 
 ficial figures, and lolid of fuch as are folid : for, of every figure, this is fuch a 
 fuperficies, and that is fuch a folid. But genus is that which is the fubje6t 
 of differences. 
 
 Again: genus alfo is that which is firft inherent in definitions fignifying 
 the effence of a thing, the differences of which are called qualities. In fo 
 many ways, therefore, is genus predicated : for it is either denominated ac- 
 cording to a continued generation of the fame fpecies, or according to the firft 
 mover of the fame fpecies ; or it is predicated as matter. For that of which 
 there is difference and quality, is that fubjed which we call matter. But 
 things are called different in genus, of which the firft fubje£t is differ- 
 ent, and one is not refolved into the other, nor both into the fame. Thus, 
 form and matter are different in genus, and fijch things as are denominated 
 according to a different figure of the predication of being. For, of beings, 
 fome things fignify what a thn'g is, others •what knid of a thing it is, and 
 others fignify conformably to the divifion we have previoufiy made. For 
 neither are thefe refolved into each other, nor into one certain thing. 
 
 C H A P. XXIX. 
 
 The false is denominated after one manner, as a thing filfe : and thisin 
 the firft place, becaufe it is not compofi.d ••■, or becaufe it is impoffible for it 
 
 • In dijcourjt^ truth and falfchood merely confift in corripofition : not fo in things. 
 
 T 2 to
 
 140 ARISTOTLE'S METAPHYSICS; Book V, 
 
 to be compofed ; as when It is faid that the diameter of a fqiiare is commen- 
 furable with its fide, or that you fit. For, of thefe, the former is always falfe, 
 bat the latter fometimes ; fo that thefe are non-entities. But other things are 
 falfe, which are indeed entities, but are naturally adapted to appear either not 
 fuch as they are, or things which are not, as, for inftance, pictures and dreams. 
 For thefe are indeed fomething, but not the things of which they caufe the 
 imagination. Things, therefore, are thus faid to be falfe, either becaufe they 
 are not, or becaufe the imagination which emerges from them is the imagi- 
 nation of that which is not. 
 
 But difcourfe is falfe, which is of non-entities, fo far as it is falfe. On this 
 account every falfe difcourfe is employed about fomething different from that 
 refpedling which it would be a true difcourfe. Thu-^, the difcourfe refpedting 
 a circle is falfe when applied to a triangle. But the difcourfe about any thing 
 which explains its eflcnce, is partly one and partly many, fince a thing itfelf, 
 and itfelf confidered as the recipient of fomething elfe, are in a certain refpedl 
 the fame ; as, for inftance, Socrates, and Socrates the mufician. But a falfe 
 difcourfe is fimply confidered as a difcourfe about nothing. On this account 
 Antifthenes entertained a ftupid opinion when he thought that nothing could 
 be faid, except one thing of one thing, by a proper difcourfe ; the confequencc 
 of which opinion muft be, that there can be no contradidion, and it will be 
 fcarcely poffible to make a falfe affertion. Any thing, however, may be 
 afferted, not only by a difcourfe peculiar to that thing, but alfo by that which 
 belongs to another thing ; and this fo as to be perfeQly falfe, and yet in a cer- 
 tain refped: true. After this manner, the number 8 is double from the defi- 
 nition of the duad. Some things, therefore, are after this manner denomi- 
 nated falfe. But a man is falfe who readily and voluntarily admits falfe affer- 
 tions, not for the fake of any thing elfe, but merely becaufe they are falfe, and 
 who is the caufe of others adopting fuch like allertions. Juft as we fay that 
 things are falfe which produce a falfe phantafy. Hence the reafoning in the 
 Icffer Hippias of Plato deceives, which endeavours to Ihow that the fame man 
 is both falfe and true : for he confiders him as falfe who is capable of de- 
 ceiving ; but fuch a one pofl!effe8 both knowledge and prudence. Befides, it 
 alfo fays that he who is voluntarily depraved is the better man. But the falfe 
 here is coUedled by induction. For he who is voluntarily lame is better than 
 him who is involuntarily fo : for here voluntary lamenefs is confidered as the 
 fame with an imitation of lamenefs. Since, if he were voluntarily lame, he 
 
 would
 
 BookV. ARISTOTLE'S metaphysics. 141 
 
 would perhaps be worfe ; jufl as this would alfo be the cafe in moral 
 condud. 
 
 CHAP. XXX. 
 
 Accident is called that which is inherent in fomething, and of which 
 fomething may be truly afferted, yet neither neceflarily, nor for the moft 
 part ; as, for inftance, if any one di}.'ging for a plant in a ditch fliould find a 
 treafure, the finding the treafure wou'd be an accident to him who digs in the 
 ditch. For neither does the one follow from the other, nor after it. Nor, if 
 any one plants, will he for the mofl part find a treafure. A mufician alfo 
 may be white ; but fince this takes place neither from neceffity, nor for the 
 moft part, we call it an accident. Since, therefore, there is fomething which 
 has a fubfiftence, and a fubfiftence in fomething, and fome of thefe are in a 
 certain place, and at a certain time, whatever has a fubfiftence indeed, but not 
 becaufe it is this particular thing, or becaufe it is now, or here, will be an 
 accident. Nor is there any definite caufe of accident, but the caufe of it is 
 cafual ; and this is indefinite. Thus, fome one may have accidentally come to 
 .^gina, if it was not his defirjn to go to that place, but he was driven thither 
 by a ftorm, or taken by robbers. Accident, therefore, was generated and is, 
 but not fo far as itfelf is, but fo far as fomething elfe is. For the ftorm 
 was the cau'e of his going to that place, to which he did not fail : but 
 this was ^gina. Accident is alfo after another manner denominated that 
 which effentially belongs to a thing, but yet is not contained in the eflence 
 of that thing ; as, for inftance, the poffeflion of angles equal to two right in a 
 triangle*. And it hippens, indeed, that accidents of this kind are eternal : 
 but this is not the cafe wiih any of the others ; the reafon of which we have 
 elfewhere afllgned f. * 
 
 * For thefe are not contained in the definition which explains the eflence of a triangle. For 
 the definition ot a triangle is this : a figure contained by three right lines. 
 
 t Refpeding thofe things which arc after this manner eflentially prefent, Ariftotle difputes 
 in his Lalt Analytics. 
 
 ARISTOTLE'S
 
 ARISTOTLE'S METAPHYSICS. 
 
 BOOK VI*. 
 
 C H A P. I. 
 
 Jl H E principles and caufes of beings are inveftigated ; and it is evident 
 that they are inveftigated of beings fo far as beings. For there is a certain 
 caufe of heahh and a good habit of body. Of mathematical entities, too, 
 there are principles, elements, and caufes. And, in fhort, every dianoetic 
 fcience, or which participates any thing of the dianoetic power, is converfant 
 ■with caufes and principles, which are either more accuraie or more fimple. 
 But all thefe circumfcribing one particular thing, and a particular genus, are 
 employed about this, but nut about being fimply, nor fo far as it is being, 
 nor do they pay any attention to the inquiry what a thing is : but from this, 
 fcme making it manifeft from fenfe, but others affiiming it from hypothefis, 
 thus demonftrate in a more neceflary or more remifs manner things eflentially 
 prefcnt with the genus, about which they fubfift. On which account it is 
 evident that there are not demonftrations of efTcnce, nor of definition from 
 an indu(Slion of this kind, but there is fome other mode of rendering thefe 
 
 * Ariflotle, fays Alexander, obfcurely aflerts in this book, more openly in the following, and 
 flill more clearly in the eighth book, that the firft philofophy is converfant with the knowledge 
 of being fo far as being ; that it confiders the definition of every thing; unfolds how every 
 thing is to be defined, whether it be intelligible or any thing clfc ; and explains of what things 
 there are definitions, and of what there are not. 
 
 apparent.
 
 Book VI. ARISTOTLE'S METAPHYSICS. 143 
 
 apparent. In like manner, they are entirely filent as to the genus with which 
 they are converfant, wliether it is, or is not, becaufe it belongs to the fame 
 dianoetic power, to make manifeft ■■liar a thing is, and if it is this thing. 
 
 But fmce the phyfical fciente is converfant v\itl) a certain genus of being 
 (for it is converfant with f ich an effence as contains in itfelf the pinciple of 
 motion and reftj it is evident that it is neither pradtical nor effedive. For of 
 things which are effed:ive *, the principle, whether it is intelledl, or art, or a 
 certain power, is in the efficient ; but of things pradical the princ'ple, viz. 
 free-will, is in the agent. For the tame thing is pradicable, a.d the objed 
 of free-will. So that if every dianoetic energy is either pradic, or effcdtive, 
 or theoretic, the phyfical dianoetic energy will be a certain theoretic fcience ; 
 but it will fpeculate being of fuch a kind as is capable of being moved, and an 
 eflence which is for the moft part known through delinition, and has not alone 
 a feparate fubfiftence. 
 
 It is, however, rcquifite to underftand in what manner the formal caufe and 
 definition fublifl. For, to inveftigate without this knowledge is to do no- 
 thmg. But of things defined, and to which the inquiry what they are be- 
 longs, fome fuSfift in the fame manner as the flat nofc, and fome as the ho/low. 
 But ttiefc dift'er, becaufe the flat nofe is conceived together with matter: for a 
 flat nofe is a hallow nofe ; but hollownefs is without fenfible m tter. If, 
 therefore, all phyfical things are predicated in a manner fimilar to a flat nofe ; 
 as, for inftance, nofe, eye, face, flefli, bone, and, in fhort, animal, leaf, root, 
 bark, and plant (for the definition of no one of thefe is without motion f, but 
 it always poffefles matter;, it is evident in what manner in phyfical inquiries 
 it is r.qaifite to inveftigate and define the effence of a thing, and why it be- 
 longs ro the natural philofopher to fpeculate refpeding a certain foul, viz. fuch 
 a foul as is not unconneded with rriatter. That the phyfical dianoetic energy, 
 therefore, is theoretic, is from what has been faid evident. 
 
 But the mathematical fcience alfo is theoretic. Whether, however, it con- 
 templates things immoveable, and wluch have a fubfiftence feparate from fen- 
 fibles, is at prefent im manifeft. But that there are fome mathematical difci- 
 plines which contemplate things fo far as they are immoveable, and fo far as. 
 
 * The effeftive fcience, as Ar-ftotle more fully explains in his Nicomachaean Ethics, is rirat 
 the work of which remains after its energy. Of this kind is the builders art : for tlie work of 
 this art, viz. the houfe, endures after the operation of building. 
 
 t »'. e. Matter. 
 
 they
 
 144 A R I STOTLE'S MET A PH YS I C S, Eook VI. 
 
 they have feparate fubfiftence, Is evident. If, indeed, there Is fomething Im- 
 moveable, eternal, and feparate from fenfibles, it Is manifeft that It Is the pro- 
 vince of the contemplative fcience to know It, and not of the phyfical (for the 
 phylical fcience is converfant with certain moveable natures) nor of the ma- 
 thematical, but of a fcience prior to both thefe. For the phyfical fcience is 
 converfant with things Infeparable Indeed, but not Immoveable : but of the 
 mathematical fciences, fome are converfant with things Immoveable indeed, yet 
 not (ep^iV^te perhaps, but fubfifting as In matter. The firil of fciences, how- 
 ever, Is employed In the fpeculatlon of things feparate and Immoveable. But 
 It Is necelTary t'nat all caufes. Indeed, fliould be eternal, and efpecially thefe : 
 for thefe* are the caufes to the ph:Enomena of things divine. So that there 
 will be three contemplative philofophies, viz. the mathematical, the phyfical, 
 and the theological. For It is not Immanifeft, that if a divine nature any 
 where fubfifts. It fubfids In a nature of this kind. And it is requifite that 
 the mod honorable fcience {hould be converfant with the moft honorable 
 genus of things. The theoretic fciences, therefore, are more eligible than 
 other fciences ; but this (or the theological fcience) Is more eligible than the 
 theoretic. 
 
 But fome one may doubt whether the firft phllofophy Is unlverfa), or con- 
 verfant with a certain f genus and one nature. For neither in the mathe- 
 matical fciences is there the fame mode of fpeculatlon ; but geometry and 
 aftronomy are converfant with a certain peculiar nature:];, while the mathe- 
 matical fcience itfelf is, in Iliort, common to all the branches of that fcience. 
 If therefore, there is not any other effence befides things which have a natural 
 fubfiftence, the phyfical will be the firft fcience. But if there Is a certain 
 immoveable elTence, this will be prior, and will be the firft philofophy. It 
 will thus alfo be univerfd, becaufe It is the firft of fciences : and it will be the 
 province of this fcience to fpeculate refpeding being fo far as being, and to 
 contemplate what it is, and what, in ihoit, are the things inherent in It fo far 
 as being. 
 
 * That is, fays Alexander Aphrodifienfis, thefe immoveable and feparate natures are the 
 caufes of the celeftial fpheres, and of divine bodies. We have already obferved, that the exift- 
 cnce of thefe feparate natures is proved by Arillotle in the latter part of the tvi'elfth book of this 
 work. 
 
 f Inftead of Tift yew;, as in the original, it (hould doubtlefs be Trcpi ri ytvoj. 
 
 t /. e. Continued c^uantity. 
 
 CHAP,
 
 SookVI. ARISTOTLE'S METAPHYSICS. US 
 
 C H A P. ir. 
 
 Since, however, being, fimply fo called, is multifariouny predicated, of 
 ■which predication one is according to accident, but another as that which is 
 ^rue, to which non-being is oppofed, as that which is falfe. But befides thefe 
 there are the figures of the categories, as, for inftance, fubftance, quality, quan- 
 tity, where, when, and whatever elfe there may be of this kind. Again : befides 
 all thefe, there is that which fubfifts in capacity, and that which fubfifts in 
 energy. But, fince being is predicated multifarioufly, v.'e muft in the firll 
 place fay, refpe<fting that which fubfifts according to accident, that there is no 
 fpeculation concerning it ; of which this is a token, that no fcience is atten- 
 tive to accident, neither the pradic, nor the effedive, nor the theoretic. For 
 neither does he who makes a houfe, at the fame time make fuch things 
 as happen to the houfe when built (for thefe are infinite) ; fince nothing 
 hinders but that the houfe may be to fome pleafant, to others noxious, and to 
 others beneficial, and, as I may fay, different from all things, of none of 
 which the building art is effective. After the fame manner, neither does the 
 geometrician fpeculate things which thus happen to figures, nor whether a 
 wooden* triangle and a triangle which has angles equal to two right are dif- 
 ferent from each other. And this happens rationally ; for accident itfelf is 
 only as it were a name. Hence, Plato j" after a certain manner does not im- 
 properly difpofe non-being about the fophiftic art. For the arguments of 
 fophifts are, as I may fay, the moft of all things employed about accident. 
 For they afk, whether a mufician and a grammarian are a different or the 
 fame perfon ; whether the mufician Corifcus and Gorifcus are the fame ; and 
 if every thing which is, but is not always, is generated. So that if he is a 
 mufician he is made a grammarian, and if he is a grammarian he is made a 
 mufician, and whatever other arguments there are of this kind. For acci- 
 dent appears to be fomething near to non-entity. And this is evident from 
 what has beenjull now faid. For, of things which fubfift in a different 
 manner from accident, there is generation and corruption ; but this is not tlve 
 cafe with things which fubfift according to accident. 
 
 * From the Commentary of Alexander AphrodiGenfis on this part, it appears that to iuf^tvot 
 ought to be here inferted. There is nothing more in the printed text than duo' si Itc^ov BffTt ta 
 ■Tfiyuvov. The verfion of Argyropylus alfo has '' neque fi triangulus ligneus" &c. 
 
 ■\ In the Sophida. 
 
 U But
 
 me ARISTOTLE'S METAPHYSICS; Book.VK 
 
 But at the Hime time let us fpeak ftlU further about accident, as much aS-- 
 poffible Ihowing what the nature of it is, and through what caufe it fubfifts, 
 for, at the fame lime, perhaps it will be evident why there is not any fcience 
 of accident. Since, therefore, in beings fome things always fubfifi; in a fimilar 
 manner*, and from neceflity (not from that neceffity which is denominated 
 according to the violent, but from that by which we fay a thing cannot fubfiff 
 otherwife), but others, though they are not neceflarily, nor always, yet they 
 are for the moft part f, this is the principle, and this is the caufe of the fubfift- 
 ence of accident. For whatever is neither always, nor for the nioji part, this 
 ivefay is accident %. Thus, for inftance, if, when the fun is in Canis, ftormy 
 and cold weather fhould be produced, we fliould fay that this happened ; but 
 we fhould not fpeak in this manner if fufTocation and heat were produced ;- 
 becaufe the latter is always, or for the moft part, but this is not the cafe with 
 the former. That man is white is alfo an accident ; for this is neither always 
 the cafe, nor for the moft part : but that man is an animal is not from acci-^ 
 dent. Likewife that a builder fhould give health, is an accident, becaufe a 
 builder is not naturally adapted to effeil this, but a phyfician : but here ic 
 happens that a builder is a phyfician. A cook, alfo, intent upon giving plea- 
 fure, may make fomething falubrious, but not from the art of cooking.. 
 Hence, we fay that this happens, and in a certain refpeit he makes fomething 
 falubrious, but fimply confidered he does not. For of other §" things the 
 powers are fometimes effedive ; but of thefe no art nor power is definite. 
 For, of things which either are, or are generated according to accidents^ 
 the caufe is alfo according to accident. So that, fmce all things are noc 
 from neceffity, nor either always arc. entities, nor are in generation (/'. ^.. 
 
 • Thus,^man is always and from neceffity an animal. 
 
 t Thus, man has not always five fingers, but for the moft part. 
 
 % The agreement between accident (in Greek <jv(iSiZmoi) and the cafual or contingent, ac- 
 cording to AriLlotle, is obvious from this definition of the word -, and hence, {hortly after, he- 
 joins a fubfiftence according to accident with cafual fabfillence. Yet Dr. Gillies, infpired with 
 the fame lawlefs rage for novelty which fo eminently diltinguiflies modern wit, has prefumed to 
 pervert the genuine meaning of thi.s word in the following note. (See vol. i. of his AriflotlCj 
 p. 65.) " The Greek word cajJiiQ-nMii is as far as I know,.unlverfally.tranilatcd ' accident V 
 wufi-iiZwdTa. in the plural, ' accident^.' (Obferve, gentle reader, that this word has a plural, and 
 alfo that, accident in the fingular maies accidents in the pluial.) But accident, in its proper 
 fenfe of what is cafual or fortuitous, lias nothing to do with it; and Ariftotle's meaning of (ri//tbt- 
 ffwoj ought to be exprefled by a Latin or Englifli word derived, not from accido, but from atceao.-' 
 
 5 Inllead of -ruy (ity ya^ a?.^«i, 1 read t«v mev yaf cO^a^^ 
 
 becoming.
 
 ^ookVI. ARISTOTLE'S METAPHYSICS. 1-17 
 
 becoming to be, or tending to being), but mod things have a fubfiftence 
 for the moft part, it is neceffary that there Ibould be fomething which 
 fubfifts according to accident, and that it fhould be luch as is a white mu- 
 fician, who is neither always fo, nor for the moft part. But, fmce it is 
 fometimes effeded, there will be a fubfiftence according to accident : for, if 
 not, all things will be from neceflity. So that matter will be the contingent 
 caufe of accident, which fubfifts differently from that which has a fubfiftence 
 for the moft part, or which feldom fails of fubfifting. But this fliould be the 
 beginning of the inquiry. Whether there is nothing which neither fubfifts al- 
 ways, nor for the moft part, or whether this is impoflible. There is, there- 
 fore, fomething befides thefe things which have a caiual fubfiftence, and a 
 fubfiftence according to accident. But ftiall we admit that there is fuch a 
 thing as that which fubfifts for the moft part, but that there is not in the na- 
 ture of things that which has a perpetual fubfiftence ? or are there certain 
 eternal entities ? Thefe things, therefore, will be the fubjeil of a pofterior 
 •confideratlon *. But that there is not a fclence of accident is evident : for 
 every fcience is of that which is always, or of that which is for the moft part. 
 How, otherwife, can a man learn any thing, or teach another ? For it is 
 neceiTary that the objed: of fcience fhould be defined either by the perpetual, 
 or by a fubfiftence for the moft part ; as, for inftance, that, to a perfon in a 
 fever, mead is, for the mofl part, beneficial. But no one will fay that mead 
 adminiftered during the new moon is beneficial in a fever f : for during the 
 new moon this is efficacious, either aKvays, or for the moft part. But acci- 
 <3ent is fomething different from thefe. We have, therefore, declared what 
 .accident is, and through what caufe it is, and that there is not a fcience of it. 
 
 CHAP. III. 
 
 That there are principles and caufes which rife into exiftence and perifli 
 -v\'ithout being generated and corrupted is evident. For, if this were not the 
 cafe, all things would be from neceflity, if it is neceffary that, of that which is 
 -generated and corrupted, there fhould be a certain caufe which does not fub- 
 
 * i. e. In the eleventh and twelfth books of tliis work. '' 
 
 f For, as Alexander obferves, it (hould rather be faid, that becaufe he who drinks mead in a 
 
 fcver is for the moft part benefited, it therefore happens to be efficacious during the mc\r 
 
 jaiooa. 
 
 • U 2 {It
 
 148 ARISTOTLE'S METAPHYSICS. Book VL 
 
 fift from accident. For, whether will this thing take place or not ? If this is 
 done, it will ; but if not, it will not take place. But this will take place, if* 
 fomething elfe is effedled. And thus, by always taking away time from a 
 definite time, you will at length arrive at the tiow^ So that this man will die 
 either by difeafe or violence, if he goes out of the city : but this will take place, 
 if he fhould be thirRy ; and this will happen, if fomething elfe happens : and' 
 fo we (hall arrive at that which now is, or at fomething which is part. As, for 
 inftance, if he fhould be thirfty ; but this will happen, if he has eaten fait meat ; 
 and this either is or is not. So that, from ncceflity, he will either die or not. 
 In like manner, if any one diredts his attention to part tranfadicns, the fame 
 reafoning will take place. For nov/ this will fubfift in fomething ; I meaa 
 that which has been effefled. All future events, therefore, will be from ne- 
 ceflity ; as, for inftance, death to that which has life. For now fomething 
 has been cfRded ; as, for inftance, contraries in the fame body. But it from 
 difeafe or violence, this will not yet be the cafe, but if this fhall have beea 
 efFe(fted. It is evident, therefore, that this redudion tends to a certain prin- 
 ciple ; but this principle does not tend to any thing elfe. This, then, will be 
 the principle of that which is cafual, and there will not be any caufe of its ge- 
 neration. But it muft be efpecially confidered to what kind of a principle, and 
 to what kind of a caufe, a redudion of this kind tends, whether as to matter,, 
 or as to that for the fake of v/hich a thing fubfifts, or as to that- which moves. 
 But we fliall omit the further fpeculation of that which fubfifts according to 
 accidenr ; for it has been fufficiently difcufled by us. 
 
 But that which fubfifts as true is being, and that which fubfifts as falfe is 
 non-belngf, becaufe they are employed about compofition and divifion, and 
 entirely about the divifion of contradidion. For the true has affirmation in 
 comp ifition, but negation in divifion ; but the falfe has the contradidion of 
 this divifion. But in what manner things which fubfift together, or which 
 have a feparate fubfiftence, are to be underftood, is another queftion. But I 
 mean things which fubfift together, and which fubfift apart, not in a confe- 
 quent order, but fo as to become one thing. For the falfe and the true are.- 
 
 * Eai' is omitted in this part of the original : for, inftead of touto J^e a^^o, it fliould evidently 
 be TCUTO S's £av a't>.<i. 
 
 t The original in this place is defeftive. Inftead of to Je a; aXtiSfs ov uf 4-et/3b{, the fenfe re- 
 quires we (hould read to li «j a.U.ti ov, to it »f ^euh; /xi ov. And this emendation is juftified by 
 the verfions of Bcfl'arion and Argyropylus. 
 
 y nofe
 
 DookVL ARISTOTLE'S metaphysics. 1-19 
 
 not in things (fo that, for inftance, that which is good is true, but that which 
 is evil falfe); but they fubiift in the dianoetic * part. But the truth and 
 fa!f, hood refpeding things fimple, and eflences, are not in the dianoetic part. 
 Such things, therefore, as it is requifite to fpeculate concerning that whi.h 
 is thus being and non-being, we fhall afterwards confidcr. But fince com- 
 pnfuion and divifion are in the dianneiic part, and not in things, and that 
 which is after this manner being is different from thofe things which are pro- 
 perly beings (for the dianoetic part conjoins or divides either fubftance, or 
 quality, or quantity, or fomething elfe), that which is as accident, and that 
 which is as true being, are to be omitted. For the caufe of the one is inde- 
 finite, but of the other a certain affedion of the dianoetic part ; and both 
 are converfant with the remaining genus of being, and do not render maniteft 
 a certain nature which fiirpajfes helng-\; on which account thefe are to be 
 omitted. But the caufes and principles of being itfelf are to be confidered, 
 fo far as it iS being. And it is evident, from what we have faid refpeding the 
 multifarious predication of every thing, that being is multifarioufly predicated. 
 
 * The dianoetic part compofes and divides the predicate from the fubjecSl ; and hence dia- 
 noetic truth and falfehood are not in things themfelves, but in this part of the foul. However,, 
 as truth is one of tlie firft of things (for, according to Plato, it tharaflerifes the eflence of 
 divine natures), its illuminations confequently extend to the laft of beings. It is, therefore, par- 
 ticipated by things in an appropriate manner, viz. according to the nature of the things by. 
 ■which it is participated. But the Cmple forms of things are not perceived by the dianotJcic 
 power, becaufe in thefe there is no compofition and divifion, and they are eternally true. They 
 are, therefore, only to be apprehended by intelle£l;ual intuition and contact ; and there cannot 
 be any deception refpedling the vifion of thefe, fince, as Ariftotle fhows at the end .of the ninth, 
 book, intelleft either fees them truly, or does not fee tliem at all. 
 
 t That is the ineffable principle of things, which Plato denominates the one and the gaod ; and 
 in his Republic aflerts, and in his Parmenides proves, to.be fapereflential. 
 
 ARISTOTLE'S
 
 ARISTOTLE'S METAPHYSICS. 
 
 BOOK VII. 
 
 CHAP. I. 
 
 ±5eING is multifarioufly predicated, as we have before evinced In what we 
 have faid refpeding multifarious predication. For one fignlfication of being 
 is what a thing Is, and this particular thing*; another, quality, or quantity, or 
 each of the other things which are thus predicated. But fince being is in fo 
 many ways predicated, it is evident that the firft being among thefe is, what a 
 ih'uig isy which fignifies eflence. For when we fay, ijohat kind of a thing is 
 this particular thing ? we either fay it is good or bad, but we do not fay It Is 
 of three cubits, or that it is a man. But when we fay, ivhat it is, we do not 
 aflert that it is white, or hot, or of three cubits, but that it is a man or a god. 
 But other things are called beings, becaufe, as belonging to true being, fome of 
 them are quantities and others qualities, fome are participated properties, and 
 others fomething elfe of this kind. Whence fome one may doubt, whether to 
 ivalk, to be in health, and to fit, are being or twn-being. And in a fimllar manner 
 with refpe£l to other things of this kind. For no one of thefe is naturally 
 adapted to fubfift by Itfelf, nor can be feparated from eflence ; but this ought 
 rather to be faid of that which zvalks, and of that which ftSy and of that which 
 
 * It Is well obfervcd by Alexaiuler, thnt Ariflotle ufually aflumes for eflence hoc aliquid et 
 ^u'td ejl, i, e. Tc?E T( KM Ti i7ik : in Eiiglifti, this partieular individual thing, and what a thing is. 
 
 is
 
 Si)OK Vir. ARISTOTLE'S METAPHYSICS. tSl 
 
 is in health. For thefe rather than thofe appear to be beings, becaufe they 
 have a certaui definite fubjeiSt. But this is eflence, and that which is parti- 
 cular, which appears in a predication of this kind. For the good, or that 
 •whicli fits, is not allerted without this. It is evident, tlierefore, that each of 
 tliole fublills through this. So th:\t, that which is primarily being, and not 
 fome particular being, but being fimply, will be eflence. 
 
 That which is firil, indeed, is multifarioufly predicated ; but at the fame 
 time elTence is the firft of all things, in definition, knowledge, time, and na- 
 ture. For no one of the other predicates has a feparate fubfiftence, but this 
 alone. This alfo is firfl in definition. For it is neceflary in the definition 
 of every thing, that the definition of eflence fhould be inherent ; fince w? 
 then, think that we efpecially know any particular, when we know lahat man 
 is, or fire is, rather than when we know the quality ^ or quantity, ox fttuation 
 of a thing. For we then think that we know each of thefe things themfelves, 
 when we know ivhat the quantity or the quality is. Indeed, that which for- 
 merly has been, and which now is, continually inveftigated and continually^ 
 doubted, viz. what being is, is an inquiry what eflence is. For this is by 
 fbme faid to be one, but by others more than one ; by fome it is called things 
 finite, and by others infinite. Whence we alfo mufl: efpecially, and in the 
 firft place, and only, as I may fay, fpeculate refpedting that which is thus 
 being. 
 
 CHAP. ir. 
 
 But eflence appears * to fubfift moft manifeftly in bodies. On which- 
 account w^e fay that animals and plants, and the parts of thefe, are efl!ences, as 
 likewife natural bodies, v)Z. fire, water, and earth, and every thing of this 
 kind; and fuch things as are parts of thefe, or are compofed from thefe, 
 either partly or entirely ; fuch as heaven and its parts, the ftars, fun, and 
 moon» But whether thefe alone are eflences, or likewife other things,, or 
 
 * Ariftotle here with great propriety ufts the word Jokei, it appears. For eflence in bodie-s 
 has only an apparent.^ and not a real fubfiftence ; true ejjence being entirely feparate from body, 
 and perfeftly incorporeal. Suidas, therifore, rightly defines Sojoij^ij by uTiOwia, Jujpicion ; and no 
 lefs properly clalTes a perception of this kind with the perception of a phantafm, a dreamj-atuJ:- 
 a fliadow. Plato alfo ufes this wcrd with the fame accuracy, v.\\tn fucaking of the objefts of 
 opinion, phantafy, or fenfe ; but he never ufes it when fpeakiiig of true being, or, in othsr 
 words, the proper object of intelleiilual vifion. 
 
 "vvhethcic
 
 152 ARISTOTLE'S METAPHYSICS. Book VIT. 
 
 •whether none of thefe, but certaui other thhigs, mufl: be confiJered. To 
 feme, indeed, the boundaries of body, as for infhance fuperficies, line, point, 
 and monad, appear to be eflences, and to be more fo than body and folid. 
 
 Again, fome are of opinion that nothing has any fubfiftence befides fenfi- 
 b!es*; but others afiert that there are many kinds of eflences, and particularly 
 eternal entities. Among thefe is Plato, who eftabliflied two kinds of eflences, 
 viz. forms and mathematical fpecies ; and a third, the elfence of fenfible bodies. 
 But, according to Speufippus, there are many eflences beginning from the one^ 
 and principles of every efl'ence, one of numbers, another of magnitudes, and 
 another of foul ; and after this manner he extends efl'ences. Some again fay 
 that forms and numbers have the fame nature, but that things in a following 
 
 order 
 
 * " Such as Hippo," Tays Alexander, *' furnamed the Atheift, who denied that there was any 
 •thing beiides fenfibles, and after him the Epicureans." I am concerned to find, that this doc- 
 trine of Hippo and the Epicureans prevails fo much in the prefent age; though, indeed, this is 
 the natural confequence of an immoderate attachment to experimental inquiries, which, fo far 
 from leading the mind to the fpeculation of an incorporeal elTence, caufe it to gaze on nothing 
 but the dark and deformed face of matter, and to be the fpe£lator of nothing but delufion and 
 non-entity. Such, indeed, is the prevalence of this opinion, that a 'R''%ht Re-jermd Di-uU:e, fome 
 few years fince, delivered a fermon at the Magdalen ! in which he endeavours to prove 
 that the felicity of a future (late will be in a great meafure corporeal, confifting in certain ex- 
 quifite fenfations of delight. How much more pure, how much more fublime, the do(3:rine of 
 THE TRULY DIVINE PLATO, that the happinefs of the good man hereafter will alone 
 .con fill in intelletlual energies, and in the beatific vifion of divinity I For, in the Phaedrus, he 
 defcribes the felicity of the virtuous foul prior to its defcent into body, in a beautiful allufion to 
 the arcane vifions of the myfleries : Kaxxoj St tote w iSiiv >.atM7rpovy hit am (u^atf/.ovt x"??' naxa^iav cnj^ir 
 Ti uai Siav, I'lro/xcvct //.era fttv Sioj >i|U£i;, aXKoi Jt /*et' aXKou ^tav, ethv te kou eteXouvto teAetwv w Se/xi; Myen 
 fiaxx^tararm' nv qfyiafc.nEv oAoxAnfoi ftEv auToi svte;, xari ayraSiii xaxuv Ida nixa^ zv VTiptf x^"'''-? uTTi/^ifvcv. 
 OxoxXvfa hxat a'TTT^a xat aTpzym xai tuSai/xova ^airtiaTa -/ivoufA.evct te xat ETojrrEi/ovTf; iv aiyv xaSa^a xaSa^ot 
 evTci, xat ajflfisivnit tcutou o vi/v f» auna iTEfipsfoi/TEj ovcfiaio/itv offT^sou rpOTTOv li^d/xiufitvoi, 1 hat is, 
 " But it was then la-vful to furvcy fplcndid beauty, when we obtained, together with that happy 
 choir (/. e- the c'.ioir of mundane gods and dxnions), this bleded vifion and contemplation ; 
 and we, indeed, enjiiyed this felicity, following the choir together with Jupiter, but others in 
 conjunclion with fome other god ; at the fame time beholding and being initiated in thofe myf- 
 teries, which it is lawful to call the mod blcfled of all myfteries. And thefe divine orgies were 
 celebrated by us, while we pod'cficd the proper integrity of our nature, and were freed from the 
 ■iiiolcfl.ations of tliofe evils which awaited us in a fucceeding period of time. Likewife we became 
 initiated fpe£lators of entire, fimple, immoveable, and felicitous vifions, refident in a pure liglit ; 
 and were ourfclves pure and immaculate, and liberated from this furrounding veftment, which 
 we denominate body, and to which we are now bound like an oyller to its (hell." 
 
 .Such being the felicity of the foul according .to Plato prior to its tlefcent, fuch alfo will be its 
 
 felicity
 
 Book VII. ARISTOTLE'S METAPHYSICS, ' 153 
 
 order, viz. lines and fuperficles, as far as to the eflence of the heavens and 
 fenfibles, [are fecond eflences *]. But with refpe6t to thefe things we muft 
 conllder what has been well or III f fald, what etlcnces there are, and whe- 
 ther there are certain eflences befides fenfibles or not, and, If there are, in what 
 manner they fubfifl j alio, whether there is any feparate eflence, and why 
 there is, and how it fubfifts ; or whether there is no efl'ence befides fenfibles, 
 having lirft of all fummarily defcribed what effence is. 
 
 CHAP. III. 
 
 Essence then, if not multlfarioully, yet at leaft is predicated according to 
 
 felicity when it afcends, and acquires the perfeilion of i's nature. This, too, is conformable to 
 the doflrine of Ariftotle. For, in his Nichomachxan Ethics, he fliows that the eflence of man 
 confifts in intelle£l : and in his books On the Soul, that intelleft is the only part of us that is 
 immortal ; the irrational part perifhing after the death of the body. 
 
 Which of thefe two do£trines mod entitles its author to the epithet of divine, let the man of 
 jiiteHfH determine. For my own part, I am of opinion, that a Paradife, the felicity of which 
 partly confifts in certain exqiiifue fenfations of delight produced by objcBs acling on the organs ofjenfe, 
 very little differs from that of the poor Indian in Pope, 
 
 " whofe untutor'd minb 
 
 Sees God in clouds, or hears him in the wind. 
 
 His foul proud fcience never taught to ftray 
 
 Far as the folar walk, or milky way ; 
 
 Yet fimple nature to His hope has giv'n 
 
 Behind tlis cloud-topt hill, a humbler Heav'n : 
 
 Some fafer world in depth of woods embrac'd, 
 
 Sonle happier ifland in the wat'ry wafte, 
 
 Where flaves once more their native land behold. 
 
 No fiends torment, no Christians thirft for gold. 
 
 To BE contents his natural defire. 
 
 He afks no angel's wing, or feraph's fire ; 
 
 But thinks, admitted to that equal iky, 
 
 His faithful dog fhall bear him company." 
 
 And fuch a hope is very natural in a Right Simple Indian. 
 
 * The words within the brackets are omitted in the Greek text ; but it appears from the 
 Commentary of Alexander, and alfofrom theverfion of Argyropylus, that they properly belong 
 to it. The text of Alexander is, " fecundas aflerunt fubftantias efie." So that there is want, 
 irg to the Greek the words ffUTE^-af tivai oujria:,', 
 
 t 'H /«« alfo is here omitted in the original. 
 
 X four
 
 154 ARISTOTLE'S MET A PHYS I CS. Book VII. 
 
 four modes. For the formal caufe, unlverfal, and genus, appear to be eflence 
 to every thing ; and the fourth of thefe is the fubjedt. But the fubjed is thai 
 of which the reft are predicated, while itfelf is no longer predicated of any- 
 other thing. Hence this muft be the firft objeft of our inquiry. For eflence 
 appears to be efpecially the hrft fubjed. Such alfo matter is faid to be, after a 
 certain manner; form, in another refped ; and the third, that wliich is com- 
 pofed from thefe. But I mean by matter, for inftance, brafs ; by form, the 
 figure of the idea ; and by that which is compofed from thefe, the whole 
 ftatue. So that, if form is prior to matter, and is more being, that alfo which 
 is compofed from both will be prior for the fame reafon. Now, therefore, 
 we have, by a rude delineation, as it were, faid what eflTcnce is, viz. that it is 
 not predicated of a fubjed, but is that of which other things are predicated. 
 It is, however, necellliry not only to fpeak of it in this manner, for it is not 
 fufhcient. For this definition is obfcure ; and, befides this, matter is eflence. 
 For, if matter is not eflTence, what elfe is will efcape detedion : fmce, other 
 things* being taken away, nothing elfe appears to remain. For other things 
 are the participated properties, produdions, and powers of bodies ; but length, 
 breadth, and depth, are certain quantities, and not elfences. For quantity is 
 not eflence, but rather that in which thefe very things are primarily inherent, 
 that is, eflence. But, indeed, length, breadth, and depth, being taken away, 
 we fee that nothing remains except that which is defined by thefe. So that, 
 to thofe who thus confider the aff*air, matter alone mufl: neceflarily appear to 
 be eflence. But I mean by matter, that which of itfelf is neither called eflTencet 
 
 nor 
 
 * i. e. Quantities, qualities, liardnefs, foftnefs, &c. 
 
 + The following account of matter, principally collected from the writings of Plotlnus, as 
 it perfe£lly accords with, and at the fame time illuftrates, what is here faid by Ariftotle refpe£l- 
 ing this lad and mod obfcure of all things, will doubtlefs be acceptable to the truly philofophi- 
 cal reader. 
 
 That it is necelTary there fliould be fome general fubjed in bodies, the receptacle of every 
 form, is fufficiently evinced by the continual mutations of corporeal qualities ; fince nothing 
 that is tranfmutcd is entirely deftroyed, and no being is produced from that which does not exift. 
 Hence a change arifes from the departure of one quality and the acceflion of another ; the fub- 
 jecl matter always remaining, which receives a conftant fucceffion of generative forms. This 
 general fubjed, which is called the firft matter, in order to diflinguifh it from that matter which 
 is the objedl of fenfc, lias the fame proportion to whatever is fafliioned from it, as filence to 
 found, as darknefs to light, and as body rude and misfliapen to fome artificial form wliich it may 
 afterwards pofiefs. Thus the formlefs air admits the harmony of found ; and thus darknefs, 
 
 which
 
 Book VII. A Tx I 3 T O T L E'S M E T A P H Y S I C S. 15S 
 
 nor quantity, nor any one of thofe things by which being Is defined. For 
 there is fomething of which each of thefe is predicated, and from which 
 
 being 
 
 vLicli is neither fuffufed with colour nor dlverfified with form, becomes the fubjeft of both. 
 And as body, confidcred matliematically, is bounded by fuperficies, which pofieffing only length 
 and breadth cannot be body; fo body, confidered phyfically, or with refpe£l to its internal con- 
 llitution, is every where bounded in the fupreme part of its effence, by form, and in the loweft 
 part by matter, which is no longer a compofite, but is entirely denudated of form. For as, in an 
 afcending feries of caufes, it is neceflary to arrive at fomething which is the firft caufe of all, 
 and which even tranfcends every perfe£lion of being ; fo, in a defcending feries of fubjecls, it is 
 equally necedary to ftop at fome general fubject, the loweft in the order of things, and of which 
 ev'cry perfeclion of being is denied. 
 
 Form, therefore, refpe£ts the quality and figure of bodies, and matter pertains to the fubjed ; 
 and this becaufe it is deflitute of form, and without bound. This general receptacle, then, 
 which is faid to be void of quality, cannot be body. For, fince it is neceflary fimply to refer 
 rnatter to all things, we muft not attribute to it according to its nature any thing which is per- 
 ceived in the genera of fenfible beings. Hence, befides denying to matter other qualities, fuch 
 as colours, heat and cold, we muft neither afcribe to it levity nor gravity, neither rarity nor 
 denfity, neither figure nor magnitude. For magnitude itfelf is different from the fubje£l which 
 is great, and figure itfelf cannot be the fame with that which is figured. And matter can then 
 only be void of all form, when it is confidered as nothing compofite, but as fimple and one. 
 But it may be alked, after what manner we can apprehend a thing which is deftitute of magni- 
 tude ? Shall we fay. In the fame manner as we perceive the indefinite itfelf ? For, if fimilitude 
 is in a certain refpeft apprehended by the fimilar, the indefinite muft be perceived by the indefi- 
 nite itfelf. Reafon, indeed, by a difcurfive proceffion round the indefinite may become defined ; 
 but the intuition of the indefinite becomes an indefinite perception. Hence the phantafm of 
 matter is not legitimate, but fpurious ; for, as Plato fays, matter is only to be perceived by an adul- 
 terated reafon. In fhort, what darknefs, the fubjcdl: of all vifible colours, is to the eye, that mat- 
 ter is to the foul ; fo that the foul, by abftracting whatever in the genera of fenfible beings is, as 
 it were, of a luminous nature, and being incapable of bounding what remains, becomes fimilar 
 to the eye fixed in the depths of darknefs. But is the formlefs nature of matter by this mean 
 perceived .'' Perhaps it is beheld as fomething deftitute of figure, colour, and light; as pofleflT- 
 ing no magnitude, and bounded by no form. Nor muft we fuppofe that, when the foul under- 
 ftands nothing, flie is affe<Sled in the fame manner as when flie beholds the darknefs of matter. 
 For, when flie underftands nothing, flie afiirms nothing, or rather is paffive to nothing; but her 
 perception of a formlefs fubjedl is dark and (hadowy. When, therefore, in any compofite fub- 
 ftance, Ihe receives the fubjed together with its inherent properties, if ftie analyfes and feparates 
 the attendant forms and qualities, fhe flenderly perceives as fomething flenderthe refidue which 
 reafon leaves, beholds obfcurity obfcurely, and underftands as it were without intelledion. And 
 becaufe matter itfelf is never deftitute of form, but continually receives a variety of fuper- 
 vening forms, hence the foul quickly invefts it with form, not enduring any longer its dark in- 
 finity, as if fearing left it fhould rufli beyond the order of things, and impatient of longer abode 
 in the region of perfect non-entity. 
 
 X 2 This
 
 156 ARISTOTLE'S METAPHYSICS. Book VII. 
 
 being and each of the predications are dlfFerent. For the reft are predicated 
 of ellence ; but this of matter. So that the laft of all things is of itfelf neither 
 
 eflence, 
 
 This being the cafe, matter is incorpdreal ; for body is fomethi'ig pofterior and a compoflte, 
 :ind form, in conjunaion with fomething elfe, makes body. For thus it is allotted the fame 
 appellation according to an incorporeal genus, becaufe both being and matter are different from 
 bodies. But, fmce matter is neither foul, nor intellect, nor form, nor reafon, nor bound (for it- 
 is a certain infinity), nor power (for, what can it do .?j, but falls below all thefe, neither can it 
 properly receive the appellation of being, but may be jullly called non-being. Yet not as motion 
 is non-being, or reft is non-being, but it is true non-entity, the image and phantafm of bulk, and 
 the defire of fubfiftence ; abiding, indeed, yet not in permanency^ of itfelf invifible, and fiylng from 
 him who widies to perceive it. Likewife, when fome one does not perceive it, then it is palling 
 into e.\iftence, but is not feen by him who ftrives to behold it. In itfelf, too, contraries always 
 appear; the fmall and the great, the lefs and the more, the deficient and the tranfcendent. Sa 
 that it is an image, neither able to abide, nor yet to fly away. For neither has it power even 
 to effeft this, fuice it received no ftrength from intellect, but was generated in the deled of all 
 being. Hence, whatever it announces itfelf to be is falfe ; fo that, if it appears to" be fome- 
 thing great, it is fmal! ; if fomething more, it is lefs; and the being which prefents itfelf in the 
 imagination of it is non-being. It is, therefore, as it were, a flying mockery; and, in confe- 
 quence of this, whatever appears to be generated in it is itfelf a mockery, being nothing more 
 in reality than an image in an image ; jult as with rtfpect to a mirror, where a thing itfelf is 
 fituated in one place, and its refemblance in another, and which is apparently filled, and is appa- 
 rently all things, yet pofTefles nothing. Bur the things which enter into and depart from mat- 
 ter are imitations and refemblances of beings, flowing about a formlefs refemblance; and in 
 confeqnence of becoming vifible through its formiefs nature, they appear indeed to effeil fome- 
 thing in it, but effeift nothing. For they are evanefcent and imbecil, and have no repercufilve- 
 power. And as this alfo is the cafe with matter, they pervade without dividing it, like images in 
 water, or as if any one fliould introduce forrns into that which is called a vacuum. Indeed, if 
 the things beheld in matter were fuch as the forms whence they are derived, it might be faiJ 
 that matter is pailive to thrir reception. But now fince the thi-gs which are reprefented are 
 difl^erent from thofe which are feen in its dark receptacle, we may from hence alfo learn that its 
 paflion is falfe, fince that wliich is feen witiiin is falfe, and pofl^cfles no fimilitude to that wlience- 
 it originates. As thefe reprefentations, therefore, are imbecil and falfe, and fall into that 
 which is falfe, fo as to refemble images in water, or in a mirror, or a dream, they necefl"a- 
 rily permit matter to remain impaflive ; though, in the particulars juft now adduced, there is a 
 certain fimilitude, in tlie phantafms beheld within, to their originals. 
 
 In (hort, as Simplicius well obferves (in Arili. Phy f p. 50, b.), matter, according to the Pythago- 
 rjeaiis and Plato, is nothing elfe than the permutation and vicifFitude of fenfible forms, with re- 
 fpect tointelligiblesj fince from thence they verge downv.-ards and extend to perfe£l non-entity, 
 or the lad of things — that is, to matter itfelf. Hence, fays he, becaufe dregs and matter are al- 
 ways the laft of things, the Egyptians alfert that matter, which they enigmatically denominate 
 water, is the dregs of the firft life, fubfilting as a certain mire or mud, the receptacle of gene- 
 rated and fenfible natures ; and which is not any definite form, but a certain conftitution of fub- 
 
 fillence.
 
 EooKVn. ARISTOTLE'S METAPHYSICS. 157 
 
 eflence, nor quantity, nor any thing elfe ; nor yet negations : for thefe alfo 
 fubfift according to accident. From thefe confiderations, therefore, matter 
 
 appears 
 
 fiftence, in the fame manner as that which is indlvifible, immaterial, and true being, is a confti- 
 tution of an intelligible nature. 
 
 Such then being the true condition of matter, and fuch the (hadowy nature of the forms 
 which (he contains, Plotinus * beautifully obferves that being, properly fo called, is neither body . 
 nor is fubjefl to corporeal affeiSlions ; but body and its properties belong to the region of non- 
 entity. But you will a(k (fays he), How is it polhble that vifible matter fhould pofH^fs no real 
 being ; that matter which contains (tones and mountains, the folid earth, and bodies v/hich mu- 
 tually refift ; fince bodies which impel each other confefs by tlieir collifion the reality of their 
 exigence ? You will likewife afk, After what manner things which neither ilrike againfl: nor 
 refift each other; which neither externally aft, nor internally fufFer, nor are in any refpecl the 
 objecVs of fight, viz. foul and intellett, are to be reckoned true and real beings ? We replvj- 
 That, on the contrary, things more corpulent are more fluggifti and inert, as is evident ia bulky 
 mafles of earth ; but whatever is lefs ponderous is more moveable and alert, and the more ele- 
 vated the more moveable. Hence fire, the mod moveable of all the elements, flies in a manner 
 from a corporeal nature. Befides, as it appears to me, whatever is more fufficient to itfelf dif- 
 turbs others lefs, and brings lefs inconvenience : but fuch things as are more ponderous and 
 terrene, unable from their defect of being to raife themfelves on high, and becoming debile and 
 languid, ftrike and opprefs furroundlng bodies by their falling ruia and lluggifli weight; — fmce 
 it is evident that bodies deftitute of life fall with moleftation on any proximate fubllance, and 
 move vehemently impel and pain whatever is endued with fenfe. On the contrary, animated 
 beings, as participating more of entity, by how much the more of being they poflefs, by fo much 
 the more innoxioufly they impinge on their neighbouring bodies. Hence motion, which is a. 
 kind of life, or foul, or an imitation of life in bodies, is more prefent with whatever is lefs 
 corpulent ; as if more of body was neceffarily produced where a defect of being happens in a 
 greater degree. 
 
 Again : it will more manifeftly appear from pafiivity, that whatever is more corpulent is more; 
 paflive ; earth in a greater degree than the other elements ; and the refl in a fimilar proportion. 
 For fome things, when divided, fuddenly return to their former union, when no obftacle prevents 
 their conjuction ; but, from the fe£tion of a terrene body, the divided portions always remain 
 feparate, as if dclHtute of natural vigour, and without any inherent defire of union and con- 
 fent. Hence they are ready, by every tiifling imptilfe, to remain as they are impelled ; to 
 rufh from the embraces of bound, and haften into multitude and non-entity So that, whatever 
 becomes. corporeal in an eminent degree, as rapidly falling into non entity, has but little power 
 of recalling itielf into one. f- nd on this account ponderous, and, at the fame time, vehement 
 concuffions are attended with ruin, when by mutu.il rufhing one thing impels another. But 
 ' when debility falls on debility, the one is valid againit the other, in the fame manner as non- 
 entity rufhing on non-entity. And this wc think a fufficient confutation of their opinion, who- 
 only place being in the genus of body, perfuaded by the telHmony of impulfes and concuffions, 
 and the phantafms perceived through the fenfes, which tcltify that fenfe is alone the fl.indard o£ 
 
 '* Eiincad. 3, lib. 6, 
 
 trutlij
 
 153 ARISTOTLE'S METAPHYSICS. Book VII. 
 
 appears to be eflence. It is, however, impoffible : for a feparate fubfiftence, 
 and iubfifling as this particular thing, appear efpecially to belong to effence. 
 Hence form, and that which fubfifts from both, appear to be more effence 
 than matter. That effence, therefore, which fubfifts from both (I mean from 
 matter and form) muft be omitted : for it is pofterior and manifeft. Matter 
 alfo is in a certain refpe£l: manifeft*. But let us confider refpeding the 
 third f ; for this is moft dubious : and as it is acknowledged that there are 
 certain effcnces of fenfibles, let us make our firft inquiry in thefe. 
 
 CHAP. IV. 
 
 Since, then, In the beginning of this book, we have fhown In how many 
 ways we divide eiTcnce, and one of thefe is the very nature of a thing, let us 
 contemplate this. For it is very advantageous to pafs on to that which is 
 more known. For thus all men acquire difcipline, by proceeding through 
 things Icfs known to nature if, to fuch as are more known. And as in prac- 
 tical affairs it is requifite from thofe things which are good to fome one to 
 efFedt fuch as are altogether good, and the good of every one ; fo, from 
 things more known to every one, thofe things which are known to nature 
 and to lome one are to be made known. But things which are known to 
 individuals, and fuch things as are firft to thefe, are often but little known, 
 and have little or nothing of being. At the fame time, however, from things 
 which are known in a depraved manner, but are known to fome Individual, 
 we fhould endeavour to know things which are altogether known, proceeding 
 as we have before faid through thefe very things themfelves. 
 
 truth. Such as thefe are affected in a manner fimilar to thofe in a dream, who imagine that the 
 perceptions of fleep are true. For fenfe is alone the employment of the dormant foul : fince 
 as much of the foui as is merged in body, fo much of it fleeps. But true elevation and true vigi- 
 lance confift in a refurreclion from, and not with, the dull mafs of body. For indeed a refurrec- 
 tion with body is only a tranfmigration from fleep to fleep, and from dream to dream, like a man 
 pafl"mg in the dark from bed to bed. But that elevation is perfe£lly true, which entirely rifes 
 from the c e id weight of bodies : for thefe, pofleffing a nature repugnant to foul, poflcfs Ibme- 
 thing opptfite to eilence. And this is further evident, from their generation and their conti- 
 nual flowing and decay ; properties entirely foreign from the nature of being, fubflantial and 
 real. 
 
 * That is to fay, it is manifeft by analogy. 
 •}• Viz. Form. 
 
 J Particulars are Icfs known to nature, ;. e. have naturally lefs of the fplendor of truth. 
 
 And
 
 BooKVir. ARISTOTLE'S METAPHYSICS, 159 
 
 And in the firfl: place, we fliall fay fomething refpeding tliem logically. 
 The very nature of a thing *, therefore, is that which a thing is faid to be 
 efTentialiy. For your eifence does not confid in being a mufician ; fince you 
 are not a mufician according to yourftlf. Yet, not every thing which is efTen- 
 tialiy prefent to a thing is the very nature of that thing. For this is not the 
 cafe with that which is fo eflentially prefent as a white fuperficies, becaufe the 
 being of a fuperficies is not the fame as the being of whitenefs. But neither 
 is that which is compofed from both, viz. the eflence of a white fuperficies, 
 the fame as the eflence of fuperficies. Should it be alked. Why is it not ? we 
 reply, Becaufe fuperficies is contained in the definition of a white fuperficies. 
 Hence, that is a definition fignifying the very nature of a thing, in v\'hich the 
 thing defined is not inherent. So that, if the being of a white fuperficies is 
 the being of a fmooth fuperficies, the being of white and fmooth is one and 
 the fame. But fince there are alfo compofites according to the other catego- 
 ries (for there is a certain fubjedl to each, as, for inftance, to quality, to quan- 
 tity, to when, where, and to motion), let us confider whether there is a defi- 
 nition of the very nature of each of them, and whether the very nature of a 
 thing is prefent with thefe ; as, for inftance, what the very nature is of a 
 •white man. But let his name be garment. What then is the being of a 
 garment ? But, indeed, neither is this among the number of things which 
 are predicated effentially. Or fliall we fay that a thing which is not eflential 
 is predicated in a twofold refped ? and that of this, one thing is from addi- 
 tion, but another not ? For one thing is faid to be that which is defined, be- 
 caufe it is added to another thing; as, if any one defining the being white 
 fhould aflume the definition of man : but another thing is fo denominated, 
 becaufe fomething elfe Is not added to it; as, if a garment fignifies a white 
 man, but foiiie one fliould define the garment as white. A white man, there- 
 
 * The very nature of a thing : in the original to ti w ttvai. The following is part of the com- 
 ment of Alexander Aphrodifi.'nfis on thefe words : " Ariftotle calls to tj >jv hvcu a thing itfelf, , 
 and its conjoined nature which is at the fame time underftood, and which is fignified by its 
 name. For man is a name fignifying the very nature of the thing which is fignified by the 
 name man." And fliortly after he adds: " liut definition is a conception, according to Ari- 
 ftotle, arifing from explaining and enunieratinE; the parts from which form confifts. The to tj 
 w eivai, therefore, diffsrs from definition in rhis, that it is a certain confufed intelle(3:ion, and^as 
 it were, expreffion, and v hich contemplates a thing as one ; but definition is a certain unfold- 
 ing of a thing, and a narration of its parts." This to t( w tivai was called by the fchoolmen 
 qutdditaSf quiddity, 
 
 fore,.
 
 160 ARISTOTLE'S METAPHYSICS. Book VII. 
 
 fore, In this cafe is fomething white, yet his very nature does not confift in 
 being white, but in being a garment. 
 
 Is there then, in fliort, luch a thing as the very nature of beings, or not ? 
 For the very nature of a thing is the eflence of that thing. But, when one 
 thing is predicated of another, it is not properly this particular thing \ as, a 
 white man is not tb'n particular things if the being this particular thing 
 belongs to eirenc«.s only. So that the very nature of a thing pertains to thofe 
 things the difcourfe rclpeding which is a deliniticn. But not every dif- 
 curfus which fignifics the fame thing as a name is a definition (fince if this 
 were the cafe aU difcourfes would be definhions : for name will be the fame 
 with any difcourfe whatever ; fo that the word Iliad will be a definition) : but 
 adifcouife is then a definition when it is of fome fir.l thing. But things of 
 this kind are fuch as arc denominated, not from one thing being predicated of 
 another. The very nature of a thing, therefore, does not belong to any thing 
 befides the fpecies of genus, but to thefe alone. For thefe appear to be predi- 
 cated, not through participalion, and p^fTion, nor as accident, but there will 
 be a difcourfe of each thing; and it will fignify fomething of other things, if 
 it Is a name ; I mean, that this thing is Inherent In this, or, inftead of a fimple 
 aflTertion, is more accurate : but it will not be definition, nor the very nature of 
 a thing. Or fliall we fay that definition, as well as the eflence of a thing, is 
 predicated multifarioufly ? For the inquiry what a thing is, In one way, fignl- 
 iies eflence, and this particular thing ; but, In another, each of the categories, 
 viz. quantity and quality, and the reft of this kind. For, as the Inquiry vyhat a 
 thing Is, belongs to all things, though not in a fimilar manner, but to one thing 
 primarily, and to others in a confequent order ; in like manner definition, 
 /imply indeed, pertains to effence, but in a certain refpeB to other things. For 
 ■we may afk what quality is ; (o that quality Is of things to which the inquiry 
 what they are, belongs ; yet not fimply, but juft as of non-entity : fome, logi- 
 cally arguing, fay that it is non-entity, yet do not fimply aflert that it />, but- 
 that it is non-entity ; fo alfo with refpeft to quality. 
 
 It is requifite, therefore, to confidcr how we ought to fpeak refpcffling each, 
 yet not more than in what manner each fubfift:s. Hence, now alfo, fince that 
 which is afferted Is manlfeft, the very nature of a thing in a fimilar manner will 
 be primarily and fimply inherent In eflence, and afterwards in other things, 
 juft as in the inquiry what a thing is. So that the very nature of a tFvtg will 
 fubfift v.'ith the addition of quality or quantity. For it is requifite to aflert, 
 
 that
 
 BookVII. ARISTOTLE'S METAPHYSICS, I6l 
 
 that thefe things are beings, either equivocally, or with addition and ablation, ia 
 the fame manner as that which is not the objedl of fcientiiic knowledge, is 
 fcientifically knowm ; fmce it is right neither to fpeak of thefe equivocally, nor 
 after the fame manner : juft as with refped; to the medicinal art, which is 
 predicated with relation to one and the fame thing, without being one and 
 the fame, and yet is not equivocally predicated. For no medicinal body is 
 called a work and an apparatus, neither equivocally, nor according to one 
 thing ; but with relation to one thing. With refped: to thefe things, however, 
 it is of no confequence in what manner any one may be willing to fpeak of 
 them. This, indeed, is evident, that definition primarily and fimplv confi- 
 dered, and the very nature of a things belong to eflences ; and in a fimilar 
 manner they alfo belong to other things, though not primarily. For, thouo^h 
 it fhould be admitted that any name has the fame (Ignification with a dif- 
 courfe, yet it does not necelTarily follow, that a difcourfe about that which the 
 name fignifies is a definition ; but this will take place when a name has the 
 j'amc fignification with a certain difcourfe. This, however, happens, if it is 
 of one thing, not by continuation as the Iliad, or fuch things as are one by 
 conjundion, but if it is multifarioully predicated as one thing. But unity is 
 predicated in as many ways as being ; and being partly fignifies fubflance, 
 partly quantity, and partly quality. Hence there will be a certain difcourfe 
 about, and definition of, a white man ; and after another manner, of that alfo 
 which is white, and of cflence. 
 
 CHAP. V. 
 
 A DOUBT, however, arifes, If any one fliould deny that definition is a dif- 
 courfe fubfifting from addition, of what will the definition be of things not 
 iimple but conjoined ? For it is necellary that they fliould be rendered mani- 
 feft from addition. But, I fay, for inftance, there, is nofe, and concavity, and 
 flatncfs, and * that which is denominatedfrom both f, becaufe this is inherent 
 in that, and neither concavity nor flatnefs is an accidental, but an ellcntial, pro- 
 perty cf the nofe; nor do tlicy fubfift as whitenefs in Callias or man, becaufe 
 Callias is white who happens to be a man ; but they fubfift as the male in 
 animc-^l, and the equal in quantity, and in the iamc manner as all fuch things 
 
 * Inftead of to ik toiv SVoiv, the fenfc re*]U!rcs km to ty. toiv 5i/oiv, &c. 
 t /'. e. From nofe and (l.tnefs. 
 
 Y as
 
 162 ARISTOTLE'S METAPHYSICS. Book VIL 
 
 as are fald to be effentially inherent. But thefe are things in which either the 
 definition or the name of which this is the property is inherent, and which 
 cannot be manifefted feparately, in the fame manner as whitenefs can be ma- 
 nifcfted without man ; but the feminine cannot be rendered apparent without 
 animal. So that the very nature and definition of thefe are either of noihing^ 
 or, if there is a definition of thefe, it is in the manner we have previouily 
 related. 
 
 There is alfo another doubt refpeding thefe things : for, if a flat nofe and 
 a concave nofe are the fame, the fl at and the concave will be the fame : but if 
 not, becaufe it is impoffible to ufe the word flat-nofe, without the thing of 
 which it is an effential property, and flatnefs of nofe is a hollownefs in the 
 nofe, either it is not poflible to fay a flat nofe, or the fame thing will be faid 
 twice, /. e. nofe, concave nofe : for a flat nofe will be a concave nole. Hence, 
 it is abfurd, that the effential fhould be inherent in things of this kind : for, if 
 it were *, there would be a progrefHon to infinity ; fince in nofe, concave nofe, 
 fomething elfe eflential would be inherent. It is evident, therefore, that defi- 
 nition is of elTence alone, Foi", if it were alfo of the other categories, it 
 mud neceffarily be from addition, as, for inftance, in the definitions of qua- 
 lity and the odd. For it is not framed without number ; nor the definition 
 of feminine without animal. But I fay, that thofe definitions are compofed 
 from addition, in which the fame thing happens to be faid twice, as in thefe : but 
 if this be true, neither will there be definitions of things conjoined, as, for in- 
 ftance, of an odd number. However, they do not perceive that the definitions 
 of thefe things are not accurately afl[igned by them. But if there are alfo de- 
 finitions of thefe things, they are either after a different manner, or, as we have 
 faid, definition and the very nature of a thing have a manifold fubfiftence. So 
 that in one refpedl definition and effence will not be inherent in any one of 
 thefe except effences, and in another refpeft they will be inherent. That de- 
 finition, therefore, is a defcription of the very nature of a thing, and that the 
 very nature of a thing either alone belongs to effences, or efpecially, both 
 primarily and fimply, is evident. 
 
 * The original here has erroneoufly fi Si im, inftead of ti h. That it is an error is evident, 
 from the fenfc of the paflage, and the text of Alexander. 
 
 CHAP.
 
 BookVIL ARISTOTLE'S metaphysics. 16| 
 
 CHAT. VI. 
 
 Let us now confider, whether the very nature of a thhig is the lame with 
 each individual thing, or different from it. For this will very much contribute 
 to the fpeculation refpeding effence ; fince each particular thing does not ap- 
 pear to be different from its own effence ; and the very nature of a thing is faid 
 to be the effence of that thing. But in things which are predicated according 
 to accident, thefe two may appear to be different ; as, for inftance, a white 
 man, and the being of a white man. For if a white man and the being of 
 a white man were the fame (for man and a white man are, as they fay, the 
 fame), then, the being of a white man would be the fame with the being of 
 man feparately confidered. Or is it neceffary, that things which fubfifl: 
 according to accident fhould be the fame [as thofe things which have an 
 effential fubfiftence] * ? For the extremes do not become fimilarly the fame. 
 But perhaps it may appear to happen, that the extremes will become the fame 
 according to accident ; as, for inftance, the being of white and the being of a 
 mufician. This, however, does not appear to be the cafe : but in things 
 which are effentially predicated, it is always neceffary that they fhould be the 
 fame, as muft be the cafe with certain effences, if there are fuch, to which 
 there are no other effences, nor natures prior, fuch as fome affert ideas to be. 
 For, if the good itfelf were different from the being of good, animal from the 
 being of animal, and being from the effence of being, there would be other 
 effences and ideas befides thofe which are faid to be, and thofe would be prior 
 effences, if there is an effence of effence itfelf. And if, indeed, they are un- 
 conneded with each other, of thefe f there will not be fcience, and thofe \ will 
 not be beings. But I mean by being unconneded with each other, if neither 
 the being of good is inherent in good hfelf, nor to be good pertains to this. 
 For a fcientific knowledge of a thing is a knowledge of the very nature of 
 that thing : and the like takes place with refpea: to good and other things. 
 So that, if neither the being of good is good, neither will the effence of 
 bdng be being, nor of the one be one ; and in a fimilar manner, all or none of 
 
 • The words v/ithin the:brackets are added from the Commentary of Alexander, becaufe, as 
 he juftly obferves, they are requifite to the completion of the fentence. 
 tf Viz. Of map itfelf, horfe itfelf, and of other ideas, there will not be fcience. 
 t Viz. The being of man itfelf, horfe itfelf, will not be beings. 
 
 Y 2 . the
 
 164 ARISTOTLE'S METAPHYSICS. Book Vm 
 
 the eflences of ideas have a fubfiftence. So that if the eflence of being is not 
 being, neither will the eifence of any one of the reft. 
 
 Further ftill : that in which the eflence of good is not inherent is not 
 good. It is neceffary, therefore, that good and the eflence of good fliould be 
 one ; alfo the beautiful and the eflence of the beautiful, and fo of all fuch 
 things as are not predicated through another, but are firft natures, and have 
 an eflential fubfiflence. For this is fufficicnt if it takes place, though forms 
 Ihould have no fubfiflence, though perhaps it is more fo if they do fubffl *. At 
 the fame time it is evident, that if ideas are fuch things as fome fay they are, 
 eflence will not be as a fubje£t to them. For it is neceflary that thefe (hould 
 be effences, and that they fliould not be predicated of a fubjedt ; for, if they 
 were, they would fubfift according to participation. From thefe reafons, 
 therefore, it is evident that each particular itfelf, and the very nature of a 
 thing, are one and the fame, not according to accident ; and that to have a 
 fcientific knowledge of any thing, is to know fcientifically the very nature of 
 that thing. So that, from indudion it is necefl"ary that both fhould be one 
 thing. But it is not true to affirm, that a thing which is predicated according 
 to accident, as a mufician, or that which is white, is the fame as the very nature 
 of a thing itfelf, becaufe that to which it happens, and the accident itfelf, have 
 a twofold fignification. So that in a certain refpedt a thing itfelf is the fame, 
 and in another refpedl is not the fame, with the very nature of a thing. For 
 the being of man is not the fame thing with that of a white man ; but fo far as 
 the eflence of man is paflive to whltenefs, or is whitened, it is the fame. But 
 it may appear to be abfurd alfo, if fome one fliould call an individual the very 
 nature of a thing ; for there wiU be another very nature of a thing befides that, 
 as, befides the eflence or very nature of a horfe f, there will be another very 
 nature of a horfe. Though what hinders but that now certain effences them- 
 
 felves 
 
 * If this is more true if ideas have a fubfiftence, there muft be ideas ; for Ariftotle himfelf 
 in the fccond book of this work fays, " As is the being of every thing fuch alfo is its truth," 
 For the folution of Arillotle's objeftions to the dotlrine of Ideas, fee the Notes to the thirteenth 
 and fourteenth books. 
 
 \ The demonflration of Ariftotle in this place proceeds on the hypothefis of ideas. But his 
 meaning appears to be as follows : If horfe and the very nature of horfe are not the fame but 
 difFcrcnt, let a name be given to this very nature of a horfe, and let it be called garment. Since, 
 then, every name fignifies fome very nature of a thing, the very nature of a garment will be differ- 
 ent from the garment. Again : let the very nature -of this garment be called plant, and the 
 
 very
 
 BookVII. ARISTOTLE'S metaphysics. 165 
 
 felves in continued fucceflion may be the fame as the things of which they 
 are the very natu'^es, if the very nature of a thing is effence ? They are, 
 how^ever, not only one, but the definition alfo of them is the fame, as is evi- 
 dent from what has been fald. For to be one, or the being of one, and one, 
 are not one according to accident. Again : if they are different, there will be 
 a progrefhon to infinity. For the one, being as it were the effence of one 
 thing, will be the very nature of that thing, but the other will be that one 
 thing itfelf. So that there will be the fame definition of them. That in 
 things firft, therefore, and fuch as are effentially predicated, the effence of a 
 thing, and the thing itfelf, are one and the fame, is evident. But it is alfo 
 evident, that fophiflic arguments againi^ this pofition are folved by the fame 
 folution. For the fophifts inquire. Whether Socrates is the fame with the 
 effence of Socrates ? For there is no difference with refped: to the things 
 from which the interrogation may be made, nor thofe which may be em- 
 ployed by him who folves the queftion. We have, therefore, fhown, after 
 what manner the very nature of a thing is the fame, and in what refpetfl it 
 is not the fame with any particular thing. 
 
 CHAP. VIL 
 
 Of things which are generated, fome are produced by nature, others by art, 
 and others by chance: but all things which are generated are generated by fome- 
 thing, and from fomething, and become fomething. But I mean that they 
 become fomething according to each of the categories : for they either become 
 fubftance, or quantity, or quality, or where. But natural generations are thofe 
 the generation of which is from nature : and that yrora which they are gene- 
 rated is that which we call matter. That by which they are generated is fome 
 one of the things which have a natural fubfiftence. And that which is fome 
 particular thi?igy is man or plant, or fome one of fuch like things which we fay 
 are efpecially effences. All things, indeed, which are generated either by na- 
 
 very nature of a plant will be different from plant. And if this name plant be affigned another 
 name, it will alfo have another very nature different from itfelf, and this will be the cafe ad inj^- 
 tiitum. If, therefore, any one gives a name to a thing, fince of every word fignifying effence there 
 is a very nature, befides that name there will be another very nature, as, befides the veryjjature 
 of a horfe, there will alfo be another very nature. So that if there is another very nature of 
 the very nature of a horfe, there will be two natures of a horfe and two efl'ences,, and not two 
 only, but an infinite number. 
 
 ture
 
 166 ARISTOTLE'S METAPHYSICS. Book VII. 
 
 ture or art, have matter : for it is poffible for each of them to be and not to 
 be ; which capabiUty is the matter in each. And, in fhort, nature is that from 
 which, and that according to -which. For that which is generated has matter, 
 as, for inftance, a plant or animal : and alfo that froin ivhich^ viz. Nature her- 
 felf, which is predicated according to form, and is, indeed, of a fimiiar fpecies. 
 But this fubfifts in another : for man generates man. After this manner, 
 therefore, are things generated generated through nature. But other gene- 
 rations are called makings. All makings, however, are, either from art, or from 
 power, or the dianoetic part. But of thefe fome are alfo generated from 
 chance and fortune, juft as in things which are generated by nature. For 
 there, alfo, fome things are generated the fame, both from feed, and without 
 feed. Concerning thefe things, however, we Ihall confider hereafter. But 
 things are produced from art, the form of which is in the foul. But / mean 
 by form the -very nature of every thing and the firjl ejfence. For after a man- 
 ner there is the fame form * of contraries. Thus, an oppofite eflence is the 
 elTence of privation, as, for inftance, health of difeafe. For the abfence of 
 health manifefts difeafe. But health is reafon in the foul and in fcience. 
 Health, therefore, is produced, when the phyfician thus reafons : — If this is 
 health, it is neceffary that the inequality of things hot and cold fhould pafs 
 into equality. And if this is to be efFeded, it is neceffary that heat fliould 
 arife. In this manner he perpetually reafons, until he arrives at that which at 
 laft he is able to effeil. Afterwards, that motion which now begins from 
 this, is called the making which leads to health. So that it happens after a 
 manner, that health is produced from health, and a houfe from a houfe, viz. 
 that which pofTefTes matter is produced from that vi'hich is without matter. 
 For the medicinal art is the form of health, and the building art of the houfe. 
 But I call effence without matter, the very nature of a thing. 
 
 Moreover, of generations and motions this is called intelle£lion, and that 
 Tsiaking. That, indeed, which begins from the principle and form is intellec- 
 tion ; but that which commences from the end of intellection is making.. In 
 like manner, each particular thing is produced in other things which fubfift as 
 mediums. I fay, for inftance, if health is to be reftored, it is neceffary that a 
 redu£lion to equality ftiould take place. And this will be effeited if heat is 
 introduced. And what is this ? It is this particular thing. But this particu- 
 
 » Becaufe form gives fubfiftencc to beings, and is the caufe that privations are numbered 
 among beings. 
 
 lar
 
 Book VII. ARISTOTLE'S METAPHYSICS. 167 
 
 lar tiling fubfifts in capacity. And this is now placed in the power of the 
 phyfician. 1 hat which makes, therefore, and that whence the motion of re- 
 ftoring health begins, if it is from art, is form in the foul ; but if from chance, it 
 begins from that which is finally the principle of making to him who makes 
 according to art: as alfo in healing, the principle perhaps is from imparting 
 heat ; but this is accompliflied by friction. Heat, therefore, in the body, is^ 
 either a part of health, or fome fuch thing which is a part of health follows- 
 it either immediately, or through many mediums. But this which makes is the 
 laft, and is in fuch a manner a part of health, as ftones are parts of a houfe, or 
 other things of fomething elfe. So that, as it is faid, it is impofTible for any 
 thing to be generated, if nothing pre-exifts. That a part, therefore, exifts 
 from neceflity is evident : for matter is a part, fmce it has an inherent fubfift- 
 ence, and is itfelf generated. But does it rank among things which belong to 
 definition ? Indeed, in both refpe£ls, we aflert what many circles are ; and 
 fpeaking of the matter, we fay it is brafs ; and of the form, that it is fuch a 
 figure: and this is the genus in which it is firft placed. But a circle of brafs 
 contains matter in its definition. Some things, however, when they are pro- 
 duced, are not called that from which they are produced as from matter, but 
 are called fomething of that kind ; as a ftatue is not called a ftone, but ftony. 
 But a man who is recovering his health is not called that from which he re- 
 covers his health. But the caufe of this is, that they are geuerated from pri- 
 vation, and a fubjedt which we call matter. Thus, for inllance, both man and 
 he who is fick are made well. Yet, health is rather faid to be produced from 
 privation, as, for inftance, from him who is fick, than from man. Hence, he 
 who is healthy is not faid to be tending to ficknefs ; but this is faid of man,, 
 and man in health. But with rcfped to things of which the privation is un- 
 certain and namelefs, as in the brafs of any figure, or in the tiles or wood of a 
 houfe, thofe tilings appear to be generated from thefe, as, in the former in- 
 ftance, from him who is tending to ficknefs. Hence, as, there, that which h 
 produced is not called by the name of that from which it is produced j fo nei- 
 ther here is the ftatue called wood, but derivatively wooden ; brazen, and not 
 brafs ; ftony, and not ftone. The houfe alfo is not called tiles fplinthoi), but 
 plinthine *. For, if any one attentively confiders, he will not fimply fay that 
 the ftatue is made from wood, or the houfe from tiles j becaufe it is requifite 
 
 * This word Is a derivative from tiles, in the fame manner as brazen from brafs. 
 
 that
 
 168 ARISTOTLE'S METAPHYSICS. Book VII. 
 
 that whatever is generated from any thing fliould be changed from that from 
 which it is generated, and fhould no longer remain that which it was before. 
 On this account, therefore, it is thus denoniinated. 
 
 CHAP. viir. 
 
 Since that which is generated is generated by fomething (but I call this 
 that whence the principle of generation is derived) and from fomething ; let 
 riiis not be privation but matter (for the manner in which we denominate this 
 has been alresdy defined). There is alfo that which is generated ; but this is 
 either a fphere or circle, or whatever elfe may cafually prefent itfelf. [*More- 
 over, as that whence the principle of motion is derived] neither makes the 
 fubjedl, I mean the brafs itfelf, fo neither does it make the fphere, unlefs from 
 accident, /. e. becaufe a brazen fphere is a fphere ; but the fphere itfelf it does 
 not make. For, to make this particular thing, is to make it this particular 
 thing from the whole fubjedt. I fay, for inftance, that to make the brafs 
 round, is not to inake the round, or the fphere, but fomething elfe, viz. this 
 form in another thing. For, if it makes, it will make from fomething elfe : for 
 this was fuppofed ; as, for in Ranee, to make a brazen fphere. But this he thus 
 makes, becaufe, from this which is brafs, he makes this which is a fphere. 
 If, therefore, he alfo makes this very thing itfelf, it is evident that he makes in 
 a fimilar manner, and the generations will proceed to infinity f. It is evi- 
 dent, therefore, that neither \% /pedes (or by whatever other name it may be 
 proper to call ihejorm in fenfibles) generated, nor is it that which is the very 
 nature of a thing. For it is generated in another, either from art, or from 
 nature, or from capacity. But the efficient caufe makes the fphere to be 
 brazen : for it makes from brafs and fphere. For in this it makes this form : 
 and this is a brazen fphere. 
 
 '^ The words within the brackets are omitted in the printed text, but are fupplled from the 
 text of Alexander. 
 
 f As he who makes a brazen fphere, makes it to be this compofite fpliere from brafs; fo, if it 
 were poffible to make the form and very nature itfelf of a fphere, it mufl be made from fome 
 fubjedl : and therefore, this form being itfelf a compofite from matter and form, that form alfo 
 would require to be generated ; and fo the generations would proceed to infinity. Hence, the 
 form which is produced in afenfible fubjeft is not introduced through generation, but is inge- 
 nerated in it, in a point of time and an indivifible moment. And this inftantaneous union of 
 form with matter imitates the at-once-colle£led and eternal proceflion of all things from tl.ke 
 ineffable principle of all. 
 
 But,.
 
 BooKVir. ARISTOTLE'S METAPHYSICS. 169 
 
 But, in (hort, if there is a generation of the eflence of a fphere, it will be 
 from a certain fomething. For it will be requifite that that which is generated 
 fhould always be divifible *, and that this fhould be one thing, and that an- 
 other ; I mean, that this fhould be matter, and that form. But, if a fphere is 
 a figure equal from the middle, of this, one part will be that in which the 
 produdion of the efficient will be inherent ; but the other, that which will be 
 inherent in this part f ; but the whole will be that which is efFcded, as, for 
 xnftance, the brazen fphere. It is evident, therefore, from what has been faid, 
 that that which is denominated as form, or as efTence, is not generated ; but 
 that the concourfe J which is faid to take place according to this, is generated : 
 alfo, that in every thing which is generated matter is inherent ; and that one 
 part is matter, but the other form. Is there, then, any fphere befides thefe, or 
 houfe, befides tiles ? Or fhall we fay that, if this were the cafe, this particular 
 thing% would never have been generated, but becaufe it fignifies fuch a particu- 
 lar thing. This, however, is not definite, but makes and generates fuch a parti- 
 cular kind of thing from this particular ; and when it is generated it is this thing 
 with fuch aparticular quality. But the whole of this is Callias or Socrates, juft as 
 this is a brazen fphere. But man and animal are altogether as a brazen fphere. 
 It is evident, therefore, that forms themfelves (as fome are accuftomed to fpeak 
 of forms), if there are certain natures of this kind befides particulars, are of 
 no ufe with refped to generations and eflences, nor will eflences effentially 
 fubfift through thele. Indeed, in fome things it is evident that the genera- 
 tor is fuch as the thing generated, yet is not one and the fame in number, 
 but in fpecies, as is manifeft in things phyfical : for man generates man, and 
 horfe horfe {|, unlefs when fomething contrary to nature is generated, as when 
 a horfe begets a mule. And thefe alfo are fimilarly affeaed. For that which 
 
 * Viz. Into form and a fubjeiS. 
 
 -j- Viz, Of this figure, one part will be thc/«(^><.7, in which the form produced by the efficient 
 i« inherent ; but the other will be the form which is inherent in the fubjeci:. 
 
 X t. e. The cotnpoCte from matter and form. 
 
 § Alexander well obferves, that by this particular thing (toJe ti) Arlftotle fignifies fenfibles, 
 things \\hich can be pointed out with the finger, and, in fliort, things which are able to fubfift 
 
 fiom themfelves. 
 
 y 
 
 U Kcti WTo; lienor is omitted in the printed text \ but the fenfe requires it fhould be inferted ; 
 and it is in the text of Alexander. 
 
 Z is
 
 170 ARISTOTLE'S METAPHYSICS. Bcok VII. 
 
 is common to a horfe and an afs, viz. the moft proximate genus*, is not 
 named: but both, perhaps, will be as a mule. So that it is evident, that it 
 is not by any means neceflary to introduce form as a paradigm (for, in fenfibles, 
 forms fhould be efpecially inveftigated, fmce thefe are efpecially eiTences), but 
 that which generates is fufficient to make, and to be the caufe of form in mat- 
 ter. But now the whole of fuch a form in thefe fleih and bones is Callias 
 and Socrates ; who are, indeed, different, on account of the matter (for the 
 matter in each is different), but the fame in fpecies : for fpecies or form is 
 indivifible. 
 
 CHAP. IX. 
 
 But fome one may doubt why fome things are produced both by art and 
 chance, as heahh ; but others are not fo produced, as a houfe. The reafon, how- 
 ever, is this: that matter, which is the principle of generation, in making and 
 generating fomething of things artificial, in which a certain part of the thing is 
 inherent, is partly of fuch a nature as to be moved by itfelf f , and partly not ; 
 and of this, one part is capable of being moved in this particular manner, but 
 another part is incapable of being fo moved. For many things are capable 
 of being moved by themfelves, but not in this manner J ; as, for inftance, to 
 leap. It is impoffible, therefore, for things, the matter of which is of this 
 kind, as, for inftance, ftones, and fire, to be thus moved, unlefs by fomething 
 elfe. Hence, fome things will not be, but others will be, without that which 
 pofieiTes art. For they will be moved by thofe things which do not indeed 
 polTefs art, but which are able to be moved themfelves, either by other tilings 
 which do not poftefs art, or from a part. But it is evident from what has 
 been faiJ, that all things are after a manner generated from equivocals §, as 
 
 " By the mod proximate genus Ariflotle means the common nature through which the mule 
 generates. 
 
 f Thus fire moves from itfelf upwards, and a ftone downwarJs. 
 
 J Thus fire, which moves from itfelf upwards, cannot be fo moved as to fufe brafs from itfelf,. 
 but through the fmith. 
 
 § This is faid of things artificial : for a houfe is not conftru£led from an exifting houfe, in 
 the fame manner as a man from a man. A houfe, therefore, is in a certain refpett conftrufted 
 from that which is univocal, or from an univocal part. For the definition of a houfe is predicated 
 of this houfe. But in another refpeiSt it is not conflruiftcd from that v/hich is univocal, bccaufe 
 there is no exifting houfe from which it is made. 
 
 things
 
 BookVII. ARISTOTLE'S METAPHYSICS. 171 
 
 things which have a natural fubfiftencc, or from an equivocal part; as, for 
 inftance, a houfe from a houfe, or from intelledl. For art is i'orm *, either 
 from a part, or from that which poflefTcs a certain parr, if it is not produced 
 accoi-ding to accident. For the caufe of making is the firft effential part : for 
 tlie heat which is in motion produces heat in the bodv. But this is either 
 health, or a part of health ; or fome part of health, or health itfelf, fo!lov/s ir. 
 Hence it is faid to make, bccaufe that which follows, and to which heat hap- 
 pens, produces health. So that, as in fyllogifms effence is the principle of all 
 things (for fyllogifms are from ibe ic/Wf), fo here generations. Things alfo 
 which are conRituted by nature fubfifl in a manner firailar to thefe. For feed 
 makes juft as the artift operates ; for he pofieifes form in capacity, and that from 
 which feed originates is in a certain refpe£l uaivocal, unlefs an injury happens 
 to take place : for it is not proper to inveftigate all things, as man from man ; 
 for woman is from man ; and hence mule does not originate from mule. But 
 thofe things are produced by chance, the matter of vdiich, as there, is capable of 
 being mos'ed by itfelf with that motion with which feed moves. And thofe 
 things the matter of which is not capable of being fo moved cannot be produced 
 in any other way than from generations. But this reafoning not only fhows, 
 refpeding effence, that form is not generated, but it alfo in a fimilar manner 
 evinces this in commoa of all firft natures, as of quality, quantity, and the 
 other predicaments. For, as a brazen fphere is that which is generated, and 
 not the form of the fphere, nor the brafs ; for it is always neceffary that mat- 
 ter and form ihould preexift ; the like muft be underftood refpeding effence, 
 quality, quantity, and the other predicaments. For quality is not generated, 
 hvxfuch like wood ; nor quantity, but wood, or an animal of a certain di- 
 menfion. However, from thefe things the peculiarity of effence may be 
 apprehended, viz. that another effence w^hich makes, having a fubfiftence in 
 energy, muft neceffarily always preexift ; as, for inftance, an animal muft 
 preexift, if an animal is generated : but it is not neceffary that this fliould 
 be the cafe with quality, or quantity, except in capacity alone. 
 
 * Thus, the art through which a houfe is confl;ru£ted, is nothing elfe than the form of the 
 houfe. 
 
 t By ejfence, and the ivtat, Aiiftotle in this place means axioms ; for demonflrations are pro- 
 <luced from thefe. / 
 
 Z a CHAP*
 
 172 ARI ST O TLB'S METAPHYSI C S. BookVII. 
 
 CHAP. X. 
 
 Moreover, fince definition is a fentence, but every fentence has parts, 
 and as a fentence is to a thing, fo is a part of a fentence to a part of a thing, 
 it is now doubted, whether it is neceflavy or not that the parts fliould be 
 inherent in the definition of the whole. For in fome things they appear 
 to be inherent, and in others not. Thus, the definition of a circle does 
 not contain the fedlions of the circle defined : but the definition of a fyl- 
 lable contains the parts of a fyllable ; though a circle is divided into fedlions, 
 as a fyllable into the elements of fpeech. Further ftill : if parts are prior to 
 the whole, but an acute is a part of a right angle, and a finger of an animal, 
 the acute will be prior to the right angle, and the finger to man. Thefe, how- 
 ever, do not appear* to be prior : for wholes are introduced in the defini- 
 tion of parts f; and they are prior becaufe they can fubfift without parts. 
 Or fhall we fay, that part is multifariouily predicated? Of which one mode 
 is that which meafures according to quantity. The confideration of this, 
 however, mufl be omitted : but our attention mud be directed to the fpecu- 
 lation of what thofe things are from which effence confifhs as parts. If, there- 
 fore, one thing is matter, another form^ and a tliird that which is compofed 
 from thefe, and effence is matter and form, and that which confifls from thefe, 
 matter alfo is in one refpe£l faid to be a part of fomething, and in another 
 is not faid to be a part ; but this is true of thofe things from which the defi- 
 nition of form confifts. Thus, for inftance, flefli is not a part of concavity 
 (for this is matter in which concavity is generated), but it is a certain part of 
 flatnefs of nofe. And the brafs, indeed, is a part of the whole flatue ; but by 
 no means of the ftatue which is denominated as form. For form is predicated 
 in every thing, and every thing is to be denominated fo far as it has form. 
 But that which is material is never to be efl'entially predicated. Hence, the 
 definition of the circle does not contain the definition of its fedlions ; but the 
 definition of a fyllable contains that of the elements from which it is compofed. 
 For the elements of fpeech are parts, and not the matter of form ; but the 
 fedtions of a circle are parts, as the matter in which the circle is produced ; 
 
 * Tlie fenfe requires we fliould read ou Joxei J' tKzna eivai ■jr^ori^a, inflcad of Sokei ^ x. t. a. 
 t Thus, in defining an acute angle, we fay that an acute angle is an angle lefs tlian a right-: 
 angle. And hence a right angle or a whole is aflumed in the definition of an acute angle. 
 
 yet
 
 Book VII. A R I ST O T L E'S M E T A P H Y S 1 C S. 173 
 
 yet they are more proximate to form than the brafs, when roundnefs is inge- 
 nerated in the brafs. But in a certain refped: neither will all the elementc be 
 contained in the definition of a fyllable ; as, for inftance, thefe waxen letters, 
 or thofe which are in the air*. For now thefe alfo are a part of a fyllable, 
 as fenfible matter. For it does not follow, that becaufe a line is corrupted, 
 when divided into equal parts, or a man when divided into bones, and nerves, 
 and flcfh, that they are fo compofed from thefe as parts of effence ; but it fol- 
 lows, that they are compofed from them, as matter only. And they are, in- 
 deed, parts of the whole; but they are not parts of form, and of that which 
 is the fubjed of definition : and, therefore, neither are they introduced in 
 definitions. In fome definitions, therefore, a definition of parts of this kind 
 will be inherent ; but, in others, it is neceffary that it fhould not be inherent, 
 unlefs it is the definition of both taken together. For, on this account, fome 
 things confift from thefe as principles, into which they are corrupted, but 
 others do not confift from thefe. Such things, therefore, as are taken toge- 
 ther, are form and matter ; as a flat nofe, or a brazen circle : for thofe, indeed, 
 are corrupted into thefe, and matter is a part of them. But fuch things as are 
 not affumed in conjunction with matter, but wdthout matter, as the definitions 
 of form alone, thefe are either altogether not corrupted, or at leaft not after 
 this manner. So that the things which they contain, are in.deed the principles 
 and parts of them ; but, of form, thefe are neither principles nor parts. Hence, 
 a ftatue of clay is corrupted into clay, and a fphere into brafs, and Callias intO' 
 flefli and bones : and further ftill, a circle is corrupted into fediions. For 
 there is fomething which is afllimed together with matter. For the circle is 
 predicated equivocally, both that which is fimply predicated f , and thofe 
 which are taken feverallyij:, becaufe thofe that are taken feverally have not a 
 proper name. 
 
 We have now, therefore, unfolded the truth ; but at the fame time it is ne- 
 ceffary that, by making a repetition, we fhould fpeak more clearly. For fuch 
 things as are the parts § of a definition, and into which definition is divided, 
 
 * For, fince voice, fays Alexander, is a percuffion of air, when we fpeak, the air is, without 
 doubt, conformed to our words. 
 
 •J- Viz. Univerfal circle. 
 
 X Viz. Particular circles. 
 
 § Viz. Such things as are the parts of form ; as animal and biped are parts of the form of 
 man, and are prior to. man. 
 
 the^e
 
 174 ARISTOTLE'S METAPHYSICS, Book VII. 
 
 thefe are prior, either all or feme of tl.em. But the definition of a right angle 
 is not divided into the definition of an acute angle, but the definition of an 
 acute into that of a right ai,g!e. For he vv'ho defines an acute, ufes a right 
 angle ; fince an acute is lefs than a right angle. The like takes place with 
 refped to a circle and femicircle. For the feinicircle is defined by the circle ; 
 and the finger by the whole. For a finger is fuch a part of the man. So that 
 fuch parts as have, indeed, the relation of matter, and into which, as into mat- 
 ter, the whole is divided, — thefe are, indeed, pofierior; but fuch as have the 
 relation of definition, and of eflence according to definition, are prior, either 
 all or fome of them. 
 
 But fincc tlie foul of animals is their form* (for this is the eflence of the 
 animated nature, an eflence according to definition and form, and the very na- 
 ture of fuch a body ; for a part of any thing, if it is well defined, is not defined 
 without its proper employment, and which here does not fubfifi: without fenfe) 
 — this being the cafe, the parts of foul are prior, either all cr fome of them, to 
 the whole animal. And the like takes place in other things. But the body 
 and its parts are pofterior to this eflTence, and are divided into thefe as into 
 matter. This is not the cafe with eflTence, indeed, but with the entire whole. 
 Thefe, therefore, are partly prior, and partly not prior, to the whole. For, 
 ■when feparated, they are not able to fubfift. For neither is a finger according to 
 every mode of fubfiftence the finger of an animal ; but a dead finger is only 
 equivocally fo called. But fome things perifli together with the whole itfelf ; 
 and thefe, indeed, are principal parts, in which definition and eflence are pri- 
 marily inherent ; fuch, for inftance, as the heart, if it is this principal part, or 
 the brain. For it is of no confequence which of thefe is of this kind. But 
 man and horfe, and the like, are in particulars : and univerfal eflence does not 
 fubfifl: feparate from the particulars to which it belongs, but a certain whole 
 confifting from tins definition and this matter j" fubfifl:s as univerfal. But a 
 particular, confifi;ing from ultimate matter, is now Socrates ; and in a fimilar 
 manner with refpcd; to other things. 
 
 Definition, therefore, is a part of form (but I mean by form the very nature 
 or eflence of a thing), and of the whole which is compofed from form and 
 matter. But the parts of definition are alone the parts of form ; and defini- 
 
 * T!ie text of Alexander, and indeed the fenfe, require that after ^uxi, in the printed text, 
 we fliould add eiJo; avrav. 
 t By the matter of man univerfal, Ariftotle means genus and difFcrence. 
 
 tion
 
 BooKVir. ARISTOTLE'S METAPHYSICS. ]75 
 
 tlon is of that which is univerfal. For the eflence of a circle and a circle are the 
 fame, and in like manner the eflence of foul and foul are the fame. But 
 of that which is now a whole, as, for inflance, of this circle, and, in fhort, of 
 that which is a particular, or fenfihie, or intelligible whole (but I mean by in- 
 telligibles fuch things as mathematical entities, but by fenfibles, fuch things 
 as are compofed of brafs and wood); of thefe I fay there is no definition, but 
 they are known by intelledllon or fenfe. But when the energy ceafes by 
 which they were vifible, it is not manifeft whether they are or are not ; ncver- 
 thelefs, they are always predicated and known by univerfal reafon : but mat- 
 ter is of itfelf unknown. With refpedt to matter, however, one kind is fen- 
 fible, and another intelligible. And fenfible matter, indeed, is fuch as brafs 
 and wood, and whatever matter is moveable : but intelligible matter is that 
 which fubfifts in fenfibles, yet not fo far as they are fenfibles, as, for inftance, 
 mathematical entities. AVe have, therefore, fliown in what manner this 
 takes place refpedting whole and part, and alfo refpedling prior and pofterior. 
 But it is neceflary to anfwer the interrogation, when any one afks. Whe- 
 ther a right angle, a circle, and an animal, are prior to the parts into which 
 they may be divided, or whether the parts from which thefe are compofed are 
 prior to their wholes ? And we muft reply, That part is not fimply predi- 
 cated *. For, if foul is the animal, or that which is animated, or every ani- 
 mal is its own foul ; and in like manner, if the circle is the eflence of the 
 circle, and the right angle of the right angle, what part is each of thefe, and to 
 what whole muft we fay it is pofterior? For inftance, of thofe parts which 
 are in a definition, which fhould we fay is pofterior to the whole, viz. to the 
 whole of a certain right angle ? For both the angle of brafs which fubfifts in 
 conjundion with matter is a right angle, and that alfo contained in lines 
 which fubfift as particulars. But the right angle which is without matter, is 
 pofterior to the parts which are contained in definition, but is prior to the 
 parts which fubfift as particulars. It muft not, liowever, be faid that this is 
 true of part fimply confidered. But if foul is fomething elfe, and not the 
 animal, thus alfo fome parts muft be faid to be prior, and others not prior, 
 as we have already obferved. 
 
 * Ariftotle here, with wonderful brevity, fays notliing more dian on av% «TAa>j. 
 
 CHAP.
 
 176 AR I STOTLE'S METAPH YSI C3. Book VIL 
 
 CHAP. XL 
 
 It may juflly be doubted what the quality is of the parts of form, and alfo 
 of the parts of that which is a compofite ; fince, this not being manifeft, it is 
 not poffible to define every particular. For definition is of that which is 
 univerfal, and of form. If, therefore, it is not apparent which of the parts 
 have the relation of matter, and which have not, neither will the definition of 
 the thing be manifefl:. Such things, therefore, as are ingenerated in different 
 fpecies, as, for inftance, a circle in brafs, in ftone, and in wood, thefe appear 
 indeed to be manifeft, fince neither the brafs nor the ftone is any thing of 
 the effence of the circle, bccaufe it is feparated from them. But fuch things 
 as are not perceived to be feparated * are not in any refped prevented from 
 fubfifting fimilar to thefe ; juft as, if all circles were of brafs, brafs would ap- 
 pear to be of the efience of the circle, yet, neverthelefs, brafs would not then 
 be a part of form. Neverthelefs it is dilficult to feparate this in our dianoetic 
 part. For the form of man always appears in flefla and bones, and fuch-likc 
 parts. Whether, therefore, are thefe parts of form and definition ? or, are 
 they by no means parts, but matter ? However, as the form of man is not 
 ingenerated in another, it is impoflible to feparate it. But fince this appears 
 to happen, and it is immanifeft when, fome '[ alfo have taken occafion to 
 doubt refpeding the circle and triangle, as if it did not pertain to lines and 
 to continued quantity to be defined ; but all thefe were fimilarly predicated, as 
 the fleih or bones of a man, and brafs and ftone of a circle. They likewife refer 
 all things to number, and fay that the definition of aline is that of the duad. 
 
 Of thofe alfo who aflcrt that there are ideas, fome fay, that line itfelf is 
 the duad, but others the form of line. For, in fome things, fay they, form 
 and that of which it is the form are the fame, as, for inftance, the duad and 
 the form of the duad. But this is not the cafe in a line. It happens, there- 
 fore, that there is one form of many things of which the fpecies appears to 
 be different ; which thing likewife happens to the Pythagorseans. The con- 
 fequence alfo will be that there will be one form only of all things, and that 
 other things will not be forms j though, after this manner, all things will be 
 
 • Thus, man confidered as united with bone, fiefli, and nerves, cannot be confidered feparate 
 from thefe, as tin; circle cun be from briifs and wood. 
 
 t Alexander informs us, that Ariitotle here alludes to the Pythagoreans. 
 
 one.
 
 EooKVIf. ARISTOTLE'S METAPHYSICS. 177 
 
 one. We have fliown, therefore, that the particulars refpedling definitioa 
 are connedied whh a certain doubt, and llkewilc through what caufe this 
 takes place. Hence, to refer all things after this manner, and to take away 
 matter, is fuperfluous. For in fome things, perhaps, this is in ihat*, or this 
 thing thus fubfifting. And that is not a good comparilbn refpefting an ani- 
 mal, which the junior Socrates f was accuftomed to adduce. For it leads us 
 from the truth, and caufes us to apprehend that it may be poflible for man to 
 fubfift without parts, in the fame manner as the circle without brafs. The 
 latter inftance, however, Is not fimilar to the former; for animal, perhaps, is 
 fomething fenfible, and cannot be defined without motion ; and therefore 
 neither without its parts fubfifting after a certain manner. For the hand is 
 not in every refpetfk a part of man, but that which is able to accomplifh the 
 proper office of the hand. So that it is a part when- animated ; but, when not 
 animated, it is not a part. 
 
 But, with refpedl to mathematical entities, why are not definitions parts of 
 definitions ? For inftance, why are not femicircles parts of the definition of a 
 circle? For thefe are not fenfibles. Shall we fay this is of no confequence ? 
 For they will be the matter of certain things, and of fuch as are not fenfible 
 and of every thing which is not the very nature of a thing. Thefe, there- 
 fore, will not be parts of univerfal circle, but of particulars, as we have before 
 fiid. For, of matter, one kind is fenfible, and another intelligible. But It is 
 manifeft that foul is the firft efTence, but body, matter; and man or animal Is 
 that which is compofed from both as univerfal. But Socrates or Corlfcus, If 
 foul Is the form of each, is two-fold. For fome call Socrates as foul, but 
 others as a whole. But If fimply this foul, and this body, they will have the 
 relation of univerfal and particular. Whether, however, befides the matter of 
 fuch like efiences, there Is fome other effcnce, and whether it is proper to in- 
 veftlgate a certain other eflcnce of thefe, as, for Inftance, number, or fome- 
 thing of this kind, muft be a pofterior confideration X- Indeed, for the fake 
 of this we endeavour to define refpefting fenfible effences ; fince, afier a 
 manner, the Ipeculatlon of fenfible efiences Is the buiinefs of natural and the 
 fccond philofophy. For the natural philofopher ought not only to have a 
 
 * Viz. Form is in matter. 
 
 t Who this junior Sjcrates was is uncertain. ^ 
 
 I See ihc Notes to tlie fourteenth book. 
 
 " ^ knowledge
 
 ]78 A R I STOTLE'S MET A PH YSIC S. Book VIL 
 
 knowledge of matter, but much more of that eflcnce which fubfifls accord- 
 ing to definition. However, with refpedl to definitions, how thofe things are 
 parts which are aflumcd in definition, and why definition is one reafon (for 
 it is evident that the tiling is one, and a thing polTefTing parts is one definite 
 particular) ; this muft be confidcred afterwards. We have, therefore, fliown 
 what the very nature of a thing is univerfaliy, and how itfelf fubfifts by itfelf :. 
 likewife on what account the definition of the very nature of fome things 
 contains the parts of that which is defined ; but in other things this is not the 
 cafe : and alfo that, in the definition of eflence, thofe parts which fubfifl as 
 matter are not inherent ; for they are not parts of that effence, but the whole. 
 But of this in a certain refpe£l there both is and is not definition. For with 
 matter there is not a definition (fince it is indefinite) ; but according to the 
 lirft effence there is. Thus, the definition of man is the definition of fouL 
 For eflence is the inherent form, from which and matter the whole eflence is 
 denominated ; as, for inftance, concavity. For, from this and nofe, a flat 
 nofe and flatnefs of nofe are compofed. For nofe is twice inherent in thefe» 
 But in the whole eflence, as in a flat nofe, or CalUas, matter alfo is inherent. 
 We have alfo fhown that the very nature of a things and each particular things 
 are in fome things the fame, as in firft: eflences. Thus, for inlfance, curvature 
 is the fame with the eflience of curvature, if it is the firfl:. But I mean by 
 firfl:, that which is not denominated, becaufe one thing is inherent in another^ 
 and is in a fubjed: as matter. But in things which fubfift as matter, or as 
 aflumed together with matter, thefe are not the fame; nor in things which, 
 are one according to accident, as Socrates and a mufician ; for thefe are the; 
 fame according to accident* 
 
 CHAP. Xlf. 
 
 It is now requifite, in the firfl: place, that we fhould difcufs what we have- 
 omitted in our Analytics * refpefting definition. For a doubt which was not 
 there diflblved will conduce to the difcourfe refpeding efl~ence. But the 
 deubt is this : Why that which is defined, of which we fay the reafon is de- 
 finition, is one thing ? For infliancc, if the definition of man is a biped ani- 
 mal (for let this be his definition), why is this one thing, and not many, animal 
 
 • Ariftotle here alludes to the fecond book of his Laft Analytics. 
 
 and
 
 SookVII. ARISTOTLE'S METAPHYSICS. 179 
 
 and biped ? For man and white are Indeed many things, when the one is not 
 inherent in the other. But when the one is inherent in the other, and the 
 fubjed:, viz. man, Is affeiled with fomething, they are one. For then a white 
 man becomes and is one thing. But here the one does not participate of the 
 other. For genus does not appear to participate of differences ; fmce, at the 
 fame time, the fame thing would participate of contraries. For differences are 
 contraries, In which the genus is different. But if It does participate*, the 
 fame reafoning will take place, if the differences are many, as capable of walk- 
 ing, biped, and without wings. For, why are thefe one, and not many ? [It 
 cannot be, that they are one becaufe they are inherent f]. lor thus there 
 will be one from all. But fuch things as are contained in definition X ought 
 
 to 
 
 * In this fentence, fays Alexander, much is wanting; but (he adds) from what Ariftotle 
 adduces, I fufpe£l his meaning to be as follows : " If any one fliould fay that genus does not 
 participate of contrary differences, but of capable of walking, biped, and without wings, the 
 fame reafoning will recur. For, if there are many differences, why are thefe one thing, and not 
 many things ? If they ought to be called one, becaufe they are inherent in genus; for the fame 
 reafon, every thing in which certain things are inherent will be one with the inherent particu- 
 lars. Hence, wine, and the veflel which contains it, will be one; and alfo a bufhel, and grains 
 of wheat. Moreover, if animal, capable of walking, biped, and without wings, are one thing, 
 becaufe thefe are inherent in animal, it follows, that animal will be one with all differences, and 
 fo all things will be one." ., , 
 
 t The words within the brackets are omitted in the printed text. It is evident, however, 
 both from the text of Alexander, and the verfion of Beffarion, that they ought to be inferted. 
 It appears, therefore, that there is wanting in the Greek ou yaf iv on uTrctpxn. 
 
 X It is well obferved by Alexander, that Ariftotle fubjoins a very obfcure folution of this 
 queftion, becaufe he has folved the fame in his fecond book On the Soul : and that in this place, 
 though after much difcuffion he has, without doubt, folved it, yet he does not appear to have 
 folved it. 
 
 Alexander then gives us the following folution of it : " A fphere in brafs is nothing elfe than 
 fpheric brafs ; and the brafs is as matter, but the rotundity as form. Moreover, matter and 
 form are naturally adapted to be one, when nothing impedes their conjunction. For in this 
 the very eflence of matter and form confifts, that when there is matter, and the form which it is 
 able to receive is prefent, they are immediately united, and become one thing. And as this is 
 the cafe with thefe, fo alfo in natural things, viz. in genus and differences. For, if I rightly 
 remember, Ariftotle, in his book On Demonftration (viz. his Laft Analytics), teftifies tlrat all 
 differences, except the ultimate difference, together with genus, poffefs fomething fimilar to 
 matter ; but that the ultimate difference is form. Thus, for inftanje, animal partaking of reafon 
 is the matter of the human form ; as is alfo mortal animal partaking of reafon : but capable of 
 intelleft and learning is the form of man. And, becaufe form and matter are naturally adapted 
 
 A a 2 to
 
 180 ARISTOTLE'S METArHYSICS. Book VIL 
 
 to be one. For definition is one particular reafon and eflence ; fo that it is 
 necelTary that it fliould be the definition of one certain thing. For efTsnce, as 
 we fay, fignifies one particular thing, and this definite thing. 
 
 It is requifite, however, in the firft place, to confider rei'pefting thofe defi- 
 nitions which fubftl\ through divifions. For there is nothing elfe in defini- 
 tion than the genus which is called firft, and difference *. Buc other things 
 are genera, both that which is firft, and together with it the aflumed differ- 
 ences. Thus, for inftance, tlie firft genus is animal ; but that which is con- 
 iequent to this is animal biped ; and again animal biped, and without wings. 
 And the like confequence will enfue, if there is a greater multitude in the de- 
 finition. And, in fliort, there is no difference, whether it fubfifts through 
 many things, or through few things, or through two things. But if through 
 two things, the one will be genus, and the other difference. Thus, for in- 
 ftance, of biped animal, animal is the genus, but the other is difference. If, 
 therefore genus, fimply confidered, is not any thing feparate from its own 
 fpecies, or if it is, indeed, yet it is as matter (for voice is genus and matter ; 
 but differences make forms and elements from this). This being the cafe, it 
 is evident that definition is a fentence compofed from differences. But it is^ 
 alfo requifite that difference fliould be divided into its differences. Thus, for 
 inftance, the difference of animal is the poffeffion of feet. Again ; it Is re- 
 quifite to know the difference of animal pofleffing feet, fo far as poffeffing 
 feet. So that we muft not fay of things pofTeffing feet, one is winged, and 
 another without wings, if we wilh to fpeak accurately ; but he will do this 
 who is unable to divide properly: but we fhould fay, that one has filTured,: 
 feet, and another feet without a fiffure. For thefe are the differences of feet, 
 fince the fiffure of the feet is a difTerence of feet. And thus we muft always 
 divide, till we arrive at things without difference. But then there will be as- 
 niany fpecies of foot as there are differences, and the number of animals with 
 feet will be equal to their differences. If, therefore, this be the cafe, it i$ 
 
 «o be one, hence thefe are one. But that the ultimate difTerence is form, and thofe which- 
 precede matter, Ariftotle himfelf will (horcly explain. After the fame manner, animal capable- 
 -of walking is matter, but biped form." 
 
 * It is alfo well obferved by Alexander in this place, that the word lajl muft be here under- 
 wood. So that the fcnfe will be, that in definition there is nothing elfe than firft genus, and 
 ultimate difference j or, in other words, thefe conflitute definition, and tliat which is explained 
 by it. 
 
 evident
 
 Boon VII. ARISTOTLE'S METAPHYSICS. rSl 
 
 evident that the laft difference will be the effence and definition of a thing, if 
 it is not neceffaiy often to affert the fame things in definitions ; for it is 
 fuperfluous. Neverthelefs, this fometimes happens. For, when any one fays 
 an animal having feet, and a biped, he fays nothing elfe than this, an animal 
 having feet, and having two feet. And if he divides this by a proper divifion, 
 he will often fay the fame thing, and as often as the number of differences. 
 If, therefore, a difference is produced of difference, one, Which is the laft, will 
 be form and effence. But if the divifion is made according to accident, as, if 
 in a divifion of things having feet, it fhould be faid, one is white and another 
 black, there will be as many differences as there are divifions. So that it is 
 evident that definition is a fentence compofed from things different, and from 
 the laft of thefe, when it is properly framed. But this will be manifeft if any 
 one tranfpofes fuch definitions, as, for inftance, the definition of a man, and 
 fays, animal biped, having feet. -For, having faid he is biped, renders the 
 addition of having feet fuperfluous. But there is no order * in effence. For 
 in what manner is it requifite to underftand this as pofterior, and that as- 
 prior? Thus much, therefore, we have in the firft place faid refpeding the 
 quality of dcliiiitions which fubfift through divifion. 
 
 CHAP. XUL 
 
 Since, however, our fpeculation is refpeding effence, let us again return 
 to this. As, therefore, a fubjed, the very nature of a thing, and that which 
 is compofed from thefe, are each of them faid to be effence, in like manner 
 that which is univerfal is called effence. Concerning two of them, therefore, 
 we have already fpoken. For we have fpoken refpeding the very nature of 
 a thing, and alio of a fubjed, which we have faid is fubjeded in a twofold 
 manner, either as this particular thing, as an animal to paflions (/*. e. partici- 
 pated properties), or as matter to energy. Univerfal alfo to fome appears to 
 be efpecially a caufe and principle. On which account it is neceffary that we 
 fliould alfo make this the fubjed of difcuilion. For it feems to be impoflible- 
 that effence ftiould be any thing of univerfals : for the firft effence of every 
 thing is that which does not belong to another thing f ; but that which is 
 
 • Thus, in the brafs of a ftatue, fo far as brafs, one part is not prior and another poflerior. 
 f Ariftotle here confiders that effence alone which is infeparable from an individual; but 
 iocs not openly admit effence univerfal. See the reafon of this in the Introdu(^ion. 
 
 univerfal
 
 1S2 ARISTOTLE'S MEJTAPHYSIGS, Book. VII, 
 
 unlverfal is common. For that is called univerfal which is naturally adapted 
 to be inher£nt in many things. Of what, therefore, will this be the eflence ? 
 For it will cither be the efltnce of all things, or of nothing. But it is not 
 poffible that it can be the eflence of all things : and if it fhould be the efTence 
 of one thing, other things alfo will be this. For things of which the eflTence 
 and very nature are one, are themfelves alfo one. Further ftill : eflience is 
 faid to be that which is not predicated of a fubjed ; but univerfal is always 
 predicated of a certain fubjeft. Shall we fay, therefore, that it cannot fubfiil:, 
 indeed, in the fame manner as the very nature of a thing, but that it is inhe- 
 rent in it, as animal in man and horfe ? It is evident, therefore, that there 
 will be a certain definition of it. But it is of no confequence if there is not 
 a definition of every thing which eflence contains. For, neverthelefs, this will 
 be an efl"ence of fomething, as man of man, in which he is inherent. So that 
 the fame thing will again happen. For eflence will be the eflence of man, as 
 animal of that fpecies in which it is inherent as peculiar. 
 
 Again : it is impoflible and abfurd, that this particular individual thing, and 
 eflence, if they are compofed from certain things, lliould not be compofed 
 from eflfences, nor from a particular individual thing, but from quality. For 
 that which is not efllence, and alfo quality, will be prior to efl'ence, and this 
 particular individual ; which is impoflTible. For it is not pofllble that partici- 
 pated properties can be prior to efllence, either in definition, or time, or gene- 
 ration ; fince they would thus have a feparate fubfiftence. Further ftiU : in 
 Socrates, who is efllence, efllence will be inherent ; fo that Socrates will be an 
 efl"ence in two eflfences. And, in fhort, if man is efl*ence, and fuch things as 
 are thus denominated, it will happen that nothing contained in definitions is 
 the eflence of any thing, and that it has not a fubfifl;ence feparate from them, 
 and does not fubfifl; in another. I fay, for inflance, that there is not any 
 animal befides thofe which rank as particulars, nor any thing elfe of the things 
 contained in definitions. From thefe confiderations, therefore, it is evident 
 that nothing which has an univerfal fubfiftence is eflence, and that nothing of 
 things predicated in common fignifies this particular individual, but a particu- 
 lar quality. For, if this be not admitted, many other things will happen, 
 and, among the reft, that there will be a third man. 
 
 This, too, will be evident from the following confideration : It is impoflible 
 that eflTence can be compofed from efl'ences, which are inherent in fuch a man- 
 ner as to be in energy. For, two things thus fubfift.ing in energy are never 
 
 one
 
 Book VII. ARISTOTLE'S METAPHYSICS. ISS 
 
 one in energy. But, if they are two things in capacity, they will be one. 
 Thus, the double is compofed from two halves in capacity ; for energy fepa- 
 rates them. So that, if eflence is one thing, it will not be compofed from in- 
 herent efl'ences, and after that manner which Democritus* rightly aflerts. 
 For he fays it is impoffible that one atom fhould be generated from two, or two 
 from one : for he makes indivifible magnitudes to be effences. It is evident, 
 therefore, that the hke will take place in number, if number is a compofitioa 
 of monads, as it is faid to be by fome. For, either the duad is not one, or it 
 does not contain the monad in energy. But that which happens is attended 
 with a doubt : for, if it is neither poffible that any efTence can fubfift from uni- 
 verfals, becaufe univerfal does not fignify this particular individual, but a thing 
 with a particular quaUty, nor poffible for any compofite effence to confift from 
 effences in energy, every eflence will be incompofite. So that neither will 
 there be definition of any eflence. However, it appears to all men, and we 
 have formerly aflerted, that definition is either alone or principally of eflence. 
 But now it is concluded, that neither is there a definition of eflence. There- 
 will not, therefore, be a definition of any one thing. Or fhall we fay that 
 after a certain manner there will be, and after a certain manner there will not 
 be, a definition of efl'ences ? But what we have now faid will be more ma-;- 
 nifeft hereafter. 
 
 CHAP. XIV. 
 
 From thefe very things, that which happens to thofe who aflertthat ideas- 
 are feparate tfl!ences, and who at the fame time make form to confifl: from 
 genus and differences, is manifefl. For, if forms and animal are in man and 
 horfe, there is either one and the fame, or a different animal in number. For 
 by definition it is manifefl that there is one and the fame ; fince he who fays- 
 that it is in each will affign the fame reafon. If, therefore, there is fome man,, 
 itfelf fubfifling by itfelf, this particular individual, and feparate,, it is necefTary 
 
 * " That is," fays Alexander, " as Democritus denied that one atom could be produced from, 
 two, becaufe, according to his do£lrine, atoms are impalfive, or tw6 from one ; for he affirmed 
 them to be indivifible : fo we (fays Ariftotle) a.Tirm it to be impoffible that one effence ffiould 
 be produced from two effeuces in energy, but that this can alone be effefted by two fubfifting in 
 capacity." 
 
 alfo^
 
 1^. ARISTOTLE'S METAPHYSICS. Book VII, 
 
 alfo, that thofe things from which It confifts, as, for Inftance, animal and 
 biped, fhcLild fignify this particular individual, and fliould be feparate, and 
 effences : fu that this wiil hkewife be the cafe with animal. If, therefore, 
 animal is the faine in man* and in horfe, as you in yourfelf, how will it be 
 one ill things which are feparate, and why will not this animal alfo fubfift 
 feparate from Itfelf ? In the next place, if it participates of biped and multi- 
 ped, it will be impoffible that any thing fhould happen. For contraries will 
 be at the fame time inherent in the fame thing, fubfiiting as one, and as this 
 definite particular. But if it does not participate, what is the mode, whert 
 any one fays an animal Is biped, or capable of walking? But, perhaps they 
 form a compofite, and touch, or are mingled. All thefc modes, however, are 
 abfurd. Shall we fay that that which is different in number Is in each ? 
 There will, therefore, be infinite particulars, as I may fay, of which the 
 eflence is animal : for man is not from animal according to accident. Fur- 
 ther ftill : animal itfelf will be many things. For animal, which is in every 
 individual, Is effence ; fince it Is not predicated according to any thing elfe. 
 But If this be not the cafe, man will fubfill from that, and that will be the 
 genus of man. And again, all things from which man confifts will be Ideas. 
 Idea, therefore, will not be of one thing and eflence of another : for this is 
 impofTible. Hence each of thofe things contained In animals will be ani- 
 mal Itfelf. Befides, this will fubfift from a certain particular, and how will 
 animal fubfift from It ? Or how Is it poffible that there fliouId be animal, 
 which Is Itfelf effence, befides animal itfelf? Further ftill : thefe things will 
 happen In fenfibles, and things ftill more abfurd than thefe. But if it Is Im- 
 poffible that this can be the cafe, it Is evident that there Is not it' »+ of them, 
 in fuch a manner as fome aifert there Is. 
 
 CHAP. XV. 
 
 Since, therefore, the whole and form are of a differeat eflence (but I fay, 
 that the former is efl'ence as matter afllimed together with form, but the latter 
 
 * The words iv ra avSfonra are omitted in the printed text ; but both the fcnfe ami tlie text 
 jof Alexander require that they fliould be inferted. 
 
 f Again we refer the reader to the Notes on the thirteenth and fourteenth books of this work, 
 in which he will find a folution of all the appaisnt objc6lions of AriHotle to th-' do£lri le of 
 ideas. 
 
 is
 
 BookVII. ARI STOTL E'S- META PH YSICS, 135 
 
 15 entirely form), hence, of fuch things as are denominated according to the 
 former of thefe, there is corruption ; for there is alfo generation. But of form 
 there is not corruption ; for neither is there generation. For the being or 
 form of hoiife is not generated, but of this particular houfe. But forms are 
 and are not, without generation and corruption : for it has been fliown that 
 thefe are nei'.her generated nor made by any one. Hence there is neither de- 
 tinirion * nor demonftration of fenfible particular effences, becaufe they have 
 matter, the nature of which is fuch, that it is pofhble for it both to be and 
 not be. On this account all the individuals of fenfibles are corruptible. If, 
 therefore, demonftration is of things: necefl'ary, and alfo fcientific definition, 
 and it is not poflible that fcience can be at one time fcience, and at another 
 time ignorance, but a thing of this kind is opinion ; in like manner demon- 
 ftration and definition cannot pertain to things which may fublill differently, 
 but fuch as thefe are the objects of opinion. It is evident, therefore, that 
 things which may fubfift differently at different times, are not the objedls of 
 ei'.her demonftration or definition. For things corruptible are not manifeft to 
 thofe who pcffefs fcience, when they are not prefent to fenfe. And though 
 the fame reafons are preferved in the foul, there will no longer be either defi- 
 nition or demonftration. Hence he who defines any thing vvrhich ranks 
 among particulars, ought not to be ignorant that a definition of this kind may 
 always be fubverted. For it is not poffible that fuch things can be defined. 
 
 Neither is it poflible to define any idea : for idea ranks, as they fay, among 
 the number of particulars, and has a feparate fubfiftence. It is alfo neceffary 
 that definition ftiould confift from names. But he who defines does not make 
 a name ; for it will be unknown : but the things which are admitted are com- 
 mon to all things. It is neceffary, therefore, that thele fliould alfo fublift in 
 other things : juil as, if any one ihould define you, he would (ay that you are 
 a {lender animal, or white, or fomething elfe which alfo belongs to another. 
 
 * In particulars, though the thing which is c'emonftrated remains, and though he remains 
 vho poilcfies t!ie definition and demoiiilation oi" it, and alio, though the definition itfeli' which 
 is poflefled in the foul is preferved free from oblivion, yet there will neither be definition nor 
 dciaonftratioii. For, after tlie departure of that objecl from fcufe of which I polTefs the defi- 
 nition, though I remain, and the tiling of which I pofTtfs the drtiniticn remains, and the defi- 
 nition itfclf fubfiils in full perfedion, yet I am ignorant whether this object exills or not. But 
 the proper objeiSls of fcience and definition arc in e-Jtry rt'fpcH nianifcll ; and cotifequcntly 
 there can neither be any definition ncr demonftration of particulars, 
 
 Bb If
 
 18^ ARISTOTLE'S METAPHYSICS; Book VIL 
 
 If fome one, however, fhould fay. Nothing hinders but that all thefe may fepa- 
 rately belong to many perfons, but that all colledively only belong to this in- 
 dividual, we muft fay, in the firft place, that animal biped pertains to both, 
 viz. to animal and to biped. And this, indeed, muft necefTirily take piace in 
 things perpetual, fmce they have a prior fubfiftence, and are parts of a compo- 
 fite. But they are alfo feparate, if man is feparate ; for either nothing will 
 be feparate, or both. If, therefore, nothing, there will not be genus befides 
 fpecies ; but if both are feparate, there will alfo be difference. In the next 
 place, becaufe they are prior in effence ; thefe, on the contrary, will not be 
 taken away. And, befides this, ideas are from ideas ; for thofe things from 
 which others confift are more incompofite. Further ftill : it is requihte that 
 thofe things from which idea confifts, fhould be predicated cf many things; 
 as, for inftance, animal and biped. For, if not, how can it be known ? For 
 there will be a certain idea which cannot be predicated of more things than 
 one. This, however, does not feem to be the cafe ; but every idea appears to 
 be partlcipable. As we have, therefore, faid, they are ignorant that it is im- 
 poffible for definition to take place in things eternal, and Specially in fuch as 
 are fmgle, as the fun and moon. For they not only err in adding things 
 of this kind, which being taken away the fun will flill remain, fuch as is that 
 of revolving round the earth, or being concealed by night ; for if the fun 
 fhould ftop in his courfe, or become apparent by night, he will be no longer 
 fun ; but it will be abfurd if, in this cafe, he fhould not be fun : for the fun 
 fignifies a certain effence. Befides, they affume thofe particulars which may 
 alfo be aflerted of another thing. Thus, for inftance, if fomething elfe fhould 
 become a thing of this kind, it is evident that it will be fun. The definition, 
 therefore, is common. But the fun ranks among particulars, in the fame 
 manner as Cleon or Socrates. In fhort, why has no one of them given a de- 
 finition of idea * ? For the truth of what we have now faid will become appa- 
 rent to him who fhall make the attempt. 
 
 * Idea, confidered in itfelf ns an eflence perfeflly fimple and without parts, cannot be 
 defined, becaufe deiinition is of tilings complex -, but confidered as having a fubfiftence by 
 participation in the dianoetic part of our foul it is definible. 
 
 CHAP.
 
 floosVir. ARISTOTLE'S M.E T A P H Y S I C S. 187 
 
 CHAP. XVI. 
 
 But it Is evident that mofl: of thofe things wliich appear to be efleiices, as 
 the parts of animals, are only fo in capacity* ; for none of them has a fepa- 
 rate fubfiflence. But, when they are feparated, then they are all of them as 
 matter, and earth, and fire, and air. For none of thein is one thing, but 
 each is as it were a heap, before they are digefled, and one thing is produced 
 from their conjunction. But fome one may efpecially apprehend that the 
 parts of animated natures and of the foul very nearly approach to a fubfift- 
 ence both in energy and capacity, becaufe they poflefs the principles of motion 
 from fomething in their flexures. Hence fome animals Uve fwhen divided. 
 But at the fame time all of them will fubfift in capacity, when they are one 
 continued thing by nature, and not by force, or coalefcence. For a thing 
 of this kind is mutation. But, fince the one is denominated as being, and the 
 elTence of the one is one thing, and thofe things of which the eflence is one 
 in number are one in number, it is evident that neither the one nor being can 
 be the eflence % of things, as neither the eflence of element or principle is the 
 efTence of all things. But we inquire, what, therefore, the principle is, that 
 we may proceed to that which is more known. Of thefe, then, that which 
 is being and one, is more eflence than either principle is, or element, or 
 caufe. But yet neither are thefe eflences, if nothing clfe which is common 
 is eflence. For eilence is not inherent in any thing but itfelf, and that by 
 which it is pofl^eflTed, of which it is the eflience. 
 
 Further ftill : the one will not be in many places at the fame time ; but that 
 which is common is at the fame time prefent with all things in many places. 
 So that no univerfal can have a fubfiftence feparate from particulars. But 
 thofe who fay that there are forms in one refpedl fpeak rightly, in giving 
 them a feparate fubfiflience, if they are efl'ences ; but in another refpeiSt not 
 
 * In tlie printed test Si/vajWEif; but the fenfe requires that we (hould read fwva/^fi. The text 
 of Alexander alfo has pote>itia . 
 
 t For ferpents, fays Alexander, when cut into two parts, fllll poflefs motion, as alfo the feet 
 of locufts, and of fpiders called phalangia. And this is eminently the cafe with the ftar fifti 
 and the polypus. 
 
 X Neither being., nor i/je one, confidered as merely fubfifting by an abRra£lion from fenfibles, 
 is the eflence of things ; but this is not the cafe with tei/ig iffelf, and the one itfelf. See ihe 
 Notes to the thirteenth and fourteenth books. 
 
 B b 2 rightly,
 
 188 A R I S !• O T L E • S M E T A P H Y S I C S. Book Vn. 
 
 lightly, becaufe they fay there is one form in many. But the reafon of thTs 
 is their inability to aflign what fuch like edences are which are incorruptible^ 
 and which have a fubfiftence independent of particulars and fenfiblcs. They, 
 therefore, make them to be the fame in fpecies with corruptible * natures (far 
 thefe we know), viz. man itfelf, and horfe itfelf, adding the word it/elf lo fen- 
 fibles. Though, even if we did not fee the ftars, yet I think tl-.ere would no 
 lefs be eternal effences befides thofe of which we have a knowledge. So that 
 alfo now, though we are not able to fee what eternal effences are, yet perhapsf 
 it is neceffary that certain eternal effences flrould have a fubfiRence. It is, 
 therefore, evident, that none of thofe things which are called univeifals is 
 effence, and that no effence is compofed from effences. 
 
 CHAP. xvir. 
 
 But, again, as if making another beginning, let us fay what, and wha-f 
 kind of a thing we ought to caH effence. For, perhaps, from thefe things, the 
 particulars refpe<3:lng that effence which is feparate from feafible effences will 
 alfo be apparent. Since, therefore, effence is a certain principle and caufe. It 
 is requifite that we fhould proceed from hence in our inquiry. But the in- 
 veftigation, on what account a thing fubfifts, always proceeds as follows, viz. 
 on what acccount one thing is inherent In a certain other thing. For to in- 
 quire on what account a mufical man is a mufical man, is either to inquire, 
 as we have faid, on what account a man is a mufician, or to inquire fomething 
 eife. To inquire, therefore, on what account a thing is that thing which it 
 is X, is to inquire nothing. For it Is requillte that to be inherent § in fome- 
 
 * Ideas properly fo called are not diftrlbuted into the multitude of particulars, but hnve a 
 fubfiftence prior to the many, as vill be fully flioun in the Notes to the two laft books of this 
 work. Hence they cannot be the fame in fpecies with corruptible natures ; for they are per- 
 fe£lly incorporeal and eternal effences. Aridotle, therefore, cannot be ferious in what he now 
 fays. 
 
 t Al'Nander well obferves, that Ariftotle in this place ufes the word perhaps, becaufe he has 
 not yet d'emonftrated that there are certain effences befides fenfibles, though to us invifible. 
 That there are, however, fuch effences, is demonftrated by Ariftotle in the twelfth book of this 
 work. 
 
 X '. t. To inquire Why man is man ? 
 
 § It appears from the Commentary of Alexander that, inftead of to w tj here, as in the 
 printed text, wc fliould read to ev tih. 
 
 thing.
 
 Book VII. A R I S T O T L E'S M E T A P H Y S I C S. 189 
 
 thing, and to be, fhould fubfill: as manifcft. I fay, for inftance, that the moon 
 is eclipfed : but of the inquiry. Why a thing is that thing which it is? there 
 is one leafcn, and one caufe in all things; as, on what account a man is a 
 man, or a mulician a mufician, unlefs fome one fhould fay that every thing is 
 indivifible with refpe£l to itfelf. But this is to be one ; and this is common 
 to all tilings, and is conclfe. Some one, however, may inquire, On what ac- 
 count man is that kind of animal which he is ? This, therefore, is evident, 
 that fuch a one does not inquire on what account he who is a man, is a man ? 
 He, therefore, inquires. Why a certain tiling fubfifts in a certain thing ? But 
 that it is inherent ought to be manifeft : for if not, he inveftigates nothing. 
 Thus, for inftance, on what account does it thunder ?. Becaufe a found is 
 produced in the clouds : for thus one thing is inquired refpeifling another. 
 And, on what account are thefe things, as, for inftance, tiles, and ftones, a 
 houfe ? It is evident, therefore, that he inveftigates the caufe. But this is, 
 as I may fay, fpeaking logically, the very nature of a thing; which in fome 
 things is that for the fake of -which, as, perhaps, in a houfe, or a bed. But in 
 other things it is that which firft moves : for this alfo is a caufe. A caufe, 
 however, of this kind is inveftigated, when a thing is generated or corrupted; 
 but the other caufe * is inveftigated when a thing already is. But that which 
 is inveftigated, is efpecially latent in things not conveniently predicated ; as, 
 for inftance, in the inquiry. What man is ? becaufe it is fimply alTerted, and 
 not definitely, that he is this or that. It is, however, requifite to inveftigate 
 definitely, otherwife it will come to pafs that fomething and nothing will be 
 inveftigated in common. But, fince it is requifite that eflence Ihould be 
 poffefied and fhould fubfift, it is evident that the inquiry will be on what ac- 
 count the matter is. As, for inftance, thefe particulars are a houfe : But on 
 what accoutit ? Becaufe thefe are that which a houfe is. Thus, too, in the 
 inquiry. Why man is this particular thing, or why this body poflefTes this par- 
 ticular thing ? the like inquiry is made. So that the caufe of the matter is 
 inveftigated : but this is the form by which any thing is ; and this is eftence. 
 It is evident, therefore, that there is not any inveftigation nor difcipline refpedt- 
 ing things which have a fimple fubfiftence, but that there is another mode of 
 inveftigating things of this kind. 
 
 But, becaufe that which is compofed from fomething is fo compofed as that 
 
 * That is the formal caufe. 
 
 the
 
 Wo ARISTOTLE'S METAPHYSICS. Book VII. 
 
 the whole is one thing, and not as a heap, but as a fyllable ; but a fyllable is 
 noc the elements of fpeech, nor is it the fame as h and ^, nor is flefh, fire, 
 and earth; for when a dlflblution takes place, flefli and fyllable no longer re- 
 main, but the elements, fire and earth, continue to fubfift ; — this being the cafe, 
 fyllable is fomething befidcs the elements, viz. befides vowel and mute : and 
 flefh is not only fire and earth, or the hot and the cold, but alfo fomething elfe. 
 If, therefore, it is neceflary, that flefh fhould either be an element, or that 
 which is compofed from elements ^ if it is an element, the fame reafoning will 
 again take place. For from this fire and earth will confift, or fiefli, and ft ill 
 further, fomething elfe ; fo that a progreflinn will take place to infinity. But, 
 if it is compofed from element, it is evident that it will not conlill from one 
 but from many, or it will be that very clement itfelf. So that, again, the fame 
 reafoning mufl: take place in this as in flefh or fyllable. But it fliould feem 
 that there is a thing of this kind, and that it is not aii element, but the caufe 
 that this thing is flefh and that a fyllable: and in a firailar manner with re« 
 fpedt to other things. But this is the effence of every thing : for this is the 
 firft caufe of fubfiftence. However, fince fome things are not the effences of 
 things, but this is the cafe with thofe alone which are naturally efiences and 
 which are conftituted by nature, it may appear to fome that this nature alfo, 
 vdiich is not an element but a principle, is eflence. But an element is that into 
 which, being inherent as matter, a thing is divided, as, of the fyllable ab^ 
 a and b, 
 
 * i, e, Form. 
 
 ARISTOTLE'S
 
 ARISTOTLE'S METAPHYSICS. 
 
 BOOK VIII. 
 
 CHAP. I. 
 
 PROM what has been fald, it is requifite to fyllogife, and, by a fummary 
 CQlledion, form a conclufion. But we have faid that the caufes, principles, 
 and elements of eflences are inveftigated. And, with refpe£l to eflences fome 
 are granted to have a fubfiftence by all men ; but concerning others, fome 
 have entertained peculiar opinions. Natural eflences, indeed, have been 
 granted to fubfift ; fuch as fire, earth, water, and other fimple bodies ; in the 
 next place, plants, and the parts of thefe ; animals alfo, and the parts of ani- 
 mals ; and, laftly, heaven, and the parts of heaven. But thofe who have en- 
 tertained peculiar opinions refpeding eflences, fay that forms and the mathe- 
 matical fpecies are eflTences. However, it happens, from the reafonings about 
 things, that the very nature of a thing, and that which ranks as a fubjed:, are 
 efl^ences. Again : in another refpedl, genus is more efltnce than fpecies, and 
 univerfal than particulars. Ideas alfo are conjoined with univerfal and genus ; 
 for, according to the fame reafoning, they appear to be eflences. But fmce 
 the very nature of a thing is eflence, and the reafon of this is definition, 
 hence we have unfolded the particulars refpecfting definition, and the efllen- 
 ti il. And, fince definition is a fentence, and a fentence has parts, it was alfo 
 neceflary to perceive relpeding a part, what are the parts of eflence, and what* 
 
 are
 
 192 A R I STOTL E'S M ET A PH YS I C S. BookVII'I. 
 
 are not ; and, likewife, whether it is neceflary that thefe fliould be the fiime 
 ^ith the parts of definition. 
 
 Further ftill : neither is univerfal nor genus, eflence. But we fhall after- 
 wards fpeak concerning ideas, and mathematical entities : for feme fay that 
 thefe have a fubfidence befides feiifible efTences. At prefent, however, we 
 fhall difcourfe refpeding thofe effences which are acknowledged to have a 
 fubfiftence. But thefe are fenfible : and all fenfiLIe eflences have matter. 
 But cifjnce is that which ranks as a fubjedl; and this is in one reri:!eft mat- 
 ter, but in another defiiution. And I cah mitter that which is not this defi- 
 nite particular in energy, but in capacity. But definition and form are fub- 
 jeds in a different refpecl, which are definire particiilars, and are feparable 
 by reafon. But the tliird is that which confills from thefe, of which alone 
 there is generation and corruption, and which is fimply feparable. For of 
 thofe efTences which fubfifl: according to reafon *, fome are feparated, and 
 others not. But that matter is effence is manifeft : for in all oppofite muta- 
 tions, there is fomething wl^ich is as a fubjed to thofe mutations ; as, for in- 
 flance, according to place, that which is now here, is again elfcwhere. Thus, 
 too, according to increafe, he who is now fo much, is again lefs or mere ; and 
 according to internal change, he who is now well, is again ill. In like man- 
 ner alfo, according to effence, that which is now in generation, is again in cor- 
 ruption : and that whioh is now a fubjedt as this definite particular, is again a 
 a fubjed as according to privation. And other mutations follow this ; but 
 this does not follow one or two of the reih For it is not neceffary, that if any 
 thing has local matter, it fliould alfo have this matter generable and corrup- 
 tible. What the difference, however, is between the being fimply and not 
 fimply generated, we have declared in our Fhyfics. 
 
 CHAP. K. 
 
 But, fmce the cxiflence of that effence which is as a fubjed, and as matter, 
 is acknowledged by all men, but this is that which fubfifls in capacity, it now 
 remains that we fbould declare what that effence is amongft fenfiblesf which 
 fubfifls as energy. Democritus, therefore, appears to have thought that there 
 
 * Cy efTences which fubfifl; according to reafon, Arifiotle means forms. 
 ■f By aa effence among fcnGbles fubfifUng in energy, Ariltotle means form. 
 
 are
 
 Book VIII. ARISTOTLE'S METAPHYSICS. - IDS 
 
 arc three differences. For he confidered the fubjedl body and matter to be 
 one and the fame ; but that it differed either by ryfm^ which is figure ; or by 
 trope which is pofition ; or diathcge which is order. But there appear to be 
 many differences. Thus, fome things are faid to be from the compofition of 
 matter, and thefe are fuch things as are mingled, as for inflance mead ; but 
 others from a nail, as a little coffer ; others again from a bond, as a bundle ; 
 others from glue, as a book ; and others again from many of thefe thin'^s. 
 Some too, are faid to be from pofition, as athrefliold, and the lintel of a door. 
 For thefe in a certain refped differ from pofition. Others again derive their 
 being from time, as fupper and dinner : others from place as winds ; others 
 from the paffions of fenfiblcs, as from hardnefs and foftnefs, denfityand rarity, 
 drynefs and molfture : and fome things are from fome of, but others, from 
 all thefe. And, in (hort, fome things are from tranfcendency, others from 
 deficiency. So that is is predicated in fo many ways. For a threfliold 
 iV, becaufe it is fo fituated ; and its effence fignifies that it has this pofi- 
 tion ; and to he ice, is to be thus condenfed. But the being of fome things 
 is defined by all thefe, and this becaufe fome things are mingled, and others 
 confift from temperament ; fome are bound, and others are condenfed ; and 
 others ufe other differences, as the hand, or the foot. The genera of differences 
 therefore are to be taken into confideration : for thefe will be the principles of 
 being ; as, for inftance, things which have thefe* fubliftence in the more and 
 the lefs, or the denfe and the rare, and ether things of this kind. For all 
 thefe belong to tranfcendency and deficiency. But, if any thing has its fub- 
 filtence in figure or fmoothnefs and roughnefs, every thing of this kind is 
 fuch through the right-lined and the curved. The effence likewife of fome 
 things confiils in being mingled, and their non-exiftence in the oppofite. 
 But it is manifeft from thefe things that if effence is the caufe of being to 
 every thing, in thefe we muft invelligate what the caufe of the being of each 
 of thefe is. 
 
 Effence, therefore, is none of thefe, nor is it thefe combined ; but at the 
 fame time it fubfifts analogoully in each. And, as in effences that which is 
 predicated of matter is energy itfelf, this is efpecially the cafe in other defi- 
 nitions ; as, for inftance, if it were requifite to define a threfhold, we {ho rid 
 fay that it is wood or ftone thus placed ; and if a houfe, that it is tiles and 
 wood placed in this particular manner. Or fliall we fav that in fome thin i:s 
 there is that for the fake of which they are falliioned ? But, if we fliou'd 
 
 C C define
 
 194 ARISTOTLE'S METAPHYSICS. Book VIIL 
 
 define ice, we fhould fay that it is water congealed or condenfed in this man- 
 ner : and if fymphony, that it is fiich a mixtuie of the {harp and the flat. 
 And after the fame manner alfo in other things. It is evident therefore, from, 
 thefe things, that energy and foriu are different from matter. For of fome 
 things compofition* is the energy and form, of other; mixture^, and of others 
 fomething elfe of the above mentioned particulars. Kence, of fuch as define, 
 thofe who fay that a houfe is flones, tiles, and v/ood, define a houfe in capa- 
 city. For thefe are matter. But thofe who fay that a veffel is that which 
 which preferves poiTeffions and bodies, or add fomething elfe of this kind, 
 define energy. And thofe who add both thefe define a third efTence, and an 
 efl'ence confifting from capacity and energy. For the definition which lub- 
 fifts through differences appears to be that of form and energy ; but that 
 which is from things inherent appears to be rather the definition of matter. 
 The likealfo takes place with refpeft to thofe definitions which Archytas ad- 
 mitted : for they are compofed from both. Thus, for infl:ance, What is 
 ferenity ? Quietnefs (according to him) in an abundance of air. For air is 
 matter, but quietntfs, energy and efTence. Y/hat is tranquillity ? Smoothnefs 
 of the fea. The fubjedl indeed, as matter, is the fea ; but energy and form, 
 fmoothntfs. It is evident, therefore, from what has been laid, what a fenfibk 
 efTence is, and how it fubfifts. For one thing is as matte, another as form, 
 becaufe it is energy ; but the third is that which is compofed from iliefe, 
 
 CHAP. III. 
 
 But it is neccfTary not to be ignorant that it is fometimes concealed from 
 us whether a name fignifics a compofite efTence, or energy and form j as for 
 inflance whether a houfe is the fign of that which is common, viz. of a co- 
 vering from tiles and wood and flones thus placed ; or whether it is a fign of 
 energy and form, becaufe it is a covering. Likewife, with refped to a line, 
 whether it is a duad in length J or the duad §. And, with relpedi to animal, 
 whether it is foul in body, or foul. For foul is an efTence, and the energy of 
 
 * As in water and honey. 
 
 t As of grains of wheat and barley. 
 
 * For a duad in length is a compofite ; the duad being fornn, and length matter. 
 
 § Atiftotle, fays Alexander, calls aline the duad, becaufe the duad in numbers is the firfl; in- 
 terval or extenfion, as in lengths a line. 
 
 a certain
 
 Book VIII. ARISTOTLE'S METAPHYSICS. 195 
 
 a certain body ; but animal will be in both, not as predicated in one de- 
 finiti m, but as with relation to one thing. Thefe things however contribute 
 to fomething elfe, but do not at all contribute to the inveftigation of a fenfible 
 elR'nce. For the very nature of a thing belongs to form and to energy. 
 For foul, and the being of foul are the fame. But the being of man and 
 man are not the fame, unlefs the foul is called man. So that man, and the 
 effence of man, will be the fame in one refpeft, and not the fame in another. 
 
 From inveftigation, therefore, it does not appear that a fyllable * confifls 
 from letters and compofition, nor that a houfe is tiles and compofitiun : and 
 this rightly : for neither the compofidon nor mixture of any thing is with 
 thole things of which it is the compofition or mixture f. And in a fimilar 
 manner, neither is this the cafe with any thing elfe. Thus, for inftance, if 
 a threlliold is from pofuion, pofition is not from a threfhold, but rather this 
 is from that. Nor is man animal and biped ; but it is necefiary that there 
 fhould be fomething which is befides thefe, if thefe are matter, and which is 
 neither an element, nor from an element, but which they call eflence, fepa- 
 rating it from matter, ij: If therefore this is the caufe of being, and elTcnce, 
 they will fay that this is effence itfelf. 
 
 But it is necefl'ary that this fliould be either eternal, or corruptible without 
 being generated §, and generated without generation. We have however 
 elfewhere fhown and rendered manifeft that form is not made by any one, 
 nor generated, but that it becomes this particular form and that which con- 
 fifts from thefe ||. But whether there are feparate eflences of things corrupt- 
 ible, is not yet manifeft; except that it is evident that there cannot be of 
 
 * Viz. the form itfelf of a fyll.ible. 
 
 f This obfcure fentence, which is dill more obfcure in the original, is thus well explained 
 by Alexander. " If there is a compofition, for example of water and honey, the mixture does 
 not unite with either of thefe, viz. with water or honey, or with both; for the purpofe of 
 forming mead. For if mixture was a thing able to fubfift by itfelf, it v/ould not be improper 
 to fay that it produced mead by a conjundlion with water or wine, or with both thefe ; but 
 fince it is not fo, this cannot be faid ; but mead is the mixture itfelf." 
 
 J The fenfe requires that, inftead of £i ouii tout aniov tou tivai, nai oua-ia tovto, outw av t>)v ouaiav 
 tv XtyoiEv, we fljould read, ei om tout' ujitiov Toy tivai xat ova-la^, auTnv av Tnv ov^iav \syoiEv. And this 
 emendation is juftified by the text of Alexander, which 1 have accordingly adopted in my verfion 
 of this paflage. 
 
 § For in the former book it has been demonftrated that form is not generated, but that which 
 confifts from matter and form. 
 
 Jl ;. (. from matter and form. 
 
 C c 2 feme
 
 196 ARISTOTLE'S METAPHYSICS. Book VHI. 
 
 fome corruptible natures, which are not able to fubfift independently of 
 fenfibles, as a houfe, or a veflel. Perhaps, therefore, neither are thefe efllnces, 
 nor is any thing elfe effence which has not a natural iubfiitence : for fome 
 one may confider nature, as alone that effence which lubfifts in things cor- 
 ruptible. So that the doubt entertained by the followers of Antiithenes, and 
 thofe fimilarly unlearned, viz. that effence cannot be defined, may now be 
 opportunely folved ; for, fay they, definition is a longfentence ; but it is pof- 
 fible to inffrudl oth.ers in the pajrtlcular quality of a thing, though it cannot 
 be defined : for you cannot fay what filver is, but you may fay that it refem- 
 bles tin ; fo that of a certain effence, as, for inftance, of that which is a ccm- 
 pofire, whether it be fenfible or intelligible, there may be a definition and 
 reafon ; but there cannot be of thofe things from which thefe firft confift, if 
 definitive reafon fignines fomething of fomething ; and it is rcquifite that 
 this fhould be as matter, but that as form. It is alfo evident why, if in a 
 certain refped: numbers are effences, they are fo after this manner, and not 
 becaufe they are a multitude * of monads ; for definition is a certain number : 
 (for it is divifible and may be refolved into indivifibles, fince reafons are not 
 infinite) and number is a thing of this kind. And as, when any one of thofe 
 things from which number confifts is fubtrafted from, or added to a number, 
 there is no longer the fame, but a different number, though that which is the 
 leaft fhould be fubftraded or added ; in like manner, neither will definition 
 nor the very nature of a thing, be any longer the fame, if any thing be taken 
 away or added. Befides, it is requifite that there fliould be fomething through 
 which number itfelf is one, and which now they cannot aflign, if number is 
 one thing ; for either it is not one thing, but is as it were a heap, or, if it is, 
 it mufc be faid what that is which makes it to be one from many things. De- 
 finition alfo is one thing compofed from the many ; but neither can they 
 affign a reafon why this is one ; and this very properly happens on the fame 
 account. EiTence alfo is after this manner one, and not according to fome, 
 who affert that it is as it were a certain monad, or point, but each is energy 
 and a certain nature j and as number has neither more nor lefs, Co neither has 
 that effence which fubfifls according to form ; but if there is any effence 
 which has the more and the Icfs, it is that which fubfifts according f to matter. 
 
 * riAtificf is omitted in the printed text. 
 
 t Inftead of lutra ix)); luitJ: matter, as in the printed text, the fenfe requires we fhould read, as 
 -in my tranflation, xut' uMv- The verlion of Bcflarion alfo \\^s Je^undum matalivn 
 
 Concerning
 
 BookVIII. ARISTOTLE'S metaphysics, 197 
 
 Concerning the generation therefore and corruption of the above mentioned 
 eflences, how each may be admitted to take pLicc, and in v/hat rcfped each is 
 impoffible, and alfo concerning the redudion of definition to number, let it 
 be thus far determined. 
 
 CHAP. IV. 
 
 Concerning a material effence we ought not to be ignorant, that, though 
 all things are from the fame firft nature *, or from the fame things as thofe 
 which are firft, and though the fame matter is as a princii>le to generated 
 natures, yet at the fame time there is fomething which is proper or domeftic 
 to every thing. Thus, for inftance, the firft matter of phlegm is the fweet or 
 the fat ; but of bile the bitter or fomething elfe : and thefe things alfo, are 
 perhaps from the fame thing ; but many matters of the fame thing are gene- 
 rated when one thing is the matter of another : thus phlegm is from the fat 
 and the fweet, if the fat is from the fweet ; and it is alfo from bile, becaufe it 
 is analyfed into bile, as into the firft matter : for one thing is from another in a 
 twofold refpedt, viz. either by progreffion, or analyfation into its principle ; 
 but;, one matter exifting, it happens that different things;are generated, through 
 the moving caufe. Thus, from wood a cheft and bed are formed. Of fome 
 things, however, which are different, the matter is neceffarlly different. Thus 
 a faw can never be made from wood, nor is it in the power of the moving 
 caufe to cfFe:T: this ; for it can never make a faw from wool or from wood. 
 But, if it is poffible for the fame thing to be made from different matter, it is 
 evident that art, and the principle as moving are the fame : for if matter and 
 that which moves are dilTerent, that alfo which is generated will be different. 
 When therefore any one inveftigates the caufe of a thing (fince caufes are 
 predicated multifarioufly) it is requifite to enumerate all the contingent 
 caufes. Thus, for inftance, what is the caufe of man as matter ? is it not the 
 menftrual blood ? But what is the caufe as that which moves ? is it not 
 feed ? V' hat is the caufe as form ? that which Is the very nature of a thing. 
 What is the caufe as that for the fake of which he fubiifts r the end ; but 
 perhaps both thefe are the fame. It is requifite however to enumerate the 
 moft proximate caufes : What is the matter of man ? not fire or earth, but 
 that which is proper or domeftic f . 
 
 * By the fame firjl nature Aridotle means formlejs matter, 
 f Viz. The menftrual blood. 
 
 With
 
 J98 ARI STOTL E'S META PH YS I C S. Book VIIL 
 
 With refped to phyfical and generated effences, therefore, it is neceflary 
 that he fliould proceed in this manner, who proceeds rightly, if there are 
 thcfe caufes, and they are fo many in number, and a knowledge of caufes is 
 neceflary. In * phyfical ejfences however^ but -which are perpetual^ a difierent 
 mode of proceeding muft be adopted ; for fome of them perhaps are with- 
 out matter, or have not a matter of this kind, but fuch only as is moveable 
 according to place. Nor does matter belong to fuch things as have indeed a 
 natural fubfiftence but are not tfl!ences, but that which is the fubjed to 
 thefe is effence. Thus, for inftance, what is the caufe of an ecllpfe ? what 
 the matter of it ? No matter f however can be afligned, but the moon is that 
 which fuffers j but what is the caufe as that which moves, and corrupts the 
 light ? the earth. An eclipfe however, has not perhaps that caufe for the 
 fake of which it fubfifts ; but the caufe which is as form is definition. This 
 however is immanifeft, unlefs it fubfifts together with caufe : as, for inftance, 
 what is an eclipfe ? a privation of light ; but if it is added that this privation 
 of light is occafioned by the intervention of the earth, this will be a definition 
 together with the caufe. Moreover with refped to fleep it is immanifeft what 
 that is which is firft pafflve : fhall we fay that it is the animal ? be it fo. 
 But according to what is this paflive ? and v^hat is firft paflive ? the heart, or 
 fomething elfe ? and in the next place, to what is it paflive ? likewife what 
 is its paflion, and which is not the paflion of the whole ? fliall we fay it is 
 fuch a particular kind of immobility ? be it fo. But this is becaufe there is 
 Something which is firft paflive. 
 
 CHAP. V. 
 
 But, fince fome things both are and arc not without generation and cor- 
 ruption, as points, if they have a fubiiftence, and, in fliort, forms (for white- 
 nefs is not generated, but the white wood, if every thing which is generated is 
 generated from foinething, and is generated fomething) ; this being the cafe, 
 all contraries are not generated from each other, but a white man is in one 
 
 * Viz In the celedial fplieres, the eflence of which is perpetual, as is fhown by Ariftotle 
 in the 13th book of this work. 
 
 t It is well obferved here by Alexander that, if the moon was the maiter of an eclipfe, but 
 form the eclipfe itfclf, when tlie eclipfe ceafecl, the moon would be no more : for, forms being 
 ^3ken away, the things alfo are taken away which fubfift through them. 
 
 way
 
 EookVIII. ARISTOTLE'S METAPHYSICS. 199 
 
 way generated from a black man, and In anotlier way vvhitenefs from b'ack- 
 ncls. Nor of every thing is there matter ; but of tbol'e things of which there 
 is generation and mutation into each other. But fuch things as either are or 
 are not without mutation, thefe are without matter. It is, however, dubious, 
 how the matter of every thing fubfifts with refpeil to contraries. Thus, for 
 inftauce, if the body is well in capacity, but diteafe is contrary to health, (hall 
 we fay that both are in capacity ? Shall we alfo fay that water is both vinegar 
 and wine in capacity ? Or iball we fay that the body is the matter of health, 
 according to habit and according to fo/m, but that it is the matter of difeafe 
 according to privation, and unnatural corruption ? But there is a certain 
 doubt why wine is not the matter of vinegar, nor vinegar in capacity, al- 
 though vinegar is produced from it. Alio, with refpedt to that which has 
 life, it may be doubted, whether it is a dead body in capacity or not. The 
 doubt, however, may be folved, by faying that corruptions fubfirt; from acci- 
 dent. But the matter itfelf of an animal is, according to corruption, the ca- 
 pacity and matter of dead body, and water alfo of vinegar. For they are ge- 
 nerated from thefe, in the fame manner as night from day. And it Is requifite 
 that fuch things as thus change into each other, ftiould return into matter. 
 Thus, in order to the generation of an animal from a dead body, it is requi- 
 fite that the dead 'body fliould firft be refolved into matter*, and, that thus 
 an animal fhould atterwards be generated from It. In like manner, vinegar 
 muft be refolved into water, and thus from it wine will afterwards be produced* 
 
 CHAP. vr. 
 
 With refpedl to the abovementioned doubt concerning definitions and 
 numbers, what is the caufe of their being one ? For, of all fuch things as 
 have many parts, and where the whole is not as it were a heap, but is fome- 
 thing befules the parts, there is a certain caufe. For in fome bodies contadl Is 
 the caufe of their being one, in others vifcofity, or fome other paflion of this 
 kind. But definition is one difcourfe, not by a bond, as the Iliad, but becaufe 
 it is of one thing. What then is it which makes man to be one, and why is 
 he one, and not many things, fuch as, for inftance, animal and biped, efpe- 
 clally if, as fome fay, animal itfelf and biped itfelf have a fubfiftence ? For 
 
 * /. e. Into the four elements. 
 
 why
 
 200 A RI STOTLE'S METAPHYSICS. Book VIII. 
 
 why is not man thofe very things? And will men fubfift, not by the parti- 
 cipation of one man, but by the participation of two things, animal and 
 biped ? In fhort, man will not be one thing but many things, animal and 
 biped. It is manifeft, therefore, that thofe who are thus accuftomed to define 
 and fpeak, cannot affign the reafon of this, and folve the doubt. But if it is 
 as we have faid, that one thing is m.atter and another form ; and again, one 
 thing is in capacity and another in energy, the doubt which is inveftigated will 
 no lono-er appear to exift. For the doubt is the fame as if the definition of a 
 garment were round brafs. For this name would be a fign of the definition. 
 So that the objed of inveftigation is, what the caufe is that the round and tlie 
 brafs are one. The doubt, therefore, appears no longer to remain, becaufe 
 this is matter, and that form. What elfe then caufes that which was in ca- 
 pacity, in things in which there is generation, to fubfift in energy, except the 
 efficient caufe ? For there is no other caufe of the fphere in capacity becoming 
 a fphere in energy ; fince this * is the very nature to both. But with relped 
 to matter, one kind is intelligible and another fenfible : and always with re- 
 fpe£l to definition, one thing is matter and another energy, as, a circle is a plane 
 figure i". But fuch things as have neither intelligible nor fenfible matter, of 
 thefe each is immediately one particular thing, as that which is this particular 
 being (/'. e. fubftance), alfo quantity and quality. Hence, in definitions there 
 is neither he'mg nor the one, and the very nature of a thing is immediately one 
 particular thing, as alfo a particular being. Hence, too, there is no other caufe 
 that each of thefe is one, nor that each of thefe is a particular being. For im- 
 mediately each is a certain being, and a certain one ; yet nehher being nor the 
 one is the genus of thele, nor have they a fubfiftence feparate from particulars. 
 But in confequence of this doubt, fomc fay that participation is the caufe ^ ; but 
 they are dubious v\hat the caufe of participation is, and how it is efieded. 
 S 'me affign the copula of the foul as the caufe, as Lycophron, who fays that 
 fcien. e is the copula of fcientific knowledge and the foul ; but others aflert 
 that life confifts in the compofition or conjundion of the foul with the body ; 
 though the fame reafon may be affigned in all things. For to be well, will 
 cither be a copula, or conjundion, or compofition of the foul and health. 
 
 * By ihis, Arlftofle appears to me to (igiiify energy; for tins is the very nature or eflence of 
 every tiling, ami confequently of both man ami fphere. 
 
 t For XiQXi: fgure is the matter, and Jiluue tl»c energy or form of the dofuiltion. 
 J Viz. is the caufe of the unity of animal and biped. 
 
 And
 
 Book Virr. A R I S T OT L E'S M E T A P H Y S 1 C S. 201 
 
 And for brafs to be a triangle, will be a compofition of brafs and triangle : and 
 for a thing to be white, will be a compofition of fuperficies and whitenefs. 
 But they fpeak in this manner, becaufe they inveftigate the uniting reafon 
 and difference of capacity and energy. However, as we have before faid, the 
 laft matter * and form are the f mie, the one being in capacity, and the other 
 in energy. So that to inveftigate the caufe of unity, is fimilar to an invefti- 
 gation of the caufe of a thing being one. For every thing is one particular 
 thing; and that which is in capacity, as alfo that which is in energy, is in a 
 certain refpedl one thing. So that there is no other caufe except that which 
 fublifts as moving from capacity into energy. But of fuch things as are with- 
 out matter, each is fimply and properly one and being "f . 
 
 • That is to fay, the proximate matter of a thing is that in capacity, which the form of it is 
 in energy. 
 
 f Inftead of aw^wj oirtfonart, as in the printed text, the fenfe requires that we (hould read 
 
 » d ARISTOTLE'S
 
 fix 
 
 ARISTOTLE'S METAPHYSICS. 
 
 ■..:f ■ 
 
 B O O K IX. 
 
 CHAP. I. 
 
 \\ E have, therefore, difcourfed concerning eflence which is primarily 
 being, and to which all the other predicaments of being are referred. For 
 other things, viz. quantity, quality, and the reft which are thus denominated, 
 are denominated according to the definition cf efllnce : for all thefe have the 
 definition of eflence, as we have before o'>ferved. But, fince being is deno- 
 minated either fubOance, or quantity, or quality, and is either in capacity or 
 energy, it is requifite that we Ihouid now fpeak concerning capacity and 
 energy. And in the firft place rtfpe£ling that capacity* which is moft pro- 
 perly fo denominated, it does not contribute to our prefent defign. For ca- 
 pacity and energy are more extended than thofe things which are alone predi.- 
 cated according to motion "j". But, when we fpeak concerning this in our 
 explanations of energy, we fliall alfo render manifeft the particulars refpedling 
 the reft. That capacity or power, therefore, and fo be able, are predicated 
 multifarioufly, we have elfewhere ftiown. But, of thefe, fuch as are equivo^ 
 cally called powers are omitted. For fome are denominated by a certain fimi- 
 
 • By that capacity which is moft properly fo denominated, Ariftotlc means the firft and 
 /ormlefs matter, as Alexander well obferves. 
 
 f (. t. According to energy. 
 
 litude,
 
 JookIX. ARISTOTLE'S metaphysics, 203 
 
 litude, ap, in geometry *, we fpeak of powers, or things poflible, alfo of things 
 impoffible, becaufe in a certain refpedl they are, or are not. But fuch things 
 as are referred to the fame form, are all of them certain principles, and are 
 predicated with relation to one firftf , which is the principle of mutation in 
 anotlier, fo far as it is another. For there is a capacity of fuffering, which in 
 the patient itfelf is the principle of paiTive mutation from another, fo far as it 
 is another. But there is a habit of impaffivity and corruption into that 
 which is worfe, which proceeds from another tranfmuting principle, fo far as 
 it is another. For, in all thefe defmitions, there is the definition of the firft 
 capacity. 
 
 Again ; thefe are alone called either the capacities of acting or fuffering, 
 or ot ading or fuftering in a becoming manner. So that, in the definitions 
 of thefe, the definirions of the former capacities are in a certain refpedl 
 inherent. It is evident, therefore, that in a certain refpedl there is one power 
 of adling and fuffering (for a thing is able, both becaufe it lias a capacity of 
 fuffering, and becaufe fomething elfe may fuffer from it), a'ld that in another 
 refpeiSl there is a different power : for there is one power in the patient. For, 
 becaufe it has a certain principle, and matter is a certain principle, the patient 
 fuffers, and one thin^ fuffcrs from another. Thus, that which is fat is com- 
 buftible, and that which yields after this manner may be preffed ; and in a 
 fimilar manner with refpect to other things. But there is another power in 
 the agent ; as, for inflance, the hot and the power of building : the former in 
 that which is able to ^ve heat, and the latter in the builder. Hence, nothing 
 which naturally poffeffes unity and continuity is itfelf pafTive to iifelf ; for it 
 is one thing, and not another: but impotency, which is contrary to fuch a 
 power, is privation. So that all power and impotency are of the fame thing, 
 and fubfifl according to the fame. But privation Is predicated multifarioufly : 
 for we fay that a thing has privation which does not poffefs a certain thing, 
 and which Is naturally adapted to poffefs, if it does not poffefs, either altoge-' 
 ther, or when it is naturally adapted ; and after this manner we fay that it 
 either entirely, or in a certain refpedt, has privation. We alfo fay of fomc 
 
 ♦ In geometry, if one line is double, or triple, &c. of another, the power or fquare of it is 
 faid to be four times, or nine times, &c. the power or fquare of that other line. Thus the 
 fquare of 4, viz. 1 6, is four times the fquare of 2, viz. 4 ; and the fquare of y, viz. 81, is nine 
 times the fquare of 2, viz. 9. 
 
 t Viz. Are predicated with relation to formlefs matter. 
 
 D d 2 things
 
 204 ARISTOTLE'S METAPHYSICS. Book IX. 
 
 things which through violence do not pofTefs that tvhich they are naturally 
 adapted to pofTels, that they ruiler a privation of fuch things. 
 
 CHAP. II. 
 
 But fince fuch-like principles of capacities fubfin: in inanimate natures, 
 "and fome of them in animated natures, in foul, and in that part of the foul 
 which poflefles reafon, it is evident, that of capacities or powers alfo, fome 
 will be irrational, but others accompanied with reafon. Hence all arts, both 
 fuch as are efiedive, and fuch as are fciences *, are powers ; for they are the 
 principles of mutation in another thing, fo far as it is another. And all 
 thofe powers which are accompanied with reafon are effe£live of contraries ; 
 but each of thofe which are irrational, is alone efTeQive of one thing. Thus, 
 for inftance, the hot is alone effedive of heat ; but the mediciml art is effld:- 
 ive both of difeafe and health. But the caufe of this is, that fcience is rea- 
 fon : and the fame reafon manifefts both a thing and its privation, though not 
 after the fame manner. In a certain refpeft, indeed, reafon knows both, but 
 alfo in a certain refpcdl it has a greater knowledge of the thing, than of its 
 privation. So that it is neceflary that fuch fciences fhould poflefs a know- 
 ledge of contraries, but of the one f eflentially, and of the other not elFen- 
 tially. For reafon knows the one elTentially, but the other after a manner ac- 
 cidentally ; fince by negation and ablation it manifefts the contrary. For firft 
 privation is that which is contrary ; but this is an ablation of the other. But 
 fince contraries are not ingenerated in the fame thing (and fcience is a power 
 from the polLfTion of reafon, and the foul alfo has the principle of motion), 
 hence that which is falubrious alone produces health, and that which is cale- 
 fadive heat, and that which is frigefadive cold ; but he who poflelles fcienti- 
 fic knowledge produces both. For reafon has a knowledge of both, though 
 not fimilaily ; and this reafon fubfifts in foul which poffelfes the principle of 
 moion. So that foul will move both from the fame principle, conjoining 
 them with chefamc thing. Hence natures wliich are endued with power ac- 
 cording to reafon, cffeit things contrary to the produdions of thofe endued 
 
 •' Alexander here well obferves tliat Ariftotlc, by a more common appellation, calli fciences 
 arts, becauTe they are motive principles in another thing. 
 
 t Viz. Of habits eflentially, but of privation not eflentially. 
 
 wit
 
 Book IX, A R I 3 T O T L E'S M E T A P H YS I C S. 205 
 
 with power without reafon. For one principle is comprehended in reafon. 
 But it is evident that the power of alone ading or fufFering follows that 
 power which is the principle of ailing or fufFering well ; but the latter does 
 not always follow the former. For it is neceflary that lie who ads well fhould 
 ad ; but it is not ncceffary that he who alone ads fliould alfo ad well. 
 
 CHAP. III. 
 
 There are, however, fome, as the Megaric * philofophers, who fay that 
 a thing when it energifes is then alone endued with power, but that when it 
 does not energife, it does not poffefs power; as, for inftance, that he who does 
 not build has not the power of building ; but that he who builds pofTefles this 
 power when he builds ; and in a fimilar manner with refped to other things. 
 But it is not difficult to perceive the abfurdities which attend this opinion. For 
 it is evident f that he who does not build will not be a builder. For the 
 very eflence of a builder confifts in the power or capacity of building ; and in 
 a fimilar manner alfo in other arts. If, therefore, it is impoffible that any one 
 can poffefs arts of this kind, unlefs he has once learned and received them ; 
 and again, that he fhould be without the pofleffion of them J, unlefs he fome 
 time or other lofes them, viz. either through oblivion, or a certain difeafe, or 
 time (for he will not lofe the thing itfelf, becaufe it is perpetual), this being 
 the cafe, when fuch a one ceafes to operate, he will not be in poffeflion of art. 
 But how will he again immediately build on refuraing the art which he had 
 loft ? The like alfo happens with refped to things inanimate. For neither 
 will there be any thing hot or cold, or fweet, or, in fhort, any thing fenfible, 
 when they are not perceived by us. So that it happens to thetn, that they 
 affert the fame thing as Protagoras. But, indeed, neither will a man have any 
 fenfe, if he neither perceives nor energifes. If, therefore, that animal is blind 
 which does not fee, though naturally adapted to fee, and when it is naturally 
 p.dapted, and further as it is naturally adapted, the fame animals will often in 
 the fame day be blind §, and in like manner deaf. 
 
 * Ey the Megaric philofophers, fays Alexander, Arillotle means Zcno and his followers, who 
 confulered energy and capacity as one and the fame thing. 
 
 f Viz. It is evident from the aflertions of thefc Megaric philofopjiers. 
 
 % When he has acquired ihem. ^ 
 
 ^ For this will be the cafe with him who winks. 
 
 -Again :
 
 206 ARISTOTLE'S METAPHYSICS. Book IX. 
 
 A'^ain; if that is irnpoffible which is deprived of power, it will be im- 
 pofTible for that which is not generated to be generated : but he who fays that 
 a thing which cannot be generated, either is, or will be,, will fpeak falfely. 
 For this will fignify that which is impofhble. So that thnfe afTertions fub- 
 vert both motion and generation. For that which ftands will always ftand, 
 and that which fits will always fit. For a man will not rife if he fits; fince 
 it will be impoffible for that to rife which is not able to rife. If^ therefore,, 
 thefe aflertions cannot be admitted, it is evident that capacity and energy are 
 different from each other. But thofe alTertions make capacity and energy to 
 be the fame. Hence it is not a fmall thing which they endeavour to fubvert. 
 So that it happens, that it may be poffible for a thing to be, and yet it may 
 not be ; and that it is poffible for a thing not to be, which yet may be. In a 
 fimilar manner too, in the other predicaments, that which is able to w^alk may 
 not walk, and that which does not walk may be able to walk. But that is 
 poffible, to which, when the energy is prefent of which it is faid to have the 
 capacity, nothing will be impoffible. My meaning is this, if, for inftance, it 
 IS poffible for any one to fit, and it happens that fuch an one fits, nothing im- 
 poffible will take place when he fits : and in a fimilar manner, if it is poffible 
 for any thing to be moved or to move, to fland, or to be flopped, to be, or to 
 be generated, not to be, or not to be generated. But the name energy, which 
 accords with entclecheia *, and alfo with other things, is principally derived 
 from motions. For motion efpecially appears to be energy. Hence, to things 
 which are not, motion is not attributed, but other predications. Thus, for 
 inftance, things which are not, are dianoetic and defirable objedls, but are not 
 moved. But this is, becaufe not being in energy, they may be in energy. 
 
 * " Becaufe energy (fays Alexander) is denominated in a twofold refpeft, according to one 
 of thefe modes, ends themfelves are called energies. For the end of luhitening which is the 
 ivhite, in which whitening ceafes and ftops, is called energy ; and in like manner the ends of 
 other motions are denominated energies, which ends themfelves are properly called enteleche'ia. 
 Eut according to another mode, motion itfelf\% called energy. Thus, in the inftance already ad- 
 duced, whitening is both in capacity and energy. It is in capacity, indeed, becaufe it has not 
 yet arrived at enteleche'ia and the end ; but in energy, becaufe it poflefles fomething of energy, 
 entelecheia, and the end : fince in whitening, or certainly in the thing which becomes white, 
 fomething of the white, and of entelecheia are inherent. Since, therefore, energy is twofold, 
 the energy, fays Ariftotle, which accords with entelecheia and the end, is derived from motions. 
 Por becaufe motion is properly called energy (for energy is confidered in motion), but motion 
 is the motion of a certain end, hence end is alfo called energy, becaufe, as I have faid, the 
 energy which is confidered in motion, is effecled on account of the end." 
 
 For,
 
 BooRlX. ARISTOTLE'S METAPHYSICS. 207 
 
 For, of things which are not, fonie are in capacity, but yet are not, becaufe 
 tliey are not in entelecheia. 
 
 CHAP. IV. 
 
 If, therefore, the pofTible is that which we have faid it is, to which energy 
 is confequent, it is evident that it cannot be true to fay that this thing is 
 pofTible, and yet will not be. For if this were admhted, things which are 
 poflible * would elude our fearch. I fay, for inftance, as if fome one fhould 
 aflert that it is poffible for the diameter of a fquare to be commenfurate with 
 the fide, but that it never will be commenfurate, not confidering that this is 
 impoflible, and, therefore, conceiving that nothing hinders but that a thing 
 which is poffible to be, or to be generated, neither is, nor will be. However, 
 from what has been laid down, this is neceflary. For, if we fuppofe that a 
 thing may be, or may be generated, which is not indeed, but which is 
 poffible, there will be nothing impoffible in fuch a fuppofition. But t 
 if it is admitted that the diameter is commenfurable with the fide, it will 
 follow that even are equal to odd numbers, which is impoffible. For the 
 falfe is not the fame with the impoffible. For, that you now fland is falfc 
 indeed, but not impoffible. At the fame time alfo, it is manifeft, that if, in 
 confequence of the exiftence of a, it is neceffary that b fhould exifl, if it is 
 poffible for a to be, it neceffarily follows that it is alfo poffible for b to be. 
 For if it is not neceffarily poffible for it to be, nothing hinders but that it may 
 not be poffible for it to be. Let it, therefore, be poffible for a to be : fmce, 
 then, it is poffible for a to be, nothing impoffible will happen from confidering 
 a as exifting. It is alfo neceffary that b fhould exift; but it was impoffible. 
 Let it, therefore, be impoffible. But if it is impoffible that b fhould exift, it 
 is neceffary that it fhould alfo be impoffible for a to exifl. But the firft is, and 
 therefore the fecond is. Hence, if a is poffible, b alfo will be poffible, if 
 they fubfift in fuch a manner, as that in confequence of the exiftence of a 
 k is neceffary that b fhould exift. If, therefore, a and b thus fubfifting, it is 
 not poffible for this to take place with refpedt to ^, neither will a, b, fubfift in 
 
 • Indead of ta aiuvara, as in the printed text, I read ra Juvara. 
 
 f The text in this place appears to be very corrupt, which I have endeavoured in my tranila- 
 ^on to rcftore from the comment of Alexander,. / 
 
 the
 
 208 ARISTOTLE'S METAPHYSICS. Book iX- 
 
 the manner in which they are fuppofed to fubfif^. And if a being pofTible, 
 it is alfo neceflary tliat b Ihould be pofTible ; if a is, it is necefTary that b alfo 
 fhould exift. For, that it is pcffible from neceffity for b to exift, if it is 
 poflihle for a to cxift, fignifies this, that if a is, and when it is, and as it is 
 pt flible to be, then this is alfo nccefiary with refped to b. 
 
 C H A P. V. 
 
 But fince of all powers fome are connate as thofe of the fenfes, but others^ 
 are from cuftom, as the power of playing on the pipe, and others again are 
 from difcipline, as thofe of the arts, it is neceflary that thofe powers which 
 are derived from cuflom and reafon fhould be acquired through antecedent 
 energies. But it is not neceflary that thofe which are not of this kind, and 
 which are paffive powers, fhould fubfift after this manner. Since, 'however, 
 that which pofTefTes power is able to effe£l fomething, it is neceflary to add 
 io the definition at a certain time, and after a certain manner, and fuch other 
 particulars as are confequent to thefe. And fome things, indeed, are able to 
 move according to reafon, and their powers are accompanied with reafon ; but 
 others are irrational, and their powers alfo are irrational. And it is alfo ne- 
 cefTary that thofe fliould fublifl in that which is animated, but thele in both. 
 This being the cafe, it is necefTary with refpedH: to fuch like powers, that when 
 the adlive and paffive approximate as far as they are able, the one fliould a€t 
 and the other fuffer. But in the rational powers this is not neceflary : for 
 with refped to all thefe, each is eiTedive of one thing *; but thofe are efTedt- 
 ive of contraries f . It is, however, impoflible that the rational powers fhould 
 at the fame time produce contraries. It is necefl"ary, therefore, that fome- 
 thing elfc fhould be that which has dominion. But I call this appetite, or 
 free-will: for whatever it defires, this it will principally efTe£l when it ap- 
 proximates as far as it is able to that which is paffive. So that every thing 
 which is endued with power according to reafon, mufl: necefl!arily accomplifli 
 this, when it defires that of which it poflefl^es the power, and as it poflefTes. 
 But it has the power of ading, that which is paffive being prefent, and fub- 
 fifiing in this manner ; for if not, it will not be able to ad. For there is no 
 longer occafion to add the words, nothing external impeding ; fince, as it is a 
 
 • As fire of heat. 
 
 t As mcJicine of health and difeafc. 
 
 power
 
 Book IX. ARISTOTLE'S METAPHYSICS. 209 
 
 power of a£llng, it poffefles power. It does not, however, poflefs this power 
 univerfally, but when it fubfifts in fuch a manner that external impediments 
 are removed. For thus certain things in the definition are taken away. 
 Hence, the efficient will neither at the fame time effed; two things or contraries, 
 though he fhould at the fame time wifh or defire to effect them. For he will 
 not thus poffefs the power of them at the fame time ; nor is power capable 
 of effeiling contraries at once. For he will thus effed: things of which he 
 has the power. 
 
 CHAP. VI. 
 
 Since then we have fpoken concerning the power which isdenomlnated 
 according to motion, let us now confider what energy is, and what the qua- 
 lity which it poffeffes. For by divifion the nature of that which is endued 
 with power will at the fame time be manifeft ; becaufe we not only fay that 
 a thing is endued with power which is naturally adapted to move another, or 
 to be moved by another, either fimply or after a certain manner, but we alfo 
 fay this in another refpedt. Hence in our inquiry we fhall alfo difcufs thefe 
 particulars. But for a thing to fubfift in energy, is not fuch a fubfiftence as 
 when we fay a thing fubfifts in capacity. But we fay a thing is in capacity, 
 as Mercury in the wood, and the half in the whole, becaufe it can be taken 
 away from the whole ; and we call him fcientifically knowing in capacity, 
 although he does not contemplate, who is able to contemplate. However, by 
 an induction of particulars, what we wifh to fay will be manifeft. For it is 
 not neceffary to inveftigate the definition of every thing, but it is fufficient to 
 perceive the analogous, viz. that as building is lo the architect, he who is 
 awake to him who is afleep, he who fees to him whole eyes are clofed, but 
 who poflelTes fight, and as that which is feparated from matter is to matter, 
 and that which is effedled by art to that which is uneffeded, fo is energy to 
 that which is endued with power or capacity. But all things are not fimilaily 
 faid to be in energy, but analogoufly, as this thing in this, or with relation to 
 this ; but that in that, or with relation to that. For fome things are as mo- 
 tion with refped to power, but others as clTcnce with refped to a certain 
 matter. But the infinite and the void, and fuch-Iike things, are after one 
 manner faid to be in energy and capacity, and after another manner many 
 other things 3 as, for inftance, that which fees, that which walks, and that 
 
 E e which
 
 K9 . ARISTOTLE'S METAPHYSICS. Book IX, 
 
 which Is feen. For it fometimes happens that thefe are fimply verified. Thus,. 
 one thing is faid to be feen, becaufe it is feen; but another, becaufe it has the 
 power of being feen. But the infinite does not fo fubfift in capacity, as that 
 it will at length become feparate in energy, but in knowledge*. However, 
 that this energy fubfifts in capacity is owing to a divifion which never fails "f ; 
 but this never-failing divifion will not cau-fe it to become feparate in energy^. 
 With refpeft, therefore, to a fubfiftence in energy, what it is, and what the 
 quality which it poffefTes, let it be manifeft to us from thefe and fuch-Iike par- 
 ticulars. 
 
 CHAP. VII. 
 
 It Is now requifite to determine when a thing Is in capacity, and when it 
 is not. For a thing is not in capacity at any time. Thus, for inftanee, is 
 earth man in capacity or not ? Or is not this rather the cafe when feed is 
 generated ? Nor even then, perhaps. As neither Is every thing healed by the 
 medicinal art, nor by fortune j but there is foracthing which is capable of being, 
 healed, and this is fane in capacity. But the definition of that which from 
 a fubfiftence In capacity acquires through the dianoetic part a fubfiftence ia 
 energy, is this : that which is reduced into energy, when he by whom It is fo 
 reduced is willing, nothing external impeding. But this takes place in him wha 
 is healed, when nothing within him impedes. In like manner, a houfe alfo is in 
 capacity, if nothing in this, and in the matter of it, prevents the houfe from 
 being conftru<fled, and when there is nothing which ought to be added, or taken 
 away, or changed : for this Is a houfe in capacity. And in a fimilar manner with 
 refped: to other things, the principle of the generation of which is external, and 
 with refpe£l to thofe which contain this principle within themfelves, and which, 
 ■when nothing external impedes, energife from themfelves. Thus, feed § is not 
 yet In capacity : for it Is requifite that it fhould fubfift in another, and be changed. 
 
 * For we know both that number can be increafed, and magnitude divided, to infinity; byt 
 this can never be effe£led in energy. 
 
 f For magnitudes are divifible to infinity. 
 
 J Several lines follow this word in the printed text which are not to be found in the Com- 
 mentary of Alexander, and are not tranflatcd either by Beflarion or Argyropylus, the mod an- 
 tient tranflalors of Ariftotle. I have, therefore, omitted them in my verfion, as undoubtedly 
 fpurious. 
 
 § Viz. Seed when it is contained in a veflel is not wheat in capacity ; but this is only trua 
 when it is placed in the earth, that it may be changed, i. c. that it may germinate, through its 
 own innafe principle. 
 
 But
 
 Book IX. ARISTOTLE'S METAPHYSICS. S-U 
 
 But when it Is now a thing of this kind through its own principle, then 
 this is in capacity ; but that * requires another principle. J uft as earth is not 
 yet a ftatue in capacity; for when changed it will be brafs. But it appears 
 that this is not what we now fay, but the following, viz. that a cheft is not 
 wood, but wooden, nor wood earth, but earthly. Again, if earth is after this 
 manner not any thing elfe, but is confidered denominatively, that which is 
 always fimply in capacity, is that which is pofterior. Thus, for inftance, the 
 cheft is neither earthly, nor earth, but wooden. For this is the cheft in capa- 
 city, and this is the matter of the cheft ; fimply, indeed, of that which is 
 fimply, but of this particular cheft, this particular wood. Indeed, if there is 
 fomething which is firft, and which is no longer denominated from another, 
 this is the firft matter. Thus, if earth is aerial, but air not fire, but fiery, fire 
 in this cafe is the firft matter, as that which is this particular thing, and which 
 is eflence. For in this that which is umverfal'\ and a^fubjcEl difFti-, that the 
 one is this particular thing, and the other not. Thus man, body, and foul, 
 are each the fubjedt of paiTions ; but paffion is the being a mufician, and the 
 being white. However, when mufic is ingenerated, that is not called mufic, 
 but a mufician ; and man is not called whitenefs, but white ; nor walking or 
 motion, but that which walks or is moved. In things, therefore, which are 
 thus denominated that which is the laft is eflence. But in things which are 
 not fo denominated, but of which a certain form and this particular thing are 
 predicated, that which is laft is matter, and a material eflence. And, indeed, 
 it very properly happens that the one is predicated of the other, both accord- 
 ing to matter and paflions ; for both are indefinite. And thus we have fliown 
 when a thing may be fald to be in capacity, and when not. 
 
 CHAP. viir. 
 
 But fince we have fliown in how many ways the prior is predicated, it is evi- 
 dent that energy is prior to capacity. I mean not only that definite capacity 
 which is called the principle of mutation in another fo far as another, but in 
 fhort every principle of motion and reft. For nature :j: is in the fame genus with 
 
 . .* Viz. Seed while in the veflel. 
 
 t According to. Alexander, by univerfal here, Ariftotle means every'predicate, whether it be 
 fiflence or accident -, but hy fubjeB he means eflence. 
 
 X Ariftotle in his PhyCcs defines nature to be the principle .of motioa and reft of that in 
 " which it is primarily and eflentially inherent. 
 
 Ee 3 capacity.
 
 J12 ATIISTOTLE'S METAPHYSICS. Book IX. 
 
 capacity ; fince it is a motive principle, yet not in another, but in itfelf, fo far 
 as it is itfelf. But energy is prior to every thing of this kind, both in defi- 
 nition and edence. It is alfo in a certain refpeiit prior, and in a certain re- 
 fpedt not prior, in time. That it is therefore prior in definition is evident. 
 For that v/hich primarily pofTefTes power, on that account pofTeffes it, becaufe 
 it is capable of energifmg. Thus, that is fabricative which is able to build ; 
 that is vifive which is able to fee ; and that is vifible which is capable of being 
 feen. The fame reafoiiing alfo applies to other things. So that it is neceflary 
 that the definition and knowledge of energy fhould precede the definition and 
 knowledge of capacity. 
 
 Energy is alfo prior in time to capacity in the fame fpecles. For that an- 
 tecedes in time which effects the fame thing in fpecies, but not in number. 
 But my meaning is this, that of this particular man who is now in energy, 
 and of this corn, and this horfe, and of that which fees, the matter, and the 
 feed, and the vifive power, are prior in time ; thefe being in capacity, man, 
 corn, and that which fees, but are not yet thefe in energy. But other things 
 which are in energy, and from which thefe are generated, are prior to thefe in 
 time. For always, from that which is in capacity, that which is in energy 
 is generated, through that which is in energy. Thus, from man man is gene- 
 rated, from a mufician a mufician, fomething firft always moving. But that 
 which moves is now in energy. Flowever, in what we have faid concerning 
 effence, we have fhown that every thing which is generated is generated from 
 fomething, and by fomething, and that this is the fame in fpecies. Hence it 
 appears to be impoflible that there fhould be a builder who has never built any 
 thing, or a harper who has never played on the harp. For he who learns to 
 play on the harp learns to play by playing on the harp ; and the refl: in a 
 fimilar manner. Hence that fophiftic argument originates, that fome one not 
 pofleffing fcience will produce a fcientific efFedt. For he who learns does not 
 poflefs fcience. But in anfwer to this we reply, that, of that which is ia 
 generation, or pafling into exiftence, fomething is already generated ; and, in 
 Ihort, of that which is in motion, fomething is moved, as we have demoa- 
 ftrated in our books* concerning Motion. This being the cafe, it is perhaps 
 
 alfo 
 
 * Ariftotle, by his books On Motion, means the laft books of his Phyfics, in which he de- 
 
 nionftrates, That every thing -which is in motion was prior to this moved; and. That every thing 
 
 •which is now moved was prior to this in motion. Thefe two propofiti-ons are demonftrated by 
 
 Proclus in hi$ lirfl book On Motion, as follows : . 
 
 " I. Every
 
 Book IX. A H I S T O T L E* S M E T A P H YS I C S. 21S 
 
 alfo neceflary that he who learns fhould poflefs fomething of fcience. And 
 from this alio it is evident that energy is thus prior to capacity, both accord- 
 ing to generation and time. 
 
 It is like wife prior in effcnce. In the firft place, becaufe thofe things which 
 are pofterior in generation are prior in form and efTmce ; as a man is prior 
 both to a boy and feed * : for the one now poflelfes form, but the other does 
 not. And in the next place, becaufe every thing which Is generated proceeds to 
 a principle and an end. For, that for the fake of which a thing fubfifts is the 
 principle ; but generation is for the fake of the end. And the end is energy ; 
 and power or capacity is received for the fake of this. For animals do not 
 fee in order that they may have fight ; but they have fight in order that they 
 may fee. In like manner, men poffefs the capacity of building that they may 
 build, and of contemplating that they may contemplate ; but they do not contem- 
 
 " I. Every thing which is in motion was prior to this moved. 
 
 " Let the magnitrde A B be in motion in a firfl time H R, and let this fird time be divided in 
 the point K. Something, therefore, of the magnitude A B was moved; and, indeeJ, in the 
 whole time H R it was in motion, but in the time H iC it was moved. For an inftant, or thr 
 flow, is the boundary of the time H K. But in this, to have been moved is poffibk, but to be 
 in motion is impoflible. In a fimilar manner alfo, by dividing the time H K, we may demon- 
 ftrate that the having been moved muft be prior to the being in motion. For the now is In every; 
 time, and confequently the having been moved. Q^E. D. 
 
 " II. Every thing which is now moved was prior to this in motion. 
 
 <' Let there be fome thing which has been changed from A into B. Either,- therefore, it was 
 changed in time, or in an inftant. But if in an inftant, it muft alfo have been through the fame 
 inftant, in A and B at the fame time. For if it is according to one inftant in A, and according 
 to another in B, there will be time between the two ; for an indivifible is not contiguous to an in- 
 divifible. It was changed, therefore, from A to B in time. But all time is divifible. So that it 
 was changed in the half of that time, and in the half of that half, and fo on ad iirfiniium. 
 Every thing, tlierefore, which is now moved was prior to this in motion. CK_t. D." 
 
 * " For, as the architeft (fays Alexander) firft forms the houfe in himfelf, then lays the foun* 
 dations, and afterwards builds the walls and the roof; fo nature, looking to man, for inftance, as 
 a mark (fince flie operates for the fake of fomething, as Ariftotle demonftrates in the third book 
 of his Phyfics), iirft produces the genital feed, and the female menfes, afterwards the heart, 
 then the liver, after this the flefli, nerves, and bones, then the boy, in the next place the youth, 
 and laft of all the man || Thus, things which are pofterior in generation are prior by nature ; 
 but things pofterior by nature, as feed and the menfes, are prior to us. Hence, the man is by 
 nature prior to the boy, and the boy to feed. 
 
 II The feven ages of man were dengminated by the Greeks as follows : B(t^ct, iraif, lusipaxiov, not, avsf,"srfiir?uTHc, 
 j'tfKv, Which I thus tranflate i The infant, the boy, the l»d, the youth, the man, the elderly man, and the old 
 man. / 
 
 plate 
 
 ^
 
 214 ARISTOTLE'S METAPHYSICS. Book IX. 
 
 plate that they may poflefs the power of contemplating, except thofe who 
 meditate. Thele, however, do not perfedly contemplate ; but they either 
 contemplate in a certain refpe£t, or they have no occafion for contemplation. 
 Further ftili : matter is in capacity, becauie it may arrive at form. But when 
 it is in energy, then it is in form ; and a fimilar reafoning takes place in other 
 things, and of which the end is motion. Hence, as teachers, when they ex- 
 hibit their difciple energifing, think that they have accomplifhed the end of 
 teaching, this is alfo the cale with nature, ror, if it were not (o, a circum- 
 ftance like the Hermes of I'affo * would take place ; fince it would be imma- 
 nifeft, whether Icience is internal or external, as was the cafe with his Hermes : 
 for a work is the end, and energy is a work. Hence the word energy is 
 denominated from work, and tends to entelecheia. But fmce the laft of fome 
 things is the ufe, as of fight feeing, and no other work befides this is pro- 
 duced by the fight, but by certain things fomething elfe is produced, as by the 
 building art, befides building, a houfe is produced ; yet, neverthelefs, energy 
 will be the end of capacity in both thefe inftances, though it is more the end 
 of it in the latter than the former. For building is in that which is built, 
 and at the fame time is generated, and is with the houfe. Of fuch things, 
 therefore, of which that which is generated is fomething befides the ufe, of 
 thefe energy is in that which is made. Thus, for inftance, building is in that 
 which is built, and weaving in that which is woven ; and in a fimilar manner 
 in other things. And, in Ihort, motion is in that which is in motion. But 
 with reipecfl to things of which there is no other work befides energy, in the 
 things themfelves energy fubfifts. Thus, feeing is in him who fees, and 
 contemplation in him who contemplates, and life is in the foul. Hence feli- 
 
 * The hiftory of Paflb, according to Alexander, is as follows : " The flatuary Paflb had rc- 
 prefented in a certain (lone the form of Mercury, and Mercury was fcen in the ilone ; but whe- 
 ther it was within or without the flone was uncertain. It could not be faid to be external to 
 the flone, becaufe, if it were, the (lone mud have been carved, and v ould have po(re(red in- 
 equalities; but the whole was as fmooth as a mirror. But neither could it be faid to be within 
 the flone. For if, in the (lone in which Adercury was reprefented, there had been any com- 
 mifTures or joinings, it might have been faid that Mercury had been carved in another (lone, ar4 
 had been afterwards inclofed in very fmooth (tones placed upon it, and that, thefe being pellucid, 
 it could be feen through them ; but as the floTie was every way continuous and one, and had no 
 joining, this could not be faid to be the cafe. It was, therefore, uncertain, whether the Mer- 
 cury was within or without the Aone. It was dubious whether it was external, on account of 
 the equality of the (lone -, and alfo, whether it wns internal, becaufe it could not be conceived 
 hpw within one continued ftone Mercury could be fafliioncd," 
 
 ci-y
 
 »oorHC AtirsrOTLE'S MET APBrYSICS, SI5 
 
 city alfo is In the foulj for it is a certain life. So that it is evident that 
 effence and form are each of them a certain energy. And according to this 
 reafoning, it is alfo manifeft that energy is prior in effence to capacity : and, as 
 we have faid, on€ energy always precedes another in time, as far as to the 
 energy of that which firft eternally moves. 
 
 Energy, indeed, is prior to capacity in a more principal and excellent man- 
 ner. For things eternal are prior in effence to things corruptible j but no- 
 thing eternal is in capacity. The reafon of which is as follows: — Every 
 power or capacity is at the fame time a capacity of contraditftion : for that 
 which is not capable of fubfifting will not fublifl: in any thing. But it is 
 poffible that every thing endued with capacity may not energlfe. Hence, 
 that which is capable of being may both be and not be. The fame thing, 
 therefore, is capable both of fubfifting and not fubfifting. But that which is 
 capable of not fubfifting may not fubfift. And that which may not fubfifl; 
 is corruptible, either fimply, or it is not this very thing which it is faid to be, 
 either according to place, or according to quantity, or according to quality ; 
 but it is fimply corruptible according to effence. No one, therefore, of things 
 fimply incorruptible is (imply being in capacity. Nothing, however, hinders 
 but that it may be fo in a certain refpedt, either according to quality or place. 
 Neither, therefore, things which are fimply, nor things which have a neceffary 
 fubfiftence, are in capacity, but all thefe are in energy ; and thefe are firft na- 
 tures : for, if thefe were not, nothing would be. Nor, again, if there is a cer- 
 tain motion which is perpetual, is fuch a motion in capacity. Nor, if that 
 which is moved is perpetual, is it moved according to capacity, unlefs fo far 
 as it proceeds from this to that boundary. Nothing, however, hinders but 
 that it may poffefs a capacity * of this kind. Hence, if the fun, and ftars, 
 and all heaven, perpetually energife, there is no occafion to fear, as certain na- 
 tural philofophers have feared, that they will ever ftand ftill. For they are not 
 wearied in accomplifhing this ; fince their motion does not fubfift about the 
 capacity of contradidion (as is the cafe with corruptible natures), fo as to 
 render the continuity of their motion laborious. For an effence which is 
 matter and capacity, and which does not fubfift in energy, is the caufe of this. 
 
 But thofe natures which fubfift in mutation, as, for inftance, earth 
 and fire, imitate incorruptible natures f. For thefe too always energife ; 
 
 fince 
 
 * Inftead of rourou V iAnf I read rovrou Je hva/Aiv. 
 
 j Viz. The whoks of the fublunary bodies, fire, air, water, and earth, are immortal. For an 
 
 account
 
 <2r6 ARISTOTLE'S METAPHYSICS, Boon IX 
 
 ilnce they poflefs motion effentlally, and in themfelves. But all the other 
 powers about which we have difcourfed are converfant with contradidion. 
 For that which is able to move in this particular manner is alfo able not fo 
 to move. I mean by the other powers, fuch as are rational : but the irra- 
 tional powers will be converfant with contradidion, through being prefent, 
 and not being prefent. If, therefore, there are certain natures or effences of 
 fuch a kind as thofe who are (killed in difciplines aflert ideas to be, fome one 
 will be much more knowing than fcience itfelf ; and fomething will be much 
 more moved than motion itfelf f. For the former will be rather energies, 
 but the latter are the capacities of the former. It is evident, therefore, that 
 energy is prior both to capacity and to every mutable principle. 
 
 CHAP. IX. 
 
 From hence alfo it is evident that energy is better and more truly excellent 
 than capacity which is excellent. For, fuch things as are faid to be capable 
 are alfo capable of contraries. Thus, it is the fame thing which is faid to be 
 capable of health and ficknefs, and at the fame time. For there is the fame 
 capacity of acquiring health and ficknefs, reft and motion, and of building and 
 deftroyinga houfe ; and it is alfo the fame capacity, by which a houfe may be 
 built, and may be thrown down. The capacity, therefore, of effeding contra- 
 ries fubfifts at the fame time, but to effed contraries at the fame time is im- 
 poflible. It is alfo impoflible that contrary energies fhould be prefent at one 
 and the fame time, as, for inftance, to be well, and to be ill. So that it is ne- 
 ceflary that one of thefe fhould be good. But to be capable is equally accom- 
 modated to both, or to neither. Energy, therefore, is the more excellent of 
 the two. 
 
 In things evil, however, it is neceflary that the end and energy fhould be 
 ivorfe X than capacity : for it is the fame thing which is capable of effeding 
 
 account of thefe wholes, which form one of tlie moft important parts of the pliilofophy of Ari- 
 ftotlc and Plato, but the theory refpeifbing which appears to have been utterly unknown to 
 Dr. Gillies, fee the Introduftion to my tranflation of the Timseus of Plato. 
 
 f This is true only of ideas confidered according to their ultimate participations. 
 
 J For the capacity of evil, fays Alexander, is mingled with the capacity of good ; but tlic 
 (Jicrgj of evil is not mingled with any energy of good. 
 
 both
 
 Book IX. A R I ST OT L E'S M ET A P H Y S I C S. 217 
 
 both contraries. It is evident, therefore, that evil is not any thing befides 
 things themfelves. For evil is by nature pofterior to capacity *. Hence, in 
 
 things 
 
 * As Ariftotle, by aflerting that evil is fomething naturally pofterior even to capacity, ac- 
 cords with the doftrine of Plato on this fubjecl, the following Platonic account of evil is fub- 
 joined for the fake of the philofophic reader. 
 
 The nature of evil then is involved in fo much obfcurity, that fome of the antients were in- 
 duced to believe that it had no kind of exiftence whatever ; otliers, on the contrary, admitted 
 its exiftence, indeed, but at the fame time aflertcd that there was no fuch thing as providence 5 
 and others, who acknowledged a providence, believed, in confequence of this, that all things are 
 good : for, if divinity was willing that evil fliould exift, how can he be good ? (ince every thing 
 which is eflentially good benefits all things, in the fame manner as that which is eflentially hot 
 imparts heat ; but it is not lawful for that which is good to produce any thing elfe than good. 
 But, if divinity was not willing that evil fliouId exift, how is it poflible that it can have a fubfift- 
 cnce ? For, if this were admitted, fomething would exift contrary to the will of the father of 
 all things. 
 
 In anfwer to this doubt It muft be obferved, that the habitude or relation which divinity has 
 to things differs from that of ours ; and again, things are related to divinity in a manner different 
 from what they are to us ; for there is one kind of relation of wholes to parts, and another 
 of parts towards each other. With reference to divinity, therefore, nothing is evil, not even 
 among things which are called evils ; for thefe he employs to beneficent purpofes. But, on the 
 other hand, with refpefl to partial natures, there is a certain evil vvith which they are naturally 
 conne£ted ; and the fame thing is evil to a part, but to the univerfe, and to vvholes, good ; for, fo 
 far as a thing has being, and fo far as it participates of order, it is good. 
 
 To be convinced, however, that there is no fuch thing as perfefl evil, it will be necefTary to 
 make the following divifion : Of all things in the univerfe, fome arc wholes, /. e. natures which 
 participate of one perfect form ; and others are parts. And of parts, fome eternally prefcrve 
 their own good, fuch as partial intellefts and partial daemons, but others are not always able to 
 preferve it ; and of thefe, fome are moved by other natures, but ethers are felf-motive. And of 
 the felf-motive natures, fome pofTefs evil eftablifhed in the will, but others extend it to aftion. 
 But as -to wholes, they are entirely good, not only fupplying themfelves, but likewife parts, with 
 good. And as to fuch things as are parts but preferve their proper good, thefe poflefs good fe- 
 condarily and partially; but parts which are moved by others, and derive their fubfiftence from 
 others, are likewife fufpended from the providence of the natures through which they fubfift, and 
 are tranfmuted by them in a becoming manner : and this js the cafe with fuch bodies as are ge- 
 nerated and corrupted. For, if it is necefTary that there fhould be generation, it is likewife ne- 
 cefTary that there fhould be corruption, fince generation fubfifts according to mutation, and is 
 itfelf a certain mutation ; but if there is corruption, it is alfo necefTary that the unnatural 
 fliould be introduced amtnj things. As, therefore, that which is corrupted is indeed corrupted 
 with refpeft to itfelf, but is not deftrcyed with refpcd fo the ujiiverfc, (for it becomes 
 jeither air or water, or fome one of the other particulars into which it is changed,) in like 
 manner that which is contrary to nature is difordered with refped to itfelf, but is orderly and 
 regular with refped\ to the univerfe. / 
 
 F f But
 
 218 ARISTOTLE'S METAPHYSICS. Book IXT. , 
 
 thlno-s which fiibfift from the principle, and in eternal natures^ there Is neither 
 evil, nor error, nor corruption. For corruption belongs to things evil. 
 Diagrams alio are found to be in energy ; but they are found to be fo by 
 divifion. For if they virere divided they would be manifeft. But now they 
 are inherent in capacity. Why has a triangle angles equal to two right ?^ 
 Becaufe the angles which are about one point are equal to two right If,, 
 
 therefore,. 
 
 But as to fucli natures as are partial, but felf-motlve, and wliich energifing according to ex- 
 ternals caufe evil to take place with refpecl to thcmfelves, this alfo is good in a certain de- 
 gree with reference to divinity; for though the adion arifing from a depraved will is not. 
 funply good, yet it is goodJo far as it p.irtakes of divine juftice, and is indeed beneficial to this 
 or that particular life. For, of goods, fome fubfift as good to all things, others as good to things 
 which differ .according to fpecies, and others as good to individuals confidered as individuals. 
 Thus, for iuftance, hellebore is neither good to all things, nor yet to all bodies, nor to all bodies 
 that are difeafed, but to a body with a particular difeafe, and is from a certain principle condu- 
 cive to health. Every intemperate and unjuft a£lion, therefore, is good to thofe-by whom it is 
 committed, fo far as it is attended with punifhment from divine juftice. For, again, of goods,, 
 fome are precedaneous and others preparative ; and the precedaneous are fuch as are defirable 
 for their own fakes, but the preparative for the fake of other things. The punifhment, there- 
 fore, which is infli£led by divinity on evil adlions is a preparative good ; for the defign of divi- 
 nity in punifliing is to purify the foul, and properly difpofe it for the reception of the higheft. 
 good. Hence unjuft actions, by being attended with punifliment, become the means of good to- 
 the offending foul, but, fimply confidered, are very remote from the nature of good, 
 
 Jn fhort, there is no evil which is not in a certain refpecSt good, bccaufe the beneficent illumi- 
 nations of providence extend to all things, and even irradiate the dark and formlefs nature of- 
 matter. But if any one fliould afk, whether divinity was willing that there fhould be evil, or 
 was unwilling ? we reply, that he was both willing and unwilling : for, confidered as imparting 
 being to all things, \\& was willing ; fince every thing in the univerfe, which has in any refpedt 
 being, proceeds from a demiurgic caufe. But he was not willing, confidered as producing all 
 things good •,. for he concealed evil in the utility of good. Evil, therefore, neither fubfifts in 
 intelledlual natures (for the whole intelledual order is void of eviH nor in fouls which rank as 
 •wholes., nor in bodies which are •wholes j for all wholes are free from evil, on account of their 
 perpetually fubfifting according to nature. Hence evil muft either fubfift in partial fouls or 
 partial bodies •, but yet not in the eflences of thefe, bccaufe all their eflences are of divine ori- 
 gin ; nor in their powers, for thcfe fubfift according to nature. It remains, therefore, that evil 
 niuH: fubfilt in tlieir energies. But, among fouls, it cannot be in the energies of fuch as are 
 rational, for all thefe afpire after good ; nor in the energies of fuch as are irrational, for thefe 
 energife according to nature ; but it mult take place in the privation offymmetry between the two. 
 And with refpedl to bodies, evil can neither fubfift in their form, for it defires to rule aver 
 matter; nor in matter, for it afpLres after the fupervening irradiations of form ; but in the 
 efymmetry of form luith refpecl to matter. And from lience it is evident that every thing evil 
 fubfifts according to Ti. parypojlnfis, i. e. has a Ihadawy kind of being ; that at the fame time it is 
 
 coloured
 
 Book IX. ARISTOTLE'S METAPHYSICS, 2I9 
 
 therefore, the line about the fide * is produced, this will Immediately become 
 evident. Why univerfally is the angle in a femicircle a right angle ? Becaufe 
 there are three equal lines ; two into which the bafe is divided, and that 
 which is raifed upon it from the middle point. When this conftrudion is 
 {sen hy him who previoufly knew it, he will alfo immediately perceive that 
 which follows from it. It is evident, therefore, that mathematical entities are 
 in capacity, and that they are difcovered when reduced into energy. But the 
 caufe of their being reduced into energy is this, that intelle£tion is energy. 
 So that capacity proceeds from energy : and on this account thofe who aO: 
 know. For energy according to number is pollerior in generation. 
 
 C H A P. X. 
 
 Since, therefore, being and alfo non-being are partly denominated accord- 
 ing to the figures of the categories, and partly according to the capacity or 
 energy of thefe, or contraries ; and fince that which is moft principally being 
 is true or falfe, and this in things themfelves coufifls in compofition or divi- 
 fion ; fo that he aflerts the truth, who is of opinion that a thing which is 
 divided is divided, and that a thing which is a compofite is a compofite ; but 
 he fpeaks falfely who, either when things are, or when they are not, fpeaks 
 of them in a manner contrary to that in which they fubfiftj — this being the 
 
 coloured by good; that confequently all things are good through the will of divinity ; and that 
 even evil is neceflary to :he perfccflion of the univerfe, as without its fliadowy nature generation 
 could not fubfift. 
 
 From all that has been faid, therefore, it follows that evil is fomcthing contrary to Intention 
 and nature, to caufe and principle, to end and bound, to will and fubfillence. It is, therefore, 
 privation and defect, imbecility and incommenfuration, error, and deviation froni defign, void of 
 beauty, life and intellett, irrational and imperfcft, without a foundation and without a caufe, 
 indefinite and unprollfic, fli:ggil1i and inefficacious, deprived of order and fimilituile, infinite, 
 dark and unciTcntial. 
 
 * What Ariftotlc now fays, will be evident by referring to the t'lirty-fecond propofitio;! of 
 the lirft book of Euclid's Elements. For by the /i/ie about t! e fide he means the line B C 
 (I refer to Earrov.-'s Euclid); and by i]v:/ule, the line AC. If the line U C, therefore, be pro- 
 duced to D, it follows that the two angles which (land about the point C arc equal to two right 
 
 arglcs. 
 
 By referring alfo to the thirty-fivll proprjfition of the third book of Euclid, what Ariftotle in 
 this place darkly aflertf,Tnd (as Alexander fays), as it were enij^matically, will become apparent. 
 For tlie three equal lines are AB, AD, and DC, and that which is raifed upon it from the middje 
 
 pclntisDB. / 
 
 F f 2 cafe
 
 2291 iCRISTOTLE'S METAPHYSICS" Book IX. 
 
 oafe, let us cortfider what that is which is called true or falfe. For it is not 
 that you are white becaufe we truly think that you are white; but, becaufe 
 you are white, we who aflert this, affert the truth. If, therefore, certain 
 things are always conipofitep, and cannot be divided, others are perpetually- 
 divided, and can never become compofites, and fome become the recipients of 
 contraries : to be, indeed, is to be a compofite and to be one thing ; but not to 
 be, is not to be a compofite, and to be more than one. About things contin- 
 gent*, therefore, the fame opinion and the fame difcourfe become falfe and 
 true ; and it happens that at one time they are true and at another falfe. But 
 about things which cannot fubfift differently, the true is not at one time gene- 
 rated, and at another time the falfe, but thefe are always true and falfe. 
 
 With refpe(fl to incompofite natures, therefore, what is the being or non- 
 being, what the true and the falfe of thefe ? For it is not any thing compo-- 
 fite, fo as to be, v/hen it is joined together, and not to be, when it is divided ; 
 juft as white wood, or the diameter of a fquare which is incommenfurable 
 with its fide : nor will the true and the falfe be fimilarly inherent in things 
 incompofite. Or fhall we hj, that as neither the true in thefe is the fame,, 
 fo neither is their being the fame ? But the one indeed is true, and the other 
 falfe. For m thcfc truth is obtained by conta£l \ and ajfcrtion. For aflirmation 
 
 * Viz. Wliich may become the recipients of contraries. 
 
 f Intelledt obtains the truth refpefting incompofite or fimple eflences, by a fimple extenfion 
 or projedtion of its vifive power, in the fame manner as tlie fight perceives colours. As fight, 
 too, does not affirm any thing concerning colours, but only beholds them, in like manner intei- 
 lecl does not affirm any thing refpeding the fimple objefts of its vifipn. For affirmation is 
 afierted of that which is a compofite from a fubjeft and predicate. When, therefore, it comes 
 into contact; with them, it aflerts that which is true ; but when it does not, and has no percep- 
 tion of them, it is faid to be ignorant of them, but not to be deceived. For the fight, when it 
 does not perceive colours by night, is not faid to be deceived, but to be ignorant of them : for 
 deception is ufurped in compofite natures, when a thing is faid to be fomething which it is not, as 
 jf wood which is not white fliould be faid to be white, or that fliould be faid not to be which is; 
 as, for inflance, that man is not an animal. Truth, therefore, is obtained in fimple eflences by 
 contad and affcrtion, but it is not poffible to be deceived refpedling them. For deception and 
 fallacy are convcrfant with compofite natures, when what is abfent from a thing is faid to be 
 prefent with it, or when what is prefent is faid to be abfent. 
 
 I only add, that this fimple and felf-vifive energy of intelleft, by which it fpeculates things 
 themfelves, and by intuition and contadl becomes one with the obje£l of its perception, is called 
 by Plato in the Phxdo, Seioj Xoyof, divine reafoii, which many, and among the reft Dacier, from 
 :not underftanding the philofophy of Plato, have crroneoufly and with barbaric arrogance tranf- 
 lated a divine revelaiicii. 
 
 and
 
 Book IX,- A R I S T O T L E'S M E T A P H Y S I C S. 221 
 
 and aflertion are not the fame. But not to pafs into contadl with them^ is to be 
 ignorant. For we cannot be deceived about the effence of a thing, unlefs by 
 accident. And in a fimilar manner with refpedl to incompofite effences : for 
 we cannot be deceived about thefe. All of them too are in energy, and not 
 in capacity. For, if they were in capacity, they would be generated and 
 corrupted : but now being itfelf is not fubjeil either to generation or corrup- 
 tion. For it would be generated from fomething. But ivltb rcfpeSl to fiich 
 things as are beings and in energy, about thefe it is not pojfihle to be deceived, but 
 they are either ifttelleElually apprehended or not. But concerning thefe effence 
 is inveftieated, whether it is of fuch a kind or not. 
 
 Moreover, after one manner being is confidered as true, and non-being as 
 falfe ; if it is a compofite, as true, but if not a compofite, falfe. But after 
 another manner, if it thus fubfifts, it is ; but if not thus, it is not. Truth 
 confifts in the intelle£lual apprehenfion of thefe ; but the falfe is not decep- 
 tion but ignorance, though not an ignorance which refembles blindnefs. For 
 blindnefs is jufl: as if fome one fhould be wholly deprived of the intelledive 
 power. It is evident alfo, that there will not be occafionally deception con- 
 cerning things immoveable, if they are confidered as immoveable. Thus, he 
 who does not confidtr a triangle as mutable, will not think that at one time it 
 has angles equal to two right, and that at another time it has not. For if this 
 were the cafe it would be changed. But he may entertain this opinion of 
 one thing, and not of another. Thus, for inftance, he may think that no 
 even number is a firft number, or that fome numbers are firft numbers, and 
 others are not. But he cannot entertain this opinion about one thing in num- 
 ber. For he will no longer think that it is now- this thing, and at another 
 time will be fomething elfe ; but he will either aflert that which is true or 
 falfe concerning it, as of a thijig which always fubfifts after this manoer,. 
 
 ARISTOTLE'S
 
 ARISTOTLE'S METAPHYSICS. 
 
 BOOK X. 
 
 CHAP. I. 
 
 JL HAT the one'^ is predicated multifarioufly was before obferved by us, 
 when we explained in how many ways every thing is denominated. But 
 fince it is manifoldly predicated, the modes of things primarily and effentially 
 denominated one, are, when colieded into one fum, four. For that which 
 is continued either fimply, or elpecially by nature, and not by contaQ, nor 
 by a bond, is one. And that is more one and in a manner prior to thefe, of 
 which the motion is more indivifible, and more fimple. Further ftill : that 
 is a thing of this kind and more fo, which is a whole, and has a certain form 
 and fpecies ; efpecially if there is a thing of this kind by nature and not by 
 violence, (as things which are one through glue, or a nail, or a bond,) and 
 which contains in itfelf the caufe of its continuity. But it is a thing of this 
 kind, through its motion being one, and indivifible in place and time. So 
 that it is evident that, if any thing naturally poffeffes the principle of the firft 
 motion, it is the firft magnitude; I mean, for inftance, a circular motion ; for 
 this is the firft of motions. Some things, therefore, arc after this manner 
 one, cither as continued, or as a whole. 
 
 * Concerning the one, the fubfidcnce of which h tlifcufied by Ariftotlc in this booli, fee 
 my tranflation of the Parmenides of Plato, the Notes to the thirteenth and fourteenth books of 
 this work, and the Diflertation on Nullities at the end. 
 
 But
 
 Boor X. A R I S T O T L E ' S M E T A P H Y S I C S, 2^23- 
 
 But fome things are called one of which the definition is one. And things 
 ©f this kind are thole of which the intelleftion is one. But the intelleftion 
 ©f that is indivifible, which is indivifible in fpecies or number. That which 
 ranks among, particulars, therefore, is indivilib'e in number ; but that is indi- 
 vifi! le in fpecies, which is indivifible in that which is known, and in fcience. 
 Hence that will be the firfl: one, which is the caufe to eflences of unity. In 
 fo many ways, therefore, is the one predicated, viz. that which is continuous 
 by nature, a whole, particular, and univerfal. But all thefe are one ; becaufe- 
 of fome the motion- is indivifible, but of others the intelledion, or the defini- 
 tion. 
 
 This, however, ought to be confidered, that it is not the fame thing to In- 
 quire what things are one, and what the eflence and definition are oi the one. 
 For the one is predicated in fo many ways, and each of thefe will be onCj in 
 which any one of thefe modes is inherent. But the eiTence of the one will' 
 fometimes accord with one of thele, and fometimes with another, which is 
 alfo nearer to the name: but thofe* are one in capacity. Juft as, if it were 
 requifite to fpeak of element and caufe, it would be neceflary to diftinguifh 
 the things, and to affign the definitionof the name. For fire perhaps, or the 
 infinite itfelf, or fomething elfe of this kind, in a certain refpe£t is, and in a 
 certain refped: is not, an efl'ential element. For there is not the fame eflence 
 of fire and of an element ; but fo far as fire is a certain thing and nature, it 
 is an element. But the name fignifies that this particular thing happens to 
 it, becaufe fomething fubfifts from this, as that which is primarily exiftent. 
 And the like takes place with refpedt to caufe and the one, and every thing* 
 elfe of this kind. Hence the eflence of the one confifls in being- indivifible, 
 viz. in being this particular thing, and infeparable either in place, or fpecies, 
 er the dianoetic part, or in that which is a whole and definite. 
 
 But the eflence of the one efpecially confifts in this, that it is the firfl:mea* 
 fure of every genus, and principally of quantity. Hence alfo it appears to* 
 have acceded to other things. For that is a meafure by which quantity is 
 known. But quantity, fo far as quantity, is known by the one, or number. 
 And every number is known by the one. So. that every quantity, fo far as 
 quantity, is known by the one, and that by which it is firft known is the one 
 
 * That is to fay, thofe natures which have been enumerated, and of which the one is- predi- 
 cated-
 
 ^i ARISTOTLE'S MET ATHYSICS. BookX. 
 
 itfelf. And hence the one is the principle of number fo far as number. 
 Hence alfo, in other things, that is called a meafure by which each particu- 
 lar is firft known, and the meafure of every thing is one, in length, in 
 breadth, in depth, in gravity, and in celerity. For gravity and celerity are 
 common in contraries : for each of thefe is twofold. Thus, for inflance, that 
 is heavy, which has any momentum whatever, and that which has an ex- 
 cefs of momentum. That alfo is fwlft wiiich has any motion whatever, 
 and that which has an excefs of motion. For there is a certain celerity of 
 that which is ilow, and gravity of that which is light. But in all thefe, that 
 which is the meafure and the principle is a certain one, and fomething indi- 
 vifible. Thus, in lines, the meafure of a foot is ufed as indivifible. For 
 every where one certain meafure and that which is indivifible are invefti- 
 gated. J3ut this is the fnnple either in quantity or quality. Hence, where it 
 appears that nothing is to be taken away or added, this is accurately the mea- 
 fure. Hence, too, the meafure of number is the moft accurate of all mea- 
 fures : for the monad is confidered as every way indivifible. But in other 
 things a meafure of this kind is imitated. For, from a ftadium and a talent, 
 and always from that which is greater, more may be taken away than from 
 that which is leifer. Wherefore that among fenfibles which is firft confidered 
 as indivifible, is by all men made the meafure of things moift and dry, of 
 weight and magnitude : and they then think that they know the quantity, 
 when they know through this meafure. Motion, too, is meafured by a fimple 
 and the moft rapid motion. For this has the fhorteft time. Hence, in aftro- 
 nomy, a one of this kind is the principle and the meafure. For the motion 
 of heaven is fuppofed to be equal and moft fwift, by which other motions are 
 determined. In mufic, likewife, diefis is the meafure, becaufe it is the leaft 
 fenfible found : and in voice a letter. And all thefe are a certain one ; yet 
 not fo as that the one is fomething common to them, but in fuch a manner * 
 as we have before fhown. 
 
 A meafure, however, is not always one in number, but is fometimes more 
 than one ; as, for inftance, two diefes, which are not underflood according to 
 the hearing, but in definitions. Voices f alfo are ipany by which we raea- 
 
 * Viz. As things which are denominated from, and with reference to, the one. 
 
 + AlexaAder well obferves, that Ariftotle here by voices means the elements of fpeech, 
 
 furc;
 
 EookX. ARISTOTLE'S metaphysics. 225 
 
 fure ; and a diameter is alfo meafured by two things*; and this Is the cafe 
 with a fide, and with all magnitudes. And thus the meafure of all things 
 is the one ; becaufe we know tliofe things from which effence confifts, by 
 making a divifion either according to quantity, or according to form. Hence 
 the one is indivifible, becaufe the firft of every thing is indivifible ; but 
 everv thing is not fimilarly indivifible, as, for inftance, a foot and the monad. 
 But the latter is in every refpedl indivifible, while the former is aflumed indi- 
 vifible with refpe£t to fenfe, as we juft now^ obferved. For, perhaps every 
 thing continued is divifible ; but meafure is always of a kindred nature. For 
 magnitude is the meafure of magnitudes and of individuals, length of length, 
 breadth of breadth, found of founds, weight of weight, and monad of monads. 
 For in this manner it is requifite to fpeak, and not to call number the mea- 
 fure of numbers. Though this would be necelfary if meafure is to be fimi- 
 larly affigned. But he who entertains this opinion does not think fimilarly, 
 but juft as if he fhould think that monads are the meafure of monads, and not 
 the monad. However, number is a multitude of monads : and on the fame 
 account we fay that fcience is the meafure of things, and alfo fenfe, becaufe 
 we know fomething through thefe ; for they are meafured rather than they 
 meafure. But it happens to us juft as if, another meafuring us, we fhould 
 know the quantity we contain, becaufe he fo many times applies to us a 
 cubital meafure. But Protagoras fays that man is the meafure of all things, 
 juft as if he had faid that he who poffeffes fcientific knowledge, or fenfible 
 perception, is a meafure ; and this becaufe the one poflefles fenfe and the other 
 fcience, which we fay are the meafures of their fubjeds. Hence, though 
 afleiting nothing excellent, he appears to fay fomething pertinent. That the 
 eflence of the one, therefore, confifts in being a certain meafure, and the moft 
 principal meafure of quantity, and efpecially according to the name by which 
 it is diftinguitlied from other things, and that it is, in the next place, the mea- 
 fure of quality, is evident. But a meafure will be of one kind, which is indi- 
 vifible according to quantity, and of another, which is indivifible according to 
 quality. So that the one is indivifible either fimply, or fo far as it is one. 
 
 * Thus, for inftance, fays Alexander, if a diameter is meafured by tlic finger, finger is two- 
 fold, viz. the very nature and form of the finger, and the finger itfclf which meafures the dia- 
 •jnctsr. 
 
 Gg / CHAP.
 
 226 ARISTOTLE'S METAPHYSICS. Book X. 
 
 CHAP. II. 
 
 It Is now requifite to inquire in what manner the one fubfifts with refpedt 
 to its eHcn'-c and nature, as in the doubts which we formerly made we dif- 
 culFed what the one is, and how we ought to conceive refpedlins; it ; whether 
 the oneitjelfh a certain elTence, as the Pythagora^ans formerly faid, and Plato 
 , afterwards, or rather a certain nature is fubjeded to it ; and how it ought co 
 be confidered after a manner more known, and whether the conceptions of na- 
 tural phi'ofophers concerning it are to be admitted. For, of thefe, one .'uTerts 
 . that fiiendihip is the one, another air, and another the infinite. But if nothing 
 of univerfals can be effence^, as we have afferted in our dfcourfe concerning 
 effcnce and being, nor this very thing efiei^ce can be one certain thing feparate 
 from the many (for a thing of this kind is fomething common, and alone 
 fubfifts as a predicate) — this being the cafe, it is evident that the o?ie is not 
 effence. For being and the one are the moft ot all tilings univcrfally predi- 
 cated. So that neither are genera certain natures and ellences feparable from 
 other things ; nor can the one be genus, through the fame caufes by which- 
 neither being nor effence is genus. 
 
 Further ftill : it is neceffary that the like fliould take place in all things. 
 But being and the one are predicated equally. Wherefore, fince in qualities 
 there is a certain one, and a certain nature, and in a firailar manner in quanti- 
 ties, it is evident that what the one is, muft, in Ihort, be inveftigated, as alfo 
 what being is ; fo that it is not fufficlent to aff.^rt that this very thing is the 
 nature of it. In colours alfo tl:ere is one colour, as, for inftance, the white ; 
 afterwards, other colours appear to be generated from this and black. But 
 black is a privation of white, in the fame manner as daiknefs of light ; for 
 this is a privation of light. So that, if beings vv'ere colours, beings would be 
 a certain number. But of what? Evidently of colours. And the one vvould 
 be a certain one, as, for inftance, the white. In like manner, if beings were 
 melodies, they would indeed be a number, but of diefisf; but the effence of 
 them would not be number ; and the one would hi fumeihing, the effence of 
 which would not be the one, but diefis. In a fnnilar manner toe, with refpedl 
 
 * Tliis is apparently fliown by Arlflotlc in the fcventlfboolc of this work. See the Intro- 
 duclion ta tliis work. 
 
 •y ;. e. The fmalleft fenfible found. 
 
 to
 
 BookX. ARISTOTLE'S metaphysics. 227 
 
 to founds, if all beings were founds, they would be the number of the ele- 
 ments, and the o?ie would be a vocal element. And if beings were right- 
 lined iigures, they would be the number of figures, and the one would be a 
 triangle : and there will be the fame reafonir.g in the other genera. So that, 
 if in participated properties, in qualities, in quantities, and in motion, there 
 are numbers, and there is a certain one in all thefe, number being the number 
 of certain things, and the one a' certain one, but this is not the eflence oi the 
 one, it is neceflary that the like fliould take place in efiences. For this will 
 fimilarly happen in all things. That the one, therefore, is a certain nature in 
 every genus, and that this very thing the one is not the nature of any thing, is 
 evident. But, as hi colours we inveftigate one colour as the one, fo in eflence 
 wc inveftigate one eflence as the one itfelf. Moreover, that in a certain refpedt 
 the one and being fignify the fame is evident, from this, that the one equally fol- 
 lows the categories, and is not in any of them ; as, for inftance, it is neither in 
 fubfl:ance nor in quality, but fubfifts in a manner fimilar to being. It alfo 
 follows from this, that in predication one man does not add any thing elfe be- 
 fides man, as neither is being any thing befldes fubftance, or quality, or quan- 
 tity : and the being oi the one* is the fame as the being of fome individual 
 thing. 
 
 CHAP. IIL 
 
 The one and the many are oppofed multifarioufly ; according to one 
 of which modes the one and i7iultitude are oppofed as indiviflble and divifible. 
 For that which is either divided or is divifible is called a certain multitude ; but 
 that which is indiviflble or is not divided is called one. Since, therefore, 
 oppofltions are fcurfohi, and one of thefe is denominated according to priva- 
 tion, thefe indeed will be contraries, and will neither be denominated as con- 
 tradidion nor as relatives. But the one is denominated and rendered appa- 
 rent from its contrary, viz. the indiviflble from the diviflble, becaufe multi- 
 tude and the diviflble are more manifefl: to fenfe than the indiviflble. So that, 
 through fenfe, multitude is prior in deflnitioa to the indiviflble. But the 
 fame, the flmilar, and the equal are oi the one, as we have fliownf in the divi- 
 
 * It mud be carefully obferved that this is trus of the one which fubfifts in fenfibles. 
 
 f Ariftotle here, according to Alexander, refers to his treatife On the Good, in which, fays he, 
 by divifion, he reduces all contraries into multitude and the one. This work, as we have before 
 cbfcrved, is unfortunately loft. 
 
 Gg 2 ■ / fioa
 
 228 ARISTOTLE'S METAPHYSICS. Eook X. 
 
 fion of contraries ; but the different, the dlflimilar, and the unequal, are of 
 multitude. But Cmce/ame is predicated multifarioufly, it is predicated in one 
 way according to number, which we fometimes call iffcif; but in another way, 
 if a thing is one in definition and number. Tlius, for inftance, you are one 
 with yourfelf, both in form and matter. 
 
 Further ftili : thofe things are faid to be the fame, of the firft * effence of 
 which there is one definition. Thus, equal right lines are the fame, and equal 
 and equal-angled quadrangular figures, though they are many in number ; 
 for in thefe equality is unity. But things are faid to be fimilar, which are 
 not indeed fimply the fame, nor without difference according to their lubjedt 
 effence, but yet are the fame according to form. Thus, a greater fquare is 
 fimilar to a leffer, and alfo unequal right lines. For thefe are indeed fimilar, 
 but are not fimply the fame. But fome things are called fimilar, if they have 
 the fame form, and in which though the niore and the lefs are ingenerated, 
 yet the things themfelves are neither more nor lefs. Other things are fo de- 
 nominated, if there is the fame paffion and one in fpecies. Thus, that which 
 is very white and that which is lefs white are faid to be fimilar, becaufe the 
 form of them is one. But fome things are called fimilar, if they have more 
 of the fame things than of fuch as are different, either fimply, or which ar(2 
 more obvious to fenfe. Thus, tin is more fimilar to filver than to gold ; but 
 gold Is fimilar to fire, fo far as it is yellow and ruddy. So that it is evident 
 that the different and the diffimilar are denominated multlfarioufly. 
 
 The different alfo and the fame have an oppofite mode of fubfifience. 
 Hence, every thing with relation to every thing, is either the fame or differ- 
 ent. But that is faid to take place, if the matter and definition are not one. 
 Hence, you, and that which is next to you, are different. But the third fig- 
 nification of the fimilar is when things fubfift as in mathematical fpecies. 
 All fuch things, therefore, as are denominated one and being, are, with re- 
 ference to each other, different or the fame. For there is not any contradic- 
 tion of the famef. Hence, it Is not afferted of non-entities, but of all 
 beings ; but not the fame is alfo predicated of beings. . For fame and different 
 are naturally either one, or not one, which non-one is both being and one. 
 
 * By the. fifjl ejfetice here, we muft; underftand the proximate ejpnce. 
 
 t That is, fays Alexander, fame and different are not oppofed contradi<5lorily, fo as to pertain 
 io non-cntitics alfo, and not to beings alone. 
 
 Different,
 
 Book X, ARISTOTLE'S METAPHYSICS. 229 
 
 Different, therefore, and fame, are after this manner oppofed. But difference 
 is not the fune with diverfity. For it is not neccflary that a thing which is 
 another^ and that with relation to which it is another, fliould he another by a 
 common fomething. For every thing whatever which is a being is either 
 the fame or different. But that which is different from fomething is different 
 by fomething *. So that it is neceffary that there fliould be fomething the 
 fame by which they differ. But this fomething the fame is either genus or 
 fpecies : for every th-ing which differs, differs either in genus or fpecies. And 
 thofe things, indeed, differ in genus, of which neither the matter is common, 
 nor the mutual generation ; as, for inftance, thofe things of which there is 
 another figure of predication ; but thofe things are different in fpecies, of 
 which there is the fame genus. But genus is faid to be that by which both 
 the things that differ are called the fame according to effence. So that con- 
 traries are things different, and contrariety is a certain difference. But that 
 this is well afferted by us is evident from indudion. For all things appear to 
 differ^ and not only to be diverfe ; but fome are diverfe in genus, and others 
 in the fame co-ordinatioa of predication. So that they are in the fame genus, 
 and are the fame in genus t. But we have elfewhere fliown what kind of 
 things are the fame or different in genus. . 
 
 CHAP. IV. 
 
 But fmce it happens that things which differ from each other differ ' 
 more or lefs, there is a certain greatefl: difference, and this I call contra- 
 riety. And, that this is the greatefl: difference, is evident from induc- 
 tion. For things which differ in genus have not a way to each other, but 
 are much diflant, and cannot be compared together. But to things which 
 differ in fpecies the generations are from contraries, as from extremes. And 
 the laft interval is the greatefl:: fo that the interval of contraries is the 
 greatefl:. But the greatefl: in every genus is the perfect : for that is greatefl 
 which cannot be tranfcended ; and that is perfect beyond which nothing can be 
 affumcd. For perfect difference has an cad, jufl: as other things from having 
 
 * Viz. Whatever differs has fomething in common with that from which it differs, 
 
 \ In the printed text tjj eiSei; but as the text of Alexander has gcncre (ra ysvei), I have 
 
 adopted this reading in my verfion. Befides, the concluding fentence of this chapter favors 
 
 this alteration. 
 
 an
 
 230 ARISTOTLE'S METAPHYSICS. BookX. 
 
 an end are called perfcd. But nothing is beyond the end : for this is the lad 
 in every thing, and comprehends that of whii-h it is the end. Hence, no- 
 tliing is beyond the end, nor is the perfect indigent of any thing That 
 contrariety, therefore, is perfe<ft difference, is from hence evident. 
 
 But, fuice contraries are predicated multilariouily, the perfedl will follow In 
 fuch a manner as accords with their fubfiftence as contraries. But, this being 
 the cafe, it is evident that there cannot be many contraries to one thing. For 
 neither will there be any thing more extreme than that which is laft, nor of 
 one interval will there be more than two extremes. And, in fliort, it" con- 
 trariety is dlfxerence, but difierence is the difference of two things, this will 
 alfo be the cafe with perfedl difference. But it is neceffary that the other de- 
 finitions alfo of contraries Ihould be true : for perfect difference differs in the 
 greateft degree. For we have fhown that of things which differ in genus and 
 fpecies, nothing externa! can be aQumed, fmce there is no difierence with re- 
 fpect to things beyond genus ; but of thefe this is the greateft. And things 
 which being in the fame genus differ in the greateft degree, are contraries. 
 For the greateft difference of thefe is that which is perfedl. Things alfo 
 which being in the fame recipient differ in tlie greateft degree, are contraries: 
 for the fame matter is the fubjedl of contraries. And, likewife, thofe tilings 
 are contraries, which differ in the greateft degree under the fame power. For 
 one fcience is coni'erfant with one genus of things in which perfedt difference 
 is the geaieft. But the firft contrariety is habit and privation ; yet not every 
 privation (for privation is predicated nniltifaricufly), but fiich as is perfeifl:. 
 But other contraries are denominated accordin;; to thefe ; feme from poffeff- 
 ing ; fome from a^^ting, or being efi'etilive ; and fome, becaufe they receive or 
 reject thefe or other contrarieties. But if conti-adidion, privation, contrariety, 
 and relatives are oppoled ; but of thefe contradidion is the hrft, and of con- 
 tradiclion there is no medium, but there is of contraries, it is evident that 
 contradiftion and contrariety are not the fame. But privation is a certain 
 contradiction : tor, either there is a privation of that which cannot by any 
 means be polfeflcd, or of that which, when it is naturally adapted to be pof- 
 felJed, is not pofteiled ; and this either altogether, or in fome definite manner. 
 For we fpcak of this muicifarioufly, as we have elfewhere fhown. So that 
 privation is a certain contradidioUj or a definite impotency, or comprehended 
 together i^ ith its recipient. Hence there is no medium of contradicflion, but 
 there is a certain medium of privation. For every thing is either ec^ual or 
 
 not
 
 Book X. A R I S T O T L E' S M E T A P H Y S I C S. 231 
 
 not equal, but not every thing is equal or unequ il, except alone in that wliich 
 is the recipient of'the equal. If, tiierefore, generations are in matter irom 
 contraries, but they are produced from form and the habit of form, or from 
 a certain privation of fpecies anJ form, it is evident that every contrariety 
 will be a certain privation, but not every privation perhaps is contrariety. 
 But the caufe of this is, that whatever fuffers a privation of any thing, may 
 fufFcr this privation in a manifold refpedl. For thcfe things are contraries 
 from the extremities of which mutations are produced. This alfo is evident 
 from indu£lion. For every contrariety has a privation of the other of con- 
 traries ; but not all things in a fimilar manner. For inequality is a privation 
 of equality, diflimilitude of fimilitude, and virtue of vice. But there is a dif- 
 ference, as we have already obferved : for one tiling is faid to fufFer privation, 
 if it is alone deprived of fomething ; but another, if it does not poffefs when 
 it is naturally adapted to poiTefs, as in a certain age, or in that which is prin- 
 cipal, or altogether. Hence, of fome contraries there is a medium, and a man 
 is neither good nor bad ; but of others there Is not a medium, but it is necef- 
 fary that a number fliould be even or odd. Further ftill : fome things have a 
 definite fubjeifl:, and others have not. So that it is evident that the other of 
 contraries is always denominated according to privation. But it is fufficicnt 
 if firft natures and the genera of contraries, as, for inftance, the one and the 
 many, are fo denominated. For other things are referred to thefe. 
 
 C H A P. V. 
 
 But fince one thing is contrary to one, it may be doubted how the one and the 
 many are oppofed, and how the equal is oppofed to the great and the fmall. For 
 we always Ipeak of the whether in oppolition ; as, for inflance, whether a thing 
 is white or black ; and whether it is white or not white. But we do not fay whe-- 
 ther it is man or white, unlefs from hypothefis, and when inveftigating, as, whe^ 
 /^^•/•Glecn came or Socrates. This inquiry, however, is not neceflary in any 
 genos. For oppofites alone cannot fubfift together, as is evident in this inquiry^ 
 which of the two came. For, if it were poffihle for both to have come, the in- 
 terrogation v.-ould be ridiculous. But if this were poffible, he who makes the 
 inquiry falls into oppofition, viz. into the one and the maiiy ; as, for inftance, 
 whether both came, or one of tihe two. But if the inquiry refpcding the whether 
 is always in oppofites (out it is faid whether a thing is greater, or lelfer, or equal V, 
 
 3 / -whiU
 
 232 ARISTOTLE'S METAPHY SIC 3= Book X, 
 
 vv-hat Is the oppofition with refpedt to thefc of the equal ? For It is not alone 
 contrary to one of them, nor to both. For why is it rather contrary to tiie 
 o-reater than the lefler ? Further ftill ; the equal is contrary to the unequal ; 
 fo that it will be contrary to more than one. But, if the unequal figniiies the 
 fame thing with both thefe together, it wall indeed be oppofue to both ; and 
 the doubt will aflift thofe who fay that the unequal is the duad. It happens, 
 however, that one -will be contrary to two ; which is impoffible. 
 
 A"-ain : the equal appears to be a medium between the great and the fmall ; 
 but contrariety neither appears to be a medium, nor, from the definition of it, 
 is it poffibie that it fliould. For it would not be perfed, if it was the me- 
 dium of any thing, but rather it always has fome medium whh refpeft to it- 
 felf. It remains, therefore, that the equal muft either be oppofed as negation 
 or as privation. Bat it is not poffibie that it can be alone oppofed to the 
 o-reat or to the fmall. For why fhould it be rather oppofed to the great 
 than to the fmall ? Negation, therefore, is privative of both. Hence, tbe 
 ivhcther is predicated with refped to both, but not with refped to either. 
 Thus we do not fay, ixihether is it equal or greater ? or, •whether is it equal or 
 lefs ? But the whether is always aflerted with reference to three things. It 
 is not, however, privation from neceffity : for it does not follow that every 
 thing is equal which is not greater or lefler ; but this takes place in things in 
 which the greater and the lefler are naturally inherent. The equal, therefore, 
 is that which is neither great nor fmall, but which is naturally adapted to be- 
 come great or fmall ; and it is oppofed to both, as negative privation. Hence 
 it is a medium. That alfo which is neither evil nor good is oppofed to both, 
 but is namelefs. For each is predicated multif.\rioufly ; and that which is the 
 recipient is not one thing, but rather that which is neither white nor black ; 
 thouo^h neither is this called one thing. But colours are in a certain refped 
 definite, of which this negation is privatively predicated. For it is necefl^iry 
 that this negation fl-iould be brown, or pallid, or fomething elfe of this kind. 
 Hence, they are not rightly reproved who think that all things are fimilarly 
 denominated ; fo that, between a flioe and a hand, the medium is that which 
 is neither a Ilioe nor a hand, fince alfo that which is neither good nor evil is 
 the medium between good and evil, as if, with refpeft to all things, there would 
 be a certain medium. It is not, however, neceflary that this ihould happen. 
 For this co-negation of oppofites is of things which are naturally adapted to 
 :|jave a certain medium, and a certain interval. But with refped to thefe 
 
 there
 
 Book X. ARISTOTLE'S METAPHYSICS. 233 
 
 there is no dIfFeience : for thofe things are in another genus, of which thefe 
 were co-negations * ; fo that the fubject of them is not one. 
 
 CHAP. VI. 
 
 In a fimilar manner, alfo, fome one may doubt refpefling tlo^ one and fhe 
 many. For, if the many are fimply oppofed to the one, certain impufTi'jIe 
 confequences will happen ; for it will either be a fmall multitude, or fmall 
 multitude':-, f , fnice the many is alfo oppofed to the few. Befides, two things 
 are many, fince the double is multiplex ; and thus alfo two is called 
 double. So that the one is few. For, with relation to what are two things 
 many, unlefs with relation to the one and the few ? For nothing elfe appears- 
 to be lefs. Further ftill : what the long and the fhort are in length, that the 
 much an { the few are in multitude, and whatever is much is alfo many, and 
 the matiy i much. Unlefs, therefore, fomething intervenes in continued inde- 
 finite quantity, the few will be a certain multitude. So that the one is a certain 
 muhitude, if it is the few. But this is neceffary if two things are many. 
 Perhaps, however, the many is denominated in the fame manner as the muchy 
 yet as differing, as water which is much, but not many. But with refpe£t to 
 fuch tlungii as are divifible, in thefe the many fubfifts, according to one mode, 
 if the multitude has a tranfcendency either fimply or relatively ; and in a 
 fimilar manner the few, when the multitude is deficient. But, according to 
 another mode, the many fubfifts as number, which is alone oppofed to the one. 
 For thus we fpeak of the one or the many ; juft as if fome one ihould fay one 
 and ones, or white and things white, and things meafured with refpe£t to mea- 
 fure, and that which is meafured. Thus, alfo, things which are manifold are 
 called many : for every number is many,, becaufe it is one many, and becaufe 
 each is meafurable by one, and is as that which is oppofed to the one, and not 
 to the few. After this manner, therefore, two things alfo are many ; but as 
 having tranfcendent multitude, or as relatives, or fimply confidered, they are 
 not many ; but two is the firft multitude in numbers. Two is, however 
 fimply few ; for it is the firft multitude having a defe 1. Hence, Anaxagora& 
 did not fpeak rightly in aflerting, that all things fubf fed together^ and were 
 
 * But things of which there are co-negations are fubje(^cd to the fame genus. 
 f In the original e?jyov n oMy«. 
 
 ^ "^ infmie
 
 234 ARISTOTLE'S METAPHYSICS, Book X. 
 
 infinite in mult'itiule and fmallnefs : for, inftead oi fmallnefs^ he ought to have 
 laid in pciHcily. F,or tlie few is not infinite ; fince it does not fubfilt through 
 the one, as fome fay, but through tivo. They are, therefore, after this man- 
 ner oppofed. But the one and the many are oppofed in numbers, and the one 
 is oppofed to the many, as meafure lo that which is meafured. And thefe are 
 oppofed as relatives, which have not an effential fubfiftence. But vve have 
 th'ewhere iliovv'n that relatives are denominated in a twofold refpedl. For 
 fome things are fo called as contraries, others as fcience to the objedl of fcience, 
 becaufe fomething elfe is predicated with refpeift to it *. Nothing, however, 
 hinders but that the one may be lefs than a certain thing ; as, for inftance, than 
 tivo. For it does not follov/, that if it is lefs, it is alfo few. But multitude is 
 as it were the gerus of number. For number is multitude, which may be 
 meafured by the one. And the one and number are in a certain refpedl oppofed, 
 not as contraries, but, as we have faid, in the fame manner as certain relatives. 
 For, fo far as the one is a meafure, but number meafurable, fo far they are op- 
 pofed to each other. Hence, not every thing which is one is number, as, for 
 inftance, if there is any thing indivifible. But, though fcience is in a fimilar 
 manner denominated with refpedt to the object of fcience, yet it is not fimi- 
 larly attributed : for fcience may appear to be a meafure, but the (>bje>St of 
 fcience that which is meafured. But it happens that every fcience is the 
 obje«fl of fcientific knowledge, though not every thing which may be f:ien- 
 tifically known is fcience, becaufe in a certain refpedt fcience is meafured by 
 the object of fclentihc knowledge. Moreover, neither is multitude contrary 
 to the few ; but to this the much is oppofed, in the fame manner as multitude 
 which tranfcends is oppofed to the multitude which is tranfcended ; nor is mul- 
 titude altogether contrary to the one. But with refpedt to the one, as vve have 
 faid, one kind is divifible, and another indivifible, which fubfifts as a relative, 
 juft as fcience whh refpedt to the objedt of fcience, if fcience were number: 
 but the one is a meafure "f. 
 
 * That is, fcience is a relative, not becaufe it is predicated of him who poJenes fcientific 
 knowledge, but becaufe the objed: of fuch knowledge is predicated with reference to'fcience. 
 
 t The Commentary of Alexander on this book extends no further than to the eiul of this 
 chapter j the remaining part being unfortunately loft. 
 
 C II A P.
 
 Book X. ARISTOTLE'S METAPHYSICS. 2S5 
 
 CHAP. VII. 
 
 But fince It happens that between contraries there Is a certain medium, It 
 is neceflary that the media fhould derive their fubfiflence from contraries. 
 For all media, and the things of which they are media, are in the fame genus. 
 For we call thofe things media into which that which is changed is necefla- 
 rily firft changed. Thus, he who pafles from the hypate * to the nete "f , if 
 the tranfition is made in a fhort time, will firft arrive at the founds which 
 fubfiil between. And in colours, if any one pafTes from white to black, he 
 will arrive at the red and the brown before he arrives at the black. And in 
 a fimilar manner In other things. But a tranfmutation from one genus to 
 another cannot take place, except from accident; as, for inftance, from co- 
 lour to figure. It Is neceflary, therefore, that media and the things of which- 
 they are media fhould be in the fame genus. But all media are the media of 
 certain oppofitcs ; for, from thefe alone eflentlal mutation fubfifts. Hence^ 
 It is impoffible that there fhould be any medium between things which are 
 not oppofites ; for othcrwife there would be a mutation from things not op- 
 pofed. But in oppofites there is no medium of contradidlon. For contra- 
 divSlion Is antithefis, and an oppofition of which one of the parts Is prefent, 
 without having any medium. But, of the reft, fome are relatives, others are 
 privation, and others are contraries. And of thofe which are relatives, fuch 
 as are not contraries have not a medium ; and this becaufe they are not in the 
 fame genus. For, what is there between fclence and the ohje£l of fclence ? 
 There is, however, a medium between the great and the fmall. But If media 
 are in the fame genus, as we have fliown, and are media of contraries, it Is ne- 
 ceflary that they alfd fhould be compofed from thefe contraries. For, either 
 there Is a certain genus of them, or none. And if there is a genus, and it 
 fubfifts in fuch a manner that fomething will be prior to contraries, thofe 
 contrary differences will be prior which make contraries as fpecles of genus; 
 for fpecits fubfift from genus and differences. Thus, if white and black are 
 contraries, and the one Is a fegregative, but the other a congregative colour, 
 thefe very differences themfelves, the fegregative and the congregative, wilt 
 have a prior fubfiftence. So that thefe contraries are prior to each other» 
 
 * The bafe chord. 
 
 f The feventh chord in the harp. 
 
 Hh 2 . But
 
 S36 ARISTOTLE'S METAPHYSICS. Book X. 
 
 But contraries whicli are diiTercnces are more contraries. The reft alfo, and 
 the media, will confift from genus and differences. Thus, it is requifite 
 that whatever colours are between white and black fliould be faid to confift 
 from genus (but colour is a genus) and certain differences. But thefe will not 
 be the firft contraries j for otherwife each will be black or white. There are, 
 therefore, other colours. And hence thefe colours will be the media of firft 
 contraries. But the firft differences are the fegregative and the congregative. 
 So that the firft thing to be inveftigated with refped to fuch contraries as are 
 not in genus is this, Fiom what the media of them confift. For it is neceflary 
 that things in the fame genus fhould be either compofed from things incom- 
 pofite in genus, or fhould be incompofites. Contraries, therefore, are not 
 compofed from each other; and hence they are pri ciples. But media are 
 either all th;ngs or nothing. From contraries, too, fomething is generated. 
 So th.it, before there is a mutation into contraries, there will be a mutation 
 into this : for of each there will be the more and the lefs. There will there- 
 fore be a medium, and this will be the medium of contraries. Fience, all 
 other media are compofites. For that which is more than one thing and 
 lefs than another, is in a certain refped compofed from thole things of which 
 it is faid to be more and lefs. But fince of contraries other things which are 
 prior are not .^of the fame kind, all media will be from contraries. So that 
 all inferiors, and contraries, and media will be from firft contraries. That all 
 media, therefore, are in the fame genus, and that they are media of contra- 
 ries, and are compofed from contraries, is evident. 
 
 CHAP. Viir. 
 
 But that which is different in fpecies is different from fomething, and it is 
 neceffary that this fhould fubfift in both differenees. Thus, it animal is dif- 
 ferent in fpecies, both will be animals. It is neceffary, therefore, that things 
 which are different in fpecies fhould be in the lame genus. But I mean a 
 genus of that kind, by which both are called one and the iame, not poffeffing 
 difference from accident, whether it fubfifts as nia.ter, or as fomething differ- 
 ent from matter. For it is not only requilite that a common fomething fhould 
 be prefent, as, for inftance, that both fhould be animals, but, that this very 
 aniii.al iiielf fhould be different from either, as that the one Ihould be horfe, 
 and the other man. Fience, this fomething common belongs to things dif- 
 ferent
 
 Book X. ARISTOTLE'S METAPHYSICS. 237 
 
 ferent from each other in fpecies. i\nd hence, too, this will be fuch a particu- 
 lar animal eflentially, and that an animal eflentially difFerent ; as, for in- 
 ilance, that will be a horfe, and this a man. It is neceflary, therefore, that 
 this difference fhould be a diverfity of genus. But I call that difference 
 of genus diverfity, which makes this very thing to be different. Hence 
 this will be contrariety. And this is evident from indudion : for all 
 things are divided by oppofites ; and it has been fhown that contraries are in 
 the fame genus. For contrariety is perfect difference. But every difference 
 which is in fpecies is fomething belonging to a certain thing. So that this is 
 the fame, and is genus in both. Hence all contraries are in the fame co- ordi- 
 nation of predication, which differ in fpecies and not in genus, and are efpe- 
 cially different from each other. For the c'ifference between them is per*e<fl, 
 and they are not at the fame time general -d together. Difference, therefore, 
 is contrariety. For this is to be different in fpecies, viz. for things which are 
 individuals, when they are in the fame genus, to poffefs contrariety. But 
 things are the fame in fpecies, which fubfifting as individuals have not con- 
 trariety. For in divifion and in media contrarieties are produced, before we 
 arrive at individuals. So that it is evident that none of thofe things which 
 accord as fpecies of genus, is, with refpedl to that which is called genus, either 
 the fame, or different in fpecies. For matter is rendered manifeft by negation ; 
 and genus is the matter of that of which it is faid to be the genus ; not, how- 
 ever, as the genus of the Heraclidx, but as that which fubfifts in nature. Nor 
 is genus denominated from things which are not in the fame genus, but 
 which differ in genus from them. But things differing in fpecies differ from 
 thofe in the fame genus. For it is neceffary that contrariety fhould be the 
 difference of that from which it differs in fpecies. But contrariety alone fub- 
 fiQs in things which are in the fame genus. 
 
 C H A P. IX. 
 
 Some one, however, may doubt why woman does not differ in fpecies from 
 man, fince the male and female are contraries, and contrariety is difference. 
 But neither are male and female animals different in fpecies, though thefe are 
 the effential differences of animal, and are not as whitentfs or blacknefs, but 
 are inherent in animal fo far as it is animal. The following doubt likewife is 
 nearly the fame with this, viz. Why, with refpeit to contrariety, one kind 
 
 / makes
 
 538 ARISTOTLE'S METAPHYSICS. Eook. X. 
 
 makes things different in fpecies, and another does not : as, for inftance, why 
 it makes that which is capable of walking and that which is winged, but does 
 not make whitenefs and blacknefs. Sliall we fay it is becaufe fome things are 
 tlie proper paffions of genus, but others are not ? And fmce one thing is 
 reafon or form, hut another matter, fuch contrarieties as are in form produce 
 difference in fpecies ; but fuch as are in that which is affumed together with 
 matter do not produce fpecific difference. Hence, neither whitenefs nor black- 
 nefs makes man *, becaufe thefe are not the fpecific differences of a white and 
 black man, though one name fhould be affigned to both. For man is as matter; 
 but matter does not produce difference: for man is not man from the matter, but 
 from the form of man. Hence, though the flefli and bones from which this and 
 that man confift are different, yet the entire whole is different indeed, but is 
 not different in fpecies, becaufe there is no contrariety in reafon or form. But 
 this entire whole is an individual ; and Callias is form in conjun(5tion with 
 matter. This is likewife the cafe with a white man, becaufe Callias is white. 
 Man, therefore, is white according to accident. Nor do a brazen and wooden 
 circle, nor a brazen triangle and wooden circle, differ in fpecies through mat- 
 ter, but becaufe there is contrariety in the form f. But whether fhall we fay, 
 that matter does not make things different in fpecies, though in a certain re- 
 fpeit it is itfelf different, or that it partly does ? For, why is this horfe dif- 
 ferent in fpecies from this man, fmce the forms of thefe fubfill: together 
 with matter ? Shall we fay it is becaufe contrariety is inherent in form ? for 
 there is a fpecific difference betvvreen a white man and a black horfe, but not 
 fo far as the one is white and the other Hack ; fmce, even if both were white, 
 they v^ould in a fnnilar manner be fpecitlcally different. But the mafculine 
 and the feminine are the proper paffions of animal, yet not according to 
 effeuce, but in matter a. id body. Hence tlie fame feed, in confequence of 
 fuffering a certain paffion, becomes either female or male. And thus we have 
 fhown what it is to be d.ff I'ent in fpecies, and why fome things are fpecifi- 
 cally different, and others are not. 
 
 • Inftead of avflfw^rru, as in the printed text, the feufe requires we fliould read avS^amn. 
 t Viz. Becaufe the form of th.. circle is contrary to that of the triangle. 
 
 CHAP.
 
 Book X. ARISTOTLE'S METAPHYSICS. iS9 
 
 C H A P. X. 
 
 But fince contraries are dlfFercnt in fpecles, and the corruptible and the 
 incorruptible are contraries (for privation is definite impoteacy), hence the 
 a rruptiblc and incorruptible mull neceirarlly be generically different frorrt 
 each other. We have novv', therefore, already fpoken concerning thefe uni- 
 verfal appellations. In confequence of tiiis, it may feem not to be neceflary 
 that the corruptible and incorruptible fhould be different in fpecies, as neither 
 are white and black. For it would happen that the fame thing would be both 
 corruptible and incorruptible*, if any thing of univerfals fubfifts, juft as man 
 will be black and white ; and after the fame manner as it happens in parti- 
 culars, that one and the lame man is white and black fucceffively, and not at 
 once; though white is contrary to black. But, of contraries, fome are inhe- 
 rent in certain things according to accident, luch, for inftance, as the particulars 
 which have been juft now mentioned, and many others ; but in other things 
 this is impoflible, among which are the corruptible and incorruptible. For 
 nothing is corruptible according to accident. For accident may happen not 
 to be J but the corruptible is of things which neceffirily fubfift in the parti- 
 culars in which it is inherent. Or the corruptible and incorruptible will 
 be one and the fame, if it is poflible that the con-uptible may not fubfift. 
 It is neceffary, therefore, that the corruptible muft fubfift in each of the 
 things which are corruptible, either efl'entially or in the effence of each. The 
 fame reafoning alio applies to that which is incorruptible : for both are 
 of things which have a neceffary fubfiftence. So far, therefore, as one 
 is piimarily corruptible and the other primarily incorruptible, fo far they 
 are oppofed to each other ; fo that they are neceffarily generically different. 
 Kence it is evident that there cannot be fuch forms as fome affert there 
 are. For, with refpedt to man, one will be corruptible and another in- 
 corruptible, though forms are faid to be the fame in fpecies with particulars']", 
 
 and 
 
 * See the Note to pnge 47. 
 
 t Neither Phuo, nor any of liis genuine clifciples, confidercd ideas as the fame in fpecies with 
 fenfible particulars. For, according to them, ideas are eternal aud pcrfecliy incorporeal na- 
 tures. 
 
 /
 
 240 ARISTOTLE'ft METAPHYSICS. Book X. 
 
 and not with refpedl to them equivocal. But things generically dif- 
 ferent are more diftant from each other than fuch as are fpecifically 
 different. 
 
 tures. Ariftotle, therefore, cannot be ferious in what he now fays ; or, if he is, his reafoning 
 n>uft be fuppofed to be direfled againft certain Platonifts and Pythagorseans of his own time, 
 who corrupted the genuine doilrine of ideas. 
 
 ARISTOTLE'S
 
 ARISTOTLE'S METAPHYSICS. 
 
 BOOK XI.* 
 
 CHAP. I. 
 
 J. HAT Wisdom, therefore, is a certain fclence concerning principles, is 
 evident from the firft books, in which we doubted againft the aflertions of 
 others refpeding principles. But fome one may doubt whether it is requi- 
 fite to confider wifdom as one fcience, or as many faiences. For, if it is one 
 fcience, there is always one fcience of contraries. But principles are not con- 
 traries. And if there is not one, of what kind are thefe many fciences ? 
 Further ftill : is it the province of one, or of many fciences, to contemplate 
 demonftrative principles ? For, if of one, why is it the province of this more 
 than of any other ? And if of many, of what kind are thefe many ? Again: 
 whether is there one fcience of all eflences, or not ? For, if not of all, it will 
 be difficult to fhow what kind of effences thofe are of which there is one 
 fcience. But if there is one fcience of all, it is immanifeft how it happens 
 that there is the fame fcience of many effences. And further ftill : whether 
 is demonftration converfant with effences alone, or alfo with accidents ? For, 
 
 • In this book Ariftotle repeats what he has before demonftrated, and fuggcfts to us that 
 a dodrine of this kind is different from the phyfical and matliematical fciences, and alone de- 
 ferves to be called wifdom. And, as in the third book he enumerated the doubts which per- 
 tain to the metaphyfical fcience, he purfues the queftions there propofed, in the other books as 
 far as to this eleventh bock. See the Notes to the thiid book, 
 
 U if
 
 242 ARISTOTLE'S METAPHYSICS. Book XL 
 
 if wuh accidents, It is not converfant with eflences. But if there is one 
 fclence of efiences and another of accidents, what is the charaderiftic of each, 
 and which of the two is vvifdom ? For demonftrative wifdom is converfant 
 with accidents ; but the wifdom which confiders hrft principles is converfant 
 with ellences. But neither rnuft the fcience which we inveftigate be eRa- 
 bUflied about the caufes which we have mentioned in our Phyfict. ; nor about 
 that caufe for the fake of which other things iubfift. For a thing of this kind 
 is the good; but this fubfifts in pradlcal things, and in things which are in 
 motion. And this firfl: moves : for the end is a thing of this kind. But in 
 things immoveable there is not that v^hich tirft moves. And, in fhort, it is 
 dubious whether the fcience which is now inveftigated is converfant with 
 fenfible cffences, or not with thefe, but with certain others. For, if with cer- 
 tain others, it will either be converfant with forms or mathematical fpecies. 
 But that forms are not is manifeft. And at the fame time, though any one 
 fhould admit that they do fubfift, it will be dubious why the like does not 
 take place in other things of which there are forms, as in mathematical enti- 
 ties. But I fay, that they place mathematical entities between forms and fen- 
 fibles, as certain third natures, befides forms, and things which are here. 
 However, there is not a third man, nor a third horfe, befides man itfelf and 
 horfe itlelf and particulars. But if they are not as they fay, about what kind 
 of things muft the mathematician be confidered as converfant \ For it cannot 
 be with things which are here ; fince none of thefe are fuch as the mathema- 
 tical fciences inveftigate ; nor, indeed, is the fcience which we now invefti- 
 gate converfant with mathematical entities. For none of thefe has a feparate 
 fubfiflence. Nor yet is it converfant whh fennble eflences ; for thefe are 
 corruptible. And, in fhort, it is dubious to what kind of fcience it belongs 
 to doubt concerning the matter of mathematical entities^ For neither can it 
 be the phyfical fcience, becaufe the whole employment of phyfics is about 
 thofe things which contain in themfelves the principle of motion and reft. 
 Nor yet that which is converfant with demonftration and fcience ; for it 
 makes this very genus itfelf the objedl of its inveftigation. It remains, 
 therefore, that the firft philofophy mull make thefe * the objed; of its fpecu- 
 laiion. 
 
 * In the printed text wtfi avTwv, but the fcnfe requires we fliould read tte^i awTuj. For the 
 propofed doubt is, what the Icience is which fpeculates the matter of mathematical entities. 
 
 Some
 
 BookXI. ARISTOTLE'S METAPHYSICS. 243 
 
 Some one, however, may doubt whether it is requifite to eflablifli the 
 fcience which we now inveftigate, as converfant with thofe principles which 
 are called by fome elements. But thefe are confidered by all men as inherent 
 in compofite natures. However, it will rather appear that the fcience which we 
 inveftigate, ought to be converfant with univerfals. For every reafon and every 
 fcience are employed about univerfals, and not about the laft of things ; fo that 
 thus this fcience will be converfant with firft genera. But thefe will be being 
 and the one. For thefe are efpecially confidered as comprehending all t^ngs, 
 and as in the moft eminent degree affimilated to principles, becaufe they 
 rank as things firft by nature. For, thefe being corrupted, othei: thi/;.^ a'llo 
 are at the fame time deftroyed : for every thing is bch>^ and one. But fo far 
 as it is neceflary that differences fhould pa'^'ic'ipate of thefe, if any one admits 
 the fubfiftence of thefe gener^^ fmce no difference participates of genus, fo far 
 it will not appear neceffary to eftablifti thefe either as genera or principles. 
 Further ftill : if that which is more fimple is more a principle than that 
 which is lefs fimple ; but the laft of things* which proceed from genus are 
 more fimple than genera ; for they are indivifibles ; but genera are divided 
 into many fpecies and differences; — hence fpecies will appear to be more 
 principles than genera. But fo far as fpecies are taken away together with 
 genera, genera will appear to be more fimilar to principles. For that is a 
 principle which takes away other things together with itfelf. Thefe, there- 
 fore, and other fuch-like particulars, are the things which are dubious. 
 
 CHAP. 11. 
 
 Further ftill: it may be doubted whether it is neceflary that fomething 
 befides particulars fhould be admitted or not, fince the fcience which we now 
 inveftigate is converfant with thefe. Thefe, however, are infinite : and things 
 which haye a fubfiftence befides particulars, are either genera or fpecies. But 
 the fcience which is. at prefeiit inveftigated is not the fcience of either of 
 thefe. And why this is impoffible we have already fhown. For, in fhort, 
 it is dubious, whether a certain eflence feparate from fcnfiblc eifences, and 
 things which are here, ought to be admitted or not. Or fliall we fay that 
 
 * By the laft of things which proceed from genus Ariftotle means the moft fpecial fpecies, 
 under which there is no other fpecies ; fuch, for inftaace, as man. 
 
 li 2 fenfibles
 
 244 ARISTOTLE'S METAPHYSICS, Book XL 
 
 fenfibles are beings, and that wlfdom is converfant with thcfe ? We appear, 
 however, to inveRigate a different eficnce ; and this efl'ence is the objedl of 
 our prclent invelligation. I fay, it feems that we inquire, if there is any thing 
 effentially fenarate, and which does not fubfift in any fenfible nature. 
 
 Asrain: if there is another cert.un effence befides fenfible eilences, what 
 
 O 
 
 kind of fenfibles are they, befides which it is requifite to eftablifh t'nis effence ? 
 For, why Ihould any one admit that it fubfifts befides men, rather than befides 
 horfes, or other animals, or, in fhort, than things inanimate ? But, indeed, he 
 ■who devifes other eternal natures equal to fenfible and corruptible effenqes 
 vrOuId appear to fall beyond the boundaries of realbn. However, if the prin- 
 ciple which is now inveftigated is not feparate from bodies, what elfe can any 
 one admit rather than matter : But this has not a fubfiftence in energy, but 
 in capacity. Species, therefore, and forms will appear rather than this to be 
 the moft proper and powerful principle. But this alfo is corruptible : fo that, 
 in fhort, there is not an eternal effence feparate, and fubfifting by itieif. This, 
 however, is abfurd : for it appears that there is fuch an effence ; and a certain 
 principle and ejfcnce of this kind is invejligatcd by men of the mof elegant minds. 
 For, how will there be order, if nothing eternal, feparate, and peruianent fub- 
 fifts ? Again : if there is a certain effence and principle, naturally fuch, as we 
 are now inveftigating, and this is one principle of all things, and the fame is 
 the principle of things eternal and corruptible *, it is dubious why, fince there 
 is the fame principle, fome things under this principle are eternal, and others 
 are not eternal. For this is abfurd : but if there is one principle of things 
 corruptible, and another of things eternal, if the principle of things corrup- 
 tible is alfo eternal, a fimilar doubt will arife. For why, fince the principle 
 is eternal, are not the things which fubfift under this principle eternal ? 
 But, this principle being corruptible, there will be fome other principle of this 
 principle, and again another of this, and this will be the cafe ad infinitum. If, 
 again, any one admits the fubfiftence of being and the one, which efpecially 
 appear to be immoveable principles, in the firft place, unlefs each of them fig- 
 nlfies this particular definite thing and effence, how will they be feparate, and 
 have an effential fubfiftence ? But we inveftigate fuch-like eternal and fiift 
 principles ; and if each of them fignifies this particular thing and effence, all 
 things will be effehces : for being is predicated of all things, and of fome 
 things the one. But that all things are effences is falfe. 
 
 • Sec the Notes to the third book. 
 
 Again :
 
 Book Xr. ARISTOTLE'S METAPHYSICS. 245 
 
 Again : how can that which is afTerted by fome be true, viz. that the firft 
 principle is the one^ and that this is effcnce^ and that from the one and matter 
 the firft number is generated, which is eflence ? For, in what manner is it 
 requifire to underftand as one, the duad, and each of the otiier compofite num- 
 bers ? For they neither fay any thing, nor indeed is it eafy to fpeak concern- 
 ing this. But if any one eftabiiOies lines as firft principles, or the things 
 confequent to thefe (I mean fuperficies), thefe are not feparate efiences, but are 
 fedions and divifions, the former of fuperficies, and the latter of bodies ; but 
 points are fedions and divifions of lines : and befides this, they are the bounda- 
 ries of thefe very fame things. But all thefe have a fubfiftence in others, and no 
 one of them is leparate. Further ftill ; in what manner ought we to conceive 
 the efi!ence of the one, and of a point ? For, of every efience there is a genera- 
 tion, but there is not of a point. For a point is divifion. This alfo is an 
 occafion of doubt, that every fcience is of things univerfal, and of that which 
 is of this kind ; but eflence is not of univerfals, but is rather this particular 
 definite thing, and has a feparate fubfiftence. So that if fcience is converlant 
 with principles, in what manner ought we to conceive that elTence is the 
 principle of things ? 
 
 Again : whether is there any thing befides the whole, or not ? But I mean 
 matter, and that which fubfifts together with this *. For, if there is not, every 
 thing in matter is corruptible. But if there is any thing befides, it will be 
 fpecies and form. It is difficult, therefore, to determine in what things this 
 fubfifts, and in what it does not. For, in fome things it is evident thac there 
 is not a feparate form, as, for inftance, in a houfe. Likewife, whether are 
 principles the fame in fpecies, or in number? For, if they are one in num- 
 ber, all things will be the fame. 
 
 CHAP. iir. 
 
 Since, however, the fcience of the philofopher is converfant with beino- fo far 
 as being, and this univerfally, and not according to a part, but being is predicated 
 multifarioufly, and not according to one mode ; — this being the cafe, if being 
 is predicated equivocally, and not according to any thing common, it is not 
 under one fcience. for there is not one genus of things of this kind. But if ic 
 
 • Viz. Form. 
 
 is
 
 246 ARISTOTLE'S METAPHYSICS, Book XI. 
 
 is predicated according to any thing common, it v»'ill be under one faience. It 
 feems, therefore, that it is predicated after the fame manner as that whicli is 
 medicinal, and that which is fahibrious. For each of thefe is predicated multi- 
 farioufly. But each of them is predicated after this manner, becaufe tliis is in a 
 ceriain refpe£l referred to the medicinid art, but that to health ; and again fonie- 
 thing elle is referred in a different refpeS, but each is referred to the fame. For 
 a medicinal difcourfe and a liitle knife are predicated; the former becaufe it pro- 
 ceeds from the medicinal fcience, and the latter, becaufe it is ufefiil to this 
 fcience. The falubrious, too, in a fimilar manner is partly fo denominated 
 becaufe it is fignifnant, and partly becaufe it is effedive of heal'.h. And there 
 is the fame mode with refped to the reiu After the fame manner, likewife, 
 all beings are predicated : for each of tliem is called being, becaufe it is either 
 a paffion, or habit, or difpofition, or niotion, or fomething elfe of this kind, 
 of being fo far as being. 
 
 But as there is a redudion of every being to a certain one, and fomething 
 common, fo of contraries each is reduced to the firft differences and contrarieties 
 of being, whether multitude and the onc^ ox ftm'ilitude and diffimiUtnde are the 
 firft differences of being, or certain other things : for let thefe be the fubjed 
 of future fpeculation *. There is, however, no difference, whether the reduc- 
 tion of being is made to being or to the one. For, if they are not the fame but 
 different, yet they are converted : for the one is alfo in a certain refped being ; 
 and being is the one. But fmce it is the province of one and the fame fcience to 
 fpeculate all contraries, and each of thefe is predicated according to privation 
 (though refpeding fome things of which there is a certain medium, as of the 
 unjuftand the juft, it may be doubted how they are predicated according to 
 privation), this being the cafe, about all thefe, it is rcquifite to place privation, 
 not of the whole definition, but of the laft fpecies ; as, if he is a juft man 
 who obeys the laws according to habit, he who is unjuft f will not be altoge- 
 ther deprived of the definition of the jiift man. However, as he is in a cer- 
 tain refped deficient as to obedience to the laws, in this refped a privation 
 of this definition will be inherent in him. And the like reafoning will take 
 
 * Alexander informs us, that this was confidered by Aiillotlc in his treatife Ilffi r'ayaflou, or 
 Concerning the Good; which, as we have before obfeiJved, is unfortunately >loft. 
 
 f It is well obferved by Alexander, that Arillotlei by i/nju/l, hcrCf me?.as one who is neither 
 juft nor unjuft, but fubfifts between both. 
 
 place
 
 BooKXIi ARISTOTLE'S METAPHYSICS. 247 
 
 place in other things. But, as the mathematician fpeculates from abftradion 
 (for he contemplates by abftrafting all fenfible natures, as, for inftance, gra- 
 vity and levity, hardnefs and its contrary, and, befides thefe, heat and cold, 
 and other fenfible contrarieties), but alone leaves quantity and the continuous, 
 of which fome pertain to one, others to two, and others to three*, and the 
 participated properties of thefe fo far as they are quantities and continuous, 
 and does not fpeculate them according to any thing elfe ; and of fome, indeed, 
 he contemplates the natures and pofitions with reference to each other, and the 
 things which are inherent in thefe, but of others the commenfurations and 
 incommenfurations, and of others again the ratios, yet at the fame time we 
 eftablifh one and the fame geometrical fcience of all thefe, — the like alfo takes 
 place with refpetfl to being ; fince, to contemplate the accidents to this fo far 
 as it is being, and its contrarieties fo far as it is being, is the bufinefs of no 
 other fcience than philofophy. For fome one may attribute to the phyfical 
 fcience the fpeculation of thefe, not Co far as they are beings, but rather fo far 
 as they participate of motion. But the dialedic and fophiftic fciences are 
 converfant indeed with the accidents of beings, but not fo far as they are 
 beings, nor do they fpeculate being fo far as being. It remains, therefore, 
 that the philofopher contemplates the things we have juft mentioned, fo far 
 as they are beings. But fince every being is predicated according to a certain 
 one, and fomething common which is multifarioufly denominated, and after 
 the fame manner contraries (for they are referred to the firft contrarieties and 
 differences of being); and alfo, fince it is poffible that things of this kind 
 may be under one fcience, hence the doubt which was mentioned in the be- 
 ginning is folved : I mean the doubt, how there will be one fcience of many 
 things which are generically diiferent.^ 
 
 CHAP. IV. 
 
 But fince the mathematician ufes things common in an accommodated 
 manner f, to fpeculate alfo the principles of thefe things will be the bufinefs 
 
 * By pertaining to one, two, and three, Ariilotle means lines, fuperficies, and folids ; the firft 
 •being of one, the fecond of two, and the laft of three dimenfions. 
 
 t See the DilTertation on the Demonftrative Syllogifm prefixed to my tranflation of Proclua 
 on Euclid. 
 
 of
 
 248 ARISTOTLE'S METAPHYSICS. Book XI. 
 
 of the firfl: philofophy. For that, when equal things are taken away from 
 things equal, the remainders are equal, is common to all quantities. But the 
 mathematical i'cience receiving this fpeculates about a certain part of its pro- 
 per matter ; as, for inftance, about lines, or angles, or numbers, or fomething 
 pertaining to other quantities ; not, however, fo far as they are beings, but fo 
 far as each of them is continuous in one, or two, or three dimenfions. Philo- 
 fophy, however, does not make particulars the objeds of its fpeculation fo 
 far as fomething is accidental to each of thefe ; but it contemplates every thing 
 of this kind about being, fo far as it is being. And after the fame manner 
 the firft philofophy fpeculates about the phyfical fcience : for the pbyficai 
 fcience contemplates accidents, and the principles of beings, fo far as they are 
 in motion, and not fo far as they are beings. But we have faid, that the 
 firft fcience is employed about thefe, fo far as the fubjeds of them are beings, 
 and not fo far as they are any thing elfe. Hence this* and the mathematical 
 fcience mull be confidered as parts of wifdom. 
 
 CHAP. V. 
 
 There is, however, in beings a certain principle, about which we cannot 
 fpeak falfely j but it is always neceffary to do the contrary to this, I mean, to 
 fpeak conformably to truth ; as, for inftance, that it is not poffible for the fame 
 thing, at one and the fame time, to be and not to be, and fo of other things 
 which are after this manner oppofcd. And concerning things of this kind, 
 there is not indeed fimply demonftration [but it is pofRble to confute him 
 who affirms that eontradidion can be at the fame time true j"]. For it is not 
 polFiblc to fyllogife concerning it from any principle more worthy of belief 
 than this J, which, however, would be necelTary if it could fimply be demon- 
 ftrated. But to him who fhows it is falfe, that oppofite aflertions are at the 
 fame time true, fomething of fuch a kind muft be aflumed, which, though it 
 
 * Viz. The phyfical fcience. 
 
 t Of the words within the brackets, there is nothing more in the original than wee; rovh 
 
 «' EJTIV. 
 
 X It is well obferved here by Alexander, that fince all demonftration and every demonftra- 
 tive fyllogifm confirt from things prior and more known, but nothing is more known than 
 contradidion, there can be no fyllogifm and demonftration of it; fincc to effe^ this fomething 
 »iore known and credible ought to be aflumed. 
 
 V'ill
 
 Book XI, ARISTOTLE'S METAPHYSICS. 249 
 
 will be the fame with that which cannot be and not be the fame at one and 
 the fame time, yet will not appear to be the fame with it. tor tnus alone a 
 demonftration can be effedled againft him who contends that oppofite aflertions 
 may be verified refpeding the fame thing. In the next place it mull be 
 affumed, that thofe who are about to difcourfe together ought to underlland 
 each other ; for, unlefs this is effedted, bow will there be a mutual communica- 
 tion of difcourfe ? It is requifite, therefore, that each of the appellations 
 fhould be known, and fhould manifeft one thing alone, and not many things ; 
 becaufe, if it fignifies many things, it is evident that the fenfe in which it is 
 ufed muft be explained. He, therefore, who fays that this thing both is and 
 is not, afferts that this is not, which he fays is ; fo that he aflerts that the 
 name does not fignify that which it does fignify. But this is iinpoffi'lle. 
 Hence, if there is any meaning in afTerting that this thing fignifies this thing, 
 it is impoflible that contradidl'on concerning the fame thing can be verified. 
 
 Again : if a name fignifies any thing, and this is verified, it is requifite 
 that this fhould be from necefTity : but that which is from neceffity cannot 
 then not be. Oppofite affirmations therefore and negations cannot be veri- 
 fied concerning the fame thing. Further ftill : if affirmation is not more 
 verified than negation, he who afitrts that any one is a man, will not fpeak 
 more truly than if he afl'erts that he is not a man. But it will appear that 
 he who fays man is not horfe, fpeaks either more or not lefs truly than if he 
 aflerted that man is not man ; fo that he will fpeak truly in afl!erting that 
 the fame is a horfe ; becaufe, according to this doctrine, oppofite afiertions 
 kre fimilaily true. It happens, therefore, that the fame thing is man and 
 horfe, or fome other animal. Hence, there is fimply no demonftration of 
 thefe things ; but againft him who makes thefe pofitions there is demon- 
 ftration. Any one Hkewife may eafily compel Heraclitus himfelf, if inter- 
 rogated after this manner, to confefs that oppofite aflertions cannot by any 
 means be verified concerning the fame thing : but now, not being confcious 
 of what he faid, he entertained this opinion. In fhort, if that which is 
 aflTerted by him is true, neither v;ill this be true, that it is poffible for the 
 fame thing, at one and the fame time, to be and not to be. For as when 
 thefe aflertions* are divided, affirmation is not more true than negation, 
 after the fame manner when they are conjoined and united, and affirmation 
 
 * Viz. Such aflertions as Socrates is not a man, Socrates is a man. 
 
 K k . is
 
 250 ARISTOTLE'S METAPHYSICS. Book XI. 
 
 is confidered p.s one thing, negation will not be more true than the whole 
 aflumed in affirmation. Further ftill : if nothing can be truly affirmed, 
 this alio will be falfe, to fay that no affirmation is true. But if any affirma- 
 tion is true, the affertion of thofe who oppofe things of this kind, and who 
 entirely fubvert difcourfe, will be diffolved. 
 
 CHAP. VI. 
 
 Similar alfo to what has been faid is the aflertion of Protagoras. Fof 
 he faid :hat man is the meafure of all things ; fignifying by this nothing 
 elfe than that whatever appears to every one is firmly that which it appears. 
 If this however be admitted, it will happen that the fame thing will both be 
 and not be, and will be good and evil, and whatever elle is faid according 
 to oppofite alTertions ; becaufe frequently this thing appears to fome to be 
 beautiful, and to others the contrary : but that which appears to every one 
 is a meafure. This doubt, however, will be folved, by contemplating 
 whence this opinion derived its origin. For to fome, indeed, it appears to 
 have originated from phyliologifts ; but to others, from all men not pof- 
 feffing the fame knowledge about the fame things : but to fome this thing 
 appears pleafant, and to others the contrary. For that nothing is generated 
 from non-entity, but every thing from being, is nearly the common dogma 
 of all phyfiologifts. Since, therefore, from that which is perfedly white*, 
 
 and 
 
 * The fenfe of this paflage, which Alexander Juflly calls very obfcure and dark, is, 
 according to that celebrated commentator, as follows : 
 
 " Some of thofe who admitted the dodtrine of the phyfiologifts, that nothing is generated 
 from non-entity, falfely aflumed from induction, that as man is generated from man, and 
 horfe from horfe, fo non-white is generated from non-white, and not from while : which pro- 
 pofition is indeed f.ilfe : for though man is generated from man, yet he is proximately generated 
 from the male feed, and female menfes, which are not men. Afluming, therefore, this falfc 
 proprfiticn, that non-white is generated from non-white, and not from white, and alfo an- 
 other falfe propofition, viz. that all negations fignlfy non-entities from non-entities, they rea- 
 foned as follows : If non-white is generated, it is generated from non-white ; but non-white is 
 non-being, non-white tliercfore is generated from non-being. But phyfiologifts are unanimous 
 in. affcrting that from non-being nothing is generated. Non-white, therefore, is not generated 
 from non-white, or from non-being. Hence it is generated from being. But if non-white is 
 non-being, white will doubtlefs be being ; and hence, white, or, which is the fame thing, 
 being, will be that from which non-white is generated, fmce that which is generated ought to 
 Ijp, generated from being. But again : fo far as non-white, according to them, is produced 
 
 front
 
 BooK.Xr. AR I STOT LE'S METAPHYSICS. 251 
 
 and by no means not white, that which is not white is generated ; if now 
 that whii h is not white is generated from that which is not white, accord- 
 ing to their doarine, it will be generated from non-entity ; unlefs that which 
 is not white and that which is white were the fame. 
 
 It is not however difficult to dilTolvc this doubt. For it has been faid by 
 us in our rhyiics, how things which are generated are generated from non- 
 entity ; and how they arc generated from being. And, indeed, to attend 
 funilariy to both the opinions and phantafies of thofe who oppofe each 
 ether, is flupid : for it is evident that one of them mufl; neceffarily affert 
 that which is falfe. This alfo is evident from the things which are effeifled 
 according to fenle : for tlie fame thing never at any time appears to fome to 
 be fweet, and to others the contrary, when that organ which has the power 
 of perceiving and judging the above-mentioned taftes is not corrupted and 
 injured in the other of thefe. This being the cafe, fome of thefe muft be 
 confidered as a meafure, and the others as not a meafure. 1 alfo aflert this 
 in a fimilar manner of good and evil, of the beautiful and the bafe, and 
 of other things of this kind. For to admit nothing but appearances does 
 not in any refpeft differ from thofe who, by placing the finger under the 
 eye, and caufmg two things to appear from one, fhould think that there are 
 two, becaufe there appears to be fo many, and again, that there is one : for to 
 thofe who do not move their fight, one thing appears to be one. In fhorr, 
 it is abfurd, becaufe things which are here appear to be changeable, and 
 never abide in the fame flate, to form from this circumftance a judgment of 
 truth: for it is requifite to inveiligate truth from things which always fub- 
 fift according to the fame, and never change. But of this kind are the na- 
 tures which the world* contains. For thefe do not appear to be different 
 at different times, but they are always the fame, and participate of no 
 mutation. 
 
 Again : if there is motion, and fomethlng which is moved, but every 
 thing which is moved is moved from fomethine;, and into fometliing, it is 
 
 from non-wliite, that from wl.ich non-white is produced will be non-wliite. And hcnco, 
 that from which white is generated will be both white and not wliite. Ariltotle, therefore, 
 folving this queflion, fays that it is true to aflert tliat non-white is generated from non buing, 
 yet not from non-being fimply, but from that which is partly being and partly non-being j 
 about which lie difcourfes in the firft book of his Pliyfics." 
 
 * Ariftotlc, fays- Alexandcir, calls the celeftial fphere and the flars, ihi world. 
 
 K k 2 neccffary
 
 252 ARISTOTLE'S METAPHYSICS. Book Xf. 
 
 neceflary that a thing which is moved fhould ftill be in that from which it 
 is moved, and yet fliould not be in it ; and that it fhould be moved in this 
 particular thing, and yet not be in it, or according to thefe men contradic- 
 tion will not be verified. And if things which are here continually 
 flow, and are moved according to quantity, and this is admitted by 
 feme one, although it is not true, why are they not permanent according to 
 quality ? For theie men appear in no fmall degree to predicate contradidlions 
 of the fame thing, in confequence of conceiving that quantity is not perma- 
 nent in bodies. Hence, according to them, the fame thing is and is not of 
 four cubits. But eflence is according to quality : for this is of a definite 
 nature. But quantity partakes of the indefinite. Again : why, when the 
 phyfician orders this particular food, do they take it ? For why is this ra- 
 ther bread than not? So that it will be juft the fame thing to eat as not to 
 eat. But now, becaufe the ph) fician aflerts the truth refpefting it, and this 
 which they are ordered to take is food, they take it ; they ought not, how- 
 ever, fince no nature whatever among fenfibles firmly abides, but all things 
 are perpetually in motion, and perpetually flowing. 
 
 Further ftill : if we are perpetually changing, and never abide the fame, 
 is it wonderful, if things fhould never appear the fame to us, in the fame 
 manner as it happens to the difeafed ? For to thefe, becaufe their habit is 
 not fimilarly difpofed as when they are in health, things which prefent 
 themfelves to the fenfes do not appear in a fimilar manner ; the fenfibla 
 things themfelves not partaking through this of any mutation, but prc-^ 
 ducing different and not the fame fenfations in the difeafed. It is therefore 
 perhaps neceflary that the fame confequences fliould be produced in us^ 
 if the above-mentioned mutation takes place : but if we are not changed, 
 but continue the fame, there will be fomething permanent. Hence, it is 
 not eafy to confute the afTertions of thofe who entertain thefe doubts from 
 reafoning, when they do not admit fomething, and no longer require a 
 reafon to be given for thefe things : for after this manner all reafoning and 
 demonftration fubfift ; for, by admitting nothing, they, in fhort, fubvert 
 difputation and difcourfe ; fo that no reafoning can be addreffed to men of 
 this kind. But, from the above-mentioned doubts, it is eafy to reply to thofe 
 who are dubious, and to diflTolve the particulars which occafion them to 
 doubt, as is evident from what has been laid : fo that from thefe things it is 
 manifeft that oppofite afTertions cannot be verified at one and the fame time 
 
 about
 
 Book XI. A R I S T OT L E'S M E T A P H Y S I C S. 253 
 
 about the fame thing, nor yet contraries ; becaufe thefe are denominated 
 according to privation. But this will be evident, by analyfing the defini- 
 tions of contraries to their principle. And in a fimilar manner, neither 
 can any medium be predicated of one and the lame thing : for, if the fuhjedl 
 is fomething white, by laying that it is neither black nor white we fliall fpeak 
 falfely ; for it happens that it is, and yet is not white : for the other of 
 the extremes will be verified concerning it ; but this is a contraditlion of 
 the white. Neither, therefore, fliall we affert that which is true, by fpeak- 
 ing either like Heraclltus, or Anaxagoras ; for, otherwife, it would happen 
 that contraries would be predicated of the fame thing : for, when Anaxagoras 
 fays that a part of every thing is in every thing, he fays that a thing is not 
 more fweet than bitter, or any one of the other contraries ; if all things fub- 
 fift in all, not only in capacity, but in energy, and feparate from each other. 
 In like manner, neither is it poffible that all afiertions can be falfe, nor all 
 true ; as well on account of many other difficulties which attend this pofiiion, 
 as becaufe, all aflertions being falfe, neither when any one afTerts that they 
 are all falfe, will he fpeak the truth : and all afTertions being true,, he viha 
 fays all are falfe will not f^eak falfely. 
 
 CHAP. VII. 
 
 But every fcience inveftigates certain principles and caufes about the 
 relpeftive obje£ls of its knowledge ; as, for inftance, the medicinal and gym- 
 naltic, and each of the remaining effedive or mathematical fciences. For 
 each of th'-fe, circumfcribing for itfelf a certain genus, is converfant with 
 this as fubfiftlng, and as being, yet not fo far as it is being y but this is the 
 province of another fcience, different from thefe fciences. But each of the 
 above-menti'^ned fciences, receiving in a certain refpedl definition in each 
 genus, endeavou''S to demonftrate what remains more ntgligently or 
 more accurately : and they receive dcfinitit n, fome of them through 
 fenfe, and others from hyporhefis. Hence, from an indudlion of this 
 kind, it is evident that there is no demonitration of eir.nce and defini- 
 tion. Since, however, there is a certain fcience concerning nature, it is 
 evident that it is different from the pradic and tffedive fciences : for the 
 principle of motion of the effedive fcience is in that which makes, and not 
 in that which is made ; and this is either a certain art, or fome other power. 
 
 And
 
 2jt ARISTOTLE'S M ETA PHYSIC?, Book XI. 
 
 And la a fiinilar manner in the praftic fcience ; motion is not In the thing 
 which is done, but rat'uer in the agents. But the phyfical fcience is con- 
 verfant with things which contain in jhemfelves the principle of motion. 
 That the •phyfical fcience, therefore, is neitiier pradic nor efFeflive, but is 
 neceffarily theoretic, is from thele things evident: for it muft neceffarliy 
 fall into one of thele genera- 
 
 Moreover, fmce it is neceflary that each of the fciences fhould, In a cer- 
 tain refpecrt, have a knowledge of definition, it is rcqulfite not to be igno- 
 rant how the phyfical fcience is to be defined, and how the definition of 
 cffence is to be affumed ; whether as the flat noie, or rather as the concave : 
 for of thefe, in th-s definition of the flat nofe, the matter of the thing is aflumed; 
 but the definition of t!ie concave is without matter : for flatnefs is venerated 
 
 o 
 
 in the nofe. Hence, the definition of It is contemplated toge'her with this i 
 for tlie fiat nole is a hollow nofe. It is evident, therefore, that the definition 
 of fleQi, of the eye, and of the other parts of the body, mufl: always be af- 
 figned in conjundion with matter. But fince there is a certain fcience of 
 being io far as being, and fo far as It is feparate, we mult confider whether 
 It Is to be admitted as the fame with the phyfical fcience, or rather as differ- 
 ent from it. The phyfical fcience, therefore, Is converfant with thofe 
 things which contain in themfelves the principle of motion ; but the mathe- 
 matical fcience is fpeculative Indeed, and about things which are permanent ; 
 but not feparate from fenfibles. There is therefore another fcience befides 
 both thefe, which is converfant with feparate and Immoveable being, if an 
 eflence of this kind fubfiRs : I fay an elfence feparate and immoveable, the 
 fubfiftence of which we fliall endeavour to evince: and if there is an effence 
 of this kind in beings, there alfo divinity will refide ; and this will be the 
 firft and moll powerful prlncirle. It Is evident, therefore, that there are 
 three genera of contemplative fblences, the phyfical, the mathematical, and 
 the theological. Hence, too, the genus of the contemplative fciences is the 
 moft excellent ; and of thefe, that which vvas mentioned in the laft place ; 
 for it is converfant with the moft honorable of beings : for every fcience 
 is called better or worfe, according to the proper objedl of Its knowledge. 
 Some one, however, may doubt whether It Is requifitc to eftablilh univer- 
 fally the fcience of being, fo far as it Is being, or not. For each of the 
 mathematical fciences is employed about one certain definite genus ; but the 
 univerfal fcience fpeculates in common about all things. If, therefore, phy- 
 fical
 
 Book XI. ARISTOTLE'S METAPHYSICS. 255 
 
 fical efTences are the firft of beings, the phyfical fcience alfo will be the firft 
 of fciences : but if there is another nature and eflence feparate and immove- 
 able, it is alfo necelTary that there fhould be another fcience of it, and that 
 this fliould both be prior to the phyfical fcience, and univerfal becaufe prior. 
 
 CHAP. VIII. 
 
 Since, however, being, fimply confidered, is predicated according to 
 many modes, of which one is that which is faid to fubfift according to acci- 
 dent, let us in the firft place fpcculate concerning being which thus fubfifts.. 
 That none of the fciences, therefore, which are delivered to us is converfant 
 with accident is evident. For neither does the architectural art confider 
 what will happen to thofc who are to ufe the houfe ; as, for inftance, whether 
 they will inhabit it painfully, or the contrary : nor is accident the objeiSt of 
 attention to the weaving, ftioe-maklng, and cooking arts ; but each of the 
 fciences alone confiders that which is effentially peculiar to itfelf ; and this 
 is its proper end. Nor does it confider any one fo far as he is a mufician 
 and grammarian ; nor aflert that he who Is a mufician, if he fhould become 
 a grammarian *, will at the fame time be both, though he v/as not before. 
 But that which is not always, was generated ; fo that at the fame time he 
 becomes a mufician and grammarian. This, however, none of thofe which 
 are acknowledged to be fciences inveftlgares, except the fophiftic fcience : 
 for this alone is converfant with accident. Hence, Plato does not fpeak 
 badly when he faysf that the fophiftic art is employed about non-entity. 
 
 * The aflertion of the antient fophift';, to which Ariftotle alludes in this place, is, according 
 to Alexander, as follows: " They fuppofe a man, as for inftance Callias, perfectly ignorant of 
 grammar, to have been firft a mufician, and that he afterwards became a grammarian ; and 
 then they thus reafon» Callias is now at the fame time both a mufician and a grammarian; 
 If this therefore be true, when he was made a grammarian, he was alfo made a mufician: 
 for, fince he is now at the fame time both a grammarian and mufician, he is at the fatnfr 
 time made a grammarian and a mufician. Hence, when he is made a grammarian, he was- 
 not a mufician |. According, however, to the hypothefis, he was a mufician before he was 
 made a grammarian. Before, therefore, he began' to be a grammarian, hie bdth was and 'was 
 rot a mufician. The paralogifm, however, is in the aflertion, v\'hich is doubtlefs filfe, that 
 the generation of things which exift together is alfo efTedled at the fame tim€." 
 
 t In the Sophifta. 
 
 J Becaufe according to the fophifm he is made' both at the fame time. 
 
 But,
 
 Ii.56 ARISTOTLE'S M ETAPHYSICS. Book XlV 
 
 But, that it is not polTible there can be a fcience of accident will be evident, 
 if wc endeavour to perceive what accident is. With reipe<St to all things, 
 therefore, fome things are always, and from neceffilyj (1 do not mean a 
 neccflity v\..ich is denominated according to violence, but that which we ufe 
 in demonftrations) but others fubfift as for the moft part ; and others neither 
 fu .(ift as for the moft part, nor always, and from neceffity, hut as it happens. 
 Thus, cold may be prod.:ced under the dog-ftar ; but this will neither be pro- 
 duced as always from neceffity, nor as for the moft part, /^nd thus we have 
 fliown what accident * is. 
 
 But why there is not fcience of a thing of thi^ kind is evident : for every 
 fcience is of that which always is, or which is for the moft part; but acci- 
 dent does not rank among either of thefe. ]t is alio evident that there are 
 not fuch like caufes and principles of being according to accident, as there are 
 of that which is eflentially being : fo-, if this were the cafe, all things would 
 be from neceflity : for, if this thing is in confequence of that, and that in 
 confequence of this, and this thing is not contingent, but from neceflity, 
 that alfo W'ill be from necefTity of w'hich this was the caufe, as far as to that 
 which is called the laft f efFedl : but this was according to accident. Hence, 
 
 all 
 
 * As the word ufetl here by Ariftotle is (7u/^Si.*mo(, we may again fee how egregioufly 
 Br. Gillies is miflaken, in afferting that this word in Aiiftotle never fignifies accident. 
 
 t The comment of Alexander on this part is as follows : " As, if there is a houfe, there are 
 neceir.iriiy wal's, and if tliefe, a foundation ; in like manner, accident will have a necefl'ary fub- 
 fiftence.. if its caufes are definite. But this will be more evident from the following example : 
 When the fun is perpendicularly oppofed to the moon, an eclipfe is necefTarily produced. But 
 Jet it be admitted to have happened, that a (reafure was found in an eclipfe. If, therefore, the 
 caufes of finding the treafure are definite, let the caufes of it be the eclipfe, and the caufe of the 
 eclipfe. 1 hen we may thus reafon : When the fun perpendicularly oppofes itfelf to the moon, 
 an eclipfe is neceflarily produced. But an eclipfe is the caufe of finding a treafure : the treafure 
 therefore is necelTarily found. The difcovery, however, of a treafure is an accident, for it is 
 among the number of things which rarely happen. But now, becaufe its caufes are faid to be 
 definite, it is concluded that it is among the number of things necefl'ary. All things, therefore, 
 are necefl'ary, and nothing is contingent. But Ariltotle calls the lalt form or fpecies the lalt 
 cQccl : lor the firll c.iufe is the perpendicular didance of the fun ; but the eft'cct is the eclipfe 
 itfelf. Atrain : the fecond caufe is the eclipfe ; but the lall efFe£t is the difcovery of a treafure, 
 •which, if it were the caufe of any thing, that would be the laft effed. If we, therefore, ad- 
 mit that there is a caufe of accident, it follows that accident has a neceffary fubfillence ; bur, 
 if we deny that tliis caufe is, and admit that it \s generated, accident will necejfarily be elRtied: 
 for, if to-morrow a treafure will be difcovered, if there is an eclipfe, but there will be an 
 i:cUpfe if there is aa oppolition under the earth, and this will take place if the fun becomes 
 
 perpendicular.
 
 Book XI. ARISTOTLE'S METAPHYSICS. 25? 
 
 all things will be from necefTity ; and to fubfift cafually after this or that 
 manner, to be contingent, and to be generated, and not to be generated, will 
 be taken away from generated natures. And although caufe is fuppofed not 
 to be being, but that which fubfifts in generation, or becoming to be, the fame 
 things will happen. For every thing will be generated from necefhty. For 
 to-morrow there will be an eclipfe. If this particular thing takes place; but this 
 will be effetSted if fomething elfe takes place, and this laft if fomething elfe. 
 And after this manner, if time Is taken away from that definite time whiclv 
 Is from the prefent inftant till to-morrow, we fhall at length arrive at that 
 which exifts. So that, fmce this is the cafe, all things after this will be gene- 
 rated from neceffity ; fo that all things will be generated from neceflity. 
 
 But, with refped to that which is truly being, and which does not fubfift 
 according to accident, one kind is that which fubfifts in the comprehenfion of 
 the dianoetic power, and is a pafllon in this ; and hence, caufes are not In- 
 veftigated about that which is after this manner being, but about that which 
 is being external to this, and has a feparate fubfiftence. That, however, 
 which fubfifts according to accident Is not neceflary, but Indefinite. But of 
 a thing of this kind the caufes are inordinate and infinite ; but that which 
 fubfifts for the fake of fomething ranks among things generated by nature, 
 or proceeds from the dianoetic power*. And fortune then fubfifts when 
 fome one of thefe Is produced according to accident : for, as with refpcifl to 
 
 perpendicular ; and this again if it fhould rain, and this if it (hould thunder ; fo that thunder 
 is the laft : then, by a retrograde procefs, becaufe it thunders, it will neceflarily rain. If it rains, 
 the fun will be neceflarily perpendicular. If this takes place, there will neceflarily be an oppofi- 
 tion ; and if this, the moon will be eclipfed ; and if the moon is eclipfed, a treafure will necef- 
 farily be difcovered. All, therefore, will be from neceflfity. Hence, fays Ariftotle, if, beginning 
 from this point of time, we fliould fay, To-morrow the moon will be eclipfed, fince every thing 
 which is generated is generated in a finite time, we fhall arrive at that which exifts. For, let it 
 be fuppofed that the treafure is difcovered at the fame time that the eclipfe ceafes ; that after 
 this rain immediately follows ; and after the rain thunder ; then, fince every time is finite, if 
 you take away the time of the eclipfe, and afterwards that of the rain, though it (hould be a 
 hundred or a thoufand months, you will arrive at that which exiflis, viz. at the thunder. Be^ 
 ginning, therefore, from thence, wc fliall aflTert that every thing after the thunder was from ne- 
 ceflity." 
 
 • The Commentary of Alexander on this book ends at the word power. For, as what follows 
 is extraded from the Phyfics, he refers the render to his comment on that work for an explana- 
 tion of the rell of this book. The reader will find all that follows in the fccond, third, and 
 fifth books of the Phyfics. 
 
 L I being,
 
 258 - AR I STOTLE'S METAPHYSICf5. Book XI. 
 
 being, one kind is efiential, and another according to accident, fo alfo with 
 refpeft to caufe. But foitiine * is a caufe from accident in things which are 
 produced according to free-will for the fake of fomething. Hence, fortune 
 and the dianoetic power are converfant with the fame thing: for free-will is 
 not without the dianoetic power. But the caufes are indefinite by which the 
 
 * Ariftctle alone co.nficlers Fortune ns a caufe with which all men are acquainted, viz. as a 
 caufe which obtains an end difTcreut from tliat which was prnpofcd ; but he leaves the ipecnla- 
 tion of forturie confidered as an occult and divine caufe to theologlfts. However, the following 
 account of Fortune, as a certain divine power rooted in th.e ineffable principle of things, will, I 
 doubt not, be g-iate£ully received by the pliilofophic reader. It is extra£led from that admirable 
 work the Commentaries of ^implicius on Arillotle's Phyfics, lib. ii. p. 8l. " 'H tmj t^xh; tm- 
 KoaTSia rw u7roinXr,vr,v /xxMCTa rou ttkvtoj /Mi^av $iJcxoaf/.it, ita^ h xai ii -nv it^ixo/xivov fucrii, I'jv araxTov 
 Bvaav xa.S ixuTrfl, it T^x» /J-na rav a'KXuv a^x"/'""^'-'' cktmv KaTiuSi/VEi, y.at raTTii, y.at HvSi^r::. mo Kai ■^ni'a- 
 Mor aurn JiJouai k^^jteiv, iif iii/Ss^vuan Ta iv ra iiovrco th; yntffsnK^ my.toira. Kc.t rj TiniaXiO'; i-tti afctipa^ 
 t\vou(nv, (L'5 tt aaTurcv th; ysfe^tai KarcuQuvoua-tK. ui^a^ h a/ji.a>'8stai ev tw fTtftx raw x^^foiv Ka^'nuv 'TTMpii, 
 fj; Tou Ti/yj"' TtxtiioiM Ssiwv Ka^'Trav ania. ^ta tovio li, xai rroXim xai oiHuiv, Kai tvoj inaij-Tov ri/^u/xiv Tuxai, 
 OTi Trcpfoi iiccJiavTii t>i{ Seicij ivuciui, Kiviuvsuoixiv haiJiz^riiv Tuf £7ri€a>\Xovcini fiiSi^cuc. xxi 0£o,ue6a Wfoj 
 70 Tuxf"' ''"15 "^^ ^^O" i'''Xl>> "*' '^'^^ ^^ ''''•'5 '^fEiTTOiri yevEO-ii inv avTnv fxoycii' ihuTraa. iiai i(7Ti f/.Ev itaaa 
 T\i%ti ayadri. huh yap ri waaa tei-Ii; ayaOcu tivoj fittiv, cuie uTncrTv ti Kaaov v7io rou Seou. tmv Si aya6av, la 
 ficv tcTTi TTfonyouiJiiva, ra h Kof^aa-rma « iifiUfa, a%ip km nay.a Uynv sita/xiOa. xai ?ia tci/to km rvxnv, TW 
 Hiv ay aim cnnaiofiiv, ri 7ij tow ti/x;£iv twv w^oriyoutJ-evav aya.9o)v anta. mi, inv I't KctKw, h tis KoT^aa-eaii i) 
 rt/Aupiai «/*«5 TiapaaKivaiii Tvxeiv.—Thzt is, " The power of fortune particularly difpofes in ati 
 orderly manner the fublunary part of tlie univerfe, in wliLch the nature of that which is contin- 
 gent is cont.Vmed, and which being effentially difordered. Fortune, in conjundion with other 
 primary caufes, direfts, places in order, and governs. Hence fhe is reprefented guiding a 
 rudder, becaufe fhe governs things failing on the fea of generation. Her rudder, too, is fixed 
 on a globe, becaufe fhe direfts that which is unftable in generation. In her other hand flie 
 liolds the horn of Amalthea, which is full of fruits, becaufe flic is the caufe of obtaining all 
 divine fruits. And on this account we venerate the fortunes of cities and houfes, and of each 
 individual; bcci'ufe, being very remote from divine union, we are in danger of being deprived 
 of its participation, and require, in order to obtain it, the afliftance of the goddefs Fortune, and 
 of thofe naturcb fuperior to the human, who pofrefs the charaO:eriftic of this divinity. Indeed, 
 every fortune is good ; for every attainment rcfpeds fomething good ; nor does any thing evil 
 fubfift from diMuity. But of things good, fome are precedaneous, and others are of a punifh- 
 ing or revenging charaderiftic, which we are accuftomeu to call evils. Hence we fpenk of two 
 fortunes, one of which wc denominate good, and which is the caufe of our obtaining preceda- 
 neous goods, and the other evil, which prepares us to receive punifhment or vengeance." Thus 
 far the admirable Simplicius. 
 
 Fortune, thtrefore, confidered as a divinity, is that power which difpofes things differing from 
 each oilier, and happening contrary to expedlation, to beneficent purpofes. Or it may be de- 
 fined that dcific diilributipn which caufes every thing to fill up the lot alTigned to it by the conr 
 .dition of its being. 
 
 things
 
 BoaK XI. 'ARISTOTLE'S METAPHYSICS. 259 
 
 things proceeding from fortune are produced. Hence, fortune Is a thing 
 immanifeft to human reafoning, and a caufe according to accident ; but, fun- 
 ply, it Is not the caufe of any tiling. Fortune, likewife, Is good or evil, 
 when any thing good or evil happens; but profperous* and adverfe fortune 
 fubfift about the magnitude of thefe. But, fince nothing v^'hlch fubfifts ac- 
 cording to accident is prior to things which have an etfential fubfiflence, 
 neither are accidemal prior to eflential caufe:?. If, therefore, fortune, or that 
 which Is cafual, Is the caufe of the univerfe, intelledl and nature will be a prior 
 caufe, 
 
 CHAP. IX. 
 
 Of things, fome are In energy only, others In capacity, and others both In 
 energy and capacity. And of thefe, one Is fubftance, another quantity, and an- 
 other fome one of the reft f. But there is not any motion belldes things them- 
 feivesj : for that which Is changed Is always changed according to the categories 
 of being. But in thefe there is nothing common in any predication. But 
 every thing fubfifts In a twofold relation in all things. Thus, with refped to 
 this particular thing, this Is the form of It, and that Its privation : and, accord- 
 ing to quality, this is white and that black. Thus, too, according to quantity, 
 this Is perfed and that Imperfe£t ; and according to latlon, this Is upwards 
 and that downwards, or this Is light and that heavy. So that there are as many 
 fpecles of motion and mutation as there are of being. But fince in every 
 genus there is a divlfion into capacity and energy, I call motion § the energy 
 
 of 
 
 * For aruxia, as in the printed text, in this place I read cuTuxnt- 
 
 •j- /. e. Of the other categories. 
 
 J Since motion, according to Ariftotle, is-convivfant with aftion and paflion, he very properly 
 fays, that there is not any motion befides things themfelves, /. e. befides the genera of bein?. 
 
 § Simplicius, in commenting on this definition of motion, whicli Ariftotle repeats from the 
 third book of his Phyfics, obferves as follows : " That Ariftotle has wonderfully defined motion 
 we may learn from hence. That which is in energy, as long as it continues fo, is not, accord- 
 ing to this, faid to be moved. Thus man, as long as he is man, is not moved according to the 
 human form : but neither if he were white in energy, as long as he continued white, would he 
 be moved according to whitenefs. But if man being white in energy was black in capacity, as 
 having the power of becoming black, when his departure commences from whitenefs into black- 
 nefs fo far as he is naturally adapted, that is, to him energizing according to his power of becom- 
 ing black, then he is faid to be moved to blacknefs. And again, when he is faid fo be black, 
 then blaeknefs is permanent in him, and he is no longer moved according to blacknefs, but he is 
 
 L 1 2 black
 
 %60 ARISTOTLE'S METAPHYSICS. Book XL 
 
 of that which is in capacity, fo far as it is in capacity. And that our affertion 
 is true, is evident from hence : for, when there is that which may be built fo 
 far as it is a thing of this kind, we fay that it is itfelf in energy fo far as it is 
 built ; and this is building. In a fimilar manner with refpedt to mathefis, 
 healing, rolling, walking, leaping, growing old, and becoming thick. But a 
 thing happens to be moved when there is cntelechcia itfelf, and when it is 
 neither prior nor pofterior to this. But the entelccheia * of that which is 
 in ca[>acity, when being in etitelecheia it energifes, not fo far as it is that which 
 it is, but fo far as it is moveable, is motion. My meaning is this : Brafs is the 
 ftatue in capacity; but at the fame time the entdecheia of the brafs, fo far as 
 
 black in energy. Nothing, therefore, is moved fo far as it is in energy. Nor yet fo far as it is 
 in capacity, abiding in capacity and in aptitude alone, can it be faid to be moved; but when it 
 changes from a fubfiilence in capacity to a fubfiftence in energy, a fubfiflence in capacity flill 
 remaining in it, then it is faid to be moved. Ariftotle, therefore, very properly adds, " fo far 
 as it is in capacity," that the energy of that which abides in capacity may be gradually perfeded. 
 For, capacity ceafmg, iTiotLon is no more. And when it is in energy, fo far as it Is in 
 energy it is in reft and permanency, but not in motion. Nor yet, if it is in capacity alone, will 
 it be now moved. For that which is capable of being built, fo long as it continues unenergetic 
 according to the capacity of being built, is immoveable. But when, fo far as it is capable of 
 being built, it has energifed according to this, ftill poflefling in the enevgifing the capacity of 
 being built, then it is moved, that is, when it is built ; and building, being the energy of that 
 which is then capable of being built, is motion." 
 
 Oti ?£ Sai/j«ao'iU{ apitraTO tui/ y.iViia-iv, iA.a9otiMV av ivTcuSev. to /j,zv yx^ tvffytia ov imip ^tyiTai iu; av 
 cuToi; EX"} ""* '^'' ^^yono Kara touto mvciaBar oiov o avS^uTTo; ed; av a'.'6pu7rc; ■/•, cuK av Htvono xc-ra rt 
 avBpiji'TTEiOV. ah>i' cuii ei >.£uxo; eiii EvtjyEia, Eojf av 7^iuxoi >), KiiEirai Kara hiuKOTraa. lav Se >,iuKOi uv av- 
 BeuTTo; evtpyEia ^uva/xti iAt\ai w iii ^uvaiJ-ivoi nz\amcr5ai, orav SHravi; auTu aiia J^iuxormo; ysvy^Txi itti jj-iha- 
 vjav, xa&o fizKpvKu TOi/Ttri xaia. ro iuvajxcvov ycvtffSai /UEXav, ivs^youtri, tote ?.eyirai xivEitrfiai £7n to ixO^av, 
 tiai TraXiv orav ^iynai izF.>.a(, tote trarai tv aura, xai oi/xetj xivsnat xaza to ixcf^av, aT^fJ is-iv evi^yiia ^sAa;. 
 ovTa; aea xa&o tveoyita. sriv, ou^iv Kii'EiTai. ou /Kevtoi ou^t xa9o ^v'ja/J.£t ficvov Si/va/XEi xat ev f^ovn rri I'^rnwetO' 
 t)iti, ouk av /.E701T0 xivao-Sai, a;A^' orav utto tou luvaixa /xsiaSahh-n ti; to tvt^yzia, //evovtoj ev awTji tou 
 ^uvaijitt, TCTE ?,£7£Tai Kivzio-Oai. iiKorui ouv TT^oaiOrixtv yi TOiourov, tva ri ci^yEia rou ^uvai/.ci /^evovtoj £n-iT£>.)iTai. 
 ■7raucra,acv!>u yap roj iuva/jtit, ouxiTt in xivwi;- to yaf EVEfyEia ycvof^BVOV xaQoTov ivipyeia, iv raan xai iv ficvn 
 trtv, a^x' ovx cv xivnuu. on /xcvroi ci/Je ei ti tii $uva/i£i Eri /jiovov, touto jiJh xivsnai. to youv oMel'onmov oTiCf 
 tri TO Oi/vc/xEVOv otxeiouv6nvai, eaf fASv avivi^ytiTOv /xevti xara to ouoJo^htov, axivnTov ertv. brav Je xa9o axo- 
 Si/xnTov tri xara touto evipyri, etj Exof ev tw eve^^eiv to o;xoJ'o/z)itoi', tote «ii£iTai, toutitiv iiTav Oixolofinrai, 
 xai M oiKOOo^w<5 tvtp')iia ouaa tou oixo^o/xyitou tote xivnaii Eri. — Smiplic. in Arilt. 1 hy(. p. 94. 
 
 In fliort, motion is the internal perfeclion of that which is moveable, fo far as it is moveable ; 
 and that perfection is the form or energy which fubfifts in that of which it is the internal 
 perfeclion. 
 
 * Foj the accur ate meaning of enielecheia^ fc^ Note to page 2o6. 
 
 brafs,
 
 >M 
 
 BooKXr, ARISTOTLE'S METAPHYSICS. 261 
 
 brafs, is not motion. For the eflence of brafs is not the fame as the effence of » 
 
 a certain capacity ; fmce, if it were fimply the fame according to definition, 
 the entelecbeia of the brafs would be a certain motion. But it is not the fame 
 as is evident in contraries : for the capacity of becoming well, and the capa- 
 city of becoming ill, are not the fame; for, if this were the cafe, to be well 
 would be the fame as to be ill. But the fubjeil which is capable of being 
 made well and ill, whether it be moifture, or whether it be blood, is one and 
 the fame. Since, therefore, the eflence of a thing is not the fame with the 
 elTence of a certain capacity, as neither is colour the fame with that which is 
 villble, motion is the entelecbeia of that which is capable fo far as it is capable. 
 For that motion is, and that a thing happens to be moved, when it is itfelf 
 entelecbeia, and neither prior nor pofterior to this, is evident. For it happens 
 that every thing at one time energifes, and at another time does not, as in 
 tliat which is capable of being built, fo far as it is capable of being built ; and 
 the energy of that which may be built, fo far as it polTefles this capacity, is 
 building : for * the energy of it is either building or the houfe. But when the 
 houfe is the energy, it will no longer be capable of being built ; and that 
 which is capable of being built is built. Building, therefore, is neceifarily 
 an energy, and building is alfo a certain motion. There is likewife the fame 
 reafoning refpecling other motion?. 
 
 But the propriety of what we have now faid is evident from the aflertlons 
 of others concerning motion, and from its not being eafy to define it in a 
 different manner. For, neither can it be placed in any other genus. And 
 this is evident from their aflertions : for fome of thefe fay, that it is diverfity 
 and inequality, and non-being, none of which is neceifarily moved. But, 
 neither is mutation a change into thefe, nor from things of this kind rather 
 than from their contraries. The rcafon, however, why they placed motion 
 in thefe, is becaufe motion appears to be fomething indefinite. But the prin- 
 ciples of the other co-ordination, in confequence of being privative, are inde- 
 finite. For no one of them is either this particular thing f, or a thing w ith 
 a certain quality, or any one of the other predicaments. And motion ap- 
 pearing to be fomething indefinite, is the caufe that it cm neither be placed ii^ 
 
 * Inftead of -n yap tcuto iciiv n otiicoo,f.r,ji;, « I'.cpycia, « eiHix, as in tlie prlateil text, I read n yaa 
 
 t By this particular thing, and a thing with a certain quality, Ariftotle m;ans the two prcdU 
 gftOiPiits fubilaiice and quality. 
 
 the
 
 262 ARISTOTLE'S METAPHYSICS. Book Xi; 
 
 the capacity nor in the energy of beings: for neither that which Is capable' 
 of being quantity is moved from necifllty, nor that which is quantity in 
 energy. Motion, however, appears to be a certain energy, though this energy 
 is impcrfed. But the caufe of this is, that the capable of which it is the 
 energy is imperfefl: ; and on tlus account it is difficult to comprehend what 
 it is. For it is either neceffary to place It in privation, or in capacity, or in 
 fimple energy. But it does not appear that it can be any one of thefe. It 
 remains, therefore, that it muft be what we have faid, viz. both energy, and yet 
 not fimply energy ; which is indeed a thing difficult to perceive, but yet is 
 capable of fubfifting. That motion alfo is in that which is moved is evident : 
 for the entelecbeia of this is from that which is motive ; and the energy of 
 that which is motive is no other than this. For it is neceffary that there 
 fhould be entelecbeia in both : for that which is motive is motive from pof- 
 feffing the capacity of moving ; and that which moves moves from ener- 
 gifmg : but it is energetic of that which is in motion. So that, in a fimilar 
 manner, there is one energy of both, juft as there is the fame interval of one 
 to two *, and cf two to one, and of afcent and defcent, but the eflence is not 
 one. And the like takes place in the mover and the thing moved. 
 
 C H A P. X. 
 
 Infinite is either that which it is impoffible to pafs over, becaufe it isf 
 not naturally adapted to be permeated, in the fame manner as voice j is invi- 
 fible ; or it is that which has a boundlefs paffiige, or that which fcarcely |, or 
 which is naturally adapted to have, but has not, a paflage § or an end. Again r 
 it either fubfifts from addition, or ablation, or from both. And, indeed, that 
 infinite Ihould be fomething feparate and fenfible is impoffible. Fcr, if it is 
 
 * In the fame manner as the interval of one to two, and of two to one, and of afcent and 
 defcent, is one in fubjecl but two according to ratio, that of one to two being half,, but that of 
 two to one double ; fo the motion of that which moves and that which is moved is one in fub- 
 ie(fl; but when it is beheld as proceeding from that which moves, it is not the fame as when be- 
 held in that which is moved. 
 
 ^ Voice is invifible according to negation, becaufe it Is not naturally adapted to be feen, from, 
 not pofleiring colour. 
 
 J As a labyrinth. 
 
 ^ As a way where there is intcnfe heat or coldi 
 
 neither
 
 -SookXI. AR I STO TL E'S metaphysics, 263 
 
 jieithcr magnitude nor multitude, but the infinite is the eflence of it and not an 
 ^iccident, it will be indivifible. For that which is divifible is either magnitude 
 -or multitude. But if it is indivifible, it is not infinite, except in the fame 
 manner as voice is invifible. Neither, however, do they thus fpeak, nor do 
 we thus inveftigate, but we confider it as Impermeable. Further flill : how 
 is it poffible how there can be the eifentially infinite, if there is neither eflien- 
 •tial number nor magnitude, of which the infinite is a paffion ? 
 
 Again : if the infinite fubfifts according to accident, ic will not be fo far as 
 infinite an element of things, as neither is the invifible an element of fpeecb, 
 though voice is invifible. And that the infinite is not in energy is evident : 
 for any part whatever of it which is alfumed will be infinite *j fince the 
 efi^ence of the infinite and the Infinite are the fame, if the infinite is eflTence, 
 and does not fiibfift in a fubjed. So that it Is either indivifible or divifible 
 into infinites, if divifible f. But it is impoffible that the fame thing can be 
 many infinites : for, as a part of air is air, fo infinite is a part of Infinite, if it is 
 eflence and a principle. It is, therefore, impartible and indivifible. But it is 
 impoffible that a thing which is In etitelecheia fliould be infinite ; for it mull 
 neceflarily be quantity. Hence it fubfifts according to accident. But thus 
 fubfifting, we have fliown that It cannot be a principle, but this mufl: be aflerted 
 of that to which it happens, viz. number or the even. This inquiry, therefore, 
 is univerfal. 
 
 But that the infinite is not in fenfibles Is evident from hence : for, If the 
 definition of body is, that which Is bounded by fuperficles, there will not be 
 an infinite body either fenfible or intelligible. But neither will it be num- 
 ber as feparate and infinite: for number, or that which poflefles number, is 
 
 * If infinite is confidered as a principle and as an effence infinite in energy, the infinite in it 
 witi be the fiiine as the eflence of the infinite, becaufe its eflence is infinite. It will^ therefore, 
 be (imple, and, if fimple, every way fimilar. But if this be the cafe, it will either be divifible, 
 and thus by no means infinite, or, if divifible, it will be divided into infinites. For the eflence of 
 that which is fimple is the fame witli its fubfiftcnce as this definite particular thing (toJIe ti). 
 Thus, foul is the fame as the eflence of foul ; but in compofites, that which fubfifts as this defi- 
 nite particular is a compofite, but its eflence is according to form. The parts of infinite, there- 
 fore, thus confidered are infinite, in the fame manner as a part of air is air, of water water, and, 
 in fhort, juftas the parts of eflence are eilences. 
 
 f Inftead of w /xt^iffTov, as in the printed text, the fenfe requires we fliould read « lAt^wroi. 
 BcOfaiioa alfo has fi partibile ejl. 
 
 numerable. 
 
 /
 
 264 ABISTOTLE'S METAPHYSICS. Book X!'. 
 
 numerable. But, that the infinite is not in fenfibles will be phyfically mani- 
 feft from the following confiderations : It can neither be any thing compofite. 
 nor fimple : for, if a compcfite, it will not be a body, if the elements are finite 
 in multitude. For it is requifite that contraries fhould be equalifcd, and that 
 one of them fliould not be infinite. For, if the power of the other body fails 
 in any refpe£l whatever, the finite will be corrupted by the infinite body. 
 But that each of the elements fhould be infinite is impoflible : for that is body 
 which every way pofTefl^es interval; but that is infinite which has interval 
 without end. So that, if there is an infinite body, it will be every way infi- 
 nite. Nor yet is it poflible that there can be one infinite fimple body, nor, as 
 foine fay, different from the elements, which according to them it generates. 
 For there is not befides the elements a body of this kind ; fince all things are 
 refolved into the natures from which they originate. But this does not appear 
 to be, befides the fimple bodies, either fire, or any other of the elements : for 
 it is impoflible, if it be admitted that the univerfe is finite, that the infinite 
 can either be, or be generated from, fome one of the elements, as Heraclitus faid 
 that all things were once fire. There is alfo the fame reafoning refpeding 
 that one thing * which the natural phrlofophers introduce befides the elements. 
 For every thing changes from a contrary, as, for inftance, from the hot into 
 the cold. 
 
 Again : a fenfible body is in a certain place ; and there is the fame place 
 of the whole and the part, as, for inftance, of the whole earth and one clodf . 
 So that, if the infinite is of fimilar parts, it will either be immoveable, or will 
 always be impelled forward. But this is impoflible : for, why fliould it be 
 rather impelled downwards than upwards, or in any other diredion ? Thus, 
 for inftance, if it is a clod of earth, where will it be moved, or where will it 
 abide? For the place naturally adapted to this body is infinite. It will, 
 therefore, occupy the whole place. But after what manner ? What, there- 
 fore, will be its reft, and what its motion ? Shall we fay that it will be every 
 where at reft ? It will not, therefore, be moved. Or fliall we fay that it is 
 every where moved ? It will not, therefore, abide. But if the univerfe i» 
 diflimilar, j^laces alfo will be difllmilar, and in the firft place the body of the 
 
 • Vi7. Matter. 
 
 t The text !i re is defeiSive ; but I have fuppfied what is wanting from the third book of the 
 Phyfics. It mir> be obferved, that a clod of earth and the wliole earth have the fame place 
 according to form, but not according to quantity, which place is the centre of the univerfe. 
 
 univerfe
 
 BookXI. ARISTOTLE'S metaphysics. 26S 
 
 unlverfe will not be one, except by contad alone. In the next place, thefe 
 things will either be finite or infinite in fpecies. But that they fliould be finite 
 is impofhble. For Tome things will be infinite, and others not, if the univerfe 
 is infinite ; as, for inRance, fire or water. But a thing of this kind is cor- 
 ruption to contraries. But if they are infinite and fimplo, places alfo will be 
 infinite, and the elements will be infinite. However, if this is impoffible, and 
 places are finite, the univerfe alfo is necefTarily finite. In fh ort, it is impoffible 
 that there can be an infinite body, and at the fame time a place for bodies, 
 if every fenfible body has either gravity or levity : for it will either be im- 
 pelled to the middle, or upwards. But it is impoffible that either the whole 
 or the half, or any part whatever, of the infinite fliould be pafiJive to any 
 thing. For, how will you make a divifion ? Or how of the infinite can one 
 part be uf'wards and another downwards, or this the extremity, and that the 
 middle ? 
 
 Further ftill : every fenfible body is in place ; and of place there are fix 
 fpecies* : but it is impoffible that thefe fliould fubfift in an infinite body. 
 And in fliort, if it is impoffible that place can be infinite, it is alfo impoffible 
 that body can be infinite : for that which is in place is fomewhere ; but this 
 fignifies either upwards or downwards, or fome one of the other differences 
 of place : and each of thefe is a certain boundary. But the infinite is not 
 the fame in magnitude, motion, and time, as if it were one particular nature; 
 but the pofterior is denominated according to the prior. Thus, motion is 
 denominated infinite, according to the magnitude upon which a thing in 
 moved, or changed, or increafed : but time is denominated according to 
 motion. 
 
 CHAP. xr. 
 
 Of things which are changed, one thing is changed according to accident ; 
 as when we fay that the mufician walks ; but another thing is fimply faid to 
 be changed, becaufe fomelhing belonging to k is changed ; as, for inllance, 
 fuch things as arc changed according to parts : for the body is healed, be- 
 caufe the eye is healed. There is alio fomething which is of itlelf hr(l 
 moved ; and this is that which is moveable from itfelf. There is a like 
 
 * Viz. Upwards and downwards, before and behind, to the right hand and to the left 
 hand. 
 
 M m diftindioa
 
 266 ARISTOTLE'S METAPHYSICS. Book XI. 
 
 diftindlon too in that which moves: for one thing moves according to ac- 
 cident ; another thing according to a part ; and another from itfelf, or eflen- 
 tially. There is alfo thit which firfl: moves; and there is foraet'ning which 
 is moved. There is befides the time in which, and from which, and with 
 reference to which, a thing is moved : but the forms and paffions, and place 
 to wliich thinps in motion are moved, are immoveable ; as, for inftance, 
 fcicnce and heat. Likeaife not heat but calefaftion is motion*. But mu- 
 tation, which is not according to accident, is not in all things, but is in con- 
 traries, and media, and in contradi(flion : and the credibility of this is de- 
 rived from induiftion. That alfo which is changed, is either changed' from 
 a fubjed into a iubjedl:, or from a non-fubjed: into a non-fubjeft, or from a 
 fubjed into a non f-fubjed, [or from a non-iubjed into a fubjed]. But I 
 mean by a fubjed, that which is manifelled by nffirmation. So that there are 
 neceflarily three mutations : for that which is from a non-fubjed into a non- 
 fubjed is not mu'ation. For it is not between contraries, nor between con- 
 tradidorie-, becaufe, in paffing from a non-fubjed to a non-fubjed, there is 
 not oppofiticm. Mutation, therefore, from a non- fubjed ijl into a fubjed 
 according to contradidion, is generation ; and fuch a mutation when it is 
 fimple is a fimple, bvit when partial a partial generation. But the mutation 
 from a fubjed into a non-fubjed is corruption ; which when it is fimple 
 is a fimple, but when partial a partial corruption. If, therefore, non-being 
 is predicated multifarioufly, and that which fubfifts according to compofition 
 or divilion cannot be moved, neither can that which lubfifts according to 
 capr.city, which is oppofite to that which fmiply is j for non-white or non- 
 good can be moved according to accident, fince that which is not white may 
 be a man ; but this can by no means be the cafe with that which is not fimply 
 this : for it is impoluble that non-being can be moved. But if this be the 
 
 * Viz. Heat, which is a pafTion, is not motion, but calefa£i;ion is motion becaufe it is a mu- 
 tation to heat. Hence that which is '^affively alTedied, i. e. that whicli becomes hot, is moved 
 with an internal tnotion : but this is not the cafe with heat. 
 
 f ^M is omitted here in the printed text, as alfo are the words within the brackets, which I 
 have added from the verfion of Beflarion. Sj that there is wanting in the Greek u ex /j,>i uttckii- 
 
 Ht'JOU Eli VTOKttlJievOV. 
 
 * That is, from that wliich is not in energy, but yet is in capacity. Aiiflotlc very properly 
 adds here, according to contradiction; for a mutation does not take place from non-white into 
 fwect, c.\ccpt according to accident. 
 
 cafe.
 
 Book XI. ARISTOTLE'S M E f A P H Y S 1 C S. 267 
 
 cafe, it is impofTi'oIe that generation can be motion* : for, if it were, non- 
 being woaLi be generat^^d. For though it fhoulJ be efpecially generated 
 according to accident, yet at the fame time it would be true to afTert of that 
 which is fimply generated, that it is non-being. And in a fiaiilar manner 
 with refpcdl to bt;lng at rcll. Sach are the ahfjrdities, therefore, which 
 attend this hypothefis. And again : if every thing which is moved is in 
 place, but non being is not in place ; for it would Le Ibmewhe: e ; — hence, 
 neither is corruption mouon : for motion or reH: is contrary to motion, hut 
 corruption to generation. But fince every motion is a certain mutation, 
 and there are three mutations as above enumerated, and fiace of thtfe the 
 mutations according to generation and corruption are not motions (btit thefe 
 fubhrt according to contradidion) — hence it necefiarily follows, that muta- 
 tion from a fubjed into a fubjed is alone motion. But fubje£ls are either 
 contraries or media : for privation is admitted to be a contrary, and is 
 manifefled by affirmation "j" ; as, for iuftance, the naked, the toothlclsij:, and 
 the black. 
 
 CHAP. XII. 
 
 If, therefore, the categories are divided by fubftance, quality, place, adion 
 and paffion, relation and quantity, it is neceflary that there fhould be three 
 motions, viz. of quality, of quantity, and of place. But there is not any 
 motion according to fubfl:ance§, becaufe nothing is contrary to fubftance. 
 
 * For generation is of that which is not in energy, and not of that which is ; but that which 
 is moved now is, fince motion, as we have before fliown, is a certain energy. 
 
 t Generation and corruption, fays Simplicius, fubfift according to the contradiction of that 
 which is, and of that which is not ; but motion is from a contrary into a contrary, to which it 
 is neceffary that permanent fubftance (hould be fubje£led, as thjt which is natuially adapted to 
 receive feparately contraries, or thii;gs intermediate, or a privation oppofite to accident, as the 
 being fick, or naked, Sec. which, becaufe they are inherent in permanent fubftances, are both 
 affirmatively predicated, and after a manner reduced into form. 13ut the pri.ation ot fubftance 
 is truly that which is not. 
 
 X In the fecond chapter of the fifth book of the Phyfics, inftead of vaisbv we find muxov the 
 •white. 
 
 § Ariftotle (hows that there is not any motion according: to fubftance, becaufe all motions 
 are from contraries into contraries. But nothinc^ is contrary to fubftance. Hence, in fub- 
 ftance, there is not a mutation from a contrary lubftance, but from privation ; and again, a 
 mutation is not produced from fubftance into fubftance, but into privation and corruption. 
 
 M m 2 Nor
 
 268 ARISTOTLE'S MET APHYSIC S. Book XI. 
 
 Nor is there any motion of relation : for it Is poflible that, one of the rela- 
 tives being changed, it may be truly faid of the other that It is not at all 
 changed ; lb that the motion of them is according to accident. Nor is 
 there any motion of agent and patient, or of that which moves and that 
 which is moved, bccaufe there is not motion of motion, nor generation of 
 generation, nor, in fliort, mutation of mutation, f'or it happens that there 
 is motion of motion in a twofold refpeiS ; viz. either as of a fubjed, as man 
 is moved, becaufe he changes from white into black ; fo that thus alfo mo- 
 tion is either made hot or cold, or is changed in place, or is increafed. 
 Tliis, however, is impofliblc ; for mutation is not any lubjedl. Or, there is 
 motion of motion, becaufe fome other fubjed is changed from mutation 
 into another form. Thus, man is changed from difeafe into health. But 
 neither is this poflible except according to accident : for every motion is a 
 mutation from one thing into another, and in a fmiilar manner generation 
 and corruption ; except that mutations from oppofites are in this or that 
 manner; but this is not the cafe with motions. Man is, therefore, at the 
 lame time changed from health to ficknefs, and from this very mutation 
 into another. But it is evident that, when he becoines fick, he will be 
 changed into a certain difeafe : for it is poflible to reft. It is likewife evi- 
 dent that he will not always he changed into whatever may cafually take 
 place ; and that will be a mutation from a certain thing into fomething elfe. 
 So that convalefcence will be an oppofite motion, but from accident; juft as 
 if he fliould be changed from reminifcence into oblivion, becaufe that in 
 which oblivion is inherent is fometimes changed into fcience, and fometimes 
 into health. 
 
 Further ftill : there will be a progrefllon ad infinitum if there is a muta- 
 tion of mutation, and generation of generation. But it is neceflary that 
 there fl:iould be the former, if there is the latter. Thus, if fimple generation 
 is at any time generated, that alfo which is fimply in generation, or becoming 
 to be, will be generated, fo that a thing which is fimply in generation will not 
 yet be : but there was fomething which was in generation, and that fomething 
 was formerly generated, and this again was once in generation or becoming 
 to be; fo that what was then in generation was not yet. But fince there is 
 not any thing firft in things infinite, there will not be that whicli is firft gene- 
 rated ; fo that neither will that which is confequent be. Neither, therefore, 
 yvjll it be poflible for any thing to be generated, nor to be moved, nor to be 
 
 changed.
 
 Book. XL ARISTOTLE'S METAPHYSICS. 269 
 
 changed. Again : contrary motion, and reft, and generation and corrup- 
 tion are of the fame thing. So that a thing which is generated, when it 
 becomes that which is generated, will then be corrupted *. For it is not 
 immediately corrupted as foon as it is becoining to he, nor pofterior to this : 
 for that mufl: neceilarily be which is corrupted. Further ftiil : it is requifite 
 that matter + fliould be fubjecSl to that ivhich is in generation and mutation. 
 What, therefore, will it be ? As that, indeed, which is variable is either 
 body or foul, fo that which fubfifts In becoming to be is either motion or 
 generation. And, again, what is that into which it is moved ? For it is re- 
 quifite that there fhould be motion and generation of this thing from this 
 into this. After what manner, therefore ? For the generation of difcipline 
 is not difcipline ; fo that neither is there generation of generation. 
 
 But, fince there is neither any motion of fubftance, nor of relation, nor of 
 aftion and paffion, it remains that there can be alone motion according to 
 quality, and quantity, and place: for in each of thefe there is contrariety. 
 But I do not mean by quality, that which is in fubftance (fmce difference alfo 
 is quality) ; but I mean paffive quality, by which a thing is faid either to fuf- 
 fer, or to be ImpafTive. 
 
 With refpe£t to the immoveable, that which is wholly Impoffible to be 
 moved is immoveable ; and that which is fcarcely moved in a long time, or 
 which flowly begins to be moved ; and that which is naturally adapted to be 
 moved, but yet Is not able when it is naturally adapted, and where, and as 
 it is naturally adapted, which alone among things immoveable, I denominate 
 that which refts. For reft is contrary to motion ; fo that it will be a priva- 
 tion of that which is capable of motion. 
 
 Again : things are faid to fubfift together according to place, which are in 
 one 111 ft place ; and thofe are faid to fublift feparately, which are in a different 
 
 * If there is generation of f^ener.ition, fmce tlie generation of one thing Is the ccrruption of 
 another, generation when generated will be corrupted. It will not, however, be corrujtL-d in 
 the beginning of its generation, fince it would not be generate.-' any longer; nor yet pcilerior 
 fo its generation, becaufe when generated it is corruj ted. Hence it is nccefl'ary that when it 
 is compI.;tc!y generated it iliould then perilh. 
 
 f In the fame manner as brafs is the fubje£l rrratter of the ftatue, and as the body or foul 
 is the fubject of alteration, fo, likev^ ife, matter n-.u'l be fabji.cl to that which is in generation ; 
 and not only to that which is fimply in generation, but alfo to a certain gener.itlon and motion, 
 and, in flioit, to mutation. For, if there were no fubjedl, neither would any thing be gene- 
 r.ited. 
 
 place.
 
 270 ARISTOTLE'S METAPHYSICS. Book XI. 
 
 place. But tilings arc faiJ to touch each olher, tlie extremities of which 
 fubfiil: together. A inecliuin is that into wliich a thing wliich is changed is 
 naturally adapted to proceed, hefore it arrives at that into which it is ulti- 
 mately changed, when it is continually changed according to nature. That 
 is contrary according to place which is very much diilant according to a right 
 line. But th.it is fucceflive, hetween which and that to which it is confequent 
 nothing of the lame kind intervenes; when it is after the princip'e, either by 
 jiofition alone, cr form, or fome other mode thus defined. Thus, \'\x\t\ifucceeii 
 or are confeciuent to a line, monads the monad, and houfes a houfe. Nothing, 
 however, hinders but that fomething elfe may fubfift between them. For that 
 which is fucceflive is fucceffive to fomething, and is fomething pofterior : for 
 one is not fucceffive to two, nor the Calends to the Nones. That is coherent 
 which hc\r\g/acce£ive touches. But, fince every mutation is in things oppo- 
 fite, and thefe are contraries and contradidion, and there is no medium of 
 contradidion, it is evident that there is a medium in contraries. But the conti- 
 71U0US has fomething of the nature of the coherent, or of the tangent. And 
 things are called continuous, when the boundaries of each by which they 
 touch and are continued are one and the fame. So that it is evident that 
 the continued is in thofe things, from which one thing is naturally adapted to 
 be produced according to contadl. And it is alfo evident that the fucceffive 
 ranks as the firft : for it is neceflary that whatever touches fhould be fuccef- 
 five, but not every thing which is fucceffive touches. Likevvife, if a thing is 
 continuous, it is neceffary that it fhould touch ; but if it touches it is not yet 
 continuous. But in thofe things in which there is not contadt there is not 
 natural coherence. So that a point is not the fame with the monad ; for 
 with points there is contad, but this is not the cafe with monads : for thefe 
 are fucceffive to each other ; and fomething fubfifts between points, but not 
 between monads. 
 
 ARISTOTLE'S
 
 ARISTOTLE'S METAPHYSICS. 
 
 BOOK XII.* 
 
 CHAP. I. 
 
 
 JL H E prefent fpeculatlon is concerning eflence ; for the principles and 
 caufes of eiTences are here invefligated. For, if the univerfe is as one whole 
 eflence will be its firft part ; or, if things fubfift in a confequent order, after 
 this manner alfo eflence will be firft;, and afterwards quality or quantity. 
 But at the fame time, in fhort, neither are thefe beings, but qualities and 
 motions, in the fame manner as that which is not white, and that which is 
 not ftraight. For, we alfo fay that thefe are^ as for inftance, that fuch a thing 
 is not white. Further ft:ill : no one of the reft has a feparate fubfiftence. 
 And the truth of this is in reality teft:ified by the antients : for they invefti- 
 
 * It is well obferved by Alexander, that Ariftotle in this book difcouifes of the firft prin- 
 ciple of things, for the fake of which the whole of the prefent work was compofed. But, 
 bscaufe, fays he, the appellation of principle is multifarioufly aflumed, for matter, form, and 
 privation are each of them called a principle ; hence, Ariftotle in the firft place fummarily 
 difculTes whatever pertains to a divifion of this kind, that by a convenient method, and in a 
 compendious way, we may eafily and rightly inveftigate the difference between this and other 
 principles. He further obferves ; that fince one among the propofed qucftiors was, whether 
 there are the fame principles of all things, or different principles of different things, which has 
 not yet been folvedt by Ariftotle ; hence, he again mentions caufes, that he may demonflrate 
 that in one refpecl there are the fame, and in another different principles of all things. 
 
 ■f A folutlon, however, of tiiis is given in the Notes to the third book. 
 
 / 
 
 gated
 
 272 ARISTOTLE'S METAPHYSICS. Book XII 
 
 gated the principles, elements, and caufes, of efTcnce. Thofe, indeed, of the 
 prefent time rather confider univerfals as eflences : for genera are univerfals, 
 which they fay are rather principles and efTunces, becaufe they inveftigate 
 logically. But the antients called particular-* eiTences, luch as fire and earth, 
 but not a common body. But there are three eiTences : one, feniible ; of 
 which one part is eternal *, and another corruptible, as all men ackuovvledge, 
 fuch as plants and animals. Of this fenlible elTcnce it is neceffary to admic 
 the elements, whether one cr many. But another elTence is immoveable, 
 which, according to fome, has a feparate fubfiftence. Others, again, give it a 
 twofold divifion ; others place in one nature forms, and mathematical entities ; 
 and others confider mathematical entities alone. The fenfible eflence, there- 
 fore, belongs to the phyfical fcience (for it fubfifts with motion): but the 
 immoveable eflence, to another fcience, if they have no principle in common. 
 
 CHAP. II. 
 
 But fcnfible eflence is mutable. If, therefore, mutation is from oppofites, 
 or from things fubfilling between oppofites, but not from all oppofites (for a 
 white colour is not from voice), but from that which is contrary, it is neceflary 
 there (hould be fomething which may be changed into contrariety ; for con- 
 traries are not changed. Befides, this abides, but that which is contrary- 
 does not abide. Hence there is a certain third thing befides contraries, 
 viz. matter. If, therefore, mutations are four in number, viz. either in ful)- 
 ftance or in quantity, in quality or in place, and fimple generation as alfo 
 corruption is a mutation according to fubftance, but augmentation and di- 
 minution according to quantity, alteration acci rding to paflion, and lation 
 according to place ; if this be the cafe, the feveral mutations will be into 
 contrarieties. It is neceffary, therefore, that matter Ihould be changed, 
 which is able to pafs into both. But, lince being is twofold, every thing 
 w' ich is changed is changed from that which is in capacity into that which 
 is in energy : as, from white in capacity, into white in energy ; and in a fimi- 
 lar n;anner with refpedl to augmentation and diminution : — hence, not only 
 all things may be generated accidentally from non-entity, but likewife from 
 being ; from being indeed in capacity, but from non-being in energy. And 
 
 * Viz. The celeftial fpheres, and the ftars which they contain. 
 
 this
 
 BookXII; ATIISTOTLE'S METAPHYSICS, 273 
 
 this is the one of Anaxagoras. For it is better to aflert this, than that all 
 things fubfifted together : it is likevvile preferable to the mixture of Enipe- 
 docks and Anaximander; and, as Democritus fays, all things were together 
 in capacity, but not in energy : fo that thefe men touched upon matter. But 
 all fuch things as are changed have matter, though in fome things it is of a 
 different kind from that of others : for the matter of thofe perpetual natures * 
 which are not generable, but moveable according to local motion, is itfelf not 
 generable, but is only moved from one place to another. But it may be 
 doubted from what kind of non-being generation fubfifts : for non-being is 
 threefold f . If, therefore, any thing is in capacity, from this generation 
 will fubflft, yet not from any thing indifcriminately, but one thing will be 
 generated from another. Nor is it fufEcient to fay that all things fubfifted 
 together ; for things differ in matter. For why were things infinite in 
 number produced, and not one thing, fince intelledl is one ? So that, if mat- 
 ter is one, that would have been generated in energy of which the matter is 
 in capacity. There are, therefore, three caufes and three principles; two 
 indeed contrariety, of which one kind is reafon and form, but the othec 
 privation : and the third principle is matter, 
 
 CHAP. III. 
 
 In the next place It is requifite to know that neither matter nor form Is 
 generated ; I mean that matter:): and that form which fubfift at the extremity 
 of things: for every thing which is changed is changed by fomething, and 
 into fomething. By fomething, indeed, viz. the firft mover ; but that In 
 which it is changed is matter ; and that into which it Is changed is form. 
 An infinite progreffion, therefore, muft take place, if not only the brafs is 
 made round, but the roundnefs alfo, or the brafs, is generated. It is therefore 
 neceffiry to ftop. After this, it muft be fhown that every effence is generated 
 from that which has the fame appellation with itfelf : for thofe things which 
 
 * Viz. Of the celeftlal bodies. 
 
 f Viz. Non-being is either that which is falfe, in the fame manner as being is that which is 
 true ; or it is that which in no refpe£l is ; or that wliich in capacity is not. 
 
 I Thus, fays Alexander, the four humors which are the matter of Socrates are generated, but 
 not the laft and formlefs matter : and again, flefh is a certain form of Socrates, but not the laft, 
 ilnce Socrates himfelf is the laft form. 
 
 N a are
 
 274 ARISTOTLE'S METAPHYSICS, Boor: XII. 
 
 are generated by nature, and alfo other things, are effences. For things are 
 generated either by art, or nature, or fortune, or chance. Art, therefore, is a 
 principle which fubfifts in another ; but nature is a principle fubfifting in the 
 thing itfelf : for man generates man. But the remaining caufes are the pri- 
 vations of thefe. Eflences, too, are three in number ; and one of thefe indeed 
 is matter, which is fome particular thing in confequence of that wh ch it ap- 
 pears to be : for fuch thing5 as are one by contadl, and not by coheficn, are 
 matter and a fubjcd. But another of thefe is nature, which is fonie particular 
 thing, and a certain habit, fubfifting as a boundary. Further ftill : the third 
 effence is that which confifts from thefe, and ranks among particulars ; fuch 
 as Socrates or Calllas. In certain things, therefore, that which is fome parti- 
 cular thing has not any fubfiftence independent of a compofite eflence ; as 
 for inftance, the form of a houfe, unlefs art is this form : nor is there any 
 generation and corruption of thefe : but the houfe itfelf, which is without 
 matter, likewife health, and every thing effefted by art, both are and arc not 
 after a different manner : for if forms have any fubfiftence they are in things 
 produced by nature. Hence, it is not badly faid by Plato that forms are fuch 
 things as have a natural fubfiftence, if there are forms different from thefe, 
 fuch as fire, flefh, the head, and the like : for all thefe are matter, and efpe- 
 cially belong to that effence which is the laft of things. Moving caufes, 
 therefore, are antecedent to produdions : but caufes which fubfift as reafon* 
 are confubfiftent whh produdtions. For, when a man is well, then health ia 
 prefent ; and the form of the brazen fphere fubfifts together with the brazea 
 fphere itfelf. But whether forms remain after feparation muft be conlidered ; 
 for nothing hinders this from taking place with fome forms : as, for inftance, 
 if foul fhould be a thing of this kind, not indeed every foul, but intelledl f ; 
 for perhaps it is impoffihle that this fhould be the cafe with every foul. It is 
 evident, therefore, that ideas are not requifite on account of thefe things; for 
 man generates man, fome particular, fome certain man. And in a fimilar 
 manner with refpedt to arts : for the medicinal art is the reafon of health. 
 
 * Viz. Formal caufes. 
 
 t Viz. The rational foul which is intelledual. 
 
 CHAP.
 
 BooKXIt ARISTOTLE'S METAPHYSICS. 275 
 
 C H A P. IV. 
 
 The caufes and principles of all things are partly the fame and partly differ- 
 ent ; tor, if any one fpeaks univcrfally, and according to analogy, the caufes 
 and principles of all things are the fame *. But it may be doubted whether the 
 principk's and elements of eflences, and of things which fubfift as relatives, 
 are different or the fame ; and In like manner with refpeil to each of the predi- 
 caments. But an abfurdity will enfue, if there are the fame principles and 
 elemen.s of all things. For relatives and effence will fubfift from the fame 
 things. What, then, will this be ? For, befides eiTence and the other predi- 
 caments, there will be nothing common. But an element is prior to the 
 things of which It is the element. Nor yet is effence the element of rela- 
 tives, nor Is any one of thefe the element of effence. Further ftill : how can 
 there be the fame elements of all things ? For no element can be the fame 
 with that which is compofed from elements ; as, for inflance, neither b nor a 
 can be the fame with ba. Nor is it poffible that any one of the Intelligible 
 elements, viz. the one or beings can be the element of all things : for thefe are 
 prefen: with every compofite nature. No compofite nature, therefore, will 
 have any fubfiftence, nor yet effence, nor relatives. It is, however, neceffary 
 that thefe ftiould fubfift. There are not, therefore, the fame elements of all 
 things. Or, as we have faid, are there partly the fame caufes and principles 
 of things, and partly not ? As, with refpeft to fenfible bodies, the hot Is as 
 form, and after another manner the cold, as privation ; but matter is that 
 which Is firft'effentially both thefe in capacity. But effences are as well thefe 
 as the things which confift from thefe, and of which thefe are the principles. 
 Or if any thing becomes one from the hot and the cold, as flefli, or bone, ftill 
 that which is thence generated muft be different from thefe. Of thefe things, 
 therefore, there are the fame, but of other things different elements and prin- 
 ciples. We cannot, however, fay that the principles of all things are after 
 this manner the fame ; but we may affert that this is the cafe according to 
 analogy: juft as if any one fhovild fay that there are three principles, form, 
 privation, and matter. But each of thefe is different about every genus ; as in 
 colours, white, black, fuperficics, light, darknefs, and air ; but from thefe day 
 
 * Viz. Matter, form, and privation, ;ire univerfally, and according to analogy, the caufes and 
 |)rinciples of material natures. 
 
 N n 3 emerges,
 
 S76 ARISTOTLE'S METAPHYSICS, Book XII. 
 
 emerges, and the night. However, fince not only things inherent are caufes, 
 but, of things external, fuch as that which moves is a caufe, it is evident that 
 principle is different from element. Yet both are caufes ; and into thefe prin- 
 ciple is divided : but that which moves or ftops is a certain principle and effence. 
 So that there are three elements according to analogy, but four caufes and 
 principles ; which four are different in different things. And the fiifl caufe, as 
 that which moves, is different in different things. Thus, health is as form, dif- 
 eafe as privation, body as matter, the medicinal art as that which moves. Again : 
 a houfe is as form, a certain confufion as privation, the bricks as matter, and 
 the builder's art as that which moves. And, indeed, into thefe things is prin- 
 ciple divided. But, fmce that which moves is Indeed in natural men* man, 
 but, in things proceeding from the dianoetic power, form, or the contrary, in 
 one refpedl there will be three caufes, but in another four. For the medicinal 
 art is in a certain refpedl health ; and the builder's art the form of the houfe ; 
 and man generates man. Further flill : befides thefe, as that which is the 
 firft of all things, there will be the mover of all things. 
 
 C H A P. V. 
 
 But fmce fome things are feparable and others Infeparable, the former are 
 effences, and on this account are the caufes of all things ; becaufe, without 
 effences paffions and motions have no fubfiftence. In the next place, thefe 
 will be perhaps foul and body, or intelled, appetite, and bodyf. Further 
 ftill ; principles are the fame after another manner by analogy, fuch as energy 
 and capacity : but thefe alfo are different in different things, and in a differ- 
 ent manner. For, in fome things, indeed, the fame thing is at one time in 
 energy and at another time in capacity ; as, for inftance, wine, or flefh, or 
 man. But thefe alfo fall into the above-mentioned caufes. For form is 
 energy, if it is feparable, as alfo that which confifts from both J ; but privation 
 is as darknefs, or as one that is fick, and matter is in capacity : for this is that 
 
 * Inftead of tv /xsv toi« tpvamoi;, as in the printed text, it appears from the Commentary of 
 Alexander, that we fliould read iv niv roi; ^utnxoij avflfwn-cij. For that commentator obferves that 
 Ariftotle fays natural men, on account of man itfelf, (/. c. the ideal man) who is not natural. 
 
 t Viz. The proximate caufes of animated natures are perhaps foul and body, as in plants ; or 
 intclle(S,body, and appetite, as in man i or body and appetite, as in brutes. 
 % Viz. Form and matter. 
 
 which
 
 BookXII. ARISTOTLE'S M ETAPHYS ICS. 277 
 
 which is able to become both. But thofe things which have not the fame 
 matter, and of which there is not the fame, but a different form, differ in an- 
 other manner in energy and capacity. Thus, the caufes of man are the 
 elements fire and earth as matter ; his proper form ; and if there is any 
 thing elfe external, inch as his father; antl, befides thefe, the fun and the 
 oblique cicle, which are neither matter, nor form, nor privation, nor of the 
 fame fpecies, but are motive natures. - Further ftlll: it is requifue to perceive, 
 tliJt of caufes, fome may be called univerfal and others not. The firft -■' prin- 
 ciples of ail things, therefore, are^ that which is in energy this firft thing "f, 
 and fomething ehe which is in capacity :{:. But thole things \\ hich are uni- 
 verfal have no fubfiftence. For that which is particular is the principle, as 
 one man is the principle of another; but there is no univerfal man. For 
 Peleus is the caufe of '\chilles, and your father of you ; and this letter i> is the 
 caufe of the fyllable Ba ; and, in (liort, l> is the caufe of da fimpiy confidered. 
 in the next place, the forms of efl'ences are principles : but, as we have faid^ 
 of different things there are different caufes and elements. Thus, the caufes 
 of thofe things which are not in tlie fame genus, fuch as colours, founds, 
 effences, quantity, are not the fame except according to analogy. The caufes 
 alio of thofe thingf. which are in the fame fpecies are different, but tbey are 
 not different in fpecies ; but becaufe of particulars, your matter, form, and 
 that which moves, differ in number from mine, though according to univerfal 
 reafon they are the fame. But in an inquiry, what are the principles and 
 elements of effences, of relatives, and qualities, whether they are the fame or 
 different, it is evident that, if they are predicated multlfarioufly §, there are 
 the fame principles and elements of every effence ; but if they are divided, 
 there are not the fame but different principles, except that there are the fame 
 in a certain refped ; for, according to analogy, there are the fame ; becaufe 
 there is matter, form, privation, and that which moves. So that, after this 
 manner, the caufes of effences are as the caufes of all things ; becaufe, effences 
 being taken away, all things are taken aw^ay. Further ftill : that which is 
 firft is in energy. Hence, contraries are in a different manner things firft, as 
 
 * That is to fay, the proximate principles. 
 
 f Viz. This particular thing, as Sophronifcus is the proximate principle of Socrates. 
 
 I I. e. This particular matter, 
 
 § /. e. Upiverfally. 
 
 they
 
 278 ARfSTOTLE'S METAPHYSICS, Book XII. 
 
 they are neither predicated as genera, nor as things multifarious. And, again, 
 different kinds of matter are called caufes : and thus- we have fliown what are 
 the principles of fenfibles, how many there are, and in what refpeit they are 
 the lame, and yet diiFereat from each other. 
 
 CHAP. VI. 
 
 Since it has appeared there are three cflences, two indeed phyfical, hut 
 one immoveable, refpeding this we muft fay, that it is neceffary there fliould 
 be a certain eternal and immoveable effence. For effences are the firft of 
 things ; and if all elTences are corruptible, all things will be corruptible. It 
 is, however, impoffible for motion either to be generated or corrupted ; for it 
 always was. This is likewife true refpecling time : for it is not poffible that 
 there can be prior and pofterior, time not exilling. There is the fame conti- 
 nuity, therefore, of motion, as of time : for time is either the fime as motion, 
 or a certain paflion of motion. But there is not any continued motion, except 
 that which is local ; and local continued motion is that which is circular. If, 
 however, there is fomething motive or effe^live, but not energetic, motion is 
 not. For it is poffible for that which has capacity not to energife. No uti- 
 lity, therefore, will enfue, though we fhould make eternal effences, in the fame 
 manner as thofe who make forms or ideas, unlefs a certain principle is inhe- 
 rent which has the power of producing mutation. Neither, therefore, will 
 this be fufficient, nor any other effence different from forms : for, if it does 
 not energife, there will not be motion. Nor yet will this be the cafe if it 
 energifes, but the effence of it is capacity : for there will not be perpetual 
 motion : for that which is in capacity may happen not to be. It is requifite, 
 therefore, that there fhould be fuch a principle, the effence of which is energy. 
 Further ftill : it is requifite that thefe effences fliould be without matter : for 
 it is neceffary they fliould be eternal, if there is any thing elfe eternal. They 
 are, therefore, in energy. A doubt, however, here arifes : for every thing 
 which energifes appears to have the capacity of energifmg ; but every thing 
 endued with capacity does not energife ; fo that capacity will be prior to 
 energy. But, indeed, if this were the cafe, nothing will have any fubfift- 
 ence ; for it will happen, that a thing will have the capacity to be, but will 
 not yet be. 
 
 But,
 
 BooKXir. ARISTOTLE'S METAPHYSICS. 2?9 
 
 But, if the. cafe is as theologifta aflert, who generate all things from 
 night, or if as the natural philofophers, who fay that all things fubfifted to- 
 gether, the fame impoflible confequence will enfue. For how could matter 
 be moved if there was no caufe in energy ? For the matter of a houfe does 
 not move itfelf, but the builder's art : nor does the menflrual blood move 
 itfelf, nor eanh, but feeds, and human feed. On which account fome have 
 recourfe to a perpetual energy, as Leucippus and Plato ; for they fay that 
 motion always is, but they do not lay why and what it is, nor why fome 
 things are moved differently from others ; nor do they afTign the caufe of 
 this perpetuity of motion. For nothing is cafually moved : but it is requifite 
 that fomething fhould always have fubfifted ; as at prefent, one thing is 
 moved naturally after this manner, and another is moved by force, either by 
 intellect or fomething elfe after a different manner. In the next place, what 
 is the nature of the firft motion ? for this makes an immenle difference. But, 
 neither is it poffible for Plato to call that a principle which moves itfelf, and 
 which fometimes he confiders as a principle. For, foul, as he fays, is pofte- 
 rior * to, and at the fame time confubfiileat with, the heavens. To confider, 
 therefore, capacity as prior to energy, is partly right and partly not. But in 
 what refpe£l it is right we have already declared. However, that energy is 
 prior to capacity Ana\-agoras teftifies ; for intelledt is energy. Empedocles 
 alfo teftifies this, by introducing friendlhip and ftrife ; and this is confirmed 
 by thofe who affert that motion is perpetual, as Leucippus. So that chaos or 
 night did not fubfift in an infinite time, but the fame things always were 
 which now are, either by circulation or otherwife, if energy is prior to capacity. 
 But if things are always the fame, either by circulation, or in fome other way, 
 it is requifite that fomething fhould always remain which poffcffes famenefs 
 of energy. But to the exiftence of generation and corruption it is neceffary 
 there Ihould be fomething v.'hich always energifes varioufly f . It is ncceffiry, 
 therefore, that after this manner it ftiould energife from itielf, but in a different 
 manner according to fomething elfe if. It muft, therefore, either energife 
 
 * Soul, according to Plato, in the Tiniseus, is reprefented as pofterior to the heavens, merely 
 hypothetically, or for the fake of doctrinal order. 
 
 f i. e. Obliquely, as the fun in his annual courfe. 
 
 % i, e. Says Alexander, according to the fphere of Saturn. 
 
 according 
 
 /
 
 280 A R I STOTLE'S METAPHYSICS, Book XII. 
 
 acordlng to that which is different, or according to the firft *. But it muft 
 neceilarily energife according to this f : for, again, this is the caufe of energy 
 botti to the one and the other. Hence, that which is firft J is the better 
 caufe : for it is the caufe of a perpetual famenefs of energy ; but fomething 
 ehe § is the caufe of variable energy. And both thefe are the caufe of an 
 energy eternally variable. After this manner, therefore, motions fubfift. 
 Why, then, is it requilite to inveftigate other principles ? 
 
 CHAP. VII. 
 
 Since, therefore, this Is the cafe (and if it were not fo, thm2;s would fub- 
 fift from night, from all things colledively and from non-entity), thefe quef- 
 tions may be folved ; and there is fomething which is always moved with an 
 unceafing motion; but this is a circular motion. And this is not only evi- 
 dent from reafon, but from the thing itf If So that the firft heaven will be 
 eternal. There is, therefore, fomething which moves. But, fince there is 
 that which is moved, that which moves, and that which fuhfifts as a medium 
 between thefe, hence there is fomething which moves without being moved, 
 which is eternal, and which is eifence and energy. But it moves in the fol- 
 lowing manner : That which is defirable and that which is intelligible move 
 without being movd. But the firft intelligible is the fame as the firft defir- 
 able : for that which appears to be beautiful is defirable. But the firft ohjedl 
 of the will is that which is really beauuful. However, we rather afpire after 
 it becaufe it appears to be beautiful, than it appears to be beautiful becaufe 
 
 * By the firft Ariftotle means the inerratic fphere. 
 
 + That is, fays /\lexander, it is ncccflary that the fun fliould be above and under the earth, 
 through the motion of the inerratic fpt ere, and not through the fphere of Saturn. But Ariftotle 
 fuggefts tli£ caufe why the fun is daily above and under the earth, when he fays, For this is the 
 caufe of energy, both to tie one and the other. That is, for again the body of the inerratic fphere 
 is the caufe of the itar which revolves in the fphere of Saturn becoming above and under the 
 earth, and alfo to the other, that is to the fun, fuice the motion of the inerratic fphere is the 
 caufe that the fun and Saturn daily rife and fet. 
 
 X That is, the inerratic fphere is the caufe that the fun always revolves above and under the 
 earth. 
 
 § That ip, the obliquity of the zodiac is the caufe that the fun is at one time in Scorpio and 
 at .another time in Capricorn.
 
 BookXIL ARISTOTLE'S metaphysics, 281 
 
 we afpire after It. For the principle is intelligence ; but intellect is moved 
 by the intelligible. And the other co-ordination* is effentially intelligible. 
 To this co-ordination alfo the firft eflence belongs, and likewife that which 
 fubfifts fiinply, and according to energy. But the one is not the fame with 
 the fimple : for the one fignifies meafure ; but the fimple^ the mode of fub- 
 fiftence. Likewife the beautiful, and that which is eligible for its own fake, 
 are in the fame co-ordination : and that which is the firft is always the beft, 
 or analogous to that which is beft. But, that in immoveable natures there is 
 that for the fake of which other things fubfif! . divifion manitefts : for there is 
 fomething to which that for the fake of which a thing is done belongs, of 
 which the one is different from the other f. But the firft mover moves as 
 that which is beloved ; and through that which is moved it moves other 
 things. But if there is any thing which Is moved, it may fubfift in a various 
 manner, ii, therefore, the firft lation is energy, fo far as it is moved, it may 
 fubfift difF.rently according to place, though not according to eflence. But 
 fince there is fomething which moves, itfelf at the fame time being immove- 
 able, and fubfifting in energy, this cannot fubfift in a various manner : for 
 lation is the firft of mutations; and of this that which is circular. But this 
 the firft mover moves. Hence, he is neceffarily being ; and fo far as he ne- 
 cefTarily fubfifts, fo far he fubfifts according to reditude, and is thus the prin- 
 ciple of things : for the neceflary is multifarious. For it either fignifies that 
 which is effetSled by violence, becaufe contrary to the will ; or that without 
 which a thing Is not well conditioned ; or that which does not admit of a 
 various, but pofTeffes a fimpllcity of, fubfiftence. From fuch a principle, 
 therefore, heaven and nature are fufpended. 
 
 But the life which he lives is the moft excellent, and fuch as we enjoy X 
 for a fmall portion of time j for fuch a life is with him perpetual. To us, 
 
 * By the other co-ovdinatioii Ariftotle means the co-ordination of the beautiful ; to which, 
 -according to the Pythagoreans, eflence, light, triangle, the odd number, &c. belong. 
 
 t That is to fay, that for the fake of which a thing is efFetSled is different from the thing 
 effeded. 
 
 X That is : "When from tlie exercife of the cathartic and theoretic virtues intelleft pafTes 
 into contaft with intelligibles, or, in other words, with thofe feparate incorporeal forms which 
 are the caufes of the fenfible univerfe, then it becomes intelligibles in energy, and enjoys the 
 mod excellent and blefled life, the felicity of which is indefcribable, and is only known to thole 
 who are capable of fuch an exalted energy : for intellect may then be faid to be ineliriated, 
 and to deify itfelf with nedar. 
 
 O o indeed, 

 
 282 ARISTOTLE'S METAPHYSICS. Book XIT. 
 
 indeed, tTiis is impoffible ; but not to the firil mover, becaufe his energy Is 
 pleafnre *. And on this account vigilance, the energies of fenfe, and intel- 
 lection, are moft delightful. Hope, too, and memory are pleafnig through 
 entrgie?. But effential intelle<fl:ion is the intelIe£tion of that which is effen- 
 tially the moft excellent ; and the moft effential of that which is moft effential. 
 Intelled, too, underftands itfelf by the affumption of the intelligible : for it 
 becomes intelligible by contadi and intellediion : fo that intellect is the fame 
 with the intelligible. For intelledl is the recipient of the intelligible, and of 
 effence. But it encrgifes poffeffing. Hence, that which intelle£t appears 
 to poffefs as divine, belongs more eminently to the firft intellect than to ours : 
 and his contemplation Is the moft delightful, and the beft. If, therefore, 
 God always poffcffes that excellent condition of being which we fometimes^ 
 poffefs, It is admirable ; but, if he poffeffes It In a ftill higher degree, It is ftill 
 more admirable. In this manner, however, he fubfifts. 
 
 Life alfo is prefent with him : for the energy of intelle£l is life ; and he is 
 energy. But effential energy is his moft excellent and eternal life ; and we 
 fay that God is an animal eternal, and the moft excellent : fo that life and 
 duration continued and eternal are prefent with God. For God Is this. 
 
 But thofe who are of opinion, like the Pythagorceans and Speufippus, that 
 the moft excellent and the moft beautiful are not inherent in the principle of 
 things, becaufe the principles of plants and animals are indeed caufes, but the 
 beautiful and the perfect are in things proceeding from thefe, do not think 
 rightly : for feed Is from other perfedt natures which have a prior fubfiftence : 
 nor Is feed the lirft thing, but that which is perfedl ; juft as fome one may 
 fay that man is prior to feed, not Indeed the man who is generated from feed, 
 but another from whom feed flows. That, therefore, there is a certain eternal 
 immoveable effence, and which Is feparated from fenfibles, is evident from 
 what has been faid. It has alfo been ftiownf that this effence cannot poffefs 
 any magnitude, but that It Is impartible and indivifible ; for It moves In aa 
 infinite time. But nothing finite pofleffes an infinite power. Since, however, 
 every magnitude is either infinite or finite ; hence, this effence will not poffefs 
 
 * For, (ince the employment or energy of the firft intellt£l is alone the intellection of him- 
 felf, i. e. an eternal and all-comprehenfive view of the divine forms contained in the unfathom- 
 able depths of his eflcnce, and fince this very energy is pleafure^ hence, in this pleafure he per- 
 petually* lives. 
 
 t In the eighth book of tlic PhyCcs. See the Inttodudion to this work^ 
 
 a finite
 
 BookXII. ARISTOTLE'S metaphysics. 283 
 
 a finite magnitude : and It cannot poflefs an infinite magnitude, becaufe an 
 infinite magnitude has not any exiftence. It has Ukewife been ftiown that 
 he is without palfivity, and unchangeable : for all other motions are pofterior 
 to that which is local. Thele arguments, therefore, evince why he fubfifls 
 in this manner. 
 
 CHAP. VIII. 
 
 But we ought not to be ignorant whether one eflence of this kind is to be 
 admitted, or more than one, and if more than, one how many ; but we fhould 
 alio call to mind the opinions of others, becaufe, concerning the multitude 
 of fucli like effences, they have faid nothing certain and clear. For the opi- 
 nion refpedling ideas has not any appofite fpeculation, fince thofe wlio 
 alfert that there are ideas call them numbers. Eut, refpeding numbers, they 
 fometinies fpeak of them as of things infinite, and fometimes as of things 
 limited as far as the decad. Nothing, however, is afferted by them with 
 demonftrative diligence, why there is fuch a multitude of numbers. This 
 then muft be declared by us, from the things pre-fuppofed and determined. 
 
 The principle and the firft of beings is immoveable both eflentially and 
 according to accident ; but he moves the firft, eternal, and fingle motion. 
 But fince that which is moved muft neceffarily be moved by fomething, and 
 that which firft moves is eflentially immoveable, and an eternal motion muft 
 be moved by an eternal mover, and one by one ; and fince we fee that be- 
 fides the fimple lation of the univerfe, which we fay the firft and immoveable 
 eflence moves, there are alfo other eternal lations of the planets — (tor a body 
 which revolves in a circle is eternal and unftable, as has been (hown in the 
 Phyfics) — fince this is the cafe, it is necejfary that each of thefe lations Jlooiild 
 be moved by on ejfentially immoveable and eternal ejfeuce : for the nature of 
 the ftars is a certain eternal elTence, and that which moves is perpetual, and 
 prior to that which is moved ; and that which has a prfority of eUcnce is 
 neceffarily eflence. // is evident^ therefore^ that there are necessarily /» 
 many ejfaices^ naturally eternal^ ejfentially immoveable^ and ivithout mognitiide^ 
 for the reafon already aftigned. That there are therefore efl'ences, and which 
 of thefe is firft and which fecond, according to the fame order as that of the 
 revolutions of the ftars, is evident. 
 
 But the multitude of thefe lations muft be confidered from that philcfophy 
 
 O o 2 of
 
 28 i _ ARISTOTLE'S METAPHYSICS. Book XIL 
 
 of the matlienialical fciences which is mod: peculiarly adapted to this piirpofe, 
 viz. aftronomy. For this contemplates an eflence, fenfibie indeed but eternal; 
 but the other mathematical fciences Ipeculate no eflence whatever ; for this 
 is neither efiecled by the fcience which is converfant with numbers, nor by 
 geometry. That there are thefefore many lations of the ftars is evident to 
 thofe who are hut moderately converfant vv^ith thefe things : for each of the 
 planets is borne along with more than one lation. But how many thefe are 
 we fhall now explain ; and, that we may underfland their definite number, 
 relate what certain* mathematicians afiert. As to what remains, it is proper 
 that we ourfelves fliould inveftigate fome things, and afk fome queftions of 
 thofe who fearch into thefe affairs, that we may know whether any thing 
 appears to them in addition lo what we have faid. Both, however, are to be 
 beloved, but aflent is to be given to the more accurate* 
 
 Eudoxus, therefore, places the lation of the fun in three fpheres, and alfo 
 that of the moon ; of which the firft is that of the inerratic ftars f j the fe- 
 cond is through that circle which pafles through the middle figns of the 
 zodiac ; and the third through that circle which is oblique J in the latitude 
 of the figns. But that oblique circle through which the moon is carried, 
 is in a greater latitude than that through which the fun is carried §. But 
 Eudoxus places the lation of each of the planets in four fpheres ; and of thefe 
 he confiders the firft and fecond as the fame with thofe of the fun and moon j 
 but the fphere of the inerratics is, according to him, fimilar to that hrtt fpliere 
 of the heavens which carries all the orbs ; and that which ranks under this,, 
 and is carried through the middle of the zodiac, is common to all of them. 
 He is alfo of opinion that the poles of the third fphere, which is comm<m to 
 all, are in that fphere which is in the middle of the figns j and that the lation 
 
 * By certain mathematicians, Ariftotle according to Alexander means Eudoxus and Calippua. 
 
 t That is, fays Alexander, (Ince the lation of the fun is effefled by three ipheres according 
 to Eudoxus, the firft of thefe, which comprehends the other two, and which revolves fimilar to 
 the inerratic fphere, viz. from eaft to weft, was confidered by Eudoxus as inerratic with reference 
 to the other two. Nor did he only call this firft fphere of the fun. inerratic, but likewife the 
 lirft and largeft fphere of each of the other planets. 
 
 X That is, according to Alexander, that circle which the fun appears to defcribe from its 
 centre, while it is borne along by that fphere to which it is fixed. 
 
 § The latitude, fays Alexander, of the obliquity of that circle which the moon appears to 
 defcribe with its centre, is greater than the latitude of the obliquity of that circle which the fun 
 appears to defcribe. 
 
 of
 
 Book XH, ARISTOTLE'S METAPHYSICS. 285 
 
 of the fourth declines from the middle of the third. Likewife that the poles 
 of the third fphere are the proper poles of the other fpherts; but that Venus 
 and Mercury have the fame poles. 
 
 But Calippus gives the fame pofition to the fpheres, that is, the lame order 
 of diftance, as Eudoxus : and, wi'h refped to their multitude, he agrees v\Mth 
 him in the number belonging to Jupiter and Saturn, but is of o[)inion that 
 ftill two fpheres require to be added to the fun and moon in order to folve 
 the phenomena ; and to each of the remaining fpheres of the planets he 
 adds one. But it is necefTary, in order, when all of them are collecled toge- 
 ther, to affign the caufcs of the phenomena, that there fhould be other re- 
 volving fpheres lefs in number by one, than thofe which cai ry the planets, 
 *nd which always reflore in the lame polition the firft fphere of that ft ir 
 ■which ranks in an interior order : for thus alone can all things be effected 
 by the lation of the planets. Since, therefore, with refpedl to thofe fpheres 
 in which the planets are carried, fome are eight, and others twenty-five ; of 
 thefe. thofe only ought not to have revolving fpheres in which the lowed* ftar 
 is carried. And thofe, indeed, which revolve the fpheres of the two firft 
 flars will be fix; but thofe which revolve the fpheres of the four pofterior 
 ftars will be lixteen. The number, therefore, of all the fpheres, that is, 
 both of thofe that carry and thofe that revolve the ftars, will be fifty-five. 
 But, if thofe motions of the fun and moon which we have mentioned are not 
 addeJ, the number of all the fpheres will be forty-feven. Let this then be 
 the multitude of the fpheres : fo that it is rational to conceive that there are 
 as many immoveable and as manyfenfible eflences and principles as we have 
 enumerated; for to prove "f that there muft neceftarily be tliis nuuiber, muli 
 be left to thofe who are better qualified for fuch an undertaking. 
 
 But if it is not polfible that there can be any lation which does not contri- 
 
 * Viz. The moon; for fhe is the loweft of the planets. 
 
 f " Ariftotle, fays Alexander, having related the number of the fpheres, which according to 
 Eudoxus are ^6, according to Calippus 33, and according to his own invention 55 ; and having 
 befides this demonftrated that one fimple and eternal motion emanates from one fimple and 
 indivifible mover, he confidently aflerts that it is rational to conceive that there are as many 
 immoveable and as many fenfible eflences and principles as he has enumerated But becaufe 
 he has only related, but has not alfo demonftrated, that there are 55 fpheres, and has aflerted 
 that it is reafonable to conceive that there are as many immoveable eflences as there are fpheres; 
 htnce he fubjoins, that a dcmonltration that there muft neceiiarily be this number, muft be 
 left to ihofe who are better qualified for fuch an undertaking." 
 
 bute 
 
 /
 
 2»fl AHISTOTLE'S METAPHYSICS. Book XIL 
 
 bute to the lation of a ftar; and if it is requifite to conceive thai every nature 
 and every elTence which is impaffive, and capable of fubfifting from itfeif, is 
 allotted the befl end, there will be no other nature befides thefe, but this 
 will neceflarily be the number of efiences. For, if there are others, they will 
 be motive, as being the end of lation : but it is impoffible that there can be 
 any other lations than thofe which we have enumerated. But this hiay be 
 rationally inferred from thefe revolving bodies themfelves : for, if every thing 
 which carries naturally fubfifts for the fake of that which is carried, and every 
 lation is of fometr.ing which is carried, no lation will lublift ibr its ov^'n fake, 
 nor for the fake of another lation, but it will fubfiil for the fake of the flaro. 
 For, if lation fhould fubfifl: lor the fake of lation, it will alfo be requifite that 
 this latter Ihould fubfift for the fake of other lations,. So that, fince it is im- 
 poffible that there can hs an infinite .progrefllon, the end of every lation will 
 be fome one of -the divine bodies which revolve in the heavens. But that 
 heaven * is one is manifeft : for, if there were many heavens, as there are men, 
 the principle about each will be one in fpecies, but many in number. But 
 fuch thinj^r- as are many in number are connefted with matter : for there is one 
 and the fame reafon of tliC many, as of man, but Socrates is one. But that 
 which ranks as -the firfl among formal cauies is not conneft^d with matter ; 
 for it fubfifts in energy. Hence, that which firfl moves immoveably is 
 one both in reafon and number; and, confequently, that Vv'hich is always 
 and continually moved is alfo one. There is therefore only one heaven or 
 univerfe. 
 
 But OtJR ANCESTORS AND MEN OF GREAT ANTIQUITY HAVE LEFT 
 
 US A TRADITION INVOLVED IN FABLE, THAT THESE FIRST ESSENCES 
 
 ARE GODS i', AND THAT THE DIVINITY COMPREHENDS THE WHOLE OF 
 
 NATURE. 
 * i. e. The univtifc". 
 
 •j If the tloiSlrine of polythcifm confided in admitting that there is a multitude of principles 
 equal in dignity and power to the great and ineffable principle of things, the cenfure which has 
 been repeatedly paffed on this doflrine, with fo much zeal, by modern tlieologifts, would be 
 highly juft, fmce it is a hypothefis no lefs falfe in its principles than dire in its confequences. 
 This, however, was far from being true of the polytheifm of the antient world, as is largely 
 {hov,n by Dr. CuJworth in his Intelledual Syftem, and nuift be obvious to every one who 
 reads with attention the temains of -Grecian and Roman literature. But, on the other hand, 
 to cenfure the doctrine, that producing eaufesof things fubfift concentred and rooted in one fivft 
 producing caufe, but with due fubordinalion to their comprehending principle, is to oppofe one 
 of the mod fublime conceptions of the human mind, endeavour to lubvert the heaven-buik 
 
 fabric
 
 FooKXrr. ARISTOTLE'S METAPHYSICS. 2«7 
 
 NATURE. The reft indeed is fabuloufly introduced for the purpofe of per- 
 fuading the multitude, enforcing the laws, and benefiting human life. For 
 
 they 
 
 fabric of intellectual pliilofophy, and, in mythological language, to war on the Olympian 
 gods. 
 
 To fuch, indeed, as have not regularly ftudied the fcientific writings of Plato and Ariftotle, it 
 will doubtlefs in the firft place feem abfurd to introduce a multitude of principles in order to 
 the production of the uaiverfe. To thefe, one principle appears fufficient for the purpofe ; and 
 the hypbthefis of a multitude fubfilling in conjundtion, and co-operating, with him, is confidered 
 as ufelefs, and as tending to diminifli the power and fully the dignity of the parent of things. 
 They will likewife deem it impoOible to conceive how a multitude of principles can have a dif- 
 tincl energy of their own, at the fame time that they are comprehended in, and energife toge- 
 ther with, a higher caufe. 
 
 The firfl of thefe objeaions may be eafily removed, by confidering that the mofl: perfed mode: 
 of produdion is the ejfential, or, in other words, when a beiiig produces by its very nature or 
 eflence. Inftances of this ejfential mode of producliou are feen in fire and fnow, the former 
 tjfentially imparting heat, and the latter eold. This mode is more perfedl than that which is 
 attended with deliberation, becaufe more extended. Thus, all fuch beings as produce delibe- 
 ratively, as is the cafe with rational fouls like ours, are at the fame time connecled with the 
 tjfential operation; fuch as is the energy of nature in generation, nutrition, and increafe. But 
 the energy of nature is prefent with beings to whom the power of deliberation is unknown* 
 And hence the ejfential is more extended than the deliberative energy. 'I he effential energy, 
 therefore, muft be the prerogative of the higheft producing caufe, becaufe more poweilul 
 than the deliberative : for fuperiority of power is always the charaderifticof a fuperior caufe. 
 
 If, therefore, the great principle of things operated from his very nature in producing all 
 things, and this without the conjundion of fubordinate caufes, and if he is the one itfelf (fmce 
 nothing is more excellent than unity), all things would have been profoundly one, without any 
 apparent di[lin£tion and feparation : for, in produdions of this kind, the efled is always /■««- 
 darily what the caufe is according to 2l primary mode of fubfiftence. The exiltence,.therelore,. 
 of the corporeal world neceflarily proves the exiftence of leffer producing caufes co-operating, 
 with the one father of all in the produftion of things. 
 
 The fecond objedion, refptfting ilic diftind: energy of fubordinate caufes, or principles, may 
 be removed by diligently attending to the diiferent powers of the human foul. Eor in thefe 
 powers, as images, we fhall confpicuoufly fee, how a multitude of divine natures may poffefs a 
 diftinit energy of their own, at the fame time that they are comprehended in, and cnergiie to- 
 gether with, a fuperior nature. If we furvey, then, the gno ilic powers of the faul, we Ihall find, 
 that they are accurately five in number, viz. intelUS, the diametic power, opitiiin, phaniafy, and 
 fenfe. 
 
 Intelha is that power by which we underftand fwnple felf-evident truths csklled axioms, »nd- 
 are able to pafs into contad with intelledual forms fcparatedfrom.allconnedion with matter. 
 
 By the diarjoetic pctuer we reafon fcientifically. 
 
 Opinion is that which knows the univerfal in fenfible particulars, as that every man iS a, 
 
 biped ; and the conclufion of the dianois'tic power, as that every rational foul is immortal ; but 
 
 it only knows the en, or that a thing is, but is perfedly ignorant of the 3ioT<, or why it is. 
 
 The
 
 258 ARISTOTLE'S METAPHYSICS, Book XII. 
 
 they afcrlbe to the firft eflences a human form, arid fpeak of them as re- 
 fembhng other animals, and affert other things confequent and fimllar to 
 
 tliefe. 
 
 The phnfitajy is that power which apprehends things clothed with figure, and may be called 
 ^figured intdligence [ij.cff!i]riiivt vonii;.) 
 
 Laftly, ft'i^ife is that power which is diftributed about the organs of fenfation, which is 
 mingled with paffion in its judgment of things, and alone apprehends that by which it is exter- 
 nally agitated. 
 
 Now, it is evident, fince the energies of thefe powers are perfecflly dlftin£t from each other, 
 that the powers thcmfelves, which are the fources of thefe energies, muft alfo be diftncl. 
 
 Again : it is evident that ilejirt, which tends to one thing, a/iger, which afpires after another 
 tiling, and free-^vil!, or that delibemtive tendency to things in our poiver, which the Greeks call 
 proairefis (Trfoaijifo-ij), are fo many diflinft vital powers of the foul. But above both lae gnoftic 
 and vita! powers is the one, or the fummit of the foul, by means of which we are enibled to fay, 
 I percsivc — i opine — I reafon — I defire — I deliberate — which fummit follows all ti.efe energies, 
 and energifes together with them ; for we Ihould not be able to know all tliefe, an-i to appre- 
 hend in what they differ from each other, uniefs we contained a certain indivUibl? nature, v.hich 
 fubfifts above the common fenfe, and which, prior to opinion, defire, and will, kiiowj all that 
 diefe know and defire, according to an indivifible mode of apprehenfion. 
 
 It mult, however, be carefully obferved, with refpe(3: to thofe mighty privprs which fubfift 
 in unproceeding union in the ineffable principle of things, that, as their union with this prin- 
 ciple is infinitely more tranfcendent, their chara6feriftic properties are iikeviife i;ifinitdy more 
 diftinft from each other, and from the one caufe of all, than the union and dillinction between 
 the human foul and its different powers. 
 
 But as tliis is a fubjecl of all others the mofl important, it is requifite to be more explicit. If 
 then it is neceffary that the progrefllon of beings fhould be continued, and that no vacuum fliould 
 Intervene cither in incorporeal natures, or in bodies themfelves, it is alfo necefliiry that every 
 thing VI hich has a natural progreffion (hould proceed through, fimilitude ; fince it is by no means 
 lawful that the thing caufed fliould be the fame with its caufe : for, if that which is fecond were 
 the fame with that which is firll, each would be fimilarly the fame, and one wouiJ not be the 
 caufe, and the other the thing caufed. But if they are alone different, they can never be con- 
 joined with each other, nor can the one participate of the other : for conjunction and partici- 
 pation are a communion and fympathy of participants, and the natures they participate. And if 
 tliey are at the fame time \tQr\\ fame and different ; fince in this cafe there is identity, defeft, and 
 fomcthing which is vanquiflied by a power contrary to famenefs ; the one itfelfvt'iW no longer be 
 the principle of the progreffion of beings, nor will every generative raufe have a fubfiflence in 
 the order of the good piior to fecondary caufes : for the one is not the caufe of divifion, but of 
 friendfliip ; and the good converts generated natures to their caufes. But the converfion and 
 friendfhip of fecondary towards prior natures fubfifts through fimilitude, and not through a dif- 
 fimilar nature. If, therefore, the one is the caufe of the univerfality of things, and if the good 
 Is the objeft of vehement defire to all things, it will everywhere conftitute ihrough fimilitude 
 the progeny of antecedent caufes : fo that the progreffion of things will fubfilt according to the 
 0ne, and the converfion of thefe progrellions will be directed to the ^ood. For neither is conver- 
 
 fioa
 
 BookXII. ARI STOTLE'S METAPH YS IC S. 28? 
 
 thcfe. But if among these assertions any one separating the 
 
 REST RETAINS ONLY THE FIRST, VIZ. THAT THEY CONSIDERED THE 
 
 FIRST 
 
 fion without fimilitude, nor can t!ie generation of efFc£ls wliich return to tlieir kindred principles 
 ever fubfifl; without this. 
 
 But riiat which immediately follows, and is demonflrated from this, is, that it is neceflary every 
 n-.onad fliould produce a number of the fame order with itfelf, viz. Nature, a natural number. 
 Sou!, one that is animadic, and IntellcJ, an intellectual number. For, if whatever pOiTeflcs a 
 power of generating generates finiilars prior to dilfimilavs, as we have already demonilratjd, 
 hence every caufe muft deliver its own form and idiom to its progeny; and before it generates^ 
 that which gives fubfiflence to progreffions far diftaut and fep.iratc from its riature, it mult con- 
 ftltute things proximate to itfelf according to eflence, and conjoined with it through fimilitude. 
 Every monad, therefore, conftitutes a multitude, indeed, as generating fomething pofterior to 
 itfelf, and dividing the powers which had a prior occult fubfilteiice in itfelf- For things which 
 fubfifted uniformly, and conjointly, in the monad appear feparately in the progeny of tlie monad. 
 And the truth of this, indeed, iimvci-fal Nature herfelf declares, comprehending in one the pro- 
 dudtive principles of all things contained in the heavens and in the fublunary regions ; but dif- 
 tributing her own powers to the natures which, proceeding from her monad, are divided about 
 the fluctuating empire of bodies. For the nntuivs of fire, earth, and the moon, poilefs their 
 idioms and forms from uiuvcrfal nature, with whicli theyenergife, and contain its peculiar diflri- 
 butions. But this alfo the monad of mathematics and numbers evinces: for, fince this is pri- 
 marily ;dl things, and fince it fpermatically conftitutes the forms of numbers in itfelf, it diftri- 
 butes difrcrent powers to numbers externally proceeding froni its nature. For it is impoflible 
 that a generated nature fliouUl at once receive the ^vhole abundance of its generating caufe : and 
 it is neceflary that the caufe of all things, having a prior fubfiltence, (hould appear as a prolific 
 power. Multitude, therefore, fubfifts about the monad, and number, diftributing the propertica 
 which abide colleiTtively in the monad. Becaufe, therefore, as we have before obferved, that 
 which is fimilar is more conjoined with its caufe than that which is diffimilar; hence one pro- 
 grellion will be a multitude fimilar to the monad from wliidi it proceeds ; but tlic other will be 
 a multituile of diffiniilars. Hut the multitude whicii is fimilar to the monad will be tliat in a 
 divided manner which the monad is indivifibly. For, if the monad poffeiTes power, and a pe- 
 culiar hyparxis *, the multitude proceeding from it will likewife contain the fitme form of 
 hyparxis, with a remiflion as io the whole. 
 
 But after this it is neceflary to confider in the third place, that, of progrelTions, fuch as are 
 nearer to their caufe are indicative of a greater multitude of things, and are at the fame time 
 In a certain refpc<n: equal to their containing caufcs : but that fuch as are more remote polTefs 
 3 lefs extended power of fignification ; and, on account of the diminution of tlieir power, change 
 and diminifh at the fame time the amplitude of produdion. For if, of prcgrefiions, that which 
 fubfifts the firft in order is more fimilar to its principle, and that Vvhich gives fubfiftence to tlic 
 greateft number is both with refpecft to eflence and power more fimilar to the generatmg prin- 
 ciple of all things, it is neceflary that, of fecondary natures, fuch aj are nearer to the monad, and 
 .which receive dominion after it, fliould give a greater extent to their productions ; but tha* 
 
 * Hyparxis fignilics in any being tlie fiimmit, or as it wcic flower, of xK oittire. 
 
 PP fur^ 
 
 /
 
 2<?0 A R I S T O T L E ■ S M E T A P H Y S I C S. Book Xlf. 
 
 FIRST LSSENCIS TO BF. GODS, HE WILL THINK IT TO BE DIVINELY SAID ; 
 AND IT MAY BE PROBABLY INFERRED, THAT AS EVERY ART AND PIII- 
 
 LOSOPUY 
 
 fuch things as arc more fcp.irateil from t'acir priinary monad fliould neitlier pervade in a fimilar 
 manner through all things, nor extend their elficacious energies to far diftant progreiTions. And 
 again : as fimiljr to this, it is necelfary that the nature which gives fubfiflence to the greateft num- 
 ber of effeds fliould be placed next to the monad, its principle ; and that the nature generative 
 of the moil numerous progeny, becaufe it is more fimilar to the fupplying caufe of all things tliaii 
 that which is generative of a few, mud be placed nearer to the monad, according to hyparxis. 
 For, if it is more remote, it will be more diffimilar to the firft principle ; but, if it is more difli- 
 milar, it will neither poflefs a power comprehending the power of fimilar natures, nor an energy 
 abundantly prolific. For an abundant caufe is allied to the caufe of all. And univerfally, 
 that which is generative of a more abundant, is more naturally allied to its principle than that 
 which is productive of a lefs numerous progeny. For a defeft of power is effeflive of fewer 
 produflions : but a fubje£tion of efience is a defeft of power; and a fubjedlion of eflence be- 
 comes redundant, on account of diffimilitude with its caufe, and diftance from its principle. 
 
 Again, therefore, in addition to what we have previoufly demonflrated, we fliall aflert ihat 
 which polTefies the mofl indubitable truth -, I mean, that it is requifite, prior to the caufes which 
 are participated, that imparticipable ' caufes (hould every where have a prior fubfiftence in the 
 univerfality of things. P'or, if it is requifite that a caufe Ihould have the fame relation to its 
 progeny as the oiieio the univerfal nature of beings, and that it fhould naturally poflefs this order 
 towards things fecondary ; and it the one is imparticipable, as being equally exempt from all 
 beings, and as that which is produ£live of all things uniformly; — in conletjuence of this, it is 
 neceflaiy that every other caufe which defcribes the excellency of the sue in ail things fliould be 
 exempt from the beings fubfifl;ing in fecondary ranks, and from the natures participated by 
 them. And again, it is requifite that every imparticipable and primary caufe which is fimilar to 
 the one-, fliould ellablith monads of fecondary natures fimilar to itfelf prior to fuch as are difli- 
 milar. 1 fay, for inilance, it is requifite that one foul fliould dillribute many fouls to different 
 natures; and one intelleft participated intellects to many fouls. For thus every firft exempt 
 "enus among the divine orders will be univerfally dillributed analogous to the one. And fecond- 
 ary natures which participate kindred caufes will be analogous to rhefc exempt genera ; and, 
 through the fimilitudc of their kindred caufes, will be conjoined with their imparticipable prin- 
 ciple. Hence, prior to the forms fubfifling in other natures, thofe arc eltabliflied which fubfill 
 in themfelves; and prior to compofite caufes fuch as are exempt ; and imparticipable monads 
 prior to fuch as are participable. And confequently (as that which is demonflrated at the fame 
 time with this) the exempt caufes are generative of fuch as arc compofite, and imparticipable 
 natures extend participable monads to their progeny. And natures which fubfifl in themfelves 
 produce the powers which are refident in other natures. 
 
 It is therefore necclTary from the preceding axioms, fince there is one unity, the principle of 
 the univerfc, from which every hyparxis derives its hypoflafis, that this unity fliould produce 
 
 . • One thing is f.iid to be imparticipable with rifpeft to another, to which it is fupcrior, when it is not confubfiftcnt 
 with it. 
 
 from
 
 BookXH. ARISTOTLE'S METAPHYSICS. 291 
 
 LOSOPHY HAS BEEN INVENTED AS OFTEN AS POSSIBLE, AND HAS 
 AGAIN PERISHED, THESE OPINIONS ALSO OF THE ANTIENTS HAVE 
 
 BEEN 
 
 from itfelf, prior to every thing elfe, a multitude of natures charadlerifed by unity and a num- 
 ber the mod of all things allied to its caufe. 
 
 For, if every other caufe eflabliflies a progeny fimilar to itfelf, prior to that which is diffimi- 
 lar; much more mufl the one, fmce it is fuperior to fimilitude, and is the one iifilf, produce 
 according to union its firll progeny. For how can the one eftablifh its proceflions, except in a 
 manner characlerifed by unity .' For nature generates things poilerior to itfelf naturally, foul 
 animaflically, and intellect intellcdiually. The one, therefore, is through union t'lc caufe of tlic 
 univerfality of things: and the progreilion from the one is uniform. But \i the one is that whlcli 
 firft produces all things, and the progrefTion is characlerifcd by unity, it is requlfite that the 
 multitude produced from thence fhould he felf-perfefT unities, the inoft allied of all things to their 
 producing caufe. Befides, if every monad eftablKhcs a number allied to itfelf, as we have pre- 
 vioufly ilemonflrated, by a much greater priority muft the one itfelf produce a number of this 
 kind. For, in tlie progreffion of things, that which is produced is often diffimilar to that virhicli 
 produces, through the over-ruling fway of diverfity : and fuch are the laft of beings, and thofe 
 wh.ich are far diflant from their principles. But the firfl number, and that which coheres to the 
 one, is uniform, ineff.iblc, and fupercffential, and is entirely fimilar to its caufe. For, neither can 
 divcr.'iiy jiappeniiig to firfl canfes feparate generated natures from their generating caufe, and 
 transfer them into another ortkr ; nor can a motion of the caufe, producing a fubjcdlion of 
 power into dilTimilitude and infinity, produce the generation of the univerfality of things : but 
 the caufe of all, excelling all motion and divifion, according to the chara£leriilic of unity efla- 
 bllQies about itfelf a divine number, and conjoins it with its own fimplicity. The one, there* 
 fore, prior to beings eflabliflies the unities of beings. 
 
 For, again, according to another mode of fpeculation, it is neceflary that fuch things as are 
 firft fhould participate the firO: caufe through their proximate unities : for all fecond natures are 
 conjoined witli their anteceilents ihrou^^h fimilars. Thus, bodies through particular fouls are 
 conjoined with univerfal foul ; fouls with univerfal intellect, through intelleftual monads; and 
 firil beings with the one itfelf, through uniform hyparxes. I"or, being itfelf, according to its oun 
 nature, is diffimilar to the one. For elTeiice, becaufe indigent of an unity externally afi'iimed in 
 order to accomplifh the firll union, cannot of itfelf be conjoined with that \»h;i;h is fuperefien- 
 tial, and is far diftant from its nature. But the utiities of bcitigs which fubfifl from the im- 
 pavticipable and exempt unity are able to conjoin beings with the one itfelf, and convert tiiem to 
 their own fupereflential naUires. And Parinenides, demonftrating this in his fecond liypothefis, 
 connefts ihe one with being, contemplates all things about the one, and dL;nonn.rat<a that this na- 
 ture, which proceeds and finiflies its progrelfion with the laft of things, is the one it'elf. For it 
 is neceflary that the unities fliould be cftabliflied prior to true beings themf;lvcs ; fince, ns 
 TimKUs obferves, it is not lawful for him who is the firfi-, to produce any thing except that 
 which is the moll beautiful of all. But this is tlie mofi fimilar to t!ia: which is fingui.irly the 
 beih 
 
 But a multitude cliaraflcriftd by unity is the nioft fimilar to the one. For the Demiurgus cf 
 the univi.rfe, becaufe he is gooil, conflituted all things fimilar to Isimfglf. Much more, ihcre- 
 
 P p 2 fore, 
 
 /
 
 292 ARISTOTLE'S METAPHYSICS. Boose XIK 
 
 BEEN PRESERVliD AS RELICS TO THE PRESENT TIME. Of the Oplnl.^lS 
 
 of onr fathers, therefore, and men of the highefl: antiquity, thus much only is 
 
 tnanifeft to u?. 
 
 CHAP. 
 
 fore, muft the fountain of univerfal good produce and cRablifh in beings gocdm-ffes naturally 
 ccnjo-ned with himfclf. There is, therefore, one god, and many gods ; one unity, and many 
 unities, prior to beings themfclves ; and one goodnefs, and many poflerior to the firll goodnefs, 
 through wliich that beneficent intelleiS the Demiurgus, and every intellect, is divine, whether it is 
 an intellectual or intelligible intelleft. And that which is the firft fuperefTential is the one ; 
 after which many fuperelTcntials fubfifl:. Whether, then, is this multitude of unities imparti- 
 cipable, as the one itjclf, or is it participated by beings, fo that the unity of every being is as the 
 flower, fummit, and centre of chat being about which it fubfifts ? But if thefe unities are impar- 
 ticipable, in what refpecTt do they differ from the one? For each of thefe unities is one, and has 
 the firfl: fubfiflence after the cue. Or how, fince they are exuberances of the firft caufe, vvere they 
 conftituted by it ? For it is every wliere neceflary that the nature which is fecond fliould be fub- 
 ject to that which is prior to itfelf, fhould fall off from its union, and en account of fome addi- 
 tion fliould diminfli the monadic fimplicity of that which is firfl. What addition, therefore, or 
 redundancy can we aflert in addition to the om, if each of thefe unities is an unity by itfelf? 
 For, if every unity is both one and many, we fhall appear to transfer the property of being to 
 the unities themfelves. But if it is one only, in the fame manner as that which is one itfelf, 
 why does this latter pofTefs a caufe exempt from all other caufes, while each of the unities is 
 allotted a fecondary dignity ? On this hypothefis, therefore, we fliall neither preferve the fupre- 
 macy of the firfl. caufe over pofterior natures, nor eftablifh the progreffion of the unities from 
 the firft, unconfufid either with refpe£l to themfelves, or the one principle of their fubfiftence. 
 
 But neither fliall we believe in Parmenides*, producing the one together with being, and de- 
 monftrating that there are as many parts ot the one as of being, and that every being participates 
 of the ctie ; that the one fubfifts every where together with being ; and laftly, that the one of tlie 
 fecond hypothefis participates of, and is participated by, being; the mode of participation not 
 being the fame in either : for tliis one participates of being, as that which is not the firft one, 
 nor exempt from being ; but as illuminating truc-fubfifting efTence. But being participates of 
 the one, as contained by the one, as repleniflied with divine union ; and as returning to that 
 which is the one itfelf, and imparticipable : for the unities which are participated conjoin beings 
 with the one, which is exempt from the univerfality of things ; in the fame manner as partici- 
 pated intellcdls unite fouls with univerfal intellect, and participated fouls conjoin bodies with 
 univcvfal foul. For it is not poflible that the diflimilar genera of fecondary natures fliould be 
 immediately united with that caufe which is exempt from all poflible multitude. But it is 
 neceflary that this conjuntflion fliould take place through fimilar natures : for a fimilar multi- 
 tude, fo far as it is multitude, participates of that which is diflimilar : but, fo far as it is fimilar 
 to the monad prior to itfelf, fo far it is conjoined with this monad. This fimilar multitude, 
 therefore, being eftabliflicd in the midft of fimilitude and multitude, becomes united with the 
 whole, and with the one, which is prior to all multitude ; but contains in itfelf far-diflant pro- 
 greflions, and fuch as are diflimilar to the one of its own nature. And through this one all 
 
 ' See iny tranflaiion of that Dialogue. 
 
 things
 
 B^okXIU ARISTOTLE'S met a physics. 293 
 
 CHAP. IX. 
 
 But there are certain doubts refpedling intelledl ; for it feems to be th^ 
 moft divine of things which are apparent : yet, by what mode of lubfillence 
 
 things return to this fimilar multitude, and extend themfelves towards the firft caufe of the 
 univerfe ; dilTimilars indeed through fimilar natures, but fimilars through themfelves. For 
 fimilitude eflentially collefts and conjoins many things in one, and converts fecond natures 
 to the monads which are prior to themfelves : for the very fubfiftence of fimilitude proceeds 
 from /Zv 0/1,;. Multitude, therefore, is conjoined with t/^e one, from which it derives its pro- 
 grelTion : and hence, (Imilitude is that which caufes many things to be allied and fympathife 
 with each other, and to fubfift in friendfliip among themfelves and with the one. 
 
 No obje£lions of any weight, no arguments but fuch as are fophiftical, can be urged againfh 
 this fublime theory, which is fo congenial to the unperverted conceptions of the human mind, 
 that it can only be treated with ridicule and contempt in degraded, barren, and barbarous ages» 
 It is this theory, which thofe who declaim againft the theology of the antients fhould firft en- 
 deavour to undevftand, before they attempt to fubvert. At the fame time, unfortunately, it is 
 a theory which has been fo entirely neglefted, that it is not to be difcovered in any writing 
 fince the time of the emperor Juftinian. Indolence and prieftcraft have hitherto confpired to 
 defame tliofe ineflimable works*, in which this and many other fublime and important theo- 
 ries can alone be found ; and the theology of the Greeks has been attacked with all the infane 
 fury of ecclefiaftical zeal, and all the imbecil flaflies of miflr.ken wit, by men whofe conceptions- 
 on the fubject, like thofe of a man between ilecping and waking, have been turbid and iviU^ 
 phantajlic and confufed, prepojlerous and vain. 
 
 "We find, however, from the paflage before us (which is certainly of ineflimable value) that 
 the dodrine that firft efiences are gods is derived from men of great antiquity, and we have 
 the teltimony of Ariftotle himfelf that it is a divine doclrinc. He likewifc very juftly obferves» 
 that a human form and the forms of other animals were afcribed to the firft efllnces, for the 
 purpofe of perfu.iding the multitude, enforcing the laws, and benefiting hinnr.n life. For, the mul- 
 titude being merged in fenfe can only by fenfibie images obtain a far-diftant gliinpfe of incor- 
 poreal natures; and the whole of the human nature is from its connection with body adapted 
 to be led back through images to exemplars, and through fenfe to intellect. Hence, Ariftotle 
 very properly adds, that human life was benefited by the fabulous part of the antient theology. 
 For, as Sallult, On the Gods and the World, beautifully obferves, •' fince the providence of the 
 gods is every where extended, a certain habitude or fitnefs is all that is requifite in order to 
 receive their beneficent communications. But all habitude is produced through imitation and 
 fimilitude. Hence, temples imit.ite the heavens, but altars the earth ; fiatues refemble life, and 
 on this account they are limilar to animals -, and prayers imitate that which is intelleftual ; but 
 chariiHcrs fuperior ineffable powers ; herbs and Ihnes refemble matter ; and animals which are 
 facrificed, the irrational life of our fouls. But, from all thefe, nothing happens to the gods 
 beyond what they already pofTefs ; for, what accefilon can be made to a divine nature ? But a 
 conjunclion with our fouls and the gods is by thefe means produced." 
 
 • Tlioff of the latter Platonifti, viz. Plotiuus, Porphyry, Jiml'licl-.us, Proclus, Ammonius, Olympiodorus, &:c. 
 
 it 
 
 /
 
 594 ARISTOTLE'S METAPHYSICS. Book XII. 
 
 it is fo, it is difficult to determine. For, if it is void of intelledion, and is 
 like one fleeping, what will there be venerable in fuch a,condition of being? 
 But, if it pofleffes intelle£lion, and yet fomething elfe has dominion over or 
 is the author of thi?, then its eflence will not be intelligence, but capacity, and 
 fo it will not be the mod excellent elTence. For that which is honorable is 
 prefent with it through intelleftion. Further ftill : whether its elTence is in- 
 tellect or intelligence, what does it underrtand ? For, either itfelf underftands 
 itfelf, or it underftands fomething elfe. And if fomething elfe, either always 
 the fame, or a different thing. Is it, therefore, of no confequence whether it 
 underftands that wlrich is beautiful, or any thing which may cafually pre ent 
 itfelf ? Or is it ablurd to fuppofe that it cogitates about certain things ? It 
 is evident, therefore, that he underftands that which is moft divine and moft 
 honorable, and that he is not changed. For the mutation would be into 
 -fomething worfe, and a thing of this kind would now be a certain motion. ' 
 In the firft place, therefore, if his effence is not intelligence, but capacity, it is 
 reafoaable to conclude, that continuity of intelledion is laborious to him j and 
 in the next place it is evident that there will be fomething elfe more honor- 
 able than intelle61, viz. the intelligible, or the objedl of intelledion. Befidef, 
 intelledion and intelligence will be prefent with him when underftanding the 
 worft of things. This, therefore, muft be avoided. For, not to perceive 
 certain things is better than to perceive them. Hence, intelligence * will not 
 be that which is moft excellent. He underftands himfelf f, therefore, if he is 
 the beft of all things ; and intelligence is the intelligence of intelligence. 
 
 But 
 
 * Since, according to Ariftollc, the firfl caufe is tlic object of dcHre to ;!ll things, he cannot 
 lubfift as iritdligence. For, that which is tlie objecT; of defire to all things is that of which all 
 tilings participate, or this defire would be vain. But all things do not participate of intelli- 
 gence, fince fomc things poficfs being alone. Tilings, therefore, originate from the iiitJ/igiMe, 
 and not from intelligence. 
 
 t The firft intelka: underftands liimfelf, and by knowing himfelf knows every thing of which 
 'he is the caufe, poflefiing a knowledge tranfcendently more accurate thin that which is co-ordi- 
 nate to the objeds of knowledge ; fince a caufal knowledge of evtry thing is fiiperior to every 
 other kind of knowledge. Without bufily attending, therefore, to the objc£ls of his intellec- 
 tion, by alone knowing himfelf he knows all things. Kor i:i he indigent of fuTe, or opinion, or 
 fc;encc, in order to know fenfil le natures; for it is himfelf that produces all.ihefc, and that iit 
 the unfathomable depths of the intelkaion of Iiimfeif comprehends an united knowledge of 
 them according to caufe, and in one fimplieity of perception : — juft as if fonie one, having built a 
 jliip, lliould place in it mcH of his cnvi; formation, and, in confequence of podening a various 
 
 art,
 
 Book Xir. ARISTOTLE'S METAPHYSICS. 295 
 
 But fclence, fenfe, opinion, and the dianoctic power always appear to be 
 employed about I'omething different from themlelves ; lo that the principal 
 delign of each of thele is not the fpeculatlon of itfelf. Further ftill : if in- 
 tellecflion is different from that which is apprehended by intelledl, according to 
 which of thefe is excellence of fuhfifleiice prelent with him ? For the being 
 of intelligence is not the fame as that of the inteliigible. Or fliall we fay, 
 that in fonie things icience is the thing itfelf which is the objedl of fcience ? 
 In effedivc fciences*, indeed, effence and form are without matter; but 
 in the contemplative fciences tliis muft be affirmed of reafon, the thing, 
 and intelligence. Hence, in things without matter f , fince the intelligible 
 is not different from intelledl:, it is the fame with it. Intelligence alfo is 
 the fame with the intelligible. Further ftill : a doubt remains, whether 
 the intelligible is a compofite nature ; for, if this be the cafe, it will be 
 changed in the parts of the whole. Or, fhall we fay that every thing with- 
 out matter is indivifible ? In the fame manner, therefore, as the human intel- 
 lect, or the intelledl of compofue natures, fubfifts for a certaiatime (for this in- 
 art, ftioulcl add a fea to the fliip, produce certain U'inds, and afterwards launch tlie (hip into the 
 new-created main. Let us fuppofe, too, that he caiifes thefe to have an exiiience by merely 
 conceiving them to exift, fo that, by imagining all this to take place, he gives an external fabGll- 
 cnce to his inward phantafnis, it is evident that in this cafe he will contain the caufe of every 
 thing whicli happens to the Ihip through Uie winds on the fea; and that by contemplating his 
 own conceptions, without being indigent of converfion to outward obje£l3,.he will at the fame 
 time both fabricate and know thefe external particulars. Thus, and in a ftill greater degree, the 
 firll or intelligible intelledl, poirelhiig the caufcs of all things, both gives fubfillence to and con- 
 templates whatever the univerfe contains, without depaning from the fpeculation of himfelf. 
 
 * It is well :bferved by Alexander, that Ariftotle here by efreflave fciences means the art of 
 building, and the like. 
 
 + Viz. In intellif^ibles properly fo called. Hence the firft intellefl: is at the fame time both 
 iiitelUcl and irdelligible. It is intc!le(St confidered as underjiaiiduig itfelf, but intelligible as nm'er- 
 jlood by itfelf. But participable which fubfifts pofterior to imparticipable intellect \ — or, in other 
 words, intellefl confubfiftent which is pofterior to intellecl uncouneiSled with foul, — underflands 
 itfelf, and the intellect prior to itfelf. For every inttlleit muft either underltnnd itfelf, or that 
 which is above, or thr.t which is pofterior to itfelf. But if it underftands that which is pofterior 
 to itfelf, it will be converted to that which is worfe than itfelf. If it underftands that which is 
 above itfelf, if thi^ is through the knowledge of iifeli, it will at the fame time underftand itfelf 
 and tliat which is fuperior. But if it alone underftands that which is fuperior, it will, though 
 intellect, be ignorant of itfcJf. However by knowing that which is prior to itfelf, it alfo 
 knows itfelf There is therefore, in :inelled the intelligible, and in the intelligible intellect ; 
 and one intell-^c^t is more total,^ and another more partial. 
 
 tellecl 
 
 X
 
 296 ARISTOTLE'S METAPHYSICS. Book XIL 
 
 telled does not poflefs the excellent condition of its being in this or that portion 
 cf time, but in a certain whole *), lb does the firil iatelled fubfill for ever ; 
 and thus through all eternity itfelf poffeffesthe intelligence of itfelf. 
 
 C H A P. X. 
 
 It mufl alfo be confidered in what manner the nature of the univerfe pof- 
 icfles the good and that which is mofl: excellent, whether as Ibmething fepa- 
 rate, and itfelf fubfifling by itlelf, or as order 1, or as both thele, in the fame 
 manner as an army. For the good of this confiils in order, and in its com- 
 mander, who is the good of the array in a ftill greater degree. Tor the 
 commander is not on account of the order, but the order on account of the 
 commander. But all things are in a certain refped co-ordinateJ, though not 
 in a fimilar manner, f\ich as aquatic and aerial animals and plants. Nor do 
 they fubfift in fuch a manner as that one has nothing in common with the 
 xDther, but there is fomething in which they all agree : for all things are co- 
 ordinated to one thing. But as, in a houfe, thofe who are free are permitted 
 to adt juft as they pleale, in all or in moft things which contribute to the com- 
 mon good ; but this is only granted in a fmall degree to flaves and irrational 
 animals, fince they a£l for the a^oft part cafually (for the nature X of each of 
 them is a principle in them of this kind) ; I fay, in this manner it is neceflary 
 that all things fliould fubfill in order to efFeil feparation. And as in a houfe, 
 fo in the univerfe, there are other things of which all participate in order to the 
 conflitution of the whole. 
 
 But we ought not to be Ignorant of the impolTible or abfurd confequcnces 
 which happen to thofe who fpeak differently, nor yet of their aflertions who 
 fpeak more elegantly, and whofe opinions are attended with the feweft doubts. 
 For all philofophers confider all things as produced from contraries. But 
 
 * IntelleiS, when it apprehends that whicli is intelligible, does not underftand one part of it at 
 this time, and another part of it at a different time ; for, thus, the intelligible or proper object 
 cf intelle£l would be divifible ; but it underllands it in an iudivifible initant. For [his is wh.it 
 Ariftotle means by a certain whole. 
 
 t Since Ariftotle, as we have alfo obferved in the Introdu£lion, admits that there is a twofold 
 order, one in the univerfe, and another in the caufe of the univerfe, he muft alfo admit that 
 there is a twofold feries of forms; one incorporeal and intelligible, fubfifting in this caufe, and 
 die other corporeal and fenfible. 
 
 t Thatjs to fay, the nature of thofe things which contribute to the nature of the uniyarfe. 
 
 neither
 
 ?5ooK XII, A R ISTOTLE'S M E T A P H y S 1 C S. 297 
 
 neither are all things generated; nor Is it rightly faid that all thir.gs are from 
 contraries ; nor do they appear to have informed us how thofe things in 
 which contrariety Is inherent confifl: from contraries : for contraries are not 
 paffive to each other. But this difficulty is folved by us in a rational manner, 
 by introducing a certain third nature. Others make one of the contraries to 
 be matter, as thofe who fubje£l the unequal to the equal, or multitude to the 
 cue. This, however, Is folved after the fame manner : for matter which is 
 one is not contrary to any thing. Further ftlll : all things will participate of 
 evil, except the one ; for evil Itfelf Is the other of the elements. But, accord- 
 ing to others, good and evil are not principles, though in all things the good 
 is rnoft eminently a principle. Others, again, are right in confidering the 
 good as a principle ; but they do not fay how it is a principle, whether as the 
 end, or as that which moves, or as form. Empedocles * too ads abfurdly ; 
 for he makes frlendlhlp to be the good. For friendflilp, according to him, is a 
 principle, and that which moves (for it congregates) ; it Is alfo as matter, for 
 it is a part of that which is mixed. However, though friendfhip fhould hap- 
 pen to fubfift as matter, as a principle, and as that which moves, yet its eflence 
 would not be the fame with the effence of thefe. Which of thefe, therefore, 
 will friendfhip be ? But It is alfo abfurd that ftrife fhould be incorruptible*; 
 fince this very thing Is the nature of evil itfelf. 
 
 But, according to Anaxagoras, the good is a principle fo far as motive. For 
 intelledl moves ; but It moves for the fake of fomething ; fo that it will be differ- 
 ent from that for the fake of which it moves, unlefs it fubfifts as we affirm It to 
 fubfift : for the medicinal art is in a certain refpe£l health. He has alfo adled 
 abfurdly, In not making a contrary to the good, and to intelled:. But all thofe 
 who fpeak of principles as contraries do not ufe contraries, as will be obvious 
 to him who does not negligently confider their opinions. And no one affigns 
 a reafon why fome things are corruptible, but others incorruptible : for they 
 make all things from the fame principles. Further ftill : fome generate all 
 things from non-entity : but others, that they may not be compelled to do 
 this, make all things to be one. Again : no one affigns a reafon why genera- 
 tion will perpetually exift ; nor does any one fay what is the caufe of genera- 
 tion. And both thofe who make two principles, and thofe who introduce 
 ideas, necefTarily require another more powerful principle j becaufe there is a 
 
 • See the Notes to the thirteenth book. 
 
 Q^q principle
 
 298 ARISTOTLE'S METAPHYSICS. Book XIF, 
 
 principle more powerful than thefe. For why is matter participated, or 
 why does it ftill continue to participate ideas ? And to others, indeed, it is 
 neceflary that there (hould be fomething contrary to wifdom and the moft ho- 
 norable fcience ; hut this is not neceffary to us. For there is not any thing 
 contrary to that which is firft ; fince all contraries have matter, and thefe are 
 in capacity. Ignorance, too, is oppofed to its contrary ; but nothing is con- 
 trary to that which is firft. 
 
 Further iVill : if there are no other natures befides fenfibles, there will not 
 be a principle and order, generation, and the celeftial orbs ; but there will 
 always be a principle of a principle, as is alfo aflerted by theologifts and all 
 natural philofophers. But if there are forms* or numbers they will not be 
 the caufes of any thing. And if this is not admitted, they will not at leaft be 
 the caufes of motion. Again : how can magnitude and that which poflefles 
 continuity emerge from things void of magnitude ? For number will not 
 make continued quantity, either as that which moves, or as form. Indeed 
 there will not be any one of things contrary which has the power both of 
 making and moving ; for it may happen not to be. But energy is in a certaia 
 refped pofterior to capacity. There will not, therefore, be eternal beings i 
 BUT THERE ARE. Hence fomc one of thefe hypothefes muft be re- 
 jedled. But we have fhown in what manner capacity antecedes energy. 
 Further ftill : how numbers are one, or foul and body, and, in fhort, form 
 and a thing, no one inJorms us: nor is it poflible to explain this, ualefs he 
 fays as we do, that the caufe of this, in effedling it, operates as that which 
 movts. But thofe who fay that mathematical number is firft, and fo always 
 fuppofe another effence adhering in fucceffion and other principles of every 
 thing — thefe make the eflence of the univerfe to be adventitious ; (for, thus^ 
 one thing do.s not contribute any thing to another, whether it exills or does 
 not exift-.; and befides this, thty introduce many principles. But beings are 
 unwilling to be governed ill. 
 
 The domination of many f is not good ; there is, therefore, one fupreme» 
 
 * See the Notes to the thirteenth and fourteenth books. 
 
 + T hat is to fay, the domination of many principles independent of each other is not good.; 
 for ATi''o;le in the preceding eighth chapter has proTed that tlicre is a multitude of principles 
 ef a nature Jimilar to the firft caufe. 
 
 ARISTOTLE'S
 
 ARISTOTLE'S METAPHYSICS. 
 
 BOOK XIII. 
 
 CHAP. I. 
 
 Jtv ESPECTING the eflence, therefore, of fenfibles, we have Ihown what 
 it is in the mode of inveftigation employed by us in our Phyfics, concerning 
 matter, and afterwards in our inquiry concerning energy. But fince our 
 prefent defign is to confider whether, befides fenfible effences, there is a cer- 
 tain immoveable and eternal nature, or not, and if there is what it is, in the 
 firft place we fhall take a furvey of the aiTertions of others, that, if in any thing 
 they have not fpoken well, we may not be liable to the fame accufation ; and 
 that, if there is any dogma common to us and them, we may receive it fepa- 
 rately, and not be indignant as with a thing hoftile to our defign. For we 
 muft be contented if any one afferts fome things better than us, and others 
 things not worfe. But there are two opinions on this fiibjedt : for they fay 
 that mathematical natures are certain effences, fuch, for inftance, as numbers 
 and lines, and things allied to thefe, and again, ideas*. However, fmce fome 
 
 coniider 
 
 * Prior to a folution of the objections of Ariflotle to the doiFlrine of ideas, it will perhaps 
 be better to give the reader a fummary vie.v of the opinions of tlic Pythagorxans and Platonills 
 on the fubje<fl, that he may be at once convi;-ccd that tlie arguments of Arittotle are not direcfled 
 to the true and genuine, but merely to the apparent meaning of thefe philofophers. 
 
 T^e divine Pythagoras, and all thofe who have legitimately received his dodrines, aiTerted 
 
 Q^q a that 
 
 /
 
 ^00 ARISTOTLE'S METAPHYSICS. Book Xlir. 
 
 confider Ideas and mathematical numbers as two genera ; but others are of 
 opinion that there is one nature of both ; and others again alfert that mathe- 
 matical natures are alone eflences, in the (irlf place let us make mathematical 
 entities the obje£l of our confideration^ without adding to them any other 
 
 nature j 
 
 that there are many orders of beings, viz. int<?lligible, intelleflual, dianoetic, phyfical, or, in 
 fliort, vital and corporeal efTences. For the progrefTion of things, the fubjedtion which natu- 
 rally fubfiils together with fuch progreihon, and the power of diverfiLy in co-ordinate genera, 
 give fubfiftence to all the multitude of corporeal and incorporeal natures. They faid, there- 
 fore, that there are three orders in the whole extent of beings, viz. the iiiti'/ligiHe, the diatioetic, 
 and the fenfible; and that in eacli of thefe ideas fubfift, charafterifed by the refpeftive effential 
 properties of the natures by which they are contained. And with refpeft to intelligible ideas^ 
 thcfe they placed among divine natures, together with the producing, paradigmatic, and final 
 caufes of things in a confequent order. For if thefe three caufes- fometimes concur, and arc 
 united among themfelves (which Arlftotle fays is the cafe), without doubt this will not happen 
 in the lowed works of nature, but in the firft and mofl excellent caufes of all things, which, on ac- 
 count of their exuberant fecundity, have a power generative of all things, and, from their convert- 
 ing and rendering fimilar to themfelves the natures which they have generated^ are the paradigms 
 or exemplars of ail things. But as thefe divine caufes a£t for their own fake, and on account 
 of their own goodnefs, do they not e.xhibit the final caufe ? Since, therefore, intelligible forms 
 are of this kind, and are the leaders of fo much good to wholes, they give completion to the 
 divine orders, though they largely fubfift about the intelligible order contained in the artificer of 
 the univerfe. But dianoetic forms or ideas imitate the intelle£lual, which have a prior fubfift- 
 ence, render the order of foul fimilar to the intellectual order, and comprehend all things in » 
 fecondary degree. 
 
 Thefe forms, beheld in celeftial smd divine fouls, poffefs a fabricative power, but with us 
 they are only gnollic, and no longer demiurgic, through the defluxion of our wings. For, as 
 Plato fixys in the Phasdrus, when the winged, that is, the intelleclual, powers of the foul are 
 perfe£l, and plumed for flight, the foul dwelk on high, and in conjundlion with divine natures 
 governs the world. In the Timseus, he manifeftly alTerts that the Demiurgus implanted thefe 
 dianoetic forms in fouls, in geometric, arithmetic, and harmonic proportions ; but in his 
 Republic, (in the feaion of a line) he calls them images of intelligibles ; and on this account 
 •loes not for the mod part difdain to denominate them intellei5fual, as being the exemplars of 
 fenfiblc natures. In the Phxdo, ae favs that thefe are the caufes to us of reniinifcence ; becaufe 
 difciplines are nothing c\k than reminifcences of middle dianoetic forms, from which the pro- 
 ductive powers of nature being derived, and infpired, give birth to all the mundane phenomena. 
 
 What we have juft now advanced, may be thus illuftrated. In a divine foul fubhfting in the 
 heavens, the bifediou of the greateft circles in a fphere pre fides with gnolHc, energetic, and 
 fabricative power, but in our fouls it has only a gnoftic fubfiftence. In the v.ituye which is 
 fufpended from fuch a foul, the zodiac, the equinoctial, and the meridian, vitally bifett each 
 «jther, and poflefs a fabricative power, but not a gnoftic energy ; a divine foul comprehending 
 all thefe in its intellecTtions in profound union, and with demiurgic energy, but a celeftial body 
 receiving divifibly thofe tilings only which are rcquifite to the perfcttion of its nature. 
 
 Hence,
 
 BooKXIlt. ARISTOTLE'S METAPHYSICS. 
 
 301 
 
 nature ; viz. without inveftigating whether they are ideas or not, and whe-^ 
 ther or not they are the principles and elTences of things ; alone attending 
 to this, whether mathematical entities have any fubfiftence or not, and if 
 they have, in what manner they fubfift. 
 
 In the next place, we (hall feparately fpeculate concerning ideas them- 
 felvcs, and this fimply, and in a fmall degree, for the lake of law*- for 
 many things are divulged refpeding them, even in exoteric difcourfes. 
 Further flill : it is requifite that greater attention fliould be paid to that 
 part of our inquiry, in which we confider if the eflences and principles of 
 
 Hence, alfo, demonftratlons are produced by aftronomers from univerfal and particular propo- 
 fitsons; from univerfal, which indesd have a caufal power, fince they pre-exift in foul, which 
 imparts eflence to all mundane natures ; and from particular propofitions, which are derived 
 from fenfiDles. 
 
 Of this threefold order of ideas, viz. thofe in divine fouls, in our fouls, and in nature, tlie 
 Pythagoraans confidered thofe which fubfift in nature, and which are the infeparabie caufes of 
 fenfibles, as the lall images of feparate forms, on which account they did not difdain to call 
 them by the fame appellations. Laftly, by thefe, (which they called <Tuv^£Tay|xiVM /Mvah; or 
 monads co-ordinated with fenfibles) the foul which has defcended into the realms of generation- 
 being roufed and excited, proceeds to the reminifcence of middle or dianoetic forms. She 
 alfo reduces her own peculiar reafons to intelleftual and firft exemplars ; and, in confequence 
 of this, fight and hearing are advantageous to the philofopher, and contribute to the re-elevation 
 of the foul. 
 
 Thefe things being well underftood, it will be found that Pythagoras and Plato, and their 
 followers, did not differ from each other about the dotlrine of ideas, as the reader might be in- 
 duced to think they did from what Ariftotle with apparent ferioufnefs afTerts. But the Pytha- 
 goreans, when they difcourfed about thofe forms which have a middle fubfiftence, and alfo about 
 thofe which are the firll of things, gave them the fame appellations with fenfibles ihemfelves, 
 transferring thele names by a certain fimllitude from the latter to the former. 
 
 Thofe antient writers, however, fays Syiianus, who have given an hiftorical account of the 
 do£lrine of thefe phllofophers refpe£ling ideas, from not having by any means fathomed the depth 
 of their meaning, have afferted that their attention was alone diretted to infeparabie forms. 
 Some, again, have affirmed that they alone venerated a mathematical effence, iince they have 
 called firft, middle, and laft forms by mathematical names. And to others, ftill more pcrverfe, 
 fome of thefe philofophers have appeared to confound intelligible with dianceiic forms ; when, 
 at tiie fame time, thefe mighty mafters of wlfdom have done nothing ot this kind •, but, in 
 reality, a falfe fufpiclon has been er\gendeied in the minds of their hiltorians, through the com- 
 munion of names with each other. But Plato, exhibiting in tills refpeft his great philanthropy, 
 has clearly ditUnguiflied by difference oi appellation, intelligible from dianoetic elfence : and. 
 hence, the pretended obje£tions of Ariftotle in what follows are directed againlt Piaco, as fup- 
 pofing that there art two orders of feparate efi'ences. 
 
 • That is, (as it appears to mt) for the fake of order. 
 
 things 
 
 X
 
 302 ARISTOTLE'S METAPHYSICS. Boos. XIII. 
 
 things are numbers and ideas : for, after ideas, this remains as the third con- 
 fideration. But it is neceflary, if there are fuch things as mathematical enti- 
 ties, that they fliould either be in fenfibles, according to the aflertions of 
 fome ; or that they fhould be feparated from fenfibles, as is afferted by others : 
 or, if neither of thefe is to be admitted, either they have no fubfiftence, or 
 they fubfift in fome other way. So that the controverfy with us will not be 
 Tefpeding their being, but their mode of fubfiftence. 
 
 C H A P. II. 
 
 * That it is impoflible, therefore, that they ftiould fubfift in fenfibles, and 
 that the reafoning adduced in defence of this mode of fubfiftence is at the 
 
 fame 
 
 * " Neither any one of die Pythagorasans," fays Syrianus, " nor Plato himfelf, nor any of his 
 genuine followers, has placed geometrical figures and magnitudes in fenfibles. But if Severus, 
 -or any of thofe who have attempted to explain the doctrines of Plato from the philofophy of 
 Ariftotle, have perverted the mathematical fciences, in applying them to the demondration of 
 natural caufes, this is nothing to the antients, whofe opinions Aviltotle now endeavours to con- 
 fute." Perhaps, however, the objections of Ariftctle are direded againfl: fuch an hypothefis, in 
 confequence of forefeeiiig that it would probably be adopted. 
 
 But, fays Syrianus, becaufc he again refers us to the doubts in the third book, we mud fay, 
 in addition to what has there been aflerted, that neither is it entirely impoffible that two folids 
 fhould be contained in the fame fpace. Nor is it requifite in order to oppofe the objc6tion» 
 of Ariflotle to regard the Stoics, who did not deny that material mafles may permeate each 
 other, but we (hould rather attend to thofe who, fuppofing interval (Jiaarij^ia) to permeate 
 through the univerfe, and to receive into itfelf the whole of a corporeal nature, aflert that it 
 by no means divides, or is divided by the air, and is co-divided with other bodies ; but that it 
 is void of inclination and fixed; and, being exempt from all mutation, is extended through the 
 univerfe, and brings with it place, receptacle, termination, circumfcription, and other things of 
 this kind, to the natures wliich give completion to the fenfible world. Thefe philofopliers, 
 .therefore, regarding a body of this kind, do not indeed aflert that it is mathematical, but fimilar to 
 a mathematical body, fo far as it is immaterial, immoveable, void of contaft, liberated from 
 contrariety, ami puriiied from every paffive quality. 
 
 Befides, they were alfo of opinion, that as matliematical body, through the energy of the 
 dianoetic part, is emitted as it were into the phantafy, (for when the dianoetic part has an in- 
 corpor-eal conception of a fphere, for initancc, the imagination alfo beholds at tlie fame time 
 the mathematical fphere, fubfiiling with immaterial bulk,) in like miunier in the will, and in 
 jhe intellecfl^on of the muiulane foulj this fpherical fpacc in the univerfe receives a kindred fub- 
 fiftence: for the muiulane foul, in confcqumce of looking to intellect, caufes this fpace to be 
 fpherical, but, in confequence of furveying all forms, caufes it to be the receptacle of all bodies, 
 and to comprehend them in one ; f.ntc the intclle<?Jons of tiiis foul are both continued and 
 
 tri'.nfitive,
 
 BookXIII. ARISTOTLE'S METAPHYSICS. 503 
 
 fame time fnftltlous, has been evinced in the doubts in which we have fhown 
 the impoffibility of two folids occupying the fame place. Further ftill : by 
 the fame reafoning, it appears that other powers and natures are in fenfibles, 
 and that no one of them has a feparate fubfiftence. Thefe things, therefore, 
 have been already difcufled. But, befides this, it is evident that it would be 
 impoffible for any body to be divided : for it would be divided according to 
 a fuperficies, and this according to a line, and a line according to a point. 
 So that, if it is impoffible to divide a point, it is alfo impoffible to divide a 
 line ; and if a line, it is impoffible to divide the refl. What is the difference, 
 therefore, in admitting, either that there fhould be fuch natures, or that there 
 Ihould not be, but that fuch natures fhould be contained in fenfibles ? For 
 the fame thing will happen ; for, fenfibles being divided, they alfo will be 
 
 tranfitive, becaufe the intelligible ideas which are the objects of its vifion, have both an united 
 and at the fame time a diftinG fubfiftence, although one nature comprehends them all. Hence 
 the fenfible univerfe, being replete with imitations of thefe, receives them attended with, 
 liimenfion and magnitude. 
 
 It appears, therefore, that the opinion of thefe philofophers is- not impoffible, nor yet of thofe 
 who think that fimple and immaterial bodies may permeate each other without divifion ; but that 
 two material bodies replete with contraries fliould occupy the fame place, they fay is in the 
 higheft degree impoffible. They further add, that immaterial' bodies are fimilar to the illumina- 
 tions which are emitted from different lamps, which at the fame time extend through the whole 
 of the fame houfe, and mutually pervade each other without confufion and divifion : for thefe 
 illuminations are commcnfurate with bodies themfelves^and are co-extended in three dimenfions,, 
 and yet are not prevented from occupying the fame place among themfelves, and with other 
 bodies. No other reafon can be affigned for this, than the fimplicity and immateriality of their 
 nature, and their being impartibly divided. But as they are united to their principle, and are 
 fufpended from it, they are prefent when it fhines, and, when it departs, they at the fame time 
 recede; and this the immaterial bodies, which are the vehicles of fouls, are by no means pre- 
 vented from accomplifliing. 
 
 Ariftotle, therefore, does not now oppofe thofe who venerate » fpace of this kind, but thofe 
 who introduce another order of bodies among fenfibles-, bodies which are folid in confequence 
 of having'triple dimenfions, and mathematical, becaufe they are perfe£Hy immoveable ; which 
 hypothefis, fays Syrianus, was not adopted by any one of the antient Uluftrious philofophers 
 with whofe writings we are acquainted. For the five regular figures, which are mentioned in 
 the Timseus of Plato, and which are employed in the formation of the mundane elements, ar« 
 indeed explained by mathematical names, but occultly fignify certain aftive and demiurgic- 
 powers of nature. If any one, too, fhould fay that the luminous vehicle alfo of our fouls poflefles 
 ttipie dimenfions, and is void of refiftance, he would not on that account openly affert that it is 
 a geometrical body. For how can that which is full of life and motion, and tlie moft moveable. 
 of all things which belong to us, (with a motion I fay allowed by Ariltotle himfelf) be placed 
 SS immoveable among geometrical bodies i 
 
 diyidtdfc 
 
 /
 
 304 ARISTOTLE'S METAPHYSICS. Book Xllf. 
 
 divided, or they will not be fenfibles. But neither can fuch like natures 
 have a feparate iubfiftence * : for if there Ihould be other folids, befides fuch 
 as are fenfibles, feparate from thefe, and prior to fenfibles, it is evident that, 
 befides fuperficies, there muft neceffarily be other fuperficies having a fepa- 
 rate fubfiftence, and in like manner other lines and points : for this muft 
 follow from the fame reafoning. And if this be admitted, again, befides 
 the fuperficies, lines, and points of a mathematical folid, there will be others 
 fubfifting feparately, fmce incompofites are prior to compofites. And if 
 bodies which are not fenfible are prior to fenfibles, for the fame reafon, thofe 
 fuperficies which fubfift by themfelves will be prior to thofe which have 
 their fubfiftence in immoveable folid : : fo that both thefe fuperficies and 
 lines are different from thofe which have a co-fubfiftence in feparate folids: 
 for the la'aer fubfift together with, but the former are prior to, mathematical 
 folids. Again, therefore, of thefe fuperficies there will be lines, prior to 
 which it will be requifite that there (hould be other lines and points, and other 
 points prior to thofe contained in the lines which have a fubfiftence prior to 
 fenfibles ; to which there will no longer be any that are prior. But this 
 co-acervation is Indeed abfurd ; for it will happen, that there is only one 
 order of folids bt fides fuch as are fenfible, but that there are two ranks of 
 fuperficies befides fenfibles ; viz. thofe which are in the feparate bodies, and 
 
 * Ariftode cannot be ferious in what he now fays -, for it contains notliing demonflirative, 
 nor does the deduction lead to an abfurdity : for thofe antients wliom he apparently confutes, 
 confidered points, lines, fuperficies, &c. as fubfifting in the effential reafons of the foul, both 
 in a divided and united manner. Nor is there any abfurdity that a point, or rather the pro- 
 dui£\ive principle (xoyoj) of a point, (hould neither be mingled with line, fuperficies, &c. and 
 yet Ihould contribute to the produilion of thefe. For thofe divine men every where confirm 
 and venerate the union and feparation of incorporeal forms ; and it is mod clearly fliown by 
 the more antient philofophers, (fays Syrianus), that the fame thing is both one and many in 
 dianoetic forms, and by a much greater priority in fuch as are intellectual. See what has been 
 faid on this fubje£l; in the notes to the third book. 
 
 But, if any one (hould be unwilling to grant that the reafon or produ£live principle of di- 
 
 ■ menfions in the foul has a manifold fubfiftence, it may be faid to fuch a one, that it is not 
 
 necefTiiry there fhould be four points, or three lines, or two fuperficies; but that, as the letter a 
 
 in a fyllable, in a word, and in a fentence, is confidered as one and the fame in fpecies, and has 
 
 every where the fame nature, in like manner a point, and a line, both confidered by thcmfelv(.'s, 
 
 •and with compofites, preferve one and the fame fpecies. And further : that as the grammatical 
 
 •art knows the power of the letter a-, both confidered as exifting feparately,. and as in a fyllable 
 
 -and a word ; in like manner the mathematical fciences, knowing thofe things which have a 
 
 feparate fubfiftence, know alfo thofe which fubfift in conjunQion vjjth otliers. 
 
 thofe
 
 JJookXIII. ARISTOTLE'S METAPHYSICS. 305 
 
 thofe which have a fubfiflence feparate from bodies ; and again : that there 
 are triple lines, viz. thofe v?hich are in folids, thofe which are in fuperficies, 
 and thofe which are feparate ; and, from the fame reafoning, that there are 
 quadruple points and quintuple monads*. So that, about which of thefe 
 will the mathematical fcience be employed ? For it cannot be employed 
 about fuperficies, lines, and points, which are in an immoveable folid ; fmce 
 fcience Is always converfant with things which have a priority of fubfiftence. 
 The fame reafoning alfo will take place refpecSting numbers : for befides 
 points there will be other monads, and befides beings fenfibles, and after- 
 wards intelligiblcs j fo that there will be infinite genera of mathematical 
 numbers. 
 
 Further ftill : how will it be pofllble to folve the doubts f which we 
 
 have 
 
 * The original in this fentence is corrupt, which I have corre£led from the commentary of 
 Syrianus. 
 
 f Since all univerfal forms are contained in divine fouls, and alfo in our fouls, prior to the 
 partial comprehenfion of them by the corporeal nature of the world, it would be ridiculous 
 to inquire in each of thefe where thei-e will be another heaven, or another fun, or any thing elfe 
 which contributes to the apparent mundane order. But becaufe, fays Syrianus, thefe things' 
 do not fubfifl once only, but as I may fay infinitely, in beings, according to the aflertions of the 
 moft antient theologifts, Ariftotle is not willing to purfue this inquiry, but notices as an abfur- 
 dity, that there fliould be one heaven only above this fenfible heaven. But he who, like the 
 Coryphxus in the Thextetus of Plato is able to aflronomize above the heavens {tou ouoamu 
 v7rt§airTpow//.ouyr£i), to view efFe£ts in their caufes, and all beings fubfifting intellectually, in the 
 great exemplar of the univerfe, — fuch a one will perhaps be indignant with him who fhould 
 neither afTent to the do£\rine of ideas, nor admit that the intelleflual foul has forms in energy, 
 but that it only contains them in capacity. How, therefore, will the demonftrations of aftro- 
 nomers any longer confifl: from things firft and proper caufes, unlefs they proceed from thofe 
 univerfal reafons, which our fouls contain gnofliically only, but divine fouls both gnoftically, 
 and pofTeding a fabrlcative power ? For, if this be not admitted, it is impoflible that aftronomers, 
 mathematicians, and natural philofophers, can demonftrate any thing, or that dcmonftrations 
 ftiould be the offspring of caufe. 
 
 But thole who admit that fenfibles have a real exiftence, and that unlverfals are merely tilings 
 of pofterior origin, fubfifting in the foul by an abftra£lion from fenfibles, forget that they make 
 the foul more ignoble than matter. " For, as Proclus well obferves, (fee his Commentary on 
 Euclid, lib. i. p. 3. of the original, or p. 56 of my tranflatiop) if matter derives from nature 
 beings elTential, and participating a high degree of entity and evidence ; but the foul, by a 
 pofterior energy, receives thefe from fenfible objects, and fafiiions in herfelf refcmblances and 
 images of pofterior origin, contemplating vile eflenccs, and abftradling from matter tlie forms 
 infeparable from its nature ; do not tlie authors of this hypothcfis make the foul more obfcure 
 ai)d indigent tlian matter itfelf ? For matter is the receptacle of forms mateiialized, as the foul 
 
 Rr "is 
 
 /
 
 306 ARISTOTLE'S METAPHYSICS^. Book Xlir, 
 
 have already enumerated ? For the particulars about which aftronomy is 
 converfant, are in a fimilar manner things different from fenfibles, and this 
 is alfo the cafe with the objects of geometric fpeculation. But how is it 
 poffible that heaven and the parts of it can fubfift, or any thing which pof- 
 felTes motion ? The like will take place in optics and harmonics *. For 
 there will be voice and found, beiides fuch as are fenfible and particular. 
 So that it is evident there will both be other fenfes and other fenfibles. 
 But why thefe more than thofe ? And if thefe, there will alfo be other 
 animals, fince there will be other fenfes. Befides, fome things are exhibited f 
 
 through 
 
 is of forms immatcrialized. But in this cafe aiatter would be the place of primary beings^ and 
 the foal of fuch as are fecondary and fubordinate: matter and its forms obtaining the lead hv 
 being, and exifting as the fources of the fubfiftence of immaterial forms." 
 
 * There is no abfurdity in admitting that all thefe fubfift in thcreafons, i. e. in the produc- 
 tive principles, of the foul, and alfo that they fubfilt in images, which are refemblanccs of 
 reafoTis, not only prior to fenfibles, but even to thofe phyfical reafons by which fenfibles are 
 formed. Thefe things being granted, Ariftotle fubjoins as a moll abfurd conftquence, that 
 there will alfo be other animals, fince there will be other fenfes. But though Plato, in the 
 Timaeus, allL-rrs that animal itfclf, or the extremity of the intelligible order comprehending in 
 jtfelf all intelligible animals, is both the caufe of thofe animals whicli fubfiil in the order of 
 foul, and of thole which fubfift in the fenfible order ; yet Ariftotle feigns as if he had never 
 he.ird of thiuits of this kind ; which is one confiderabl* proof among many others,, that he is not 
 ferious in his objedtions to Plato's doctrine of ideas. 
 
 It deferves alfo to be remarked, that Ariftotle himfelf in the twelfth book of this work calls 
 the firft intelledl an animal ; and, in his Nicomachtean Ethics, he alTerts that man, properly 
 confidered, is intelle£l. If therefore intellect, which is our principal part, is tlie true man,, 
 fince every man is an animal, it Is evident that our intelleft alfo is an animal. We contend, 
 therefore, that there are other animals befides fuch as are fenfible, but that they fubfift in a 
 different, and not in the fame manner as fenfibles. He, therefore, who calls the knowledge of 
 fuch' animals fenfe, and the objedls of their knowledge fenfibles, though thefe are the caufes of 
 fenfibles, does nothing more tlian transfer to caufes the names of their efFe£ls. 
 
 -(■ The whole re.ifoning of Ariftotle is as follows : If certain things are evinced by mathemati- 
 cians and natural pl.ilofophers, through particular axioms, as, for inftance, that if from equal things 
 you take avu.iy equals the remainders are equal, and that, if four quantities are proportional, the 
 rectangle under the extremes is equal to that under the means, and many other of this kind ; it 
 is neceflary; fince magnitudes and numbers have a fep. ..tc fubfiftence, that the things fignihed 
 by tl\cfe axioms fliould alfo be feparate, having a fubfiftence fuperior indeed to oiagnitudes and 
 mathematical numbers, but inferior to ideas; or, in othe words, they muft be placed between 
 cffential and mathematical magnitude. This Ariftotle objedls to as impoflible, in order appa- 
 rently to deftroy the feparate fubfiftence of mathematical entities. It is however, in a certain 
 refpcci true : for, of the reafons or produd^ive principles contained in the foul, fomc are more 
 
 jBmple,
 
 BooiiXni. A RI STOTL E'S xMETA PHYSICS. 307 
 
 through unlverfal reafons by mathematicians, befides thefe eflences. Thi^ 
 therefore, will be another feparate eflence, rubfifting between ideas and things 
 which have a middle fubfiftence, and which will neither be number nor 
 points, neither magnitude nor time. But if this is impoflible, it is evidently 
 impolllble that thole natures can have a fubfiftence feparate from fenfibles. 
 In Ihort, the very contrary * to that which is ufually apprehended will take 
 
 place, 
 
 fimple, unlverfal, and comprelienfive tlian others, and on this account are more proximate to 
 iiitellcct, and more manifeft and known than particulars; but others are deUitute of all thelc 
 properties, and receive their completion from more antient principles, by which alfo they are 
 contained. Is it not, therefore, neceflary, fince conceptions are then true when they accord 
 with and are accommodated to things thenifelves, that if the axiom is true which affirms that, 
 if from equals you take away equals, the remainders arc equal, there fliould be fome reafon in 
 which this is primarily inherent, and which is neither the reafon of magnitude, nor number, nor 
 t-ime, but comprehends all thefe, and likewife other things in which this axiom is naturally in- 
 herent ? At the fame time, this reafon is neither in place nor in fenfibles : for, how can that 
 which is univerfal, and moft fimple, and on this account indemonftrable, fubfift in matter, which 
 willingly (ayaTtira;) receives the imprelTions of forms ? Indeed, if we admit this, how can that 
 aflertion be any longer defended, that every demonflrative caufe is primarily inherent in fome- 
 thing, fo as that it may be co-equal to it, and may be univerfal, as Ariftotle in his Laft Analy- 
 tics aflerts of univerfal ? 
 
 Befides, on what account are axioms more manifeft and known than particulars and thing* 
 demonftrable, if we give fubfillence to them by indutlion from things lad, when prior to this 
 they had no fubfiftence ? After what manner, likewife, do all men agree in aflenting to their 
 truth, unlefs they had an eflential pre-exiftence in our conceptions ? For it is not neceflary that 
 we Ihould be unanimous refpecling things which we receive through the fenfes. 
 
 Again : how is that true which Ariftotle openly admits, that intelle£t delivers the principles of 
 demonftration to the foul, unlefs we eflentially received them in our conceptions prior to the 
 energies of fenfe ? For intelledl does not become miniftrant to us in things of which the gene- 
 ration is fubordinate. Either, therefore, we muft reafon in a circle, if we aflume and give fub- 
 fiftence to axioms from particulars, but demonftrate particulars from axioms; or, fince demon- 
 ftrations are from things prior, as Ariftotle proves in his Laft Analytics, we muft derive our 
 more fimple conceptions of axioms from intellect. But the variety of forms which the foul con- 
 tains fubfifts in us from the compofitiou of thefe. And thefe alfo again fubfift according to intel- 
 k£l and from intellect. For whatever we effentially poflefs muft be derived from intellect, fince 
 through more Cmple forms and reafons fuch as are more particular derive their fubfiftence. 
 And by thus fpeaking we fliall fpeak conCfl^eatly, fince we fhall affirm that demonftrations arc 
 perfected from caufes themfelves. 
 
 • Thofe divine men are indeed neither difcor t with rcfpccl to each other, nor to things 
 themfelves : for, neither did they conceive that the form of magnitude which is in intellect 
 is imperfect, or the magnitude which is conjoined to this form in imagination, nor yet that it is' 
 inanimate. For how is this poffible, fince they are placed in foul ? But, fince demonftrations 
 
 R r 2 arc 
 
 /
 
 308 A U I S T O T L E • S M E T A P H Y S I C S. Book XHf. 
 
 place, if any one cotifiders mathematical entities as certain frparate natures, 
 l-'or it is neccHary, if they ful)^!! in ihis manner, that they nioi.Id be prior to 
 fentible nugnitudes, when at the fame lime in reality they are poflerior to 
 theni : for an imperfe^ft magnitude is in generation prior, but in eflence 
 poflerior; as, for Inftance, the inanimate to the animate. Further ftill : ia 
 what and when will thcfe mathematical magnitudes be one * ? For thofe 
 
 which 
 
 are from caufcs which have an eflential fubfillence, as Ariftotle erinces in his Laft Analytics, 
 map-nitudes alio mull have an elTential iubfiflence in the foul, unlets vie are wiDinsr to admit 
 that the unelTential is the caufe cf eflence. Since Ariltotle likevi'ife often aihrnis that univer- 
 fals are things prior by nature to particulars (becaufc, if they no longer fubfill, the fubftftence 
 of other things is dePiroyed, but tho;igh ether things fnoutd pcrifli, th.eir fubfiflence would 
 net be fub«rted), he cannot be ferious in aflerting that thefe again have their fubfiftence from 
 ■fenfibles. 
 
 If, indeed, we admit that univerfal is twofold, one the caufe of a fenfible thing, and the other 
 of poflerior origin, being nothing more than a general phantafm as it were derived from fenfi- 
 bles, we fhall fpeak agreeably to i'lato and all the Pythagorseans. We muft alfo, in confequence 
 of this, aJmit that there is a twofold magnitude, the one lubfifting in the dianoctir part, and at 
 the fame time accompanied with the imagniable form of magnitude ; but the other obtained by a 
 denudation of fenfible magnitude. Nor fhall we fay, that geometry is converfant with denudated 
 magnitude, fince it does not pofiefs indubitable certainty. To which we may add, that we have 
 never feen fo many multangles and fuperficies, fuch a variety of multilateral figures, fuch divl- 
 Cons of angles, fides, or fpaces, as geometry confiders, and of which the reafons or productive 
 principles of the foul are full, but matter is naturally unadapted to receive. 
 
 But the Pythagorasans and Platonifts afl'ert that geometry is converfant with imaginable 
 forms, fo far as thefe are fufpended from the eflential reafons of infelleft, from which through a 
 demonflrative caufe they proceed. Or rather, that geometry wifhes indeed to contemplate the 
 impartible reafons of the foul; but fince it cannot ufe intelle£lions void of imagination, it ex- 
 tends itfelf to imaginable figures, and to magnitudes fubfifting with dimenfion, and thus in thefe 
 fpeculates thufe } in thf^ fame manner as, when imagination is not fufficient for this purpofe, it 
 even proceeds to external matter, in which it defcribes its theorems. Its principal intention, 
 however, in this cafe is, not to apprehend the fenfible form which has an external pofition, but 
 that interior vital form in the mirmr of imagination, M'hich the inanimate exterior form imi- 
 tates. After tlie fame manner alfo, when geometry is converfant about the imaginable foim, it 
 is not employed about it as tlie principal objedl of its energy-, but fince, through the imbecility 
 of its intt lleftion, it is incapable of apprehending form diverted of imagination, it directs its 
 eye to the imaginable figure. As every imaginable firm, therefore, ranks among particulars, 
 but demonftration is diredled to that which is univerfal, the principal employment of geometry 
 is not about imaginable form, but about that which is univerfal and immaterial. 
 
 * Again Ariftotle recurs to his former reafonlng, in which he inquired how mathematical 
 entities are both more imperfe£l than and prior to fenfibles. But he here inquires what the 
 caufe is by which mathematical magnitudes arc united. For, to fenfibles, nature, or material 
 
 form.
 
 SooK XIH. ARISTOTLE'S METAPHYSICS. 309 
 
 which are here either refiue in the foul, or in a part of the foul, or in fome- 
 thing which participates of reafon. But, if this is not the cafe, they will be 
 many, and will be diiroved. However, as thofe are divifible and quantities, 
 what is the caufe of their being one, and fubfifting in conjunction ? Further 
 ftill : this Is evinced by generations ■=. For that which pertains to length is 
 firlt produced, aftervvfards that which pertains to breadth, and, laftly, that 
 which pertains to depth ; and thus the end is obtained. If, therefore, that 
 which is pollerior in generation is prior in eflTence, body will be prior both 
 to fuperficles and length ; and thus will be perfect and more a whole, becaufe 
 it is animated. But how will a line or fuperhcies be animated ? For this 
 will be an a::iom above the reacli of our fenfes. 
 
 Again : body indeed is a certain eifence f ; for it already podefles in a 
 certain refpect the pcrfedT:. But how can lines be faid to be eflences ? For 
 they are nor eflences, in the fame manner as a certain fpecies and form, as if 
 a thing of this kind were foul j nor are they elTences after the fame manner as 
 
 form, is the cement or bond : but what is the bond to mathematical entities ? We reply, that 
 tb.e impartible reafons of magnitudes are better, lince they fubfiH in profound union, than ima- 
 ginable magnitudes, and, in confequence of depending on their impartibk' caufe, are free from 
 the difperfion with which interval is attended. And befides this, as they fubfift in foul, they 
 receive from it a far greater union than fenfibles. 
 
 • As mathematical entities are without generation, the only thing that can be evinced by the 
 prefent reafoning of Ariftotle is this, that in fenfibles body itfelf is eflt;ntially prior to, and more 
 perfect than, fuperficies. 
 
 f Ariftotle here apparently wifhes to evince that lines and fuperficies are pofterior to bodies. 
 For if, fays he, lines are elTences, after what manner are they elTences .'' As form, or as matter ? 
 But if they are not elTences, they will be pollerior to eflences. We reply, therefore, that thingi 
 void of dirnenfion, fuch as reafons and forms, are elTences ; but, that things which fubfift with di- 
 mcnfion in the phantafy, are as the matter of right lines or circles. If any one indeed aflerts that 
 imaginable caufe in the imagination fubfifts there as in a fubje(Sl, he mull necefTarily admit that it 
 is pollerior to, and more imperfedl than, its fubje(Sl. But it does not follow, that it is pollerior to 
 fenfible eflence. For not every thing which is in a fubjecl is pollerior to every ellence -, lince, 
 if tills were the cafe, the virtues of the foul and the fciences would be fuboi-dinate to Hones and 
 other material bodies. But it is univerfally true, that whatever eilentially refides in a fubjeft 
 is pollerior to that fubje£l ; at the fame time that it is neither pollerior to, nor more imperfect 
 than, another thing which is of an inferior nature. Unlefs fomc one (hould have the hardinefs 
 to alTert that Icience and virtue are things fubordinate to body. But, furcly, foul and what be- 
 longs to foul are more excellent than body and all corporeal properties. And foul, indeed, fur- 
 palTes thofe things that refide in it as a fubjecl, whether they are in capacity or in energy -, but 
 body is more honorable than its accidents. 
 
 matter, 
 
 /
 
 5Ja ARISTOTLE'S METAPHYSICS. Book XIIL 
 
 matter, as if a thing of this kind were body. Tor it does not appear that any- 
 thing is capable of fubfilling either from fuperficies or points. But if it 
 were a certain material elfcncc, it might appear capable of fufFering this. 
 Mathematical natures, therefore, are prior in definition * to fenfibles ; yet it 
 does not follow, that all luch things xTS are prior in definition are alio prior 
 in eflence. For, things prior in effcnce are fuch as, having a feparate fubfift- 
 ence, tranfcend i'n being: but things prior in definition are thofe, the defini- 
 tions of which are conipofed from definitions, Thefe, however, do not fub- 
 fift together : tor, if paOlons do not fubfift apart from eiTences, as, for inftance, 
 lomething moved, or fomething white, whitenefs is prior to a white man, 
 according to definition, but not according to eflence ; for it cannot have a 
 feparate fubfiftence, but always fubfifl:s together with the whole: but 1 mean 
 by the whole, the white man. So that it is evident that neither is that prior 
 which fubfifts by ablation, nor is that pofterior which fubfifts from addition : 
 for, by the addition of whitenefs a man is denominated white. That mathe- 
 matical natures, therefore, do not poflefs a greater degree of entity than 
 bodies, and that they are not prior in eflence, but only in definition, to fen- 
 fiblcs ; and alfo, that they cannot have a feparate fubfift;ence, has been fuffi- 
 cienily fliown. Since, however, they cannot fubfifl; in fenfibles, it is evident 
 that, either they altogether have no fubfiftence, or that they fubfift after a 
 certain manner, and on this account fimply are not : for we fpcak of being 
 multifarioufly. 
 
 * Ariftotle here granfs that mathematical entities are prior in definition to fcnfibles, fince he 
 who defines a ftnfible body requires the three dimenfions which limit mathematical body ; but 
 he apparently denies that they are prior in eficnce. But, that he is not ferious in what he fays 
 IS evident from lience, that, according to the rules delivered by him in the feventh book of this 
 work, in fimple eflences (viz. eflences which are confidcred without accidents), that which is 
 prior in definition is alfo demonftrated to be prior in eflence. For he there fays that things 
 which are prior in definition are alfo prior in fpecics ; but things prior in fpecics are prior in 
 eflence ; and confequcntly things prior in definition are prior in elTencc. Mathematical entities, 
 therefore, are, according to Ariftotle, prior to fenfibles both in definition and eflence. Indeed, 
 he who rightly confiders the dimenfions about which geometry is employed, will find them to 
 be in all things prior to a material body, if it be univerfally acknowledged that immaterial na- 
 tures are prior to majteiial, univerfals to particulars, and things eternal to fuck as are corrup- 
 tible. 
 
 CHAP.
 
 BookXIIT. AR'ISTOTLE'S METAPHYSICS. 3fl 
 
 CHAP. III. 
 
 As upiverfiils In the mathematics are not converfant with any other fepa- 
 rnted natures than magnitudes and numbers, but are employed about thefe, 
 th3Ui;n not ib far as they are fuch things as poilefs magnitude, or are divi>- 
 fib's^ \z is evident that definitions alfo and demonftrations take place about 
 fenfi'-iie magnirudes, but not fo far as they are fcnfibles *, but fo far as they 
 are confidered univerfally. For, as there are many reafons of things in mo- 
 tion, 
 
 * We hnve already fliown, that mathematical entities do not fubfift by a denudation from fcn- 
 fibles. We fliall no-v obfcrve, in reply to what Ariftotle fays refpeding the non-exiftence of 
 motion feparate from fenfibles, that the arguments concerning motion are not (imilar to thofe 
 concernint^ figures. For he who is not willing to admit the exiftence of motion feparate from 
 fenfioles, does not undcrltand a motion more certain than that which is in moveable entities; 
 but geometry underftands things more certain than fenfible figures. In fliort, we may fay, in 
 anf-.ver to the whole of his reafoning, that we neither behold all the figures nor all the numbers 
 contained in fenfibles, nor is it poifible for things derived from fenfibles to pofiTefs mathematical 
 accuracy and certainty. But if it Ihould be faid, that v/e add what is wanting, and make the 
 things abltraaed from fenfibles more fcertain, and after this manner coufider them ; in the 
 firil place, indeed, it is requifite to fay whence we derive the power of thus giving them perfec- 
 tion. For we Ihall not find any more true caafe than that affigned by the antients ; I mean, 
 that the foul, prior to the energies of fenfe, eflentially contains the reafons of all things. But 
 in the next place, by adding fomething to the things abftra£led from fenfibles, we do not make 
 them more certain and true, but, on the contrary, more fictitious^ For, if any one blames 
 the perfon of Socrates, while he accurately preferves in his imagination the image which he has 
 received from the fenfible Socrates, he will have an accurate knoA'Iedge of his perfon ; but if he 
 wifhes to tranbform it into a more elegant figure, he will rather confider the transformed figure 
 h.in -he form of Socrates. But nothing of this kind takes place in equal and fimilar numbers 
 amt figures ; but by how much the nearer we bring them to the more certain and perfect, they 
 become by fo mu h the more manifefl and known, in confequence of approaching fo much the 
 n-'arer to their ow.i impartible form. "We may fay, indeed, that we are excited to the percep- 
 tion of mathematical truth-s by fenfible objeifts ; but it mull by no means be admitted that they 
 derive their fubfiftence by an abftracftion from fenfibles. For the forms, indeed, which are 
 tranfuiitted to us through the fenfcs, may proceed as far as to the imagination, in wliich they 
 wifh to retain an individual fubfiftence, and to continue fuch as they entered. When intelleft, 
 however, afterwards pafles beyond thefe to univerfal, and to things which are apprehended by 
 fcientific reafoning, it plainly evinces that it confiders objefts allied to Itfelf, and which, indeed, 
 are its legitimate progeny. Hence, this energy is emulous of divine energy and not laborious, 
 and has a power of exciting, purifying, and enlightening the dianoetic eye of the foul, which is 
 blinded and buried by ftudies of a different kind. But how could this be effefted, if it were 
 employed about things which alone fubfift by a denudation from fenfibles? The contrary to 
 this, indeed, would rather be effefted j the fplendid eye of intellect would be darJcened' and
 
 Srj ARISTOTLE'S METAPHYSICS. TBook XIII. 
 
 tion, fo far as they are in motion only, without confidering what the nature 
 is of each, or what the accidents which belong to them ; and yet it is not ne- 
 cciTary on this account, that there fliould be any thing in motion feparated 
 from fenfibles, or that in things in motion there fhould be any feparated 
 nature ; in like manner there will be reafons and fciences about things which 
 are moved, yet not fo far as they are moved, but fo far as they are bodies 
 only: and again, io far as they are luperficies only, and fo far as they are 
 lengths only, and fo far as they are diviiible ; likewife fo far as being indivi- 
 fible they have pofition, and fo far as they are indivifible only. So that,- 
 fmce it is hmply true to fay that there are not only things feparable, but alfa 
 things not feparable, fuch as things in motion, and fuch as are mathematical : 
 (lince it is fimply true to affert that thele are fuch things as they are faid ta 
 be,) and as. with refpedl to other fciences, it is fimply true to fay that they 
 are converfant with this definite particular, and not with that which is acci- 
 dental ; as, for inftance, with that which is white, if that which is falubrious 
 fliould be white, but yet fo far as it is falubrious ; they are not converfant, I 
 fay, with that which is accidental, but with that to whicli each particular be- 
 longs—if falubrious with the falubrious, if with man {o far as he is man. In 
 like manner with refpeft to geometry, it does not follow that, though the 
 objects with which it is converfant are fenfible, and though it is not converfant 
 with them fo far as they are fenfible — it does not follow, 1 fay, though this be 
 admitted, that the mathematical fciences do not depend on fenfibles, or that 
 they are employed about other feparate natures. But there are many eflen- 
 tial accidents to things, fo far as each has its peculiar charaderiftic ; fince, fo 
 
 fixed in body, and ks native tendency to true beings reflrained, by being bufily employed, as in 
 the perception of fliadows, about things of pofterior origin, dark imitations of reality, and 
 more vile than matter itfelf. 
 
 In fliort, one of thefe two things mufl follow : either that mathematical demonftrations are 
 lefs certain than phyfical reafons, or tliat the mathematical fciences are converfant with things 
 •which poflefs more reality than phyfics. For it is not reafonable to fuppofe that things which 
 have more of reality fliould be more obfcurely known, nor that things which are Itfs real fliould 
 be more manifeflly known. But whenever tliis happens in the fpeculation of any intelligible 
 cflencc, it is the confequence of our imbecility, and does not arife from the thing itfelf : for 
 the afiertion of Plato in this refpedT: is moft true, that every thing participates of fplendor and 
 knowledge, in proportion as it participates of truth and being. The fame thing alfo is mani- 
 fellly adcrted by Ariflotle in the fecond book of this work ; for he therj exprefsly fays, " Js it 
 the being of every thing, fuch alfo is its irtith." So that it clearly follows, from Ariilotle himfelf, 
 that fenfible objeiSls have Icfs reality than matliematical entities. 
 
 far
 
 BookXIII. ARISTOTLE'S METAPHYSICS. 31S 
 
 far as an animal Is feminine, and fo far as It is mafculine, thefe are Its peculfar 
 paffions ; although there is not any thing feminine nor any thing mafculine 
 feparate from animals. So that, fo far as geometry confiders lengths alone, 
 and fiiperficies alone, and by how much the more it is employed about things 
 which are prior in definition and more fimple, by fo much the more will it 
 poflefs the accurate and the certain : but the accurate is that which is fimple. 
 Hence, geometry rather fpeculates things without magnitude, than according 
 to magnitude, and in a particular manner it fpeculates things without motion. 
 But if it contemplates motion, it efpecially contemplates that motion which 
 is firft ; for this is moft fimple and regular. The fame reafoning will alfo 
 take place refpecting the harmonic * and optic fcience : for neither fpecu- 
 lates fo far as fight or fo far as found, but fo far as the objeds of fpeculation 
 are lines and numbers ; for thefe are the proper paflions of thofe. And in a 
 fimilar manner with refpedt to the mechanic fcience. So that, if any one, ab- 
 ftradling from accidents, confiders any thing refpeding thefe fciences fo far 
 as they are fuch, he will not through this be in the fmalleft degree deceived f, 
 as neither when he defcribes any thing in che earthj, and calls that pedal 
 
 * The optician does not fpeculate the form of fight, or the mufician the form of voice j but 
 the former directs his attention to the rays of light, and the latter to numbers which have a rela- 
 tion to each other ; thefe being the eflential properties of fight and found. The truth is, how- 
 ever, that optics makes the rays emitted to fenfible obje£is from the luminous fpirit or vehicle 
 of our foul, fimilar to the lines which fubfift in the phantafy, and the fame luminous fpirit- 
 Hence, alfo, Ariftotle fomewhere obferves that optics ufes phyfical, as if they were mathemati- 
 cal lines, thus properly referring images to their proximate exemplars ; fince it is not poffible to 
 know an affimilated thing, except by its relation to a paradigmatic caufe. The mufician alfo 
 refers numbers which are contained in a fubje£l, and which fubfift in other things, to feparate 
 numbers, which are both produ£live of them and are their exemplars, and whence they can alone 
 participate of certainty. After the fame manner, the mechanic alfo, in giving (hape to matter, 
 refers the whole of his operation to immaterial figures, which fubfift; in the phantafy with di- 
 menfion, and impartibility in intelleft. For all thefe difciplines, though they recur to matter, 
 and are inclined to things exterior, yet as they operate under the pure mathematical fciences, 
 they are referred to them, and ufe the theorems of thefe fciences. 
 
 f The true reafon why this takes place is, becaufe he who abflrails from accidents paiTes 
 from conjoined to unconjoined figure, and from the partial and material to the univerfal and 
 immaterial, in which both a variety of reafons, and multitude of theorems, prefent themfelves 
 to the view. 
 
 J This is not fimilar to the inftance juft before adduced ; for the quantity of the thing de- 
 fcribed is not aflumed in the propofition. But demonftration makes mention of, and is compofed 
 from, univerfals. So that the mathematician principally difcourfes concerning thele, and not of 
 the things which are in fenfible figures, or magnitudes. 
 
 S i which 
 
 /
 
 314 ARISTOTLE'S METAPHYSICS. Book XIII, 
 
 which is not pedal : for there Is nothing fa1fe in the propofitions. But 
 each particular will thus be contemplated in the beft * manner, if any one 
 confidcrs that as feparate, which has not a feparate fubliftence, as the arithme- 
 tician f does, and alfo the geometrician : for man is one and Indivifible fo far 
 as man. But the arithmetician eftablifhes an Indivifible one ; and after- 
 wards confiders, whether any thing happens to man fo far as he is Indivifible. 
 On the other hand, the geometrician confiders man neither as man, nor as 
 indivifible, but as folid. So that on this account geometricians fpeak with 
 redltude, and dlfcourfe about beings : for being is twofold ; one kind fub- 
 fifting in energy, and the other materially. But fince the good is different 
 from the beautiful if (for the one is always converfant with pra<5lical affairs, 
 
 but 
 
 * This is perfectly true. For that which is in a fubje£V, and has rot one feparable caufe, 
 will be known in the bed manner, in its fubjeft: as the form of Socrates will be more known 
 and manifeft in the body of Socrates than when by abftraftiou it is confidered feparate. And 
 becaufe this happens to be the cafe with every thing which fubfifls in common in bodies, or, in 
 other words, with univerfal, confidered according to its ultimate participation, the intelleftioii 
 of this, when it is feparated, can for no other reafon be the beft, than becaufe we effentially 
 contain the forms of all things, (the foul being as it were an omnlform image, wa^/uofipov aya^fjia,) 
 which revolving and unfolding by a dianoetic energy, we produce every fpecies of fcience. 
 
 t It may here be afked. What is that which leads figure and magnitude from capacity into 
 energy? For certainly the geometrician, by preferving capacity, does not underfland thefe in 
 capacity, but he then undcrftands them when he has brought them into energy. But, if this 
 be the cafe, he gives form to them, makes them more certain, and perfefts them. How, there- 
 fore, could he accomplirti this, unlefs he pofTefled in himfelf things in energy ? Hence, 
 Ariftotlc fays, that by that alone which is energy that which is in capacity is perfected, and led 
 into energy. Befides, neither can the geometrician entirely derive the obje&s of his fpeculation 
 from fenfibles : for he contemplates many figures, and pofitions of figures, which the fenfible 
 world does not receive. And, in the next place, if thefe things fubfift in energy in fenfibles, 
 but are confidered feparate from fenfibles in capacity, how is that wliich is in capacity more 
 certain than that which is in energy i 
 
 t In addition to what has here been well faid by Ariftotle, againfl; Ariftippus, we may aflc 
 whence mathematical entities derive the good, the commenfurate, and the finite .' For intelli- 
 gibles arc better than tliis divifion and evolution of reafons. It remains, therefore, that they 
 muft pofiefs a middle nature between intelligible and material forms ; fo that they will be more 
 divided and multiplied than intelligibles, but more united than fenfibles. They will alfo be 
 orderly difpofed and meafured by certain univerfal reafons, and immaterial forms, which per- 
 petually endure in a becoming manner, and proximately prefide over fenfibles. But, above all, 
 it may be confidently aflerted, that the mathematical fciences can only have been treated with 
 contempt, from not confidering their objects a;, having a feparate fubfiftence. For in things 
 void of eflence, of pofterior origin, and which are the fimilitudes of fenfibles, what can there be 
 
 which
 
 Book XIII. ARISTOTLE'S METAPHYSICS. 315 
 
 but the beautiful Is alfo in immoveable natures), thofe who fay that the 
 mathematical fclences aflert nothing refpedling the beautiful or the good, 
 fpeak falfely : for they fpeak about thefe, and efpecially render them mani- 
 feft. For though they do not employ thefe names, yet when they exhibit 
 the operations and reafons of thefe, do they not fpeak concerning them ? 
 Indeed, the greateft fpecies of the beautiful are order, fymmetry, and the 
 definite, which the mathematical fciences efpecially evince. And fmce thefe 
 appear to be the caufes of many things, (I mean, for inftance, order and the 
 definite) it is evident that they fpeak of fuch a caufe as is after a certain 
 manner beautiful. But about thefe we fhall elfewhere fpeak more perfpi- 
 cuoufly. Concerning mathematical* natures, therefore, that they are 
 
 beings, 
 
 which depends on good or order ? fince, thus fubfifting by a denudation from fenfibles, they 
 will be full of obfcurity, nothingnefs, and ignorance. They will poffefs no good, nothing of 
 order, nothing adorned with the fplendors of bound. For ultimate good, the moft obfcure 
 gradation, and the laft boundaries are to be found in fenfibles. So that, any nature pofterior 
 to that which is fenfible (and fuch is that which fubfifts by abftraftion from fenfibles) muft ne- 
 ceffarily be unadorned, inordinate, infinite, and non-eiTential. But, if the mathematical fciences 
 are the receptacles of beauty, of a fair variety of propofitions and theorems, and of an admirable 
 order, their objefts muft be better than fenfibles, and muft as far tranfcend them, as that which 
 fubfifts perpetually the fame, furpafles that which fubfifts ditFerently at different times. 
 
 * He who reads and underftands the admirable work of Jamblichus IlEfi thj xoivh; naSn/jtaTixnt 
 £7n(7T>ifi)i,-, i. e. On the commcn Mathematical Science, publifhed by Villoifon in his Anecdota Graeca, 
 will clearly perceive the eflence, power, and energies, of the whole of the mathematical fcience ; 
 what the common fpeculation of it is, and to what genera it is extended ; what the principles 
 arc of the mathematical fciences, and in what they differ from other principles ; what the na- 
 ture is of the principles of other efTences, and how principles of this kind impart a common 
 caufe to all the mathematical fciences. He will likewife know what the principles are of each 
 of thefe fciences, as of numbers, figures, harmonies ; how they accord, and in what they differ 
 from each other ; what the beft ufe is of the ftudy of the mathematics, and to what end the beft 
 treatife concerning them ought to be referred ; what that is, which is fubje£led to each of thefe 
 fciences, as the proper objedt of fcientific knowledge ; what the common judicial inftrument 
 is of all the mathematical fciences, and how this is difcovered by the fe£lion of a line, delivered 
 by Archytas, and by Plato in his Republic ; whether the efTence of thefe difciplines is firft ter- 
 minated in foul, or prior to foul, becaufe foul is felf-motive, but thefe are immovcible. He 
 will alfo learn that the foul principally confifts from mathematical reafons, as Plato, and, prior 
 to Plato, the Pythagoric Timaeus demonflrates -, and will know what the employment is of 
 mathematical fpeculation, and how it is acquired ; and that thefe fciences were properly deno- 
 minated mathematical, as producing in us a reminifceiice of feparate incorporeal forms. He 
 will likewife perceive what the powers are of the mathematical fcience, their orders with rela- 
 tion to each other, the differences by which they are divided, and in how many ways.they are 
 
 S f 2 underftoodj
 
 316 ARISTOTLE'S METAPHYSICS. Book XIII. 
 
 beings, and how far they are beings, how they are not in one refpedl prior 
 to fenfibles, and yet how in another they are prior, thus mych has been 
 faid by us. 
 
 CHAP. IV. 
 
 With refpedl to ideas*, in the firfl: place that opinion concerning Idea 
 is to be confidered, which does not in the leaft aflbciate it with the nature of 
 numbers, but is that which was adopted from the beginning by thofe who 
 
 underftood ; what the genera and objecTls are of this fcience, and how they differ from intel- 
 ligible eflences; what the fimilitude and diflimilitude are of the mathematical fcience, and hovv 
 far they are extended ; and in what they differ from intelligible and fenfible f3militi;..cs and 
 difTimilitudes ; how the knowledge of thefe faiences pervades through the whole of philofophy, 
 and how many advantages they confer on theoretic and pra£lical fciences ; what are ihe Piodes 
 peculiar to the Pythagoreans in treating on thefe fciences, ard how they employed them ; 
 what the Pythagoric divlfion is of the whole of the mathematical fcience into genera, and mod 
 proper fpecies; what the definitive method is of this fcience, how it is effected, and what 
 utility it confers on fcience ; what the demonftrative method is, and whether it derives this 
 from itfelf, or clfewhere. 
 
 All this, and ftill more than this, the reader may learn from this invaluable work ; and, if 
 together with this he has experimentally learned, in the language of the divine Plato, that the 
 foul, through thefe difciplines, has an organ purified and enlightened, which is blinded and 
 buried by ftudies of another kind, an organ better worth faving than ten thoufand eyes, fince 
 truth becomes vifible through this alone, — if he has learned this, he will indeed be fearful 
 of drawing down to an uneffential fubjecl; a fpecies of fpeculation fo beautiful and varied with 
 fcientific and intellectual reafons, and fo calculated to lead us back to the true purity and per- 
 fection of our nature. 
 
 * The Pythagoraeans and Plato did not denominate idea from one thing, and ideal number 
 from another. But fince the affertion is eminently true, that all things are fimilar to number, 
 it is evident that number, and efpecially every ideal number, was denominated on account of 
 its paradigmatic peculiarity. If any one, however, wifhes to apprehend this from the appella- 
 tion itfelf, it is eafy to infer that idea was fo called, from rendering as it were its participants 
 fnnilar to itfelf, and imparting to them form, order, beauty., and unity ; and this in confequence 
 of always preferving the fame form, expanding its own power to the infinity of particulars, and 
 invefling with the fame fpecies its eternal participants. Number alfo, fince it imparts proportion 
 and elegant arrangement to all things, was allotted this appellation : for the antients, fays 
 Syrianus, call to adapt or compoje, a^t/ai arfai, whence is derived a^tS/iOf arithmos number. Hence 
 avapaioi' anarfion, among the Greeks fignlfies incompojtte. Hence too, (he adds) thofe Grecian 
 layings, you luill adapt the balance, they placed number together -with them, (aj ifi/<ov iQtvro (/.era afinv), 
 and alfo number and friendjbip. From all which, number was called by the Greeks arithmos, 
 as that which meafures and orderly arranges all thirgs, and unites them in amicable league. 
 
 fuft
 
 BookXIII. ARISTOTLE'S metaphysics. 317 
 
 firft aflerted the exiflen'^e of ideas. But the opinion * refpeding forms was 
 entertained by the advocates for their fubfiRence, in confequence of their 
 being perfuaded of the truth of the Heracliisean arguments, that all fenfible 
 things are in a perpetual flux ; fo that, if any thing is the objed of fclence 
 
 and 
 
 * The followers, however, of Socrates and Plato did not perfeflly accord with Heraclitus 
 in their dogmas refpeding a fenfible nature, as is evident from the Thesetetus and Cratylus of 
 Plato; nor did they, from the ever-flowing nature of thefe, arrive at a knowledge of the deter- 
 minate caufes of beings. But that there is no fcience of things in a continual flux, was not 
 only the opinion of Plato, Socrates, and the Pythagorxans, but alfo of Ariilotle. Nor is there 
 any fcience of particulars, whether they flow in toto, according to Heraclitus ; or are perpetu- 
 ally generated and corrupted, but ar» permanent, collectively confidered, or according to the 
 whole of themfelves, through an ideal caufc, according to Plato ; or are the only things that 
 have a fubfiftence, according to the Stoics : for all ph'lofophers deny that there is any fcience 
 of individuals, unlefs we are willing to call fenfation fcience, which will not be attempted by 
 any one who is in the lead Ikllled in the mathematical difciplines. 
 
 But, omitting the further confideration of tliefe things for the prefent, it niuft by no means 
 be granted, as the words of Ariilotle feemlngly imply, that Socrates arrived at unlverfals for 
 the fake of definitions, and that he confidered thefe as infeparable from particulars, but that 
 Plato and Socrates, either being ignorant of or paffingby the ufe of unlverfals, afcrlbed to them 
 an abflraft eflence. For neither did Socrates confider things definable as the only unlverfals, 
 but, prior to thefe, he eftablllhed thofe reafons or principles produdlive of fcience which efien- 
 tlally refide in the foul, as Plato fhows in the Ph.edrus and Phxdo. In the tenth book of the 
 Republic, too, he introduces Socrates as venerating thofe feparate forms which fubfifl in a 
 divine intellefl: ; and in the Phaedrus, as aflerting that fouls, elevated to the fuperceleftial plate, 
 behold juftlce itfclf, temperance itfelf, and, befides thefe, fcience itfelf; and laftly, in the 
 Phxdo, evincing the immortality of the foul, from the hypothefis of feparate forms. For how, 
 as Syrianus juftly obferves, is it pofTible that Plato fhould not have delivered to us the genuine 
 do(flrine of Socrates, fince he was the moft juft of all men, and the moft worthy to be believed ? 
 
 Syrianus further obferves, that this dodtrlne was not derived fronr Socrates, but had a higher 
 origin, from Pythagoras, and the leaders of the Eleatic fedl. For Timxus, who was a Pytha- 
 gorean, afcribes the generation of the univerfe to feparate forms, and aflerts both that they are, 
 and that they are the caufes of fenfibles ; and Parmenides fays, " that he who does not permit 
 the idea of every thing which exifts to be always the fame, will entirely deflroy the difcifrfive 
 power of the foul." 
 
 Syrianus then proceeds to (how, in defence of Socrates, Plato, the Parmenidaeans and Py- 
 thagora:ans, that ideas were not introduced by thefe divine men, according to the ufual meaning 
 of names, as was the opinion of Chryfippus, Archedemus, and many of the junior Stoics ; ios 
 ideas are diftinguiflied by many differences, from things which are denominated from cuftom. 
 Nor do they fubfift together with intelleCl, in the fame manner as thofe flender conceptions, 
 which are commonly called abftraft ideas, or unlverfals abftradt'-d from fenfibles, which was 
 the hypothefis of Longinus : for, if that which fubfifls is unfubftar .i-.d, it cannot be confub- 
 fiftent with intellect. Nor are ideas according to thefe men notions, as Cleanthes afterwards 
 
 aflerted
 
 3J8 ARISTOTLE'S METAPHYSICS, Book XIII. 
 
 and inlelletflual prudence, there mufl neceflarily be certain other permanent 
 natures befides Tenfibles ; for there is no fcience of things flowine;. But 
 Socrates, employing himlelf about moral virtues, iirll of all explored the 
 manner of defining refpedting thefe : for Democritus touched only upon 
 
 phyfics 
 
 alTertcd them to be. Nor is idea, definitive reafon, nor material form, and the obje£l of 
 definition, as here and ell'ewhere Ariltotle pretends it is, according to Socrates -, for thefe indeed 
 fubfifl; in compofition and divifion, and verge to generation and matter. But ideas are perfe£l, 
 fimple, immaterial and impartible natures. And what wonder is there, fays Syrianus, if we 
 fhould feparate things which are fo much dillant from each other ? Since neither do we imitate 
 in this particular thefe Platonifts, Plutarch, Atticus, and Democritus, who, becaufe univerfal 
 reafons perpetually fubfifl in the elTence of the foul, were of opinion that thefe reafons are ideas: 
 for though they feparate them from the univerfals in fenfible natures, yet it is not proper to 
 conjoin in one and the fame, the reafons of foul, and an intelleift fuch as ours which is called 
 material, with paradigmatic and immaterial forms, and demiurgic intelleftions. But, as the 
 divine Plato fays, it is the province of our foul to collect things into one by a reafoning pro- 
 cefs, and to poflefs a reminifcence of thofe tranfcendent fpe£lacles which we once beheld, when 
 governing the univerfe in conjunction with Divinity. Boethus the Peripatetic too, with whom 
 it is proper to join Cornutus, thought that ideas were the fame with the univerfals in fenfible 
 natures. However, whether thefe univerfals are prior to particulars, they are not prior in 
 fuch a manner as to be denudated from the habitude which they poflefs with refpedl to them, 
 nor do they fubfift as the caufes of particulars; both which are the prerogatives of ideas : or 
 whether they are poRerior to particulars, as many are accuftomed to call them, how can things 
 of polterior origin, which have no eflentia! fubfillence, but are nothing more than (lender con- 
 ceptions, fuilain the dignity of demiurgic ideas .' 
 
 In what manner, then, do ideas fubfifl: according to the contemplative lovers of truth ? We 
 reply, Intelligibly and tetradically (voma; xai TeTfaSixu;) in animal itfelf (ev tm auroiuui) or the 
 extremity of the intelligible order * ; but intelleftually and decadically (voc^u; nai hua^MUi) in 
 the intelka; of the artificer of the univerfe : for, according to the Pythagoric hymn, " Divine 
 number proceeds from the retreats of the undecaying monad, till it arrives at the divine tetrad 
 which produced the inother of all things, the univerfal recipient, venerable, circularly invefting 
 all things with bound, immoveable and unwearied, and which is denominated the facred decad, 
 both by the immortal gods and earth-born men." 
 
 TT^otKrt yap o Seio; ajiS^o;, u( fri<rtv I YluSayoptic; £:{ auTOv i/xvij, 
 
 Movaio; IK xiii9iJi.iiivoi axr]^arou eitt', av ixiiTai 
 TfTfafa trri fafie>iv, v Jo tskc junrffa ttouituv, 
 ni»5£Xf<*» wfEirffifav, ofov ijrcpi Trari Ti6£i<rav, 
 ArpoitoVf axa/jiaTov, iexaSa xhtiouat /uiv ayviiv 
 
 AdavaTOI T£ ^£01 XCl 7»I7£V££1{ UvS^UTTCt -f , 
 
 • For as account of this order, fee my Introduftions to the Timaeus and Parmcn cIl^ of Plato. 
 t Froclus in Tim. p. i6^. But t ic laft line is from Syr.anus. 
 
 And
 
 BookXIII. ARISTOTLE'S metaphysics. 319 
 
 phyfics in a fmall degree, and defined how the hot and the coM fubfift : but 
 the PythagorcGans prior to him invented definitions refpedling a certain few 
 particulars, the realbns of which they referred to numbers ; as, for inftance, 
 what opportunity is, what the yV//?, or what marriage is. Socrates, indeed, 
 rationally inquired tihtv- the what : for he fought how to fyllogife ; but the 
 principle of fyllogifms is the what. For dialedic ftr^ngth did not then 
 exift ; fo that they were able without the pofTeffion of the whiit, to con- 
 fider contraries, and whether there is the fame fcience of contraries : for 
 there are two things which may be juftly attributed to Socrates, indudive 
 arguments, and the definition of univcrfal : for both thefe fubfift about the 
 principle of fcience. But Socrates did not confider univerfals and definitions 
 as things which have a feparate fubfiflence; but others feparated them, and 
 denominated things of this kind the ideas of beings. So that, for the fame 
 reafon, it nearly happened to them that there are ideas * of all things which 
 
 are 
 
 And fuch is the manner of their fubfiflence according to Orpheus and Pythagoras. Or, if 
 it be requifite to fpeak in more familiar language, an intelle£l fuflicient to itfclf, and which is 
 a moft perfeft caufe, prefides over the wholes of the univerfe, and through thefe governs all its 
 parts i but at the fame time that it fabricates all mundane natures, and benefits them by its 
 providential energies, it preferves its own moft divine and immaculate purity ; and while it 
 illuminates all things, is not mingled with the natures which it illuminates. This intellecSt, 
 therefore, comprehending in the depths of its eflence an ideal world, replete with all various 
 forms, excludes privation of caufe, and cafual fubfiftence, from its energy. But as it imparts 
 every good and all pofiible beauty to its fabrications, it converts the univerfe to itfelf, and 
 renders it fimilar to its own omniform nature. Its energy, too, is fuch as its intelle£lion ; but 
 it underftands all things, fince it is moft perfe£l. Hence, there is not any thing which ranks 
 among true beings, that is not comprehended in the eflence of intelledl ; but it always efta- 
 bliflies in itfelf ideas which are not different from itfelf and its effence, but give completion to 
 it, and introduce to the whole of things a caufe, which is at the fame time produ£live, paradig- 
 matic, and final : for it energifes as intellect \ and the ideas which it contains are paradigmatic, 
 as being forms ; and they energife from themfelves, and according to their own exuberant 
 goodnefs. And fuch are the dogmas which he who truly oppofes the advocates for the doc- 
 trine of ideas ought to confute ; but which Ariftotle does not any where attempt to contradift. 
 
 * From the Platonic theory of ideas, it follows, that though thefe lucid beings arc univerfals, 
 yet there are not ideas of all^univerfal conceptions of the mind : " for, in the firft place, fays Syri- 
 anus, there are no ideas of things evil and bafe, becaufe thefe fubfift in nature rather by a privation 
 and abfence of ideas. And on this account they are faid to exift contrary to nature. Nor fecondly, 
 of negations, for thefe are deftruftive of the bound and limitation, which are attributed to every 
 thing from the unifying and comprehending nature of ideas ; and hence, feparation is rather 
 the refult of material infinity, than of that which is formal or ideal. Nor, again, are there any 
 
 ideas
 
 320 ARISTOTLE'S METAPHYSICS. Book XIII. 
 
 are predicated unlverfally : and this is juft as if fome one wifliing to enu- 
 merate *, ftiould be of opinion that when there are fewer things he cannot, 
 but when he has made more he will be able to enumerate : for, as I may 
 fay, forms are more in number than fqnfible particulars, from an inquiry 
 
 into 
 
 ideas of things which at different times receive a variety of conditions : for thefe participate of 
 tranfmutatlon from 3 moveable caufe, but not from the immoveable and (table illuftration of 
 ideas. Further ftill : there are no ideas of parts, fuch as the hand, head, fingers, and the like : 
 for the caufes of things exifling entire, produce vvhole fpecies and forms, and are not divided 
 about the parts of tliefe, like the reafons of nature. 
 
 " But neither did thefe wife men place in intelle£l the determinate caufes of accidents in 
 bodies, fuch as fweetnefs and whitenefs : for they confidered that natural reafons were fuffi- 
 cient for the produdtion of accidents. Nor again, of compofites, as of a wife man. For, fince 
 ideas are fimple, they prefide over the fimple elTence of every thing. But the compofition and 
 divifion of things is the bufmefs of our intelledl ; ideas at the fame time, and that intelle£lion 
 which is co-ordinate to ideas, being exempt from all thefe, on account of tranfcendent fimpli- 
 city. Neither, therefore, muft we eftabliQi ideas of things generated from dilTimilars, fuch as 
 mules ; nor of fruit produced by ingrafting from different trees : for all thefe have a poflerior 
 and adventitious generation, and are not the vv'ork of nature alone, nor of nature proceeding 
 according to her own reafons, but, as it were, compelled to labour contrary to her own deter- 
 minations. Hence, it is manifefl that all art which imitates nature, and alone minifters ta 
 the ufe of the mortal life, is feparated from ideal caufe. But neither are the works 
 which, depending on the purpofe of the foul, are perfe(Sted by a concourfe of many caufes, 
 and which we are accuftomed to call the operations of fortune, to be conjoined with an ideal 
 caufe. For things which are there perfe^led are eternal, and fubfifl perpetually the fame, 
 free from the nature of contingent events. It remains, therefore, that ideas muft be confined 
 to univerfal and perfedl effences, and to whatever confers to their natural fubfiftence ; as for 
 inflance, to man, and every thing perfe£live of man, fuch as wifdom and virtue : for, as ideas 
 are the generative and energetic caufes of the perfe£lion of every thing, they diftribute being 
 and perfeftion to effences, and convert them to the ineshauftible plenitude of their own omni- 
 form natures." 
 
 * That Ariftotle is not ferious in this place is evident ; for what he firft fays is a mere 
 cavil, and not a confutation ; and, in the next place, he confiders the Platonifts as attributing 
 ideas to accidents. This, however, is falfe : for, according to the more accurate of the an- 
 tJent Platonifts, there are no ideas of particulars, nor of the accidents to bodies. In reply to 
 the cavil we may fay, that it is not polhble to number horfes, without employing monadic 
 number, (that is, number compofed from units), and which is different from the numbei of 
 things numerable ; number in this latter cafe, being confubfiftent with the numerated natures. 
 But, in fliort, if we do not diredt our attention to material caufes, but to fuch as are firft- 
 operative, and feparate from their effects, it is neceffary to pafs to the contemplation of other 
 natures, which, filling all things in an eternal time, with an immoveable energy, and from 
 their very cflence, with beauty and order, comprehend the caufes of things generated in them- 
 felves ; thefe caufes bcjng fewer in number than mundane natures from their proximity to
 
 Book XIII; ARISTOTLE'S METAPHYSICS. 
 
 321 
 
 in to the caufes of which, thefc men proceeded from fenfibles to ideas : for 
 ideas are homonymous with fenfible particulars, and bt fides cffcnces * 
 they are inherent in many other things, both in feafibles and things 
 eternal. 
 
 Further ftill : it does not appear from any one of thefe, according to what 
 modes f the fubfiftence of forms is evinced : for from fome, it is not necef- 
 
 fary 
 
 the one, but poflcfTing an ineffable power which comprehends the infinitude of the whole of 
 time, and the things generated in it, through a tranfcendency of nature which is exempt from, 
 and unco-orditiated with, the fenfible univeife. 
 
 * As there are many problems refpefling ideas, there are four of principal importance ; viz. 
 if there are ideas ; what are the things of which there are ideas; what are their participants, 
 whether generated natures alone, or alfo fuch as are eternal, and whether all, or only fome 
 things eternal ; and, in the fourth place, in what manner ideas are participated. The prefent 
 reafoning of Ariliotle, therefore, feems to relate to the third of thefe problems, viz. whether 
 the defenders of thefc lucid beings admitted that there is any form or idea common to things 
 generated and eternal, as, for inllance, the idea of fimilitude, or equality, or identity, which 
 both the heavens and the realms of generation participate. There is indeed no abfurdity in 
 admitting this : for though it is the fame thing which is participated, yet the mode of partici- 
 pction is difterent ; fince every thing participates principal caufes, in a manner adapted to its 
 rank in the order of things. But, left any perturbation (fays .Syrianus) fhould be occafioned 
 by arguments of this kind, let us confidcr what were the opinions of the bed of the Platonifts 
 refpe(£1:ing the participants of ideas. Numenius, then, Cronius and A melius confidered all in- 
 telligible and fenfible natures as participating ideas -, but Porphyry confinLd this participation to 
 fenfibles alone, and a(!erted that the firft and befl of intelligibles were the things which were 
 participated, but that the natures thence originating, viz. the order belonging to fouls, and the 
 fenfible univerfe, were the participants of ideas. And indeed there is no abfurdity in admitting 
 that the ideas of famenefs, equal, and fimilar, are after one mann('r participated by foul, and 
 after another manner by nature ; in one way by the heavens, and in another by the realms of 
 generation; and ihat of thefe there are indeed alliances, fynipathies, and peculiarities in the 
 participation of one idea ; notwithftanding which, tiie poilerior always depend on the prior. 
 After this.manner, indeed, idea, by no means departing from itfelf, may be conceived to be 
 impartibly prefent to all its participants. It will alfo follow that participants are adorred by 
 things prior to ihemfelves, and kd back to idea itfelf; body through nature ; this iljrcugh 
 foul ; and this again through its own intelltiS, which lubfifts in unproceeding union with 
 liiviue forms, and is therefore conjoined with them better than things which fubfill; accord- 
 ii^g to the idioms af tlu;lr participants. 
 
 f There are many ways by which the cxiftence of ideas may be proved. At prefent it 
 may fufHce to relate one of them; for we propofe, on account of its importance, to confidef 
 tliis fubjeft very fully in the additional notes which will be annexed to this work. He who 
 fabricated the univerfe is a god. Every god produces by his very eflence ; in the fame manner 
 iS fire burns, and fnow refrigerates. Every thing which produces from its very eflence, pro- 
 
 T t dues
 
 323 ARISTOTLE'S M E T xV P H Y S I C S, Book XIII. 
 
 fary that f) Uoglfin fliould take place ; but from others, even of thihgs of 
 which they do not think there arc forms, forms arifc. For, according to the 
 reafons criguiating from the fciences *, there will be forms of all things of 
 which there are fciences ; and, according to tlie one in the many, there will 
 alfo be forms of negations f : but, from our underftandlng fomething of that 
 which is corrupted, there will be forms of things corruptible J ; for there is a 
 
 certain 
 
 duces an image of Itfelf. He, therefore, who fabricated the univerfe made the world an image 
 of himfclf. If this be the cafe, he contains in himfelf paradigmatically the caufes of the uni- 
 verfe : but ihefe are ideas. 
 
 Kor is that argument in favor of their fubfiftence to be defpifed, which confiders the perfeil 
 as prior to the imperfe£l, unity to multitude, the impartible to the partible, and that which al- 
 ways fubfifis after the fame manner to that which has a mutable efience. In which the patrons 
 of ideas f\iow, that things do not begin from degraded natures, but that they end in thefe. 
 But they begin from things the mod perfect, the bell, and the moft beautiful. For it would be 
 abfurd to fuppoff; that we can form conceptions of the equal and the fimilar, and every thing 
 of this kind; confidered acccrding to their principal f.ibfiftence, but that the intellect of the arti- 
 ficer of tlie univerfe fliould not contain in himfelf the equal itftlf, the jufl itfelf, tlie bcauiifui,. 
 and the good, and every thing elfe of a fimilar nature. 
 
 * This alfo was faid by the Pythagoreans and Platonifts. If fciences are converfant with 
 beings, they are univerfals ; for fciences are of things univerfal ; fo that the fyliogifm will be in 
 the third figure. The objedls of fcience are univerfals ; the objects of fcience are beings ; there- 
 fore fome univerfals are beings. For this is not true of all univerfals ; not indeed of univerfals of 
 pofterior origin, viz. which are abflradted from fenfibles, nor of thofe which are in individuals.. 
 But there is no abfurdity in admitting that all objedts of fcience are beings, if objefls which are 
 properly fcientific are aflumed, but not the medicinal or the mechanical. For thefe are not pro- 
 perly fciences -, but thofe alone deferve to be lo denominated, which are employed about things 
 eternal, felf-fubfiltent, and perpetually the fame. 
 
 ■f That they placed unity before multitude is evident ; but they confidered this unity or 
 monad as effential and generative of multitude, and not that which is peculiar to privation. 
 For this is pofterior, and the foul perceiving the common privation of men, produces in herfelf 
 non-man, or the conception of that which is not man. But we muft not fuppofe, that, as there 
 is a certain ideal and terminated caufe in the univerfe, through M'hich all the different fpecies of 
 animals derive their perfe<Slion, fo there is fome caufe which makes all thefe privations or non- 
 men to fubfifl. For thof natures which have a principal fubfiftence in things, muft not be 
 fuppofed to depend from one and the fame caufe with thofe which are only conlidered in them 
 through a flender conception of the foul. 
 
 X The things which true intellect reaches by its proje£ting energy (coffa ETtiSof^n] are 
 real beings : for the intelledlions of true intelle£t cannot be deprived of eflence. But Ariftotle, 
 as it ap ears to r. e, drawing down intellect to imagination, for the purpofc of concealment (for 
 in other places he calls imag'nation pafTive intellefl), favf, there will thus alfo be an efience of 
 things corrupted : for any one may imagine that which is corrupted. By this, therefore, we 
 fee, that thofe who oppofe ideas aye comi'cUed to defcend from beings to privations, and from 
 
 intellea
 
 BookXIIL ARISTOTLE'S M eta physics, 323 
 
 certain phantafm of thefe. Again, with refpeift to the moft .accurate argu- 
 ments of the advocates for ideas, fome ePcabUdi ideas of things relative *, of 
 which we do not fay there is an effential genus ; but others introduce a third 
 man. And, in fhort, the aOertions refpeding forms fubvert the very things 
 the exiftence of which the advocates for forms are more willing to admit than 
 that of ideas themfelves. For it happens that the duad f is not firft, but 
 
 number ; 
 
 Intellecl: which is in energy to imagination and opinion. For we can imagine and form an opi- 
 nion of non-entity ; but it is not pollible to apprehend it by intelledual energy, or know it 
 fcientifically. 
 
 • We do not fay that there are ideas of unefTential habitudes, nor of things la motion, nor of 
 thofe things which are perfeiSted according to fome unnatural pofition, whether upwards or 
 downwards, to the right or left hand, or other things of this kind. But fuch things as become 
 relatives through the participation of any idea, as fimiiars, equals, or things different, participate 
 of thefe, indeed, with a certain genus of being, but others receive among themfelves one defi- 
 nite co-ordination of ideas. And is there any thing wonderful in alTerting that fome fenfible 
 particulars become relatives through divine forms, fince we admit that relation fubfifts alfo ia 
 the intelligible world ? But, that relatives have not an eflential fubfiflence here, is not only 
 afferted by the Platonifts, but alfo by Ariflotle himfelf : for, when we fay that this thing is a 
 caufe or principle, but another a thing caufed from a principle, do we not endeavour to fliow the 
 order which divine natures preferve amongft themfelves ? According to Ariftotle alfo, of the 
 feparate forms which he places over the mundane fpheres, fome are firfl, others middle, and 
 others lall ; and thofe are of a greater, but thefe of a lefs ambit ; fince they have the fame 
 order among themfelves, as that of the ethereal fpheres, 
 
 Ariftotle in the next place afks, how tlie advocates for ideas introduce a third man. For, as 
 all ideas fubfift in the feveral orders of beings, there \yill not only be three, but many men, be- 
 caufe all things may be multiplied : for they will fubfift in intelleft and in intellects, in one foul 
 and in fouls, in univerfal nature and in particular natures. In the heavens, therefore, and 
 the earth, and nearly in all parts of the univerfe, the fpecies man will fubfift in a manner 
 adapted to the places by which it is received. So that there will not only be t'aree men, but a 
 multitude incomprehenfible by our reafoning power. It muft, however, be carefully remem- 
 bered, that fenfible natures are not univocnl with ideas : for, how can images be univocal with 
 their exemplars ? Nor muft it by any means be thought that idea participates of any thing: 
 for ideas prefent themfelves to be participated by all things, fince they are eminently primary 
 forms. 
 
 t Thofe divine men faid, that after the one principle of all things, which they were of opi- 
 nion fliould be called the good itfelf, and the fuperciTential one, there are two ciufes of all 
 things, a monad and a duad, of infinite power ; and thefe principles they placed in an accom- 
 modated manner in tlie feveral orders of beings. For there is fomething which correfponds to 
 the good itfelf in every difpofition of things, and fomething which is appropriated to the? firft 
 iDonad, and the firft duad. But Ariftotle fays, that as they introduce among ideas the eflential 
 
 T t 3 duad
 
 324 A R I S T O T L E ' S iM E T A P H Y S I C S. Book XUl. 
 
 numLer ; and tir't, prior to this, that which is relative and the eflentlal fubfiil:. 
 And this will be the cafe wiih ati fucli particulars as, being confequent to tiie 
 opinions refpe^ting forms, are contrary to principles. 
 
 Further 
 
 tliiati and the eflential monad, in the firfl place, becaufe they nre accu'tomed to diftribute things 
 more venerable than ideal caiifes, they defbroy the nionud and duad, wl.ich r;;nk among prin- 
 ciples. For, of the firft duad or monad, which will be tlic more antient, the monad or the 
 duad? A->d in the next place, becaufe the efTentiai tetrad is double of the eflential duad, and 
 tl.'- elTentiai duad of the clTential monad ; this being the cafe, not only efiential number will ba 
 prior to the principles, but alio relative number : and, i:i (liort, Ariftotle fays that there are 
 many things of this kind, through which wifiiing to defend the theory refpetting ideas, they 
 ignorantly oppofe their proper principles. 
 
 But that all this is foreign to what thefe divine men have aflerted, Is evident to the more fag*-. 
 <;ious, prior to all reafoning ; which I think fufficiently proves that the objections of Arilfotle; 
 are merely pretended, and not ferious. However, as fome one may demand- a folution of thi; 
 fallariou? reafoning, we fay th;U the nature of priricipks is different from the nature of ideas, 
 though (bnieihing takes place about them equivocally; or rather not about them : for what cau 
 fupervene the mod divine of beings .' But it takes place about our dlfcudion of them : for the 
 duad, which ranksf^as the fecond of the two great principles, ■sXtzx the hie_ffMe one, imparts to 
 all things prolific power, progrefllon, multitude, and multiplication, and excites and moves all- 
 things to the fpontaneous generation, providential, care, and prefervation of poilerior natures. 
 Hence it fills all the divine and intelle6tual orders, and alfo the order belonging to fouls, the 
 phyfical and the fcnfible, with fuch numbers as are adapted to each; but it does not fuffer any, 
 thing to be unproduced which is in any refped naturally adapted to proceed Into exigence. 
 ^nt the duad it/elf , which has a fubfillence among ideas, imparts its own yirwz to fouls, na-^ 
 tures, and bodies. Hence,, whether the univerfc is divided, or the heavens alone, or the reafons 
 of foul alfo, or, prior to thefe reafons,cIrcles themfelves (for thefe firft employ a twofold dlvi-r 
 fion) ; or whether alfo any animal has two eyes, or two hands, or two feet, or any otlier of the. 
 works of nature poflelTes the duad, this proceeds to things from the effential duad, which ranks 
 in the order of ideas, but not from the principal duad, which is prior to ideas, and from whicl^ 
 the Ideal duad and every intelle6l derives its fubfillence. The fame alfo with refpetl to the, 
 monad : for there is one monad which has the relation of a principle, which, together with tha 
 higheil duad. Imparts fubfiftence to ail things, aijd is the leader of identity, inability, continuity, 
 and eternal life to ivholes : but another monad is the efleiitial (auro/AOvas) which lias a priority in the. 
 order of ideas, through which participating effe£ls are united, and are continued in their proper, 
 habit. As, therefore, thefe divine men introduced a leading monad and duad among ideas, they, 
 did notaffign them this dignity for the purpofe of deflroying the monad and duad which rank as. 
 principles; for how could they .■* fince they alTert that the ideal monad and duad, together with., 
 the whole of an Intelleclual and intelligible efllnce, fublill from tiie principles. 
 
 In anfvi-er llkewife to what Ariftotle fays, that they introduced monadic number, or number, 
 confiding from unities, and on this account made the efiential duad double of the efTentiai. 
 oionad, we reply, that ideal numbers are not denominated from a quantity of units, but from. 
 
 J A certain,
 
 3ccK.XrHv AR I STOTLE'S MET AP n Y S r CS, 325- 
 
 Furihci- ftill ; agreeably to that opinion * by which they fay that there are 
 idea*;, there will not: only be forms of ellences, but a'.fo oi' m.iny other things. 
 For there is not only one conception of eiTences, but ai^o of things which are 
 not effences ; and fcienccs will not alone be converfant with effence ; and ten 
 thoufand iamilar confequences will enliie. But, according to the neceffary,. 
 and the opinions refpecling Ideas, if forms may be participated, it unavoidably 
 follows, that there are alone ideas of effences : for they are not participated 
 according to accident ; fince each is necelTarily participated, fo far as it is aot 
 predicated of a fubjeift. I fay, for inftance, if any thing participates of the. 
 
 a cerfaiii character or feal of a mofi: divine and fimple eflence. Individuals participate of thefe 
 according to their nature j and, as fenfible man participates with colour, figure, and form, of the 
 eflential or ideal man, which in without colour, figure, and form ; in like manner fenfibles parti- 
 cipate with quantity of the triad itfelf, which is devoid of all quantity. To invefligate, there- 
 fore, monadic multitude among ideal numbers, is jufl the fame as to inveftigatc in the ideal' 
 man the liver, fpleen, inteftines, and the like. Hence, thefe divine men neither fubvert their! 
 principles through ideal numbers, nor introduce among intelligibles number fubfifling in habi- 
 tude. 
 
 * We have before obferved that there are ideas of unlverfal eflences, as of man, horfc, and 
 the hke, and of all fuch things as perfect thefe effences, as virtue and fcience, together with' 
 fuch things as fimiliiude, equality, and magnitude, which accede to fouls, to bodies, and' 
 to numbers. But things which accede to bodies alone, or corporeal accidents, have their 
 determinate caufes, according to Jamblichus, in the reafons or produOive powers of na- 
 ture. For the divine Plotinus obferves that the idea of whitenefs is not to be placed in intel-- 
 !ect. It does not follow, therefore, that there are ideas of all univerfal conceptions^ though the 
 converfe is true, viz. that of whatever there are ideas there are univerfal conceptions ; for, if 
 this were admitted,, there would alfo be ideas of things contrary tc> nature. But neitlier are 
 tliere ideas of all fuch things of which there are fciences improperly fo called ; though, as they 
 are eflences, it is rightly faid that they participate ideas. Yet it does not follow, that a thing is 
 eifence which participates of eflence : for we fay that fcience itfelf and juftice itfelf are eflences^ 
 but our habits are not eflences. It mufl alfo be obferved, that nothing belonging to ideas is ia 
 a fubje£l:, but that every thing which they contain tends to elTence. For Ariftotle himfelf, in 
 the eleventh book of this work, manifeftly demonftrates that nothing corporeal or incorporeal 
 has an accidental fubfiftence. We fliouid rather therefore fay, that every immaterial and divine 
 form is all-powerful in an unmultlplied, fingle, and mofl: fimple eflence, and is participated by. 
 fenfible natures partially, and not according to all its powers. The duad itfelf, therefore, con- 
 tains in its eflence the impartible, the intelligible, the produdlve, and the eternal, and none of 
 tliefe as in a fubjeft. But it is participated by a fuperior foul, according to more, but by ours 
 sccording to fewer, of its powers ;. and by bodies, or corporeal powers, fo far as pertains to one- 
 or two of its powers. Yet, as we have before obferved, it is not necefiary that all things which 
 participate of eflences ftiould be eflences ; but as certain things participate impartibles partibly,, 
 and intelligibles without intelleclion and intelleft, fo likewife they participr.te eflences widiout: 
 dleuce. < 
 
 double-
 
 3'26 ARISTOTLE'S ME TAP HYS I C S. Book XIII. 
 
 double, this alfo participates of the eternal, but according to accident : for it 
 happens to the double to be eternal j fo that forms will be effence : but thcfe 
 both here and there fignify eflence. Or, can we fay that the one in the many 
 is any thing befules thefe ? If, indeed, there is the fame form * of ideas and 
 their participants, there will be fouiething common : for why, of corruptible 
 duads, and of duads which are many indeed, but eternal, is there rather one 
 and the fame duad, than of this, and fome particular duad ? But if there is 
 not the fame form it will be homonymous, and will be juft as if fome one 
 fhould call Callias and a piece of wood a man, perceiving no communication 
 whatever between them. But if we confider other thing?, /. e. common 
 reafons f, as adapted to forms, as, for inftance, a plane figure to the circle it- 
 felf, and the other parts of the definition of a circle, that to which it belongs 
 being added, if this be done, it is requifite to confider whether or not this is 
 altogether vain. For, to what is it added ? to the middle, or to the plane, 
 or to all? For all things w^hich are in eifence are ideas, as, for inftance, ani- 
 mal and biped. Further ftill ; it is necefiary that a thing itfelf, as for inftance 
 a plane, fliould be a certain nature, which, in the fame manner as genus, is 
 inherent in all fpecies. 
 
 * But neither are ideas univocal with fenfible natures, nor are they equivocal in the fame 
 manner as things which fubfifl from fortune ; but they Iiave the fame relation as a paradigm 
 and its image ; efpecially fince the paradigm, by its very efli;nce giving fubfiftence to the images, 
 converts them to itfelf. 
 
 t In anlwer to what is now faid by Ariflotle, it is neceflliry to obferve that ideas are not, pro- 
 perly fpeaking, objefts of definition. For impartible, fimple, and intelledual forms are 
 exempt from definitive reafons, and from every thing which is naturally adapted to be confi- 
 dered by a difcurfive and evolving energy, fuch as is that of the dianoetic power. Hence Plato, 
 in his feventh epiftle, fays that the circle Itfelf is diflerent from that which is capable of being 
 defined, and which is the object of fcientific knowledge. And Ariftotle himfelf, in the eighth 
 book of this work, thinks it juft that there fliould be no definition of the moft fimple forms. 
 However, though ideas were capable of being defined, it is not neceffary that we ftiould ufe the 
 fame definitions in fenfibles as in the exemplars themfelves. For there is not the fame defini- 
 tion of the image of Socrates, and of Socrates himfelf, though the image of Socrates fhould be 
 made conformably to the Socratic form. But if any one fliould fay that there is the fame defi- 
 nition of both, what fliould prevent us from underllanding intelligible in the one and lenfible in 
 the other ? For it is fit that all things fliould fubfift intelligibly in idea (if they are altogether 
 inherent), but pliyfically in fenfibles the obfcure refemblances of ideas. Hence, idea is not in 
 reality capable of being defined ; nor, if it were,, would it be comprehended by the lame defini- 
 tion as its effcfts. Or, though all thefe particulars fliould be granted, nothing will prevent us 
 from admitting that the fame things arc intelligibly diftributed in exemplars, but imaginably or 
 phyfically in imajres. 
 
 ^ CHAP.
 
 Book Xlir. ARISTOTLE'S METAPHYSICS, 327 
 
 C H x\ P. V. 
 
 But moft of all it may be doubted* what forms contribute either to 
 things perpetual among fenfibles, or to things generated and corrupted : for 
 they are neither the caufe to them of any motion, nor of any mutation what- 
 ever. Nor yet do they afford any afli fiance to the fcience "[ of other things : 
 for, neither are they the effence of thefe (fince they would be in thefe), nor 
 do they contribute to the being of any thing, fmce they are not inherent in 
 their participants : for, if this were the cafe, they might thus perhaps be confi- 
 dered as caufes, as white mingled with white. But that reafon which Anaxa- 
 goras firft, and Eudoxus afterwards, introduced, doubting, and likewife certain 
 others, may be eafily confuted. For, to this opinion it is eafy to colleifl many 
 
 * Ariftotle inquires, refpe(fiiiig the utility of ideas, whether their fubfiftence contributes any 
 thing to fenfibles. To this we reply, that all divine natures are fuch as they are, both from 
 their own principles and from themfclves. But, becaufe their eflence is both generative and 
 providential, though they do not fubfill for the fake of fecondary natures, yet they communicate 
 eflence, power, and every perfection to things fubordinate to themfelves. Indeed, through ideas, 
 fuch things as are eternal among fenfibles, both fubCfl and perpetually endure ; natures of this 
 tind being excited to unceafing life and motion, through love of thefe all-beautiful and all- 
 perfeft edl-nces. We may likewife afk, how the mortal and material efFe£l:s of nature could 
 proceed into being, unlefs nature and thofe demiurgic caufes which employ nature as an inftru- 
 ment referred their energy to things terminated, and which have a perpetual famenefs of fubfiit- 
 cnce. For, why is not any thing produced from any mutation ? And why do the mutations 
 and progreffions of nature appear to be bounded ? Surely for no other reafon than becaufe 
 there is a pre-exiftent order in the reafons of nature. 
 
 f That the fpecuUition of ideas efpecially contributes to the fcience of other things, the divine 
 Plato every where evinces, but efpecially in the Parmenidcs, in which he fays, That he who does. 
 not admit the fubfiflience of ideas will entirely dellroy the difcurfivepower of the foul ; and in the 
 Phaedo his demon ftrations of the immortality of the foul are principally founded on the hypothefis 
 of ideas. But to urge that the infpedlion of ideas does not contribute to the fcience of fenfibles, 
 rather becomes any one than a man converfant with demonftration. For, if demonftrations are 
 from things prior and which have a more caufal fubfillence, as Ariftotle Ihows in his Lad Analy- 
 tics, it follows that nothing is fcientifically known through its own elements (for neither are thefe 
 proper caufes, except fo far as fubfervient to things more true than themfelves \ nor by a much 
 Itronger reafon through its own accidents. The affertions, therefore, of Anaxagoras refpeding 
 things of fimilar parts, and alfo the doubts of Eudoxus concerning certain things of this kind, 
 are eafily fubverted. Neverthelefs, fince ideas are to fenfibles the caufes of goodnefs and per- 
 manency, they neceJTarily impart every perfeflion to the fcience of fenfibles which it is capable 
 of receiving, 
 
 thingSj
 
 328 ARISTOTLE'S METAPHYSICS. Book XIII. 
 
 things, and fuch as are '•ipoffible. Eut neither do other * things fubfift fron 
 forms accordir- _ .o any one of the modes which are ufually adduced. And 
 to fay that ideas are paradigms, and that other things participate of them, is 
 to fpeak idly, and to employ poetic mttaphors. For. w-iat is that which ope- 
 rates looking to ideas? For It is poinhle that any thing may be, and may be 
 generated, though it be not alfimilated to a paiadigm ; fo th^t, Socrates both 
 cxifting and not cxifling, there v.-il' be fiich a perlon as Socrates. In a fiml- 
 lar manner, it is evident, though Socrates fliould be eternal, there will be 
 many paradigms f of the fanie thing, and therefore alfo forms ; as, for in- 
 ftance, of man, animal and biped, and man rub;:Pting as an idea. Further 
 flill : forms will not only be paradigms of fenfiblesi but alio of themfeb es ; 
 as, for inftance, genus, of generic fpecics ; fo that the 'c/ne thing will be both 
 paradigm and image. Again : it may feem to be impoifible that eflence, and 
 
 that 
 
 * That fenfibles do not confift from ideas, neither as from matter, nor as from pu.';uion, nor 
 -as from material form, is evident ; becaufe no one of thefe is a true caufe. Bat ii/eas contain 
 the mod proper and the mod comprehenfive caufes of all mundane nature^ ; Ciufes wh'ch 
 through tranfcendency of power are exempt from their effecls, and are boti: tffei,l.ive and 
 final. ; 
 
 f It is not proper to refer whatever appears in fenfibles and efFefts to the fi-fl producing and 
 intelle£lual caufes of thefe ; but while the fenfible man is an animal, biped, rational, mortal, and 
 an infinity of other particulars, the ideal man, or man itfelf (auro ai''§a'7ro;), is none of tlicfe, fince 
 it comprehends in itfeif impartibly the caufe of natural and fenfible men. Tliere is no necet 
 lity, therefore, that the fenfible man fhould participate of many ideas fo far as he is man ; bur, 
 becaufe he is fenfible, and on that account participat.-s the caufe of man which ^lbfif!^ in nature, 
 that which is in foul, and that wliich is in intellecl, fo far it may be granted tliat he participates 
 of many ideas. Indeed, there is no abfurdity in admitting chat things lall participate of ajl the 
 caufes prior to themfelves, (ince, according to AniL-lius, the reafons or produclivc principles of 
 nature may be properly faid to participate of ideas, but fouls receive their refemblunccs. So 
 that we mufl coiifider a diftribution and moft exacft divifion of reafons as taking place in cffedls 
 themfelves ; but to abflr3,cl caufes we mull aflign a profoundly indivifille comprehcnfion of 
 wholes. 
 
 J It mud be granted that, of the caufes contained in intel'efl, fome are more univerfal and 
 others more particular, becaufe Ariftotle hlmfclf, as we have iecn In the tu-elfth book acknow- 
 ledges that tlie divine caufes of thp univeri'e have the fame order among themfelves with the 
 ttliereal fpheres ; and of thefe, fome are evidently of a gr<;ater, and others ef a lefler ambit. 
 However, it does not follow irom tliis, either according to Ariftotle or the Platonifts that tlie 
 fi'cond in rank are images of the firft •, but it muft.be faid that divine and inrellinible natures 
 are profoundly united together, and pervade each other wnh perfe£l purity and without confu- 
 /iqn j bi\t it muft not bj any means be admitted, that the fecoiid participates of the firft, in the 
 
 fame
 
 Book XIII. AR I S T O T L E'S M ET A P H Y S I C S; 32> 
 
 that of which It Is the effence, fhould be feparate*. So that, how can Ideas, 
 which are the effences of things, have a feparate fubfiftence ? But, in the 
 Phsedo, it is aflerted that forms are the caufes both of being and generation ; 
 and yet, notwithftanding the fubfiftence of forms, things will not be produced, 
 unlefs there is that which moves. To which we may add, that many other 
 things are made f , as, for inftance, a houfe and a ring, of which they do not 
 affert there are forms. So that it is evident that other things alfo, of which 
 they fay there are ideas, may both be, and be generated, through fuch-like 
 caufes as we have juft now mentioned, but not through forms. But, indeed, 
 relpeding ideas, many things fimilar to thofe already confidered, may be col- 
 4e(3:ed, both after this manner and through arguments more logical and more 
 accurate. 
 
 fame manner as fecondary and imperfe£l natures participate of ideas. All the caufes, there- 
 fore, which fubfift in intelleft are the true exemplars of things pollerior, and receive in them- 
 felves no fubingreflion of image. 
 
 * It is neceflary that the univerfal energies of divine natures fliould be eternally in energy ; 
 and from this caufe total /pedes or idea can never defert the univerfe. For, fince it is a caufe of 
 infinite power, it is neceflary, on account of its fimplicity and immenfity, that it fhould be a 
 never- failing caufe to its effefls. But a partial nature would never participate of idea unlefs it 
 had matter difpofed for its participation. The preparation, therefore, of material caufes which 
 are converfant with motion, participates of immaterial caufes. 
 
 t The Pythagorxans and Platonifts do not admit that there are fabricative ideas of things 
 which are neither in nature, nor are produced by nature. Ariftotle therefore rightly informs us 
 that they were not of opinion that there are intelligible and divine ideas of things artificial. 
 But, that in the foul of artifts there are reafons or produ£live principles which are the exemplars 
 of artificial produQions, is not only aflerted by thefe divine men, but is admitted in many places 
 by Ariftotle himfelf. The friends of ideas, tlierefore, in anfwer to his pretended objeftions, 
 may very juftly aflc how it can be confiftently granted that things artificial are accurately fabri- 
 cated according to their exemplars refident in foul, and yet, that the works of nature are 
 efFefted without a paradigmatic caufe, though art is faid to imitate nature in her operation ? 
 Indeed, on this hypothefis natural energy can be referred to no definite caufe, though Ariftotle, 
 in the firfl book of his Phyfics, fays that nature defires form. We therefore afk, what form ? 
 Shall we fay, that which fubfifls in motion, and is material ? But nature has not yet made this, 
 and it is pofterior to nature herfelf, and is united with a formlefs fubject : to which we may add, 
 the abfurdity of fuppofing that nature fliould defire that which has not yet a being, which is 
 pofterior, is borne along in conjunction with privation, and on this account is bafe and unlovely. 
 But, if nature afpires after tliat form which has a feparate fubfiftence, which is both true and 
 prior to herfelf, and is a divine and real form, it is neceflary that this fliould be intelleftual and 
 immaterial, and fliould poflefs a perpetual famenefs of fubfiftence, that the defire of nature may 
 ie unextinguifhed, and its energy never-failing. 
 
 U u CHAP,
 
 330 ARISTOTLE'S METAPHYSICS. Book XIIH 
 
 CHAP. VI. 
 
 Since, then, we have concluded thus much concerning ideas, it will be 
 well again to fpeculate the confequtnces refpeifling numbers, which happen 
 to thofe who alTert that they are feparate ellences, and the firft c.iufes of 
 things. But it is neceflarv, if number * is a certain nature, and there is 
 net any other eflence of it, but this very thing itfelf is its efllnce, as fome 
 affert,- if this be the cafe, it is necelTary, either that fomething belonging 
 to it fhould rank as firft, and fomething as confequent which is iecond, 
 and is diiferent in form ; and this either diredly fubfifls in monads, and 
 every monad is incapable of being compared with every monad ; or all 
 of them arc dire£lly confequent, and, each may be compared with each, as- 
 they fay is the cafe with mathematical number ; for in mathematical number 
 no one monad differs from another: or fome monads may be compared with 
 others, and fome not ; jufl as if the firft duad fubhfts ^fter ihe one, in the 
 next place the triad, and then another number. But the monads in each num- 
 ber are capable of being compared, as, for inftance, thofe which are in the firft 
 duad, and thof; which are in the firft triad ; and in a fimilar manner, in 
 
 * That Ariftotle is not ferious in the following divifions which he makes through monads, is, 
 I think, evident from hence, that all thefe divifions are fuperfluous, and the inquiry which they 
 produce foreign to the purpofe. For, if tliefe divine men fuppofed that feparate numbers have 
 their fubfidence in a quantity of monads, it would be right to doubt whether all the monads 
 are incapable of being compared, in the fame number with each other, and in a different num- 
 ber with other monads ; or whether they are all indifilrent, like the monads in mathematical 
 number ; or wliether ihefe are indeed indifferent, and without comparifon in different numbers. 
 But, on the contrary, they confidered fuch of thefe numbers as are feparate from tlie univtrfe as 
 impartible, and without quanlity, and as occultly fubfifling in divine forms. However, as thefe 
 numbers proceed together with ideas into the fenfible world, they affertedthat fome of tiiem are 
 itiftparable from mundane natures. Hence, fome of the Pythagoraeans, fays Syrianus, dif- 
 courfed about infcparable numbers alone, but others of fuch as have a feparate fubfifience, in 
 ■w ich as in paradigms they faw thofe numbers are contained which are perfefted by nature.. 
 But others, making a didindlion between the two, unfolded their doiSlrine in a more clear and 
 perfect ma-.n_;. If it be rcquifite, however, to fpeak concerning the difference of thefe monads, 
 and thf ir privation of difference, we mull fay that the monads which fubfift in quantity are by no 
 means to be extended to effentia! numbers ; but when we call effential numbers monads, we muft 
 affert that all oi tt.em mutual'/ differ from each other by difference itfelf, and that they poffefs a 
 privation of diilcience Uom jametiefs. It is evident, alfo, that thofe which are in the fame order 
 ate combined through mutual comparifon, in famenefs rather than in difference, but that thofe 
 which are in different orders are converiant with much diverCty through the dominion of dif- 
 ftrence. 
 
 Qibcr
 
 Book XIII. ARISTOTLE'S METAPHYSICS. 33,1 
 
 Other numbers. Bur the monads In the duad itfelf cannot be compared with 
 thofe in the triad itfelf, and in a fimilar manner in the other following num- 
 bers. Hence, the mathematician after one numerates two, with the former 
 one another one : and in numerating three he adds another one to thefe two ; 
 and fo of the reft. But Plato, after the otic, confiders two other unities with- 
 out the firft one, and the triad without the duad, and. In a fimilar manner, 
 other numbers. Again, therefore, one kind of numbers muft. be fuch as that 
 which was firft mentioned, but another that which is employed by mathema- 
 ticians, and a third that which we have fpoken of as the kft. Further flill ; 
 thefe numbers muft either be feparate from things or not feparate, but fubfift 
 in fenfibles ; yet not in fuch a manner as was confidered by us at firft, but as 
 from numbers exlfting in fenfibles. Or one kind of thele muft have a fub- 
 fiftence, and another not, or all of them muft exift. The modes, therefore, 
 according to which it is poflible for them to be, are neceflarily only thefe. 
 But thofe who affert that the one is the principle, eflence, and element of all 
 thing'5, and that from this and another certain one, number fubfifts, each of 
 thefe nearly adopts fome one of thefe modes, excepting this, that all the 
 monads are not comparable ; and this reafonably happens. For it is not 
 pcffible that numbers can have any other mode of fubfiftence befides thofe 
 which have been enumerated. Some*, therefore, aflert that both are num- 
 bers, and that one of thefe modes which poffeftes the prior and the pofterior 
 accords with ideas : but that mathematical number is difftrent from ideas and 
 fenfibles; and that both ideas and mathematical numbers are feparate from 
 fenfibles. But according to others, the mathematical \ number alone is the 
 firft of things, and is feparated from fenfibles. The Pythagoreans % alfo cele- 
 brate 
 
 * Arirtotle here, fays Syrianus, alludes to Pinto, as Alexander A phroclifienfis alfo obferves. 
 Pl.ito indeed afferted thefe things, and not thefe only: for, accordiag to him, there is ideal 
 number, or number fubfifting in the various orders of ideas ; and there is alfo mathematical 
 number, which has indeed a more excellent fubfjftence than phyfica!, but is fubordinate to ideal 
 number ; juft as our foul is fupcrior to nature, but podcrior to intellccl. 
 
 f Alexander, fays Syrianus, aflerts that Ariftotle here alludes to the followers of Xenocrates, 
 who feparate indeed mathematical number from fenfibL's, but do not think it is the only num- 
 ber. Indeed, as Syri-inus obferves, how is it poftible, fince ihey were Platonics and were will- 
 in t to Pythagorize {■nti^u.too.Km') that thsy (liould not direct their attention to imjiartible num. 
 bsrs fepirated -"rom the GtTonc* of foul ? Hut it appears that by mathematical names they 
 confidered things which-psrtain to more excellent numbers. 
 
 J That the PytlagoiaennSj fays Syrianus, afferted that nature produces fenfibles by numbers 
 
 U u ? muJt
 
 332 ARISTOTL E'S M ETAPH YSI C S. tooK XIIL 
 
 brate the mathematical one, but not as having a feparate fubfiRence ; but they 
 fay that from tliis fenfihle eflences are derived. For they farbricate all 
 heaven from numbers, only not from the monadic : but they confider monads 
 as pofTefTing magnitude. At the fame time they feem to doubt how the hnl 
 one confifts, polfeffing magnitude. But a certain other philolopher * aflcrts 
 that the firft nuniber ranks among forms ; and according to others f, the 
 mathematical number is the firll number. In like manner with refped to 
 
 muft be confeffed ; but then thcfe numbers were not mathematical but phyfical ; and as they 
 fpoke fymbolically, it is not improbable that they demonftrated every property of fenfibles by 
 mathematical names. However (fays he) to afcribe to them a knowledge of fenfible numbers 
 alone, is not only ridiculous but highly impious. For they received indeed from the theology 
 of Orpheus the principles of intelligible and intellc£lual numbers, they afhgned them an abund- 
 ant progrefiion, and extended their dominion as far as to fenfibles themfelves. Hence, that 
 proverb was peculiar to the Pythagoraeans, that all th'mgs are ajjimilaled to numhcr. This being 
 the cafe, Ariftotle cannot be ferious in aflerting that the Pythagorxans vi'cre alone converfant 
 with bodies, and numbers co-exiftent with bodies. " For indeed (fays Syrianus) Pythagoras 
 himfelf, in the Sacred Discouuse, clearly fays that number is the ruler of forms and ideas,. 
 and is the caufe of gods and daemons. He alfo fuppofes that to the mod antient and artifi- 
 cially-ruling deity, number is the canon, the artificial reafon, the intelleft alfo, and the moft 
 undeviating balance of the compofition and generation of all things." Ai/to{|«eii nuSayofa;, {vtm 'aca 
 \oyoi, JiaffuJiiv //.opjiuv nat liiav K^avTopa rov afiS/^ov eXevev Eivai, km Sioiv xai Sai/xovuv airiov xai rco ttpeit- 
 SuraTa kixi x^a.Ti<7riuovrt t£xvit)i Sew xavova, xai Xoyov te^vikov, vow te, km tnaS/yUtv ax'KiviaTarav tov aetd/Aov 
 iwtixe a-ucrra(rto{ xcct yiVE(reu{ tuv maxim. " But Philolaus declared that nuniber is the governing 
 and felf-begotten bond of the eterral permanency of mundane natures." 4'iXoXau; Je, t«; tjuv 
 KO^fitxuv Mcovia; Jia/*oi)is Tuv xparuTsuoua'av km auroyevTi (Tvvoxiv Eivai a'TtKpniaro iov apiS/xov, " And 
 Hippafus and all ihofe who were deftined to a quinquennial filence {axouafianxoi), called number 
 the judicial inflrument of the maker of the univerfe, and the firft paradigm of mundane fabri- 
 cation." 'Oi h 9TEJ11 'iTTTTaaov axoujfJiaTiXOi a^iO/xov uttov x^nixov xo^novpyou ^tov opyavov, xai 7ra^a$ctyix<x 
 
 !Tf4JT0V KOapLOTTOliai. 
 
 But how is it pofTible that they could have fpoken thus fublimely of number, unlcfs they had 
 confidered it as pofleffmg an eiTence feparate from feivfibles, and a tranfcendency fabricative, and 
 at the fame time paradigmatic ? 
 
 * ;. e. Plato. 
 
 f Some, fays Ariftotle, do not admit known mathematical number, but introducing one 
 number, i. e. the ideal, they call this alfo mathematical. They were perhaps induced to this, 
 bec.iufe mathematical number is twofold, one confilling from monads or unities, and the other 
 cflentiai, with which the artificer of the univerfe is faid to have adorned the rational foul. 
 They were unwilling indeed to call that number which is known to the multitude ideal, as being 
 uneffcntial, but they did not confider that number which is eflentially inherent in fouls, and 
 from which the monadic originates, as the fame with ideal number. However, they did not re- 
 fute to call it ideal, in the fame manner as we are accuftomed to call the middle reafons of the 
 ibui ideas. 
 
 lengths,
 
 Book XIII, ARISTOTLE'S METAPHYSICS. 333 
 
 lengths *, and fuperficies, and folids : for, according to fome, thofe which fub- 
 fift after ideas are different from fuch as are mathematical. But, of thofe who 
 fpeak differently, fome difcourfe of mathematical natures mathematically, and 
 thefe are fuch as do not confider ideas to be numbers, nor affert that there are 
 ideas. But others fpeak of mathematical natures not mathematically : for 
 they contend that every magnitude cannot be cut into magnitudes, and that 
 any kind of monads do not compofe the duad. All, however, confider num- 
 bers as monadic, except fuch of the Pythagorseans as affert that the one is the 
 element and principle of things. Bui thefe confider monads as endued with 
 magnitude, as we have already obferved. In how many ways, therefore, 
 numbers are confidered by thefe men, and that all the modes have been enu- 
 merated, is, from what has been faid, manlfeit. All the modes, however, are 
 impoffible, though perhaps one more than another. 
 
 CHAP. vir. 
 
 In the firft place, therefore, let us confider whether monads are capable of 
 being compared with each other, or cannot be compared f : and it they can- 
 not be n:LUtudly compared, in what way can we as it were divide them; for 
 every kind of monad will not admit of comparifon with every kind. But 
 tliofe monads which are in the duad, do not admit of comparifon with thofe 
 in the triad ; and thus the monads in each prime number cannot be com- 
 pared with each other. If, therefore, all the monads are capable of being 
 
 * The fame thing alfo may be aflerted of geometrical names. For figures fubfift after one 
 manner in intellect, and after another in fou), but in both thefe without dimenfion. Hence, 
 thofe divine men, regarding the peculiar nature of things, and not the ufe of names, fpoke of 
 impartible magnitudes, indivifible lines, and the duad without quantity, becaufe tliey directed 
 their intellectual eye to the caufal lubfiftence of thefe in intellect and foul. 
 
 f All this, if it were ferioufly fid, would be faid in vain. For no one of divine and intef- 
 le£lual numbers is monadic. But ail arithmetical monads are without any difll-rence. What 
 is afferted therefore by Ariftotle does not follow : for it will not be ideal number, fince this 
 does not confill from unities. For it is difficult to devife how many unities compofe this or 
 that idea. But if the whole propofition is falfe, which fays that every number is monadic, or 
 compofed from unities, nothing will be denionftrated from it, but we may rather from what is 
 faid conclude tlie contr.iry : for if it is true, both according to the i'ythagorveans and Ariftotle^ 
 to fay that every number which confifts from unities is not idt-al number, and the Pythago- 
 reans affert that there is fuch a thing as ideal number, every number will not confilt from 
 unities. 
 
 compared 
 
 /
 
 3** AR 1 STOT LE'S METAPH YSI CS. Book XIIl- 
 
 compared, aiul are without any difTerencc, mathematical number, and one 
 number alone will lublifl:; and it will not be poffible that ideas can be num- 
 bers : for what kind of number will man-itfelf be, or animal-itfeif, or any 
 other fpecies ? For there is one idea of each, as for inftance, one idea of man- 
 itfelf, and another one of animal-itfeif. But fimilar monads, and fuch as have 
 no difference, are infinite : fo that this triad will not in any refped be more 
 man-itfelf, tlian any thing elfe. But, if ideas are not numbers*, it is not, 
 in lliort, poffible that they can have any fubfiftence : for from what principles 
 will ideas be derived ? For number is from the one and the indefinite duad : 
 and thefe are faid to be the principles and elements of number, and cannot 
 be in order, either prior or pofterior to numbers. But if monads do not 
 admit of comparilbn, and are in fuch a manner incapable of being com- 
 pared that every one is different from every one, neither is it poffible that 
 this can be mathematical number, (for mathematical number confifts of 
 monads which are not different from each other, and the things manifefted 
 by it, harmonife with monads of this kind), nor yet can this number belong 
 to forms ; for the firil duad will net be from one and the indefinite duad ; 
 and afterwards the following numbers, as it is faid, viz. the duad, triad, and 
 tetrad : for at the fame time, the monads which are in the firft duad are 
 generated; whether they fubfift from unequal monads (for from things 
 
 * Ariftotle rightly affumes, that if ideas are not numbers, it is not poffible for them to have 
 any fubliftence. But he does not demonftrate that they are not, for it would indeed be impof- 
 fible. That ideas are not numbers confiding from unities he fome time fince defired might 
 be granted, but he is not billing to prove it. Ariftotle, however, does nut confider either 
 thi one or number, in the fame manner as they were coniidered by tlie Pythagorxans : for they, 
 when they beheld a twofold co-ordination of things about every being, aflerted that the better 
 was imparted to every thing from the one, but the ivorfe from the duad. But Ariflotle, according 
 to his ufual method, confiders thefc names rather mathematically than agreeably to the con- 
 ceptions of the anticnts. 
 
 If, therefore, there are ideas, as thofe divine men liave demonllrated, and as we alfo have 
 evinced there are, ideas will not be numbers compofed from unities, fince arithmetical unities 
 or monads are without any difference, nor will this be tlie cafe even if uniiies are fuppofcd to 
 be different from e..ch othei, unlefs numbers compofed from uniiies are conlkiercd according 
 to a different fignification. It mull here, however, be obferved, that numbers according to 
 their firll fubfiftenc-'; are fuperior to ideas, viz. coiifidere-d as charatteri.ing the hyparxes or 
 lummits of divine natures ; for in this cafe, they have a fuperefleinial fubfiHence. To thofe 
 of a tn,!y philofophical genius this will be evident, from Rudying the Parmenidcs of Plato j 
 gnd, as we learn from Syrianus, t!)is was one of the thealo^^ical dogoias of the Pythago- 
 raeaus. 
 
 made
 
 FooK XriT, ARISTOTLE'S METAPHYSICS. 335 
 
 made equal they were produced) or have a fubfiftence different from 
 this. 
 
 In the next place, if one monad is prior* to another, it will alfobe prior to 
 the duad which fubfifts from thefe : for when of any thing, fomething is 
 prior, and fomething poftcrior, then, that alfo which fubfiib from thefe, will 
 be prior to this, and pofterior to that. Further Rill f : fmce the one it/elf 
 is hrft, and afterwards a certain one of the reft ; alfo, a fecond after this, and 
 again, a third j there will be a fecond indeed, after a fecond, but a third after 
 the firfl: one : fo thac monads will be prior to the numbers which are com- 
 pofed from them. Thus, for inftance, in the duad there will be a third 
 monad, before the number three has a fubfiftence, and in the triad a fourth,, 
 and in the tetrad a fifth, before thefe numbers fubfift. None % of them, 
 however^ afferts that monads are after this manner incapable of comparifon. 
 But indeed, according to their principles, it is reafonable it fhould be fo, 
 though impoflible according to truth : for it is reafonable that monads fhould 
 be prior, if there is a certain firft monad, and a firft; one ; and in like man- 
 
 » This,, alfo Ariftotle anunies, for the purpofe of demon ftrating that the monads which are 
 In ideal number are not incapable of being compared with each other : for, if the two monads in 
 the duad cannot be compared, one of thefe is prior and the other pofterior; for, fince they are 
 different, they do not proceed together from the principles of number. But, if this be the cafe,, 
 the duad itfelf will be prior to the junior of thefe unities, and will be junior to the prior ; fince 
 it is a mixture of two monads : for, as that liquor which is mingled from wine and honey, i& 
 fweeter than wine, but lefs fweet than honey ; fo alfo the duad itfelf will be pofterior to its 
 prior part, but prior to its pofterior part. That this, however, is faid by Ariftotie rather in- 
 jeft than ferioufiy, is, as Syrianus well obferves, obvious to the more fagadous. 
 
 f What Ariftotie now fays is this : if after that unity which ranks as a principle, and has the 
 power of generating wholes, we conceive the prior monad in the duad, there will be a duad 
 from this principal one, and monad, before the duad is generated. And again : if we conjoin 
 two monads of the triad with the firft one, there will be a triad, before the triad itfelf fubfifts, 
 and univerfally a quantity of monads will always pre-occupy its proper number. Cut it has 
 often been ftiown that afTertions of this kind are rather pretended than ferious : for how can 
 feparation of this kind, and material diviGon, and a compofition from things prior and pofterior, 
 fo as to form one thing by fuch a eonjun£lion, be adapted to natures impartible, without 
 quantity, and proioundly indivifible ? 
 
 \ Ariftotie, in what he now fays, is evidently not ferious : for, if he were to call intetligible 
 ellences, or the numbers peculiar to tliem monads, there would be no abfurdity in afferting^ 
 fince there is an order in divine natures, that this is firft, and that in a following rank ; but^ 
 in confequence of conCdering mathematical monads, and yet taking away that which is peculiar 
 to them, fince he fuppofes tltem to be incapable of being compp.red with each other, he evi- 
 dently jefts through thefe bypothefes, in what lie fays refpe(Sing divine natures. 
 
 nec-
 
 336 ARISTOTLE'S METAPHYSICS. Book XIII. 
 
 ner with refpedl to diiads, if there is a firft duad. For after that which is 
 firft, it is rational and neceffiry that there fhould be a certain fecond : and 
 if a fecond, a third ; and fo of the reft in a following order. But to aftert at 
 the fame time, that there is a firft and fecond monad after t/je one^ and alfo 
 a firft duad, is impoffible. Thefe, however, introduce a monad and a firft 
 one, but no longer a fecond and a third. They alfo introduce a firft duad, 
 but not a fecond and a third. It is evident*, however, that if all , monads do 
 not admit of comparifon, it is impoffible that there can be a duad and a triad, 
 and other numbers : for whether monads are without any difference, or 
 whether each differs from each, it is ncceffary that number fhould be nu- 
 merated by addition ; as, for inftance, the duad, by the aduition of one to 
 anotlier one ; and the triad, by another one being added to two : and in a 
 fimilar manner the tetrad. But this being the cafe, it is impoffible that there 
 fhould be a generation of numbers, in fuch a manner as they generate them 
 from the duad and the one : for the duad becomes a part of the triad, and 
 the triad of the tetrad. And the like confequences enfue in the following 
 numbers. But from the firft duadj, and the indefinite duad, the tetrad is 
 
 produced, 
 
 * Ideal number, fays Ariftotle, cannot have any fubfiftence, that is, the duad itfelf, and the 
 triad itfcif, if monads are fuppofed to be incapable of comparifon, to which it is confequent 
 that it is not number compofed from unities, 'Ihis, indeed, lie omits, but infers that whether 
 unities are capable of being compared or not, it is neceflary that there fliould not be the triad 
 itfelf; becaufe every number is numerated, and completed by appofition, as the duad by af- 
 fuming unity becomes the triad ; and that on this account there are many duads in the num- 
 ber fix, in eight, and in twelve ; and alfo that the duad is a part, of the triad, indeed, two parts, 
 but the half of the tetrad. There is, however, nothing of this kind in ic'.enl numbers : for thefe, 
 according to the Pythagoreans, are generated from the monad and indefinite duad, and each of 
 them is one, and no one is a part of another. So that Ariltotle indeed is ferious in what he 
 favs of the properties of ideal numbers, but not when he previouily aflumes that every number 
 is meafured arid completed by appofition : for the properties of numbers compofed from 
 unities, cannot be transferred to all numbers. Nothing elfe, therefore, if now concluded by 
 Ariftotle, than that it is impoffible that the duad itfelf can be number compofed from unities ; 
 which, fays Syrianus, prior to all reafoning is nearly granted by all men. 
 
 f Ariftotle fays this in oppofition to himfelf. They, fays he, from the duad itfelf (for he 
 calls this the firft; duad), and from that duad which has the relation of a principle, which he 
 calls the indefinite duad, perfe£l the tetrad, neither producing nor increafing it by compofition, 
 but the Indefinite duad being multiplied into the duad itfelf generates the tetrad. On which 
 account, they by no means compofe ideal number through appofition. Having faid thus much, 
 in oppofition as it were to himfelf, he grants that they did not conftitutc number by appofition, 
 
 anrj
 
 Book Xiri. ARISTOTLE'S METAPHYSICS. 337- 
 
 , produced, being two duads befide the duad kfelf. But, if the duad Itfelf is 
 not a part, there will yet be another one duad, and the duad will fubfift from 
 the one itfelf, and another one. If this, however, is the cafe, it is not pof- 
 fible that the indefinite duad can be the other element : for it generates 
 another monad, but not the definite duad. 
 
 Further ftill * : befides the triad, and the duad itfelf, how will there be 
 other tiiads and duads ? And in what manner will they be compofed from 
 prior and pofterior monads ? For all thefe things are fictitious ; and it is 
 impoflible that there fliould be a firft duad, and afterwards the triad itfelf. 
 It follows, however, that this muft neceflarily be the cafe, if the one, and 
 the indefmite duad, are the elements of numbers. But if the confequences 
 are impoffible, it is alfo impoflible that thefe can be principles. If, therefore, 
 fome monads differ from others, thefe things, and other things of this kind, 
 neceflarily happen. But if the monads in another number are diiferent, 
 but thofe in the fame number are alone without any mutual difference, evea 
 in this cafe difficuhies as numerous will arife. As, for inftance, in the decad 
 itfelf, there are ten monads ; but it is compofed both from thefe, and two 
 pentads. Since, however, the decad is not a cafual number (for neither is 
 it compofed from cafu:d pentads, nor from cafual monads) it is neceflary 
 that the monads in this decad fhould differ : for, if they do not diff'er, neither 
 will the pentads differ from which the decad is compofed. But, fmce they 
 differ, the monads alfo will diff'er. If, therefore, they differ, whether docs it 
 follow, that there will not be other pentads, but only thofe two, or that there 
 
 and that the other of the principles whicli converts all divine natures to itfelf, and excites them 
 to the completion and generation of fccond and third fpecies, is the caufe of the produdlion of 
 niuititude and all multiplication. 
 
 * Thofe divine men after intellcclual number placed that which fubfifls In foul, and next to 
 this mathematical and phyfical number, yet they did not affert that all numbers arc compofed 
 from unities, por did they call unities prior and pofterior, as having the relation of fubjccls to 
 xIjlC quaWty of nuipbejs : for wi.th them, all numbers vrere without .quantity, except mathe- 
 matical number ■, but tlicy contemplated triads, pentads, and decads in them from tlielr powers, 
 and the properties which they poflefs with relation to divine numbers. Hence, AriRotle alfo 
 fays, it is necefi'ary that there fliould be prior and pofterior triads and duads, fince they are 
 perfecled from principles of this kind. Indeed, if we afl'ent to thefe principles, we muft admit 
 many ordsrs cf numbers. But that it is impcffible there fliould be different numbers, does 
 not feam to be co!icIu.de<J,,nor is it polhble that it fliould ; for, as Syrlanus very juftly obferves, 
 thut ivhich is true cannot he confttiei}^ and th.it luh'tch is faljc is indcmonjlrabh : to te yx^ a^^!SEJ 
 
 X X . will
 
 S38 A R I S T O T L E- S M E T A P H Y S I C S; Book XIIT, 
 
 will be ? Fcr in the decad, there is not another decad befides itfelf. But, 
 indeed, it is a'.fo neceiTary that the tetrad fhould not be compofed from: 
 cafual dunds : for the indefinite diiad, as they fay, receiving the definite 
 diiad, produces two duads. For it caufes the dua/d which it receives to be- 
 come two. 
 
 Again*: how does it happen that there is a certain nature, i.e. the 
 
 duad,. 
 
 ♦ Thefe things arc by no means doubted againft divine numbers ; for thefe are not compofed' 
 from unities, fo as that we fliould have to inquire what each of thefe numbers is, befides the 
 unities fuhjeft to it ; but thefe objections may be more aptly urged againft mathematical 
 number. In defence, therefore, of mathematical number, we may fay that as in every thing,, 
 according to the dodrine of Ariftotle himfelf, one thing correfponds to matter, and another to 
 form, ill tlie pentad alio, or number five, its five monads, and in fhort its quantity, and the 
 number which is the fubjeft of participation, are derived from the duad itfelf; but its form, 
 that is, the pentad itfelf, is from the monad : for every form is a monad, and unites its fubject 
 quantity. The pentad itfelf, therefore, which is a monad, proceeds from the principal monad, 
 or that which ranks as the highell principle, after the ineffable one, forms its fubjeft quantity, 
 which is itfelf formlefs, and conueds it to its own form. For it is again neceflary to under- 
 fiand that tliere are two principles of mathematical numbers in our fouls, the monad which- 
 comprehends in itfelf all the forms of numbers, and correfpo.-ids to the monad in intelledual- 
 natures, and the duad, which is a certain generative principle of infinite power, and which oa 
 this account, as being the image of the never-failing and intelligible duad, is called indefinite. 
 Wliile this proceeds to all things, it is not deferted in its courfe by the monad, but that which 
 proceeds from the monad continually diftinguifties and forms boundlefs quantity, gives a fpecific 
 diflindion to all its orderly progreffions, and inceffantly adorns them with forms. And as in 
 mundane natures, there is neither any thing formlefs, nor any vacuum among the fpecies of. 
 things, fo likewife in mathematical number, neither is any quantity left innumerable, for thus,, 
 the forming power of the monad would be vanquifiied by the indefinite duad, nor does any 
 medium intervene, between the confequent numbers, and the well-difpofed energy of tlie 
 monad. 
 
 Neither, therefore, does the pentad confift from fabftance and accident, as a white man 5, 
 nor from genus and difference, as man from animal and biped •, nor from five monads mutually 
 touching each other, like a bundle of wood •, nor from things mingled, like a drink made from 
 •wine and honey ; nor from things fuflaining pofition, as Hones by their pofition complete the 
 houfe ; nor laftly, as things numerable, for thefe are nothing elfe than particulars. But it does 
 not follow that numbers themfelves, becaufe they confift from indivifible monads, have nothing 
 elfe befides monads ; (for the multitude of points in continued quantity is an indivifible multi- 
 tude, yet it is not on this account that tliere is a completion of fomething elfe, from the 
 points themfelves) but this takes place, becaufe there is fomething in them which correfponds 
 to matter, and fomething which correfponds to form. Laftly, when we unite the triad with 
 the tetrad, we fay that we make feven. The afiertion, however, is not true : for monads con- 
 joined with monads, produce indeed the fubjeft of the number 7, but nothing more. Who 
 then imparts the heptadic form to thefe monads ? Who is it alfo, that gives the form of a bed 
 
 to
 
 BookXIII. ARISTOTLE'S METAPHYSICS, 339 
 
 duad, befides two monads, and the triad, helides three monads ? for either 
 one participates of the other, as a white man, befides white and man ; (for 
 he participates of thefe) or the one is a certain difference of the other, as 
 man befides animal and biped. Further Aill : foine things are one by con- 
 ta<!:l, others by mixture, and others by pofition ; none of which can pertain 
 to the monads from which the duad and the triad confift. But as two men 
 are not one certain thing befides both, the fame confequencc muft neceflarily 
 apply to monads ; nor muft ii be find that they differ becaufe they are indi- 
 vifihle ; for, on this account points alio are indivifible. But at the fame 
 time the duad of two men, is not any thing elfe befides the two. Nor yet, 
 ought this to be concealed, thafthere will be prior and pofterior duads ; and 
 in like manner with refpedl to other numbers. For the duads* in the 
 
 tetrad 
 
 to a certain number of pieces of wood ? Shall we not fay tliat the foul of the carpentar, from 
 the art which he pofieffes, fafliions the wood, fo as to receive the form of a bed, and that the 
 numerative foul, from poirefTing in herfelf a monad which has the relation of a principle, gives 
 form and fubfiftence to all numbers ? But in this only confifts the diH^erence, that the carpen- 
 ter's art is not naturally inherent in us, and requires manual operation, becaufe it is converfant 
 with fenfible mutter, but the numerative art is naturally prefent with us, and is therefore pof- 
 felTed by all men, and has an intelledual matter, which it inftantaneoufly inverts with form. 
 And this is that which deceives the multitude, who ihink that the heptad is nothing befides 
 feven monads. For the imagination of the vulgar, uiilefs it firlt fees a thing unadorned, after- 
 wards the fupervening energy of the adorner, and lalily, above all the thing itfelf perfect and 
 formed, cannot be perfuaded that it has two natures, one formlefs, the other formal, and ftill 
 further, that which beyond thefe impjrts form ; but ailerts that the fubjecl is one, and without 
 generation. Hence, perhaps, the antient theologifts and Plato afcribed temporal generations 
 to things without generation, and to things which are perpetually adorned and regularly dif- 
 pofed, privation of order and ornament, the erroneous and the boundlefs, that they might lead 
 men to the knowledge of a formal and effeflive caule. It is, therefore, by no means wonderful, 
 that though feven fenfible monads are never wichout the heptad, thefe fhould be diflinguiflied by 
 fcience, and that the former fliould have the relation of a fubjecl and be analogous to matter, 
 and the latter (hould correTpond to fpecies and form. 
 
 * This is faid in conformity to that conception, that the fecond of the two great principles 
 after the ineffable caufe of all, doubles numbers. In reality, however, this neiiher militates 
 againft ideal, and impartible number, nor againft mathefhatical, and wh'ch confifts from monads. 
 For in the latter, the quantities of the lefler numbers are placed together, and fubjedted to the 
 form of the greater number, and not the numbers themfelves. As, therefore, when water is 
 changed into air, the water does not become air, or the fubjeft of air, but that which was the 
 fubje£l of water becomes the fubjecft of air, fo, when the triad unites itfelf with the duad, the 
 fpecies or forms of the two numbers are not mingled, except in their immaterial reafons, in 
 which a: the fame time that they are feparate, they are not impeded from being united, but the 
 
 X $ 2 quantities
 
 340 ARISTOTLE-S M E f A P B Y S I C S. Book Xllf, 
 
 tetrad fubfift together with each other, but they are prior to thofe in the 
 odad ; and as the duad produces the diiads in the tetrad, fo thefe duads pro- 
 duce the tetrads in the o<flad itfelf. So that^ if the firft duad is an idea, thefe 
 alfo will be certain ideas. The iame* realbning will likewife take place 
 with refped to monads : for the monads which are in the firft duad will 
 generate the four monads which are in the tetrad. So that all monads will 
 be ideas, and idea will be compofed from ideas. And hence, it is evident 
 that thofe things alfo of which thefe are ideas will be compofites. Juft as- 
 if any one fhould fay that animals are compofed from animals : if, therefore, 
 there are ideas of thefe, ideas will be compofed from animals. And, in 
 fhort, to make monads in any refped different f, is abfurd and fiditious. 
 But, I mean by fiditious, that which is forcibly introduced to an hypothefis. 
 For we do not fee that monad differs from monad either according to quan- 
 tity or quality : and it is neceffary that every number fhould be either 
 equal J or unequal, but efpecially monadic number. So that, if neither 
 greater nor leffer, ,it mufl; be equal. But we confider things which are equal^ 
 
 quantities of the two numbers which are placed together become the fubjeft of the pentad. 
 The triad therefore is one, and alfo the tetrad, even In mathematical numbers : for although in- 
 the ennead or number nine, you may conceive a firft, fecond, and third triad, yet you fee one 
 thing thrice afiumed ; and in fhort, in the ennead, there is nothing but the form of the ennead- 
 in the quantity of nine monads. But, if you mentally feparate its fubjeft, (for form is im- 
 partible) you will immediately inveft it with forms correfponding to its divifion : for our foul 
 cr.nnot endure to fee that which is formlefs, unadorned, efpecially as fhe poflefles the power of 
 inverting it with ornament. 
 
 * Number, as fubfifting among ideas, is not compofed from monads, nor are ideas compofedi 
 from ideas-, a;, for inftance, the idea of horfe from the idea of man and dog, in the fame man- 
 ner as horfe, in this feufible region, is compofed from fenfible natures. Nor in mathematical 
 number are the monads different, but all thofe which are fubjetted to numbers are without 
 difference, except that monad which is the principle, fountain, and mother of all number of 
 this kind. Not only the many monads of mathematical number are equivocal to this monad ;, 
 but the indefinite duad of fuch number is equivoeal to the indefinite duad of intelligibles. 
 
 f Thefe things are not afTerted againft the monads which are fubjetled to numbers: for they 
 neither differ in quantity, fmce all of them are the Icaft, nor in quality, for they are formlefs. 
 
 X Equality, indeed, and inequality permeate every number, the natural, the fupernatural,, 
 and the mathematical. But it is here worthy of obfervation, that Ariflotle manifellly acknow- 
 ledges that all numbers are not compofed from monads ; for the exprefhon " but efpecially. 
 monndic number" is an evident confirmation of the dodrine of the antients. As all his argu- 
 ments, tlierefore, are taken from numbers compofed from unities, they do not in reality op- 
 f ofe thofe numbvis which rank among ideas. 
 
 and
 
 BookXIII. ARISTOTLE'S metaphysics. 341 
 
 and altogether without difference, as the fame in numbers. And, if this be 
 not the cafe, neither will the duads in this decad be without difference, fince 
 they are equal : for what caufe can he affign who fays that they are 
 without difference ? 
 
 Further ftiir* : if every monad and another monad make two, a monad 
 taken from the duad, and a monad from the triad will be two ; and this 
 duad will conHft of monads which have no diverfity. It may therefore be 
 afked, whether this duad is prior or pofterior to. the triad ? For there ap- 
 pears to be a greater neceflity that it fliould be prior ; fince the one fubfifls- 
 together with a triad of monads, but the other with a duad. And we, ia 
 fhort, apprehend that one and one are two f, whether they are equal or 
 unequal ; as, for inflance, the good and the evil, man and horfe. But, if 
 the number of the triad is not greater than that of the duad, it is wonder- 
 
 * It would be abfurd to fuppofe that Arlflotle is fc'iious in what he now fays, or was in what he 
 has before f;vid concerning ideal numbers : for neither ar€ two monads the fubjeft of the diiad 
 itfelf, nor three of the triad itfelf: nor, if they were, would it be poITible to take from both, 
 and make fomething eife, becaufe both famenefs and ditlerence are in each of thefe. And if 
 y-ou fliould take difference from each of them, or from one of them difference and from the- 
 other famenefs, you would not, indeed, produce any third thing mingled from both. Indeed, 
 all the quell ions now propofed by Ariltotle are taken from thing^s material and altogether 
 partible, and are entirely foreign from intelledtual, fimple, and impartible eflences. But, if 
 Ariftotle's queftions pertain to mathematical number, they may be eafily folvcd from what has 
 been already faid : for it is not neceflary that we fliould take from the duad or the triad, that 
 we may make other duads ; fince thefe things take place about thiags numerable, as from two 
 horfes, and three men. If, therefore, we take the duad from both, we make a tetrad from 
 diffimilar monads. But, if each be what it is,^ it may caft. away the duad. All thefe imagi- 
 nations, however, which announce numbers to be of pofterior origin, and to fubfift by an 
 abftradion from fenfibles, ferve only to lead us into tlie myderies of numbers of a much nobler 
 origi-n, and of a much fuperior order.. 
 
 t The Pythagorxans, fays Syrianus, called forms or ideas monads, as being the pre-fubfifling; 
 meafures of fenfibles. This being the cafe, as forms themfelves are different, they neceffarily 
 faid that thefe monads alfo are different. The monads, therefore, in intelleft are different 
 through intelle£luaL ditFerence, and thofe in foul poffefs a ftill greater difference in confequence- 
 of being much more remote from the i'le/fuble oiu. But again, all rhefe monads may be com- 
 pared with each other, on account of tlie union which pervades all things from the good Itfelf, 
 and through identity being vi£lorious in immaterial forms. Syrianus adds, that the Pythago- 
 raeans neither referred any of the monads which AriHotle now examines to ideal numbers,, 
 nor related their diveifitLes» 
 
 m
 
 S42 ARISTOTLE'S METAPHYSICS. Book. XIII. 
 
 ful * : and, if it is greater, it is evident that equal number alfo is inherent in the 
 duad ; and is not diiTerent from the duad Itfelf. This, however, will not 
 happen, if there is a certain firft, and alfo a fecond number ; nor will ideas 
 be numbers : for this is rightly faid by thofe who think it proper that 
 monads fhould be different ; fince, as we have before obferved, they will be 
 ideas : for the fpecies of bath is one. Bat, with refped. to monads, if they 
 are wirhout difference, this alfo will be the cafe with duads and triads. So 
 that it is neeeffiry to fay to the authors of this aflbrtion, that in enumerating 
 one, two, that which is pre-exiftent muft not be admitted : for neither is 
 generation from the indefinite duad, nor is it pofTible that idea can fubfift : 
 for one idea would be inherent in another ; and all forms would be parts of 
 one. Hence, with refped: to the hypothefis indeed, they fpeak rightly, but 
 fimply confidered not rightly; for they fubvert many things: fince they fay 
 it is dubious f, whether when v.e numerate and predicate one, two, three, 
 we aflame any thing, or effedl this according to parts. But we do both ; on 
 which account it is ridiculous to refer this to fo great a difference of eflence. 
 
 * It is by no means wonderful, if the Pythagorxans, afferting that there are fuch things as 
 the duad itfelf, and the triad itfelf, alfo faid that the triad is not more ample than the duad, and 
 that the duad is not inherent in the triad : for neither do thefe numbers participate of quantity, 
 nor is the form of e<]uality or inequality inherent in them after the fame manner as in numbers 
 compofed from unities. For in thofe, equal numbers are never alfo unequal ; but, in ideal 
 numbers, the fame are both equal and unequil to each other, juft as they are ho\.}\ fame and 
 (hjfa-ent. And tliis arifes from their receiving the illuminations of the genera of being, and the 
 mod comprehenfive of forms. Nor is this attended with any contradiiSlion : for tliey are not 
 unequal, fo far as they are equal, nor dilhmilar, fo far as they are fimilar, nor ditTevent, fo far as 
 they are the fame ; but they sre indeed fimilar, equal, and the fame through fimilitudc, equality, 
 and identity ; and difhmilar, unequal, and different, through forms, oppofite as it were to the 
 former: for it is not pofliblc, fince the monad and indefinite duad rank among the firft prin- 
 ciples of things, that the natures v\hich fubiill from them, fnould not receive the powers of both. 
 
 \ When the form of the triad itfelf is received by three monads, the triad in energy is pro- 
 duced, and becomes one thing. But this now fubfifting in energy will not become the tetrad 
 or the number four, by the addition of the monad : for how can the form of the triad be tranf- 
 muted into that of the tetrad .' But the triad, which is confidered in three monads alone, is in 
 mere capacity, which, when it is conceived witiiout the form of tiie triad, if it affumes the 
 monad will make indeed the fubjeft of the tetrad ; and this again, fo far as it is formlefs, may, 
 by aiTuming the monad, become the fubjeft of the pentad ; but, when occupied by the form of 
 the triad, it alone produces the triad. Divifions, therefore, and multiplications arife from the 
 matter and the quantity of numbers, and not from forms ; for thefe are not only themfelves 
 immoveable, but they impart their own one form to the oatures which they fupervene. 
 
 CHAP.
 
 BookXIIL ARISTOTLE'S METAPHYSICS. H9 
 
 CHAP. VIII. 
 
 In the firfl: place, however, it will be well to define the particular dif- 
 ference, if there is any, between number and the monad. But it is necelTary 
 that this difference fliould be, either according to quantity, or accordinsi; to 
 quality. Neither of thefe, however, appears to be poflible ; but the differ- 
 ence fo far as number, is according to quantity. If, therefore, monads alfo 
 differ in quantity, one number will differ from another,, though equal to it 
 in the multitude of monads. Further ftill : whether are the firfl: monads* 
 greater or leffer, and whether do they afterwards increafe, or the contrary ? 
 For all thefe particulars are abfiird. But neither can they differ according to 
 quality : for no paffion can be inherent in them ; fince they fay that quality 
 is prefent with numbers pofl:erior to quantity. 
 
 Again ]■ : this will neither happen to them from ibe one^ nor from the 
 
 duad. 
 
 * Thefe things are rightly faid againfl; monads confidered according to their ufual accep* 
 tation. Ncverthelefs, if any one attends to the generation of numbers compofed from unities, 
 he will fee that the form which brings with it quality itfelf, afterwards gives formation to its 
 fubjecl quantity. 
 
 f Becaufe Ariftotle aflumes the one, for the monad which has the rank of a principle, as he is 
 apparently unwilling to allow that it has any quality, he does not admit that it is the caufe of 
 quality. The indefinite duad, however, is rather the caufe of quantity only, and not of both 
 quantity and quality. But this again arifes from Ariftotle pretending that the triad is nothing 
 but three monads : for in reality, if this were the cafe, the duad which generates quantity, 
 would alfo produce quality. But now, this generates infinite monads \ but the other, that is, 
 the better principle, bounds and dillingulQies them by forms^ 
 
 Moreover, fays Syrianus, Ariftotle very properly defires the Pythagoreans to fiiow, not 
 only that ideal monads diiFer, but alfo in what their difference conlifts. And they will reply 
 indeed, fays he, that it is not the diiference of monads which are the fubjefts of number ; (for 
 they did not admit that there was any difference among thefe) but a difference correfponuing 
 to the various orders of being : for when they fay that unity is the leaft of quantity, or the 
 firft and common part of quantity, they define known mathematical unity. But, when tliey 
 fay that unity is the form of forms,, they exhibit the original caufe of ideas, which compre- 
 hends in Itfelf the forms of all numbers, and which the Stoics did not refufe to call one tnulti'- 
 tude. Again, fays Syrianus, when thty difcourfed concerning divine monad?, they confidered 
 one monad as intelligible, from the undecaying retreats of which, as we have before obferved, 
 number proceeds ; but another as intelle£tual and demiurgic, which they denominated Jupiter, 
 concerning which, many of the antients, and likewife many of the more recent Platonlfts have 
 written ; but cfpecially the divine Jamblichus, who has mofl clearly, fays Syrianus, difcourfed 
 on thcle monads, in the I'eventh book of his Colledlion of Pythagoric dogmas, Syrianus adds, 
 
 that
 
 Si4 ARISTOTLE'S METAPHYSICS. Book Xllf. 
 
 duad. For the one doe;^ not partake of quality, but the duad partakes both 
 of quantity and quality : for the nature itfelf of the duad is the caufe that 
 beings are many. If, therefore, this fubfifts in a certain refpedl differently, 
 it muft be faid that this is efpecially fo in the principle ; and we muft define 
 refpeding the dijfferences of the monad, that it is efpecially neceflary, and 
 why it is fo, that this fhould be the cafe. But, if monads do not differ in 
 quantity, nor yet in quality, what other difference in them can they affign ? 
 .And indeed, if ideas* are numbers, it is evident that in neither of thefe 
 ways, can all monads be compared with each other, nor yet be mutually 
 without compaiifon. Nor again, as certain others f fpeak concerning num- 
 bers is it well faid. But thefe are fuch as do not indeed admit that there are 
 ideas, neither fimply confidered, nor yet as being certain numbers, but affert 
 the fubfillence of mathematical entities, and contend that numbers are the 
 firft of things, and that the principle of them is the one ttfdf: for It is in- 
 deed abfurd if that the one fliould be fomething which is tiift of unities, as 
 they fay it is ; but that the duad fliould not be fomething, which is firO: 
 of duads, nor the triad of triads ; fince the fame reafoning will apply to all 
 
 that he who is capable of underftanding the facred difcourfe (U^o^ ^ovo,-) of Pythagoras, wiM 
 there find all the orders both of monads and numbers completely celebrated. According to 
 the PythagorKans, therefore, there is a neceflary difference among the divine monads: for, in 
 .every progreffion of things, it is requifite that the monad, which is the leader of that progreffion, 
 fhould be more multiplied, than the monads which precede it ; and therefore as many, and 
 fuch as are the order* of beings, fuch and fo many arc the differences of monads which rank 
 as principles. 
 
 * Indeed, if ideas were numbers compofcd from monads, all the hypothefes refpefting 
 monads would be confuted in them : for, v\hether the monads of ideal number are without any 
 difference, many abfurdities will foUow ; fince there willbe no difference between number com- 
 pofed from monads and ideal mimber : or whether they are diticrent, or fome of them arc 
 different, and others iiotj the difcourfe of Ariiiotlc about them will be fictitious. But he who 
 afferts that ideal rwrnber is nor compufed from monads, will not be difturbed by any of the 
 pretended objeclions of Ariftotle ; for nothing indeed is faid againfl fuch an affertion. 
 
 f lif, fays Syrianus, there were any of the antients who afferted thefe tilings, iht-y are very 
 properly reprobated by Ariftotle. But perhaps ihey did not ufe the name of ideas, but fignified 
 th»; properties of divine effences by mathematical names : for how could they give the one and 
 mimber a fubfiflence prior to wholes, unlels they had venerated the fiipen^hitial one, true 
 beings, and the order of ideas ? 
 
 X Ariftotle rightly fees that the dogma is confifteiit with itfelf: for, if in every order of 
 beings there is a monad which has the dignity of a leader, and if all thefe monads proceed 
 from a fupercffcntial one, abftraclcd from ail things, it is neceffary riint there fhould be ideal 
 number. 
 
 of
 
 BooKXrir. ARISTOTL E'S METAPHYSICS. S45 
 
 of them. If, therefore, this is the cafe * with the particulars refpedling 
 number, and fome one alone admits the fubfiftence of mathematical number, 
 the one is not the principle of numbers : tor it is neceflary that a one of this 
 kind ftiould differ from other monads. But if this be the cafe, a certain 
 firft duad alfo muft differ from other duads : and a fimilar confequence muft 
 take place with refpedb to all following numbers. But if the one is the 
 principle, there is a greater neceffity that the particulars refpeding num- 
 bers fhould fubfift (as Piato faid), and that there fhould be a tirfl duad and 
 triad, and that numbers lliould not admit of comparifon with each other. 
 But yet again, if any one adopts thefe pofuions, it has been faid by us that 
 many impoffible f confequences will enfue. It is however neceffary^, 
 that either thefe or thofe pofitions fhould be adopted ; fo that if neither of 
 them is true, it is not poffible that number can have a feparate fubfiftence. 
 But, from thefe things, it is evident that the third mode Is the worfl §, 
 I mean that which afferts that mathematical number is the fame with the 
 number belonging to forms : for it is necefTary that two errors fhould ac- 
 cord in one opinion. For neither can mathematical number fubfift in this 
 manner ; but it is necefTary that he who lays down the peculiar hypothefes 
 
 * The whole reafoning is as follows : If mathematical num her alone fubfifis, the one will 
 not be the principle of things : but if the one itfelf is the principle of things, Plato is vidorious, 
 there is ideal number, and the one kind ofc.number eiFentially differs from the otiier. But it 
 will be our province afterwards to fliow that the one is the principle of things, which, fince it is 
 neither intelleft, nor being, nor number, is the caufe of all thefe, and imparts e {fence and 
 union to all thinr;s : for, this being fufficiently eftabHflied, Ariilotle will be found to aflcnt to 
 all the legitimate dogmas of Pythagoras and Plato. 
 
 \ Nothing inipciTible will however happen, if we reafon from a true hypothefis, and con- 
 formably to the meaning of the antient philofophers. 
 
 X If number, fays he, has a feparate fubfiftence, it is necelT.iry that either mathematical 
 number fliould be firft, or ideal number. It mud be uLferved, however, that there are other 
 numbers, viz. fuch as are fuperelTential, prior to ideal nun>bers. 
 
 § Some, fays Arif^otle, make two orders of numbers, and feparate them, as Plato ; for he 
 manifeftly aflerts that mathematical is different from ideal number. But others, as fome of 
 the Pythagor^eans, admit only one kind of number, viz. the mnthcmaticd ; and others know 
 indeed both mathematical and ideal number, but make them to be one. But perhaps, fays 
 Syrianus, he means in this place Speufippus and Xenocrates, who, he fays, were the leaders of 
 this mofl depraved hvpothefis. We have, however, alixady obferved refpecting thefe philofo- 
 phers, that though they employed the fame names, yet tlicy knew the dillindlion of numbers 
 according to ideas. 
 
 Y y fhould 
 
 &
 
 346 AR ISTOTLE'S METAPHYSICS. Book XIIL 
 
 fhould be prolix, and that he fhould alfo necefTarily enumerate the confe- 
 quences which happen to thole who fpeak of numbers as if they were 
 forms. 
 
 But the mode of the Pythagoreans * has partly fewer difficulties than 
 thofe which we have before mentioned, and partly has others which are 
 peculiar. For indeed, to make number infeparable from fenfibles, takes 
 way many iirspoffibilities ; but to fuppofe that bodies are compoftd from 
 numbers, and that this number is mathematical, is abfurd : for neither is it 
 true to fay that there are indivifible f magnitudes. And, in the next place, 
 
 becaufe 
 
 * This is, in reality, the fpeculation of Pythagoras and the Pythagorasans, and of thcfe who 
 legitimately received the dogmas delivered by them refpeding numbers. But Ariltotle here 
 fubdivides, and fays that they alone venerated that, with which they were feverally converfant. 
 Laftly, he praifes the Pythagoreans, as aiTerting that numbers are infeparable from feiifibles; 
 but reproves them for faying that bodies confift and are generated from numbers. But it 
 appears to me to be very evident that Ariftotle is neither ferious when he praifes, nor wlien he 
 blames the Pythagorseans for fpeaking in this manner : for who, fays Syriaiius, can refrain 
 from laughing, on hearing that the Pythagorseans were ignorant of feparate numbers, when 
 Pythagoras himfelf was accuftomed to define numbers in two ways ? by one of which defini- 
 tions, he evinced numbers to be entirely feparated from fenfibles, and to be unpolluted by them \ 
 but by the other, he taught their demiurgic, providential, and defenfive power. For, when he 
 fays that tiumher is the extenfton and energy of the fpermat'ic reafons jubftjVmg in the monad, the 
 defines that number which proceeds from its own principle, felf-prolific, and felf- motive, 
 which is eftabliflicd in itfelf, and has a feparate fubfiftence in all various forms. But when he 
 fays that number is that luhich fuhfijls prior to all things in a divine intelkHy by -which and from 
 ivhich ail things are co-ordinated, and remaiu properly jeparated in indijfoliible order, he celebrates- 
 the paradigm, and the artificer and father of gods, daemons and mortals. In like manner the 
 followers of Hippafus faid, that number is the firjl exemplar of the fabrication of the -world, and the 
 judicial inflrument of its divine artificer. Philolaus alfo affirms, that number ;') the felf-begotten and 
 ruling bond of the eternal duration of mundane natures ; and almoft all the other Pythagorxans, in 
 conformity to this theory, afiertcd that there are different kinds of numbers. Nor muft we 
 think, that becaufe the Pythagorseans faid that bodies derive their fubfiftence from natural 
 numbers, on this account they alone dire<£led their attention to numbers infeparable from fen- 
 fibles, or afcribed magnitude to numbers ; for neither did they alone difcourfe about natural ' 
 numbers ; nor did they confider natural and mathematical number as the fame ; nor afcribe 
 magnitude to numbers which are the caufes of magnitude. 
 
 t What the Pythagoraeans afTert, fays Syrianus, cannot be fubverted, and will continue 
 through the whole of time. For that which is true, according to the aflertion of tlie divine 
 Socrates, cannot be confuted. •' But the things, (fays he,) which Ariflotle now confutes, 
 accord with any rather than the Pythagoraeans : for neither do they fay that the number 
 by which we meafure fenfibles is the caufe of fenfibles : and if they confidered in it the images 
 
 of
 
 BookXIIL ARISTOTLE'S METAPHYSICS. 347 
 
 becaufe they efpeclally fubfift in this manner, the monads do not poflefs 
 magnitude. But how is it pofTible that magnitude can be compofed from 
 indivifibles ? However, arithmetic number is monadic; but they aflert that 
 beings are number. They adapt, therefore, fpeculations to bodies, as if from 
 them numbers fubfiRed. Further ftill, therefore, it is neceflary, if number 
 IS fometliing eflentially belonging to beings, that fome one of the above- 
 mentioned modes ihould take place. But this is impoffible. It is evident, 
 therefore, that there is no fuch nature of number as thofe introduce, who 
 make number to have a feparate fubfiftence. Further ftill : it may be 
 afked* ; whether each monad confifts from the ^r eat and the y/W/equalifcd, 
 
 or 
 
 of fenfible number ; as in a fpace {Za\uti)i») of two hundred and ten, tliey affirmed that the idea 
 of body is exhibited ; but of fire in unity, of air in the triad, of earth in the heptad, and of 
 \v;iter in the ennead ; yet thefe were aflumed by them through a certain fimilitude, for the pur- 
 pofe of reprefenting natural powers. But neither were they of opinion that the monads in this 
 number either poiTefs indivifible magnitude, or are at all inherent in fenfibles ; but when they 
 fpeak of indivifible magnitudes, they refer us to the caufal reafons of magnitudes, and to the 
 paradigmatic caufe of things great, which Plato was, in reality, accullomed to call magnitude 
 Itfelf. Moreover, when they aflert that monads have magnitude, they celebrate the power 
 of demiurgic or fabricative monads pervading through all things. But, when they 
 fay that magnitude confifts from indivifibles, they do not aflert this, as if indivifibles 
 produce intervals by any kind of junftion, or coalition ; for this is the dodrine of 
 Democritus, and contradi£ls geometry, and almoft all fciences ; but they fignify, that what- 
 ever among things indivifible are intelleftual, unpolluted, fabricative, and vivific forms, thefe, 
 rot departing from themfelves, give fubfiftence to other things, and to corporeal bulk among 
 the laft of things. But fuch things as are phyfical, and which verge in their energies to matter> 
 thefe, though they arc without bulk, and have an incorporeal fubfiftence, and though they are 
 the caufes of corporeal compofition, yet after a manner they fubfift together with, and on this 
 account may be faid to be infeparable from, bodies ; but they denied for many reafons that 
 body is fabricated from bodies. If, therefore, this is true, it is altogether neceflary that bodies 
 fliould have their fubfiftence from indivifibles ; yet it does not follow that they are compofed 
 from indivifibles, or can be refolved into them, except by a mental procefs." 
 
 * In anfwer to the prefent inquiry of Ariftotle, it may be faid, that whether any one con- 
 fiders the indefinite duad according to its firft fubfiftence, i. e. as the fecoiul of thofe two great 
 principles after the ineffable caufe of all, or as intelleftual, or as fubfifting in foul, or phyfical, 
 or as participated by matter, yet we muft never afl^ert that it is either aflive or paflave divifibly, 
 through the great and the [mail, but that it imparts the great and the j mall to each of the natures 
 generated by it, in a manner accommodated to the feveral orders cf beings. But with refpe£t 
 to the monads in mathematical number, fuice Ariftotle at prefent confiders thefe, and indeed is 
 rot willing, con.fiftently with the malk which he aflumes, to fpeak of any other, of thefe we 
 fay, that they are produced by all the principles, and by the monad and indefinite duad, yet do 
 not contain the great and i'/'f^/y/j/// divifibly, nor ever did, fo th.it we might doubt in what each 
 
 Y y 2 monad
 
 348 ARISTOTLE'S METAPHYSICS. Book XIIL 
 
 or one monad from the fmall, and another from the .great ? If then thi^ be 
 the cafe, neither is each number from all the elements, nor are toe mona is 
 ■witliout difference : for, in this the great will be inherent, but in that the 
 fmall, being naturally contrary. Again: how do ihefe elements fubfift in 
 the triad itfelf ? for one of them is fuperfluous. But through this perhaps 
 they make the one itfelf the middle in the odd number. But if each of the 
 monads is from both the elements equalized, how will the duad be one certain 
 nature, compofed from the great and the fmall ? or in what will it differ from 
 the monad? Further ftill*: the monad is prior to the duad: for, being 
 taken away, the duad alio is taken away. It is neceifary, therefore, that it 
 fhould be the idea of idea, being prior to idea, and having a prior generation : 
 for the indefinite duad was effective of duality. Further iiill : it is neceffary 
 that number Ihould be either finite "j" or infinite ; for they make number fe- 
 
 parate : 
 
 monad differs from the duad itfelf; and tliat they are with refpcft to other numbers, and the duad 
 itfelf formlefs and infinite. We mult, howe\'er, aflert that they alfo are detained by the image 
 {(v3a>,«aTi) of the one. But if the inquiry is made refpefting immaterial monads (for it is lawful 
 to call intellectual forms not only numbers, but alfo monads), we may much more aflert that 
 each of thefe is from all the prinLiples, and that tliey poffefs from the one their fingle form and 
 monadic nature {inam eiJoj hoi.\. to /xjvjtJi^ov) ; but from the indefinite duad, impartibiiity and the 
 ability of pervading through all things, as well in their fabricailve ?s in their piovidential and 
 guardian powers. For it is requifice to fuppofe great and fmall of this kijid among divine na- 
 tures. 
 
 * The monad, fiys Ariftotle, is prior to the duad itfelf •, but if the duad itfelf is an idea, the 
 monad a!fo, which is more antient than this daad, is an idea. Jt proceeds, thetefore, from 
 fomething ; but it cannot proceed from the indefinite dual, for that alio doubles things fimple. 
 Here Ariftotle does not diftinguifli concerning whiit monad be I'pe.iks, but manileftly propotcs a 
 doubt re'pciSting the known duad, which is not in ideal number, but has ;m abjecl fubfiftente in 
 the lalt of mathematical numbers ; nor is it more aniient than the duad wbieh is compt^d 
 from duads, unlefs perhaps in generation, but it is not effencially more aii:i»i.t For cf {his 
 kind are material- caufes. But both this and every fubj'^t of mathematical numbers are pro- 
 duced from all the principles, but efpecially from the duad peculiar to rbem. For this, w'lea 
 numbers are divided into matter and form, is more the principle of matter ,• but when into the 
 even and the odd, it is mor; the leader of the een Producing, therefore, thefc things, and 
 many others o^ a wonderful ■ • ture about numbers, it is iielcivedly calie 1 du d-ifftB^Vt (5u:Tff,cj), 
 For the duad is after a manner .1! matter, every thing ev and every thing oblong, and wiiat- 
 ever elfe belongs to this co-ordination. 
 
 + 1 he divifion is inevitable, and the caufe is very weighty ; for neither can be afferted definitely 
 in fenfibles ; but it mull be faid, that things w Iiich (ublill in one time are finitt-, and that thofe 
 which lubfifl in an infinite time are infinite in number : but in things which (ubiift always the fame 
 and after the fame manner, and in which the energies of time are unJcuown, wc muft fav it is 
 
 Beceflaij
 
 Book XIII. ARISTOTLE'S METAPHYSICS. 349 
 
 parate : Co that it is not poffible that the other of thcfe fliould not fubfift. 
 That it cannot therefore be infinite * is manifeft : for infinite number is 
 neither odd nor even. But the generation of numbers is always either of the 
 odd number or the even : for, when unity falls upon an even number, an odd 
 number Is produced; but when the duad falls upon the even, that number 
 which is from unity is doubled ; and when it falls upon the odd number an 
 even number is produced. Again f : if every idea belongs to fome particular 
 
 thing, 
 
 neceffary to afTume either the infinite or the iinite, becaufe divine natures are indeed infinite in 
 power, but finite in number. But when, in fpeaking of divine natures, it is faid that the triad 
 is here and the tetrad there, and that the heptad is in one place and the decad in another, the 
 numeration which is adopted in other numerable natures muft not te adopted here; but lan- 
 guage of this kind is employed becaufe all things there are perfeEl, rank as unbegotten principles, 
 and comprehend in themfelves wholes. For among them a different property accords to different 
 natures, though at the fame time all are in all. In thofe divine natures, therefore, in which the 
 firft perfect is beheld, the triad is faid to fubfifl ; but the tetrad in thofe in which all mundane 
 natures are comprehended according to the caufal nature of principle [a^xfis.^ui). In like maimer, 
 the keptad is faid to fubfifl: in thofe through which generated natures receive the beneficent illu- 
 minations of providence without generation ; and laflly, the decad in thofe in which all things 
 are previoufly comprehended intelleftually, and with greater diftindtion and reparation. And 
 fuch is the theory of the Pythagorseans, as far as it is poffible to fpeak with brevity of things of 
 the greateft moment. But Ariftotle, conformably to his ufual method, again mingles known 
 mathematical monads with divine numbers. 
 
 * Some one may rather properly urge thefe doubts againfl mathematical number, but not 
 againft divine and ideal number. For the even and the odd fubfift in the latter, not as they are 
 now confidered by Ariftotle, but rather as the poets are aceuftomed to fpeak: ¥^iH,\vxt ^tu, Travrtj 
 T£ Sfoi, wacrai T£ &£aivai ; " Hear me, all ye gods and goddejfes." For there Jupiter, the demiurgic 
 intellect, fills up the two co-ordinations of divine and providential intclkftion. For, of the 
 divinities wiiich proceed from the father of gods and men, fome abiding in their parent, and 
 never departing frsm their domeftic monad, whom the poet therefore places in the abode of 
 Jupiter, providentially prcfide over the univerfe together with their father, and, in confequence 
 of polfeifing an eflence feparate from mundane nutures, are never reprefented as engaging in. 
 •war or difcord ; but others fubfide into manifold orders, become more partial and proximate 
 to the natures which th^y govern, and, on account of abundantly fympathizing with inferiors, 
 •war with each othtr. But to him who thus doubts refpefling mathc-matical number, it may be 
 faid that every number which is aflumed is finite, and is either even or odd ; but that which is 
 not yet adumed is unknown, formiefs, and infinite, and is, indeed, in capacity ehher. even or. 
 odd, but is neither in energy.. 
 
 t Let it be deraonftrated by Ariftotle, fays Syrianus, that intelkdlual numbers are not infinite 
 of their own proper nature. For, though fome one may refufe to admit the infinite in them,. 
 not for the reafons which he alTigns, yet this at Icnft is fufficiently demonftrated by Philolaus : 
 ♦' forno number (fays he) will be known if all of them are infinite." If, therefore, divine 
 
 number
 
 350 ARISTOTLE'S METAPHYSICS. Book XIII. 
 
 thing, but numbers are ideas, infinite number alfo will be the idea of fome- 
 thing, either of I'enfibles or of fomething elfe ; although this is neither pcfljble 
 according to pofition, nor according to reafon : in this manner, however, they 
 arrange ideas. 
 
 But If number is finite '*, how far does it extend ? For this ought to be 
 fhown, not only that it is, but alfo why it is. But if, as fome fay, number 
 extends as far "as the decad t> ii^ the firft place, forms will fwifdy fail ; as, for 
 inftance, if the triad is ideal man, what number will ideal horfe be ? For 
 every ideal number extends as far as the dec:id. It is, however, necefiary 
 that certain numbers fliould be in ihefe : for thefe are effences and ideas ; but 
 at the fame time they will fail, if they exceed the fpecles of animal. It is alfo 
 evident, that if the triad is after this manner ideal man :):, this will alfo be the 
 cafe with other triads : for thofe in the fame numbers are limiJar ; fo that there 
 will be infinite men. If, indeed, every triad is an idea, each will be ideal 
 man ; or, if this be not admitted, at lead it will be men. But if the tetrad 
 itfelf is the idea of any thing, as of horfe, or that which is white, man will 
 be a part of horfe, if man is the duad. It is alfo abfurd that there fliould be 
 
 number knows Itfelf, it is becaufe it is bounded in itfelf ; and if its magnitude is according to 
 the will of its principles, this will be becaufe its meafure is previoudy comprehended by their 
 will. It will, therefore,-no otherwile be infinite, than as pofleffing infinite power, or as conii- 
 dered with relation to us. 
 
 * It mud be carefully obferved, that divine natures are not numerable by our nature. But 
 when the Pythagoreans fpeak of triads, tetrads, heptads, and decads, among divine natures, 
 they are not deftitute of reafons adapted to thefe confiderations, as we have jufl. before briefly 
 ihown. 
 
 f Divine men, fays Syrianus, called the decad an ideal number, as being the mundane para- 
 digm, and the boundary to all things. They likewife aflerted, that as the decad comprehends 
 every number within itfelf, not occultly as the monad, nor effentially as the tetrad, but with abun- 
 dant diverfity and divifion, fo the intclledual fabrication (voffa lr\nioupyta), or, in other words, 
 the intelled of the mundane artificer, comprehends in itfelf the forms of the univerfe. And 
 this opinion, fays Syrianus, Ariftotle derived from Orpheus and Mufieus, and their followers 
 (xdi ravrnv rnv ^o^av utto Of(ptcc;, km Mouatu;, xm tiov txetSiv KarayoijLCMUv i/Troh^afisvos b A^iji 0Ti>yii). 
 But here .igain Ariftotle, as ufual, confiders the decad only, which is compofed from unities. 
 
 X It has been already faid, that not only every ideal number is one, but alfo every mathemati- 
 cal number, if that is aflumed which is confidered in energy, and in conjundion with its own 
 form. Dut the triad itfelf will not be the paradigm of man, but of iill the triads vhich are 
 pofterior to it. Hence there is one caufe of the many, of thcff indeed, which are proximate to 
 itfelf, but of other things, fituatcd in particulars. 
 
 an
 
 Book XIII. ARISTOTLE'S METAPHYSICS. 351 
 
 an idea of the decad *, and not of the endecad, nor of the numbers confe- 
 quent to the endecad. 
 
 Again : certain things both are, and are generated, of which there are no 
 ideas: fo that it may be aflced on what account there are no ideas of thele ? 
 Forms, therefore, are not caufes. Farther ftillj : it is abfiird that number, as 
 far as the decad, fhould be in a greater degree a certain being, and the form 
 of the decad itfelf ; although of this indeed there is no generation as of the 
 onr, but there is of that. But they fpeak as if number as far as the decad was 
 petfedl, and therefore generate the following numbers, confidering as a va- 
 cuum, analogy, the odd, and other things of this kind within the decad. For 
 they attribute fome things to principles, as, for inftance, motion and reft, good 
 and evil ; but others to numbers. Hence the one is odd : for, if in the triad, 
 how is the pentad odd ? Again : how far do magnitudes and fuch-like 
 
 things 
 
 * There is no abfurdity in admitting this, if it be confidered that there are ideas only of 
 fimple natures, and not of things compoied from kindred elements. Whence, fays Syrianus,. 
 the Pythagorasans called every ideal number the decad, for the above-mentioned reafons : ncver- 
 thelefs they alfo eflablifhed an idea of every number as far as to the decad; for thefe are mod 
 fimpIc, and poflefs among tbemfclves a fpecihc difference. But the number eleven is a compo- 
 fition of tvi'o pre-exifting numbers. 
 
 t There is a defed here, fays Syrianus, in the fentence ; but it will be perfefl: if we read : 
 " Further flill • it is abfurd that number fliould not proceed as far as to eleven ; becaufe the one 
 has more of being than the decad, and is the form of it." The one, therefore, is called by the 
 Pythagorseans the form of the decad ; not indeed any unity indifcriminately, but that which 
 ranks as a principle, and which In defining they call the form of forms. Neverthelefs, though 
 this monad is the form of all arithmetical forms, yet it is efpecially laid to be the form of the 
 decad : for what the monad is to all numbers fimply, that the decad is to all the poflerior decads, 
 hundreds and thoufands ; whence :iiro, according to a fecondary progrelTion, it is denominated a 
 monad. As, therefore, intelled is indeed the form of all things, but efpecially of the foul ; 
 after the fame manner the monad, though it is the. form of all numbers, yet is principally 
 fo of the decad. To this monad, therefore, the unbegotten particularly accords, and not to 
 that which belongs to the number eleven. But Ariftotle was not ignorant of the reafon 
 why the I'ythagorseans produced number as far as to the decad. For this number is the ulti- 
 mate perfedlon of all numbers, containing all things in itfelf. The more exact too of the 
 Pythagorean difcourfes, fays Syrianus, do not leavr; any example of a vacuum in numbers, be- 
 caufe neither is there a vacuuin in beings, asjamblichus flwws in the fifth book of his Colle£lion 
 of Pythagoric Dogmas. He further adds, But the Ipaces of numbers, and efpecially the pro- 
 portions which are themfelves entirely filled up by numbers, bring to our recolleflion the fpace 
 or region of the univerfe, whith in its own proper nature is void, but is filled by inteil'"£lual 
 fabrication, and by the circular motion of ether, which embracing and compelling all things to- 
 wards itfelf, does not falFer any part of the univene to be void, but renders the world throuirh- 
 out fympathetic and in liarmony with itfelf. In like manner, neither does the monad which 
 
 gives
 
 352 ARISTOTLE'S METAPHYSICS. Book XIII. 
 
 things partake of quantity ? as, for Inftance, the firft indivifible line, then the 
 duad, and afterwards thele alfo as far as to the decad. 
 
 Further ftill * ; if number is feparate, fome one may doubt, whether the 
 one is prior, or the triad and the duad : fur, fo far as number is a compofite, 
 the one is prior; but fo far as univerfal and form are prior, number has a pri- 
 ority of fubfiftence ; for each of the monads is a part of number as matter, 
 but that as form. And indeed the right angle is in a certain rerpe(£i: prior to 
 the acute, becaufe it is Hmit'ed by its definition ; but in anoth.er refpei^t the 
 acute angle is prior, becaufe it is a part, and the right angle is divided ii;to 
 
 gives fubfiftence to numbers, leave any void region, but fills with fucceeding numbers, without 
 intermiffion, ail the numeral receptacles. But it is evident that every proportion may be confi- 
 dered as fubfifling within the decad : for the arithmetical fublifls in the natural progrefFion of 
 the numbers I, 2, 3, &;c. ; the geometrical in the numbers I, 2, 4, and I, 3, y ; and the har- 
 monic in the numbers 2, 3, 6, and 3, 4,6. 
 
 The Pythagora'aiis, therefore, fiys Ariftotle, affigned all tilings to the priaciples, viz. to the 
 monad and the duad ; reit, indeed, and the good to the monad, but motion and evil to the duad. 
 The two co-ordinations alfo in numbers, as far as to the decad, may very properly be called 
 principles, bccaofe, in the order of beings, fome things are fufpcnded from the principles alone, 
 viz. from the ineffiible one, and the two great principles of things poftericr to it, louml and infi- 
 fiiiy ; but others alfo pre-aflume a formal caufe. But the apparent oppofition which Aiiftotle 
 makes to the Pythagorseans in the end, may be eafily folved : for he inquires, if the triad fubfifls 
 through the one, why the pentad does not alfo fubfifl through the triad, and likewifis every odd 
 number, in the fame manner as every even number fubfifls through the duad ? 1 he anfwer is 
 obvious: that the firil and iiicompoCtenumber appears to derive its fpecific diflinSion from the 
 monad alone ; but that number which is fecond and compofte, has alfo another meafure from 
 the monad. Hence the monad is the form of all odd numbers, as the duad of all even. For> 
 i.n fliort, it is requifite that the triad fliould be (iniilar to tlie dund, not from ranking as a prin- 
 ciple, but rather through the monad. Fiom thefe words, therefore, of Arillotlc, it appears that 
 even according to him there is another caufe through which the Pythagoraeans produce the pa- 
 radigms of numbers as far ae to the decad. For, if they were, willing to confider the caufes of 
 all things in: numbers; but thjey faw the caufes, of all things in the numbers as far as to the 
 decad, it would be fupetfluous to fuppofc paradigms of the following numbers. Let it be alfo 
 obferved, that the number eleven has not together with the decad that monad which is the 
 caufe of the decad ; but a monad, which is as it viere a part of the decad, auJ of the duad, and 
 01 every other number. 
 
 * Ariilotle both rightly doub's, and folves liis doubts from tliofe things which are ufually 
 affertcd by the Pythagoiaans. For this iniieed, fays Syrianus, is the monad which ranks as a 
 principle, and correfponds to the divine monnd which the Pythagorarans call the firfl number in 
 all thi'.-!gs, and the fummit cf all forms and all figures. But the other monad is that vihich be« 
 comes the fubjecl of numbers, and which the Pythagorxms defined to be the lead in quantity, 
 and the firft in generation though not in efTence. 
 
 tlxis.
 
 EooKXirr. ARISTOTLE'S METAPHYSICS. 358' 
 
 this. Indeed, as matter, the acute angle, an element, and the monad are prior ; 
 but, confidered with relation to form, and an efleriQe according to definition, 
 the right angle, and the whcle compofed from matter and form are prior : 
 for bcth are more proximate to form, and to that to which definition belongs, 
 but they are pofterior in generation. How, therefore, is the cue a principle ■ ? 
 Bccaufe, fay they, it is not divifible, but indivifible, both that which is uni- 
 vcrfal, and that which is particular, and alfo that which is an element ; but in 
 a different manner : the one^ indeed, according to definition, but the other ac- 
 cording to time. After what manner, therefore, is the one a principle ? for, 
 as we have faid f, the right appears to be prior to the acute angle, and the 
 acute to the right angle, and each is one. But, according to both:}^ thefe modes, 
 they make the one a principle. Still, however, it is Impoffible : for this is as 
 form and eflence, but that as a part §, and as matter : for each is in a certain 
 refpedt one ||, in reality indeed, in capacity ; if, indeed, number is one certain 
 
 thing, 
 
 * Ariftotle here inquires what this one of tlie Pythagoraeans is ; whether it is that which ranks 
 as a principle, or that which is the leaft in quantity. Syrianus here informs us, that according 
 to the Pytiiagorseans, there is a difference between the one and the monad, to cv km h /^ova; ; and 
 that this was a fubjeft of difcuflion to many of the more antient philofophers of that fe£l, among 
 whom is Archiras, who fays, " that the one and the monnd, though of a kindred nature, differ 
 from ea«h other." He likewife informs us, that tliis fubjedl employed the attention of thofe 
 junior Pythagoracans, Moderatus and Nicomachus. But Ariftotle, for the purpofe of conceahng 
 his defign, paiTes from the monad to the cnr, as if thefe two M'ere one and the fame. See more 
 on this fubjeft in the annexed DifTertation. 
 
 f That monad which completes the eflence of numbers, by fubfiRing as a fubjedl, when con- 
 fulcred as analogous to an acute angle, is faid to be both prior and poilerior to number; pofle- 
 rior indeed in eflence, but in generation more antient. 
 
 J We reply, But not after the fame mnnner. For that monad which ranks as a principle is 
 a principle in every refpeft, as being the caufe of wholes •, but that monad which is the leaft in 
 quantity is a principle in the fame manner as an acute of a right angle. 
 
 § That is to f;:y, it is as a part and as matter, fo far as it is fubjeft to numbers. 
 ■ II Ariftotle here fpeaks both according to truth, and the opinion of the antients For, if 
 number is not a heap of monads, but each is compofed from i'u many monads as I'ubjecls, but 
 confifts through its own form, the monad in the duad will be nothing in energy till it is invcfted 
 with its proper form. It is here, therefore, requifite to obferve, that neither is Atiftotlc of oii- 
 nion that number is a co-accrvation of monads, nor tb.at monads, in flioit, are any thing in 
 energy till they are adorned by forms. For though, for the fake of concealment, he alTumes 
 that, according to the Pythagorajans, that which is in capacity is not only prior in generation 
 and time to that which is a wholcj and has a fprcific diftinciion, but ulfo in definition and 
 
 ^ z eflence i
 
 55-i ARISTOTLE'S M E T A T H Y S I C S, Book XIII. 
 
 thing, and not as a heap, but, as they fay, different numbers fubfifl from dif- 
 ferent monads. But the monad is not each of theTe in energy. The caufe, 
 however, of the accidental error is this, that they inveftigate at the fame time 
 from mathematical natures and univerfal reafons ; fo that, from thofe as a 
 point, they have placed the one and the principle : for the monad is a point 
 without pofition. As, therefore, certain others have compofed beings from 
 that which is leaft, fo alfo they. So that the monad becomes the matter of 
 numbers, and at the fame time prior to the duad. It is, however, again pof. 
 terior, the duad fubfifting as a certain whole, as one, and as form. But, in 
 confequence of their inveftigating a univerfal predicated one, they fpeak of 
 it as of a part. It is, however, impofllble that thefe fhould fubuft at the 
 fame time in the fame thing. But if it is requifite that the one itfelf Ihould 
 alone be without pofition (for it differs in nothing, except that it is the prin- 
 ciple, and that the duad is divifible, but the monad not) —if this be the cafe, the 
 monad will be more fnnilar to the one. But if the monad alone is without 
 pofition, the otie will be more fimllar to the monad than to the duad ;" fo that 
 in eitlier cafe the monad will be prior to the duad. They do not, however, 
 affert this; for they generate the decad the firft. Laflly, if the duad itfelf is 
 one certain thing, and alfo the triad itfelf, both ^re a duad. From what, 
 therefore, does the duad itfelf confifl ? 
 
 CHAP. IX. 
 
 But fome one may doubt, fince there is no conta(fl * in numbers, whether 
 the firft monad in the duad or triad is placed in an order confequent to 
 
 effence ; yet, if we obferve in reply, that according to thofe divine men there are two monads, 
 one of wliich ranks as a principle, and the other as a material fubjeft, we fhall then fpeak fuf- 
 ficiently, both with refpe£t to truth and the concord of the antients. 
 
 * The properties of mathematical monads, as we have often obferved, are not fo be trans- 
 ferred to ideal number ; but, if what Ariftotle now fays is direded againfl mathematical num- 
 ber, we may reply, that the monads which fubfill in different numbers analogous to matter, are 
 not confequent to any thing, fince neither are they effentially in energy : but when they are in- 
 verted with the form of their proper number, then they become confequent to each other. The 
 monads, however, in another number, mufl by no means be faid to be confequent to thefe, 
 but rather the numbers which are placed in a natural order fliould be faid to fucceed to each 
 other. 
 
 the
 
 BookXIIL a R ISTOTLE'S met a PH YS I CS. S53 
 
 the one, or not; and whether the duad is prior to the monads which are in 
 a confequent order, or whether this is the cafe with any kind of monads. 
 In Hke manner, thefe difficukies take place in the pofterior genera of number, 
 of a line, a fuperficles, and a body : for fome make lengths from the fpecies 
 of the great and the fmall, as it were from the long and the fliort ; but fuper- 
 ficies from the broad and the narrow, and bulks from the profound and the 
 low. But theft? are the fpecies of the great and the fmall : but others differ- 
 ently place among things of this kind, that principle which fubfifts according 
 to the one. And in thefe a!fo ten ihoufand impofiibillties, fidlions, and things 
 contrary to all rational aflertions appear. For it happens that they will be 
 liberated from any connexion with each other, if the principles alfo do not 
 at the fame time follow ; but if the principles co-exift, a line will be the fame 
 with a fuperficles, and a fuperficles with a folid. 
 
 Further ftill : how can angles*, figures, and things of this kind be af- 
 figned ? The fame thing alfo happens to the particulars refpeding numberf. 
 For thefe are the paflions of magnitude : but magnitude does not confiil from 
 thefe, as neither does length confift from the flraight and the curved, nor 
 fjlids from the fmooth and the rough. To all thefe, however, the fame doubt 
 
 is 
 
 • Ariflotk here Inquires how the Pyihagorscans can any longer produce thefe things from the 
 monad and indefinite duad. For what, fays he, is there in thefe tranfcendent, and what defi- 
 cfcnt ? In angles indeed, it is eafy to reply, that the right angle fubfills rather according to the 
 monad, but t!:e acute and obtufe, according to the indefinite duad, in which exuberance and 
 defect are moft apparent. Of 'figures alfo, thofe which are charaftcrifed by equality, famenefs, 
 and fimilitude, have a greater relation to the monad •, but thofc in which inequality, difference 
 and ('ifiimilitude are predominant, are more allied to tlieduad. In fliort, every figure fubfifts 
 from thefe two principles : for the fphere, circle, equilateral triangle, fquare and cube, partici- 
 pate of the duad by their quantity, and their poffeffion of interval. And again, beams of timberj 
 altars, fcalene triangles, and oblong figures, accord with the n^onad, from which they receive 
 their form. Neverthclefs, as we are accuilomed to fay in number';, that every number fubfifts 
 from thefe two principles, but that the odd number is rather charatlerifed by the property of the 
 monad, but the even by the property of the duad ; after the fame manner, in angles and figures, 
 wc affirm that they all indeed fubfilt from thefe t«'o principles, but that fome are more -.'.ffimi- 
 lated to ti.e monad, and otliers to the duad. 
 
 -j- As the odd and the even are the efTential properties of numbers, in like manner the circular 
 and the ftraight are the eflcntial properties of length ; the narrow and the broad of depth ; and 
 ihe high and the low of depth. But, as thefe properties do not fubfift in their fubjects without 
 2 caufe, it is evident tiiat they proceed from an accommodated principle. And when, indeed, 
 
 Zz % they 
 
 /.
 
 356 ARISTOTLE'S METAPHYSICS. Book XIIJ. 
 
 is common*, which happens to fpecies confidered with relation to genus, whea 
 anv one admits univerfals ; viz. whether animal itfelf is in animal, or fome- 
 thing dlfierent from animal itfelf: for this not being feparate produces uo 
 doubt ; but if feparate, as thofe fay v\'ho make thefe alfertions, it is not eafy 
 
 they are united to tbeir fubjefts with rectitude and permanency, they rather proceed into them 
 from unity, as the right in angles: but if they are beheld with exuberance and defeat, they fub- 
 fifl; together with the more and tlie lefs, and receive thefe from the indefinite duad. Neither, 
 therefore, did the Pythagoreans call the pafTions or participated properties of magnitudes, the 
 principles of magnitudes, but rather thofe things from which thefe are imparted to magnitudes, 
 and of wliich there is one fountain, viz. their proper indefinite duad. 
 
 * In anfwer to the apparent objection of Ariflotle, that many impofTibllitles will follow, if we 
 admit that univerfals have a fubfiftence feparate from fenfibles, we may reply, that in every in- 
 dividual of the human fpecies tlie common nature of man is apparent ; that animal alfo is be- 
 held in lion and horfe, and man and dog ; the pentad in the five fingers, and the duad in the 
 noftriis, the eyes, hands and feet. But, fince thefe do not fubfift without a caufe, but receive 
 their perfeti^ion from certain definite natures, it is altogether necefl'ary that there fhould be fome 
 animal in the whole of nature, feparate from fenfibles, through which this which is fenfible i« 
 generated : and, flill further, that there fhould fubfift in nature a pentad through which 
 the hands are always adorned with fo many extremities, and a duad from which the two eye* 
 and noflrils proceed. But if neither nature pofTefles thefe from herfelf, but they are imparted 
 to her from another caufe, as they alfo emanate from her into matter, it is necefl'ary that there 
 ihould likewife be univerfals and numbers prior to nature, and which fubfift in a fuperior man- 
 ner. For neither does nature poflefs thefe in the fame manner as fiie imparts them to matter j 
 fmce in matter they fubfid accompanied with Interval, and diftended with bulk : but in nature 
 they fubfift indlvifibly, and with efficacious energy (Jfacrrixrus). In foul they fubfift ftill more 
 fimply and Immaterially ; and in that which is fuperior to foul, they poflefs, through tran- 
 fcendency of eflence, the prerogatives of ideas. Neverthelefs, it muft here be obfcrved 
 that Ariftotle rightly afierts, that univerfals and numbers are at the fame time feparable, or 
 at the fame time infeparable, from which many other conclufions may be deduced : for, which- 
 ever of thefe you approve, you muft conclude the other. This alfo is rightly aflerted by 
 Ariftotle, That if there are ideas, numhen are ideas. For his reafoning is, that if there are uni- 
 verfals there are ideas ; and we admit the conclufion ; not that univerfals are Ideas, for how i& 
 this pofliLle ? fince the former fubfift in foul, but the latter in Intelled. But we admit the 
 conclufion, becaufe, fince there are forms involved in the folds of matter, there are alfo formi 
 more indivifible than thefe, and which have a more principal fubfiftence. If numbers, there- 
 fore, have a feparate fubfiftence, there are univerfals ; but if there are univerfals, there are 
 ideas ; if numbers are feparate, ideas alfo are feparate. As, therefore, he who admits that 
 forms are feparate, will not ceafe in his afcent tiU he arrives at the moft fimple forms, whiclj 
 are no longer fecondary to others, but have a primary fubfiftence from themfelves ; fo he who 
 admits the exiftence of feparate number, will not ftop in his fublime career, till, arriving at tlie 
 luminous region of ideas, he perceives their profound union with numbers. For monadic num* 
 kers poffefs tpantlty feparated from formj. but in divine numbers the wbole is form, 
 
 to
 
 Book XIII. ARISTOTLE'S METAPHYSICS. 357 
 
 to folve the doubts refpeding the ont and numbers. But, If not eafy, it is re- 
 quifitc to lay that it is impoffible : for, when any one underftands the one* 
 in the duad, and univcrfally in number, whether docs he underftand fome 
 particular thing itfelf, or fomething elfe ? Some, therefore, generate magni- 
 tudes fiom matter of this kind, but others from a point, (but a point appears 
 to them not to be the one^ but to poflefs a hke qnahty witli the one) and an- 
 other matter fuch as is mukitude ; concerning which it happens that the fame 
 doubts no lefs arife : for, if the matter is one f , line, fiiperlicies, and foiid are 
 the fame ; for, from the fame things there will be one and the fame thing : 
 but if tlie matters are many, and there is one matter of a line, another of a 
 fuperficies, and another of a folid, they either follow each other, or they do 
 not. So that tluis alfo the fame things will happen : for either a fuperficies 
 will not have a line, or it will be a line. Further ftill J : no one endeavours 
 to explain how It happens that number fubfifts from the one and multitude. 
 But In whatever manner they fpeak, the fame difficulties take place which alfa 
 
 * 37y one in the duad indeed is derived from that monad which ranks^ as a principle ; buj 
 the one in number does not proceed from that monad which is material : for material monads 
 are not different from each other. 
 
 f In the firft place, indeed, the other of the principles is not as the matter of magnitudes, but 
 as that which gives fubfiftence to matter. And in the next place, what necelTity is there that, 
 one matter exifting, the fame things fhould be efFefted from it ? For the difference will arife 
 from the forming caufe, as in the mundane elements : for fire, air, water and earth have the 
 fame matter, but are evidently not the fame with each other. A fyllable alfo, a word, and a 
 fentence, employ the fame fubje£ts ; for the elements of fpeech are the matter of all thefe ; and 
 yet fome of thefe are more fimple, and others more compoGte. To which we may add, that no 
 one of the more compofite can fubfifl without the more fimple, as neither can body fubfift 
 without fuperficies and line ; bun the more fimple may be confidered as fubfilling by them- 
 felves ; as, for inflance, a line. 
 
 % Both thofe who make the other of the principles to be multitude, and thofe who denomi- 
 nate it the duad, fpeak of the fame thing under different names : for, neither is a multitude of this 
 iind fuch as is that which is generated, nor did the Pythagorieans confider the duad itfelf as 
 the fame with that duad which is a certain multitude, but as that which is generative of quantity,, 
 and derives its fpecific diftiniSlion from the monad. But Ariflotle here plainly (hows that he is. 
 not ferious ; for, though tlie inquiry at prefent is refpefling things which are void of pofitioa 
 and contaft, and which are immaterial, yet he afks whether we afcribe the continuity of num- 
 bers to mixture, or pofition, or temperament, or generation ; which modes are evidently rude 
 and inartificial, and do not even apply to thofe numbers which are more proximate to bodies : for 
 it is manifeft that each of thefe derives its fubfiftence from its proper forjiij and through this. 
 form is ailimilated to the monadic principle of numbers^ 
 
 kappea. 
 
 fe-^-
 
 35S ARISTOTLE'S METAPHYSICS. Book XIII. 
 
 happen to thofe who aflert that numher confifts from the one and the indefi- 
 nite duad : for one generates number from predicated univerfal, and not from 
 a certain muhitude, but another from a certain multitude, yet that which is 
 firftj for, according to them, the duad is the firft multitude. So that, as I may 
 fay, there is no dlflerence with refped to the difficulties that take place, but 
 the fame doubts follow, wheth'.r mixture, or pofition, or temperament, or ge- 
 neration, or any thing elfe of this kind is adopted. But eipecially it may be 
 inquired*, if each monad is one, from what it fubnfts : for ea;h will not 
 be the one itfelf. It is neceiTary, however, that it flipuld either be from the 
 07ie itfilf, and multitude, or from a part of multitude. To fay, therefore, that 
 the monad is a certain multitude is iuipoffible, fmce it is indivlfible. But to 
 fay that each monad is from a part of muhitude, is an aflcrtion attended 
 with many other difficulties ; for it is necclfary that each of the parts (hould 
 either be indivifible, or be multitude, and that the monad fliould be divifible, 
 and the one and raullitade not be an element ; for each monad is not from 
 multitude and the one. 
 
 Again : he who fays this, does nothing elfe than make another number : 
 for multitude is a number of indivifibles. Further ftill f : it may be inquired 
 
 of 
 
 * Ariftotlc rightly inquires whence each of the material monads fubfills. He alfo rightly 
 denies, that the material monad is the fame with that which ranks as a principle, and which he 
 calls the monad itfelf. We alfo have aflerted the fame. It is, however, by no means necelTarv, 
 that the remaining part of what he fays fhould follow: for, neither do we fay that this monad 
 fubfifls from a part of the duad ; fince every principle is indivifible in multitude: nor, if it fub- 
 fifted from the duad, would it on that account be raultifU le ; for the duad itfelf is not multi- 
 tude. We muft fay, therefore, in riply to t/,e firft interrogation, that this monad fubfifls indeed 
 from that caufe which generates the fuhjeft of numbers, viz. from the duad, but that it 
 alfo derives foroething from that moTiad which ranks as a principle, as Aiiftotle himfelf now 
 ad.-r.its, and fubfifts from the great principles of things. W^e muft further fay, that the duad is 
 not divided, and that number will not be in it prior to numbers, but that it contains the caufe of 
 the matter of numbers. The fiime doubts may alfo be urged refpefnng the matter of things 
 capable of being generated, and the doubts may be folved by anf«ers of this kind : for, if lie 
 afks whether this matter fubfifts from multitude or the one, we muft fiy that it proceeds indeed 
 from the fame produdive and infinitely powerful duad, but that it a!fj receives a refemblance 
 of a more excellent principle, fo far as it is in a certain refpsdl faid to be one, and fo far as it is 
 dinimilarly affimilated (avo/«ia; o/noiaTai) to the cue. 
 
 t Ariftotle docs not at prefent inquire concerning numbers, wliether they are fin'te or not ; for 
 ^his he had propofed before ; but rc;p«cling the multitude in the duad; from the divifion of \\hich 
 
 he
 
 BookXIII. ARISTOTLE'S met a PHYS IC S. 359 
 
 of thofe who fpeak in this manner, whether number is infinite or finite : for 
 the multitutie alio, as it fcems, was finite, from which and the one finite mo- 
 nads were produced ; and multitude itfelf is different from infinite multitude. 
 What kind of multitude, therefore, is an element and iJje o?ie*^ In like 
 manner, it may be inquired refpcding point and element "|", from which 
 they make magnitudes : for there is not only one point itfelf. From what, 
 therefore, does each of the other points confiil ? For it does not confift from 
 a certain interval, and the point itfelf. But neither does it happen that in- 
 divifible parts are the parts of interval, as they are of the multitude which 
 confius from monads : for number is compofed from indivilibles, but this 
 is net the cafe with magnitudes. All thefe, however :{;, and other fuch like 
 particulars render it evident, that it is impofTible for number and magnitudes to 
 have a feparate fubfiftence. Further ftill : fince the firft authors of thefe 
 hypothefes difagree refpedting numbers, it is a fign that thefe things not 
 being true are the fources of confufion to them. For fome, making mathe- 
 matical fpecies§ alone befides fenfibles, and perceiving the difficulty and 
 
 he fuppofed monads to be generated. But his meaning is evident from the conclufion. We 
 murt; fay, therefore, that difcrete muhitude by no means fubfifts in the duad ; and that the 
 duad is for the moft part called multitude, as pofleffing, and containing in itfelf, a caufe genera- 
 tive of multitude. 
 
 * For TTotov om wXiffo; uai roixeiov tn ro tr ; read wotov ouv n-Xtifloj xm roix^iov tri hm to sr ; 
 
 f To inquire, indeed, whence many points and magnitudes derive their fubfiftence, is the 
 bufinefs of a philofopher. The true folution, therefore, of the queftion is this j that the multi- 
 tude of points in a line correfpond to material monads. Hence, they poiTefs indeed a cauf» 
 produdlive of matter, but they alfo receive a refemblance of a fpecific and formal principle. 
 But magnitudes pofll'fs their divifions from the other of the principles, or the duad, which 
 generates matter ; but their ratios from the monadic principle. Neither, therefore, is it re- 
 quifite to call interval the generative principle of interval, nor to underftand points as parts of 
 interval, not only becaufe the parts of dimenfion are not impartible?, but becaufe neither is 
 diftance the otiicr of the principles; nor, in the duad which gives fubfiftence to multitude, 
 do we fay thu the monads which it contains are the caufes of externally ingrelfive monads. 
 
 X It has, I think, been fufficiently demonftrated, that none of thefe objedions oppofe th« 
 real dogmas of the Pythajorsans. " It is alfo manifeft, fays Syrianus, that neither if any one 
 fliould accumulate an infinitely infinite number of fuch objedions, could he ftiake the truth 
 itfelf from tho- intelleft of the more prudent." 
 
 § We h.ave already obferved that the followers of Hippafus, to whom Ariftotle now alludes, 
 venerated ideal number •, though, in conformity to other Pythagoraeans, they called fuch num- 
 ber by mathematical names, and thus gave occafion to others to aflert, that, feparating themfelves 
 from the firft and better fpecies of number, they direded the whole of tlieir attention to that 
 which is fecondary and fubordinate. 
 
 fidioa
 
 S60- A R I S T O T L E- S M E T A P H y S I C S. Book XI1I» 
 
 fiiStion refpeifling forms, abandoned formal, and Introduced matliematical, 
 number. But others, being willing to make forms at the fame time and 
 numbers, and not perceiving how, if any one adopts thcfe principles, mathe- 
 matical number can fubfift befides the formal, made formal and mathematical 
 number to be the fame in definition. But fince the mathematician is entirely 
 withdrawn in their aflertions, they introduce peculiar, and not mathematical, 
 hypothefes. However, he who fiift adopts forms and numbers, rationally 
 fcparates forms and mathematical entities ; fo that all of them in a certain 
 refpedi fpeak rightly, but not entirely fo. They likewife do not accord with, 
 but fpeak contrary to, each other ; the caufe of which is this : that their hy- 
 poihefes and principles are falfe. But it is difficult, according to Epicharmus, 
 to fpeak well from things which are not well prefuppofed : for in this cafe, 
 as foon as any thifig is faiJ, it immediately appears not to be well laid. 
 But, ,with refpe£l to numbers *, the doubts already enumerated and the 
 things already determined are fufEcient : for he who is perfuaded by what 
 has been faid, may yet be more perfuaded by more numerous arguments ; 
 but nothing further can be urged to perfuade him who is not yet per- 
 fuaded. 
 
 But with refpeit to flrft principles, and firfl: caufes, and elements, fuch 
 things as are alTerted by thofe who alone employ themfelves about a fenfible 
 effence, have been partly mentioned by us in our Phyfics, and what further 
 remains to be faid refpeding them does not belong to the prefent inquiry. 
 But fuch things as are afierted by thofe who introduce other effenccs befides 
 
 * Our philofopher, fays Syrianus, very rightly conjectures, that chough as many jocular 
 objeclions againft the admirers of antieut philofophy Oiould be compofed without end, they 
 would efreift nothing : for all his arguments are dircclsd againil numbers compofed from 
 monads ; but no divine number is of this kind, but perhaps mathematical number alone. 
 Syrianus adds, that Ariftotle, according to his own confelTion, has faid nothing againft the 
 hypothefes of the Fythagoraans, nor, in Ihort, againft ideal number!-, if they are different from 
 mathematical numbers. For in his fecond book On Pliilofophy (a work unfortunately no 
 longer extant) he fays : " wherefore, if ideas are numbers of a difl'crent kind from fuch as 
 are mathematical, we (hall have no coiiception of them." Hence, his arguments are- 
 now direcled againil thofe who know of no other number than that which is compofed from 
 monads, but not againft the conceptions of thofe divine men the antieut Pythagorxans. 
 
 Syrianus adds, that fome confider this book as ending here ; and therefore, as v. hat follows 
 regards the third queftion, they diftribute it in the fourteenth book. Neverthelefs, fays he, 
 many books have the divifion adopted by Alexander: and this divifion, which Syrianus alio- 
 follows, has been retained by all fucceeding ages. 
 
 fenfibles.
 
 EookXIII. ARISTOTLE'S METAPHYSICS. 361 
 
 fenfibles, form fpeculatlons confequent to what has been faid. Since, there- 
 fore, fome affert that there are fuch like* ideas and numbers, and 
 that the elements of theie, are the elements and principles of things, 
 let us confider what they fay, and how they fpeak refpeding thefe ; 
 referving for an after fpeculation the opinions of thole who alone introduce 
 numbers, and thefe fuch as are mathematical. But of thofe who affert that 
 there are ideas, fome one may at the fame time perceive the mode, and the 
 doubts which take place refpeding them : for at the fame time they make 
 ideas to be univerfal effences, and again they confider them as feparate, and as 
 particulars. But, that thefe things are not poffible, we have already doubted. 
 The caufe f, however, which induced thofe who call ideas univerfals, to 
 
 confider 
 
 * The Pythagoreans and Plato confidered ideas as efiences, according to a tranfcendency 
 with refpeft to individual or partial eflences; and aflcrted that they are more compreheiifive 
 than univerfals, and contain in profound union th& caufes both of univerfals and individuals. 
 Hence, ideas are neither univerfal after the manner of the reafons or productive principles of 
 foul, nor indivifible and one in number, according to the refemblances of lad images. 
 
 f We have already obfcrved, that neither did' the antients arrive at ideas by following the 
 dodrine of Heraclitus, nor did Socrates think that there were no other univerfals than Cuch 
 as are infeparable from particulars. But, fince Ariftotle manifeftly acknowledges that fcience 
 cannot be poflefled without univerfals, we may inquire of him what univerfals he means : for, if 
 fuch as are infeparable from particulars, thefe are indeed parts of fenfibles, and are neither 
 prior nor pofterior to them. But Ariftotle very properly afTerts that demonftrations and fci- 
 cnces aie acquired from caufes, and things which have a priority of fubfiflence ; and this noS 
 only in his Laft Analytics, but in what he has a little before faid, " that the univerfal which is 
 predicated, is different from that which fubfifts in an individual as a part, and can never become 
 one and the fame with it." If, therefore, all demonftrations are from predicated univerfals, 
 they can by no means te formed from the univerfals inherent in fenfibles. Befides, if demon- 
 ftrations fubfilt through infeparable univerfals, where will be the demonftrative power which 
 they poflefs ? For thofe who confider the things through which demonftration fubfifts as fepa- 
 late from particulars, at the fame time demonlirate from caufes, and are able to demonftrate 
 things demoiillrablc, fince they both fubfift in feparace caufes, and in fuch as are inleparable, 
 but have a more univerfal fubfiftence. But if we confider the things from which demonftrations 
 are compofed as feparate indeed, but of pofterior origin, and void of elTence, as man fubfifting 
 in our phantafy or opinion by an abftraftion from fenfibles, thus again, demonftrations will 
 neither be from things prior and caufes, but from things pofterior and caufed; and befides this, 
 we (hall know beings thcmfelves through non-entities, which of all things is the moft irrational. 
 If, therefore, we wi(h to be confiftent both with ourfelves and things, we muft place phyfical 
 reafons (i. e. productive principles) in fenfibles, but we muft eftablidi prior to thefe the con- 
 ceptions of our foul, confidering beings through univerfal reafons, from which demonftratioii 
 and every kind of fcience originate ; and again, above thefe, that ideal efTence which fubfifti 
 
 3 A ia.
 
 3Sf ARISTOTLE'S METAPHYSICS. Book XIIlV 
 
 confidcr both as one and the ii»me thing, was becaufe they did not make thera 
 to. be the fame eflences as fenfibles. Particulars, therefore, vshich are in 
 fenfibles, they confidered as having a flowing fubfiftence, and that none of 
 them had any permanent efience ; but that there was univerfal Icldes thefe, 
 and that it was different from them. But this, as we have before obferved, 
 excited Socrates through definitions, yet he did not abflradt from panlculars'; 
 and by thus not abftrading he conceived rightly. The truth of this, Indeed, 
 is evident from operations : for without univerfals fcience cannot be attained. 
 13ut to feparate them from fenfibles is the caiife of the difficulties which take 
 place refpecling ideas. But others*, as if it were neceflary tliat, if there are 
 certain elfences befides fenfible and flowing natures, they fhould have a 
 feparate fubfillence, not having any others, introduced thefe which are called 
 univerfals. Hence it happens that univerfals and particulars f are nearly 
 the fame natures. This, therefore, will itfelf be a certain eflential diflaculty, 
 with which the above-mentioned particulars are attended. 
 
 CHAP. X. 
 
 But, as we obferved J in the doubts which we enumerated before, that 
 both the allertions of thole who contend that there are ideas, and of thofe 
 
 who 
 
 in the facred and alt-fplendid receflcs of intellect, and has dominion over all things. Of the 
 obje£tions wliich have be;n made to thefe divine dognjas, both by aitients and moderns, fome 
 arc thofe of men inteile£lually blind, and others are eafily confuted. 
 
 * Though the Platonilts were mofl rich in names, yet, becaufe the progrefTion of beings 
 pofTefles images of firfl natures, in tlie lafl orders of tilings, they principally accommodated 
 thefe names to -divine natures, but fecondarily and with diminution to fenfibles. 
 
 t A fenfible nature docs not become the fame with thofe intelligibles of which it pofTefles 
 the images ; for an effective and paradigmatic caufe is very different from that which is per- 
 fected by, and according to, it. But, if laff natures are aflimilated to fuch as are middle and 
 firft, what abfurdity will there be in ufing the fame names in all thefe ? For Ariflotle himfelf 
 in the twelfth book of this work calls tlie fnfl god an animal, as v.e]l as that which is fenfible 
 and painted. 
 
 \. If it be requifite, fays Syrianus, tliat, attending to the meaning of the pliilofopher, we 
 fliould defpife verbal ambiguity, he appears to me to reject the deftru£lion of feparate elTences, 
 led .'t the fame time he fliould fubvert the exiflence of a fenfible efience, and this very pru- 
 dently and confiftently with himfelf. For, in his Phyfics, he fnows that unlefs there is fome- 
 thing which pofTefTes infinite power, there will be nothing endued witli finite power. Again : 
 It will be poffible (fays he) that a fep;ifate effence fhould appear to Ariftctle to be infinite, 
 
 becaufe,
 
 Book Xiri. ARISTOTLE'S METAPHYSICS. S^ 
 
 who contend that there are nor, are attended with a certain doubf, we muft 
 now alfo repeat the fame obfervation. For he who does not admit 
 
 THAT THERE ARE SEPARATE ESSENCES, AND THAT PARTICULARS 
 ARE AS IT W£R£ AFTER THIS MANNER THE SUBJECT OF DISCOURSE, 
 
 SUBVERTSj. 
 
 becaufc, if any one fuppofes the principles of it to be individuals, he mud al]ert that there are 
 as many principles as beings : for he will behold them as elements, and will not leave any 
 fcience of them; fince there is no faience of particulars, as dcmonJlrations and definitions 
 evince. But if the principles of a feparate eilence are univetfals, it is not reafonable that thefe 
 principles (hould be unfubftantial, while individuals have a real fubfiiLcrice. He adds : But let 
 univerfal appear to Ariftotle to be unfubftantial, we again fay, that the principles of ideas are 
 neither individuals, nor unlverfals of fuch a kind as the forms which are in foul, or in nature,. 
 or in fenfibles, or as refemblances of pofterior origin, which laft among unlverfals may be juftly 
 confidered as unfubft.mtial ; but they are prior to all thefe, fubfilling as the caufes of wholes, 
 and being entirely exempt from the nature of their efteiSts : for neither are other ideas, which 
 proceed from thefe, individuals, or unlverfals. Indeed, as that which is individual is material^ 
 but univerfal is in foul, fo that which is entirely impartible is intelleclual. 
 
 But in anfwer to what ATiftotle fays, that as the elements of fpeech make infinite words, 
 though they are infeparable from fpeech, in like manner the principles of beings operate, fince 
 they are infeparable from the fenfible elTence of individuals, we may reply, tliat in the firfb 
 place, the Pythagoreans did not introduce a monad and duad of this kind ; and, in the next 
 place, as our intelle<5l and phantafy tranfmute the elements of fpeech, and produce dlftereiit 
 words by a certaiti tranfpofitioii, we may allc what that nature is in the univerfe which tranf- 
 pofes the elements, and preferves an eternal generation of things } For, if It is fomething 
 worfe than IntelleiSl:, we muft be careful that we do not, on this hypothefis, make parts more 
 excellent than wholes, accidents than eflences, things mortal than things divine, and. things 
 which alwap energife after the fame manner with perfecSl: re£litude, than thofe which arc- 
 rarely right in their energies;, if we afTert indeed, that our aftlons are the progeny of intelle6t, 
 but that natures which rank as wholes are not governed by reafon. But if fome inteiledt 
 tranfpofes thefe, is it intelle£l in capacity, or in energy, or is it that which is both ? It is mani- 
 feft, indeed, that if it operates eflentially, or from its very eiTince, it both poflefles in itfelf the 
 caufe of its produdions, and gives fubfillence to images of itfelf; for of this kind are all 
 things which energife cfientially. But if It energifes from free-will and tranfitive intelledlion,. 
 (wfoaipt^ii xai litraSaTMtt voMti] we may aflc what are the orderly difpofed and bounded, natures. 
 in its efl'ence, which it looks to in Its energies ? Tor it cannot be fuppofed in its produftions 
 to energife with aftonilhmenr, (eHTtXnKTmui) or inconftantly, as we do in our operations ; but, 
 according to either mode, it will contain in itfelf the ideas of its produclions i for neither 
 would it be poflible for us from four-anci-twenty terminated elements of fpeech to produce 
 infinite words, unlefs we alfo contained ia ourfelvcs die idea of each of them, and principles 
 productive of the compofition of them all. For why have irrational animals fhorter words 
 enunciative of their peculiar pafiions ? But man, employing infinite permutations, never ceafes 
 from compofing the fcvera! letters. 
 
 Again,: If Ariftotle is ferious in faying that Ccience is of. unlverfals in capacity,, but of 
 
 3 A. a particulars.
 
 364 ARISTOTLE'S METAPHYSICS. Book XIII. 
 
 -SUBVERTS,AS' WE WILLINGLY ALLOW, ESSENCE ITSELF. But yet, if any- 
 one admits that there are fcparate eflences, how will he eflabllfh the elements 
 and principles of them ? For if thefe are particulars, and not univerfals, 
 there will be as many beings as there are elements, and the elements will not 
 be the objeds of fcicntitic knowledge ; for, let the fylhbles in a word be 
 tflences, but the elements of them the elements of cffences : but it is necef- 
 fary that ba and each of the fyllables fhould be one, if not univerfally indeed, 
 and the lame in fpecies, yet each mull be one in number, and this particular 
 tiling, and not homonymous. Further ilill : each one is confidered by them 
 as the very thing itfelf: but if fyllables, fo likewife the things from which 
 they are cempofed. There will not, therefore, be more than one letter a ; and 
 for the fame reafon, each of the other elements will onlv be one, as neither of 
 the other fyllabl'es will the fame lyllable be in dllierent words. But, indeed, 
 if this be the cafe, there will be no other beings than elements, but things wilt 
 be elements alone. Again : elements will not be the objedls of fcientific 
 knowledge; for they are not univerfals, but the objeds of fcience are univer- 
 fals. But this is evident from demonftrations and definitions : for the fyllo- 
 gilm will not be, that this particular triangle has angles equal to two right, un- 
 
 Icfs 
 
 partlculiri in energy, he fubverts what he has faid in his Lafl Analytics, that it is not pof- 
 iible tl ere can be fciences of particulars, and much lefs can there be the more excellent and 
 perfe£l fcience of univerfals. And, as it feems, the firil mode of the firft figure, which con- 
 cludes from two unlverfal aihrmatives, and which he fays poflcfles the greatefl demonftrative 
 power, will not produce a perfect conclufion, nor that which produces fcience in energy ; but 
 thofe fyllogifms will be more perfe<S which conclude from a univerfal and particular affirmative 
 efpecially if the minor propofition is of particulars. Ihat fenfe, therefore, is principally em- 
 ployed in<.!ced about tliat which is individu;!, but accidentally about that which is common in 
 the individual, n.ay be granted; but it is falfe, that grammar on this account is principally con^ 
 vcrfant with this particular a, but from accident about a which is common. For arts are more 
 converfant with univerfals than particulars; fince they produce and judge of particulars, in 
 confequence of poflefling the caufcs of ihat which is common. For a phyfician knows ho-.v to heal 
 man, ajid not Callias ; but when he energifes together with matter, he heals an individual, be- 
 caufe he previouily comprehended in hiraftlf the univerf^jl producing principles of licalth. 
 The grammarian alfo knows the power of the letter a, when it is attenuated and afpirated, and 
 when it is (hortened and lengthened, when it is taken feparately, and when it is compofed with 
 others; prepofitively indeed in vowels, but fobjunitively {hTro-ra.KTixaC] in confonants. But wlien 
 he is willing to pronounce it, or to judge of the pronunciation of another perfon, then he ener- 
 gifes about the individual, bccaufe he has previouily received the proilucing principles of uni- 
 verfal itfelf. 
 
 What has been now faid of the arts, which differ in tliis from experiments, that tJiey know 
 
 the
 
 UookXIIL AR ISTOTLE'S METAP H YSIC S. 365 
 
 Icfs the fame conclufion is true of every triangle ; nor that this man is an 
 anim=i!, unlefs every man is an animal. But yet, if principles are univcrfais, 
 or if the eflences which fubfill from thcfe are univciials, non-cfTcnce will be 
 prior to elfence : for univerfal is not eflcnce ; but element and principle are 
 univerfals. But element and principle are prior to the things of which they 
 are the element and principle. All thefe confequences, therefore, rationally 
 happen, both when they make ideas from elements, and when, befides ideas 
 and eflences which have the fame form, they think fit that there fiiould be a 
 certain one which has a feparate fubfiflcnce. If nothing, however, hinders, 
 but that, as in the elements of f;)eech, there is a multitude of the letter «, and 
 a multitude of the letter b, and a itfelf and b itftlf are nothing befides the 
 multitude of thefe, on this account there will be infinite fimilar fyllables. But 
 that all fclence is of univerfals, fo that it is neceffary the principles of things 
 iliould be univerfals, and fhould not be feparate effcnces, this is attended with 
 a greater doubt than any thing which has yet been faid. In a certain refpedl, 
 however, that which is now aflerted is true, and in another refpe£t it is not true : 
 for fciencc as alio fcientific knowledge is twofold ; of which one is capacity, 
 but the other energy. Capacity, therefore, being as it were the matter of that 
 
 tlie caufes of their operations, in the highcfl degree accords with Ariftotle himfelf, who mani- 
 fi.ft.ly proclaims in his books on Rhetoric, that no art confiders that which is particular. " Thus, 
 (fays he) medicine does not coniiderwhat isfalubrious to Socrates or Callias, but what is fo to 
 this Or that perfon, or to thefe ; for this is the province of art." " But that which is particular 
 (fays he) is infinite, and is not the obje£l of fcientific knowledge." But when we afcend to 
 thofe fciences which have no conne6\ion with any tiling ftnfible, but are alone converfant with 
 impartible and imn.aterial forms, how is it pofhble to conclude rcfpe£ling thefe, that tliey are not 
 princij>ally em|<loyed about univcrfalf, but about individuals ? 
 
 Nor niuft what Ariftotle fays in the end be admitted fimply, and without addition. "For if 
 (fays he) principles are univerfals, tliofe tilings which fubfift from tl.eni will alfo be univerfals, 
 as in dcmoiiftrations." But it may be faid, that in demonftrations the material principles are the 
 propofitions which produce the conclufion not abiding in thcmlelves, but giving thcmfelves 
 up lo the fabrication of the thing propofed to be demonftratcd. In eft'eclive principles, however, 
 it is not neccHary that the things which are generated Ihould be co-extended w.th their caufes. 
 Unlefs, perhaps, we are willing to fay that tliofe univerfals which proximately proceed from uni- 
 verfal principles themfclves, and which are effentially contained in foul, are principally genera- 
 tive of the reafons of nature; but, proceeding through the reafons of nature to matter, are pro- 
 dijclive of individuals. Thus, univcifal propofitions principally conclude, that the angles of 
 every triangle are equal to two right ; but propofitions lefs univerfal conclude this equality of 
 angles to two right, of fonie particular fpccies of triangle : and thofe iliil Icfs univerfal conclude 
 this of feme individual tri.uijjle in a diniiuifljed and ultimate degree. 
 
 whith.
 
 366" ARISTOTLE'S METAPHYSICS. Eook XHl'. 
 
 wliicfi IS unlverfal and indefinite, is the capacity of the univerfal and indefi- 
 nite ; but energy being definite has alfo a definite obje£t, being foinething par- 
 ticular of fomething particular. But fight perceives accidentally univerfal 
 colour ; and the grammarian fpeculates this particular a. Since, if it is necef- 
 fary that the principles fhould be univerfals, it is alfo necefiary that the things 
 which fubfifl; from them fhould be univerfals, as is evinced in demonflrations. 
 But if this be the cafe, nothing will have a fcparatc fubfiffence, nor even effence 
 itfelf. It is evident, however, that fcience is in a certain refpedl of that which 
 is univerfal, and in a certain refped not. 
 
 ARISTOTLE'S
 
 ARISTOTLE'S METAPHYSICS, 
 
 BOOK XIV. 
 
 C H A P. I. 
 
 xxND thus much, therefore, refpeding this effence. But, as we obferved 
 in our Phyfics, that all philofophers make principles to be contraries, the 
 like is alfo true concerning immoveable* eflences. However, if it is not 
 poffible that any thing can be prior to the principle of all things, it will be 
 
 impoflible 
 
 " Ariftotle in what he now fays apparently oppofes thofe who make the principles of things 
 immoveable to be contraries, jufl as he does not think it improper to aflume for the principles 
 of fenfibles, contraries, together with their fubjed. But he thus fyllogizes after his ufual 
 manner : Contraries are in a fabjeft ; principles are not in a fubjedl, left there ihould not be 
 elTence prior to a fubjeft ; contraries, therefore, are not principles. To which it may be re- 
 plied, that the Pythagoraeans did not affume in principles contraries which are not effential, 
 as being fubordinate to efTence, but as being more excellent than efTence. For it is requifite 
 that the principles of eflences (hould be fupereflential ; fince if the great principle of all tilings 
 is fupereflential, as Plato demonftratcs him to be, in his Parmenides, and the fixth book of his 
 Republic, it is, neceflTury that his immediate progeny fliould be fupereflential alfo in a fecon- 
 dary degree. But, in fliort, neither did the Pythagorseans begin from as it were oppofites. 
 And that they knew (fays Syrianus) that principle which is beyond the two elements the 
 monad and indefinite duad, is teftified by Philolaus, wlio fay?, " that God gave fubfiftence to 
 hound and infinity" which two, as we have often obferved, are the fame as the monad and in- 
 definite duad. Syrianus adds, that tliis great principle, which Is prior to bound and infinity, 
 and is abftradled from all things, was called by ArchiBnetus a caufe prior to caufe ; but by 
 
 Philolausj
 
 ■368 ARISTOTLE'S METAPHYSICS. Book XIV. 
 
 impoflible that the principle being any thing elfe fhould be the principle of 
 all. Juft as if any one fhould fay that a thing white is the principle, not Co 
 far as it is fomething elfe, but fo far as it is white, which yet according to its 
 fuhjeifl is white, and at the fame time fomething elfe: for that will be prifT. 
 But, indeed, all things are generated from contraries as from a certain fubjedl. 
 It is therefore cfpecially neceifary that this ftould take place in contraries. 
 Hence, all contraries pertain to a fubjedl, and none of them has a feparate 
 fubfiflence. But, as it appears, nothing is contrary to effence ; and reafoa 
 teftifies the truth of this affertion. No one, therefore, of contraries is pro- 
 perly the principle of all things, but fomething different from thefe. Bur 
 according to fome, the other of contraries is matter *. According to others, 
 the unequal Is contrary to ibe one, that is to ibe equal, as if this were the 
 nature of multitude. And again : according to otherSj multitude is contrary 
 to the one : for numbers are generated by fome from the unequal duad, viz. 
 the great and the fmall, but by a certain perfon j" from multitude ; by both, 
 however, from the fubftance of (be one : for he X who calls the unequal 
 
 and 
 
 Philolaus, the principle of all things ; and by Brotinus, that which tranfcends every intellcfl 
 and eflence both in power and antiquity (wj vou ttcvtcs km wo-iaj ^uva/xti Kcti crf£tr?£ia uTtifix^')'- 
 Hence the divine Plato fpeaks to the fame effe£l in his Epiflles, in bis Republic, and in his- 
 Philebus and Parmenides. Arillotle, therefore, in what he now fays cannot be ferious, fince 
 the propofuions are not found: for principles if they are contraries are not in a fubjc^; 
 fupernal natures are by no means unfubftantial ; nor are principles eflences. For principle?' 
 properly fo called, and which are the principles of all things, are fupereffential. Nor does his- 
 conclufion confute any dogma of the Pythagorseans : for, as we have before obferved, they did 
 not begin from things which are as it were oppofites, but they placed at the fummit of things 
 the one, which they confidered as tranfcending both principles and elements. 
 
 • Neither, fays Syrianus, do the Pythagorxans call the duad which is prior to all numbers 
 a material caufe; for divine numbers are not indigent of matter; nor does Plato, when he 
 demonftrates the indefinite duad through inequali/y, differ from Pythagoras, who demonftrates 
 the fame through multitude. For each endeavours to denominate it from thofe things which, 
 through it, are inherent in numbers. But it has been already obferved, that this duad is ths 
 caufe of multitude, and progrefhon, prolific power, and diverfity ; in the fame manner as tha 
 monad is the caufe to divine forms of identity, and eterr.al permanency : for eternity, fayj 
 Plato, abides in one j by the appellation of otie fignifying the monad of the Pythagora:ans, whicj* 
 is the caufe of eternal permanency in the fame things, and after the fame manner. 
 
 t Viz. Pythagoras. 
 
 X Plato, fays he, ought to aflert that thefe are two in definition, but one in number: fO 
 Syrianus obfcrves that it is better thus to explain tlie meauing of Ariftotle,, than as it is ex- 
 
 glaineil^
 
 BookXIV. ARI STOTLE'S META PH YS IC S. 369 
 
 and the one elements, but the unequal from the fmall and the great the duad, 
 fpeaks of the unequal, the great and the fmall, as if they were one, nor does 
 he clearly aflerc that they are fo in definition, but not in number. Nor yet 
 do they well explain the principles which they call elements*. For fome, 
 introducing the great and the fmall together with the one, aflert that thefe 
 three are the elements of numbers ; the two firft indeed, having the relation 
 of matter, but the o?ie of form. But according to others, the much and the 
 few are elements, becaufe the great and the fmall are naturally more allied to 
 magnitude. According to others, again, the elements are things more uni- 
 verfal in thefe, viz. the furpafhng and the furpaffed. But no one of them 
 differs, as 1 may fay, with refpedl to certain things which take place, but 
 only with refpedl to logical difEcultles which they defend, becaufe they alfo 
 introduce logical demonftrations. Indeed an inftance of this may be feen in 
 their aflertion, that principles are the furpafling and the furpalfed, but not 
 the great and the fmall, and that of the elements, number is prior to the 
 duad : for both are more univerfal. But now they aflert the one, and not the 
 other. Others again, oppofe to the one that which is different and another. 
 But others introduce as principles, multitude and the one. But if beings are 
 from contrarievS-f-, as they are willing they fliould be, but to the one either 
 
 nothing 
 
 plained by Alexander. However, Plato did not call the other of the principles, the unequal 
 and the duai", the great and the fmall, in the fenfe adopted by Arifbtle, conformably to his 
 concealed mode of writing. But, as we have often obferved, this principle according to Plato 
 is the caiife of multitude and progrelfion, and generates every thing great and fmall. And, in 
 Ihort, if this principle by an inclTable tranfcendency is feparated from the great and the fmall 
 proceeding from it, and is better than every fubjeft:, (for fuch is the truth of the cafe,) what 
 place can there be for fuch afTertions as the prefent ? 
 
 * All thefe, fays Syrianus, according to the opinion of Ariftotle, call the more divine and 
 paternal principle of numbers, the monad ; but the maternal is called by fome, as by Plato, the 
 great and the fmall ; by others, correflively (tOTJisfflou^fi'a);), the much and the few; by others 
 again, recurring to that which is more general, the exceetUng and excefs ;■ by others diflerence ; 
 and by others multirude. But we have already fliown that all thefe appellations iignify the 
 fame thing. And, in anfwer to what he fays againft the patrons of ideas 'jiev Ei^'iKiiTEfii), that 
 they make nun^ber prior to the duad, we reply, that if l.e means the indefinite duad, or, as we 
 have often obferved, the fccond of thofe two great principles after the ineffable caufe of all, 
 it is impolTible that number can be the genus of it, becaufe number is its ofFipring ; but, if he 
 means the duad itfelf, this ranks as the firft among ideal numbers, 
 
 f Nothing can more plainly evince that Ariflotle is not ferious in what he now aflerts than ' 
 this, that he contradicts w hat he has faid in the tenth book of this work ; for he there clearly 
 
 3 B aflerts
 
 870 ARISTOTLE'S METAPHYSICS. Book XIV, 
 
 nothing is contrary, or, if there be, it is multitude ; but the unequal is con- 
 trary to the equal, difference to famenefs, and that which is another ro that 
 which is the fame, — if this be the cafe, thofe who oppofe the one to multi- 
 tude, have fomething to urge in defence of their opinion : yet neither is 
 their hypothefis fufKcient : for the one will be few ; fince multitude is oppofed 
 to paucity, and the much to the few. But, with refpeit to the one, it is 
 evident that it fignifies meafure *. And in every thing there is a certain 
 other thing which ranks as afubjedt; as for inftance, in harmony, diefis j 
 but in magnitude, a finger, or foot, or fomething of this kind ; but in rhythms^ 
 the bafis, or a fyllable. In like manner, in weight, there is a certain definite 
 
 aflerts that the few is not contrary to every multitude, but to that which tranfcends •, and that 
 the one is not contrary to niultitmie and number, but is rather relativdy oppofed. So that,, 
 according to his own opinion, both the propofitions are falfe, through which he colledts the 
 conclufion of his confutation ; viz. both that which fays that the one is contrary to multitude, 
 and that which confiders every contrary to multitude to be the few. To which we may add, 
 that his objeaions are not direded againft the one which the Pythagoreans eftablifh, nor does^ 
 he confider multitude conformably to their dodlrine. 
 
 * " As thofe divine men, (the Pythagoraeans) fays Syrianus, called God the one, as the caufc 
 of union to wholes, and as beyond every being, all life, and all-perfed inteUefl ; and, befides 
 this, denominated him the meafure of all things, as illuminating eflence and end to all things, 
 and as comprehending and bounding all things by his ineffable tranCcendencies (viripoxMi), and 
 which are expanded above all bound f, this demoniacal man, dire£ling his attention to that 
 one which is the leaft in quantity, and on account of its parvitude is the common nieafure of 
 all things of the fame kind, affirms that there is neither any meafure, nor one, which does not 
 fubfilt in a fubje£l. Hence, his difcourfe falling from the one principle of beings, or the unity 
 immediately conne£ted with it, as from a certain divine foundation, fubverts the whole difcuf- 
 fion of incorporeal natures. It is worth while therefore, fays he, to compare with the afler- 
 tions of Ariftotle, what is faid by Clinias the Pythagorsean, who affirms that the one is per- 
 fe<flly exempt not only from bodies and mundane natures, but from intelligibles themfelves » 
 and who, venerating the principle of beings, fays that he is the meafure of intelligibles, that 
 he is unbegotten, eternal and alone, that he is the fovereign ruler, and that himfelf unfolds 
 himfelf into light. To this we may add the words of the divine Plato in his Laws, in which 
 he calls God the meafure of all things, as comprehending in himfelf the beginning, middle, 
 and end of all beings." 
 
 But, that Ariftotle was of the fame opinion in this refpe^l, with thofe who philofophifed 
 before him, is evident from the fecond book of his Politics ; for he there openly fays, " that 
 ihe good is the moft certain meafure of all things." So that it is evident, as Syrianus well ob- 
 ferves, that his arguments are rather logical than ferious. 
 
 'f T«v tittm »\i(m IV /uir \iymm tov &eov i>; ivarixc tut oXnc mticv, mi Trairo; tw amt, cat van; {ante, )U> Mu tsu vavrtXwf 
 MTIKtirct* /AiTpevTi Tefj watri0v, if Tratri t»v ouo-tait, Hai to tiXoc imXa/AirovTa, km v; nravTA mfi$X9VTa Xfti cft^ovTa ratf a«f»facrTflic 
 muTW, «at ?ravTC^ itTri^nirhmiAhati frig«T«» ^Vlfox"*^* ^ i^i^orifif cvTDf; K. T, Kt 
 
 meafure,
 
 Book XIV. A R I S T O T L E'S M E T A P H Y S I C S. »7l 
 
 meafure, and fo in all things, ,-^hus, too, in qualities, there is a certain defi- 
 nite quality, and in quantities a certain indlvilible quantum : for, with refpect 
 to meafure, one kind is according to form, but another according to fenfe ; 
 fo that there is not any eflence which is eilentially one. And this rationally: 
 for the one fignifies that it is the meafure of a certain multitude; and num- 
 ber, that it is multitude meafured, and a multitude of meafures. Hence, it 
 may be realbnably inferred that the ofie is not number : for neither is a mea- 
 fure meafures, but a prmciple, and the meafure, and the 072e. But it is requi- 
 fite that a meafure fhould always fubfift the fame in all things; as, for in- 
 fl:ance, if a horfe is the meafure in horfes, and if a man in men. But if man, 
 horfe, god, and animal are meafures, perhaps the number of them will be 
 animals ; but if man, white, and walking, there will by no means be a num- 
 ber of thefe, becaufe all of them fubfift in one and the fame according to 
 number. At the fame time, however, there will be a number of their genera, 
 or of fomething elfe which has a fimilar appellation. But thofe who make 
 the unequal * as one certain thing, but the indefinite duad from the great and 
 
 the 
 
 * 'The one and the equal, which are aflumed in the more paternal principle, neither fubfift as 
 relatives, nor as accidents, but arc fupereflential natures, the caufes of union and equality to all 
 things, and imparting by their illuminations permanency, (lability, unchangeablenefs and purity 
 to all things; in the fame manner as the unequal itfelf, (which. Ariflotle fometimes divides into 
 the great and the fmall, fometimes into the much and the few, and fometimes into the exceeding 
 and excefs), when it is confidered as fubfifting in the firft duad, fymbolically exhibits that caufe 
 which is the fource of increafc to wholes, and which is not only better than accidents, but than 
 the effences which are generated from it. 
 
 But neither mull we diilribute a fecond or multifarious place in principles, or afcribe accident 
 to divine ideas : for, according to the doftrine of the Pythagorxans, nothing is accidental to 
 divine ideas: but there equality itfelf and fcience itfelf fubfift. Samenefs, therefore, fimilitude, 
 and difference are eflenccs, fubfift from themfelves, and do not depend on others for their fub- 
 fiftence. This Plato alTerts in many places, bat particularly in the Phaedrus, when he fays, 
 fpeaking of the foul in a ftate of fupreme felicity, " That it hAoXAs jiijj ice itjelf^ temperance itfilf, 
 and fcitfice itjelf; not that with which generation is prefent, nor which is different from fubfilt- 
 ing in that which is different, fuch as are the things which we now denominate beings, but that 
 which is fcience from its refiding in true being." 
 
 Hence it is ufual with Plato to charaaerife i<lea by the epithets auTo uaff auro, Itfelf /•^ itfelf \ 
 by the former of thel> fignifying its fimplicity, and by the latter its immaculate purity. If 
 caufe, therefore, fubfifts among ideas, but that which is caufed here, it does not fubfift there ac- 
 cidentally, but effentially ; and the fame thing, in Hiort, muft be faid reipeaing all habitudes. 
 Hence feme things there are fupereffential, but others cffential ; and accident fubfifts about the 
 foul in generation (». e. the fublunary region), and generation itfelf. And thus much in reply 
 
 3 B 2 to
 
 872 ARISTOTLE'S METAPHYSICS. Book XIV^ 
 
 the fmall, fpeak very far from the truHi of trrr-^gs apparent and poffible ; for 
 thcfe are rather paffions and accidents, than things fubjed to numbers and 
 magnitudes. For the much and the few, the odd and the even, are the paf- 
 fions of number ; and the great and the fmall, the fmooth and the rough, the 
 rtraight and the curved, are the paflions of magnitude. 
 
 Further ftill : in addition to this error, it is alfo neceffary that the great and 
 the fmali, and things of this kind fhould be relatives. But of all the cate- 
 gories, relation is in the leaft degree a certain nature or eflence, is pofterior 
 both to quality and quantity, and, as we have faid, is a certain paflion o€ 
 quantity, but is not matter, or any thing elfe ; and, in fhort, is fomething com- 
 mon both to the parts and fpecies of quantity. For there is nothing, either 
 great or fmall, or much or few, or, in Ihort, which fubfifts as a relative, which 
 is not much or few, great or fmall, or a relative, at the fame time that it is 
 fomething elfe. But that relation is in the fmalleft degree a certain efTence, 
 and being is apparent from hence, that of it alone there is neither generation^ 
 nor corruption, nor motion, as with refped: to quantity there is increafe and 
 diminution, with refped; to quality alteration, with refpedt to place local mo- 
 tion, and with refpedt to eflence, fimply generation and corruption ; but this is- 
 not the cafe with refpe£t to relation : for, without being moved, at one time it 
 ■will be greater, and at another time leifer or equal, the other being moved 
 according to quantity. It is alfo neceflary that the matter of every thing 
 ihould be fuch as the thing itfelf is in capacity ; fo that this will alfo be the 
 cafe with the matter of eflence : but relation neither in capacity nor in 
 energy is eflence. It is abfurd, therefore, or rather impofllble, to make non- 
 eflTence to be the element of, and prior to, efl"ence : for all the categories are 
 pofl;erior. Again : elements are not predicated of thofe things of which 
 they are the elements : but the much and the few are predicated both fepa- 
 rately and together of number, and the long and the fhort of a line, and a 
 fuperficies is both broad and narrow. But if there be a certain multitude to 
 which the few always belongs, it will be, for inflance, the duad ; (for, if this 
 be much, tbe one will be few,) and if it be much fimply, it will be much after 
 the manner of the dccad ; and if this be not the cafe, it will be more than 
 ten thoufand. How, therefore, will number confifl; from the few and the 
 
 to the whole reafoning of Ariftotle -, but to fay that the feiu itfelf is the caufe of the Juacl which 
 is there, or the much of the dccad, docs not by any means fubvert any part of the doflrine of 
 the Pythagorseans. 
 
 much ?
 
 Book XIV. ARISTOTLE'S METAPHYSICS. 373 
 
 much ? For, e'uher it is necefTary that both fliould be predicated, or neither ; 
 but now one of thefe alone is predicated. 
 
 CHAP. 11. 
 
 But it Is requlfite fimply to confider whether it is poffible for things eter- 
 nal * to be compofed from the elements: for they will have matter, fince 
 every thing confifting from elements is a conipofite. If, therefore, it is necef- 
 fary that a thing fliould be generated from that from wliich it confiQs (both 
 if It always is, and if it is generated), but every thing is generated from that 
 •which is in capacity the thing generated (for it could not have been generated 
 from the impoirible, and it was not before It was generated ), but that which 
 is pofTible may energife, and may not energife ; if this be the cafe, number 
 alfo, ahhough it molt eminently always is, or any thing elfe which poflefles 
 matter, may happen not ta be, juft as that which poffelTes the fpace of one 
 day, and that which has any number of years whatever. But if this be the 
 cafe, it will be true alfo of time, when it is fo extended as to be without 
 bound. There will not, therefore, be things eternal, fmce that Is not eternal 
 ■which it is poflible may not be, as we have elfewhere fliown f . But if that 
 which is now faid is univerfally true, that no one efTence is eternal, unlefs it 
 be in energy, and elements are the matter of eflence, there will not be ele- 
 ments of any eternal efTence, from which being inherent fuch effence is com- 
 pofed. But there are fome | who make the indefinite duad together with. 
 
 * The moft antient and the beft of the philofophers, fays Syrianus, aflert that divine ideas 
 snd forms do not fubfifl: from material elements, or altogether from elements which are fo 
 called, from being affumed in the conllitution of fomething elfe. For that which confifts from, 
 material elements may be generated and corrupted ; but that which confills from immaterial 
 elements, though it may be without generation, is neverthelefs a compofite. It is, however, 
 necefi'ary that divine forms fliould be fimple and without generation, and that they fhould nei- 
 ther be arranged as foul, nor, for a much flronger reafon, have a compofite effence like the fen- 
 fible univerfe. In fliort, it fliould ever be remembered, as Syrianus well obferves, that the 
 antients called the generative cnufes of all things elements. 
 
 f Viz. In the books De Coelo. 
 
 J The antients, fays Syrianus, not fearing the admirable reafonings of logicians, nor rejefting 
 this kind of equal, were willing to call the caufe of multitude the duad ; but becaufe they were 
 alfo willing to fhoiv its alliance with the more excellent principle, as they thought proper to call 
 that the eqii.il^ they denominated this the unequal. But denominating that the monad, they called 
 this the duad, for reafons which we have repeatedly mentioned. 
 
 the
 
 S74 ARISTOTLE'S METAPHYSICS. Boor XIV. 
 
 the one, the element, but are very properly unwilling to admit the unequal, 
 on account of tlie impcffibilities which take place ; from whom, fuch of the 
 difficulties only are taken away, as muft neceiTarily happen to thofe who 
 make the unequal and relation to be the elements of things. But fuch diffi- 
 culties as take place feparale from this opinion, muft alfo neceflarily happen to 
 thefe, whether they produce from them ideal or mathematical number. There 
 are, therefore, many fources of error with refpe<fl; to thefe caufes ; but the 
 opinion of the antients is efpecially the occafion of doubt : for it appeared 
 to them that all things would be one, viz. being itfelf, uniefs fome one folves 
 the doubt, and at the fame time proceeds conformably to the reafoning of Par- 
 menides : for this cannot by any means be non-being ; but it is neceflary to 
 fhow that non-being is. For thus, from being and fomething elfe, things will 
 fubfift, if they are many ; though, indeed, this will be true in the firft place, 
 if being is manifold* : for this fignifies that a thing is effence, that its pofleffion 
 of quality, this again that it is endued with quantity, and fo of the other cate- 
 gories. What kind of one, therefore, will all things be, if non-being is not? 
 Whether will they be eflences, or paffions ; and in a fimilar manner other 
 things ? Or will they be all things ? And the one will be this thing, and fuch- 
 like, and fo much, and fuch other particulars as fignify one certain thing. But 
 it is abfurd, or rather impoffible, that one certain nature fliould be a generated 
 caufe, and that of this being, and of the fame being, fomething fhould be 
 
 * Without difference there will neither be ten genera of being, nor two, nor any thing elfe 
 except one thing in number. But fince there is difFerence there is alfo non-being: for each of 
 the ten genera of being, if it is different from the reft, is more non-being than being, even 
 though you fliould fpeak of fubftance itfelf. For, fince it is fublUnce, it is neither quantity, nor 
 quality, nor a£l:ion, nor paflion. By compofuion, therefore, we fliall perceive the force of the 
 dogma: if there are ma?iy beings there is difference; if there is difference there is non-being; 
 if there are many beings there is non-being. There is no other way, therefore, of underltand- 
 ing the Parmenidean reafoning, nor can the fubfiftence of multitude hi. admitted on any other 
 hypothefis than that of introducing at the fame time non-being. Nor on this account does 
 Plato oppofe Parmenides in that which is moft true ; but the affertions of both are indeed true, 
 tliough that of Plato is more apparent. For Parmenides, alone difcourfing about that which is 
 intelligible, and confidering its union, and the identity and Empedoclean friendfliip which pre- 
 dominates in its fplendid effence, proclaimed being to be one ; but Plato, knowing that a fenfible 
 nature alfo in a certain refpe£t had a being, knew alfo that it is differciU from true being, and 
 on this account ought rather .to be called non-beipg than being. But that which is intelligible 
 is notlefs multitude than one, and introduces to beings the nature of difference. In conformity, 
 therefore, to this doclrine, Plato demonftrates non-being to be effential ; as is proved in the 
 Sojphifta by many arguments highly worthy of belief. 
 
 thi|
 
 BooxXIV. ARISTOTLE'S METAPHYSICS. 375 
 
 this particular thing, fomething elfe fliould be endued with quality, this belong 
 to quantity, and that to lituation. In the next place *, from what kind of 
 non-being and being do beings fubfift ? For non-entity is manifold, fince 
 this is alfo true of being. And, indeed, non-man fignifies that which is not 
 this particular thing ; but not Jlraight fignifies that which does not poffefs this 
 particular quality ; and not three cubits^ that which does not poffefs this parti- 
 cular quantity. Prom what kind, therefore, of being and non-being, does 
 the multitude of beings fubfift ? This opinion t» therefore, wiflies to aiTert 
 that which is falfe, and to call this nature non-being, from which, and being, 
 the multitude of beings fubfifts. Hence, it is alfo afferted that fomething 
 falfe ought to be fuppofed, in the fame manner as geometricians admit as an 
 
 * By no means as from form and privation ; for privation is of no advantage to beings ; but 
 becaufe, as there are five genera of beings according to the Pythagorseans and Plato, one of them 
 is difference. But the bufinefs of this genus is to make every thing that which otlier things arc 
 not ; and from the non-being which fubrfts according to difference, and from effence, beings are 
 many : for effence communicates being to all things, fince it is not, as it has appeared to fonie 
 to be, the fubjcct of things, but is the principle and fountain of being, which it imparts to all 
 things without any diminution of itfelf. But difference disjoins and midtiplies beings, not lo- 
 cally, but effentially, and eaufes other things not to be the fame with others, and particulars to 
 preferve the purity of their peculiarity, and an unmingled and immaculate fubfiftence. But if, 
 fpCiiking of beings in the ufual way, we denominate them fenfibles, and inquire from what 
 being and from what non-being thefe derive their fubfiftence, again thefe divine men will fpeak 
 of other genera of being, and will affign as the eaufes of thefe effence and difference r for their 
 energy and prolific power are extended to all things which are in any refpedt beings. But as 
 the loweft beings are fubfervient to many eaufes, and employ a more various compofition, they 
 derive being from form, but non-being from matter. 
 
 f As the I'ythagoraeans and Plato, fays Syrianus, afferted that the non-being which is from 
 difference fubfills in intelligibles, fenfibles, and that which is material, and as they called matter 
 not only non-being, but that which is falfe, becaufe it feems to be all things, but is fallacious, 
 and neither is, nor is becoming to be any thing belonging to beings; the admirable Ariftotle, in 
 the firft place interrogating them from what being and from what non-being they produce the 
 multitude of effences, fuppofes them to fpeak of that non-being which fnbllfts according to 
 matter. In the next place affuming from them that they called matter falfe, which ihey fubjecled 
 to form's, he fays that they produce beings from the falfe, fyllogizing after the following man- 
 ner : Beings are from ncn-being : the falfe is non-being : beings, therefore, are from the falfe. 
 Here it is evident that he alone confiders non-being according to its loweft fubfiftence, but 
 negle£ls to confider the whole extent of non-being according to thofc divine men, which diffufes 
 itfelf as far as to an incorporeal eP.ence, and omits to mention how the falfe was predicated by 
 them of matter. For they did not call matter falfe in the fame way as we are accuftomed to 
 call a difcourfe falfe, or an opinion falfe, whicli does not accord with things themfelves ; but it 
 was thus denominated by them through the above-mentioned caufe. 
 
 hypothefis.
 
 376 ARISTOTLE'S METAPHYSICS. Book. XIV. 
 
 hypothefu-, that a thing is pedal which is not pedal. It is not, however, 
 inipoffible, that this fhould be the cafe : for neither do geometricians fuppofe 
 any tiling falfe (llnce that is not the propofition in the demonftrative fyllo- 
 gifm\ nor are things generated or corrupted from that which is after this 
 manner non-being. But fince non-being, according to cafes (TrTaiani), is 
 equally predicated with the categories, and, befiJes this, that is called non- 
 being which fubfifts as the faJfe, and alfo that which fubfifts according to 
 capacity, from this generation takes place from that which is not man, but 
 man is produced from man in capacity ; and a thing white, from that which 
 is not white in energy, but in capacity. The like confequcnces enfue whe- 
 ther one thing is generated or many. But the inquiry feems to be, how 
 being, which is predicated according to effcnces, is many: for numbers, and 
 lengths, and bodies, are things which are generated. But it is al-furd to in- 
 quire how being, which is fome particular thing, is many, and not alfo to 
 inquire how it poffefTes quality or quantity. For neither is the indefinite 
 duad * the caufe, nor yet the great and the fmall, that two things are white, 
 or that there are many colours, or taftes, or figures : for thefe will be numbers 
 and monads. Indeed, if they had attended to thefe things f, they would 
 
 * The (Juad is indeed every where the caufe of multitude fo far as it produces things from 
 the one, with their proper differences. But fo far as it is a principle, there is alfo in the feveral 
 orders of beings a proper monad ; and .a duad connate to this is four.d, and which generates 
 a number accommodated to itfelf. But if thofe divin« men faid more refpefling eflences than 
 accidents, and of intelligibles than fenfibles, it is by no means wonderful: for almoft the whole 
 of their attention appears to have been dirttfjd to that which is /// /// own nature manifeft and 
 known, which has a perpetual fanienefs of fubuftence and an intelligible eflence ; but they 
 rarely declined to the ibadows and ultimate boundaries of being. 
 
 f They confidered accidents, indee<l, (fays Syrianus) and faw that the fame princi]-'es had an 
 analogous fubiifteuce in thefe ; and that they had their proper monad and duad; the former 
 being the caufe of identity to them, and ihe latter of difference and multitude. Nor was it 
 through departing from [hara •na^exiairiv) the true caufe, nor from any other degeneration that 
 they alibciated the biformed caufe with t/:e me. But the princi(.de adduced by Ariftotle, and 
 which is predicated by negation, is material : for non-man is the matter of man. Thof; 
 divine men, however, (Syrianus adds) knew that this principle is ntcell'iry in the lait of things ; 
 but they did noi call it a caufe, but a concaufe : and in natural reafons, or produiSlive femina! 
 principles, they placed effeftive caufes. 1 hcie is, therefore, in nature one produftive principle 
 gcneriitive of all colours, and another whici) is indeed primarily perfeiled from tliis, but which 
 produces together with it the multitude and diverfity of colours : and thefe are the monad and 
 d'lind of colours. In other accidents alfo, which .ire perfeded through natural reafons, there 
 will be found a monad and duad analogous to thcle. 
 
 have
 
 Book XIV. ARISTOTLE'S METAPHYSICS. 377 
 
 have perceived the caufe alfo in them. For the fame thing, and the analo- 
 gous, is the caufe : for the deviation itfelf is the caufe, and alfo the oppofition 
 of that which they inveftigated to being and the one, which induced them to 
 fuppofe that which has a relative fubfiftenccs and the unequal, becaufe there 
 is neither a contrary to, nor a negation of, thefe, but one nature of things, as, 
 for inftance, this particular thing, and that quality. 
 
 This alfo ought to have been inveftigated, how relatives * are many, and 
 not one. But now it is inquired, how there are many monads befides the 
 firft one : but they do not alfo inquire how there are many unequals befides 
 the unequal, although they employ and fpeak of the great and the fmall, the 
 much and the few, from which numbers confift ; the long and the fhort, from 
 which length is compofed ; the broad and the narrow, which conftiiute fu- 
 perficies ; and the deep and the low, from which bulks confift ; and fo of any 
 other fpecies of relatives which they may introduce. What then is the caufe 
 to thefe of their being many ? It is neceflary, therefore, as we have faid, to 
 fuppofe in each of thefe being in capacity f . And this alfo is evinced by him 
 who makes thefe aflertions, viz. that this particular thing is being in capacity, 
 and effence, but that of itfelf it is non-being, becaufe it is relative. Juft as if 
 he fliould fpeak of fomething of fuch a nature, that it is neither the one nor 
 
 • Thofe things, fays Syrianus, which we call relatives, are one nature of beings, from which 
 all the order, fympathy, harmony, and fymphony in the world proceed ; neverthelefs the Pytha- 
 goreans did not negledl to confider the principles of this nature, but they afligned the caufes of 
 its fingle form and the multitude which it contains. But Aridotle fpcaks as if it appeared 
 wonderful to him, that fince they employed many unequah, as many monads, they did not fay 
 whence many unequals fubGft. Why, however, befides ideas, and ihe principles of ideas, (hould 
 any other caufes of the multitude of unequals be defircd ? For, as fimilitude itfelf and difh- 
 militudc itfelf are the caufes of the multitude of Cmilars and difTimilars, fo equality itfelf and 
 inequality itfelf are the caufes of the multitude of equals and unequals. And of thefe tilings, 
 indeed, Plato fpeaks in the Phasdo, and more largely in the Parmenides. But if we afcend to 
 the principles of ideas, we (hall find ft ill prior caufes, the monad itfelf and tie duad itfelf; 
 the former of which vindicates to itfelf identity, equality, and fimilitude ; but the latter differ- 
 ence, inequality and diflimilitude. 
 
 t The great and the fmall, the unequal, and the indefinite duad, fays Syrianus, were not 
 confidered by the Pythagorasans as relatives. But if any where they call matter, as bearing 
 refemhhnce of the indefinite duad, the great and the fmall, or the unequal, they exhibit by this 
 the divifion, irregularity, and degradation of forms, when they proceed into the dark recefll's of 
 matter. For not only the one is diftant from the other, but, what is truly wonderful, form be» 
 comes feparatcd and diftant from itfelf, when in its prcgr^fTion it approximates to matter. 
 
 3 C being
 
 378 ARISTOTLE'S METAPHYSICS. Book XIV. 
 
 being in capacity, nor yet a negation of the one or being,- but one certain 
 thing, which is fomething belonging to beings. But much more will this 
 be the cafe (as we have faid) if he inquires after what manner beings are 
 many ' , not by inquiring how things in the fame predicament are many 
 effences, or many things endued with quality, but how they are many beings : 
 for feme things are effences, others are paffions, and others are relatives. In 
 the other categories, therefore, the fubfiftence of the many is the fubjed of 
 another confideration. For, becaufe they are not feparable, the fubjed; be- 
 comes, and is many ; and thofe things alfo endued with qualities and quan- 
 tity are many. But though it is neceflary that there fhould be a certain 
 matter to every genus, yet it is impoffible that it Ihould be feparate from 
 effences. In things, however, which fubfift as particulars, there, is fomc rea- 
 ,fon in the inquiry, how this particular thing is many, if it is not fomething 
 particular, and this very particular thing, and a certain nature. But this 
 doubt rather originates from thence, how there are many effences in energy, 
 and not one. However, if this particular thing is not the fame with that 
 
 * The PythagorjEans, fays Syrlanus, did not negle£l: to aflert fomething of fenfibles, as hav- 
 ing the moft abje£l: fubfiftence in the lafl; of things j but as their attention was principally di- 
 retled to firft beings and intelligibles, which k-d them more frequently to confider the principles 
 of thofe eflences, they gave occafion to fuch as are buCly employed about fenfibles to aflert, that 
 they alfo contemplated fenfibles analogoufly in objeds of fenfe. It muft alfo be obferved, that 
 it is by no means arduous to ftiow how fenfibles are many : for thefe are feparated by place, 
 ufe a different fubjed, and fo great is the difference which prevails in them, that fome of thesn 
 even oppofe themfelves ; but how intelligibles are many, fince they are neither feparated by 
 place, nor detained in a fubjed, and have no habitude or tendency to fecondary natures, may 
 be very properly inquired by him, vvhofe intelle<fi:.is not perfeftly fluggifh, and fcarcely able to 
 be awakened from the fleep of oblivion. However, Syrianus adds, thefe divine men, before 
 they evinced that multitude fubfifts in intelligibles, neceflarily inveftigated the caufe of the mul- 
 titude which is there, and found that among the genera of being it is difference, which fubfifts 
 according to mn-heitig ; but that, in caufes moft eminently the firft, it is the indefinite duad, 
 which Pythagoras in the Sacred Difcourfe calls Chaos, and which he aflbciates with intelleiit ; 
 for he affigns this appellation to the monad, which is the firft of the two great principles after 
 the one. Hence, with great propriety, they ferioufly applied themfelves to this inveftigation, and 
 afligned the caufe of the multitude of true -beings -, nor did they make the other of the prin- 
 ciples (the duad) to be a relative, nor did they entirely negleft the contemplation of fenfibles, as 
 is evident from what Ocellus has written On the Nature of the Univerfe, from which (fays Sy- 
 rianus) Arillotle's Treatifc On Generation and Corruption appears to have bjcn with very little 
 alteration derived (^ovovjux' titTaQi^Ma^oa). This is alfo manifeft from the greater part of the 
 Book of 1 imaeus the Locrian, through which the Peripatetic philofophy derives a great part of 
 its theology. 
 
 which
 
 Book XIV. ARISTOTLE'S METAPHYSICS. 3?9 
 
 which is a certain quantity, it is not faid how and on what account beings 
 are many *, but how and on what account quandties are many : for every 
 number fignifies a certain quantity j and the monad is nothing elfc than a 
 mealure, becaufc it is according to quantity indiviiible. If, therefore, a quan- 
 tity is different from that which fubfills as a definite particular, it is not faid 
 from what fuch definite particular originates, nor how the many fubfifts. But 
 if it is the fame, he who aflerts this fuftains many contradi£tions. It may 
 alfo be fuggefted with refpect to numbers, whence are we to obtain convic- 
 tion of their fubfiftence ? for the dodrine of ideas Introduces a certain caufe to 
 things, fmce every number is an idea. But idea in fome way or other is the 
 caufe of being to other things : for let this be fuppofed by them. With re- 
 fpeci, however, to the man wiio is not of this opinion, becaufe he fees the 
 difficulties with which the dodrine of ideas is attended, fo that on this ac- 
 count he does not make them to be numbers, but introduces mathematical 
 number, whence is it proper to believe that there is number of this kind, and 
 that it is in any refped ufeful to other things ? For, neither does he fay that 
 it is the caufe of any thing, who alTerts its fubfiftence, but fuch a one affirms 
 that it is a certain nature, which has an eflential fubfiftence ; nor does it ap- 
 pear that it is a caufe. For, as we have already faid, all arithmetical theorems 
 are converfant with fcnfibles. 
 
 CHAP. III. 
 
 Those, therefore, who aflert that there are ideas f , and that they are num- 
 bers, ftiould endeavour to ipform us how and why they fubfift, fince, accord- 
 ing 
 
 * If the Pythagoraeans, fays Syrianus, confidered quantity and fubflance as the fame, they 
 muft have made accident to be the fame with efiencc, and fubje£l with that which fubfifts in 
 fubjed ; and, in {hort, they mufl liave oppofed the phacnomena. We muft fay, therefore, to 
 Arillotle, that they called all beings numbers. Hence, inquiring how multitude fubfilts in 
 numbers, they made all intelligible and fenfible natures the objects of their invefligation, and 
 aflerted that the duad is every where the caufe of multitude. 
 
 f \riftotle having related three opinions, viz. tliat which venerates ideal number, which he 
 ufually afcribes to his mafter Plato ; that which makes bodies to be numbers, which he attributes 
 to the Pythagorreans ; and that which alone recognizes mathematical number, he reprobates the 
 third opinion, as being lefs rational than the others. That he is not fi;rious however, in what 
 he fiiys, is I think evident from the following confideraiions. In the firft place, as we are in- 
 
 3 C 2 formed
 
 MO ARISTOTLE'S METAPHYSICS. Boox XIV. 
 
 ing to the expofition of each, every idea is one certain thing different from 
 the many. However, as thefe things are neither neceiTary nor pofTible, 
 neither muft it be faid that mathematical number has a feparate fubfiftence. 
 But the Pythagorseans, in confequence of perceiving many paflions of num- 
 bers fubfifting in fenfible bodies, made beings to be numbers, not howe\'er 
 feparate; but they confidered beings as compofed from numbers. But why ? 
 Becaufe the paffions of numbers fubfift in harmony, in the heavens, and in 
 many other things. But, to thofe who fpeak of mathematical number alone, 
 nothing of this kind follows according to their hypothefes ; but it was faid 
 by them, that of thefe there will not be fciences. We however fay that 
 there is, as we before afferted. And it is evident that mathematical natures 
 have not a feparate fubfiftence ; for, if they had, the paffions of them would 
 not be inherent in bodies. The Pythagoraeans*, therefore, fo far as relates 
 
 to 
 
 formed by Syrianus, none of the Pythagoreans thought that there was no other number befides 
 mathematical ; but perhaps, fays he, thofe who made ufe of mathematical names in fpeaking of 
 divine numbers, occafioned fome to entertain this erroneous conception. In the next place, do 
 they not employ, fays he, a fuflicient argument to prove that mathematical has a fubfirtence 
 feparate from fenfible number, when they fay : If there is arithmetic, or the phyfical fcicnce, 
 there is feparate number ; but that which precedes is true, therefore that which follows is alfo 
 true. But in anfwer to what Ariftotle now fays, that the paffions, i. e. participated properties 
 of feparate effences, do not fliine forth in fenfibles, we may reply, that he equivocally ufes the 
 words numbers and paflions, and that moft things of this kind fubfift after one manner in 
 numbers compofed from monads, and have indeed in thefe an analogous fubfiftence, and after 
 another manner, in the produdions of nature. 
 
 • Ariftotle for the purpofe of concealment having adopted the hypothefis that the Pythago- 
 raeans did not admit of feparate number, but compofed the fenfible world from numbers; but 
 that others, becaufe axioms and univerfal propofitions are not true in any thing fenfible, gave 
 a ffparate fubfiftence to number and magnitudes, he now doubts, againft the Pytliagoraeans, bow 
 from numbers void of gravity and magnitude fenfible bodies can be compofed : but againft 
 thofe who feparate, how the properties of magnitudes and numbers can be inherent in fenfibles 
 unlefs they are infeparable from numbers themfelves. In defence, therefore, of the Pythago- 
 raeans, we muft fay that they were well acquainted with other numbers, and did not only dif- 
 courfe concerning fuch as are fenfible, but alfo concerning the intellectual order of numbers, 
 together witli the orders belonging to foul and nature. And not only this, but they likewife 
 aflerted that the fenfible world fubfifts from immaterial and energetic reafons, and from more 
 antient caufes. But thofe who do not admit that nature herfelf is full of produdive powers, 
 left they ftiould be obliged to double things themfelves, thefe wonder how, from things 
 Toid of gravity and magnitude, gravity and magnitude are compofed. Though thefe are never 
 compofed from things of this kind which are void of gravity and magnitude, as from parts. 
 
 But
 
 Book XIV. ARISTOTLE'S METAPHYSICS. 
 
 S81 
 
 to a thing of this kind, are not to be reprehended : but fo far as they make 
 natural bodies from numbers, from things without gravity or levity, things 
 heavy and light, they appear to fpeak of another heaven and other bodies, 
 and not of fenfibles. But thoie who make numbers to have a feparate fub- 
 fiftence, becaufe axioms are not in fenfibles, and the aflertions of mathema- 
 ticians are true, thefe caufe a perturbation in the foul, and apprehend that 
 numbers are, and have a feparate fubfiftence ; and in a fimilar manner, ma- 
 thematical magnitudes. It is evident, therefore, that the adverfe argument 
 aflerts contraries, and that which was juft now doubted is folved by thofs 
 who fpeak in this manner, viz. why, lince thefe things by no means fubfift 
 in fenfibles, yet the paffions of them are in fenfibles ? But there are fome *, 
 who, in confequence of the fubfiftence of boundaries and extremities, viz. 
 
 But magnitude is generated from enentially impartible elements : fince form and matter are 
 the elements cf bodies ; and flill much more is it generated from thofe truer caufes which are 
 confiJered in demiurgic reafons and forms. Is it not therefore necefT.iry, that all dimenfions, 
 and all moving mafles, mu(l from thefe receive their generation ? For either bodies arc unbe- 
 gotten like incorporeal natures, or of things with interval things without interval are the 
 caufes, of partibles impartibks, and of fenfibles and contraries, things infenfible and void of 
 contact : and we muft affent to thofe who aflert that things polTcffing magnitude are thus gene- 
 rated from impartibles. 
 
 But, in defence of thofe who give a feparate fubfiftence to numbers, we mull fay, that it is by 
 no means wonderful that numbers (hould be fimilar to their caufes. Since, therefore, feparate 
 numbers poflefs a demiurgic power, which mathematical numbers alfo imitate, the fenfiblc 
 world likewife with great propriety contains images of thofe numbers by which it is adorned ; 
 fo that all things are in all, but in an appropriate manner in each. 
 
 But in anfwcr to the argument deduced from axioms and the fciences, we may fay, that either 
 thefe axioms are falfe, or they accord, and are conjoined w ith, things themfelves. If, therefore, 
 they are filfe, you take away all knowledge ; for dcmonftrations are from thefe. But, taking 
 away all knowledge, you cannot afErm any thing of any being. If, on the contrary, axioms are 
 true, and are adajned to, and conjoined with, tilings, with wliat things are they conjoined ? It 
 cannot be primarily with fenfibles ; for thefe have an individual partial fubfiitence ; and what- 
 ever of things comjnon are conjoined with them are alfo detained by matter. It remains, 
 therefore, that they mud accord with intelledual natures as their equals, but with intelligible 
 exemplars as images and figures. 
 
 • Ariftotle fays that fome of thefe divine men aflumed terms or boundaries as forms and 
 eflences ; which doftrine he apparently oppofes, becaufe, fays he, terms are not efiences, and 
 much Icfs are they feparate efiences. In defence, however, of thefe men it may be faid, tha' 
 they did not make known terms to be feparate ellVnces, but thofe which fubfift in the eflential 
 reafons of intelle£l, foul and nature ; which both terminate in a more principal manner, and 
 give limitation to generation itfclf. Of thefe, fenfible terms exhibit, like impreflions in wax, 
 an ultimate refemblance, {rtf^turMav aTcunavun airirvjtvtomt,) 
 
 from
 
 382 AR'f S'foVtE''^^ ME'rAT-H Y S ICS. Book XIV. 
 
 from ia point being tlVe bbuhHsfy of a Kne, a line of o fuperficies, and a 
 fuperficies of a folkl, are of opinion that fuch natures muft neceffarilv exift; 
 It is requilite therefore to confider, -vvhether this opinion alfo is not veiy ' 
 debile : for neither are extremities cffcnces, but rather all thefe are bounda- 
 ries : fince both of walking, and univerfally of motion, there is a certain 
 boundary. Is therefore this boundary forae particular thing, and a certain 
 elTence? But, to fuppofe this would be abfurd. Admitting, however, that 
 they were effences, all of them would be fenfibles : for the aflertion admits 
 that they" fubfift in thefe. Why therefore will they be feparate ? 
 
 ' Further ftill * :' fome one who is not very eafily perfuaded, may inquire 
 concerning every number, and mathematical natures, why fuch of thefe as 
 are prior contribute nothing' to thofe that are poflerior : for, according to 
 
 * Ariftotle doubts againfl thofe who alone admit and extol a mathematical eflence, why, 
 fince numbers according to them are prior to nvagnitudes, foul, and bodies, things pofterior are 
 not always produced from fuch as are prior ; but magnitudes are, and are generated without 
 numbers ; and likewife, though thefe fliould be taken ^way, there will neverthelefs be foul and 
 bodies. But againfl thofe who admit ideal number he doubts, whether magnitudes whicli are 
 proximately produced from numbers, are alfo ideas themfelves, or not. In defence, therefore, 
 of the former of thefe we fay, that they did not alone conCder the mathematical eflence, and ' 
 that they aflerted that things prior, by imparting an order to fubjefts themfelves, always con- 
 tribute to the fubfiflence of fecondary natures. For it is requifite that the feries of natural 
 things fliould be continued; and that every thing adventitious (hculd be excluded. But we have 
 often faid in the preceding notes, that thefe divine men Jiad not a linowledge of the mathema- 
 tical eflence alone, although in delivering the doflrine refpedling divine natures they eniployed 
 mathematical names. This, indeed, the prcfent doubt of Ariilotle clearly evinces : for if he 
 accufes them as not conipoftng the foul from magnitudes and numbers, which have a fubfiftcnce 
 prior to foul, he n^anifcftly tefiifies, that they generaie thofe numbers which arc in intelie£t 
 tluough divine numbers. 
 
 But in defence of the lattcrof thefe we may fay, that the firfl mngiittudes are ideas, viz. the 
 circle itfclf, the pyrnmid itfelf, and the triangle itfelf; but that a ru.iinifcence of them is 
 produced In us, by the mathematical reafons. Not indeed that mathematical fpeculations are 
 accommodated to thefe, fince they are difcurfive and divifible, and ci^uc.'udc through liypoth;fes, 
 but, as Plato fays in bis feventh Epillle, the circle itfelf is neither known by figure, norname, 
 nor definition, nor fcience, but is alone to be perceived fuch PS it is in itfeU'' by intelleclual' 
 intuition, projeflion, and adhefion. However, by the collifion of fcientific confidcrations, as 
 from that of ftcnes emitting fire, an intelltttual light fhines forth in the foul, in which, by itS' 
 own fpIeisdouT, it is nouriflicd and preferved. " The mathematical meth.od, therefore, fayS' 
 Syrianus, is a certain preparation, exercifing the foul, as in images, to the felf-vifive and intui- 
 tive pcrctption of t!ie paradigm: (i.e. of that divine infcl!e£l which is the paradigm of the 
 niathemailcal fcience) ( /xaSviMXTiKn (tteflcSbj TTfOKaTarxcvi) ti; sriv, u; ev axon yujAAxl^oijira tdv v-'X"" 
 5rfoj MirczTiKm Toy iraoci^itynaroi £!riQC7itiv.) 
 
 thofe
 
 Book XIV. A R I S T OT L E'S M E T A P H Y S I C S. 383 
 
 tliofe who fay that mathematical natures alone fubfift, though number (hould 
 not be, yet magnitudes would ftill have a tublifteiicc ; and though thefe 
 were not, yet ftill foul would be and fcnfiblc bodies. But from the phseno- 
 mena nature does-nct appear to be adventitious, like a bad tragedy. This, 
 however, efcapes the notice of thofe who introduce ideas : for they make 
 magnitudes from matter and number ; from the duad indeed lengths ; but 
 from the triad perhajis fuperficies ; and from the tetrad folids, or from other 
 numbers : for it is of no confequence. But whether will thefe be ideas, or 
 what is the mode of their fubfirtence, and what do they contribute to beings ? 
 Nothing indeed, as neither do mathematical natures contribute any thing. 
 But neither is there any theorem of thefe, unlefs fome one is willing to move 
 mathematical entities, and to make certain peculiar opinions. But it is not 
 difficult for thofe who affume any kind of hypothefes to be prolix and fpeak 
 inceffantly. Thefe therefore in this manner err, by conneiling mathema- 
 tical entities with ideas. But the firft of thefe making two numbers, the one 
 of forms, and the other mathematical, by no means fay, nor are they indeed 
 able to fay, how and from what a mathematician will be formed ; for they 
 place him between the formal and the fenfible : for, if from the great and the 
 fmall, he will be the fame with him who is one among the number of ideas ; 
 but if from another fmall and great, he will compofe magnitudes. If, how- 
 ever, he fpeaks of any thing elfe, he fpeaks of many elements. And if the 
 principle of each is a certain one, the one will be fomething common in thefe. 
 But then it muft be inveftigated how thefe many are one ; and at the fame 
 time, a:cording to him who makes this alTertion, it is impoffible for number 
 to be generated, otherwife than from the one and the indefinite duad. AH 
 thefe confequences, therefore, are irrational, and both oppofe themfelves, and 
 thofe who argue rationally. In thefe conclufions, too, there appears to be 
 the long difcourfe of Simonides : for a long difcourfe is like that of flaves, 
 where nothing fane is aflerted. They appear alfo, with refpedl to thofe 
 elements*, the great and the fmall, to exclaim as if they were dragged up 
 with violence: for they cannot by any means generate number, without 
 doubling that which proceeds from the one. But it is abfurd f , or rather, it 
 
 is 
 
 * It has often been faid by us, that the duad which the Pythagorxans called the great and 
 the fmall is generative of all multitude. 
 
 t Where, fays Syrianus, is the error of the Pythagorasans, if they do this for tlie fake of the 
 
 doftrinal
 
 384 - ARISTOTLE'S METAPHYSICS. Book XIV. 
 
 is one of the things impoffible, to introduce generation of thefe things which 
 are eternal. With reipect to the Pythagoracans *, therefore, there is no oc- 
 cafion to hefitate, whether they introduce, or do not introduce, generation : 
 for they cltarly affert that, the one being eftablifhed, immediately that which 
 is neareil to the infinite, whether from fuperficies, or from colour, or from 
 feed, or from fuch things as they are dubious to affert, is drawn forth, and 
 terminated by bound. But, fince they fliow how the world was fabricated, 
 and are willing to fpeak phyfically, it is juft that they fhould inveftigate 
 fomcthing concerning nature, but depart from the prefent method : for we 
 inveftigate the principles in things immoveable. So that it is requilite to 
 coafider the generation of numbers of this kind. 
 
 CHAP. IV. 
 
 They do not, therefore, fpeak of the generation of the odd f number, 
 as if it were evident that generation is of the even number. But they firft 
 of all conftitute the even \ number from unequals, i. e. the great and the 
 
 fmall 
 
 doclrinal method ? Ariflotle, however, fays this confidently with himfelf ; as lie does not 
 openly admit an effe£live caufe in things eternal. But, according to the Pythagoreans and 
 Plato, all things derive their fubfillence from principles. 
 
 • " The manner, fays Syrianus, in which Ariftotle propofes thefe reafons, will not be con- 
 cealed from the more intelligent. But that we may purfue the meaning of the Pythagoraeans 
 from what he lays down, we muft fay that, according to them, that one thing which is com- 
 peted from matter and form is a whole. But they affert chat this is conlUtuted in the follow- 
 ing manner. That reafon or productive principle which proceeds from nature, and which 
 generates colour, figure, and dimcnfjon, generates, in the firft place, body void of quality ; 
 (a?ro(pv a-u/xa), for this is proximate to the infinite, (i. e. to matter) ; and afterwards that body 
 which is compofed from matter and form, when bound and phyfical reafon 1 ave perfeclly 
 occupied this body without quality, as their fubject." But wliat thefe divine men have faid 
 refpe£\ing feparate numbers, we have before related. 
 
 t " The Pythagoraeans, fays Syrianus, afcribing the odd among numbers to ideas, very proT 
 perly fay that it is unbegotten ; but alTuming the even as analogous to material natures, they 
 call it generable, and aflbciate it with the duad : for we have often obfcrvcd that they generate 
 co-ordinate even and odd numbers from the fame principles, though they affert that the odd 
 are fimilar to the monad, and the even to the diiad." 
 
 t Here, alfo, Syrianus informs uc, " that the Pythagoraeans. afferted that tlie even number 
 poflfifled Uirough matter, as proceeding from the duad, the great and the fmall ; but tlmt 
 
 through
 
 Book XIV. ARISTOTLE'S METAPHYSICS. 385 
 
 fmall equalized. It Is tlierefore rcquifite that inequality ftiould fubfifi: prior 
 to the equalization of ihefe. But, if they were always equalized, they would 
 not have been prior to this unequal : for there is not any thing prior to the 
 even. So that it is evident that they do not make the generation of num- 
 bers for the fake of contemplating. But the manner in which elements and 
 principles are related to the good and the beautiful is dubious, and, to him 
 who doubts properly, is a fubjecl of reprehenfion. The doubt is this, 
 whether fome one of them is fuch as we wilh to call the good itfelf, and the 
 moft excellent, or whether this is not the cafe, but they are of pofterior gene- 
 ration. Indeed, by fome of the prefent theologlils this appears to be acknow- 
 ledged, who fay, that from the progreffion of the nature of things the good 
 and the beautiful become apparent. But they do this to avoid the real diffi- 
 culty which happens to thofe who affert (as is the cal^ with fome) that the 
 one is the principle of things. The difficulty, however, arifes, not from 
 their attributing to the principle good as a thing prefent with it, but from 
 their confidering the one as a principle, and that it is a principle as an ele- 
 ment *, and that number is from the one. 
 
 Thus, too, in a fmiilar manner antient poets f affert, that Jupiter reigned 
 
 and 
 
 tlirough form. It is tempered with equality. Thefe things, however, have no temporal origin, 
 but are eternal. But if they afTcrt that things without order are prior to fuch as are orderly 
 difpofed, this is the common method of all the Pythagoraeans, which they adopted for the fake 
 of the dodtrinal method (5ioa^■xiJ;^l«5 evsxa). Ariftotle alfo fays, that matter is prior to, and is 
 the principle of, body, though it is perpetually adorned." 
 
 * ^he one concurs with the good, and is not to be called a principle in the fame manner as 
 an element, from which when inherent number confifts : for the one, according to Plato, is 
 the fame with the good, and tranfcends all effence, intellect, and life. 
 
 f Ariilotle, from not enduring that caufes fliould be called by the fame names as their effeiSls, 
 relates, as it appears to me, the opinions of antient thcologifts in a fuperficial manner. *' For 
 fays Syrianus, they aflert that Night and Heaven reigned, and, prior to thefe, the mighty father 
 of Night and Heaven, who diftributcd the world to gods and mortals, and who firft poffefied 
 royal authority, the illuClrious EricapKus. 
 
 ou TTfuTOf Paji'Ktuz 7r£pi;i>.*Tn; jj^iKETraioj. 
 Night fucceeded Ericapasus, in the hands of whom flie has a fceptre. 
 (TKiTcrpov £xo"(r' Ev xffJ'iv rt^miTtcuDu' 
 To Night, Heaven fucceeded, who firft reigned over the gods after mother Night. 
 hi xffflToj /3j!!riA£i/f Ssijv ixno, ixmc^a vuiitoi. 
 
 3 D Chaos
 
 3"86 ARISTOTLE'S METAPHYSICS. Book XIV. 
 
 and governed, and not thofe firft principles fuch as Night and Heaven, or 
 Chaos, or even Ocean. But it happens indeed to thefe, to aflert things of 
 this kind, in confequence of changing the rulers of the world j fince thofe 
 among thefe, who were of a mixed clafs, and who did not fpeak of thefe 
 things fabuloufly, fuch as Pherecydes, and certain others, eftabliih the firft 
 generating principle, as the beft* of things. This is alfo the cafe with the 
 Magi, and among the wife of latter times, with Empedocles and Anaxagoras ; 
 the former making friendfliip to be the element, and the latter, intelled: to be 
 the principle, of things. But of thofe who aflert that there are immoveable 
 eflences, fome fay that the one f is the good it/elf; but neverthelefs they are 
 of opinion that the elfence of the good is efpecially the one. In which way, 
 therefore, is it proper to folve this doubt ? But it is wonderful, if to that 
 which is firft, perpetual, and moft fufficient % to itfelf, fufficiency and the 
 
 prefervatloa 
 
 Chaos tranfcends the habitude of fovereign dominion : «nd, with refpetH: to Jupiter, the Oraclea 
 given to him by Night, manifcflly call him not the firft, but the fifth immortal king of the gods. 
 
 aSavacTov liatrihna Sewv TTSfiTrrov yeviaSat. 
 According to thefe theologifts, therefore, that principle which is moft eminently the firft, i» 
 tie one, ox the good, after which, according to Pythagoras, are thofe two principles j^Lther and 
 Chaos, which are fuperior to the pofTeftion of fovereign dominion. In the next place fucceed 
 the firft and occult genera of the gods, in which firft fliines forth the father and king of all 
 wholes, and whom, on this account, they call Phanes. Neither, therefore, do the beft of the 
 philofophers depart from the gods ; nor do theologifts aflert, that things of a pofterior nature 
 are more powerful and excellent than fuch as have a more principal fubfiftence, but there is 
 one truth among them all." 
 
 * " Ariftotle, fays Syrianus, rightly admits the antient theologifts afTerting that the firft 
 caufe is the beft of all things. They do not, however, make mutations of kingdoms, though 
 in their fabulous figments they introduce things of this kind. But, more antient caufes always 
 abiding in their proper mode of fubfiftence, they fay that fucli as are of a fccond rank after 
 this manner fubGft." 
 
 •f Again Syrianus informs us, " that not only, according to Plato, the one zr\A the good are 
 fupercflential ; but alfo according to Crotinus the Pythagortcan, and almoft all who came 
 from the fchools of the Pythagoreans. Neverthelefs, the one was confidered by them to be the 
 clTence of the firft principle, which they called the good, as being the caufe of unity and goodnefg 
 to all things." 
 
 X Perfeft fufficiency is inherent in the good on account of the fimpHcity of his fubfiftence; 
 fince this is with him the fame thing as to be the good itfelf: for he is not good and fomething 
 elfe, but this very thing, and this alone, the good itfelf. So that he is the one, becaufe his nature 
 is not compofed from the good and fomething elfe : for, if this were the cafe, we fhould be in 
 want of another principle, in which good would not be mingled with any other nature, but 
 
 would
 
 Book XIV. A R I S T O T L E'S M E T A P H Y S I C S, 3*7 
 
 prefervation of itfelf fhould not be good to it the firft of all things. In- 
 deed, it is incorruptible and fuificient to itfelf for no other reafon than be- 
 caufe it has an excellent condition of fubfiftence. So .that to fay that the 
 principle of things is of this kind, may rationally be fuppofed to be true. 
 That this, however, {hould be the one, or, if not this, the element of num- 
 bers, is impoflible : for many difBculties attend this hypothefis, which fome 
 in order to avoid, acknowledge that the one is the firft principle and element 
 of things, but that this one is not the principle of mathematical number : 
 for, if this were the cafe, all the monads would becom,e .4 certain good, and 
 there would be a great abundance* of things good. 
 
 Further ftill : if forms are numbers, all forms will be a certain good. Let, 
 however, any one fuppofe ideas f to be of whatever nature he pleafes : for, if 
 
 they 
 
 troulJ be perfe£lly pure. But Ariftotle adduces a difliculty refpeQlng the cm, becaufe he 
 underflands it in his ufual way, rather than theologically. If, however, fome fuppofing the one 
 to be the principle of mathematical numbers, take away from it afterwards the good, fuch do 
 not fpeak concerning the principle of all things, but concerning the caufe of monadic numbers. 
 And it is evident indeed, that even this caufe is the good of thofe things which are generated 
 from it; yet it is not fimply the good itfelf. That which he fays is indeed certain, that all 
 monads are a certain good •, but then thefe are not material monads, but thofe which are con- 
 fidered in the forms of nuaibers. Thus tlie pentad may be f.iidto be the good of the number 
 five, viz. of the number five conGdered as confifting from five monads which correfpond to 
 natter, and the pentad wliich correfponds to form ; and, in the fame manner, the decad is the 
 good of the number ten. Yet they arc not that which is fimply good, in the fame manner as 
 the unities (evaSi;) proceeding from that principle which is nioft eminently the firfl: : for thefe 
 are not only gods, but are likewife, according to Plato and the Pythagorxans, certain connec- 
 tives, avvoxoti, of gods. Nor is there any abfurdity in admitting tiiat there Is an 'affluence of 
 good in divine natures: for that which is divine is void of envy, and is incomprehenfible by 
 liuman reafoning. Ideas alfo and numbers poflefs the form of good, as being moft eminently 
 the progeny of the firfl; caufe. 
 
 * For aTTo^tx read luTropia. 
 
 f In anfwer to what is here doiibted by Ariftotle, it may be faid, that if there are ideas of 
 die virtues, it does not follow that fuch ideas will not be eflences : for tlie image is not altoge- 
 ther fuch as is the exemplar in things of this kind ; but impartlb'es are the caufes of parables, 
 intelleclual natures of fuch as are not intelleclual, and immortal of fuch as are mortal. In 
 like manner, effcnces arc the caufes, not of any kind of qualities, but of thofe which are per- 
 feftive of eflences. There are therefore ideas of all univerfal eflences, and of whatever con., 
 tributes to the perfection of thefe; but it does not neccflarily follow from this, that every thing 
 in the fublunary region fhould be beautiful and good : for that which receives the illuminations 
 of fupernal natures does not always retain fymtnetry an4 ordei: ; but is Lurried away to the 
 
 3 U 2 coutraii?*
 
 388 ARISTOTLE'S METAPHYSICS. Book XIV. 
 
 they are of things good alone, ideas will not be effences. But if of eiri.aces 
 alfo, all animals and plants are good, and the participants of thefe. Thefe 
 abfurdities, therefore, attend this hypothefis, and the contrary element, 
 whether it be multitude, or the unequal, and the great and the fmall, will be 
 evil itfelf. Hence, a certain perfon avoids connecting the good with the one^ 
 becaufe, on this hypothefis, fince generation is from contraries, the nature of 
 multitude muft be neceflarily* evil. But others aflert, that the unequal f 
 is the nature of evil. It fo happens, therefore, that all beings participate of 
 evil J, except the one which is the one itfelf, and that numbers participate it 
 more purely than magnitudes. It alfo follows that evil is the place of good, 
 and that it participates and afpires after that which is corruptive of itfelf: 
 for one contrary is corruptive of another. But if, as we have faid, matter 
 is every thing in capacity, as, for inftance, fire in capacity of fire in energy, 
 evil will be the good itfelf in capacity. All thefe things therefore happen §, 
 
 in 
 
 contraries of thefe, through the imbecility of its nature. In the next place it may be afked, 
 whv if the one is good, mud the other principle the cluad be evil ? For, in the firft place, the 
 Pythacorsans and Plato called that one the good, which is abftraded from all compofition or 
 co-ordination with another, and tranfcends the two principles pofterior to the one. But even 
 if they had faid that the more divine of the two principles, which thty call the monad, is the 
 good, it would not follow that according to them th.e duad (though it fliould have fome other 
 oppofition to the mon.ul) is evil. For divine natures are not generated, and do not proceed 
 from an oppofition of this kind, but from the moft excellent principle, and which poTefles 
 the mofl pure and immaculate good. The impoffihilities, therefore, which Ariftctle collefis in 
 ■what follows, as confequent to the hypothefis, do not in any refpecl accord with the real mean- 
 intr of thofe divine men : for, according to them, evil is entirely excluded from principles, as 
 Plato manifeftly aflerts in the Thextetus. 
 '* For tvavTiov ov read avayux.ov ov. 
 
 f They aiTumed, fays Syrianus, that ui::qual which is the cai:fe of beings, and which is 
 more antient than difference iifilfy among the genera of being. They liLewife not only deno- 
 minated it mofl excellent, but ailerted th.nt it is efpecially generative of the mod excellent na- 
 tures. But if in the lad of things, and in material natures, there is any thing unequal, whicli 
 is reprobated by thefe divine men, tliis no further pertains to tlie caufe generative of multitude, 
 except that this alfo in a certain refpecl is derived from thence. 
 
 X It mud net be thought that Aridotle here fays any thing in reality againd the Pythago- 
 lieans : for tliey by no means placed evil among principles. 
 
 § This abfurdity follows, fays Aridotle, becaufe they make every principle an element. 
 But what are the abfurdities which he confiders as confequent to this ? 1 hat all things are 
 good, if the good is a principle as an element ; that evil is a principle, becaufe they confidcr 
 contraries as principles ; that the one itfelf is a principle, for it will no longer be good if it is 
 
 the
 
 Book XIV. ARISTOTLE'S METAPHYSICS. 389 
 
 in confequence of making every principle an element, — contraries principles, 
 — the one the principle of things, — and numbers the firft eflences, having a 
 feparate fubiiftence, and exifting as forms. 
 
 CHAP. V. 
 
 If, therefore, not to rank the good among principles, and to rank it among 
 them in the manner we have mentioned, is impoffible, It is evident that nei- 
 ther principles nor the firft eflences are rightly affigned. Nor yet does he 
 conceive rightly, who affimilates the principles of the univerfe to the prin- 
 ciple of animals and plants ; becaufe things more perfe(5l always proceed 
 from fuch as are indefinite : on which account alfo, in fiift eflences, they 
 fay, it fo happens that neither is any particular being the one itfelf. But, In 
 fenflble things alfo, the principles from which fenflbles originate are perfet:!. 
 For man generates man, and feed is not the firft thing. It Is alfo abfurd to 
 make place * together with mathematical folids : for the place of particulars 
 
 is 
 
 the one; and laflly, tliat numbers will participate of unmingled evil, becaufe they fay that firft 
 eflences are numbers. Four abfurdities, therefore, follow the four hypothefes : for all things 
 ■will be good and evil ; befides the one itfelf Caert will alfo be an evil principle ; the principle of 
 things will not be the gcorl ; and numbers will participate of unmingled evil. 
 
 We muft fay therefore with Syrianus, that the Pythagoreans did not make element a prin- 
 ciple to all things, in the fenfe in which it is adopted by Ariftotle ; nor did they make thefe 
 contraries to be principles, fo that the one is the good, and the other evil ; nor did they under- 
 lland the one, as Ariftotle now underftands it ; nor does it follow that, becaufe there are Sepa- 
 rate numbers, they participate of pure and unmingled evil. Since, according to them, un- 
 mingled evil is not only expelled from an intelligible eflence, but alfo from the whole of the 
 ethereal region. Hence, it folely wanders about a mortal nature, and is adbciatcd with par- 
 tial good. Principles therefore are rightly delivered by the Pythagora:ans ; and it is better to 
 call the good, the one, than to call it intellecl : for he who calls it the one, preferves umning'cd 
 good, and good alone ; fjnce good is not willing to be aflbciated with any thing elfe. But he 
 who calls it intelleEt, does not maka it to be good alone ; fince intellect poflefles multitude, 
 though this multitude is profoundly united. 
 
 * Alexander Aphrodifienfis, according to Syrianus, fays that this is advanced by Ariftotle 
 againft Plato. If, therefore, fays he, Alexander rightly conjedlures the meaning of Ariftotle, 
 we ftiall not aflert any thing inconfiderate refpecling the divine Plato, in laying that he made 
 our imagination the place for mathematical bodies, in the fame manner as matter is the place 
 of material forms. There is however this difference, that matter, receiving material form 
 from nature, neither knows that which it receives, nor is able to detain it. But our imagina- 
 tion, receiving mathematical body from a fuperior foul, both contemplates and preferves it, 
 3 to
 
 390 ARISTOTLE'S MET APHYS I CS. Book XIV- 
 
 is peculiar to them, on which account they are locally feparable. But ma- 
 thematical folids are not fituated in a certain place. And to fay indeed that 
 they are fituated lomewhere, and at the fame time not to fay what place * is, 
 is abfurd. But it is requifite that thofe who aflert that beings are compofed 
 from elements j, and that numbers are the firft of beings, fhould, by dividing 
 one thing from another, inform us after what manner number fubfifts from 
 
 to the utmofl of its ability. Hence, there is one place of natural bodies, another of material 
 forms, another of mathematical bodies, and another of immateri.il reafons. Nor is there any- 
 thing of innovation in thefe afTertions. For Ariftotle himfelf, in his books De Anima, calls the 
 intelleftual foul the place of forms ; and thofe who read the Timseus with attention will dif- 
 cover that Plato there fpeaks concerning the place of natural bodies. 
 
 * Jnftead of ti 3i ej-tik o TOTrog, /oi aroTTov, read ti Je ej-tiv o tottc; f^n euteiv aroTrot. 
 
 f There is not the fame reafoning refpedting the fubfiftence of mathematical and that of 
 ideal numbers ; for, though we do not attribute to the former natural quantity, yet at leall we 
 -afcribe to them mathematical matter as their fuhje£t. But ideal numbers are perfedlly impar- 
 tible, intelleflual, energetic, and demiurgic, and have their fubfiftence in fimple and immaterial 
 forms and principles. This being the cafe, it is requifite clearly to diftinguilli refpefliing what 
 numbers Ariftotle makes thefe interrogations. Neverthelefs, becaufe he feems rather to inter- 
 rogate concerning ideal numbers (for the firft of beings were called by the Pythagorasans, not 
 mathematical, but ideal numbers), we mud again fay, that neither compofition, nor fubje6l, nor 
 privations, nor element receiving corruptions, nor any thing clfe of this kind, is aflumcd in con- 
 Itituting divine numbers. For all thefe fubfift about a material nature, and a nature which is dif- 
 ferently affefted at different times. But all divine natures, fince principles always remain the 
 fame, proceed with fel-f .prolific energy, through the affluence of the prolific power of primary 
 caufes; and through their own felf-fplendid and felf- prolific prcptrty, they fubfift always in the 
 fame things, and after the fame manner, being firmly eftabliflied far remote from generation and 
 corruption, compofition and divifion, and all mutation. They likewife prefide over the whole of 
 nature, and over the mundane foul by which nature is governed, exciting them to continual ener- 
 gies about generation, left its fluctuaiing empire ihould fail, or the irregularity about matter fliould 
 be victorious. But all things are adorned by the n.itural and demiurgic powers of ideas and num- 
 bers. 1 hofe mundane wholes, therefore, which detain and renovate things naturally flowing, 
 mortal and corruptible, cannot be corrupted by the very natures which they preferve. 
 
 With refpeft likewife to what is now faid of Empedoclcs, it muft be obferved, that, as the 
 accufation is not rightly made, it is not reafonable to fuppofe that Ariftotle is ferious in making 
 it. Fcr Jlfi/e, fays Syrianus, is not corruptive, according to Lmpedocles. fince it fabricates the 
 unlverfe ; nor is the fphere which he introduces ever according to him diffolved, uulefs fome one, 
 by dwelling on the words which antecedc the whole of his theology, fliould become deprived of 
 his true meaning. But ^ri/e, according to this philofophei', is generative of multitude and difler- 
 cncc ; znA friendjlAp of famenefs and union. Hence in inieUigihUs, which he denominates a 
 i^zxt, frientipip has dominion, but in feiifibles y?///^ ; for in eaiji of thefe there is uiiiiy and 
 *nultitudc J but jn ftiendChip unity predominates, and in llrife multitude, 
 
 principles,
 
 BookXIV* ARISTOTLE'S METAPHYSICS, 
 
 391 
 
 principles, and whether this is accomplifhed by mingling. But neither is 
 every thing mingled which is generated. 
 
 Does number then fubfift from compofition, as a fyllable ? But, in this 
 cafe, it is neceflary there fhould be pofiiion ; and he who employs his intel- 
 lect on this fubjeft will underftand feparately the one and multitude. Num- 
 ber, therefore, will be the monad and multitude, or the one and the unequal. 
 And fince that which fubfifts from certain things, fubfifts indeed partly as 
 from things which are inherent, and partly not, in which way will number 
 fubfift ? For thofe things which fubfift as from things inherent, are no other 
 than thofe of which there is generation. Does it, therefore, fubfift as from 
 feed ? But it is impoffible for any thing to depart from that which is indi- 
 vifible. Shall we fay, it is as from a contrary not abiding. But things which 
 fubfift in this manner, are alfo from fomething elfe which is of a permanent 
 nature. Since, therefore, with refpcdt to the one, this perfon confiders it as 
 contrary to multitude, but that as contrary to the unequal, employing the one 
 as if it were the equal, number will fubfift as from contraries. There is, 
 therefore, fomething elfe from which, being permanent, the generation of the 
 other is effeifted. 
 
 Further ftill : why are fuch other things as are from contraries, or to which 
 there are contraries, corrupted, though they may confift from every thing, 
 but this is not the cafe with number ? For, refpeding this nothing is faid, 
 though contrary, both when it is inherent and when it is not inherent, cor- 
 rupts ; as, for inflance, ftrife that which is mixed. This, however, is not 
 requifite ; for the former is not contrary to the latter. But nothing is deter- 
 mined with refpeit to the manner in which numbers * are the caufes of 
 
 e [fences, 
 
 * Ariftotle relates two opinions refpefling the fubfiftence of effences from numbers, neither 
 of which he admits according to their literal acceptation. For, neither (fays he) are numbers 
 the boundaries of eflences, as points are of lines. For the Pythagorsean Eurytus, entertaining 
 this opinion, faid that this particular number is the boundary of this plant, and again another 
 number of tliis animal ; juft as of a triangle 6 is the boundary, of a fquare 9, and of a cube 8. 
 Nor are numbers boundaries, as others alFert them to be, becaufe eflences are generated by- 
 ratios, but ratios are certain fymphonies, and fymphonies are modulated and compofite habi- 
 tudes of numbers. For, from none of thefe hypothefes, fays he, can it be (liown how accidents 
 are produced from numbers. In anfwer to this, fays Syrianus, it mull be faid, tliat Eurytus and 
 his followers, beholding the images of things themfelves in numbers, rightly attributed certaia 
 numbers to certain things according to their peculiarity. But the fecond of thefe opinions 
 omits to fpeak of natural numbers : for thefe are truly efi'cclive of fymphony in a fubjed. For, 
 
 hovT
 
 892 ARISTOTLE'S METAPHYSICS, Cook XIV. 
 
 eflences, ^nJ of being, whether as boundaries in the fame manner as points of 
 magnitudes, and, according to Eurytus, as number of a certain thing; as, 
 for inftincc, tins number of man, and that of hnrfe. Juft as thofe who 
 refer numbers to figures, the triangle and the fquare, thus affimiiating the 
 forms of plants to calculations. Shall we fay, this is becaufe it is either ratio, 
 or the fymphony of numbers? and in a fnnilar manner, with refpect to man 
 and every thing elfe. But with refpect to paffions, how are they numbers, 
 fuch as the white, tlie fvveet, and the hot ? However, that numbers * are 
 neither eflences, nor the caufes of form, is evident : for reafon is eflience ; 
 but number is matter, as, for inftance, the number or eflence of flefh or bone. 
 Thus, too, three of fire, but two of earth ; and always number, whatever it 
 may be, is of certain things, and is either fiery, or terrene, or monadic. But 
 efTence confifts in beingyo much with refped: to^o much according to mixture. 
 But this is not number, but the ratio of the mixture of corporeal numbers, 
 or of certain things. Number, therefore, is not a caufe by making f : nor is 
 number altogether, nor monadic number, either as matter :];, or as reafon and 
 the form of things. Neither is it as that for the fake of which a thing fubfifts. 
 
 how could the dominion of one form make a fubject to be one, when the contraries which it 
 contains do not accord, and are void of modiihition ? But what other In this cafe will nume- 
 rate befides nature herfclf? For, as the mufician harmonizes his lyre through mathematical 
 numbers, fo Nature, through her own natural numbers, orderly arranges and modulates her pro. 
 du£lIons. 
 
 * Ariftotle here affumes that every number is the number of certain things, and is indigent 
 of a fubjcft ; and again, that reafon is the caufe of mixture, and not number. The Pythago- 
 rxans, however, fays Syrianus, fuppofed immaterial numbers, and aflerced that numbers are 
 the caufes of the natures in fenfibles, which are adapted to their recipients, and of the mixture 
 of every -compofite. 
 
 -j- Since there are four caufes, Aridotle fays, that number is no one of thefe. For it neither 
 (fays he) has-an effeclive power like feed, nor is it as form in fenfibles, nor as matter, nor as the 
 final caufe. This is true indeed of mathematical number, but not of that vvliich is phyfical or 
 divine. For all caufes are numbers except matter : but this is not a caufe, but is merely fub- 
 ■ fervlent to caufes in tlie generation of things. We muft fay, therefore, that divine numbers 
 are energetic, and that they communicate other numbers, viz. material forms to fubjedls, and 
 that they energife for their own fake. 
 
 X For oi/T£ h l»^yi, read ouTt wj « bhn. 
 
 CHAP.
 
 Book XIV. ARISTOTLE'S METAPHYSICS. 393 
 
 C H A P. VI. 
 
 But fome one may doubt what the good is which refults from numbers*. 
 If mixture is either in rational or in the odd number : for now nothing 
 more fAlubrious arifes, from water and honey being thrice three times 
 mingled : but it will be more beneficial if there be no proportion in t!ve 
 mixture ; and it will be watery, or in number unmingled. Further dill : 
 the ratios of mixtures confill in the addition of numbers, and not in numbers 
 themfelves ; a?, for inftance, the ratio between three and two is that of three 
 to two, but is not thrice two ; for it is requifite that there fhould be the fame 
 genus in multiplications ; fo that it is requifite that the feries abg fhould be 
 meafured by ^, and de^ by d; fo that all things mud be meafured by the 
 
 • In anfwer to what is now urged by Ariftotle, we may fay with Syrianus, that the more ufeful 
 is the more congruous mixture, and that when it is more confonant it is proportioned and coin- 
 menfurate: but this is acquired through natural arithmetic. Thus, too, f.iys he, fome one may 
 reply to thofe who dire£l their attention to occafion in the feveral adtions of life, who do not look 
 to the whole of things, nor employ reafonii-.g in conjunflion with fenfe, and who order us to truft 
 to opportunity alone, — >fhat it is better to act with prudence than from occafion ; that it is the 
 firft bufinefs of prudence to know by reafoning the opportunities accommodated to particular ac- 
 tions -, and thus to confuler other things which tend to the orderly acquifiiion of the end. In like 
 manner, the Pythagoreans fiy that numbers of a flender fubfillence and thefe mathematical arc 
 not received by nature, or chofen by prudent men, but that good accedes to particulars through 
 the bed numbers which are endued with proportion, and are not mathematical, but natural, and 
 operative : for God and nature, according to them, produce all things tlirough number. They 
 add, that prudent men exhibit the beauty of fabricative numbers through mathematical num- 
 bers ; fince they cannot in any other way inftiu(fl; thofe who do not follow the whole order of 
 beings. 
 
 But Ariftotk in what follows, obvioufly, and therefore we may conclude defignedly, paralo- 
 glfes ; for he alTumes mathematical names in natural things. However, as we are informed by 
 Syrianus, philofophers more antient than Ariftotle denominated the progrelTions of the prolific 
 powers of nature, multiplications, which progreffions rule over their fubjedl matter, and poflefs 
 proportion and fymphony. 
 
 In anfvvcr to what is faid after all this, viz. That if all things communicate with number, and 
 €very number is in things, it is neceflary that many things (liould ufe the fame number, and that 
 there fhould be many numbers of the fame thing, we may reply as follows : Though all words and 
 ^ fer.rences arc compufed from the twenty-four letters as elements, and though all letters appear in 
 fentences, it is neither neceffary tliat different fentences fhould ufe the fame letters, but that they 
 ibould partly ufe the fame and partly not ; nor is it neceflary that different letters (hould be irj 
 the fanii. v\ ovd, is, for inftince, t!:at all tlie letters of the wordPlato fliould be in the word Socrates. 
 In like manner, in natural reafons and numbers, all thefe are operative, and all natural things 
 confift t raugh them, yet different things are not immutably adorned with the fame numbers. 
 
 3 E fame
 
 394 ARISTOTLE'S METAPHYSICS. Book XIT. 
 
 fame meafure. There will be, therefore, of fire begz^ and of water the 
 number twice three. But if it is requifite that all things ihould participate of 
 number, it is alfo neceffary that many things which are the fame fhould hap- 
 pen, and that there fhould be the fame number to this thing and to another^ 
 Is, therefore, this the caufe, and is a thing through this ? Or is it im- 
 manifeft, fuch as is a certain number of the revolutions of the fun *, and 
 again of thofe of the moon, and of the life and age of every animal ? 
 What, therefore, hinders, but that feme of thefe may be fquares, others 
 .cubes, and equal to each other, and others again double ? Nothing, in- 
 deed, hinders ; but it is neceflary that they fhould be intimately conneded 
 with thefe, if all things participate of number. It will alfo happen that 
 things which differ from each other will fall under the fame number ; fo 
 •that, if the fame number happens to certain things, they will be the 
 fame with each other, having the fame form of number ; as, for in- 
 ftance, the fun and moon will have the fame numerical form. But through 
 what caufe f have they the fame form I There are, indeed, feven vowels, 
 
 fevea 
 
 * That there is a folar number, and alfo a lunar number, and a proper number of each of 
 the bodies that revolve in the heavens, is, fays Syrianus, manifeft according to the adage, even to 
 the blind. For the reftitutlons of the heavenly bodies to their priftine flate {aTronaTacrraaeii} 
 would not always be effedted through the fame things, and in the fame manner, unlefs one and 
 the fame number had dominion in each. Yet all thefe contribute to the procefTion of the celef- 
 tial fpheres (to Seiov '/snmov), and are contained by their perfecS; number. But there is alfo a 
 certain natural number belonging to every animal. For things of the fame fpecies would not 
 be diftinguifiied by organs after the fame manner, nor would they arrive at puberty and old age 
 about the fame time, or generate, nor would the foetus be nouviilied or increafe, according to 
 regular periods, unlefs they were detained by the fame meafure of nature. Syrianus further 
 obferves that, according to the molt excellent of the Pythagorseans, Plato himfelf, number is 
 the caufe of better and worfe generations. Henee, fays he, though we fometimes fpeak of the 
 fquares and cubes of natural numbers, we do not make them to be monadic, fuch as the 
 number 9 and the number 27, but we fi^nify thrcur,'h thefe names from fimilitude the progref- 
 fion of natural numbers into, and dominion about, generations. In like manner, though we 
 call them equal or double, v/e exhibit the dominion and fymphony of ideas in thefe numbers. 
 Hence different things do not ufe the fame number, fo far as they are different, nor do the fame 
 things ufe a diiTerent number^ fo far as tlu ;• are the fa 
 
 t As if he had faid, But let us fee by ^ !iat arguments they prove that thefe are the caufes of 
 things. Celebrating, therefore, the heptad, they fay that there are feven vowels through which 
 fpeech receives its completion. The fyrnphony called the diapafon alfo confifcs of fevea 
 founds ; and ftill further, the Pleiades are feven in number, and animals faed- their teeth in feven 
 years ; from all which he reprobates the conclufion, that through tliis cumber ibxne things fub-
 
 EodkXIV. ARISTOTLE'S METAPHYSICS. 31^5 
 
 feven chords or harmonies, feven Pleiades : in feven years, too, feme flied- their 
 teeth, and lonie do not; and thofe who, led an ar:ny againft Thebes were 
 feven in number. Is it, therefore, becaufe fuch a particular number is natu- 
 rally adapted to the purpcfe, that either they were feven, or that the Pleiades' 
 confifl: of feven ftars ? Or are thefc, indeed, on account of the gates of 
 Thebes, or through any other caufe ? But if we thus numerate and affifri 
 twelve ftars to the Bear, others afcribe to it a greater number : for they fiy 
 that |%|. ^ are fymphonies : and that, becaufe thofe are three, thefe alio are 
 three. However, that there are ten thoufand fuch-like things is not an objetLl: 
 of concern to any one : for y and p will be one fign j but if at one time 
 
 fift in this particular manner, and other? not. Thofe alfo who led an army againft Thebes were 
 feven in number. Afterwards he demonftrates that none of thefe fubfdts through tlie number 
 feven, but from another caufe. And indeed, as Syrianus jullly obferves, it would be ridiculous 
 to think that this number was the caufe of the Grecian leaders, or of the Pleiades. For it muil 
 not be faid that this conflellation was tluis confliituted by the providence of its divine Artificer ; 
 but rather that the whole of it participates of abundant pofition. Hence, he adds, the fixed ftars 
 are differently arranged by the Egyptians, Chaldaeans, and Grecians. Ariftotle alfo very pro- 
 perly obfcrves refpedling the double confonants, that they are not three, becaufe there are three 
 fymphonies. Nor, fays Syrianus, can each of thefe confonants be reduced to the feveral fym- 
 phonies, as, for inftance, K to the diateilaron, or I to the diapente, or ij- to the diapafon ; but 
 rather, becaufe there are three modes of pronunciation, one is accompliflied through each. Sy- 
 rianus adds, that this mode of diftribution, as Theophraftus relates, was adopted by Archinus ; 
 but nevertl'.elcfs that we muft not reprobate phyfical afl'ertions refpefting numbers, becaufe fome 
 more recent philofophers have adopted illegitimate modes of diftribution. 
 
 Indeed, if any thing of this kind had been aflerted, either by the divine Plato, or by any 
 one of the illuftrious Pythagoreans, Ariftotle might be confidered as now ferioufly oppofing 
 their doctrine. This, however, is far from being the cafe : for Syrianus informs us that Pytha- 
 goras, who was the firft that aflerted many things both vener.able and divine concerning the 
 heptad, adopted no diftribution of this kind, but prudently evinced after what manner nature 
 through feven years, or months, or days, perfects or tranfmutes many thin^js of this kind. But 
 others (fays he), difcourfing refpcfting the decad, unfolded its kingdom in the whole of the ce- 
 leftial regions, and its empire in the feveral produdlions of nature; and Pythagoras himfelf dif- 
 courfes both theologically and phyHcally concerning all the numbers from one to ten, and this 
 without employing any trifling and frigid diftribution. Ariftotle alfo himfelf, when he fpeaks 
 ferioufly about things of this kind, admires the power of numbers, and adopts the theory of the 
 Pythagoreans : for in the beginning of his treatife Ds Coelr, after having adduced, in tefti- 
 mony of what he there advances refpe(fling the number three, the dorlrine of Pythagoras, he 
 at length exclaims : " Hence receiving this number from nature, we employ it in the wor- 
 Ihip of the gods." In his treatife too On Soife t2nd ScnfilUs, finding that there are eight moft; 
 general fapois ; and again, that there are eight more fimple colours, he makes each ta be feven, 
 thinking that this number is adapted to fabrication (J^/^iowjy.a). 
 
 3^2 each
 
 396 ARISTOTLE'S METAPHYSICS. Eook XR'. 
 
 each of t^ie others is double, bat another is not, this is, becaufe one in each is 
 added to cr. On this account there are three only, and not becaufe there are 
 three fymphonies : for there are more fymphonies than three; hut here 
 there cannot be more than three. Thefc men aUb refemble the antient Ho- 
 merics*, who perceived fmall fnnilitudes, but overlooked inch as are great. 
 But fome aflert the:e are many fuch-like particulars, as, for iniiancc, with re- 
 fpedt to media, one medium is 9 and another 8 ; and a \crCe of 1 7 feet is 
 equal in number to thefe. But in fyllables they fay that 9 afcends on the 
 light hand, but 8 on the left ; and that there is an equal interval in letters 
 from a to &;, and in pipes from the moft grave found to the moft acute «^/t", 
 the number of which is the equality in the all-various melody of the hea- 
 vens. But we ought not to perceive things of this kind (for no one will 
 make them the fubjedt of doubt), nor fpeak concerning them, nor attempt to 
 difcover them in things perpetual f, becaufe they are to be found in things 
 corruptible. But thofe natures in numbers :[; which are the fubjed of praife> 
 
 and 
 
 * That fome of the interpreters of Homer (fays Syrianus) were not confiftent with them- 
 felves, and that fome of thofe who endeavoured to imitate the Pythagoreans fell from the true 
 theory of thofe philofophers, and were led to uncertain and ridiculous conjeftures, ought to be 
 granted. But this does not militate againft Horricr or Pythagoras, or againfl; thofe who are abie 
 to recur to the true fpeculation of their doctrine. He aikis : " Thofe, therefore, are to be de- 
 rided who fay that 9 and 8 are two media between 12 and 6 (for 12 : 9 : : S : 6), becaufe a verCe 
 has feventeen fyllables ; or who afl'ert that the media of two fyllables are the caufes of verfe. 
 It is alfo ridiculous to make the holes of a pipe to be (0 many in number, on account of the 
 letters of the alphabet, or to accommodate the twenty-four letters to the entire perfeftion of the 
 world. For, though there fliould je one definite caufe of thefe (as in reality there is), yet it is 
 to be confulcred in a very different manner. 
 
 f Eternal nature? are orderly difpofed through certain divine numbers, but mortal natures 
 riirough fuch as are both divine and natural. For, if eternal natures fubfirt. in this manner, 
 they thus fubfift naturally. Thus, for inftance, the fun through fuch a portion of time makes 
 a complete revolution, and this always : it, therefore, naturally revolves after this manner. But 
 this time is the number of a thing of this kind. Nature, therefore, imparted being to the fun, 
 in coniuniSlion with fucli a number ; to the moon, with fuch a number peculiar to it; and in like 
 manner to each of the celeflial orbs : but this number is not mathematical, but fabricative and 
 divine ; though in mathematical numbers we may behold certain images of this, becaufe pofte- 
 rlor numbers always depend upon fuch as are prior, proceed according to their peculiarity, and 
 lliine forth in the lad orders of things. Mortal animals alfo, as far as nature has dominion iii 
 them (but it has dominion not always, but for the moft part), are fo far orderly difpofed with 
 proper numbers. 
 
 1 Ariltotle openly admits, that in numbers and figures, in colours, and in fcnfible particularsj 
 
 thera
 
 B' OK XIV. A RISTOTLE'S M ET A r II YS I C S. 397 
 
 and the contraries to thefe, and, in fhort, the objcds of mathemalical contcm- 
 j;Iation,as they are confiderfd by fome, and made to he the caufes of nature,, 
 appear to efcape the attention of thofe who fpeculate in this manner. Tor 
 no one of them is a caufe according to any of thofe modes which are defined 
 Vtfpcding principles. Yet, as they make it manifeft that well being has a 
 fubfilknce, and that the odd number, the ftra'glit, the equal, and powers of 
 certain numbers, are of the co-ordinaion of the beau'iful (for the feafon of 
 the year and a particular number fubfift together), and fuch other things 
 as they coUedl from mathematical theorems, — all thcfe pofTtls this power ; 
 on which account they refemble cafual accidents : for they are indeed acci- 
 dentf, but all of them accord with cich other ; but the analogous is one : 
 for in each category of being there is tiie analogous, as, for inftancc, the' 
 flraight in length is analogous to the even in fuperficies ; and perhaps the* 
 odd in number, and the white in colour. Further flill : the numbers * which 
 
 are 
 
 diere is the good, and the oppofite to the good.' He alfo admits this in nature; but he does not 
 openly grant that a better co-ordination of number is the caufe of that which is more excel- 
 lent in nature : but he rather admits, for inftance, that liours, are prior to the year, and are more 
 caufes than number itfelf, and does not afTert this of the numbers of the hours. In this, indeed, 
 he is confident witTi himfelf, as, for the purpofe of concealment, he alone directs his attentioa 
 to numbers of poflerior origin. But, fays Syrianus, " in a fimilar manner we muri; afk Ari- 
 ftotle, whence the hours always fubfifl after the fame manner ; for, it is either from Jupiter, or 
 the Sun, or fome other of thofe mundane artificers. 'I hey are, therefore, thence meafured and 
 orderly dlfpofed through the efFe£live power of numbers : and, in fiiort, why, prior to tliat w hich 
 fubfifts in another, Ihould we not contemplate that which fubfills in itfelf ?" 
 
 But that Ariftotle is not ferious in what he now fays is evident from hence ; that if we admit 
 the contrary, and allert that Ariftotle, on beholding good in particulars, neither fpeaks of the 
 caufe of this good, in confequence of not admitting that it has a caufe, nor reduces all things to 
 one principle from which they derive their perpetual fimilitude of fubfiftence and famenefs of 
 progrelfion, we muft alfo neceflarily admit that he disjoins beings, and that he forgets what 
 he has faid at the conclufion of the twelfth book of this work, " that tlie domination of many is 
 not good." 
 
 * This is alone urged againft ideal numbers, which Ariftotle fays polTcfs monads which can^ 
 rot be compared with each other ; fo that the ideal triad is sot a third part of the nine itfelf, 
 nor the half of the number fix itfelf. If, therefore, fays he, ideal numbers are fuch, they will 
 by no means be the caufes of fymphonies. For in fymphonies fimilar founds are equal, and the 
 mte is double of the upate; and, in fliort, the tetrad is the half of the oclad, and fefquitertian 
 with relation to the triad. He therefore fyllogifes as follows : Ideal numbers have different 
 monads. Numbers which compofe fymphonies have not different monads. Ideal numbers, 
 3 therefore.
 
 398 ARISTOTLE'S METAPHYSICS. Book XIV. 
 
 are in forms are not the caufes of things harmonic and the like : for thofe 
 equals in fpecies differ from each other, for the monads alfo diiler ; fo that, 
 in confequence of thefe things, forms are not to be introduced. Thefe con- 
 fequences, therefore, and ftill more than thefe, may be colleded ; but they 
 appear to afford an argument that the patrons of ideas fall into many errors 
 refpeding the generation of them, and that they cannot be confiftcnt, becaufe 
 mathematical fpecies are not, as fome fay, feparated from fenfibles, nor are 
 thefe the principles of things. 
 
 therefore, do not compofe fymphonies. Hence, he who aflerts that fymphonies fubfift through 
 thefe numbers, af&rts that which is falfe. 
 
 In anfwer to this we muft again fay, that ideal numbers do not confifl. from monads, fo as to 
 become monadic numbers, unlefs fome one is wilHng to call the ideas ©f them unitiesj or things 
 charaiSerifed by the nature of the one. Nor do they poflefs the power of immediately confti- 
 tuting lyric fymphonies, but this power is rather to be afcribed to thofe numbers which fubfift 
 in divine fouls, and in the nature of the univerfe. And, in fliort, as we are informed by Sy- 
 rianus, fuch things as the Artificer of the univerfe is faid to have produced and orderly difpofed, 
 through an energy profoundly one (ewwoij), and to have rendered confonant both to himfelf and 
 to ea.ch other, derive, according to the Pythagorjeans, their confonance from ideal numbers. 
 
 ADDITIONAL
 
 ADDITIONAL NOTES.
 
 ADVERTISEMENT. 
 
 THE defign of the following additional notes is to illuftrate the Platonic doflrine concerning 
 Ideas and the principle of the univerfe. They are chiefly extrafted from what appears to me 
 to be one of the moft: precious remains of antiquity, the MS. Commentary of Proclus on the 
 Parmenides, and from the works of Plotinus, one of the mod fublime of the intelledual philo- 
 fophers. I {hall rejoice if I have been able to add any thing of my own which may contribute 
 to elucidate the conceptions of thefe divine men, and induce the reader to abandon with gene- 
 rous ardour the grovelling contemplation of fenfible objefts, profoundly dark and incelTantly 
 flowing, for the exalted furvcy of the all-fplendid and ever-permanent forms in the world of 
 mind.
 
 ADDITIONAL NOTES. 
 
 Page 30, Note X- 
 
 JN EITHER is multitude unco-ordinated to i/je one, and feparated from itfelf, nor 
 is the one unprolific, and deftitute of a multitude adapted to it ; but this is the leader 
 of fecondary monad?, and multitude poffefles an union accommodated to its nature : 
 for all multitudes, intelligible and intelle6lual, mundane and fupermundanc, are 
 fufpended from proper monads, and are co-ordinated with each other. But thefe 
 monads are again fufpended from one monad, that the multitude of monads may not 
 be feparated from itfelf, and be multitude alone deprived of union : for it is not law- 
 ful that thofe caufcs which give union to other things fhould be divulfed from each 
 other. Thus, the caufes which impart life to other things are not deflitute of life, 
 nor are the fources of intelledi deftitute of intelligence, nor are thofe which illumi- 
 nate all things with beauty,\oid of beauty ; but they have either life, intelled, and 
 beauty, or fomething more excellent and divine than thefe. So that it is neceflary 
 that the monads which impart union to other things Ihould be united to each 
 other, or fliould poflefs fomething more excellent than union. There is not, how^ 
 ever, any thing more divine than this, except the one itfelf. But if the one is prior 
 to thefe, it is neceflary that thefe monads fhould be united to each other : for things 
 which participate of the one are united. But, if they are united, whence is their 
 union derived, if not fi-om the one itfelf? It is neceflary, therefore, that the multi- 
 tude of unities fliould fubfift; from the one; that from thefe unities, both firfl; multi- 
 tudes and thofe in a following order fliould be fufpended ; and that always things 
 more remote from the one fliould be more multiplied than thofe which have a prior 
 fubfifience. 
 
 But at the fame time it muft be obfervcd that every multitude has a twofold 
 
 monad, one co-ordinated, and the other exempt. Thus, for inftance, in fpecies, we 
 
 may behold a twofold man, one exempt, viz. the ideal man in the intelligible world, 
 
 .the other participated by the apparent man. Thus, too, the beautiful is twofold, 
 
 3 F . that
 
 402 ADDITIONALNOTES. 
 
 that which is prior to the many, and that which fubfifts in the many. And in a 
 limilar manner with rcfpcdl to the equal, the juft, and every other form. Hence, a 
 monad fubfifling in another, and a monad fubfifling by itfclf, may be feen in the fun 
 and moon, and every other natural form : for it is necefTary that thofe things which 
 fnbfift in others, and that common and participated natures fliould have, prior to- 
 themfelves, that which fubfifts from itfelf, and which is imparticipable and exempt. 
 The bond, therefore, which proximately unites multitude is that which is common, 
 in multitude. And on this account, man itfelf, or the ideal man, is different from, 
 man fubfifting in particulars, or, in other words, con-diftributed with the individuals 
 of the human fpecies. And the former of thcfe is eternal, but the latter is partly 
 ■mortal and partly immortal-. The former is intelligible, the latter fenfible. As, 
 therefore, every form is twofold, fo every whole is twofold : for forms are parts of a- 
 «crtain wholenefs. Of wholes, too, one kind is im[)articipable, and another partici- 
 pable. And this is alfo the cafe with foul : for that which generates the multitude 
 of fouls is imparticipable, and that which binds this multitude together is partici- 
 pable foul. Thus alfo, with refpedl to intelle6l, one is imparticipable, and the other 
 participable ; the former producing, and the latter connecting, intelledlual multi- 
 tude. Of beings, therefore, there is likewife a twofold monad, one imparticipable^. 
 from which all beings and the number of beings proceed, and the other participable. 
 And laftly, tJiere is a twofold one, this withdrawing itfelf from multitude, and fub:- 
 Jifting ineffably exempt from beings, but that participated by beings.. 
 
 Page 47, Note •f-. 
 
 That it is necel'iiiry that being profoundly united {sv cv) fhould fubfift prior to the 
 multitude of beings may be fhown by the following logical method. Being is either 
 homonymoufly predicated of all beings, or fynonymoufly, or it is predicated as from, 
 one and to one. But it is impofliblc that it can be predicated fynonymoufly ;. 
 lince we fay that one thing is more being, and another lefs : for the more and the 
 lefs have not any fubfiflence among things tynonymous. But whether being which 
 is profoundly one is predicated homonymoufly of all things, or whether it fubfifls 
 as from one and to one, it is necefl^ary that there fhould be a certain being prior to. 
 the multitude of beings. 
 
 This alfo may be fl^iown in a more phyfical way as follows, and which is adopted 
 by the Elean gucfl in the Sophifla. It is necefiary, if beings arc many, that fo far 
 asthcy are many they fliould differ from each other, but that fo far as they arc beine:s 
 they fh-ould be the fame ; which fartienefs mufl neceflarily cither be imparted to all 
 beings from fome other nature, or from one among the multitude of beings to the 
 rell. But, if from one among the multitude to the reft, that one will be the firft 
 
 being.
 
 A D D I T I O N A L N O T E S. 40S 
 
 fjciiig, but the reft will through it participate of being. Bat if again from fome 
 other nature, that nature, being prior to all, will confer on all the participation of 
 being. 
 
 In the third place, this inay be evinced as follows, from a more theological 
 principle. Every thing which is participated, l1ncc it fublifis in other? which par- 
 tici[)ate it, has entirely its progreflion into being from that which is iniparticipable v 
 for this is niuilipiied together with its fubjcfl recipients, each of which it generates, 
 and communicates its proper eflence to the natures of its participants. Bat, prior to 
 things participated and mingled with others, it is neceflary that things imparticipable 
 and unmingled, and which lubfift from themfelvcs, fhould be cflablifhedi and that 
 things which have a tim;,>]icity of eflence flionld fubfitt prior to relatives, and which 
 have their being in others. Hence, if thefc things are true, it is neceflary that being- 
 itfelf fhould fubtift prior to the multitude of beings, from which the being in the 
 many is derived, which has a fubfillencc participated by them. But as, prior to that 
 which participates, and that which is participated, that which is imparticipable fub- 
 fifts, fo it is neceflary that between the imparticipable and participants that which is 
 participable (hould lubfilt. Or how will things which participate be that which they 
 are faid to be, if there is nothing which is participated, and which fubfifts in the 
 participants ? Neither, therefore, is there alone that which is participated by the many, 
 ibut prior to this the imparticipable fubfifls ; nor is there alone that which is im- 
 participable, but after this there is that which is participated, and which has a co- 
 ordinated lubfiftence in the man}'. 
 
 Again : that which is being profoundly united, orfimply being, is one and many : 
 • for everything pofterior to //je one immediately poflcflcs a reprcfentation (sf^rpc^a-i;) 
 of multitude. But in one order of beings this multhude is occult, and characterized 
 by the nature of ihe one. In another order, it is multitude unfolding itfelf into li^ht : 
 and in another, it has now proceeded, and is fully unfolded. And the progreirion 
 of it is again different in different orderf, and there is not in all the fame mode of 
 reparation. But fince there is every where a monad prior to multitude, it is necef- 
 fary to fuf[)end all beings from their proper monad : for, in bodies, that which fubfifts- 
 as a whole (viz. the body of the univerJe) precedes thofe which rank as parts, and, 
 being itfelf connecficd and a whole, comprehends all the diftributed bodies in the 
 world. Thus alio in natures, one nature, and which ranks as a whole, fubfifts prior 
 to the many : for, through this one nature, partial natures, which are contrary to each 
 other, are often at the lame time circularly led as it were into union and f}-mpathy. 
 And in fouls, the monad of louls iseflabliflicd in an order more anlient than the mul- 
 titude of fouls ; and about this as a centre all fouls converge : divine fouls indeed, in the 
 firfi place, the- attendants of thefc in the feeond place, and the co-attendants {(rvmitei^oi) 
 of thefe io a third order, as Socrates afTerts in the Phaedrus. In a fimilar manner, toD^ 
 
 3 F 2, ill
 
 404 ADDITIONALNOTES. 
 
 in intellect?, one whole and imparticipablc intellcft, fird emerging into light from na- 
 tures profoundly united, generates after itfclf the uhole of intel!c6^ual multitude, 
 and every indivifiblc eflcnce. It is necefKiry, therefore, that prior to all beings 
 there fhould be the monad of being, through which all beings arc co-ordinated with 
 each other, as alfo intellects, fouls, natures, and bodies, and every thing which is in 
 any refped faid to be. For, let the one be the exempt eaufe of union j but every thing- 
 fo far as one is made to be one through this. Our inquiry however is, what con- 
 necting and uniting monad they poflefs, fo far as they are beings : for every number 
 is elevated {avYiOT^zcct) to a monad adapted to and co-ordinated with it, and from which 
 it derives its fubfiftence and its appellation, neither fynonymoufly nor cafually, but as 
 from one, and as referred to one. So that beings alfo arc from one monad, which 
 is called the firft being, through which they derive their order, and arc denominated 
 beings ; and from this all beings are in fympathy with each other, and in a certain 
 refpeCl are the fame, fo far as they proceed from one being. Parmcuides, looking ta 
 this union of all beings, thought proper to call all things one; (that being the mofl: 
 principal and the primary all, which is united to the one. It is likewife fimply all :), 
 for all things, fo far as they participate of one being, arc in a certain rcfped the fame 
 with each other. 
 
 Page 68, Note f . 
 
 The manner in which forms are participated is neither corporeal nor material^ 
 
 but is exempt from all the modes of participation which are peculiar to fecondary 
 
 and partial natures : for fenfibles do not participate of forms or ideas in the fame 
 
 manner as one body participates of another ; fince, in this cafe, the participant 
 
 either draws the whole into itfelf or a part. Thus, when we eat we partake the 
 
 whole of the food : for that which is participated, being the lefler, is able to proceed 
 
 into that which is greater than itlclf ; and fince we are compofed from elements 
 
 which rank as zvholes, we participate a part of each of them : for the fire which is in 
 
 us is from the whole fphcre of fire ; and in a fimilar manner the water and each of 
 
 the other elements which wc contain. And, as Socrates fays in the Philebus, we 
 
 participate of wholes, but wholes do not participate of us. But no fenfible nature 
 
 can receive the whole power of idea, viz. its eternal efficacy, and its perfeCl life and 
 
 intelligence. And yet we perceive, that whatever is in the fame fpecics equally 
 
 receives the ideal property imparted to that fpecies ; fo that not corporeally, but in 
 
 a very different manner, idea is in one refpedl totally, and in another not totally, in 
 
 its participants. Likewife, fince ideas abide in themfelves, they are able to be 
 
 totally prefent at the fame time with many things feparated from each other ; — a 
 
 property which cannot belong to bodies, fince they require a certain place, nor to 
 
 «:orf)oreal powers, which are infeparablc from particular lubjcdls. 
 
 In
 
 -ADDITIONAL NOTES. 405 
 
 In Hiort, he who invefligates whole and part not corporeally, but in fuch a man- 
 ner as is adapted to intelligible and immaterial forms, will perceive that every fen- 
 Iible nature participates both of the whole and a part of its paradigm : for, beeaufe 
 that ranks as caufe, and ferifibles as things caufed, and effects can by no means re- 
 ceive the whole power of their caufes, hence fcnfibles do not participate the whole 
 of idea. Thus, for int^ance, the charafteriftic peculiarity of the beautiful is every 
 where and in all things, but in fome things intcllecSiually, and in others materially. 
 And it is evident, that the participations of the more perfe6l natures participate 
 more than thofe of the natures which are remote from perfedion : and fome ac- 
 cording to more, but others according to fewer, powers : for, let the definition of 
 the beautiful itfclf be this. An inteJle6lual vital form, the caufe of fyimnetry to all 
 things. Forniy therefore, and that which is efFeflive of fymmetry are prefent with 
 every thing beautiful : for this was the charadleriftic peculiarity of the beautiful. 
 So that every thing beautiful participates the whole of this peculiarity; but its intel- 
 leHiial power is not prefent with every thing beautiful, but with a nature to which 
 foul belongs. For the beautiful in this is uniform. But neither is its vital pre- 
 rogative inherent in everything beautiful, but in a cclcftial nature (for whatever the 
 heavens contain is full of life), and whatever there may be of this kind in generated 
 natures. In gold, alio, and certain ftones we behold the fplendor of the beautiful. 
 Some things, therefore, participate of its intellectual and vital powers ; but others 
 of its vital feparate from its intelledlual ; and others, again, of its characfteriftic 
 peculiarity alone. And things more immaterial receive more powers of the beauti- 
 ful than fuch as are material. In this manner, therefore, it is proper to addrefs 
 thofe who are able to behold the incorporeal eflence of ideas. But to thofe who are 
 jof opinion that forms are participated corporeally, we muft fay, that if this were the 
 cafe, one and the fame thing mull be totally prefent at the fame time with many 
 things feparate from each other ; which would be of all things the moft abfurd. For 
 if a finger, or any other corporeal part, or any corporeal power, was at the fame time 
 in many things feparate from each other, it would be feparate from itfelf : for power 
 which is in a lubjedl will thus belong to other fubjefts, and will be feparate from 
 itfelf, fince it will fubfift from both, not being able to be feparated from either. 
 But, again, that the whole of a body Ihould be in different places at the fame time 
 is impoflible : for by divilion it appears that there may be many bodies in one place. 
 Thus, lince one body can fubfift in one place, and many bodies in many places, the 
 medium between thefc will be, many bodies in one place. The fphere of the fixed 
 ftars, and the fpheres in which the planets are carried, are bodies of this kind ; for 
 they confift of pure immaterial light. But tiat the fame body fhould be in many 
 places at the lame time is impoflible. It is therefore impoflible for a whole to bs 
 corporeally prefent with many fubje<5ts at thp fame time. 
 
 That
 
 405 ADDITIONAL NOTES. 
 
 That tlic reader may be further enabled to conceive the manner in which not 
 only ideas but all incorporeal natures arc prcfent with bodies, the following extracts 
 -from the mctaphyfical auxiliaries (aJ-op/>t«/ 'tt^^cq rcn voYira) of Porphyry are added. 
 
 Every body is in place ; but nothing eflcntially incorporeal, or anj thing of this 
 kind, lubfiits in place. 
 
 Things eflcntially incorporeal, becanfe they are more excellent than all body and 
 place, arc every where, not with interval, but impartibly*. 
 
 Things effentially incorporeal are not locally prcfent with bodies, but they are 
 prefent with them whenever they arc willing; and this by verging to them, fo far 
 as thev are naturally adapted to verge. Hence, not being locally prcfent wiih 
 them, they arc prcfent by habitude, (i. e. by proximity or alliance). 
 
 Things eflcntially incorporeal are not prcfent in hypoftafis {i. e. fubfiftcnce) and 
 eflence ; for thev are not mingled with bodies ; but, by an hvpoftalis from inclina- 
 tion, they impart a certain power proximate to bodies : for inclination gives fub- 
 fiftcnce to a certain fecondary power proximate to bodies. 
 
 Soul is a certain medium between an eflenee indivifible and divifible about 
 bodies : but intellc61 is an impartible eflenee alone. And qualities and material 
 forms are divifible about bodies. 
 
 Not every thing which a6ls on anotbcr, eflcifts that which it eftc61s by approxi- 
 mation and contacl ; but thofe things which a(51 from approximation and contact 
 ulb approximation according to accident. 
 
 Soul is bound to body by converting itfclf to the pafllons originating f om 
 body ; aiid it is again liberated by becoming iinpafllvc to body. 
 
 That which nature has bound, nature alfo difiblves, and that which foul has bound, 
 f<jul alfo ciiflolves. Nature, indeed, bound body in foul, but foul bound hcrfelf in 
 body. Ilcnce nature liberates body from foul ; but foul liberates hcrfelf from 
 ■ body. 
 
 Death therefore is twofold ; one, with which all men are acquainted, when the 
 .body is liberated from the foul; but the other peculiar to philosophers, when the 
 foul is liberated from the body ; nor does the one entirely follow the other. 
 
 We do not underfland fimilarly in all things, but in a manner accommodated to 
 .the cfl"ence of each. Thus, in intellect, we underfland intelleflually ; in foul, ra- 
 tionally; in plants, fpermatically ; in bodies, idolieally, or after the manner of an 
 image; and, in that which is above all things, fuperintcIlccTlually and fupcrcflcnT 
 tially. 
 
 Incorporeal hypoftafes in defcending are divided and multiplied about individuals, 
 through a fubjecflion of power ; but in afcending they are united, and return to » 
 i;oil.e£icd fubliftcncc through abundance of power. 
 
 * i. e. Without parts. 
 
 The
 
 A D D I T I O N A L N O T E S. 407 
 
 The homonymous not only takes place in bodies, but life alio ranks among things 
 which are multitaiioufly predicated : for there is one life of a plant, another of that 
 which is animated, another of foul, another of that which is intelledlual, and an- 
 other of that nature which is above intelledl. For thefe alto live, though nothing 
 which fubfifts from them obtains a fimihir life. 
 
 The pafiior. of bodies is diflerent from that of incorporcals : for the paflion of 
 bodies is with mutation; but of foul the aptitudes and the paflions are energies. 
 They are not, iiowcver, fimilar to the heat and cold of bodies. Hence, if the paf- 
 fion of bodies is with mutation, we mull fay that all incorporeal natures are im- 
 padive. For, ihings which are feparated from matter and bodies are in energy the 
 fame ; but things which approach to matter and bodies are thcmfelvcs, indeed, im- 
 patTive, but the natures in which they are beheld fufFer. For, when the animal 
 perceives, the foul is fimilar to feparate harmony, moving from itfelf the harmonifed 
 chords, but the body is fimilar to the harmony in the chords which is infeparabic 
 from them. The caufe of motion is the animal, in confequence of its being ani- 
 mated, but it is analogous to the mufician through its harmonic arrangement ; but 
 the bodies which are ftruck through fenfitive motion are fimilar to the harmonifed 
 chords : for there alfo feparate harmony does not fufFer, but the chord. And the- 
 mufician indeed moves, according to the harmony which he contains; yet the 
 chord would not be mufically moved, though the mufician (hould be willing, unlefs 
 this were dictated by harmony. 
 
 The appellation of incorporcals is not thus denominated, like bodies, according tc 
 the communion of one and the fame genus, but according to a naked privation with 
 rcfpe<5l to bodies. Hence, nothing prevents fome of them from fubfifting as beings, 
 and others as non-beings,, fbme from being prior and others pofierior to bodies, 
 and fome from being feparate and others infeparabic from a corporeal nature. Likc-- 
 wife nothing prevents tome of them from fubfifiing from themfelves, but others 
 from being indigent of other natures to their lubfittenee ; and ibme from being the 
 fame with felf-motive energies and lives, but others from fubfilling together with 
 certain vital energies. For they are denominated according to a negation of that 
 which they are not, and not according to an afiirmation of that which they are. 
 
 In incorporeal lives while progreffions are etFe6tcd, prior natures remain (table 
 and firm, nothing belonging to them being corrupted or changed in giving fubfift- 
 ence to things inferior; fo that,, neither are the things which thence fubfifl: produced 
 with a certain corruption or mutation, nor docs any thing belonging to them fubfiH: 
 in fuch a manner as generation, which participates of corruption, and mutation; 
 They arc, therefore, unbegotten and incorruptible, and on this account are produced 
 in an unbegotten. and incorruptible manner. 
 
 Concerning that which is beyond intellect many things are afTerted by intelli- 
 gence r
 
 408 ADDITIONALNOTES. 
 
 gence ; but it is beheld by a privation of intelligence better than by intellectual per- 
 ception. Juft as, with relpccO; to him who is afleep, many things are afferted through 
 vigilance, of whieh the knowledge and apprchenfion is obtained through fleep. For 
 the limilar is known by the fimilar, becaufe all knowledge is an aniiniL.tion to the 
 ob)e(!n of knowledge. 
 
 The fubfitlence of body docs not in any refpe£t prevent that which is eflentially 
 incorporeal from being prefent where it withes to be, and as it wills. For, as that 
 which is void of bulk is incomprehenfible by body, and has no relation whatever to 
 it, lb that which fubfifis with bulk cannot oppofe (avs'TriTr^oa-SriToy) that which is incor- 
 poreal, but lies like non-entity before it. Nor does an incorporeal nature pervade 
 locally where it pleafes; for place is confubfitlent with bulk. Nor is it contra6led 
 by the prefence of bodies. For, whatever fublifls in that which has bulk is able to 
 be contradted by it, and to make a tranfition locally. But that which is entirely 
 without bulk and magnitude can neither be detained by bulk, and does not partake 
 of local motion. Hence, by a certain difpofition it is found to be there where it is 
 inclined to be, at the fame time being every where and no where in place. By a 
 certain difpofition, therefore, it is cither above the heavens, or is contained in fome 
 part of the iiniverfc. However, when it is contained in a certain part of the world,, 
 it is not vifible to the eyes, but its pretence becomes apparent from its works. 
 
 That which is incorporeal when it is detained in body, is not fo inclofcd as a wild 
 beafi; in a cage ; for no body is able thus to inclofe and comprehqnd it : nor as any li- 
 quor or vapour in a bladder. But it is rcquifite that an incorporeal efTence fhould give 
 fubfiftence to powers verging from a union with its nature to that which is external ; 
 by which powers when it defcends it becomes connected with body. Hence, its de- 
 tention in body is etFedted through an ineffable extenfion of itlelf, and on this ac- 
 count nothing elt'e binds it, but itfclf binds itfeif. Neither, therefore, is it libe- 
 rated when the body is wounded and corrupted, but when itfeif turns itfeif from cor- 
 poreal pafiion. 
 
 No whole and perfect effence is converted to its own progeny ; but all perfedl 
 Dfltures arc led back to the caufes by which they were generated, even as far as to 
 the mund:ine body. For, being perfcci, it is elevated to the mundane Ibul which is 
 intellectual, and through this is circularly moved. But the foul of this body is ele- 
 vated to intelletTt, and intellect to that which is firft. All things, therefore, ex- 
 tend themlelves to this beginning from that which is lafl, according to the peculiar 
 ability of each. But the rcdudtion to that which is firft is either proximate or re- 
 mote. Hence, thefe are not only faid to afpire after divinity, but alio to enjoy him 
 as far as they are able. But in partial natures, and which" are able to verge to many 
 things, a converfion to their progeny belongs. Hence, in Jhefe guilt, in thefe dif- 
 graceful perfidy is found. Matter, therefofc, defiles thefe, becaufe they decline to 
 
 it.
 
 A D D I T I O N A L N O T E S. -109 
 
 it, at the fame time that they poHefs the power of converting thcmfelves to a divine 
 nature. So that perfc6lion gives fiibfiftence to fecondary (rom prior natures, pre- 
 ferving them converted to things fir(l ; but the imperfcd converts things firft to 
 things fubordinatc, and caufcs them to love natures which have apodatiled [jrior to 
 themfelves. 
 
 God, intellect, and foul arc every where, becaufe they arc no where ; but God is 
 every where and no where, in all the things portcrior to him, and alone is as he is, 
 and as he wills. Intcllcft is in God indeed, but is every where and no where in 
 things pofterior to itfelf ; and foul is in intelle6l and in God, but is every where and 
 no where in body : but body is in foul, in intelledV, and in God. And, though all 
 beings and non beings proceed from and fubfill in God, yet he is neither beings, nor 
 does he lubfift in them : for, if he was alone every where, he would be all things, 
 and in all ; but finco he is alfo no where, all things are generated through him ; 
 and they are contained in him, bccaulc he is every where; but are different from him, 
 becaufe he is no where. In like manner iutelle(fl, being every where and no where, 
 is the caufe of fouls and of things pollerior to Ibuls ; and it is neither foul, nor the 
 natures pollerior to foul, nor does it fublilt in thefe ; becaufe it is not only every 
 where in things pofterior to itfelf^, but alio no where. And foul is neither body, nor 
 in body, but is the caufe of body ; becaufe, being every where with refpc6l to body, 
 it is no where. And this progreffion of things extends as far as to that which is 
 jicither able to be at the fame time every where, nor yet no where, but partially par- 
 ticipates of each. 
 
 Page 294, Note *. 
 
 A riftotle appears in his theological writings to have afcended no higher than in- 
 telligible intelledt, or the Phanes of Orpheus, and to have called this the firll caufe, 
 as being the firll eflhbie, all beyond this being according to antient theologifis inef- 
 fable. But that Ariftotle knew there was fomething even beyond this, is evident 
 from the following citation from the fecond book of the Commentaries of Simplicius 
 in Arift. de Ccelo, p. 1 13. — Or/ jj.;'/ ya^ vou ti koci vtvs^ rov 'jow h(^iTTor;Krig, kcxi vtt;^ 
 T/jy ov<nocv, drjXog stti vrct^x rois i<r'/jxTOig rov (Si^T^iov Trspi 7r^0(rsv//ig, ^tct^^Yj^yiv X-yoov, OTI 
 B=c; i'l vcvg z'fin, ■-} xi Kui v'tts^ vow. i.e. " That Ariflotlc knew that there is alfo 
 ibmething above intelledl and eflence is evident from the latter part of his book On 
 Prayer, in which he clearly fays, that God is either intellcdl, or fomething above in- 
 tclledt." 
 
 Page 3° 5' Note f. 
 
 That it is not proper to Hop at conceptions of pofterior origin, or, in modern lan- 
 guage, abftracl ideas, i. c. notions gained by an abfiradtion from fenfiblc particulars, 
 
 3 G but
 
 410 A D D I T I O N A L N O T E S. 
 
 but that we Ihould proceed to thofe cflcntial reafons which arc allotted a perpetua? 
 fubfifience within the foul, is evident to thofe who are able to furvey the nature of 
 things. For, whence is man able to collcdt into one by reafoning the perceptions 
 of many fenfes, and to confider one and the fame unapparent form prior to things 
 apparent, and feparated from each other'; but no other animal that we are ac- 
 quainted with, furvcys this fomething common, for neither does it potiefs a rational 
 eflence, but alone employs fcnfc, and appetite, and imagination ? Whence, then, do 
 rational fouls generate thefe univerfals, and recur from the fenfes to that which is 
 the obje6l of opinion ? It is becaufe they eflentially poflefs the gnoftically produc- 
 tive principles of things : for, as nature potTefles a power produ6live of fenfibles, 
 by containing reafons, or produclive principles, and fadiions and connccSls fenfibles, 
 fo as by the inward eye to form the external, and in a fimilar manner the finger, and 
 every other particular; fo he who has a common conception of thcfc, by previoufly 
 pofleffing the reafons of things, beholds that which each pofletTes in common. For 
 he does not receive this common fomething from fenfibles ; fince that which is 
 received from fenfibles is a phantafm, and not the obje6t of opinion. It likewife 
 remains within fuch as it was received from the beginning, that it may not be falfe, 
 and a non-entity, but does not become more perfe<St and venerable, nor does it ori- 
 ginate from any thing elfe than the foul. Indeed, it muft not be admitted that 
 nature in generating generates by natural reafons and meafures, but that foul in 
 generating docs not generate by animaftic reafons and caufcs. But if matter 
 pofl^effes that which is common in the many, and this fomething common is efien- 
 tial, and more effence than individuals; for this is perpetual, but each of thole is 
 corruptible, and they derive their very being from this, fince it is through form that 
 every thing partakes of eflence, — if this be the cafe, and foul alone polfcfics things 
 common which are of pofterior origin {va-Ts^oyivrj xciva), do we not make the foul 
 more ignoble than matter ? For the form which is merged in matter will be more 
 perfect and more efl^encc than that which rcfides in the foul ; fince the latter is of 
 pofterior origin, but the former is perpetual ; and the one is after and connecT.ive of 
 the many. To which we may add, that a common phantafm in the foul derives its 
 fubfifience from a furvey of that which is common in particulars. Hence it tends to 
 this ; for every thing adheres to its principle, and is faid to be nothing elfe than a 
 predicate ; lb that its very eflence is to be predicated of the many. 
 
 Further fiill : the univerfal in the many is lefs than each of the many ; for by cer- 
 tain additions and accidents it is furpaflcd by every individual. But that which is of 
 pofterior origin (i. c. univerfal abllraded from particulars) comprehends each of the 
 many. Hence it is predicated of each of thefe ; and that which is particular is 
 contained in the whole of this univerfal. For this fomething common, or abfiradl 
 idea, is not only predicated of that fomething common in an individual, but like- 
 3 wile
 
 ADDITIONAL NOTE S. 411 
 
 wile of the whole riibjc6l. How then can it thence derive its fubfiftence, and 
 be completed from that which is common in the many ? For, if from the many 
 themfclves, where do we fee infinite men, of all which we predicate the fame 
 thing ? And if from that which is common in the many, whence is it that 
 this abflradl idea is more comprehenfive than its caufe ? Hence it has a dif- 
 ferent origin, and receives from another form this power which is comprehen- 
 five of every individual ; and of this form the abfiract idea which fubfifts in opinion 
 is an image, the inward caufe being excited from things apparent. To which we 
 may add, that all demon ft rat ion, as Ariftotle has Ihown in his Laft Analytics, is 
 from things prior, more honourable, and more univerfal. How, therefore, is univer- 
 fal more honourable, if it is of poftcrior origin ? For, in things of pofterior origin, 
 that which is more univerfal is more uneflential ; whence fpecies is more eflenee 
 than genus. The rules, therefore, concerning the moft true demonftration mufl: be 
 fubverted, if we alone place in the foul miiverfals of poflerior origin : for thefe are 
 not more excellent than, nor are the caufes ofj nor are naturally prior to, particulars. 
 If, therefore, thefe things are abfurd, it is neccflary that eflential reafons fhould fub- 
 fift in the foul prior to univerfals which are produced by an abftradlion from fenfibles. 
 And thefe reafons or produdtive powers are indeed always exerted, and are always 
 efficacious in divine Ibuls, and in the more excellent orders of beings; but in us 
 they are fometimes dormant, and fometimcs in energy. Again : that the foul con- 
 tains eflential forms, and that, unlefs this be admitted, there can be no fueh thing as 
 fcience, may be thus proved. 
 
 If dianoetic and intelledual are better than fenfible knowledge, it is neeeflary 
 that the things known by the dianoetie power, and by intelleft, fhould be more 
 divine than thofe which are known by fenfe : for, as the gnoftie powers which are 
 co-ordinated to beings are to each other, fuch alfo is the mutual relation of the things 
 which are known. If, therefore, the dianoetic power and intclledl fpeculate fepa- 
 rate and immaterial forms, and likewife things univerfal, and which fubfift in them- 
 fclves, but lenfe contemplates things partible, and which are infeparable from fub- 
 jecls, it is necctlary that the fpedtaeles of the dianoetie power and of intellecl fhould 
 be more divine and more eternal. Univerfal?, therefore, are prior to particulars, 
 and things immaterial to things material. Whence, then, docs the dianoetic power 
 receive thefe ? for they do not always fubfift in us according to energy. It is how- 
 ever neceffary, that things in energy fhould precede thofe in capacity, both in things 
 intellectual and in eflences. Forms, therefore, fubfift elfewhere, and prior to us, in 
 divine and feparate natures, through whom the forms which we contain derive their 
 peifcdion. But thefe not fubfifting, neither would the forms in us fubfift: for 
 they could not be derived from things imperfcft : finee it is not lawful that more 
 excellent natures fliould be either generated or perfedlcd from lueh as are fubordi- 
 
 3 G 2 nate
 
 412 ADDITIONAL NOTES. 
 
 nate. Whence, too, is this multitude of forms in the mulliUnlc of louls derived .* 
 For it is every where nccefJary, prior to multitude, to conceive a monad liom which 
 the multitude proceeds : for, as the multitude of fenfibles was not generated, except 
 from an unity, which is better than fenfibles, and which gave fubfiftenceto that which 
 is common in particulars ; fo, neither would the multitude of forms fubfift in fouls, 
 fuch as the juft itfelf, the beautiful itfelf, &c. which fubfill in all fouls in a manner 
 accommodated to the nature of foul, without a certain generating unity, which is 
 more excellent than this animaftic multitude: juft as the monad from which the 
 multitude of fenfibles originates is fuperior to a fenfible elTence, comprehending 
 unitedly all the variety of fenfibles. Is it not alfo ncceflary that, prior to fclf- 
 motive natures, there fhould be an immoveable form ? P'or as fclf-motive reafons 
 tranfcend tliofe which are alter-motive, or moved by others, after the fame manner 
 immoveable forms, and which energite in eternity, are placed above felf motive 
 forms which are converfant with the circulations of time : for it is every where 
 requifite that a ftable fhould precede a moveable caufe. If, therefore, there are 
 forms in fouls which arc many, and of a felf-motive nature, there are, prior to ihefe,. 
 intelle6!ual forms. In other words, there are immoveable prior to felf-motive 
 natures, fuch as are monadic prior to fuch as are multiplied, and the perfecl prior 
 to the imperfed; It is alfo requifite that they fliould fubfift in energy ; fo that if 
 there are not intclle6lual, neither are there animallic forms : for nature by no means 
 begins from the imperfeft and the many ; fince it is necefiary that multitude fhould 
 proceed about monads, things imperfc6l about the perfedl, and things moveable 
 about the immoveable. But if there are not forms eflentially inherent in foul, there 
 is no place left to which any one can turn his dianoetic power, as Parmenides in 
 Plato very juftly obferves : for phantafy and fenfe neccflurijy look to things con- 
 nafcent with themfelves. But of what fliall we poffcfs a dianoetic or fcicntific 
 knowledge, if the foul is deprived of forms of this kind .? For we fhall not make 
 our fpeculation about things of pofterior origin, fince thefe are more ignoble than 
 fenfibles themfelves, and the univerfals which they contain. How then will the 
 objecfls of knowledge, which are co-ordinate to the dianoetic power, be fubordinate 
 to thofe which arc known by fenfe ? It remains, therefore, that we fliall not know 
 any thing elfc than fenfibles. But if this be the cafe, whence do demonftrations 
 originate ? Denionfiralions, indcad, arc from thofe things which arc the caufes of the 
 things demonfiratcd, which are prior to them according to nature, and not with 
 relation to us, and which are more honourable than the conclufions v.hlch arc 
 unfolded from them. But the things from which dcmonflrations are formed are 
 univerfals, and not particulars. Univerfals, therefore, are prior to, and are more 
 caufal and more honourable than, particulars. Whence, likewife, are definitions.^ 
 For definition proceeds through the cfiential reafon of the foul : for we firft define 
 
 that
 
 A D D I T I O N A L X O T E S. 413 
 
 (hat which is common in particulars, poflcfling within, that form, of which the 
 Ibmcthing common in thefe is the image. If, therefore, definition is the principle 
 of demonftration, it is neceflary that there fhoiild be another definition prior to 
 this, of the many forms and cHential rcafons which the foul contains : for fin ce, as 
 we have before faid, the jiift itfclf is in every foul, it is evident that there is fome- 
 thing common in this multitude of the juft, whence every foul, knowing the reafon 
 of the jull contained in its cfience, knows, in a fimilar manner, that which is in all 
 other fouls. But, if it poficfles fomething common, it is this fomething common 
 which we define, and this is the principle of demonftration, and not that univerfal 
 in the many, which is material, and in a certain refped mortal, being co-ordinated 
 with the many : for, in dcmonftrations and definitions, it is requifite that the whole 
 of that which is partial iLould be comprehended in univerfal and definition. But 
 the definitions of things common in particulars do not comprehend the whole of 
 particulars : for, can it be faid that Socrates is the whole of rational mortal animal, 
 which is the definition of man ? fince he contains many other particulars, which 
 caufe him to pofiefs charafleriftic peculiarities. But the reafon of man in the foul 
 comprehends the whole of every individual ; for it comprehends uniformly all the 
 powers which are beheld about the particulars of the human fpecies : And in a 
 fimilar manner with refpeft to animal : for, indeed, the univerfal in particulars is 
 lefs than the particulars themfelves, and is lefs than fpecies ; fince it does not pofl^efs 
 all differences in energy, but in capacity alone ; whence, alfo, it becomes as it 
 were the matter of the fuececding formal differences. But the reafon of man in 
 our foul is better and more comprehenfive ; for it comprehends all the differences 
 of man unitedly, and not in capacity, like the univerfal in particulars, but in energy. 
 If, therefore, definition is the principle of demonftration, it is requifite that it 
 fhould be the definition of a thing of that kind, which is entirely comprehenfive of 
 that which is more partial. But of this kind are the forms in our foul, and not the 
 forms which fubfill in particulars. Thcfe, therefore, being fubvertcd, neither will 
 it be poffible to define. Hence, the definitive together with the demonftrative 
 art will periiT), abandoning the conceptions of the human mind. The divifive art, 
 alfo, together with thcfe will be nothing but a name : for the whole employment of 
 divifions is to fcparate the many from the one, and to diftribute things pre-fubfi(ting 
 unitedly in the whole, into their proper differences, not adding the differences ex- 
 ternally, but contemplating them as inherent in the genera themfelves, and as di- 
 viding the fpecies ft om each other. Where, therefore, will the work of this art 
 be found, if we do not admit that there are eficutial forms in our foul ? For he 
 who l"uppofes that this art is employed in things of poftcrior origin, i. e. forms 
 abftraded from fenfibles, perceives nothing of the power which it poffeftes : for, to 
 divide things of poftcrior origin, is thebufinefsof the divifive art, energifing accord- 
 ing;
 
 414 ADDITIONALNOTES. 
 
 ing to opinion ; but, to contemplate the eflential difl^erences of the reafons in the 
 foul, is the employment of dianoetic and fcientific divifion, which alfo unfolds 
 united powers, and perceives things more partial branching forth from fuch as arc 
 more total. By a much greater priority, therefore, to the definitive and demon- 
 flrative arts will the divifive be entirely vain, if the foul does not contain eflential 
 reafons : for definition is more venerable, and ranks more as a principle, than de- 
 monftration, and, again, divifion than definition : for the divifive gives to the defi- 
 nitive art its principles, but not vice vcrfa. The analytic art, alfo, mufl perifli to- 
 gether with thefe, if we do not admit the eflential reafons of the foul. For, as we 
 have before obferved in the notes to the thirteenth book, the analytic is oppofed to 
 the demonllrative method as refolving from things caufed to caufes, but to the de- 
 finitiv£, asproceeding from compofites to things more fimple, and to the divifive, 
 as afcending from things more partial to fuch as are more univerfal. So that, thofe 
 methods being deftroyed, this alfo will perifh. If, therefore, there are not forms or 
 ideas, neither fhall we contain the reafons of things. And, if we do not contain the 
 reafons of things, neither will there be the dialectic methods according to which 
 we obtain a knowledge of things, nor fliall we know where to turn the dianoetic 
 power of the foul . 
 
 Page 321, Note -}~. 
 
 The following additional arguments in defence of the Platonic doctrine of ideas 
 are given for the fake of the liberal and Platonic reader. The whole is nearly 
 extracted from the MS. Commentary of Proclus on the Parmenides. 
 
 This vifible world is cither felf-fubfiftent, or it derives its fubfiflence from a 
 fuperior caufe. But if it is admitted to be fclf-fubfiflent, many abfurd confcquences 
 will enfue: for it is ncccffliry that every thing fclf-fubfiftcnt fliould be impartible; 
 becaufe, every thing which makes and every thing which generates is entirely in- 
 corporeal. For bodies make through incorporeal powers ; fire by heat, and Ihow 
 by coldnefs. But if it is neceflary that the maker fliould be incorporeal, and in 
 things felf-fubfiftent the fame thing is the maker and the thing made, the generator 
 and the thing generated, that which is felf-fubfiflent will be perfcdiy impartible. 
 But the world is not a thing of this kind : for every body is every way divifible, 
 and confequently is not felf-fubfifient. Again : every thing felf-fubfiftent is alfo 
 felf-energetie. For, as it generates itfelf, it is by a much greater priority naturally 
 adapted to energife in itfelf, fince to make and to generate are no other than to 
 cnergife. But the world is not fclf-motive, becaule it is corporeal. No body, 
 therefore, is naturally adapted to be moved, and at the fame time to move according 
 to the who'e of itfelf For neitlicr can the whole at the fame time heat itfelf, and 
 be heated by itfelf: for becaufe it is heated, it will not yet be hot, in confequence 
 
 of
 
 ADDITIONAL NOTES. 415 
 
 of the heat being grafliialiy propagated through all its parts ; but becaufc it heats, 
 it will pofTefs heat, and thus the fame thing will be, and yet will not be hot. As, 
 therefore, it is impoflible that any bqdy can move itfelf according to internal change, 
 neither can this be cfteded by any other motion. And, in lliort, every corporeal 
 motion is more fimilar to paffion than to energy ; but a felf-motive energy is im- 
 material and impartible : lb that, if the world is corporeal, it will not be felt-motive. 
 But if not felf-motive, neither will it be felf-fubfiftent. And if it is not felf-fubfiftent, 
 it is evident that it is produced by another caufe. 
 
 For again : that which is not felf fubfiftent is twofold, viz. it is either better than, 
 or inferior to, caufe. And that which is more excellent than caufe*, as is the in- 
 cfFiiblc principle of things, has fomething polterior to itfclt', fuch as is a felf-fubfiftent 
 nature. But that which is fubordinate to caule is entirely fufpended from a felf- 
 fubfiftcnt caule. It is necefiiiry, therefore, that the world fhould fubfift from an- 
 other mora excellent caufe. But with refpeA to this caufe, whether does it make 
 according to free will and the reafoning energy, or produce the univerfe by its 
 very eflence-j- ? for, if according to free will, its energy in making will be unliable 
 and ambiguous, and will fubtifb ditFerently at different times. The world therefore 
 will be corruptible : for that which is generated from a caufe moving differently at 
 different times, is mutable and corruptible. But if the caufe of the univerfe 
 operated from reafoning and inquiry in producing the world, his energy could not 
 be fpontancous and truly his own ; but his cflence would be fimilar to that of the 
 artificer, who does not derive his produdions from himfelf, but procures them as 
 fomething adventitious by learning and inquiry. Hence we infer that the world 
 is eternal, and that its maker produced it by his very effence ; for, in fhort, every 
 thing which makes according to free will has alfo the eflential energy. Thus, 
 our foul, which energifes in many things according to free v.ill, imparts at the 
 fame time life to the body by its very eflence, which life does not depend on 
 our tiee will ; for, otherwife, the animal from every adverfe circumftance would be 
 difitblved, the foul on fuch occafions condemning its aflbciation with the body. 
 But not every thing which operates from its very eflence, has alfo another energy 
 according to free will. Thus, lire heats by its very eflence alone, but produces 
 nothing from the energy of will ; nor is this effeded by fnow, nor, in fliort, by any 
 body, fo far as body. If, therefore, the eflential energy is more extended than 
 that of free will, it is evident that it proceeds from a more venerable and elevated 
 caufe. And this very properly : for the i,Teative energy of natures that operate from 
 their very eflence is unattended with anxiety. But it is cfpccially neceflary to corj- 
 
 * This is demonftrated by Proclus in his Elements of Theology. 
 
 f This mode of operation wc have explained in a note to the twelfth book. 
 
 ceive
 
 416 ADDITIONAL NOTES. 
 
 ceive an energy of this kind in divine natures ; fincc we alfo then live more free 
 from anxiety, and with greater eafe, when our life is divine, or according to virtue. 
 If, therefore, there is a caufe of the univerfe operating from his very eflence, he is 
 that primarily which his produftion is lecondarily ; and that which he is primarily 
 he imparts in a fccondary degree to his produdion. Thus, fire both imparts heat 
 to fomething elfe, and is itfelf hot, and foul imparts dife, and poffeUcs life ; and 
 this reafoning will be found to be true in every thing which operates eflentially. 
 The caufe of the univerfe, therefore, fabricating from his very eflence, is that pri- 
 marily which the world is fecondarily. But, if the world is full of all-various forms, 
 thelc will fubfift primarily in the caufe of the world: for it is the fame caufe which 
 gave fubfiftence to the fun and moon, to man and horfe. Thefe, therefore, are 
 primarily in the caufe of the world ; another fun befides the apparent, another man, 
 and, in a fimilar manner, every other form. There are, therefore, forms prior to 
 fenfibles, and demiurgic caufcs of the phscuomcna prc-fubfifting in the one caufe of 
 the univerfe. 
 
 But if any one fliould fay that the world has indeed a caufe, yet not producing, 
 but final, and that thus all thhigs are orderly difjiofed with relation to this caufe, 
 it is fo far well indeed, that they admit the good to prefide over the univerfe. But, 
 it may be aflced, whether does the world receive any thing from this caufe, or no- 
 thing according to defire ? for, if nothing, the defire by which it extends itfelf to- 
 wards this caufe is vain. But if it receives fomething from this caufe, and this caufe 
 not only imparts good to the world, but imparts it eflcntially, by a much greater 
 priority, it will be the caufe of exiftcnce to the univerfe, that it may impart good to 
 it cflentially ; and thus he will not only be the final, but the producing caufe of the 
 univerfe. 
 
 In the next place, let us direct our attention to the ph:cnomcna, to things equal 
 and unequal, fimilar and dilTimilar, and all fuch fenfible particulars as are by no 
 means truly denominated : for where is there equality in fenfibles which ""are 
 mingled with inequality ? where fimilitude in things filled with difiimilitudc ? 
 where the "beautiful among things of which the lubjecl is bafe ? where the good 
 in things in which there is capacity and the imperfect ? Each of thcfc fenfible par- 
 ticulars, therefore, is not that truly which it is faid to be : for, how can things, the 
 nature of which confifis in the impartible and in privation of interval, fubfifi pcrfedjy 
 in things partible, and endued with interval ? But our foul is able, both to conceive 
 and generate things far more accurate and pure than the phacnomcna. Hence, it 
 cprrecls the apparent circle, and ])oints out how far it falls Ihort of ihc j>cifcctly 
 accurate. And it is evident that in fo doing it beholds another form mure beauti- 
 ful and more perfed than this : for. unlefs it beheld fomething more pure, it could 
 Dot fay that this is not truly beautiful, and that is not in every rcfpcd equal. If, 
 
 therefore.
 
 ADDITIONAL NOTES. 417 
 
 therefore, a partial foul fiich as ours is able to generate and contemplate in itfclf 
 things more pcrfcdl: than the phaenomena, fuch as the accurate fphere and circle, 
 the accurately beautiful and equal, and, in a fimilar manner, every other form, 
 but the caufe of the univerfe is neither able to generate, nor contemplate, things 
 more beautiful than the phzenomena, how is the one the fabricator of the univerfe, 
 hut the other of a part of the univerfe ? For a greater power is effective of things 
 iTnoreperfed, and "a more immaterial inteile6t contemplates more excellent fpedlacles. 
 The maker of the world, therefore, is able both to generate and underftand forms 
 much more accurate and perfect than the phaenomena. Where, then, does he 
 generate, and where does he behold them ? Evidently, in himfelf : for he con- 
 templates himfelf. So that, by beholding and generating himlclf, he at the fame 
 time generates in himfelf, and gives fubfiftence to forms more immaterial and more 
 accurate than the phaenomena. 
 
 In the third place, if there is no caufe of the univerfe, but all things are from 
 chance, how are all things co-ordinated to each other, and how do things perpe- 
 tually fubfift ? And whence is it, that all things are thus generated according to 
 nature with a frequency of fubfiltence ? for whatever originates from chance does 
 not fubfift frequently, but fcldom. But if there is one caufe, the^ fouree of co-ordi- 
 nation to all things, and this caufe is ignorant of itfelf, muft there not be fome 
 nature }>rior to this, which, by knowing itfelf, imparts being to this caufe ? for it is 
 impoQible that a nature which is ignorant fliould be more excellent than that 
 which has a knowledge of itfelf. If, therefore, this caufe knows itfelf, it is evident 
 that, knowing itfelf to be a caufe, it mufl; alfo know the things of which it is the 
 caufe -, fo that it will alfo comprehend the things which it knows. If, therefore, 
 intellect is the caufe of the univerfe, it alfo co-ordinated all things to each other : 
 for there is one artificer of all things. But the univerfe is various, and all its parts 
 do not participate either of the fame dignity or order. Who is it then that mca- 
 lures the dignity of thefe, except the power that gave them fubfiftence ? Who dif- 
 tributcd every thing in a convenient order, and fixed it in its proper feat ; the fun 
 here, and there the moon, the earth here, and there the mighty heaven, except the 
 being by whom thefe were produced ? Who gave co-ordination to all things, and 
 produced one harmony from all, except the power who imparted to every thing 
 its cflence and nature ? If, therefore, he orderly difpofcd all things, he cannot be 
 ignorant of. the order and rank which every thing maintains in the univerfe : for to 
 operate in this manner would be the province of irrational nature, and not of a 
 divine caufe, and would be the chara6icrifl.ic of necefhty, and not of intellectual 
 providence. Since, if, intcllcdually perceiving himfelf, he knows himlclf, but know- 
 ing himfelf and the eflencc which he is allotted, he knows that he is an immoveable 
 caufe, and the objecft of defire to all things, he will alfo know the natures to which 
 
 3H he
 
 418 ADDITIONAL NOTES. 
 
 he is (Icfirablc : for be is not dcfirable from accident, but eflentially. He will there- 
 fore cither l)e ignorant of what he is eflentially, or, knowing this, he will alfo know 
 that he is the objccl of defire; and, together with this, he will know that all things 
 ' defire him, and what the natures are by which he is dcfired : for, of two relatives, to 
 know one definitely, and the other indefinitely, is not the charadterifiic of fcicnce, 
 and much lefs of intellectual perception. But, knowing definitely the things by 
 which he is defired, he knows the caufes of them, in confcquence of beholding 
 himfelf, and not things of a poflerior nature. Ifj therefore, he does not in vain 
 poflx;fs the caufes of all things, he muft necefllirily, according to them, bound the 
 order of all things, and thus be of all things the immoveable caufe,as bounding their 
 order by his very elience. 
 
 But whether tball we fay that, becaufe he defigned to make all. things, he knew 
 them, or, becaufe he underftands all things, on this account he gave fubfifience to 
 all things ? But if, in confequence of defigning to make all things, he knows all 
 things, he will pofi"efs inward energy, and a converfion to himfelf fubordinate to 
 that which proceeds outwardly, and his knowledge of beings will fubfill for the fiika 
 of things different from himfelf. But if this is abfurd, by knowing himfelf he will 
 be the maker of all things. And, if this be the cafe, he will make things external 
 limilar to thofe which he contains in himfelf : for fuch is the natural order of things, 
 that externally proceeding (liould be fufpended from inward energy, the whole 
 world from the all-perfedl monad of ideas, and the parts of the vifible univerfe from 
 monads which are leparated fjpm each other. 
 
 In the fourth place, we fay that man is generated from man> and from every thing 
 its like. After what manner therefore are they generated ? lor you will not lay that 
 the generation of thefe is from chance : for neither nature nor divinity makes any 
 thing in vain. But, if the generation of men is not from chance, whence is it?. 
 You will fav. It is evidently from feed. Let it be then admitted, that man is from 
 feed; but feed poflelTcs productive powers in capacity, and not in energy. For, 
 fince it is a body, it is not naturally adapted, to poflefs productive powers impartiblv 
 and in energy : for every where a fubfifiencc in energy precedes a fubfillence in 
 capacity ; fince, being imperfeCl, it requires the aflifiance of fomething elfe endued 
 with a perfective power. Tiiis fomething elfe you will fay is the nature of the 
 mother ; for this pcrfcCls and fafliions the offspring by its productive powers. 
 For the apparent form of the mother does not make the infant, but nature,, 
 which is an incorporeal power and the principle of motion. If, therefore, 
 nature changes the productive powers of feed from capacity to a fubfillence in 
 energy, nature muft herlelf poflefs thefe productive powers in energy. Hence, 
 being irrational and without imagination, fhe is at the fame time the caufe of phyfi- 
 cal reafons. As the nature of man, therefore, contains human productive powers, 
 
 docs
 
 ADDITIONALNOTES- 419 
 
 does not alfo nature in a lion contain thofe of the lion ; as, for inftance, the reafons 
 or produdlive powers of tlie head, the hair, the feet, and the other parts of the lion ? 
 Or, whence, on fhedding a tooth, does another grow in its place, unlefs from an 
 inherent power which is able to make the teeth ? How likewife does it at the 
 fame time make bone and t]efh, and each of (he other parts ? for the fame thing 
 energifing according to the fame, would not be able to fafhion fuch a variety of 
 organization. But does not nature in plants alfo poflcfs produ<5tive powers as well 
 as in animals ? or fhall we not fay that, in thete likewife, the order of generation 
 and the lives of the plants evince that they are perfefted from orderly caufes ? It 
 is evident, therefore, from the fame reafoning, that the natures of thefe alfo compre- 
 hend the apparent producSlive powers. Let us then afcend from thefe to the one 
 nature of the earth, which generates whatever breathes and creeps on its furface, and 
 which by a much greater priority contains the produ6tive powers of plants and ani- 
 mals. Or whence the generation of things from putrefadtion ? (for the hypothefis 
 of the experimentalifts is weak and futile.) Whence is it that different kinds of 
 plants grow in the fame place, without human care and attention ? Is it not evident 
 that it is from the whole nature of the earth, containing the produdlive powers of all 
 thefe in herfelf ? And thus proceeding, we fhall find that the nature in each of tlie 
 elements and celeftial fpheres comprehends the produdlive powers of the animals 
 which it contains. And if from the celeftial fpheres we afcend to the nature of the 
 iiniverfe itfelf, we may alfo inquire refpecling this, whether it contains forms or not, 
 aed we tliall be compelled to confefs, that in this alfo the productive and motive 
 powers of all things are contained : for whatever is perfc6led from inferior fubfifts 
 in a more excellent and perfecl manner from more univerfal natures. The nature 
 of the univerfe, therefore, being the mother of all things, comprehends the pro- 
 du(Hive powers of all things ; for, othervvife, it would be abfurd that art, imitating 
 natural reafons, fhould operate according to produdtive principles, but that nature 
 herfelf (hould energife without reafons, and without inward meafures. But, if 
 nature contains produdlive principles, it is neceflary that there fhould be another 
 caufc prior to nature, which is comprehenfive of forms : for nature verging to 
 bodies energifes in them, juft as if we fhould conceive an artifl verging to pieces of 
 timber, and inwardly, by various operations, reducing them to a certain form : for 
 thus nature, merged together with and dwelling in corporeal mafles, infpires them 
 with her produdiv.e powers and with motion; fince things which are movcd^by 
 otliers require a caufe of this kind, a caufe which is properly irrational indeed, 
 that it may not depart from bodies, which cannot fubfifl: without a caufc continually 
 rcfiding with them, but containing the produiffivc powers of bodies, that it may be 
 able to preferve all things in their proper boundaries, and move every thing in a 
 £Qnv.enicnt manner. Nature, therefore, belongs to other things, being merged in, 
 
 3 H » or
 
 420 ADDITIONAL NOTES. 
 
 or co-oi(HnateJ with, bodies. But it is rcqulfite that the moft principal and proper 
 caufe fhould be exempt from its prodii6iions : for, by how much more the maker is 
 exempt from the thing made, by fo much the more perfcflly and purely will he 
 make. And, in lliort, if nature is irrational, it requires a leader. There is there- 
 fore fomelhing prior to nature, which contains productive powers, and from which 
 it is requifitc that every thing in the world fhould be fufpendcd. Hence a know- 
 ledge of generated natures will fubfili in the caufe of the world more excellent 
 than the knowledge which wc pollels ; lb far as this caufe not only knov.'S, but 
 gives fubfiflenee to, all things ; but we poficfs knowledge alone. But if the demiurgic 
 caufe of the univerfe knows all things, if he beholds them externally, he will again 
 be ignorant of himfcif, and will be fubordinate to a partial foul ; but, if he beholds 
 them in himfelt", he will contain in himfelf all forms, both intellectual and gnoftic. 
 
 In the fifth place, things produced from an immoveable caufe are immoveable 
 and without mutation ; but things produced from a moveable caufe are again 
 moveable and mutable, and fubfifi: differently at diiFerent times. If this be the cafe,, 
 all fuch things as are cfTcntialiy eternal and immutable muft be the progeny of an 
 immoveable caufe ; for, if from a moveable caufe, they will be mutable ; which is im- 
 polTlble. Are not, therefore, the form of man and the form of horfe from a caufe,, 
 if the whole world fubfifts from a caufe ? From what caufe, therefore ? Is it from, 
 an immoveable or from a moveable caufe ? But if from a moveable caufe, the 
 human fpccies will fome time or other fail ; fince every thing which fublifts from a 
 moveable caufe ranks among things which are naturally adapted to perifh. We 
 may alfo make the fame inquiry re(pe6fing the fun and moon, and each of the liars : 
 for, if thefe are produced from a moveable caufe, in thefe alfo there will be a muta- 
 tion of efTence. But if thefe, and all fuch forms as eternally fubfifi in the univerfe, 
 arc from an immoveable caufe, where does the immoveable caufe of thefe fubfifi ? 
 For it is evidently not in bodies, fince every natural body is naturally adapted to be 
 moved. It therefore fubfifls proximately in nature. But nature is irrational ; and it 
 is requilite that caufes properly fb called fhould be intelledlual and divine. Hence,, 
 the immoveable caufes of thefe forms fubfifi primarily in intellecSl, fccondarily in 
 foul, in the third gradation in nature, and laftly in bodies. For all things cither fub- 
 fifi: apparently or unapparently, either fcparate or infeparable from bodies; and if 
 fcparate, either immoveably according to effence and energy, or immoveably accord- 
 ing to effence, but moveably according to energy. Thofe things, therefore, are 
 properly immoveable, which are immutable both according to efience and energy,, 
 fuch as are intelligibles ; but thofe poflefs the fecond rank which are immoveable 
 indeed according to efience, but moveable according to energy, and fuch arc Ibuls : 
 in the third place, things unapparent indeed, but infeparable from the phasnomena, 
 are fuch as belong to the empire of nature ; and thofe rank in the lall place which 
 
 are
 
 ADDITIONAL NOTES. 421 
 
 are apparent, fubfift in fenfiblcs, and arc divifiblc : for the gradual fLibjecftion of 
 forms proceeding as far as to fcnfibles ends in tliefe. 
 
 In the fixth place, let us fpeculate after another manner concerning the fubfiftence 
 of forms or ideas, beginning from demon ftrations themfelves. For Aritlotic has 
 proved in his Lafh Analytics, and all fcientifio men mud confefs, that dcmonllrations 
 arc entirely from things which have a priority of (libfiftcnce, and which are naturally 
 more honorable. But if the things from which demonftrations confift are univerfals 
 (for every demonflration is from thefe),— hence thcfe mull be cnufcs to the things 
 .which are unfolded from them. When, therefore, the allronomer fays, that the 
 circles in the heavens bife6l each other, fincc every greatcfl: circle bifccts its 
 like, whether does he demonflrate or not ? For he makes his conclufion from that 
 which is univcrfal. But where fhall we find the caufes of this fe^tiori of circles in 
 the heavens, which are more univerfal than the circles ? For they will not be in 
 bodies, fince eveiy thing which is in body is divifiblc. They muft, therefore, refide 
 in an incorporeal eflence j and hence there muft be forms which have a fubfiftence 
 prior to apparent forms, and which arc the canfes of fubfi deuce to thefe, in confe- 
 quence of being more univerfal and more powerful. Science, therefore, compels us to 
 admit that there are univerfal forms, which have a fubliflrence prior to particulars, are 
 more efiential and more caufal, and from which the very being of particulars is derived. 
 
 By afcending from motion we may alfo after the fame manner prove the cxift- 
 enec of ideas. Every body from its own proper nature is alter-motive, or moved by 
 another, and is indigent of motion externally derived. But the firft, moft proper 
 and principal motion is in the power which moves the mundane wholes: for he 
 poflefles file motion of a mover, and body the motion of that which is moved, and 
 corporeal motion is the image of that which pre-fubfills in this power. P'or that is 
 perfe(fl: motion becaufe it is energy j but the motion in body is impcrfeft energy : 
 and the imperfect derives its fubfiftencc from the pcrfedt. 
 
 From knowledge alfo we may perceive the neceffity of the fame conclufion. For 
 laft knowledge is that of bodies, whether it be denominated fenfiblc or imaginable : 
 for all fuch knowledge is deftitute of truth, and does not contemplate any thing uni- 
 verfal and common, but beholds all things invcficd with figure, and all things 
 partial. But more perfect knowledge is that which is without figure, which is im- 
 material, and which fubfifts by itfelf^ and from itlelf; the image of which is fenfe, 
 fince this is imperfcdl knowledge, fubfifiing in another,, and not originating from 
 itfelf. If, therefore, as in motion, fo alfo in knowledge and in life, that which par- 
 ticipates, that which is participated, and that which is Imparticipable, arc ditterent 
 from each other, there is aifo the fame rcafoning with refpciSt to other forms. For 
 matter is one thing, the form which it contains another, and flill diftcrent from 
 either is the feparate form. For God and Nature do not make things imperfe6t 
 which fubfift in fomething different from themfelves, and which have an obfcure- 
 
 and
 
 422 A D D I T I O N A L N O T E S. 
 
 and debile exigence, but have not produced things perfeft, and which fubfifl; from 
 themfelvcs ; but by a much greater priority they have given fubliftence to thefe, and 
 from thefe have produced things which are participated by, and merged in, the 
 darkncfs of matter. 
 
 But if it be rec;uifite fummarily to relate the caufe that induced the Pythagoracans 
 and Plato to adopt the hypothecs of ideas, we mull fay that all thefe vifiblc natures, 
 celeftial and fublunary, arc either from chance, or fubtift from a caufe. But that 
 they fhouid be from chance is impoflible : for things more excellent will fubfill in 
 things fubordinate, viz. intelleol, rcafon, and caul'e, and that which proceeds from 
 caufe. To which we may add, as Ai'iftotle obfcrves, that prior to caufes according 
 to accident, it is requifite that there fhouid be things which have an etfential fubfifl- 
 ence ; for the accidental is that in which the progretlions ot thefe are terminated. 
 So that a fubfiftence from caufe will be more antient than a fubfiftence from chance, 
 if the moft divine of things apparent are the progeny of chance. But if there is a 
 caufe of all things, there will either be many unconjoined caufes, or one caufe ; but if 
 many, we fliall not be able to aflign to what it is owing that the world is one, fince 
 there will not be one caufe according to which all things are co-ordinated. It will alfo 
 be abfurd to fuppofe that this caiife is irrational. For, again, there will be fomething 
 among things pofterior better than the caufe of all things, viz. that which being 
 within the univerfe, and a part of the whole, operates according to reafon and know- 
 ledge, and yet derives this prerogative from an irrational caufe. But if this caufe is 
 rational and knows itfelf, it will certainly know itfelf to be the caufe of all ; or, 
 being ignorant of this, it will be ignorant of its own nature. But if it knows that 
 it is efilntially the caufe of the univerfe, it will alfo definitely know that of which it 
 is the caufe ; for, that which definitely knows the one will alfo definitely know the 
 other. Hence, he will know every thing which the univerfe contains, and of which 
 he is the caufe *. and if this be the cafe, beholding himfelf and knowing himfelfi he 
 knows things poflerior to himfelf. By immaterial reafon?, therefore, and forms, he 
 knows the rnundane reafons and forms from which the univerfe confifls, and the 
 univerfe is contained in him as in a caufe fcparate from matter. This, Proclusadds, 
 was the dpdlrine of the Elcatic Zeno, and the advocates for ideas : nor did thefe 
 men alone, fays he, form conceptions of this kind refpedting ideas, but their doc- 
 trine was alfo conformable to that of the theologifts. For Orpheus fays, that after 
 the abforption of Phancs in Jupiter, all things were generated : fuice prior to this the 
 caufes of all mundane natures fubfilled unitedly in Phancs, but fecondarily and with 
 Ibparation in the Demiurgus of the univerfe. For there the fun and the moon, heaveni 
 itfelf, and the elements. Love the fource of union, and in fhort all things,were pro- 
 duced : for there was a natural conflux, fiys Orpheus, of all things in the belly of Ju- 
 piter. Nor did Orpheus flop here ; but he alfo delivered the order of demiurgic forms 
 through which fcnfible natures were allotted their prefent diflribution. Proclus fur- 
 
 thej;'
 
 ADDITIONAI.NOTES, 428 
 
 ther adds : The gods alfo have thought fit to unfold to mankind the truth refpeding^ 
 ideas ; and have declared what the one fountain is whence they proceed ; where 
 ideas firft fubfift in full perfedtion ; and how in their progreffion they affiniilate all 
 things, both wholes and parts, to the Father of the univerfe. What Proelus here 
 alludes to is the following Chaldaic Oracle : 
 
 JloijxiJioiy(pov; loscxg. "Trriy/js Ss {J-iccg ocTTOTrracrcci 
 
 E^i^opov' ■7raT^o9:-v yx^ sriv /SoliAjjt- TcAoj t.-» 
 
 AAX' su!Pia-9yi(r<xv vospco ttvpi uoi^yj^ztiroci 
 
 E/i- aXKscg voi^xg' noTu-u) yu^ avccl^ ttoXv^o^m 
 
 Tl^ov^riKiv vos^cv tvttov u(p9irov ov kxtcc y^oT^ov 
 
 IX^'O? STTityo^ivog ^o^(pv\g [xstoc x.oirjj.og i^xv^ri, 
 
 Tlocvrotxtg ^sxtg xs%ce^ia-usvog, wv jj-ix Try/yi], 
 
 E^ '/ig ^ot^ovvTxi- ^E^i^ta-^ivxi xKKxt otTvKrjot, ► 
 
 P/yyiv/^iva/ Koa-^ou tts^i crcoijcaTiy, xi Tr-fi x.o7\.7tovg 
 
 ajj-s^dxhscvg, (T^Y,Ji<r<riv soiyjjtxi <po^:OVTxi} 
 
 T^osTTOvcn TTfp; t x^ipi irx^x a-yj^ov xW\y>ig xKKij 
 
 "Evvoixi vos^xi Tryjyrjg Trxj^ntrig xtto, ttoXv 
 
 A^XTTcy.ivxi TTv^og xi/Sog xkciimtitov y^povov, XKu-n 
 
 A^iycvcvg idsxg vr^iAjzyj TT-xr^og fSAticri raf 5c 
 
 AuTorsXYjg TTYiyvi,^ 
 
 i.e. The intelledl of the Father made a cradling nolle, underftanding with un- 
 wearied counfel omniforin ideas. But with winged fpeed they leaped forth from 
 one fountain : for both the counfel and the end were from the Father, In confe- 
 ^uenee, too, of being allotted jin intellectual fire,, they are divided into other intellec- 
 tual forms : for the king previoufly placed in the multiform world an intellediual 
 incorruptible irapreflion, the vefiige of which haftening through the world, caufes it 
 to appear invefted with form, and replete with all-various ideas of which there is one 
 fountain. From this fountain^ other immenfe diftributed ideas ruili with a crafhing 
 noife, burfting forth about the bodies of the world, and are borne along its terrible 
 bofoms like fwarms of bees. They turn themfelves too on all fides, and nearly in 
 all diredlions. They are intellectual conceptions from the paternal fountain, pluck- 
 ing abundantly the flower of the fire of fleeplefs time. But a felf-perfecSl fountain 
 pours forth primogenial ideas from the primary vigour of the Father. 
 
 Through thefe things, fays Proelus, the gods have clearly fliown where ideas fub- 
 jift, who the divinity is that comprehends the one fountain of thefe, and that from 
 this fountain a multitude proceeds. Likewife, how the world is fabricated according 
 
 to.
 
 424 ADDITIONALNOTES. 
 
 to ideas; that they are motive of all mnndanc fyftems ; that they are eflentially in- 
 telledtual ; and that they are all-various according to their chara(51:eriftics. 
 
 If, therefore, he adds, arguments perfuade us to admit the hypothefis refpedting 
 ideas, and the wife unite in the fame dcfign, viz. Plato, Pythagoras, and Orpheus, 
 and the gods clearly bear vvitnefs to thcfe, we fhould but little regard fophiftical 
 arguments, which are confuted by thenifclves, and aflcrt nothing fcientitic, nothing 
 fane. For the gods have manifeftly declared that they are conceptions of the 
 Father : for they abide in his intelligence. They have likevvife af^erted that they 
 proceed to the fabrication of the world ; for the cradling noife fignifies their, pro- 
 grcffiou ; — 'that they are omniform, as comprehending the caufes of all divifible na- 
 tures ; that from fontal ideas others proceed, which are allotted the fabrication of the 
 world, according to its parts, and which are faid to be fimilar to fvvarms of bees ; 
 and laftly, that they are generative of fecondary natures. 
 
 For the fake of the Platonic reader it may not be improper to obferve that, in 
 the Supplement to Vol. III. of the Monthly Magazine, I have given as complete a 
 collecftion of thefe Clialdaic Oracles, as I believe can at prefent be obtained. Of 
 thefe invaluable remains of a theology coeval with the univerfe, I have not only 
 afccrtaincd the authenticity, but have made an accurate arrangement, and have 
 given the authors and places where each (a few only excepted) may be found. The 
 reader will likewife find that I have added fifty Ciialdajan Oracles and fragments of 
 Oracles to the collc61ion of Patricius, and that I have given a far more corredl edi- 
 tion of the text than that of Stanley and Le Clerc, who, from not underftanding any 
 thing of the wifdom with which thefe venerable fragments are replete, have by 
 their arrangement made perfc<5l nonfenlc of the greater part. 
 
 Should the reader, convinced by thcfe arguments that there is an ideal world fub- 
 fifling in incorporeal pcrfedlion, all-beautit'ul and all-divine, be fortunately led to 
 inquire how he may arrive thither, and by what guides like leading ftars he may 
 dircdl his flight from the magic power of Circe* and the detaining charms of Ca- 
 lypfo-|-, to this .Iplendid region, the paternal port, the true Ithaca of the foul, let ' 
 iiim attend to the following admirable paffiige from the Ninth Book of the Fifth 
 Enncad of Plofinus, On Intellecl, Ideas, and Being. For if, like Ulyfics, he is able 
 even in the prctcnt life to pafs from fenfe to the regions of intellc6l, he may like 
 him, after having wandered over the fca of gen?-ralion, been puritied by the cathartic 
 \irtucs, and es[)erienccd the light of fcicncc, find intellect ua! energy, and intelledl 
 itfclf thining in the rccefies of his foul. 
 
 " Since all uien from their birth employ fcnfc prior to intellect, and are necefiar. 
 fily firft convcrfant with fenfiblcs, fome proceeding no further pafs through life, con- 
 
 * The goddefs of Senfe. -j- The goddefs of Phantafy. 
 
 fidering
 
 A D D I T I O N A L N O T E S. 423 
 
 fideri'ng thefe as the firfl: and laft of things, and apprehending that whatever is 
 painful among thefe is evil, and whatever is pleafant is good ; thus thinking it fufE- 
 cient to purfue the one and avoid the other. Thofe, too, among them who pretend 
 to a greater fhare of reafon than others, efiicem this to be vvifdom, being afFeded in 
 a manner fimilar to more heavy birds, who, colledling many things from the earth, 
 and 0[)prcfred with the weight, are unable to fly on high, though they have received 
 wings for this purpofc from nature. But others arc in a fmall degree elevated from 
 things fubordinate, the more excellent part of the foul recalling them from pleafure 
 to a more worthy purfuit. As they are, however, unable to look on high, and as 
 not pofTeffing any thing elfe which can afford them retl, they betake themfelves to- 
 gether with the name of virtue to adlions and the eleiSlion of things inferior, from 
 which they at firft endeavoured to raife themfelves, though in vain. In the third 
 clafs is the race of divine men, who through a more excellent power, and with pier- 
 cing eyes, acutely perceive fupernal light, to the vifion of which they raife themfelves 
 above the clouds and darknefs as it were of this lower v/orld, and there abiding delpife 
 every thing in thefe regions of fenfe ; being no otherwife delighted with the place 
 which is true and properly their own, than he who after many wanderings is at length 
 refiored to his lawful country. 
 
 " What, then, is this region ? and how may we arrive thither ? This, indeed, may 
 be accomplifhed by him who is naturally a lover, and is truly from his birth a philofo- 
 pher ; as a lover being parturient about the beautiful, yet not enduring to be detained by 
 the beauty in body, he flies from thence to the beauty of foul, viz. virtues and fciences, 
 • inftitutions and laws ; and again from thefe afcends to the caufe of all that is beauti- 
 ful in foul ; and if any thing remains prior to this, he fiill afcends, till at length he 
 arrives at that which is firfl, and which is beautiful from itfelf. Airiving hither he 
 is freed from parturition, but not before. But how does he afcend ? Whence does 
 he derive the power ? And .after what manner does this love condud him to the 
 dcfired end ? Shall we fiy it is thus ? 
 
 " This beauty which is inherent in bodies is adventitious to bodies : for the forms 
 of bodies refule in them as in matter. The fubjcct, therefore, is changed, and from 
 being beautiful becomes bafe, Hence, reafon fays that body is beautiful by partici- 
 pation. What, then, is it which makes body to be beautiful ? This is effedled in 
 one way by the prefencc of beauty, and in another by foul, which fafliions and inferts 
 a form of this kind. Is, then, ibul beautiful from, itfelf. or not r Certainly not : 
 for, if this were the cafe, one foul would not be wife aiid beautiful, and another 
 unwife and bafc. The beauty about foul, thecefore, proceeds from wifdom. What 
 is it then which imparts wifdom to foul ? Is it not neecfUirily intellect ; an intelle<5l 
 which is not at one time intcllci^, and at another deprived of intelligence, but true 
 intelledl, and which is, therefore, beautiful from itfelf? Is it then ncceflary to 
 
 3 I flop
 
 ■<26 A D D I T I O N A L N O T E Si. 
 
 ftop here, as at that which is firft ? Or ought we not alfo to proceed beyond' iiite'^ 
 Tcdl itfelf ? Infelle6t, indeed, in our afcent prefents itfelf to the view prior to the- 
 principle of things, announcing as it were in the veftibule of the good that it con- 
 tains all things in itfelf, being as it were an imprefllon of the good., rather fubfiftino^ 
 in multitude than unity, the good on the contrary entirely abiding in one" 
 
 Wilh this we may alfo conjoin the following fublime paflages fiom Plotimis onthe- 
 Ideal World : they are extradcd from his book On Intelligible Beauty, of which I 
 have given a tranflation in my Hiftory of the Reftoration of the Platonic Theoloa:y, 
 at the end of Proclus on Euclid. I would earneftly recommend the whole of this 
 admirable book to the attention of the reader. 
 
 " Divine natures are not at one time wife, and at another time the contrary ; but 
 they are perpetually wife, with a tranquil, ftable, and pure intelledl underftanding all 
 things, and knowing not properly human concerns, but their own, that is, fuch as. 
 are divine, and fuch as inlellc6t itfelf perceives. But the gods who inhabit this vifible 
 heaven, for they abound in divine leifure, afliduoufly contemplate, as if it were above 
 them, what the primary and intelligible heaven contains. But thofe who are fta- 
 tioned in this higher world contemplate its inhabitants pofieffing the whole of this- 
 diviner heaven. For all things there are heaven. There the fea, animals, plants^ 
 and men are heaven.. Laftly, every portion ot this heaven is celeflial : the gods 
 likewife who refide there do not difdain men, nor any other of its inhabitants, be- 
 caufe every thing there is divine ; and they comprehend the whole of this intelli- 
 gible region with the moil perfe(5l repofe.. 
 
 " Hence the life of thele divinities is eafy, and truth is their generator and nurfe,. 
 their eflence and nutriment. Hence, too, they perceive all things, not fuch, indeed^, 
 as are fubjcfl to generation, but fuch as abide in eflence. They likewife perceive- 
 themfelves in others : for all things there arc perfcflly pcrtpicuous. Nothing there- 
 is dark, nothing oppofing ; but every thing is eonfpicuous to all, intrinfically and^ 
 univcrfally. For light every where meets with light. Each thing contains in itfelf 
 all, and all things arc again beheld in another : fo that all things are every -^vherc,, 
 and all' is truly all.. There every thing is all; there an hnmenje fplcndor fhines j 
 there every thing is great, fince even what is fmall is there great. There the fun 
 is all the flars ; and every (lar is a fun, and at the fame time all the fiars. Bat one 
 tbing excels in each, while in the mean time all things arc bchcJd in each. There 
 motion is perfectly pure : for in its progrefiion it is not confounded by a mover 
 foreign from the motion. Permanency alfo there is difiurbcd by no mutation : for it 
 is not mingled with an unftable nature. Bcfidcs, beauty there is beauty itfclfj bc- 
 caufe it does not fubiitt in beauty : but every thing abides there, not as if placed in 
 feme foreign land ; for the being of each is its own fiablc foundation. Nor is its 
 cflcnce different from its feat: for its fubje^l is intelledt, and ilfelf is intellet'^., 
 Juft as if any one lliould conceive this fenfiblc heaven, which is manifeft and lucid 
 
 to-
 
 A D D I T I O N A t \' O T E' S. 427 
 
 "fo the eyes, germinating into ftars by its light. In corporeal natures, indeed, one 
 part is not every where ])roduced from another, but each part is diftincl from the 
 reft. But there each thing is every where produced from the whole ; and is at the 
 fame time particular and the whole. It appears, indeed, as a part ; but by him who 
 acutely perceives, it will be beheld as a whole: by him, I mean, who is endued with 
 a fight fimilar to that of the lynx, the rays of whofe eyes arc reported to penetrate 
 the depths of the earth. For it appears to me that this fable occultly iignifies the 
 perfpicacity of fupcrnal eyes. Befides, the vifion of thefe bletfed inhabitants is never 
 wearied, and never ceafes through a fatiety of perceiving. For there is no vacuity 
 in any perceiver, which when afterwards filled up can bring intuition to an end : nor 
 can plcafurc ever fail through the variety of objecfts, or through any ditcord between 
 the perceiver and the thing perceived. Befides, every thing there is endued with an 
 untamed and unwearied power. And that which can never be filled is fo called, 
 becaufe its plenitude never fpurns at its repleniiliing obje6i: : for, by intuition it more 
 afGduoufly perceives ; and beholding itlelf infinite, and the objeds of its per- 
 ception, it follows its own nature as its guide in unwearied contemplation. Again : 
 no life there is laborious, fincc it is pure life : for, why fhould that labour which 
 lives in the beft manner ? But the life there is wifdom, a wifdom not obtained by ar- 
 guments like ours, becaufe it is always total, nor is in any part deficient, from which 
 it might require inveftigation. But it is the firft wifdom, not depending on any 
 other, yet not in fuch a manner that cfTence is firfl, and then wifdom fucceeds as 
 fecondarv and adjunct. Hence no wifdom is greater than this, but there fciencc 
 itfelf is the affociate of intellcf'^t, becaufe they both germinate and beam with divine 
 fplcndors together : in the fame manner as by a certain imitation they report that 
 Jufticerefides with Jupiter : for every thing of this kind exifls there like a lucid 
 refemblance perfpicuous from itfelf, fo as to become the fpecHaele of tranfcendently 
 happy fpecftators." 
 
 Again : in another part of the fame admirable work we have the following truly 
 fublime paflage : 
 
 " Let us then receive by our dianoeiic power this our fenfible world, fo difpofcd 
 that every part may remain indeed what it is, but that one thing may mutually refide 
 in another. Let us (uppofe that all things are colledlcd as much as polfible into one, 
 fo that each particular obje(ft may firlt prclent itfelf to the eyes ; as if a fpherc 
 Ihould be the exterior boundary, the fpe6taclc of the fim immediately fuccceding, 
 and a reprefcntation of the other flars, and the earth, the lea, and all animals appear- 
 ing within, as in a diaphanous globe: and laftly, let us conceive that it is poflible 
 1o behold all things in each. Let there be then in the foul a lucid imagination 
 of a f])here, containing all things in its tnuifparcnt receptacle ; whether they are 
 agitated or at reft, or partly mutable and partly ftablc. Now, preferving this f[>here, 
 
 3 I z receive
 
 4Zg A D D I T I O N x\ L N O T E S. 
 
 receive another in yonr foul, removing from this latl the extcnfion into biiTk, ta'ke 
 away Hkevvife place, and banifh far from yoiirfelf all imagination of matter; at the 
 fame time being careful not to conceive this fecond fphere as fomething lefs than the 
 firft in bulk, for this miifl be void of all dimenfion. After this invoke that Divinity 
 who is the Anthor of the univcrfe imaged in your phantafy, and earneftly entreat 
 him to approach. Then will he fuddcniy come, bearing with him his own divine^ 
 world, with all the gods it contains; then will he come, being at the fame time one' 
 and all, and bringing with him all things concurring in one. There, indeed, all 
 the gods are various amongfl: thcmfelves in gradations of power, yet by that one 
 abundant power they are all but one, or rather one is all : for the divinity never fails 
 by which they are all produced. But all the gods abide together, and each is again' 
 feparate from the other in a certain flate unattended with diflance, and bearing no 
 form fubjeft to fenfiblc infpeftion ; or one would be fituatcd diflcrently from the 
 other, nor each be in itfclf all. Nor, again, does any one of thefe pofiefs parts- 
 different from others, and from itfelf ; nor is every whole there a divided power,, 
 and of a magnitude equal to its meafured parts; but it is indeed an univerfe, and as 
 univerfal power proceeding to infinity in a power which is the parent of energy." 
 
 Page 32,8. And to fay ihat ideas are paradigms, &c: 
 
 Every idea is not only the paradigm, but likewife the producing caufe, of fen- 
 fibles : for fomething elfe would be rcquifite by which fenfibles are generated and 
 aflimilated to ideas, if thefe divine forms remained fluggifh and immoveable, and 
 without any efficacious power, fimilar to impreffions in wax: for it is abfurd to 
 admit that the reafons in nature poflefs a certain fabricative energy, but that intel- 
 ligible forms fhould be deprived of produdlive power. Every divine form, therefore,- 
 is not only paradigmatic but paternal ; and is by its very etfence the generative caufc 
 of the many. It likewile poflefles a perfe6live power: tor it is this which leads, 
 fenfibles from the imperfeit to the perfeii, and excites matter which is all things 
 in capacity, into a lubfiltence according to energy. It alfo pofTcflcs a guardian 
 power. For whence does the orderly arra:!gcment of the univerfe remain indif- 
 foluble, if not from ideas ? Whence thofc liable reafons which preferve the fym- 
 pathy of wholes infrangible, and through which the world remains always perfedt, 
 without the failure of any form, — whence are they derived except from flablc 
 caufes ? Jufl: as the mutability of fenfibles proceeds from moveable caufes. Add 
 too, that the divifible and diffipated nature of bodies is no otherwife comprcffcd 
 and connected than by the indivifible power of forms : for body is of itfelf divifible, 
 and requires the eonncdive power of divine reafons. But, if union precedes this 
 conncdion, for it is neccfTary that every thing connedtive ftiould be previoufly one 
 
 and.
 
 A D D I T I O N A L N T E S. 435 
 
 and indivifible, — this being the cafe, form or idea will not only be generative, de- 
 fenfivc, and perfccflive, but alfo connedlivc and imific of all fecondary natures. 
 
 Page 345, Note *. 
 
 For the ilike of the reader who is defirous and at the fame time capable of 
 afcending to a fcientific knowledge of the ineffable principle of things, the follow- 
 ing propofitions relative to tie good and the one are added. They are extra61ed from 
 that moft admirable work, The Elements of Theology, by Proclus, my tranflation of 
 which, at the end of my Proclus on Euclid, 1 would earneftly recommend to the 
 Englifli reader ; and, if he potil-fles a truly philofophical genius, would alfo urge 
 him to 
 
 " Read it by day, and meditate by night." 
 
 " The principle and firft caufc of all beings is the good. 
 
 " For if all things proceed from one caufe, it is requifite to call that caufe, either 
 the good, or more excellent than the good: But if it be more excellent than the good, 
 we afk whether any thing emanates from this caufe into beings, and into the nature 
 of beings, or nothing ? And indeed if nothing, it will be abfurd : for we cannot on 
 this hypothefis any longer preferve it in the order of a caufe, fince it is every where 
 requifite that fomething fliould be prefent from the caufe to the things caufed, and 
 efpecially from the firft caufe, from which all things depend, and through which 
 every being fubfifis. But if there is a participation of this firfl caufe in beings, in 
 the fame manner as there is of the good, there will be fomething more excellent than 
 goodnefs penetrating into beings from the firfl; caufe : for, fince it is more excel- 
 lent and fuperior to the good, it cannot beftow on fecondary natures any thing worfe 
 than the benefits difiributed by that which is poflerior to itfelf But what can be 
 more excellent than goodnefs itlelf ? fince we apply the term more exceUeiit to that 
 which participates more of the good. If, then, that which is non-good is not more 
 excellent, it mull be poflerior to the good. But if likewife all beings defire good, 
 how can any thing be prior to this caufe ? For, if good alfo defires, how can it be 
 good in the moft eminent degree ? But if it does not defire, muff not all beings 
 defire that caufe of all from which they proceed ? And if it is the good ilfelf froiii 
 which all beings depend, the good mutl be the principle and firft caufe of all. 
 
 " 2. Every good is endued with a power of uniting its participants, and every 
 union is good ; and the good itfeJfh the fame with the one. 
 
 " For \f the good ilfelf IS the preferver of all beings, and on this account isdefirable 
 by all, but the one itfelf prefervcs and contains the efi^ence of each : (for all things 
 are preferved by the one, and difperfion removes every thing from eflence) hence, the 
 good caufes thofc things to be one, to which it is prefent, and contains them by 
 
 union »
 
 4S0 ADD ITI ON A L NOTES, 
 
 union. But, il'//v one is endued with a congregating and containing power, it per- 
 fe6ls every being by its prefence : and hence, it is good to all things to be united. 
 But, if union is cffentially good, and good potrcfTcs an uniting power, the Jimply good 
 and the J/!/!]- 1)' one are the fatne ; uniting, and at the fame time benefiting beino-s. - 
 Hence it is, that things, which in a certain refpci.'^ fall from good, are alfo deprived 
 of the partidpation of unity; and that things which are deftitutc of the one, bc- 
 xaufe they arc replete with fcparation, are alio deprived of good. 
 
 " Hence, both goodncfs is union, and union is goodnefs ; and ih good is the one, 
 and the one is the firft good. 
 
 "3. The one is fupcrcdential. 
 
 •" For 4:Jfnnce is not the fame with ufiify ; nor is to he, and to he united, one and the 
 lame. But, \{ rjf.ncc is not tbe fame with tunty, that which is firft will eitha- be botli 
 thefe, and fo will not be one alone, but fomcthing befides one, and will participate of 
 the one without being the. oneitfelf; or it will be either of thcfe. But, indeed, if it is 
 eilcncc it will be indigent of the one. But it is impofliblc that the good and the jirjl 
 fhould be indigent. It will therefore, be the one alone ; and will confcquently be 
 fupcreflcatial." 
 
 Thcfcdogma?, that tie one is the principle of all" things, and that the one is the fame 
 with the good, and is fupcrcdential, are perfe6ily conformable to the do6\rine of Plato : 
 for that philofophcr, in the fixth book of his Republic, obfcrvcs, " You may fay, therc- 
 foi:e, that the good ViOt only affords to objcifis of knowledge the power of being known, 
 but likevvifc diftributes their being and eflence. while, in the mean time, the good itfelf 
 h not cjfence, hut ahove tjfence, tranfcending it both in dignity and power." And, iu 
 the firli hypothcfis of his Parmenides, he aficrts, in one of his conclufions refpedling 
 the one, " that t]:e one in no rcfptdl parlicijatcs of cfll-nce." (See p. 326 of my 
 Tranflation of that dialogue ) 
 
 1 his daxftrine concerning the incfl^able i)rincij)lc of things, which is unequalled 
 for its fublimity and profundity, infpired that divine magnificence of conception 
 which is fo confpicuous in the following patlliges, Proclus, then, in his fecond book 
 On the Theology of Plato, thus commences his contemplation of the one through 
 nca;r!tions. " Let us now, if ever, remove from ourfelvcs multiform knowledge, 
 exterminate all the variety of HI-, and in pcrfctft quiet approach near to the caufo 
 of all thifig-s. For this jiurpofc, let not only opinion and phantat}' be at red, nor 
 (he jianions alone vi'hich impede our anagogic impullc to the firft, be at peace ; but 
 let the air be fiill, and the univcrfc itfelf be Hill. And let all things extend us witl^ 
 a tjan.quil power to communion with the inefiable. Let us alfo, ftanding there, 
 having tranfcended the intelligible (if we contain any thing of this kind), and with 
 nearly clofcd eyes adoring as it were the rif.ng fun, fince it is not lawful for any 
 being whatever intently to behold him — let us furvcy the fun whence the light of 
 
 the
 
 ADDITIONAL NOTES. 431 
 
 ffi'e intelligible gods proceeds, emerging, as the poets fay, from the bo(bm of the 
 ocean ; and, again, from this divine tranquillity defcending into inteliecfl, and from 
 intelleft employing the reafonings of the foul, let us relate to ourfelves what the 
 natures are, from which, in this progreffion, we fliall confider the firft god as exempt. 
 And let us as it were celebrate him, not as eftabUfliiiig the earth and the heavens, 
 nor as giving fubfiftence to fouls, and the generations of all animals ; for he pro- 
 duced thefe indeed, but among the laft of things, But, prior to thefe, let us celebrate 
 him, as unfolding into light the whole intelligible and intellectual genus of gods^ 
 together with all the fupcrmundane and mundane divinities— as the god of all 
 gods, the unity of all unities, and beyond the firft adyta, — as more ineffable than- 
 all filence, and more unknown than all eflence, — as holy among the holies, and 
 concealed in the intelligible gods *." 
 
 Damafcius, likewife, in his MS. Trcatife, Trspi aiXi^v, or Concerning Principles^ 
 obfcrves, " This higbeft god is leen afar o,tF as it were obfcurely ; and, if yol^ 
 approach nearer, he is beheld ftill more obfcurely; and lafily, he takes away the 
 ability of perceiving other objects. He is, therefore, truly an iucomprehcnfible and. 
 inacceffible light, and is profoundly compared, by Plato, to the fun : upon which- 
 the more attentively you look, the more you will be darkened and blinded ; and. 
 will only bring back with you eyes ftupeficd with excefs of light." 
 
 Further ftill : the Pylhagorsans, and Plato the bcft of the Pythagorseans, called' 
 the principle of all t-hings tie one, becaufe, to be united is to all things good, and 
 the greateft of goods j- but that which is entirely leparated from unity is-evil, and 
 fubfifts at the extremity of evils : for divifion is the caufe of diffimilitude, and pri- 
 vation of fympathy. Hence alfo, fays Proclos, every principle, lb far as it is allotted 
 this dignity, is a certain unity, and that which is moft fingle in every order of things 
 
 * Aye 3Vf ol/v, ciTref Trdrt, xai vov Ta; ■proXviihti' a7ri>(ricsva70ijLi6a ymcti^, xu'i Tav to ttoiki^cv tv; ^iiivti: 
 i|opi(rU|t«£V a(p' ri/ttav, km ttsoituv cv n^Bfiia yiv>,u£voi, toi Travruv aiTioi TTf 07iW|tisi' '.yyu;. uth Oi if^iv an /^cioy- 
 Jbluf, irn^t tpxvraa-iai ri^ifjux, /xnh wux^a rm Traim «a")V eiiTrooi^oinuv rm vpo; to Trpuiov ayayuyov ofujjv, ■ 
 oXx' ifuxoi iitv ati^, wtrwxov 3JE to way touto, vavra Je arf e/*£i tji Suvxfiti tt^o; t>iv tosi a^^nrcu n^TO-jinav 
 Ttfjiai avatttviTU. xai iTTcaiti exei, xat to- voiitov (ei J»i ti roiourov EtrTiv iv ti/Mv) i/Trif^pafiOvrsi, xai ciov >I^l»l' 
 cvia^XOVTa Tr^oaxuvttirami, ixE/ivxCKTi toij o^fla^^oi? (ou ya^ ^^f^'S avruTriiv ouic aXAo tsjv ovrui' ov^iv) to*- 
 Tcivuv Tou <puTOi TiiiV voririiiv 5ttov mXiov e| oixzcxvou, patnv of •Komoti, '^rpofaivofuvov iSovtej, xcci auOi^ ex t>i{ 
 itSsou TOUT)); yitkriwi £15 votivxaTaSavTii;, xai a-no vou toi; t>i; ^}/uX''5 Xftu/iiEVoc ^.oytafmi, eittu/x^v Trpo^ ii/j'-oc; 
 auToui, uv flufJi/xEvov tv Tn wof Eia TxuTn tov TTfuTov Sjou TtOEipttOx. K3I biov bjXvn'Joiaiv a'jTov oux oti 7»y, 
 xai oupavov vmaTATtv XE'/ovfEj, oi/J' au In -^ux^it **' ^"'^'' CTramiv yevsacif, xcu raura /xiv yxp, aX.\' ett' 
 ffl'X't'C't" "■^o ^^ Toi/Tiav, di; Trav ^£v to voijtov rinv Sfuv ytvog, '^av Se to voe^ov flsf »v£, iravTaj Je toi/; uttep 
 TOV xoa^iJi.o-,.xai tov; tv tu xoajMi SfOi/f awavTaf, xat a; Seos e^t. Seuv aTTanav, xai a; tva; Eva&a/y xai Si; Tun 
 a^uvaTav (lege a3i/T£ov) ettekeivix tuv tt^xthv, xai ii; TraTr,; (riyn; a^onTOTEfcv, xai u; Traa'ti; intap^mi aym<TTQ- 
 rtfovy.ayioi ev ayi^tj, T015 voutoij tvaTronEx^vnnivoi Seoij. Procl. in Plat. Theol. p. 109. 
 
 is
 
 432 ADDITIONALNOTES, 
 
 is firft, not confidered as fubfifting in parts, but in wholes, nor in fome one of the 
 many, but in the monads connective of multitude. 
 
 But, as this is a fubjcdi of all others the mod interefling, the following admirable 
 paliage from the fixth book of the MS. Commentary of Proclus on the Parmenides 
 is added for the fake of thofe, who, being born with a divine dcltiny {Buot jjioi^a), are 
 capable of arriving at the fummit of philofophy. 
 
 " The firft caufe therefore, as fupplying all things with the greatefl: good, unites 
 all things, and is on this account called fhe one. Hence the gods, from their fur- 
 pafling fimilitude to the firtt god, will be unifies proceeding from this one principle, 
 and yet ineffabiy abforbed in his nature. Thus, for inftancc, (that we may illuftrate 
 this dodlrine by an example,) we perceive many caufes of light, fome of which are 
 celeftial, and others fublunary ; for light proceeds to our terreftrial abode from mate- 
 rial fire, from the moon, and from the other f^ars, and this, lb as to be different ac- 
 cording to the difference of its caufe. But if vi'e explore the one monad of all mun- 
 dane light, from which other lucid natures and fources of light derive their fubfifi:- 
 ence, we fhall find that it is no other than the apparent orb of the fun ; for this 
 orbicular body proceeds, ^s it is faid, from an occult and fupermundane order, and 
 difleiTiinates in all mundane natures a light commcnfurate with each, 
 
 " Shall we fay then that this apparent body is the principle of light ? But this is 
 endued with interval, and is divifible, and light proceeds from the different parts 
 whicli it contains ; but we arc at prefent inveftigating the one principle of light. 
 Shall vvc fay, therefore, that the ruling foul of this body generates mundane light ? 
 7'his indeed, produces light, but not primarily, for it is itfelf multitude : and light 
 contains a reprefentation of a fimple a^id uniform fubfiltenec. May not intelledt, 
 therefore, which is the caufe of foul, be the fountain of this light ? Intellect, indeed, 
 is more united than foul, but is not that whic^h is properly and primarily the 
 principle of light. It remains, therefore, that /Z-e? w/f of this intellect, its fummit, 
 and as it were flower, mud be the principle of mundane light: for this is properly 
 the fun which reigns over the vifible place, and, according to Plato in the Republic, 
 is the ofi8pring of the good ; fince every unity proceeds from thence, and every deity 
 is the progeny of the unity of unities, and the fountain of the gods. And as the good 
 is the principle of light to intelligibles, in like manner the unity of the folar order 
 is the principle of light to all vifible natures, and is analogous to the good, in which it 
 i,-, occultly cftabllOied, and from which it never departs. 
 
 " But this unity having an order prior to the folar intelle(?t, there is alfo in intelledt, 
 fo far as intelled, an unity participated from this unity, which is emitted into it like 
 a feed, and through which intclledf is united with the unity or deity of the fun. 
 This, too, is the cafe with the foul of the fun ; for this through the orie which (Tie 
 contains, is elevated through the one of intcllecft as a medium, to the deity of the fun, 
 
 In
 
 ADDITIONALNOTES^ 43j 
 
 In like manner with rcfpea to the body of the fun. there is in this a certain echo, 
 as it were, of the primary folar 07ie : for it is necefl'iry (hat the foiar body (honld par- 
 ticipate of things fuperior toitfelf; of foul according to the life which is difieininated 
 ■in it; of intelled according to its form ; and of unity according to its one, fince 
 foul participates both of intcllcft and this one, and participations are ditFerent from 
 the things which are participate d. You may fay, therefore, that the proximate 
 caufe of the folar light is this ztu'ily of the folar orb. 
 
 In like manner, if we fhould inveftip-ate (he root, as it were, of all bodies, from 
 which celeftial and fublunary bodies, wholes and parts, bloflbm into exilicnec, we 
 may not improperly fay that this is nature, which is (he principle of motion and reft 
 to all bodies, and which is eftablifl:ied in them, whether they are in motion or at 
 reft. But I mean by Nature, the one life of the world, which, being fubordinate 
 to intelle6t and foul, participates through thel'e of generation. And this indeed is 
 more a principle than many and partial natures, but is not that which is properly 
 the principle of bodies : for this contains a multitude of powers, and, through fuch 
 as arc different, governs different parts of the univerfe : but we are now invelligat- 
 ing the one and common principle of all bodies, and not many and diftributed prin- 
 ciples. If, therefore, we wifh to difcover this one principle, we muft raife ourfelves 
 to that which is mod united in nature, to its flower, and that through which it is a 
 deify, by which it is lufpended from its proper fountain, conne6ts, unites, and caufes 
 the univerfe to have a fympathetic confent with itfelf. This one, therefore, is the 
 principle of all generation, and is that which reigns over the many powers o{ 71a tare 
 over partial natures, and univerfally over every thing fubje6l to the dominion of 
 nature. 
 
 In the third place, if we inveftigate the principle of knowledge, we fball find (hat 
 it is neither phantafy norfenfe ; for nothing impartible, immaterial, and unfigured is 
 known by thcfe. But, neither muft we fay that eiiher doxaftic * or dianoetic know- 
 ledge is the principle of knowledge ; for the former does not know the caufes of 
 things, and the latter, though it knows caules, yet apprehends the objedlsof its per- 
 ception partially, and does not view the whole at once, nor poflefs an energy eol- 
 le«5livc and fimple, and which eternally fublifls according to the fame. Nor yet is 
 intelle(5t the principle of knowledge : for all the knowledge which it contains (ubfiils,, 
 indeed, at once, and is intranfitive and impartible. But, if the knowledge of intellect: 
 was entirely without multiplication, and profoundly one, perhaps we might admit that 
 it is the principle of knowledge. Since, however, it is not only one but various, 
 and contains a multitude of intelledlions; for, as the objects of intelledl are fepa- 
 rated from each other, fo alfo intclledlual conceptions, — this being the cafe, intellect 
 
 * Viz. Confiding from opinion. 
 
 3K is
 
 '*5t ADDITIONAL NOTES; 
 
 is not the principle of knowledge, but this mutl: be afcribed to tie one of intelleiSl, 
 which is generative of all the knowledge it contains, and of all that is beheld iu 
 the fccondary orders of beings. For this, being exempt from the m:iny, is the prin- 
 ci[)le of knowledge to them, not being of fiich a nature as i\\& Jamcnefs of intel- 
 k-ftuals ; fince this is co-ordinate to difference, and is fubordinate to cflcnce. But the 
 one tranfcends, and is connective of an intellectual eflence. Through this o«^ intel- 
 lect is a god, but not through faixiencfs, nor through eflence : for, in fhort, intelledl, 
 lb far as intellect, is not a god ; for otherwifc a partial intelle6l would be a god. 
 And the peculiarilv of intcllecl is to underftand and contemplate beings, and to 
 judge; but of a god to confer unity, to generate, to energife providentially, and 
 every thing of this kind. Intellect, therefore, by that part of itfelf which is not in- 
 tellec'l is a god, and by that part of itlelf which is not a god it is a divine intelledl. 
 And this unity of intelleft knows itfelf, indeed, fo far as it is intelleftual, but be- 
 comes intoxicated as it is faid with nedar, and generates the whole of knowledge, 
 fo far as it is the flower of intelle<fV, and a fupereflential one. Again, therefore, in- 
 veftigating the principle of knowledge, we have afcended to the one ; and not in 
 thefc only, but in every thing clfe in a limilar manner, we fliall find monads the 
 leaders of their proper numbers, but the unities of monads fubfifting as the mofl 
 proper principles of things." And fhortly after, the fame incomparable man 
 further obferves, " y\ll thefe unities fubfift in and are profoundly united with each 
 other: and their union is far srreater than the communion and famenefs which fublifb 
 
 ' to 
 
 in beings. For in thefe there is indeed a mutual mixture of forms, fimilitude, 
 and friendfinp, and a participation of each other; but the union of the gods, as. 
 being an union of unities, is much more uniform, inefMible, and tranfccndent : for 
 here a/I are in ei/l^ which docs not take place in forms or ideas*; and their un- 
 mingled purity and the charjjftcritlic of each, in a manner far furpaffing the diver- 
 fily in ideas, prcfcrvc their natures unconfufcd, and diflinguifli their peculiar 
 powers. Kence, fome of them are more univcrfal, and others more partial ; fome 
 of them are eharafterilcd according to permanency, others according to progreffion, 
 and others according to converlion. Some, again, are generative, others an;igogic, 
 and others demiurgic ; and, in fliort, there are different chara6ten fries of different 
 gods, viz. the connective, perfe6live, demiurgic, atlirnilative, and fuch others as are 
 celebrated prfterior to thefe ; fo that all are in ail, and yet each is i'.{ the fame time 
 fc[).ir;itc and diftintn. 
 
 Indeed, wc obtain this knowledge of their union and charadlerifiics from the 
 natures by which they arc participated : for, with refpect to the apparent gods, we 
 fay that there is one foul of the fun, and another of the earth, direding our attcn- 
 
 * J'"or in thefc all are in each, but not all in all, 
 
 , Hon
 
 ADDITIONAL NOTES. 435 
 
 tion to the apparent bodies of thefe divinities, which poflefs much variety in their 
 cflence, powers, and dignity among wholes. As, therefore, we apprehend the dif- 
 ference of incorporeal eflences from fenfible infpedlion, in like manner, from the 
 variety of incorporeal eflences we are enabled to know fomething of the unmingled 
 reparation of the firfl: and fupereflential unities, and of the charadteritiics of each ; 
 for each unity has a multitude fufpcnded from its nature, which is either intelligible 
 alone, or, at the fame time, intelligible and intelledtual, or intelledlual alone ; and 
 this lafl: is either participated or not participated, and this again is either fupermun- 
 dane or mundane : and thus far does the progreflion of the unities extend." And 
 fhortly after he adds, " As trees by their extremities are rooted in the earth, and 
 through this are earthly in every part, in the fame manner divine natures are rooted 
 by their fummits in the one, and each is an unity and one through its unconfufed union 
 with the one itfelf." 
 
 He who can read thefe paflages, and afterwards pity the ignorance of the heathens 
 in theological concerns, ishimfclfan objedl of extreme pity ; h:[\'\v\g\\\Q grcatejl eji- 
 of bis foul blinded by Ignorance, and buried in the darknefs of Oblivion,- 
 
 ^K a A DISSER'
 
 A DISSERTATION 
 
 ON 
 
 NULLITIES AND DIFERGING SERIES \ 
 
 IN wnicu 
 
 The Kaliirc of infinitely finall Quantities is unfolded; and the TO "EN, or 
 The One, of the Pythagoraeans and Platonifts elucidated. 
 
 BY THOMAS TAYLOR.
 
 DISSERTATION, &c. 
 
 CHAP. I. 
 
 X HE doctrine of nullities has been hitherto involved in impenetrable obfcurity; 
 and while feme eminent mathematicians have confidered them to be, as their name 
 implies, nothings, others have admitted that a nullity never fignifies nothing abfo- 
 lutcly, but in relation to the objcdl under contideration. Both, however, have been 
 very far from fufpe<5ling that they are in reality infinitely fmall quantities, and 
 that they have a fubfiftence prior to number, and even to the monad itfelf. To 
 prove this, is in part the defign of the following pages; in which, alfo, I perfuade 
 m}rclf the reader will find the nature of infinitely fmall quantities clearly unfolded, 
 and the fource of a new, and by no means unprofitable ftream of mathematical fai- 
 ence detected. 
 
 I. It is well known that infinite feries are diftributcd by mathematicians into 
 three clafles, the converging, the diverging, and the neutral. Thus, i — fH-- 
 — i + t) ^'-'> '^ called a converging; i — 2 + 3 — 4 + 5, &c, a diverging; and 
 I — I + I — I, 2cc, a neutral, feries. The diverging feries is fo called, becaiife its 
 terms continually dccrcafc ; and the neutral, bccaufe its terms neither increafe nor 
 diminifh. We projiofe to fhow that mathematicians have been egrcgioufiy mil^ 
 taken in the conclufions tl;ey have formed refpcding ihofe feries which they call 
 
 diverging and neutral. 
 
 1. The
 
 ■i:0 A DISSERTATION ON 
 
 2. The fratflion — = — - — , is when rcfolved into an infinito ferics, as is well 
 
 known, i — i + i — i, &c, ad infin. " In this feiies, fays Wolfius, (fee his Al- 
 gebra, p. 8^) the quotient, though never lb much continued, differs from the pro- 
 pofcd fraiStion by f ;" " whence, he adds, appears the caufe of the error which 
 Guide Grando committed in his Treatife of the quadrature of the circle and hy- 
 perbola, where he infers that, becaufc i — i + i — i, &c, = o, tlic fum of the in- 
 finite nullities is t ? which error Leibnitz knew in his Adla Eruditorum, torn, 5. 
 fup. p. 264, & feq." The reafoning of Eulcr on this fcries, which he calls " a 
 remarkable comparifon," is as follows, (Elements of Algebra, p. 143,) " If we 
 flop, (fays he) at — i, the feries gives o ; and, if we tinifh by + i, it gives i. But 
 this is precifely what folves the difficulty ; for, fincc we muft go on to infinity, 
 without flopping either at — i, or at + i, it is evident that the fum can neither 
 be o nor i, but that this refult muti be between thefe two, and therefore be=:-^." 
 Whence it appears that Euler, as well as Wolfius, was very flir from fufpcdling 
 that the fum of the infinite nullities is t ; and, as Euler is one of the latefl writers 
 on Algebra, I infer that the conclufions of thefe two great mathematicians refpedting 
 this feries are generally adopted ; particularly as I find, in that excellent work. 
 Dr. Hutton's Mathematical Didionary, that this feries is ranked among thofc of 
 the neutral order. 
 
 3. It is fingular that neither Euler, nor any other mathematician, fhould have 
 
 confidered that — = — ; ; — , — = ; and, in thort, all fradiions 
 
 3 1+1+14 i+i+i+i' ' 
 
 whofe numerators are unity, and whofe denominators are diflributed into unities, 
 
 will, when refolved into infinite feries, be equal to i — 1 + 1 — i. Sec, infinitely ; 
 
 and confcquently, the reafoning of Euler no lefs applies to all fractions whatever of 
 
 this kind, than to t? ariJ is no folution of the difficulty. But the fradtion f feems to 
 
 have been like the pillars of Hercules on this dark ocean of inquiry ; for modern 
 
 mathematicians have not ventured to explore beyond it, as the reader will perceive 
 
 in the courfe of this DlfTertation. Had they made the attempt, fair, and ampje, and 
 
 novel regions of fcience would have prefentcd themfelves to their view. 
 
 4. But, however lingular this circumftancc may be, and fingular it certainly is^ 
 
 there
 
 NULLITIES AND DIVERGING SERIES, 441 
 
 there is another which greatly furpafles it in this refped, viz. that not even the mod 
 enterprifing of our modern mathematicians fliould have ever tried the refult of 
 multiplying the infinite ferics i — i + i — i, &c, colledlivcly, by i -f i ?.s 
 below. 
 
 I — 1 + I — I + I — Ij &c 
 
 I + I 
 
 I I + l — X + I — I 
 
 + I — I + I — I + I 
 
 For, fince — - — =1 — 1 + 1 — i, &c, ad infin., it is evident that, if the quo- 
 tient is true, i — i + i — i, &c, multiplied by i 4- 1 ought to be equal to i ; 
 and, that it is fo when multiplied as above is obvious : for fince, in any finite feries 
 of terms, the produd is accurate to as many terms as are contained in the mul- 
 tiplicand, and it cannot be expefled to be accurate beyond this number, if the 
 multiplication is infinitely continued, the produdl will be accurately i, which is 
 the true produdl. But, mathematicians not attending to this, but confidering 
 I — I as equivalent to o, have concluded that, as o multiplied by i -{- i is equal 
 to o, the fum of i — i -f- i — 'j &c, was not equivalent to the fradlion f. It 
 is indubitable, however, that it is fo, and confcquently i — i is not the fame with 
 o ; or, in other words, I — • i confidered collecftively, or as one thing, is not the 
 fame with i confidered as taken from one, fo as to leave nothing. 
 
 5. This may be alfo further proved as follows : The f of the infinite ferics 
 J +- I -J- I + ij &c, produced by the expanfion of , is equal to i * -f- i * 
 
 ^ » .J • C • I+I + I + I,&C-r,,I I I 
 
 -J- I *, &c ad mfin. = — — - x . But — -— x ^ 
 
 I + i 1 1 + 1 I — I i^ —I 
 
 — i*.+ i* + '*>2cc; and confcquently — ~ = i + i + J , 9sc. 
 
 Agam : -—- x = i*-fi* + 1*, &c, and confc- 
 quently I — I + I — I, &c, = — -— . That is to fay, the ferics i — i + i — i, 
 &c, taken colledively is equal to f, and therefore i — i is not the fame with o, 
 
 3 L In
 
 442 ADISSERTATIONON 
 
 In fhort. fince X = i + i -f- i, &:c ad infin., half that feries = — ^ — = 
 
 I — 11 1 — I 
 
 X — n - — I -1 — ^j&cad infin., or z: i * + i * + i *, Sccad infin. : but 
 
 — — X ^—-^ — ^-^ LzJ.' gic ad infin. r= i * + i * + i *j 8cc; and confc- 
 
 quently i — i + i — i, he, is not to be confidered as a feries of o + o, Sec ad 
 infin., but as a feries the aggregate of which is equal to ~. 
 
 6. Since, therefore, —^ = the fum of i — i + i — i ad infinitum, let us 
 ' ' I + I 
 
 confider what will be the confequence when — ; — = — -, — ; ; ; — = — , 
 
 T i + i + i 3'i + i+i + i 4' 
 
 and fimilar fradtions are rcfolved into infinite feries. It is evident indeed, that the 
 
 quotients will be nullities, but that there fhould be the fame number of nulHties in 
 
 each is impoflible. With refpedl to |, then, when refolved it will be as follows u 
 
 i + i + i) I (i— -i* + i — I* 
 
 I + I + I 
 
 — 
 
 1 
 
 •— 
 
 I 
 
 
 
 
 
 
 
 
 — 
 
 • I 
 
 — 
 
 I — 
 
 I 
 
 
 
 
 ' 
 
 
 
 
 • 
 
 
 • + 
 
 I 
 
 
 
 
 
 
 I 
 
 + 
 
 I 
 
 + 
 
 I 
 
 
 
 
 
 — 
 
 I 
 
 
 I 
 
 
 
 
 
 
 
 
 I 
 
 — 
 
 I 
 
 — 
 
 I 
 
 + 1 
 
 ^. Hence it appears that ] is equal to an infinite feries of nullities with an inter- 
 val between each, which intervals are denoted by the flars, fo that the number of 
 nullities in ^ is lefs than the number in -^ by the aggregate of the flars. In like 
 manner it will be found that -^ is equal toi — i:;f* -fi — i-^#, &c. So that 
 in ^ there will be two intervals between each nullity j and univerfally the number of 
 intervals between two terms of any feries, will be found to be equal to the deno- 
 minator
 
 NULLITIES AND DIVERGING SERIES; 443 
 
 minator of the fracSlion producing that feries lefs by a. That this conclufion is 
 accurate will appear by multiplying any fuch feries by the denominator of the fradion 
 from whicli' it is produced ; for the produdl will always be equal to the numerator. 
 Thus, if the feries i — i#* + i — i**, Sec, ;= -^ be multiplied by i + i + i + ij 
 the produifl will be i, aS below : 
 
 I — I * *+i — I * *-hi — I 
 I 4- I + 1 + I 
 
 I I **_j_I I *5(C_{_I I 
 
 + 1 I * * + I I ^ * + I I 
 
 -f I — I * *+i — I * * + i — r 
 
 -}-i — I * * + i — I * * + i — I 
 
 But fince — ^ = i + i + i, &c ad infinitum, and confequently i + i + i, 
 
 &c, ad infin. multiplied by i — i, is equal to i ; or, in other words, an infinite feries 
 of I — I is equal to i : and fince alfo i — i + i — i, &c ad infin. is equal 
 to f, it would feem to follow, that i -J- i -|- i, &c, x by i — i, is equal to i — i 
 + 1 — I, he, or that i is equal to f. It will, however, appear that the former 
 feries is double the latter, by placing the one under the other, as follows ; 
 
 I — I + I — I + I — I, Sec, = t 
 I + I + I + I + I + I 1 ^ 
 
 Here it is evident 4hat under each unity of the upper feries there is i — i of the 
 lower, and confequently the latter is double the former. This will be more obvious 
 by multiplying i -j- i + i, &c by i — i, as follows: 
 
 I + I + I + I + I, &€, 
 1 — I 
 
 I + I + I + I -j- I 
 — I — I — 1 — I 
 
 3 L 2 Here,
 
 444 A DISSERTATION ON 
 
 Here, if under the fiift i the laft — i be placed, the arrangement will be as 
 alcove. Hence alfo it will clearly follow, that the nullities in unity are triple ihofe 
 in 7, quadruple thofe in J-, &c. ; and this will be at once apparent by placing the 
 one under the other thus : 
 
 I — I * + I ~ I '> + I — » *3 &Cj = t 
 1+ i + i + i+i + i + i+i-}- 
 
 1+ i + i + i+i + i + i+i+n 
 I — I — I — I — I — I — I — 1 — ij 
 
 For, In the upper feries there arc three nullities, and in the lower nine ; and, in like 
 manner, it will be manifeft that the nullities in unity are quadruple thofe in ^. 
 
 8. If the nullity i — 1 be continually involved into itfelf, the following nulli- 
 ties will be produced, viz. 1— a + i, i — 3 + 3 -' ^y ^ — 4 -1-6 — 4+ i, 
 I— 5 + 10 — 10 + 5 — I, i~6-fi5— ao+ 15 — 6 + 1, I — y -\- 21 
 •~~35 + 35~~*i + 7 — I, Sec, each of which will be found to poffefs a differ- 
 ent power from the reft, and will confequcntly be a nullity of a different order. 
 
 The firft remarkable property of thefe nullities is this, that each when it divides 
 unity produces the terms of the reft in a confequent order. Thus, 1 — i when it 
 divides i produces i + i +1, &c, the firft terms of the feveral feries; i — a + I 
 when it divides i produces i + 2 + 3 -+- 4, &c, the fccond terms ; 1 — 3+3 — i 
 produces i + 3 + 6 + 10, &c, the third terms, and fo of the reft, 
 
 9. In the next place, it Is remarkable that when any preceding is divided by any 
 
 immediately following nullity, the quotient is always 1 + i -f- i, &c, ad infinitum^ 
 
 I i-i I — z -H » 
 
 = YZTi' "^^"^^ I - 2 + I = I + I + I, &c, I _ 3 + 3 « 1 = I.+ 1 + I, &ci 
 
 and fo of the reft. 
 
 10. In the third place it follows, fince i — 2 + i is the fquare, and r — 3 + 3 — i 
 
 r 1 I 
 
 the cube of i — i, that i _ a + t is the fquare, and i_3-f.3_i the cube of i _ i. 
 Hence, the Caiv of the feries of numbers in a natural order, viz. i. a. 3. 4, &c, when 
 Infinitely continued is equal to the fquare of the fum of the feries 1 + i + ij 
 f<c, infinitely continued ; and 1+34-6 + 10, &c, ad infinitum, is the cube of the 
 
 faid
 
 NULLITIES AND DIVERGING SERIES. 445 
 
 laid feries. In like manner the feries arifine from the expanfion of > ■ 
 
 ° ^ 1-4+6-4+1 
 
 will be the fourth power of i + i + i, ad infin. ; and fo of the reft. 
 
 It may here be ncceflary to obferve that it is not poffible to conceive more than 
 three kinds of the adlual infinite j viz. the infinite in power, in magnitude, and in 
 number. The infinite in power is that which fubfifts in divinity ; in magnitude 
 the adlual infinite has no fubfiftence whatever; and in number it has partly a fub- 
 fiftence, and partly not : for it does not fabfift collectively, or at once, but according 
 to a part, or, in other words, according to the power of receiving an additional num- 
 ber beyond any afTignable number. Hence one infinite feries may be greater than 
 another, becaufe the terms in the one are continually greater than the terms in the 
 other. That is to fay, the one has the power of continually fupplying greater terms 
 than the other : not that the aggregate of one infinite Icries is greater than that of 
 another when the terms are adlually infinite ; for this is impoffiblc, becaufe there can 
 be no numerical infinite with an aggregate fubfiftence; but when one feries con- 
 tinued to infinity is greater than another, the terms in it are infinite only in capacitv. 
 Modern mathematicians, not attending to this diftindtion, have had no clear concep- 
 tion of the nature of the mathematical infinite, confidcred as having an aiflual 
 fubfiftence. 
 
 1 1. Thefe nullities including i — i, I call circular nullities of the firit order ; 
 thofe produced from the involution of 2 — 2, including 2 — 2, circular nullities of 
 the fecond order ; from 3 — 3, of the third order, and fo on : each of which orders 
 pofTefles different powers, as will be obvious to thofe who think fit to make the 
 trial. 
 
 12. From hence it will appear how much Emerfon was miftaken in the following 
 corollaries refpedling Nullities, in his Treatife on Algebra, p. 209. "Ifo (fays he) 
 multiply an infinite quantity, the product is a finite quantity. Or a finite quantity 
 is a mean proportional between nothing and infinity " For this is only true of nulli- 
 ties when they multiply infinite quantities formed from fradtions whofe denominators 
 
 are fuch nullities as the multiplying nullity. Thus, i — i x = i, or 2 — a 
 
 X ; = I, or I — I X — ^ = 4, &c. But this is not the cafe when the deno- 
 
 minator of the fradion by which the infinite quantity is produced is any po\^'er of
 
 4 16 A DISSERTATION ON 
 
 1 — I, or 2 — 2, &c. Tlui?, for inflance, i — i, X ^ _ ^ _^ ^ = i + i + r, &c 
 ad infinitum, viz. the produdof an infinite quantity multiplied by a nullity, may be 
 an infinite quantity. 
 
 ij. In the next place he obferves, "that if o be divided by D, the quotient is a 
 finite quantity of fome fort. But this is true only of nullities of the fame form, fuch 
 as I — i^ 2 — 2, &c : for, if i — l be divided by i — 2 + i, or i — 2 4- i by 
 I — 2 + 3 — h ^'i'^ quotient is an infinite quantity. 
 
 14. In the third place, he fays " that adding or fubtracfling any finite quantity 
 from an infinite quantity makes no alteration." This, however, is likewife falfe : 
 
 for, let 1 be added to —^^ and we fliall have ' ^ ^~ ', which is equal to 1 + 2 + i 
 
 ~h I + I, &c ad infinitum ; and is precifely more by the addition of unity than 
 
 _J or I -t- I + I + I, &c ad infin. Thus, too, lefs by unity is equal to 
 
 I — i' I — I 
 
 ^ ~ ^ "*" ^ — I * + I + I, ?cc ad infin., which is lefs than the ferics i + r + i, 
 I — I 
 
 &c by unity, as the flar indicates. 
 
 15. Nullities are infinitely fmall quantities : for let « reprefent any finite quantify; 
 then if a be divided by the infinite quantity — — , the quotient will be 1^1-f =: 
 
 I J. Hence an infinitely fmall part of 2 is 2 — 2, of 3, 3 — 3, Sec. : and 
 
 hence, that which has been hitherto called a neutral, is in reality a converging 
 feries,. 
 
 16. Nullities, when multiplied by nullities, are diminiflicd, which is a property 
 dired\ly contrary to the nature of numbers, and evinces that they arc cfTenfially dif- 
 ferent from quantities. Thus, a — a X a — a = a — 2 a + a, which is an infi- 
 Bitely fmall i)art o( a — a ; {or a — 2 a + a = a — a divided by -^. 
 
 17. Hence nullities are fomcthing belonging to, without being, quantity : for, 
 that they are not quantities is evident from the above mentioned property, and alfo 
 from this, that when they divide finite quantities, the quotient of each is an infinite 
 
 quantity,
 
 NULLITIES AND DIVERGING SERIES. 447 
 
 quantitj', which is ,nl<b a property contrary to that of quantity : and, that they are 
 not meiely nothings is evinced by this, that they arc equal to finite quantities, when 
 multiplied by infinite quantities, or when infinitely added to themfelves. Hence, 
 they may be confidered as fubfifting between nothing and quantity. 
 
 18. When a circular nullity of the firfl: order is fubtraftcd from the nullity im- 
 mediately above it, the remainder will be the nullity which immediately precedes it. 
 Thus, if I — 2+1 = I — ixi — ibe fubtradled from i — i, the quotient is 
 I — I. Thus, alfo, I — 3 + 3 — i fubtradled from i — 2 + 1 leaves 1 — 2 + i-, 
 and fo of the reft. But a nullity fubtraded from itfelf in the following man- 
 ner, is the fame as that nullity multiplied by i — j. Thus, 
 
 I — r I — a-J-r 
 
 I — I I — 2+1 
 
 I — 3 + 1, and I — 3 + 3 — I ; and fo of the reft. 
 
 X9. To divide a nullity by an infinite quantify, is the fame thing as to multiply 
 a nuUity by a nullity. Thus, i — 1 divided by - — ■ = i — 2 + 1 = i — iXi — i. 
 
 so. An infinite quantity divided by a nullity becomes infinitely increafed. 
 
 Thus divided by i — i gives . 
 
 I— I ■' ° X — 2 + 1 
 
 21. The quotient of any number divided by a nullity is different from the 
 quolient of the fame number when difiributed into unities, or numbers equal to 
 the whole, and divided by the fame nullity. Thus, 2 divided by i — 2 + 1 = 
 2 + 4 + 6 + 8, &c ad infin. ; but i + I divided by i — 2 + 1 1=1 + 3 + ^ 
 + 7, &c, and the latter feries is lefs than the former by i -f- i -f- i, &c ad infin. 
 
 = . Or, fuppofing m to reprefcnt any number whatever, = m -\- zni 
 
 + awi + 4w, &c ad mfin. but — — ^ h -%— + -^ {- -i — , &c. 
 
 ** 1—24-1 a 2 2 2 
 
 22. An
 
 ♦IS ADISSERTATIONON 
 
 22. An infinite quantity, whofe denominator is i — i, when fubtra(5led from 
 itfelf is equal to a finite quantity ; but an infinite quantity, whofe denominator is 
 I — 2 + 1, or any other circular nullity of the firll order, when fubtradted from 
 
 itfelf is equal to an infinite quantity. Thus, = a; but ; — 
 
 T T •' 'i^x I — I 1 — 2 + X 
 
 — = — — — = a + a + a, &c. ad infin. Hence, an infinite quantity, 
 
 fubtraded from itfelf, is the fame thing as a nullity divided by a nullity. Hence, 
 loo, every finite quantity may be confidered as an infinite nullity, viz. as a nullity 
 whofe terms are infinite. 
 
 Q.^. U a nullity confifring of two terms, with a finite number of intervals, be 
 divided by i — i, the quotient will always be a finite number exceeding by unity 
 the number of the intervals in the given nullity. Thus, if a . . — i» be divided 
 by I — I, the operation will be as follows, 
 
 I — i)a..-^a{a + a + a 
 
 a — a 
 
 + 
 
 a 
 
 • 
 
 
 
 
 a 
 
 
 a 
 
 
 
 
 + 
 
 a — 
 a — 
 
 ■ a 
 
 and the quotient will be 35, which is dne more in number than the number of the 
 intervals. 
 
 24. Hence, if the intervals are infinite in number, the quotient will be an in- 
 finite feries : fo that ^°°_~'' =/? + « + tf, &c ad infin. 
 
 15. Hence, too, a nullity with infiinite intervals is equal to a finite quantity; for 
 — ^ — = a -^ a-\- a. &;c. 
 
 X — I 
 
 * z6. And
 
 NULLITIES AND DIVERGING SERIES. 449 
 
 2,6. And, confequently, nullities with intervals are to each other as th(?»numbers 
 arifing from their divifion by i— I. Thus, a . . — a \s io a . . . — <?, as 
 2 to 4, and ib of others. 
 
 27. It will likewife be found that, 
 
 I . —I r 1 . . — I I I . _ J 
 
 4-4 2' 9-9 3' 
 
 . — , and — '• ■ == — ; and that = an infinite fcries of — . 
 
 4 3-^3 3- I. ..-I 4* 
 
 28. The infinite quantity —— divided by -^ is equal to a; but the infinite 
 
 quantity _ divided by — — = a + a yi a, Sec, ad infin. viz, the quotient of 
 
 a g'-eatei" infinite quantity divided by a lefTer, is alfo an infinite quantity. On the 
 contrary, the quotient of a lefler infinite quantity divided by a greater is an infinitely 
 
 fir.all quantity. Thus, divided by — — ^ =1 — i = an infinitely fmall 
 
 part of I. 
 
 29. The infinite feries of negatives i — 2 + 3 — 4 + 5 — 6, &c, is produced; 
 by the multiplication of i — i + i — i ad infin. into itfelf, as follows > 
 
 I — i + i — i + i — I 
 I — i + i — I + I — I 
 
 I — I + I — I + I — I 
 
 I + I — I + I — I+&C 
 
 +•1 I + I — I + &C 
 
 — I + I — I + &c 
 
 +■ I — I + &c 
 
 — t 4- &C 
 
 II "• - - _ - . 
 
 I — 2 + 3 — 4"'"S — ^ ^^' 
 
 Which inflance of itfelf affords a fufficient proof that i — 1 taken colledlively Jr 
 not the fame as o.- 
 
 3M: CHAP.
 
 ^0 A DISSERTATION ON 
 
 CHAP. IL 
 
 30. If 772 and a reprefent any two quantities whatever, of which m is the greater, 
 then the exprefllon — - — is faid, when expanded, to produce an infinite diverging 
 feriesj viz. according to modern mathematicians, the feries i — m -\- m"^ — vi^ 
 + m* -~ 7/7', £:c, infiniiciy diverges from the truth : that this however is falfe,, 
 
 •when every two terms of the feries are taken colledlivcly, and is only true when 
 they are atSually feparated from each other by fubtraftion, wc now propofe to evince. 
 
 31. " If the terms in the quotient (fays Wolfius in his Algebra, p. 83, fpeaking 
 of diverging feries) continually increafe, the feries, the longer it be continued, goes 
 the further from the true quotient ; nor can it be made equal to it, except when 
 the feries ends you add Jhe remainder with its fign. Ex. Let — — ——.the quo- 
 tient will be found i — 2 + 4 — 8 -{- 16 — 64+ 128, &:c. The term i exceeds 
 
 — bv -^ ; two terms want — ; three terms exceed by — , and four want — , 
 .3 -^ 3 3 ^ I 3 
 
 and fo on. Let us fuppofe the feries to end in — 8, then = i — 2 + 4 — S 
 
 ... ii; but I — 2 + 4 — 8 = — 5 _- - -11, therefore — ^ - — — -11 = -L." 
 3 3 1+23 3 3 
 
 Here again, it is fmgular in the e*;trcmc, that neiither Wolfius, though fo great a 
 mathematician, nor any other mathematician prior or poflerior to him, Newton 
 himfelfnot excepted, fliould have tried the refult of multiplying fuch feries col- 
 lectively by the denominators of their producing fracSlions ; for, as, in this cafe, the 
 produdl would have been found lo be equal to the nnmerators of fuch fraiflions, it 
 mufl necetTarily follow that the aggregates ^^ thefe feries are piecifcly equal to the 
 fractions by which they arc produced. 
 
 Thiis, in tbe infiance adduced by Wolfius if i — 2 + 4 — 84-16 — 64, 8ic^ be 
 multiplied by i + 2 as below, the produ6l will be unity. 
 
 I — 2 + 4 — S 4- 16 — 64 
 I + 2 
 
 i — 2 + 4— 8-f- 16 — 64 &c 
 + 2 — 4 + 8 — 16 + 64 &c. 
 
 For
 
 NULLITIES AND DIVERGING SERIES. -451 
 
 For the producl can only be confidcrcd as accurate lo as many terms as there are 
 in the multi[)r!cand. 
 
 32. FIcnce, 1 — 2, 4 — 8, 16 — 64, &c, taken colledlively, arc not the flimc ns 
 — 1, — 4, — 48, Sec. And hence, the fcrics which have been hitherto called 
 diverging, are in reality converging feries, as well as thofe which have been 
 erroneoufly denominated neutral. 
 
 33. But, that the reader may be fully convinced that a negative quantity, when 
 confidcred in connexion with the terms by which it is produced, is not the fame a«s 
 when conlidered foparate from thofe terms,'let him attend to the following inflance : 
 If I — 5, in whatever way it may be confidcred, was always the fame as — 4, and 
 I — 2 the fame as — 1, then, fince — i divided by — 4 is equal to -;, 1 — z 
 divided by i — 5 would alfo be equal to 7, but, on the contrary, it is equal to the 
 infinite feries i + 3 + 15 + 73, &c. And this may be further proved by an 
 infinity of fimilar iuftances, as the mathematical reader will eafily perceive. 
 
 34. When i/i is confidered as reprefenting any quantity whatever greater than a, 
 as we have already obferved, it is evident that a — ;« a will reprefent any negative 
 quantity whatever in connexion with the terms by which it is produced, and, confo 
 
 quently, fince • is equal to an infinite quantity = 1 + m + m^ + m^ -f- m'', &c, 
 
 ad infin. a — uia will be an infinitely fmall part of a ; for a divided by — — = 
 
 o' — m a» 
 
 •— z=.a — ma. 
 
 a 
 
 35. Hence 1—2, i — 3, i — 4, 8cc, will be infinitely fmal! parts of i. It 
 mull however be carefully remembered that fuch like exprellions, which I call 
 infinitely fmall quantities of the third order, are only infinitely fmall quantities when 
 confidcred cclledively ; for, taken feparately, they are. lefs than nothing,. 
 
 ^(y. There is a remarkable difference between i + i — 2 and 2 — 2; for 
 — — 7 — - = 1 — 1 +3 — 5 H- 1 1 — 21, &c ad infin., but — — = -1. 4. _I_ 4. 
 
 — — &c. ad infin. and univerfally . is very different from — - — ■. 
 
 2. •'rt + a-ma •' la — ma 
 
 3 M 2 3;r. Thus
 
 453 A DISSERTATION ON 
 
 37. TIuiP, too, fince — ^ = 1+2 + 4 + 8, &c ad infin,, and ^ ■ _ ' _ . = 
 
 1 + I -\- a + i, &CC ad infin., it is evident that i — 2 is not the fame as i — i — i -, 
 or, in olhcr words, i — 2 taken colledivcly as a whole, is very different from 
 X — 1 — I taken colledively ; and fo of all other firailar exprcliions. 
 
 38. When the middle terms of a circular nullity of the firft order are multiplied 
 by any number, the nullity is by fuch multiplication infinitely diminiflied. Thus, 
 if the middle terms of the nullity i — 3 + 3 — i he multiplied by 2, the nullity 
 produced 1 — 6 + 6 — 1 will be infinitely lefs than i — 3 + 3 — i '• and uni- 
 verfally i — 3 '« + 3 '-"^ — i will be infinitely Icfs than i — 3 + 3 — ij becaufa 
 
 ^ is infinitely greater than ; — ■ — . 
 
 I - 3m + ^m - I ■'*= 1-3+3-' 
 
 39. Of fome infinitely fmall quantities, the terms taken feparately produce finite 
 quantities. Thus 1 — 4 + 4 is an infinitely fmall part of i — 2, for it is equal to i — z 
 
 divided by — ^; ; but when its value is confidered by feparating its terms, viz. when 
 
 it is confidered as — 3 + 4, 4 being added to — 3 the refult will be unity. Thus too, 
 1 — 5 4- 6 is a flill infinitely fmaller part of i — 2 than i — 4 + 4 ; for it is equal 
 
 to I — 2 divided by — ~, > but, when taken feparately, it is equal to 2. And 
 
 this appears to mc to be an admirable property of infinitely fmall quantities of 
 this kind. 
 
 40. Hence, it appears that fome infinitely fmall quantities when taken feparately 
 -are actually noth-ng, but, v.hen taken colledtivcly as a whole, are nullities, or fome- 
 thing beloriging to quantity without being quantity ; and, that others again, when 
 taken feparately, are quantities, but are not fo when taken colledively. The firft 
 of thefe are fuch nullities as i — r, 2 — 2, &c ; and the fecond are fuch expref- 
 lions as i — 4 i- 4, 8cc, or infinitely fmall quantities of the third order. 
 
 41. Since is an infinitely greater infinite quantity than —3—, it follows that 
 
 J — 2 is an infinitely fmaller infinitely fmall quantity than i — i ; but i — 1 is 
 
 not
 
 NULLITIES AND DIVERGING SERIES; 451 
 
 ndl quantity, and confcquently i — 2 is not quantity ; and Co of all other fimilar 
 cxpreffions. 
 
 42. It will be found that (he nullity i — a + i added to itfelf, either finitely or 
 
 infinitely, in a feparate manner, is not the fair.e as the feries i — a + i + i 2 
 
 + 1, &c. Or, in other words, the aggregate of i — 2 + 1 added to itfelf is an 
 infinitely finall quantity of a different order from i — 2+1 connecled with itfelf 
 fo as to form one whole without any feparation. Thus 
 — 2+1 
 
 2 + I is very different from i — 2-f-i + i — 2-f-i. 
 
 For, ■ ' ^ = — + 1 + - + 2 + - , &c, but = 1 + 2. 
 
 -^3 + 3+3 +3 + 4+5+6 + 6, &c. 
 
 This alfo appears to be the cafe with every feries of infinitely fmall quantities, 
 except thofe of the forms i — i, a — 2, 3 — 3, See. 
 
 43. The fra6lion — — — fubtracSled from itfelf colleclHiively leaves an infinite feries. 
 
 4+-+};_ 
 
 + 
 
 I I — I 
 
 which yet is but an infinitely fmall quantity : for— — — 
 ^ a — 2 + a — 2, &c ad infin. 
 
 I + I I + I 
 
 = I 
 
 44. Since an infinite quantity is produced by dividing unity by an infinitely fmall 
 quantity, it follows that, on the contrary, an infinitely fiuall quantity is produced 
 by dividing unity by an infinite quantity. Thus, fince — — r: i -j- i -j- j^ gjc, 
 
 ^ _l + I = I + a + J + 4, Sec, and ^-1— = 1 + 2 + 4 + 8, &c ; on the 
 
 contrary, ,^.,+'^,;,e^ =1-1, , ^ , ^3 ^ ^ ^, = i -. ^ + i, and 
 
 = I 
 
 » + a + 4 + 8 &c 
 
 This being the cafe, fince alfo an infinitely fmall quantity is in reality void of quan- 
 tity, or, in other words, has a non-quantitive fubfiftence, it follows that infinite orders 
 Tof infinite feries may be conceived to have a non-quantitive fubfiftence in unity. Thus 
 .the feries i + 2 + 3 + 4> &c, fubfifts in unity according to i «— 2 + i : the feries 
 I + a + 4 + 8, &c, according to i — 2 ; and fo of the refl. Hence we fhall 
 ]»e able to difcover the true natui'C of infinitely fmall quantities : for it may be de- 
 
 mpnfiratcd
 
 454 ADISSERTATIONON- 
 
 monflratcd as follows, that they are negations of infinite multitude. In the infinitclj 
 fmall quantity, for example, i — 2, it is evident that 2 docs not tTibfifl according ta 
 quantity, fince in this cafe i — 2 would be the fame as — i, which we have clearly 
 fhown it is not ; 2, therefore, muft be non-quantilive. This being the cafe, it 
 follows that when this 2 is taken from unity, an infinite feries of non-quantitivs 
 numbers is at the fame time taken from unity. For fince unity, as wc have fliowa 
 above, contains infinite feries of numbers with a non-quantitive fubfiftencc, if a 
 non-quantitivc 2 were alone taken from unity, an infinitely fmall part only of unity 
 would be taken away, and confequently the remainder would not be an infinitely 
 fmall quantify. In like manner the expreffions 1 — 1,1 — 3, i — 4, &rc, fignify. 
 that infinite non-quantitive feries are fubtradcd from unity. 
 
 45. Hence, fince i — i, i — 2, i — 2, 2>:c, are infinite negations of non- 
 quantitive multitude, they are by a much flronger reafon infinite negations of aflual 
 quantity. 
 
 46. Hence, too, the powers of the infinitely fmall quantities 1 — i, i — 2, Sec,, 
 
 y\z, I 2 + 1, I — 4+4} &c, will by a much ftronger reafon be infinite ncga. 
 
 tions of multitude: for they are infinitely fmall parts of the infinitely fmall quanti- 
 ties of which they are the powers, as we have before fhown. 
 
 CHAP. III,. 
 
 Having thus afcertaincd the nature of infinitely fmall quantities, I now propoft 
 to {how that in continued quantity they are points; that, in confequence of this, 
 linear points, or the points properly belonging to aline, are very difi-erent from 
 thofe which properly belong to a fuperfiieies ; and the points in a fuperficies from 
 thofe which properly belong to a folid : and, in the third place, that points have the 
 fame relation tu eacii other as the lines, fuperficies, and folids to which they belong. 
 
 47. Let a then reprcfent any line, arid an infinitely fmall part of this will be 
 fi — a: for a divided by — |— = a — a. But a — a is- not quantity.: it is, how- 
 
 ever.
 
 NULLITIES AND DIVERGING SERIES. 4SS 
 
 ever, fomething belonging to the line, though it is no quantitive part of the line; 
 But there is nothing belonging to a line, and which is not quantity, except a point : 
 a — a, therefore, is a point. In like manner let a b reprefent any fuperficics, and 
 ah — ah will be an infinitely fmall fuperficies ; i. e. a point of a very diftcrent order 
 from a — a. And \i ah c be any folid, ahc — abc will be an infinitely fmall folid, 
 or point of a very different order from either ah — ah, or a — a. 
 
 48. Hence it follows, that mathematicians have been greatly miftakcn in fup- 
 poflng that infinitely fmall fuperficies may be confidered as lines ; fincc it now evi- 
 dently appears that they are points, 
 
 49. In the third place, fmce a — a is to h — ^ as (7 to /', and ah — ah to 
 ^d — ccl, as ah to cd, and ahc — abc to def — def as abc to def, it follows that 
 points have the fame relation to each other as the lines, fuperficies, and folids to 
 which they belong. 
 
 fr T I- <i'-> — 'Z^ 11/- di^ — '^■''" 1 Cil'l^ — 1^1^ 1 -i /- II 
 
 'Hence, fince —, — = a, and alio -; 7— — a, and = a!\ it follows 
 
 i — b be — b^ c — c 
 
 that the points which compofe a fuperficies and folid may alfo compofc a line, and 
 that thofe which compofc a folid may compofc a fuperficies ; but in this cafe, the 
 ■points belonging to a fuperficies when they compofe a line approximate nearer to 
 quantity than linear points, or points properly belonging to a linfi ; and thofe belong- 
 ing to a folid approximate flill nearer to quantit)-. For, as we have (hown that a 
 finite quantity is produced by the fubtra(!^ion of an infinite quantity from itf^lf, it is 
 evident that a^ approaches nearer, ancL iz/'^.^flill nearer to an infinite quantify than 
 a ; and confequently ah — ab and abc — abc are greater points than a — a. 
 Ilencc, too, we fee, in confcquencc of thcfc being greater points, that there is a 
 lefs infinity of them in a than of « — a. 
 
 There is, therefore, a threefold order of points, viz. linear, fuperficial, and fcl'd, 
 each of which is entirely impartible. 
 
 50. It mufl. here, however, be obfcrved, that when a line is confidered as confifling 
 oi points which properly belong to a fuperficics or folid, fuch line mufi: alfo be con- 
 fidered as belonging to fuperficies or folid^ and not as line fubfifting by itfcif; and 
 
 the
 
 456 A DISSERTATION ON 
 
 the like muft be nndei-ftood of fuperficies, when confidered as confining fiom points 
 which belong to a Ibiid. 
 
 51. ShouH it feem ftrange to admit that fuperficies and folicrs confift from an 
 infinity of points, it will no longer appear fo when it is confidered that m;ithe- 
 maticians univerfally acknowledge that a line confifls of an infinity of points, 
 a fuperficies of an infinity of lines, and a folid of an infinity of fuperficies : for^ 
 this being granted, a fuperficies and folid will alfo confiil: of points, though in 
 an infinitely greater infinite number when confidered as linear points tlian thofe 
 which compofe a line. It muft likewife be carefully obferved that, as a multitude of 
 monads or unities in number correfponds to matter ; (for by the acceflion of a cer- 
 tain numerical fornfi thefe rnonads become a certain definite number,) fo infinite- 
 points become the matter or recipient of continued quantity ; or, in other words^ 
 rnfinite points are continued quantity, iv Swaua, in capacity. 
 
 52. Since, as we have before obferved, points have the fame relation to each; 
 other as the lines, fuperficies, and folids to which they belong, hence the points in a 
 right line may be confidered as redtilinear, and thofe in a circle as circular points. 
 
 If, therefore,^ reprefent the periphery of a circle,.and ^ the diameter, ^ ~ ■ = p, or 
 
 the periphery is equal to an infinite number of circular points ; p — p reprefenting a-- 
 
 point of this kind. Again : ^-~ x — = ^—"^-L z= -^ = the area of the circle 
 r °i— 144-44 
 
 =: £ X -^^. In which cafe p X d — d will reprefent a point afFeefled with 
 fuperficies,. or which, in other words, is fomething belonging to a cylindric fuperfi- 
 cies ; a particular infinity of which fuperficial points, i. e. --^, is equah to the area- 
 
 4 4" 
 
 of the circle. 
 
 53. Should it feem firange that the infinity of points in the area of a circle is but 
 — the infinity of thofe iu the periphery ; for x p — p '^ p, and x 
 
 pd-r-pd zz -p, it mufl. be remembered that J5 — p is a linear, zndpd — pda fuperficial' 
 
 point;^-
 
 NULLITIES AND DIVERGING SERIES, 457 
 
 point, and confcquently that every point in the periphery is to every point in the 
 area of a circle as the periphery of the bate of a cylinder to its rupcrficies, when the 
 diameter of fuch periphery is equal to the altitude of the cylinder. 
 
 <±. Alfo, fincc ~ ' ■ =: i, ^ ~ ^ = 2, i-Hi =r 3, &c ; and fince 1 — 1 is to 
 ■J^ ' I — I 'i — I I — I •'' 
 
 2 — 2 as 1 to 3, and 2 — 2 is to 3 — 3 as 2 to 3, and fo on ; and confequently, if 
 
 I, 2, 3, &c, reprefcnt lines, Qvery point in 2 is to every point in i, as 2 to i, and fo of 
 
 tlie reft; hence points approximate to quantity in proportion to the incrcafe of the 
 
 fines with which they arc conne6led. 
 
 .. J. I — t I— 2+1 i—^ + j — i 
 
 < < . n ffaui : lince = i , = i , and = — i , and fo on ad 
 
 JJ ° I — I '1— »H-i ' 1 — 3+3 — t ' 
 
 infinitum, when the infinitely Imall quantities which form the numerators of thefe 
 
 fradtions are confidercd as reprefenting points, and the fractions themfelves as repre- 
 
 fenting lines, it follows that every line may be confidercd as confifting either of an 
 
 infinite fcrics of points of the order , or of an infinite feriesof (he order ^ 
 
 which is the Iquare of the former, and an infinitely fmall part of it, and after this 
 manner \vc may proceed ad infinitum, not only in lines, but alfo in fupcrficies and 
 folids. 
 
 i)6. \ fliall conclude this chapter with obferving that the p«/^t7fummation of every 
 kind of infinite leries can perhaps only be obtained by means of thefe infinitely 
 fmall quantities. General rules may be given for the fummation of any infinite 
 feries of \\ hole numbers, as I may perhaps fliovv at ibme future period, when I pro- 
 pofe to enter more largely into the inveftigation of this abfirufe fubjcdl. At prcfent 
 let the following inftances of the fummation of infinite foj'ies fufEce. 
 
 ■ a + i " ~ ^ — 2 -\- S — 7 + 9 — J'j ^^' which feries is the reciprocal of 
 the feries t — t + i — t + t — -tVj &c, which is equal to ^ of the circumference 
 
 of a circle, when the diameter is i. _ ' — 3— =11 + 4+9 + 16 + 25, &c, 
 
 3 N the
 
 458 A DISSERTATION ON 
 
 the reciprocal of the feries i + t + t + -rV> &c, and which is equal to t of the 
 fquare of the circumference when the diameter is i. 
 
 57. Again : according to Dr. Wallis, in his Algebra, p. 296, as ihc produdl of 
 the fquares of the odd numbers, 3, 5, 7, 9, See ad infin. is to the product of the 
 fame fquares diminifhed by unity, fo is the fquare of the diameter to the area of the 
 circle; viz. as 9 x 25 X 49 X 81 x 12 1, &;c ad infin. to 8 x 24 X 48 x 80, &c 
 ad infin. Now, though I have not difcovered two fradlions, which when expanded 
 will give the products of thefe two feries ; yet the following fradtions will give their 
 
 fum : for, ■ ^ ~ ', ^— — ^ +-25 + 49, &c, and ; =: 8 + 24 + 48^ 
 
 -f 80, &c, ad infin. ; in which laft fraction it is remarkable that the numerator 8 is 
 equal to the numerator of the other fradlion when its terms are taken feparately. 
 
 58. We have already fliown that — — — — = 1 -}-44-9 + 16, gcc, the 
 
 terms of which are the fquares of the terms of the feries 1 + 2 + 3 + 4, &:c, =: 
 
 ^ ; this beine: the cafe, it will be found that '■ — % ^ :r i + 8 -{- 
 
 1—2+1 ° 1-4 + 6 — 4 + 1 '^ 
 
 27 + 64, &c, the terms of wliich are the cubes of the feries 1 + 2 + 3 + 4, &cj 
 
 that \^~ li — i — I + 16 + 81 + 2? 6, the terms of which are the 
 
 I — 5 + 10 — 10 + 5 — I -' 
 
 fourth powers of the fame feries, and that 7—,—- ; — : — r-; — = 1 + ^2 
 
 » 1—0 + 15 — 20+1^—0 + 1 -^ 
 
 + 243 + IQ24, &c, the terms of which are the fifth powers of that feries ; and 
 
 fo on. 
 
 ijg. In thefe fra-dlions it is in the firfl: place remarkable, that the denominators- 
 I — a-f-ij I — 3 + 3 — i> J — 4 + 6 — 4+1, &:c, are the fquare, cube. Sec 
 cf the nullity x — i ; and, in the next place, that the numerator of the firft fradtion 
 
 ^ multiplied by 2, is equal to the fum of the terms of the numerator of the 
 
 fccond fraction ; tliat the numerator of the fecond fradtion multiplied by 3 is equal 
 to the fum of the terms of the numerator of the third j that of the third' multiplied 
 by 4 = the fum of the fourth, and fo on. Thus i x 2 = 1 + i the numerator of 
 
 the
 
 NULLITIES AND DIVERGING SERIES. 451 
 
 the fecond fradllon ; i + i X3 = 6z:i+4+i the numerator of the third ; 
 1+4+ 1X4 = 24 =1 + 11 + ii + i the numerator of the fourth ; and 
 fo on. 
 
 CHAP. IV. 
 
 60. Having thus unfolded the nature of infinitely finall quantities, I fliall in the 
 next place proceed to (how that they are admirable images of the to Iv, or the one, 
 of the Pythagorasans and Plato, concerning which, as we have feen, fo much has 
 been faid by Aritiotle in the thirteenth and fourteenth of the preceding books; 
 and that they beautifully illuflrate fome of the moft profound dogmas of antient 
 theology. 
 
 61. Firftthen, we have demonftrated that infinitely fmall quantities are negations 
 of infinite multitude ; and a negation of all multitude is that which charadterifes tbe 
 one, as is evident from the firft hypothefis of the Parmenides of Plato. As all fimte 
 quantities likewife may be confidered as confifting of infinite feries of infinitely fmall 
 quantities, it follows that infinite negations of multitude may be faid to conftitute all 
 finite quantity. Admirable, therefore, is the nature of negation, as is beautifully 
 fhown by Proclus in the following extracSl from the fifth book of his moft excellent 
 MS. Commentary on the Parmenides ; for the length of which the intelligent reader 
 will, I am perfuadcd, require no apology. 
 
 " Let us now confider what negations are, and whether they are better or worfe 
 than affirmations : for affirmation appears to all men to be more venerable than 
 negation ; negation, fay they, being a privation, but affirmation the prefcncc and 
 a certain habit of form. To forms, indeed, and to things invefled with form, affirma- 
 tion is better than negation ; for it is necefiary that their own habit fliould be pre- 
 fent with forms, and that privation fliould be abfent ; and, in ffiort, to be is more 
 accommodated to beings than not to be, and affirmation than negation : for being is 
 the paradigm of affirmation, but non-being of negation. But it is not immanifell 
 how Plato, in the Sophifia, fays that non-being, by which he means difference, 
 is related to being, and that it is not lefs than being. But, fince non-being 
 ■ 3 N 2 is
 
 M60 A D I S S E R T A T I O N O N 
 
 is inuhifariou?, one kind fLibfifling as more excellent than, Jinothcr as coordinatctr 
 with, and a tliird as the privation of, being-, it is evident that we may alfo fpeculatc 
 three fpccies of negations ; one' above affinnatiun, another inferior to affirnnration, 
 and a third in a certain refpcdt equal to it. Affirmation, therefore, is not always- 
 uniforr.ily more excellent than negation, fince, when negation fpeaks of that non- 
 being which is above being, affirmation is allotted the feeond order. But, fince this 
 non-being is ahb t'.vo-fold, one kind * being participated by being, and the other -}■• 
 not eon- numerated with any being, it is evident that to this latter aflirniaticn is not 
 by any means adapted, and that to the former negation more properly belongs than 
 affirmation ; though in a certain refpe6l affirmation is adapted to thi«, fo far as it 
 communicates with, being. However, though nothing can be truly faid of that non- 
 being which is uncoordinated with being, yet negation may be m.ore properly 
 aflertcd of it than affirmation : for, as affirmations belong to beings, fo negations to 
 non-being. In fhort, affirmation willies to be converfant with a certain form ; and 
 when the foul f lys that one thing is prefcnt toanother, and makes an affirmation, it 
 adduces fome of the kindred natures which it contains. But the firfl: caufc of all is 
 above form, and it is not proper to introduce to it any thing belonging to fccondary 
 natures, nor transfer to it things adapted to us : for we fhall thus deceive ourfclves, 
 and not aflcrt what the firll: is. We cannot, therefore, in a becoming manner em- 
 ploy affirmations in fpeaking of this caufe, but rather negations of fecondary 
 natures ; for affirmations haftcn to know fomething of one thing as prefcnt with 
 another. But that which is firfi is unknown by the knowledge which is connate 
 with beings, and nothing can be admitted as belonging to or prefent with it, but 
 rather as not prefcnt : for he is exempt from all compotition and participation. To 
 which we may add, that affirmations manifeft fomething definite ; for non-man is 
 more infunte than man. The incomprehenfible and uncireumfcribed nature of 
 • iJ.je one is therefore more adapted to be manifeficd- through negations : for affirma- 
 tions may be fild to vanquiQi beings, but negations poffefs a power of expanding 
 from things .circunafcribed to the uncireumfcribed, and from things diftributed in 
 proper boundaries to the indefinilc. Can it, therefore, be faid that negations are not 
 more adapted to tlic contemplation of //je out? For its ineftable, incomprehenfible. 
 
 * Viz. The divine unities. See the Additional Notes, 
 f That is, the ineffable principle of things. 
 
 and
 
 NULLITIES AND DIVERGING SERIES. 461 
 
 anil unknown nature can alone ihrougli thcfc be declared, if it be lawful fo to fpcak, 
 to partial- intelledual conceptions fuch a» ours. Negations therefore are better than 
 .ifRrmations, and are adapted to fuch as are afccnding from the partial to the totalj 
 from the coordinated to the uncfoordinated, and from the circumfcribcd and van- 
 qnifhed form of knowledge, to the uncircumfcribcd, finglc, and fimple form of energy. 
 " In the next place, let us confider how, and after what manner, negations are 
 adapted to the firft caufe. They muft not then be adapted as in things capable of 
 receiving negation, but yet which do not receive it, as if we fhould fay that Socrates 
 is not white : for, in fhort, the one does not receive any thing, but is exempt from 
 every being, and all participation. . Nor, again, mufl: negation be adapted to the one, 
 
 r 
 
 as in that which in no refpcci receives negation, which poflefles a- privation of it, and 
 is unmingled with form ; as if any one fhould fay that a line is not white, becaufe 
 it is without any participation of whitenefs. For that which is firfi is not (imply 
 chvulfcd from its negations ; nor are thefe entirely void of communion v.'ith the o?ie, 
 but Ihcv are thence produced : nor can it be faid tljat, as whitenefs neither gene- 
 rates a line, nor is generated by it, fo things pofterior to the one, neither generate 
 the one, nor are generated by it ; for they thence derive their fubfiflenee. Nor yet 
 muft negation be applied according to that middle mode, in which we fay that 
 things do not receive, indeed, but are the caufcs to others in which they are inhe- 
 rent, of receiving affirmation ; as, for inftance, motion is not moved, but that 
 which is in motion. Negation, therefore, is predicated of it, viz. the not being 
 moved, though other things are moved through it. And, in fhort, every pafTion is 
 itfelf impaffive; fince, being fimple, it either is or is not. But that which fuffcrs, 
 or the pallive fubjedt, is through paffion a compofite. Negations, therefore, are not 
 after this manner denied o{ the one : for neither is the one ingenerated in any thing, 
 but is the caufc of all the affirmations, the negations of which we introduce to it ; 
 but it is by no means ingenerated in thofe things of which it is the eaufc. But, if 
 I may be allowed concifcly to -relate what appears to me, as the one is the caufe of 
 wholes, {o negations are the caufes of affirmations ; whence fuch things as the 
 fecond hypothefis in the Parmenides of Plato affirms, the firft denies. For all thofe 
 affirmations proceed from thefe negations; and the one is the caufe of all things, as 
 being prior to all things : for as foul, being incorporeal, produces body, and as intel- 
 lfii9, by not being foul, gives fubriftence to foul, fo the one, being void of multitude. 
 
 gives.
 
 462 ADISSERTATIONON 
 
 gives fubfiflence to all multitude, and, being without number and figure, produces 
 number and figure ; and in a fim'.lar manner with refpeif to other things : for it is no 
 one of the natures which it produces ; fince neither is any other caufe the lame with 
 its progeny. But if it is no one of the natures to which it gives fubfiftence. and at 
 the fame time gives fubfiflence to all things, it is no one of all things. If, therefore, 
 we know all things afHrmativel}', we manifeft the one negatively, by denying every 
 thing of it ; and lb this form of negation is generative of the multitude of afHrnia- 
 tions. Thus, the unfigured, when applied to the one, is not like that of matter 
 which is beheld according to a privation of figure, but it is that which generates and 
 produces the order which fubfifls according to figure. 
 
 " With refped to matter, therefore, negations are worfe than affirmations, becaufe 
 lhey are privations, but affirmations are participations of which matter is efTcntially 
 deprived. But, with refpedl to beings, negations are conjoined with affirmations : 
 and, when applied to the one, they fignify tranfcendency of caufe, and are better 
 than affirmations. Hence, negations of things fubordinate are verified in caufes 
 pofterior to the one. Thus, when we fay that the foul neither fpeaks nor is filcnt, 
 we do not affert thefe things refpedling it as of fiones and pieces of wood, or any 
 other infenfible thing, but as of that which is generative in an animal of both voice 
 and filence. And again, we fay that nature is neither white nor black, but unco- 
 loured and without interval. But is fhe without thefe in the fame manner as mat- 
 ter? By no means ? for Hie is better than the things denied. But flie is unco- 
 loured and without interval, as generative of all-various colours and intervals. In 
 the fame manner therefore, we fay that the monad is without number, not as being 
 fubordinate to numbers and indefinite, but as generating and bounding numbers. 
 I mean the firft monad, and that which we fay contains all the forms of numbers. 
 All therefore that is denied of the one proceeds from it : for it is neceffiiry that it 
 fhould be none of all things, that all things may be its offspring. Hence, it appears 
 to me that Plato often denies of the one things which are oppofitc to each other, 
 fuch as that it is neither iivhole nor part, neither y2zw/e nor different, neither at reji nor 
 in motion : for it is expanded above all habitude, and is pure from every duad, being 
 the caufe of all the multitude of thefe, of twofold coordinations, of the firfl duad, 
 and of all habitude and oppofition. For nature is the caufe of all corporeal oppofi- 
 tions, the foul of all vital caufes, and intellciSl of the genera pertaining to foul. But 
 
 .the
 
 NULLITIES AND DIVERGING SERIES. 463 
 
 the one is fimply the caufe of all divifions : for it cannot be faici that it is the caufe 
 of fome, and not the caufe of others ; but the caufe of all oppofition, is not itfelf 
 oppofed to any thing : for, if it were, it would be requifite that there fhould be fome 
 other caufe of this oppofition, and the one would no longer be the caufe of all things. 
 Hence, we fay that negations are generative of afHrpnations ; thofe which are 
 afTumcd in the full: hypothefis of the Parmenides of thofe which are inveftigated in 
 the fecond : for, whatever the firft caufe generates in the firfl: hypothefis, is gene- 
 rated and proceeds in its proper order in the fecond. And thus the order of the 
 gods fubfifting from exempt unity is demonftrated." 
 
 And (hortly after he adds, " But here perhaps fome one may aflc us whether 
 we ufe negations through the imbecility of human nature, which is not able firmly 
 to apprehend the fimplicity <:>{ the one through a certain projetSlion (of intellect,) and 
 adhefive vifion and knowledge ? Or, whether natures better than our ibul know- 
 the one negatively in an analogous manner ? We reply, therefore, that intelledl 
 by its perceptions which are conjoined with forms knows forms, and comprehends 
 intelligiblcs, and this is a certain affirmative knowledge : for that which is ap- 
 proaches to that which /V, and intellect is that which it underftands,. through the in- 
 telledual perception of ilfelf. But, by an unity above intelledi, it is conjoined with 
 the one, and through this union knows the one by not being that which is being. 
 Hence, it knows the one negatively : for it poficfTes a twofold knowledge, one kind 
 as intelle<9^, the other as not intelledt ; one as knowing itfelf, the other becoming 
 inebriated, as fome one fays, and agitated with divine fury from netiar ; and one- 
 fo far as It is, but the other fo far as it is not. Much-celebrated intelledt itfelf,_ 
 therefore, poflefles both a negative and affirmative knowledge of the one. But if 
 rntellect, divine fouls alfo, according to their fummits and unities energife enthu- 
 fiaftically about the one, and are efpecially divine fouls on account of this energy ; 
 but, according to their intelle6lual powers, they are fufpended from intellcdl, round 
 which they harmonically dance. According to their rational powers they know 
 themfelves, preferve their own eiTcnce with purity, and evolve the produflive princi- 
 ples which they contain ; but according to thofe powers which are charadlerized by 
 opinion, they comprehend and govern in a becoming manner all fenfible natures. 
 And all the other kinds of knowledge which tbey poflefs are indeed affirmative ; 
 for they know beings as they are; and this is the peculiarity of affirmation. But 
 
 the
 
 464 A DISSERTATION ON 
 
 the cnthufiaflic energy about the one is in thcfe a negative knowledge : for they do not 
 know that the one is, but that he is not, according to that which is better than lie 
 is. But the intellcclion o( that which is not, is negation. If, therefore, both di- 
 vine fouls and inuch-celcbrated intellect itfclf know ths one through negation, what 
 occafion is there to def|jife the imbecility of our foui, earneftly endeavouring to 
 nianifcfl negatively its uncircunifcribed nature? for n-otliing pertaining to //^f /;_y? 
 is fuel) as we are aceullomcd to know, i. c. a certain quality of a thing, as I'lato 
 fiys in his fccond Epilllc. This however is the caufc of every thing beautiful in 
 the Ibul, viz. to invcfligate the eharadlcriflic of the firfl, to commit in a beccming 
 manner the knowledge of him to the reafoning power, ::nci to excite the one whicli 
 we contain, that, if it be lawful fo to fpeak, we may know the fimilar by the fimilar, 
 to far ^s it is pofilble to be known bv our order: for, as by opinion wc know the 
 obje6ls of opinion, and by the dianoctic j ower dianoaic o'ljeAs, and as by our in- 
 t€lle<51ual part we know that which is intelligible, fo by our one we know the one*.'' 
 
 62. In 
 
 * lea; h av ti; amo touto J/^aj ETaVEfoiTO, TCOTipay T015 aTTopxTiXOi; xfa/ztSj; Jijs T»v a^rfcvEiav r-n;av6^a- 
 Tr.vir; ^uiricii;, ou ouvaficvrii tuv a^^oTvira tou ho; '7rapa>^S£:v 01 anQoXri; tivoj sTTipEi&Tiiia;, xai 5-as km 
 V^iicrEfflj E^ii^najxiv-.i;, h xxi ia H^tirtoid. trii >i/x£Tt^a:j -^vx^i Kcna to avahcynv aTroiparuui; yiyvxaKti to Iv. 
 pctaev ?« ovv 'oti xai vou;, rsu; fji.iv culivyi'i; tt^-:; tx z:lr\ voniTEcriv, aula, yiyviiaxiiv, xai 'Trtpt'hocfi.SavH ra 
 lOATx, Kat icjiv auTYi KaTaparixn ti; ii yvuing. lov yy.p eoi'Ti TTEAaf ;i, nai 6 voei toito UTrj, oia t>i{ ixutou 
 
 VOltCEW!" Til Je UTTt^ VOUV DloSt (TUVnTTTai TT^C; TO IV, KM Jia T>)f EJUCTEa; TaUTr.i ytyiuaKH TO £», Ttf /irj OVTl TOCV. 
 
 a7ro(paTiiii>; apa yiyvuaxn to iv. oma; ya^ tx^i Ta; yvacru;, rr,v /Kv a; vcu;, Tr.v oe if ^n nvi, xm Tnv fjLiv if tautov 
 yr/v'jKTxtisv, Tvv Ss /xtOutoy f'vjiri T15 «ai awTov cvOia^nv ra vixTa^i, xai tiiv fiiv ij E<rTi, Try ?e i; cux ijTi. Ttiv 
 fyivj s^a aTTO^aTiKYy ixii r/ov yvuann-j, tm? 0; HaTcfaTtanv, xai auTc; TroT^uu/xvYim; vcvi;. aMa /xev ei von;, xai 
 fct SEiai \J-u%ai xara fj.tv ra; Ixutuv axpoTrua; xai Ta; ivoTma; ei6o'j(Xiaiouiri teoi to iv, xai ciai 5iiai \)/i>x,at 
 //.ay.iJTa TavTYi; tvtxx Tr; tvt^yzia;, Kara oe Ta; voz^x; ouvafMi; cin^TnTai Tcv vou, xai •mpixo^o^ouJiv auTcv 
 xaTa 3e Ta; wmixa;, lauTa; yiyvoxrxouai, xai tjiv £a-jToiv ouatav ax^avTx; criifouiri, xai Toi/j lavTtnv hoyouf 
 aviMTTOUji, xaTd Se Ta; ^o^aaTtxa; Ta aiair,Ta iravTc '!r^oti>.r\(pa(ri Tf xai xicTivSmovat JeovTi-;. xai naaai 
 fuj at a>->.at yviiisti; aurav itjt xarapaTixjciy ra ypcg evTa u; lUTi yiyvu^xcuci, tcuto os ktti xaTaipajKn; 
 t^ior T)» ?6 ev93U£ri37TiK>) TEfi TO IV lu^yva TO Dt^oOaTiKov EJ-Ti XXI Ell Txi/Tai; Tws yxiic'.a; o* ya^ Iti taTi to 
 h yiytauxovuiv, a^x' oti oux ej-ti, xuto. to xpiTTsv tou ecttiv « Je tov oti ojx tcrri vonui; aTiopaai; cariv. 11 
 TC:\m xxi ai Sfiai -^uxxi, xai avTo; TToP^vu/xvriTo; vov; 5i a-7ro(pa<Ttu; yiyvuuxH to h, ti x,-*i y.aTayiyvui7xu\ 
 a^uva/iiav td; ri/xETEpa; ^ux^f'y oi^oipxTixu; auTcu TO aTf^iMTTTov tthixiuaOai aTTcvSaiouff^; ; tcu yotf TTfaTov 
 ^x^'iv oiiStv eiTTtv ToiouTOv, oiov yiyvai7Kiiv eiaiSsc/j.Ev, TTOiov Ti /^nVy a; avTo; ev c7riaTo\ai; tifWE, axxa //.nv 
 jouTO tJTi TO TtavTav ai'nv th ^ux^ xa>.av, to tov i5ioT«Ta tou WfUTCu fiiTsiv, xai yoyu/tto tvv txtivou yvu<<Ti» 
 
 JTriTfsnTII
 
 KULLItlES AND DIVERGING SERIES. 465 
 
 62. In the fecond place, fince we have fhown that infinite orders of infinite 
 feries have a non-quantitive fubfiflence in unity or the monad, this evinces the 
 ti'uth of what is fo often aflerted by the Pythagoraeans and Piatonifts, that the 
 monad comprehends in itfelf all the forms of numbers, and this occuldy, and, as it 
 may be faid, fuper-numerically, and not after the manner of quantity. Hence, he 
 who is able to afcend from the mathematical monad to intelle6t, of which the monad 
 is an imitation, will perfpicuoufly fee how all forms or ideas, of which numbers are 
 images, are by a much greater priority comprehended in intelledt. He will like- 
 wife fee how they fubfifl; in occult and indivifible union, and how all are in each, 
 though at the fame time each is etientially diftin(5l from the reft. Hence intelledlj 
 from its all-comprehending nature was called by Parmenides a tphere, 
 
 'iruvTo9iv svxvkKov a-(pxi^rig svxXiyTtwv oyx-oj 
 
 The fenfe of which is, " Every way fimilar to a perfed fphere, equal from the 
 middle, and rejoicing in revolving manfion." For all forms are primarily in intel- 
 ledV, but fecondarily, and after the manner of images, in the monad and the whole 
 of a fenfible nature ; phyfically in the latter, and mathematically in the former. 
 " Hence," fays Proclus, " intellect: is an intelligible fphere, the monad a dianoetic, 
 and the world a fenfible fphere, containing in itfelf images of the eternal gods*." 
 
 Si- Since too, infinitely fmall quantities, — which, from what has been faid, are 
 evidently analogous to the fupereflential unities, of which we have fpoken fo largely 
 in note to p. 286, twelfth book, and the additional notes, — fince, I fay, they fubfift 
 infinitely in the monad, and may be confidered as conftituting the very nature of 
 it, — hence, an infinitely fmall quantity, or the one, is fuperior to the monad ; for in- 
 finitely fmall quantities compofe, but are not compofed from, the monad. And 
 hence we fee, that there is an evident diftindlion between the one and the monady. 
 
 jwiTfECTfiv 3tovT«j, xai av£ytif£iv to tv «/*iv sv, iv« Ta o/«oiw to 0|UOiov £i 9f;Mi{ ix-imv yvuvai aj xxra T»y- 
 i/iirc^xv ja^iv SuvatTo; -uvuficQa. u; yaf Join ra ^o^aara yiyvatnioiAtVytuti ii; Siavoiat tx 5iavo)iT«, xai a; Ta 
 vot^a ra (v ijuiv to vonrov, ouru xai Ta ivi to sv. Procl. in Parmenid. lib. 5. 
 
 * 'H (Tipaifa ya^ vo»t>i (Utv voi/?, fiavowTi) Jt h /i^ovajj aiaSmn ft McrfiCi iviou tiwmi fe^m ev lavra ruv 
 
 ai'Jifflv Sew. Procl. in Parmenid. lib. 5. 
 
 3 O * which^
 
 466 A D I S S E R T A T I O N O N 
 
 which, as we have obfervcd in note to p. 353, was one of the dogmas of the Py- 
 thagorasans. All numberj too, is in like manner full of the nature of ile one, or the 
 infinitely fmall ; for any number divided by an infinitely fmall quantity produces 
 an infinite ferics. 
 
 64. Again : when a finite quantity is fubtraaed from itfelf, an infinitely finall 
 quantity may be confidered as the remainder. Thus, a fubtra6led from a is a — a^ 
 which confpicuoufly ftiows us as in an image, that when all multitude is talen away 
 from beings, the one ftill remains : for numbers are images of beings, and an infi- 
 nitely fmall quantity of the one. 
 
 65. We have alfo fhown that an infinitely fmall quantity, when confidered as 
 conneded with magnitude, is a point ; and that, thus confidered, it is an admirable 
 image of the one, which is participated by the higheft beings, the following pafTage 
 from the MS. Commentary of Proclus On the Parmenides beautifully evinces; 
 " An apt refemblance of the progrefiion of the divine unities now prefcnts itfelf to 
 our view. Becaufe a line is the firfi: continuous and divifiblc nature amongft mag- 
 nitudes, hence, it participates of an irKlivifible, that is, of a point. And this point, 
 though it is allotted a fuperlincar condition, and is indivifible, yet it fubfifts in tlie 
 line, is fomething belonging to it, and is the fummit of the line. To which w:e 
 may add. that many lines in a circle touch by their fcveral points the centre of the 
 circle. In like manner an intelligible and intelledlual eflence, becaufe it is the firft 
 multiplied nature, on this account partakes of a tranfcendent unity. And this 
 unity, though it is neither eflence nor obnoxious to cflential multitude, yet abides 
 in eflence, or rather fubfifts as its vertex, through which every intelle(?tual efl^cnce 
 is a god, enjoying divine unity as the very flower of its unity, and as that which 
 conjoins it with the hiejfahle one" 
 
 66. Since too, we have fhown that infinitely fmall quantities, or points, in a line 
 have a linear, in a fuperficies a fuperficial, and in a folid a folid fubfiftence, or, in 
 other words, that in a line, fuperficies and folid, they are refpedlively aflefled with 
 the nature of line, fuperficies and folid, at the fame time that they fiill retain in each 
 their non-quantitivc nature, — hence, we niey fee as in images how incorporeal 
 
 natures.
 
 NULLITIES AND DIVERGING SERIES. -167 
 
 natures, when they become profoundly connedted with bodies, are afFe61ed indeed 
 with a corporeal nature, but fiill retain an incorporeal fubfiftence. And thus much 
 concerning infinitely fmall quantities fo far as they are images of fupernal natures. 
 
 I (hall only obferve further at prefcnt that the mathematical fciences ought never 
 to be leparated from intcllcdual philofophy. The Pythagoraeans and Platonifts, 
 from the fubfiftence of thefe fciences between fenfible and intelle6tual natures, juftly 
 conlidered them as a bridge, by which we are enabled to pafs from the obfcurity of 
 the one to the fplendor of the other. Hence the Pythagoric senigma, " a figure 
 and a tlep, but not a figure and three oboli ;" fignifying, that we fliould employ 
 thefe fciences as aftep to higher attainments, and not, by confidering them as alone 
 fubfervient to the neceffities of a mortal life, ncglecin: that elevation which rifes to an 
 intelligible eflence : for the mathematical fciencc, when thus employed as a ftep, 
 removes, like the Homeric Minerva, the darknefs of a fenfible nature from the 
 dianoi'tic eye, which is better worth fiving than ten thoufand corporeal eyes, and 
 preferves us by its Hermetic gift from the incantations and delufions of thefe 
 Circasan realms. " Hence, (fays Proclus in Eucl. p. 14,) the bufinefs of this 
 fcience is apparent from its name : for it moves knowledge, excites intelligence, 
 purifies the dianoetic part, unfolds the forms which we efTentialiy contain, removes 
 the oblivion and ignorance which we poficfs from generation, and diflblves the 
 bonds v.ith which we are held in captivity by an irrational nature. And all this 
 it efFeds according to a real fimilitude of that divinity (Mercury) who leads into 
 light intellectual gifts, fills all things with divine reafons, moves fouls to intellcd}, 
 excites them as from a profound fleep, converts them by inquiry to thcmfelves, per- 
 fects them through obftetrication, and through the invention of pure intelled con- 
 ducfts them to a blefled life *." 
 
 * Kai TO eeyov apcc th; i7naTniJ.i\; raun;, oTrom Jii ti tariv en tow ovcuaro; ^tiMUTat, HtmDcov T)i; 
 yvuirefflf, xat cyepriHov m; vodcteuj, km xaSaf twov th; ^lavoia;, ttat cKpavTMOv rm xa-r' ou<nav i.aiv (lege i,(i.n) 
 ima^XO^Tijiv eiSwv, MiSds te xai ayvoiaj apaioETixov, iiv utto rr,; ysnaiui ixof^^^t ««' aToM/Tixcv im ex rns 
 ftXoyiaf hir/iav, Kara tov Seov ovra; tov thj ettij-t);/*)),- Ta;i>T)i; £?iofov, 05 -jfiiayii nvj eij to intpam -ra voi^x 
 li^pa, Ti^npoi h Trance tbv Seiwv Myuv, kivei h ra; -i^vxa; £5" voi/v,.x«i aawt^ ik xa^ou Patka; ctvsyti^ti, Jia 
 (mwa^i h smaTfE^ti ^rpoj avr^i, km Jia ^amai (lege iMiiiai) teaeioi, km fi« ^ivaw, (lege ti/ficrsn?) 
 
 THE END.
 
 ERRATA, 
 
 P. 145, 1, 3, for luhich predication read this predication^ 
 V. 152, in the note, for ?fxa» read h xai. 
 
 Davis, Wilks, and Taylor,' 
 Printers, Chancery-lane.
 
 . P 000 128 664
 
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