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 THE 
 
 O F 
 
 L O G I C K. 
 
 In FOUR BOOKS. 

 
 THE 
 
 ELEMENTS 
 
 L O 
 
 C K. 
 
 IN FOUR BOOKS. 
 
 BOOK I. 
 
 Of the Original of our 
 Ideas, their various Di- 
 vifians, and the Manner 
 in which they contribute 
 to the Increafe of Know- 
 ledge j with a Philofo- 
 phical Account of the 
 Rile, Progrefs, and Na- 
 ture of human Lan- 
 guage. 
 
 BOOK II. 
 
 Of the Grounds of human 
 Judgment, the Doftrine 
 of Propofitions, their Ufe 
 in Reafoning, and Divi- 
 lion into felf-evident and 
 demonftrable. 
 
 BOOK III. 
 
 Of Reafoning and Demon, 
 ftration, with their Ap- 
 plication to the Inveiti- 
 gation of Knowledge, 
 and the common Affairs 
 of Life. 
 
 BOOK IV. 
 
 Of the Methods of Inven- 
 tion and Science, where 
 the feveral Degrees of 
 Evidence are examined, 
 the Notion of Certainty 
 is fixed and ftated, and 
 the Parts of Knowledge 
 in which it may be at- 
 tained, demonstrated at 
 large. 
 
 Defigned particularly for Young Gentlemen at the 
 Univerfity, and to prepare the Way to the Study 
 of Philofophy and the Mathematicks. 
 
 By WILLIAM DUNCAN, | 
 
 Profefibr of Philofophy in the Mari/hal College of ABERDEVN* 
 
 Doclrina fed Vim promovet infitaoi ; 
 Reftique cultus Pedora roborant. Hon. 
 
 The EIGHTH EDITION. 
 
 LONDON: 
 Printed for J. DODSLEY, in Pali-Mall. 1787..
 
 ( V ) (01 
 
 
 A/SA ~ ~ rSfSrS 
 
 XXX kjM( XXX 
 
 To the RIGHT HONOUR ABU 
 
 I 
 
 S I R, 
 
 F I take this Opportunity of pub- 
 lifhing to the World the Efteerri I 
 have for a Character to which Learn- 
 ing is fo greatly indebted, I hope you 
 will not think yourfelf injured by 
 fuch a Declaration from a Man that 
 
 honours
 
 Vi D E DI C A T,I O N. 
 
 honours you, and who looks upon 
 the Liberty of putting the following 
 Work under your Patronage, as one 
 of the happy Incidents of his Life. 
 
 FROM the firft Moment I form- 
 ed the Defign of it, I had it in my 
 Thoughts to addrefs it to you ; and 
 indeed what could be more natural, 
 than that I fliould be ambitious of 
 infcribing a Treatife upon the Ele- 
 ments of Philofophy, to one, who 
 has fb eminently diftinguifhed himfelf 
 by his exteniive Knowledge in that, 
 as well as all the other Branches of 
 human Learning ? 
 
 YOUR great Abilities in every Kind, 
 have defervedly recommended you to 
 the Notice of your King and Country, 
 and occafioned your being courted and 
 importuned to accept of thofe high 
 Offices of State, which others purfue 
 
 with
 
 Vli 
 
 with fo much Eagernefs, and find it 
 often difficult to obtain, by all the 
 Arts and Endeavours of Ambition. 
 Nor have your Talents been confined 
 to the View of your own Country 
 alone. Foreign Nations have feen 
 and admired you, andftill fpeak with 
 the greateft Applaufes of your wife 
 and able Conduct, when it was your 
 Province to act as a Britijh Minifter 
 abroad. 
 
 BUT theQualities of a great Statef- 
 man are not thofe alone by which 
 you have rendered yourfelf illuflrious. 
 The Virtues of private Life no lefs 
 actuate and adorn your whole Beha- 
 viour, and add a new Dignity to the 
 high Station to which your Merit 
 has raifed you. Affability, Compla- 
 cency of Manners, and, above all, an 
 extenfive Humanity and Benevolence, 
 which takes Pleafure in doing Good, 
 
 are
 
 viii DEDICATION. 
 
 are diftingui filing Parts of your Cha- 
 racter, and have contributed no lefs 
 than your other extraordinary En- 
 dowments, to that univerfal Acknow- 
 ledgment which is paid you by your 
 Country. 
 
 THAT you may long live to be an 
 Ornament and Bleffing to the Nation, 
 and to enjoy the Pleafure which arifes 
 from a Confcioufnefs of the.Efteem 
 and Approbation of all good Men, is 
 the fincere and hearty Prayer of, 
 
 S i R, 
 
 Tour much obliged, 
 and moft obedient 
 bumble Strvanf, 
 
 W. DUNCAN.
 
 ( I ) 
 
 \ 
 
 THE 
 
 ELEMENTS 
 
 O F 
 
 L O G I C K. 
 
 INTRODUCTION. 
 
 I. ^""V F all the human Sciences, 
 
 fm, r IinperteHft 
 
 tnat concerning Man is c f t bi Kem- 
 V-X certainly the moft wor- jg f // ""' 
 thy of Mao, and the moft neceflary 
 Part of Knowledge. We find ourfelves in this 
 World furrounded with a Variety of Objects ; 
 we have Powers and Faculties fitted to deal 
 with them, and are happy or miferable in pro- 
 portion as we know how to frame a right Judg- 
 ment of Things, and fhape our Actions agree- 
 ably to the Circumftances in which we are 
 placed. No Study therefore is more important 
 than that which introduces us to the Know- 
 ledge of ourfelves. Hereby we become ac- 
 B quainted
 
 quainted with the Extent and Capacity of the 
 human Mind - y and learning to diftinguifli what 
 Objects it is fuited to, and in what manner it 
 muft proceed in order to compafs its Ends, we 
 arrive by Degrees at that Juftnefs and Truth 
 of Underftanding, which is the great Perfection 
 of a rational Being. 
 
 II. IF we look attentively into 
 ^Ja"L .f Things, and furvey them in their 
 Pcrfcaion in f u ll Extent, we fee them rifmg one 
 
 Things. , i r-k 
 
 above another in various Degrees 
 of Eminence. Among the inanimate Parts of 
 Matter, fome exhibit nothing worthy our At- 
 tention; their Parts feem as it were jumbled to- 
 gether by mere Chance, nor can we difcover any 
 Beauty, Order, or Regularity in their Compofi- 
 tion. In others we difcern the fined Arrange- 
 ment, and a certain Elegance of Contexture, 
 that makes us affix to them a Notion of Worth 
 and Excellence. Thus Metals, and precious 
 Stones, are conceived as far furpaffing thofe un- 
 formed Mafles of Earth, that lie every where ex- 
 pofed to view. If we trace Nature onward, and 
 purfue her through the vegetable and animal 
 Kingdoms, we find her ftill multiplying her Per- 
 ft&ions, and rifmg, by a juft Gradation, from 
 mere Mechanifm to Perception, and from Per- 
 ception, in all its various Degrees, to Reafon and 
 Underftanding. 
 
 III. BUT
 
 ( 3 ) 
 
 III. BUT though Reafon be the vfefefaft f 
 Boundary by which Man is diftin- Culture, and 
 
 particularly of 
 
 guifhed from the other Creatures the Study of 
 that furround him, yet we are far L & uk ' 
 from finding it the fame in all. Nor is this Ine- 
 quality to be wholly afcribed to the original 
 Make of Men's Minds, or the Difference of 
 their natural Endowments. For if we look 
 abroad into the feveral Nations of the World, 
 fome are over-run with Ignorance and Barbarity, 
 others flourifh in Learning and the Sciences ; 
 and what is yet more remarkable, the fame Peo- 
 ple have in different Ages been diftinguifhed by 
 thefe very oppofite Characters. It is therefore by- 
 Culture, and a due Application of the Powers 
 of our Minds, that we increafe their Capacity, 
 and carry human Reafon to Perfection. Where 
 this Method is followed, Knowledge and 
 Strength of Underftanding never fail to enfue ; 
 where it is neglected, we remain ignorant of our 
 own Worth ; and thofe latent Qualities of the 
 Soul, by which (he is fitted to furvey this vaft 
 Fabrick of the World, to fcan the Heavens, and 
 fearch into the Caufes of Things, lie buried in 
 Darknefs and Obfcurity. No Part of Know- 
 ledge therefore yields a fairer PTofpecT: of Im- 
 provement, than that which takes account of 
 the Underftanding, examines its Powers and 
 Faculties, and {hews the Ways by which it 
 B 2 comes
 
 ( 4 ) 
 
 comes to attain its various Notions of Things. 
 This is properly the DcTign of Logick, which 
 may be juftly ftyled the Hiftory of the human 
 Mind, inafmuch as it traces the Progrefs of our 
 Knowledge, from our firft and fimple Percep- 
 tions, through all their different Combina- 
 tions, and all thofe numerous Deductions that 
 refult from varioufly comparing them one with 
 another. It is thus that we are let into the natu- 
 ral Frame and Contexture of our own Minds, 
 and learn in what manner we ought to conduft 
 our Thoughts, in order to arrive at Truth, and 
 avoid Error. We fee how to build one Difco- 
 very upon another, and by preferving the Chain 
 of Reafonings uniform and unbroken, to purfue 
 the Relations of Things through all their La- 
 byrinths and Windings, and at length exhibit 
 them to the View of the Soul, with all the Ad- 
 vantages of Light and Conviction. 
 Cftrationt of ^- BUT as ^ Undemanding, in 
 tb Mad. advancing from one Part of Know- 
 ledge to another, proceeds by r. juft Gradation, 
 and exerts various Acts, according to the diffe- 
 rent Progrefs it has made, Logicians have been 
 careful to note thefe feveral Steps, and have di- 
 ftinguifhed them in their Writings by the Name 
 of the Operations of the Mind. Thefe they 
 make four in Number, and agreeably to that 
 have divided the whole Syftem of Logick into 
 
 four
 
 ( 5 ) 
 
 four Parts, in which thefe Acts are feverally ex- 
 plained, and the Conduct and Procedure of the 
 Mind, in its different Stages of Improvement, 
 regulated by proper Rules and Observations. 
 Now, in order to judge how far Logicians have 
 followed Nature, in this Diftinction of the Pow- 
 ers of the Underftanding, let us take a fhort 
 View of the Mind, and the manner ofits Pro- 
 grefs, according to the Experience we have of it 
 in ourfelves, and fee whither the Chain of our 
 own Thoughts will without Conftraint lead us. 
 
 V. FIRST, then, we find ourfelves 
 furrounded with a Variety of Ob- 
 jects, which acting differently on our Senfes, 
 convey diftinct Impreffions into the Mind, and 
 thereby roufe the Attention and Notice of the 
 Underftanding. By reflecting too on what 
 pafles within us, we become fenfible of the Ope- 
 rations of our own Minds, and attend to them as 
 a new Set of Impreflions. But in all this there 
 is only bare Confcioufnefs. The Mind, without 
 proceeding any farther, takes notice of the Im- 
 preflions that are made upon it, and views 
 Things in order as they prefent thcmfelves one 
 afcer another. This Attention of the Under- 
 ftanding to the Objects acting upon it, whereby 
 it becomes fenfible of the Impreffions they make, 
 is called- by Logicians Perception ; and the No- 
 tices themfelves, as they exift in the Mind, and 
 3 3 are
 
 ( 6 ) 
 
 are there treafured up to be the Materials of 
 Thinking and Knowledge, are diftinguifhed by 
 the Name of Ideas. 
 
 VI. BUT the Mind does not al- 
 
 judgment. . , 
 
 ways reft latisned in the bare View 
 and Contemplation of its Ideas. It is of a more 
 a&ive and bufy Nature^ and likes to be aflembling 
 them together, and comparing them one with 
 another. In this complicated View of Things, 
 it readily difcerns that fome agree and others 
 difagree, and joins or feparates them according to 
 this Perception. Thus, upon comparing the 
 Idea of two added to two, with the Idea of four, 
 we at firft Glance perceive their Agreement, and 
 thereupon pronounce that two and two are equal 
 to four. Again, that white is not black, that 
 five is lefs than feven, are Truths to which we 
 immediately afTenr, as foon as we compare thofe 
 Ideas together. This is the firft and fimpleft 
 Act of the Mind, in determining the Relations 
 of Things, when by a bare Attention to its own 
 Ideas, comparing any two of them together, it 
 can at once fee how far they are connected or 
 disjoined. The Knowledge thence derived is 
 called intuitive, as requiring no Pains or Exa- 
 mination ; and the A6t of the Mind aflernbling 
 its Ideas together, and joining or disjoining them 
 according to the Refult of its Perceptions, is 
 what Logicians tetm Judgment. 
 
 VII. IN-
 
 ( 7 ) 
 VII. INTUITION affords the high- 
 
 _ ,_ _ . . - i i . Reafoniitf, 
 
 eft Degree of Certainty, it breaks m 
 with an irrefiftible Light upon the UnderftancU 
 ing, and leaves no Room for Doubt or Hefitation. 
 Could we in all Cafes, by thus putting two Ideas 
 together, difcern immediately their Agreement or 
 Difagreement, we fhould be exempt from Error, 
 and all its fatal Confequences. But it fo hap- 
 pens, that many of our Ideas are of fuch a Na- 
 ture that they cannot be thus examined in Con- 
 cert, or by any immediate Application one to 
 another ; and then it becomes neceflary to find 
 out fome other Ideas that will admit of this Ap- 
 plication, that by means of them we may difco- 
 ver the Agreement or Difagreement we fearch 
 for. Thus the Mind wanting to know the 
 Agreement or Difagreement in Extent between 
 two inclofed Fields, which it cannot fo put toge- 
 ther as to difcover their Equality or Inequality by 
 an immediate Comparifon, cafts about for fome 
 intermediate Idea, which by being applied firft to 
 the one, and then to the other, will difcover the 
 Relation it is in queft of. Accordingly it a/Fumes 
 fome ftated Length, as a Yard, &. and mea- 
 furing the Fields one after the other, comes by 
 that means to the Knowledge of the Agreement 
 or Difagreement in queftion. The intervening 
 Ideas made ufe of on thefe Occaflons, are call- 
 ed Proofs i and the Exercife of the Mind in 
 B 4, finding
 
 finding them out, and applying them for the Dif- 
 covery of the Truths it is in fearch of, is what 
 we term Reafoning. And here let it be obferyed, 
 that the Knowledge gained by Reafoning is a 
 Deduction from our intuitive Preceptions, and 
 ultimately founded on them. Thus, in the 
 Cafe before mentioned, having found by meafur. 
 ing that one of the Fields makes threefcore fquare 
 Yards, and the other only fifty- five, we thence 
 conclude that the firft Field is larger than the fe- 
 cof)J. Here the two firft Perceptions are plainly 
 intuitive, and gained by an immediate Application 
 of the Meafure of a Yard to the two Fields, one af- 
 ter another. The Conclufion, though it produces 
 no lefs certain Knowledge, yet differs from tho 
 others in this, that it is not obtained by an imme- 
 diate Comparifon of the Ideas contained in it one 
 with another, but is a Deduction from the two 
 preceding Judgments, in which the Ideas are fe- 
 verally compared with a third, and their Relation 
 thereby difcovered. We fee, therefore, that 
 Reafoning is a much more complicated Act of 
 the Mind than fimple Judgment, and neceflarily 
 prefuppofes it, as being ultimately founded on 
 the Perceptions thence gained, and implying the 
 various Comparifons of them one with another. 
 This is the great Excercife of the human Facul- 
 ties, and the chief Inftrument by which we pufli 
 on our Difcoveries, and enlarge our Knowledge. 
 
 A Quick-
 
 ( 9 ) 
 
 A Quicknefs of Mind to find out intermediate 
 Ideas, and apply them fkilfully in determining 
 the Relations of Things, is one of the principal 
 Diftinctions among Men, and that which gives 
 fome fo remarkable a Superiority over others, 
 that we are apt to look upon them as Creatures 
 of another Species. 
 
 VIII. THUS far we have traced 
 
 . Method. 
 
 the Progrefs of the Mind in Think- 
 ing, and feen it rifing by natural and eafy Steps 
 from its fir ft and fimple Perceptions, to the Sxer- 
 cife of its higheft and moft diftinguiftiing Faculty. 
 Let us now view it in another Light, as enriched 
 with Knowledge, and ftored with a Variety of 
 Difcoveries, acquired by a due Application of its 
 natural Powers. It is obvious to confider it in 
 thefe Circumftances, as taking a general Survey 
 of its whole Stock of intellectual Acquifitions, 
 difpofing them under certain Heads and ClafTes, 
 and tying them together, according to thofe 
 Connections and Pcpcndencies it difcerns be- 
 tween them. It often happens, in carrying on 
 our Enquiries from Subject to Subject, that we 
 ilumble upon unexpected Truths, and are en- 
 countered by Difcoveries which our prefent 
 Train of Thinking gave no Profpect of bring- 
 ing in our Way. A Man of clear Apprehenfion, 
 and diftinct Reafon, who after due Search and 
 Examination has mattered any Part of Know- 
 B $ ledge,
 
 ( 10 ) 
 
 ledge, and even made important Difcoveries in 
 it, beyond what he at firft expected, will not fuf- 
 fer his Thoughts to lie jumbled together in the 
 fame confufed Manner as Chance offered them ; 
 he will be for combining them into a regular 
 Syftem, where their mutual Dependence may be 
 eafily traced, and the Parts feem to grow one out 
 of another. This is that Operation of the 
 Mind, known by the Name of Difpofitlon or Me- 
 thod) and comes in the laft in order, according to 
 the Divifion of the Logicians, as prefuppofing 
 fome tolerable Meafure of Knowledge, before it 
 can have an Opportunity of exerting itfelfin any 
 extenfive Degree. 
 
 P<r C <p t icna*d IX ' WE fee then that this f U ^ 
 
 judgment, fold Diftin&ion of the Powers of 
 
 "Termi cf a , i r T i 
 
 ery txtenfat tn ^ Mind in Perception, Judgment, 
 
 ion. Reafoning, and Difpofition, as well 
 as the Order in which they are placed, have a 
 real Foundation in Nature, and arife from the 
 Method and Procedure of our own Thoughts. 
 It is true, there are many other Actions and Mo- 
 difications of the Underftandingj befides thofe 
 above mentioned^ as Believing, Doubting, Af- 
 jfenting, (ffr. but thefe are all implied in the Adi 
 f Reafoning, in the like manner as Comprehend- 
 ing, Abftradling, Remembering, may be referred 
 to the firft Operation of the Mind, or Perception. 
 This will appear more fully in the Sequel, when 
 
 we
 
 C ) 
 
 we come to handle the feveral Parts of Logick fe- 
 
 parately : at prefent we ftiall content ourfelves 
 
 with this general Account of Things j only it 
 
 feems neceflary to obferve, that Perception and 
 
 Judgment, in the Propriety of the Englijh Tongue, 
 
 have a much more extenfive Signification than, 
 
 Logicians commonly allow them. We not only 
 
 perceive the Ideas in our own Minds, but we are 
 
 faid alfo to perceive their Agreement or Dif- 
 
 agreement; and hence arife the common Phrafes 
 
 of intuitive Perceptions, Perceptions of Truth t 
 
 and of the Juftnefs of Arguments or Proofs; 
 
 where it is manifeft that the Word is applied 
 
 not only to our Judgments, but alfo to our Rea- 
 
 fonings. In a Word, whatever comes under 
 
 the View of the Mind, fo as to be diftin&ly re- 
 
 prefented and taken notice of, whether an Idea, 
 
 Propofition, Chain of Reafoning, or the Order 
 
 and Connection of Things, is thereby rendered 
 
 an Object of Perception, and gives Employment 
 
 to this firft and moft fimple of our Faculties. la 
 
 like manner the Word 'Judgment is feldom in 
 
 common Difcourfe confined to obvious and felf- 
 
 evident Truths. It rather fignifies thofe Con- 
 
 je&ures and Guefles that we form, in Cafes 
 
 which admit not of undoubted Certainty, and 
 
 where we are left to determine by comparing the 
 
 various Probabilities of Things. Thus a Man of 
 
 Sagacity and Penetration, who fees far into the 
 
 B 6 Humours
 
 Humours and Paflions of Mankind, and feldorn 
 miftakes in the Opinions he frames of Charac- 
 ters and Actions, is faid to judge well, or think 
 judicioufly. For thefe Reafons, it might not be 
 improper to change the common Names of the 
 two firft Operations' of the Mind, calling the 
 onefimple Apprehenfion^ and the other Intuition ; 
 which two Words feem better to exprefs their 
 Nature, and the Manner in which they are con- 
 verfant about their feveral Objects. This Accu- 
 racy of Diftinguilhing, where there is any the 
 leaft Difference, is in a peculiar Manner necef- 
 fary in a Treatife of Logick, as it is the profeff- 
 ed Defign of that Science to teach us how to 
 form clear and diftin& Notions of Things, and 
 thereby avoid being mifled by their Similitude Or 
 Refemblancc. 
 
 X. HAVING thus given a general 
 
 ided into four Idea of the four Operations of the 
 Uf<fuintfs*r>ti Mind, and traced their Connection 
 ExciL'eny. an( j Dependence one upon another, 
 I would next obferve, that in confequence of this 
 Divifion of the Powers of the Underftanding, 
 Logick is alfo divided into four Parts, which 
 treat feverally of thefe A&s, and give Rules and 
 Directions for their due Conduct and Regulation. 
 The Operations themfelves we have from Na- 
 ture, but how to exert them juftly, and employ 
 them with Advantage in the Search of Truth, is 
 
 a Know-
 
 C 13 ) 
 
 a Knowledge that may be acquired by Study and 
 Obfervation. It is certain that we meet with 
 falfe Reafonings as well as juft. Some Men are 
 diftinguifhed by an Accuracy of Thinking, and 
 a happy Talent of unravelling and throwing 
 Light upon moft obfcure and intricate Subjects. 
 Others confound the eafieft Speculations j their 
 Underftandings feem to be formed awry, and 
 they are incapable of either conceiving clearly 
 themfelves, or making their Thoughts intelligible 
 to others. If then we fet ourfelves carefully to 
 obferve what it is that makes the one fucceed fo 
 well, and how the others come to mifcarry, thefe 
 Remarks will furnifh us with an Art of the high- 
 eft Ufe and Excellency in the Conduct of Life. 
 Now this is the precife Buiinefs of Logtck to 
 expldn the Nature of the human Mind, and the 
 proper Manner of conducting its feveral Powers, 
 in order to the Attainment of Truth and Know- 
 ledge. It lays open thofe Errors and Miftakes 
 we are apt through Inattention to run into, and 
 teaches us how to diftinguifh between Truth, and 
 what carries only the Appearance of it. By 
 this means we grow acquainted with the Nature 
 and Force of the Underftanding, fee what Things 
 lie within its Reach, where we may attain 
 Certainty and Demonftration, and when we 
 muft be contented with bare Probability. Thefe 
 Confiderations fufficiently evince the Ufefulnefs 
 
 and 
 
 * i.
 
 ( '4 ) 
 
 and Benefit of this Science, which ought to be 
 eftablifhed as the Foundation and Ground-work 
 of all our other Knowledge, if we really wifh to 
 fucceed in our Enquiries. But we fhall now pro- 
 ceed to treat of its Parts feparately, according to 
 the Divifion given of them above. 
 
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 ( is ) 
 
 THE 
 
 ELEMENTS 
 
 O F 
 
 L O G I C K. 
 
 __ ____ . _ __- -- _____ .- - ---- * 
 
 BOOK I. 
 
 Of SIMPLE APPREHENSION er PER- 
 CEPTION. 
 
 CHAP. I. 
 
 Of the Original of our Ideas* 
 I.I B "VHE firft thing we obferve, 
 
 I B "V 
 
 i XT- c 
 
 when we take a View or prcbenfun and 
 what pafies within us, is, 1*""' 
 thatw are capable of receiving Impreflions from 
 a Variety of Objects, that diftinft Notices are 
 thereby conveyed into the Underftanding, and 
 that we are confcious of their being there. This 
 Attention x)f the Mind to the Objects acting upon 
 it, is what we c^lfimple^pprebenfion^n^ is in fact 
 the Mind itfelf taking a View of Things, as re- 
 
 prefented
 
 ( 16 ) 
 
 prcfcnted to it by its own Confcioufnefs. It is by 
 this means that we come to be furnifhed with all 
 thofe Ideas about which our Thoughts are em- 
 
 O 
 
 ployed. For being fenfible of the Lnprelnons made 
 upon us, and attending to the Perceptions they 
 bring, we can renew them again upon Occafion, 
 even when the Objects that firft produced them 
 are removed. Now our Ideas are nothing etfe but 
 thefe renewed Reprefentations of what we have at 
 any Time perceived and felt, by means of which 
 Things are again brought under the View of the 
 Mind, and feem to have a Kind of Exiftence in it. 
 It is true we can upon many Occafions combine 
 our Ideas variously together, and thereby form to 
 ourfelves Reprefentations of Things that never 
 had an Exiftence in Nature, as when we fancy 
 a- Centaur, or a Golden Mountain ; but it is (till 
 certain, that the original Ideas out of which thefe 
 are made, are fuch as have been conveyed into 
 the Mind by fome former Impreflions. It remains 
 therefore to enquire how we come by our fiift 
 Notions and Perceptions of iThings. Whencedoes 
 the Underftanding derive thofe original Impref*. 
 fions and Characters, which it can combine in fo 
 many different Ways, and reprefent to itfelf un- 
 der fuch infinite Varieties ? To this I anfweiy 
 that if we attend carefully to what pafTes in our 
 Minds, we fliall obferve two Inlets of Know- 
 ledge, from whence, as from two Fountains, 
 
 the
 
 the Underftanding is fupplied with all the Mate- 
 rials of Thinking. 
 
 II. FIRST, outward Obje&s, a&- 
 ing upon our Senfes, roufe in us a 
 Variety of Perceptions, according 
 
 . ,._ ... 
 
 to the different Manner in which 
 they affect us. It is thus that we come by the 
 Ideas of Light and Darknefs, Heat and Gold, 
 Sweet and Bitter, and all thofe other Impreijions 
 which we term fenfible Qualities. This great 
 Source and Inlet of Knowledge is commonly 
 diftinguifhed by the Name of Senfation, as com- 
 prehending all the Notices conveyed into the 
 Mind, by Impulfes made upon the Organs of 
 Senfe. 
 
 III. BUT thefe Ideas, numerous 
 
 i , ,, , . , Or Reflefltin, 
 
 as they are, are wholly derived to us 
 from without ; there is therefore yet another 
 Source of Impreflions, arifing from the Mind's 
 Attention to its own Ads, when, turning in- 
 wards upon itfelf, it takes a View of the Percep- 
 tions that are lodged there, and the various Ways 
 in which it employs itfelf about them. For the 
 Ideas furnilhed by the Senfes, give the Mind an 
 Opportunity of exerting its feveral Powers ; and 
 as all our Thoughts, under whatever Form they 
 appear, are attended with Confcioufnefs, hence 
 the Impreflions they leave, when we come to turn 
 the Eye of the Soul upon them, enrich the Un- 
 
 derftandin*
 
 C >8 J 
 
 demanding with a new Set of Perceptions, no 
 lefs diftindl than thofe conveyed in by the Senfes. 
 Thus it is that we get Ideas of Thinking, Doubt- 
 ing, Believing, Willing, &c. which are the dif- 
 ferent Acts and Workings of our Minds, repre- 
 fented to us by our own Confcioufnefs. This 
 fecond Source of Ideas is called Refieftlon, and 
 evidently prefuppofes Senfation, as the Impref- 
 fions it furnifhes are only of the various Powers 
 of the Underftanding, employed about Percep- 
 tions already in the Mind. 
 
 Rjt and Pro- ^ THESE Confiderations, if we 
 vrcfs cf human duly attend to them, will give us a 
 clear and diftincl: View of the natural 
 Procedure of the human Intellect, in its Advances 
 to Knowledge. We can have no Perception of 
 the Operations of our own Minds, until they are 
 exerted ; nor can they be exerted before the Un- 
 derfbnding is furnifhed with Ideas about which 
 to employ them : and as thefe Ideas, that give the 
 firft Employment to our Faculties, are evidently 
 the Perceptions of Senfe, it is plain that all our 
 Knowledge mult begin here. This then is the 
 fuft Capacity of the human Mind, that it is fitted 
 to receive the Imprefllons made upon it by out- 
 ward Objects affedingthe Senfes ; which Impref- 
 fions thus derived into the Underftanding, and 
 there lodged for the View of the Soul, employ it in 
 various A6ls of Perceiving, Remembering, Con- 
 
 (idering,
 
 ( 19 ) 
 
 fidering, &V. all which are attended with an in- 
 ternal Feeling nd Confcioufnefs. And this 
 leads us to the fecond Step the Mind takes in its 
 Progrefs towards Knowledge, viz. that it can by 
 its own Confcioufnefs reprefent to itfelf thefe its 
 feveral Workings and Operations, and thereby 
 furnifh the Underftanding with a new Stock of 
 Ideas. From thefe fimple Beginnings, all our 
 Difcoveries take their Rife : for the Mind, thus 
 .provided with its original Characters and Notices 
 of Things, has a Power of combining, modify- 
 ing, and examining them in an infinite Variety of 
 Lights, by which means it is enabled to enlarge 
 the Objedls of its Perception, and finds itfelf pof- 
 fefTed of an inexhauftible Stock of Materials. It 
 is in the various Comparifon of thefe Ideas, ac- 
 cording to fuch Combinations of them as feeni 
 beft to fuit its Ends, that the Underftanding ex- 
 erts itfelf in the Arts of Judging and Reafoning, 
 by which the capacious Mind of Man pufhes on 
 its Views of Things, adds Difcovery to Difcove- 
 ry, and often extends its Thoughts beyond the 
 utmoft Bounds of the Univerfe. Thus we fee, as 
 it were, at one Glance, the whole Progrefs of the 
 Soul, from the very firft Dawnings of Percep- 
 tion, till it reaches the Perfe&ion of human 
 Knowledge ; nor (hall we, among all its vail 
 Stock of Difcoveries, or that infinite Variety of 
 Conceptions whereof they confift, be able to 
 
 find
 
 ( 20 ) 
 
 find one original Idea which is not derived 
 from Senfation or Reflection, or one complex 
 Idea which is not made up of thofe original 
 ones. 
 
 V. HAVING thus fhewn how the 
 u7'i'jeat into Mind comes to be firft furnifhed 
 Jiittple and w jth Ideas, we (hall next proceed to 
 the Confideration of the Ideas them- 
 felves, and endeavour to give fuch an Account of 
 them as will beft ferve to explain their feveral Ap- 
 pearances, and the Manner in which they are 
 formed. It is evident, from what has been faid 
 above, that they all fall naturally under thefe two 
 Heads : Firft, thofe original Imprcffions that are 
 conveyed into the Mind by Senfation and Reflec- 
 tion, and which exift there fimple, uniform, aad 
 without any Shadow of Variety. Secondly, 
 thofe more complex Notions of Things that re- 
 fuk from the various Combinations of our fimple 
 Ideas, whether they are conceived to exift of 
 themfelves in any particular Subje&, or are 
 united and joined together by the Mind en- 
 larging its Conceptions of Things, and purfuing 
 the Ends and Purpofes of Knowledge. Thefe 
 two ClaiTes comprehend our whole Stock of 
 Ideas ; and, when confidered feparately in that 
 Order wherein they moft naturally feem to offer 
 themfelves to our Thoughts, will, I hope, give 
 fuch a View of the Conduct and Manner of the 
 
 Mind,
 
 Mind, as may contribute not a little to intro- 
 duce us to an Acquaintance with ourfelves, and 
 make us fenfible of the Capacity and Extent of 
 the human Intellect. We proceed therefore to 
 a. more particular Account of this Divifion of 
 our Ideas. 
 
 CHAP. II. 
 
 Of Simple Ideas. 
 
 I. f-r\HE firft Clafs of our Ideas 
 
 1 are thofe which I diftin- Simfk 
 
 What, 
 
 guifh by the Name of fimple Percep- 
 tion ; becaufe they exift in the Mind under one 
 uniform Appearance, without Variety or Com- 
 pofition. For though external objects convey at 
 once into the Underftanding many different 
 Ideas all united together, and making as it were 
 one whole ; yet the Imprefllons themfelves are 
 evidently diftinc\ and are conceived by the Mind, 
 each under a Form peculiar to itfelf. Thus the 
 Ideas of Colour, Extenfion, and Motion, may 
 be taken in at one and the fame Time, from the 
 fame Body ; yet thefe three Perceptions are as 
 diftinct in themfelves, as if they all proceeded 
 from different Objects, or were exhibited to our 
 Notice at different Times. We are therefore 
 
 carefully
 
 ( 22 ) 
 
 carefully to diftinguifh between our fimple and 
 primitive Conceptions, and thofe different Com- 
 binations of them which are often fuggeftcd to 
 the Mind by fingle Objects acting upon it. The 
 firft conftitute our original Notices of Thing?, 
 and are not diftinguifhable into different Ideas, 
 but enter by the Senfes fimple and unmixed. 
 They are alfo the Materials out of which all the 
 others, how complex and complicated foever, are 
 formed j and therefore ought defervedly to be 
 looked on as the Foundation and Ground-work 
 of our Knowledge. 
 
 II. Now if we take a Survey of 
 
 bimfle Idtat . . . 
 
 f Senja- thefe Ideas, and their Icveral Lmi- 
 '""' fions and Claffes, we ihall find them 
 
 all fuggefled to us either by our Senfes, or the 
 Attention of the Mind to what paffes within it- 
 felf. Thus our Notices of the different Qualities 
 of Bodies, are all of the Kind we call fimple 
 Ideas, and may be reduced to five general Heads, 
 according to the feveral Organs which are affected 
 by them. Colours, &c. and Sounds, are convey- 
 ed in by the Eyes and Ears; Taftes and Smells, 
 by the Nofe and Palate ; and Heat, Cold, and 
 Solidity, &c. by the Touch. Befides thefe, 
 there are others which make Impreffions on feve- 
 ral of our Senfes, as Extenfion, Figure, Reft, and 
 Motion, &c. the Ideas of which we receive into 
 our Minds both by feeing and feeling. 
 
 3 III. IF
 
 III. IF we next turn our View 
 
 r,, . . . r , Simple TJetl 
 
 upon what paites within ourfelves, O f 
 
 we fhall find another Set of fimple e " 
 Ideas arifing from our Confcioufnefs of the Acts 
 and Operations of our own Minds- Perception 
 or Thinking, and Volition or Willing, are what 
 every Man experiments in himfelf, and cannot 
 avoid being fenfible of. I fhall only obferve far- 
 ther, that befides all the above-mentioned Percep- 
 tions, there are others that come into our Minds 
 by all the Ways of Senfation and Reflection j fuch 
 are the Ideas of Pleafure and Pain, Power, Exig- 
 ence, Unity, Succeflion, ff>. which are derived 
 into our Underftandings both by the Action of 
 Objects without us, and the Confcioufnefs of 
 what we feel within. It is true fome of thefe 
 Ideas, as of Extenfion and Duration, cannot be 
 conceived altogether without Parts, neverthelefs 
 they are juftly ranked among our fimple Ideas j be- 
 caufe their Parts being all of the fame Kind, and 
 without the Mixture of any other Idea, neither of 
 them can be refolved into two diftinct and fsparate 
 Conceptions. Thus they {till anfwer the Defini- 
 tion given above, of being one uniform Appear- 
 ance in the Mind, without Variety or Plurality. 
 But to prevent confounding our fimple Ideas of 
 Space and Duration, with thofe complex Modes 
 of them marked out by the feveral Meafures 
 commonly in Ufe, as Yards, Miles, Days, Years,
 
 &V. it may perhaps be moft proper to confider 
 the leaft Portions of either whereof we can form 
 a clear and diftincl Perception, as the fimple Ideas 
 of that Kind out of which all their other Modes 
 and Combinations are formed. Such an Inftant, 
 or Point, may be conceived to be the fame in re- 
 fpecl of Duration or Space, as Unity is in refpect 
 of Number; and will ferve beft to (hew, how by 
 a continued Addition or Repitition our more en- 
 larged and complex Ideas are made up. 
 
 Simph id*** IV ' HAVING thus g iven a S eneral 
 ttve no Ad- View of our fimple Ideas, I have ftill 
 
 fuffioa bat by /-M / 
 
 tbt proper h- two Obfervations to make concern- 
 ktitfNaiurt. j ng t h em . The firft is, that they 
 are fuch as can only be conveyed into the Mind 
 by the proper Channels and Avenues provided by 
 Nature ; infomuch that if we are deftitute of any 
 of thofe inlets, by which the Impreffions that 
 produce them are wont to be admitted, all the 
 Ideas thence arifing areabfolutely loft to us ; nor 
 can we, by any Quicknefs of Understanding, find 
 a Remedy for this Want. A Man born blind is 
 incapable of the Ideas of Light and Colours ; in 
 like manner as one who is deaf can form no No- 
 tion or Conception of Sounds. Hence it ap- 
 pears, thatthefe our fimple Ideas are juft fuch as 
 Nature has furnifhed them, and have no Depen- 
 dence on our Will j we can neither deftrojr 
 them when in the Understanding, nor fafliioa 
 8 or
 
 ( 25 ) 
 
 or invent any new one, not taken in by the or- 
 dinary Means of Perception. So that we here 
 fee the utmoft Bounds of human Knowledge, 
 which, however mighty and enlarged, cannot ex- 
 ceed the Limits of thofe our fimple original Ideas, 
 and their various Combinations. 
 V. AXD this leads me to the fe- 
 
 , / -^., r - r r i fbey furnijb 
 
 cond Oblervation 1 propoled to ampitM&tt- 
 make, which is, that though the h ' 6 S . 
 
 ... Knowledge, 
 
 Mind cannot, in multiplying its 
 Conceptions of Things, advance one Step be- 
 yond the Materials furnifhed it by Senfe and 
 Confcioufnefs ; yet as it has a Power of com- 
 bining, modifying, and enlarging them, in all 
 the different Ways in which they can be put to- 
 gether, it therefore finds itfelf in Pofleflion of an 
 inexhauftible Treafure of Ideas, fufficient to em- 
 ploy it to the full Extent of all its Powers, and 
 furnifh Matter for all thofe various Opinions, 
 Fancies, and Views of Things, that make up the 
 Subject of its Thoughts and Contemplations. Let 
 us but reflect upon the fingle Idea of Unity or 
 One,. and obferve what a Variety of Combina- 
 tions are formed, by continually adding it to it- 
 felf j infomuch that the Underftanding finds no 
 Stop or Boundary, in its Progrefs from Number 
 to Number. In what an Infinity of different 
 Lights may Extenfion alone be confidered ! What 
 Limits can be fet to that endlefs Diverfity of 
 C Figures,
 
 ( 26 ) 
 
 Figures, which it is in the Power of the Imagi- 
 nation to fafhion and reprefent to itfelf? If to 
 thcfc we add thofe numberlefs other Combina- 
 tions that refult from varioufly compounding and 
 comparing the reft of our fimple Ideas, we fhall 
 have little Reafon to complain of being limited 
 to a fcanty Meafure of Knowledge, or that the 
 Exercife of the human Faculties is confined 
 within narrow Bounds. But having traced the 
 Progrefs of the Mind thro' its original and fim- 
 ple Ideas, until it begins to enlarge its Concep- 
 tions by uniting and tying them together ; it is 
 now time to take a Survey of it as thus employ- 
 td in multiplying its Views, that we may fee by 
 what Steps it advances from one Degree of Im- 
 provement to another, and how it contrives to 
 manage that infinite Stock of Materials it finds 
 itfelf poflefled of. 
 
 VI. WHOEVER attentively con- 
 
 *** flders his own Thoughts, and takes 
 e a View of the feveral complicated 
 
 . 
 
 tiofe framed thcmfelves to his Understanding ; 
 
 ty the Mind. 
 
 will readily obferve that many of 
 them are fuch as have been derived from without, 
 and fuggefted by different Objects affecting his 
 Perception; others again are formed by the Miud 
 itfelf, varioufly combining its fimple Ideas, as 
 feems bcft to anfwer thofe Ends and Purpofes it 
 
 has
 
 f *7 ) 
 
 has for the prefent in View. Of the firft Kind 
 are all our Ideas of Subftances, as of a Man, a 
 Horfe, a Stone, Gold. Of the fecond are thofe 
 arbitrary Collections of Things, which we on 
 many Occafions put together, either for their 
 TJfefulnefs in the Commerce of Life, or to fur- 
 ther the Purfuit of Knowledge : fuch are our 
 Ideas of dated Lengths, whether of Duration or 
 Space ; as Hours, Months, Miles, Leagues, &c. 
 which Divifions are apparently the Creatures of 
 the Mind, inafmuch as we often find therrfdiffe- 
 rent in different Countries j a fure Sign that they 
 are taken from no certain and invariable Stand- 
 ard in Nature. Many of our Ideas of human 
 Actions may be alfo referred to this Head j as 
 Treafon, Inceft, Manflaughter, &c. which com- 
 plex Notions we do not always derive from an 
 a<5hial View of what thefe Words defcribe, but 
 often from combining the Circumftances of them 
 in our Minds, or, which is the moft ufual Way, 
 by hearing their Names explained, and the Ideas 
 they ftand for enumerated. Thefe two ClafTes 
 comprehend all our complex Conceptions, it be- 
 ing impoilible to conceive any that are not either 
 fuggefted to the Underftanding by fome real Ex- 
 iftences, or formed by the Mind itfelf arbitra- 
 rily uniting and compounding its Ideas. We 
 fhall treat of each in Order. 
 
 C * CHAP.
 
 CHAP. III. 
 
 Of our Ideas of Subjtances. 
 
 I. '"T^ H E firft Head of complex 
 yw;i Calltc- *" Ideas mentioned in the fore- 
 
 timi offimpit going Chapter, is that of Bubjlqnce^ 
 
 Heat, held to- . J 
 
 gttbcr by feme which I choofe to handle before the 
 
 ynw.ut- other . bccaufe) as wm afterwards 
 appear, the Notices derived from 
 this Source very much help us in forming thofe 
 arbitrary Collections, which make up the fecond 
 Divifion. For in many of them we take our 
 Hints from the Reality of Things, and combine 
 Ideas that actually exift together, though often 
 with an Exclufion of others, as will be explain- 
 ed when we come to treat of abftract and uni- 
 verfal Notions. It has been already obferved, 
 that the Impreflions conveyed into the Umler- 
 ftanding from external Objects, confift for the 
 mod part of many different Ideas joined together, 
 which all unite to make up one Whole. Thefe 
 Collections of various Ideas, thus co-exifting in 
 the fame common Subject, and held together by 
 fome unknown Bond of Union, have been dif- 
 tinguifhed by the Name of Sub/tarices^ a Word 
 which implies their fubfifting of themfelves, with- 
 out Dependence (at leaft as far as our Know- 
 ledge reaches) on any other created Beings. Such 
 
 are
 
 ( 29 ) 
 
 are the Ideas we have of Gold, Iron, Water, 
 a Man, &c. For if we fix upon any one of 
 thefe, for inftance Gold, the Notion under which 
 we reprefent it to ourfelves is that of a Body 
 yellow, very weighty, hard, fufible, malleable, 
 &V. : where we may obferve, that the fevc-ral 
 Properties that go to the Compofition of Gold, 
 are reprefented to us by clear and evident Per- 
 ceptions; the Union too of thefe Properties, and 
 their thereby constituting a diftinct Species of 
 Body, is clearly apprehended by" the Mind : but 
 when we would pufti our Enquiries farther, and 
 know wherein this Union confifts, what holds 
 the Properties together and gives them their Self- 
 fubfiftence, here we find ourfelves at a Lo^.How- 
 ever, as we cannot conceive Qualities, without 
 at the fame Time fuppofing fome Subject in which 
 they adhere, hence we are naturally led to form 
 the Notion of a Support, which fervirtg as a 
 Foundation for the Co-exiftence and Union of 
 the different Properties of Things, gives them that 
 feparate and independent Exiftence under which 
 they are reprefented to our Conception. This 
 Support we denote by the Name Subjlance- y and 
 as it is an Idea applicable to all the different Com- 
 binations of Qualities that exift any where by 
 themfelves, they are accordingly all called Sub- 
 ftances. T-hus a Houfe, a Bowl, a Stone, &c. 
 having each their diftinguifhing Properties, and 
 C 3 being
 
 ( 30 ) 
 
 being conceived to exift independent one of an- 
 other, the Idea of Subftance belongs alike to 
 them all. 
 The Di-vijion II. IN Subftances therefore there 
 
 gfiUT are two Thi "S s to be confidered : 
 Firft, the general Notion of Self- 
 lubfiftence, which, as I have faid, belongs equally 
 to them all j and then the feveral Qualities, or 
 Properties, by which the different Kinds and 
 Individuals are diftinguifhed one from another. 
 Thefe Qualities are othcrwife called Modes, and 
 have been diftinguifhed into eflcntial and acci. 
 lcntal, according as they are perceived to be fe- 
 parable or infeparable from the Subjecl to which 
 they belong. Extenfion and Solidity are eficntul 
 Modes of a Stone, becaufe it cannot be conceiv- 
 ed without them ; but Roundnefs is only an ac- 
 cidental Mode, as a Stone may exift under any 
 Shape or Figure, and yet flill retain its Nature 
 and other Properties. 
 
 NO,** of HI. ! MIGHT run farther into 
 thefe Divifions and Sub-divifions, in 
 
 injef arable . T . . , . 
 
 frem Sut- which Logicians have been very fcr- 
 fonce,. t jj e . b ut as they tend little to the 
 
 Advancement of real Knowledge, and ferve ra- 
 ther to fill the Memory with Words and their 
 Significations, than furnifli clear and diilincl 
 Apprehenfions of Things, I fhall not trouble the 
 Reader with them. It is more material to ob- 
 fcrve, that the Change of Properties in any Sub- 
 
 itance,
 
 fiance, tho' it oft- times changes the Nature of that 
 Subftance, that is, its Species or Kind ; yet it 
 never deftroys the general Notion of Self-fubfift- 
 cnce, but leaves that equally clear and applicable, 
 as before any fuch Alteration happened. Wood 
 by the Application of Fire is turned into Charcoal; 
 but Charcoal, however different from Wood, is 
 ftill a Subftance. 1 In like Manner, Wax may be 
 converted into Flame and Srnoke, a human Body 
 will moulder into Duft, yet thefe Alterations de- 
 ilroy not their Being or Exigence ; they are ftill 
 Subftances as before, tho' under a different Form 
 and Appearance. In the feveral Experiments 
 made by Chemifts, Bodies undergo many 
 Changes, and put on fucceflively a great Variety 
 of different Shapes ; and yet, by the Skill and 
 Addrefs of the Operator, they are often brought 
 back to their firft and primitive Form. What 
 Alteration can we fuppofe the Fire, or the Ap- 
 plication of any other Body, to make, unlefs on 
 the Configuration, Texture, or Cohefion of the 
 minute Parts ? When thefe are changed, the 
 Body is proportionably changed ; when they re- 
 turn to their original State, the Body likewifo 
 puts on its firft and natural Appearance. 
 IV. ALL that is effential to Matter , 
 
 Foundation cf 
 
 therefore, is the Cohefion of folid ex- the different 
 tended Parts ; but as thefe Parts are f^jlf 
 capable of innumerable Configura- flances. 
 tions j as their Texture may be very various, and 
 C 4 the
 
 ( 3* ) 
 
 the internal Conflitution thence arifmg be of 
 confequence extremely different in different Bo- 
 dies ; we may from thefe Considerations conceive 
 pretty clearly the Source and Foundation of all 
 the different Species of corporeal Subftances. 
 Nor is this a Notion taken up at random, or one 
 of thofe chimerical Fancies in Philofophy, de- 
 rived rather from a Warmth and Livelincfs of 
 Imagination, than Obfervations drawn from 
 Things themfelves. Do we not daily fee our 
 Food, by the Changes it undergoes in the dif- 
 ferent Avenues of the Body, converted firft into 
 Blood, and thence employed in nourishing, 
 building up, and enlarging, the feveral Parts of 
 that wonderful Fabrick ? Rain defcending from 
 the Clouds, and mixing with the Mold or Earth 
 of a Garden, becomes Aliment for Trees df va- 
 rious Kinds, puts on a Diverfity of Forms, ac- 
 cording to the different Channels and Convey- 
 ances thro' which it paffes ; and at laft, after in- 
 numerable Changes and Tranfmutations, fprouts 
 forth in Leaves, opens in Buds, or is converted 
 into the Subftance of the Tree itfelf. Can we 
 conceive any greater Difference between the 
 component Parts of Gold, and thofe of Stone, 
 than between the moiftened Particles of Garden 
 Mold, and thofe new Forms and Figures under 
 which they appear, after they have been thus 
 fafhioncd by Nature for the Purpofes of Growih 
 and Nourifhment ? 
 
 V. IF
 
 ( 33 ) 
 
 V. IF this be duly attended to, it . 
 
 , r , ir EfftrceofSub- 
 
 will not appear wonderful to allert, j- tancct no ,bing 
 that the Variety of material Subftan- but . *' ''"'"" 
 
 J tial S'rufiure 
 
 ces arifes wholly from the different and Conft'nu- 
 Configuration, Size, Texture, and 
 Motion of the minute Parts. As thefe happen 
 to be varioufly combined, and knit together un- 
 der different Forms, Bodies put on a Divcrfity of 
 Appearances, and convey into the Mind by the 
 Senfes all thofe feveral Impreflions, by which 
 they are diftinguifhed one from another. This 
 internal Conflitution or Structure of Parts, from 
 which the feveral Properties that diflinguifh any 
 Subftance flow, is called the Eflence of that Sub- 
 ftance, and is in FadT: unknown to us, any far- 
 ther than by the perceivable Impreflions it makes 
 upon the Organs of Senfe. Gold, as has been 
 faid, is a Body yellow, very weighty, hard, fufi- 
 ble, malleable, &c. That inward Structure and 
 Conformation of its minute Partides, by which 
 they are fo clofely linked together, and from 
 which the Properties above mentioned are con- 
 ceived to flow, is called its Eflence ; and the Pro- 
 perties themfelves are the perceivable Marks that 
 make it known to us, and diftinguirti it from all 
 other Subftances ; for, our Senfes are not acute 
 enough to reach its inward Texture and Con- 
 flitution. The Parts themfelves, as well as their 
 Arrangement, lie far beyond the utmgrt Penetra- 
 C 5 tion
 
 C 34 ) 
 
 tion of human Sight, even when a/Tifled by Mi- 
 crofcopes, and all the other Contrivances of 
 Art. 
 
 VI. THUS, as to the EfTence or 
 h vbclly *n- interna i Conftitution of Gold, we 
 
 kmivn to us, ' 
 
 nor f,r*,ei to are wholly in the dark ; but many 
 Sfau". ' f tne Properties derived from this 
 Eflence, make obvious and diftin& 
 Impreflions, as the Weight, Hardnefs, and yellow 
 Colour, sV. Thefe Properties combined together, 
 and conceived as co-exifling in the fame common 
 Subject, makeup our complex Idea of Gold. The 
 fame may be faid of all the other Species of cor- 
 poreal Subftances, as Lead, Glafs, Water, &"c. 
 our Ideas of them being nothing elfe but a 
 Collection of the ordinary Qualities obferved in 
 them. 
 
 VII. THIS however ought to be 
 
 r " r " ,**'? o^ferved, that tho' the Efience or 
 
 f re fumed to be 
 
 <nj}ir.fi in all inward Structure of Bodies is al- 
 xf/j* together unknown to us, yet we 
 
 rightly judge that, in all the feve- 
 ral Species, the EfTences are diftinft. For each 
 Species being a Collection of Properties, which 
 taken together are different from thofe of every 
 other Species, the Conformation of Parts, on 
 which thefe Properties depend, muft in like man- 
 ner be different ; and this, as we have faid, con- 
 ttitutes the Eflence. Iron and Glafs are evi- 
 dently diftinft Kinds of Body, their perceivable 
 
 Qualities
 
 ( 35 ) 
 
 Qualities have little or nothing common ; and 
 therefore the inward Structure or Conftitution 
 from which thefe Qualities flow, cannot be the 
 fame in both. But after all, this is the only Thing 
 we can with Certainty affirm concerning thefe 
 Eflences, which lying fo wholly in the Dark, we 
 fhall do well to lay them afide in our Reafonings 
 about Things, and ftick to thofe more intelligi- 
 ble and fettled Ideas got by joining together their 
 various Properties and Powers. For thus only 
 js true Knowledge promoted, when we argue 
 from known Qualities, and not from a fuppofed 
 internal Conftitution, which, however real in it- 
 felf, yet comes not within the Reach of our Fa- 
 culties, and therefore can never be a Ground to 
 us for any Difcoveries or Improvements. 
 
 VIII. MATERIAL Subftance, asl By what S(eff 
 have faid, includes the Idea of folid, *t arrive at 
 cohering, extended Parts, and is di- LLr"'w ^ 
 vided into different ClafTes, accord- $*%?*"? 
 ing to the different Impreffions made upon the 
 Organs of Senfe. But, befides thefe fenfible Ideas 
 received from without, we alfo experiment in 
 ourfelves Thinking and Volition. Thefe Actions 
 have no Connection with the known Properties of 
 Body ; nay, they feem plainly inconfiftent with 
 fome of its moft eflential Qualities. For the 
 Mind not only difcovets no Relation between 
 Thinking, and the Motion or Arrangement of 
 C6 Parts;
 
 ( 36 ) 
 
 Parts ; but it alfo perceives that Confcioufnefs, 
 a fimple individual Act, can never proceed from, 
 a compounded Subftance, capable of being di- 
 vided into many. Let us fuppofe, for inftance, a 
 Syftem of Matter endowed with Thought ; then 
 either all the Parts of which this Syftem is com- 
 pofed muft think, which would make it not one, 
 but a Multitude of diftindt confcious Beings ; or 
 its Power of thinking muft arife from the Con- 
 nection of the Parts one with another, their Mo- 
 tion and Difpofition, &V. which, all taken toge- 
 ther, contribute to the Production of Thought. 
 But it is evident that the Motion of Parts, and 
 Manner of combining them, can produce no- 
 thing but an artful Structure, and various Modes 
 of Motion. All Machines of human Compo-r 
 fiticn, as Watches, Clocks, sV. however art- 
 fully their Parts are fet together, however com- 
 plicated their Structure j tho' we conceive in- 
 numerable different Motions, varioufly conjoin- 
 ed, and running one into another with an endlefs 
 Diverfity, yet never produce any Thing but Figure 
 and Motion. If a Clock tells the Hour and Mi- 
 nute of the Day, it is only by the Motion of the 
 different Hands, pointing fuccefllvely at the Fi- 
 gures marked on the Hour-plate for that Purpofe. 
 We never imagine this tobe the Effect of Thought 
 or Intelligence ; nor conceive it poflible, by any 
 t of Structure, fo to improve the 
 
 Com-
 
 ( 37 ) 
 
 Compofition, as that it fhall become capable of 
 Knowledge and Confcioufnefs. The Reafon is 
 plain : Thought is fomething altogether diffe- 
 rent from Motion and Figure, there is not the 
 Jeaft Connexion between them ; and therefore 
 it can never be fuppofed to icfult from them. 
 
 IX. THIS then being evident, 
 
 , , ... ..... Which tee 
 
 that Intelligence cannot ante from et ker<wijt all 
 an Union or Combination of unin- #/>'"" 
 telligible Parts ; if we fuppofe it to belong to 
 any Syftem of Matter, we muft neceflarily attri- 
 bute it to all the Parts of which that Syftem is 
 compofed ; whereby, inftead of one, we fhall, as 
 was before obferved, have a Multitude of diftindl 
 confcious Beings. And becaufe Matter, how far 
 foever we purfue the Minutenefs of its Parts, is 
 ftill capable of repeated Divifions, even to Infi- 
 nity; it is plain that this Abfurdity will fol- 
 low us through all the Suppofitions that make 
 Thought inherent in a material Subftance. 
 Finding, therefore, Confcioufnefs incompatible 
 with the Cohefion of folid feparable Parts, we 
 are neceflarily led to place it in fome other Sub- 
 ftance of a diftincl: Nature and Properties, which 
 we call Spirit. 
 
 X. AND here it is carefully to be 
 
 i r 11 i f in- r ^"Jy an ^ Spi m 
 
 obierved, that the leveral bpecies or r \ t djkn& 
 corporeal Subftances, though diftin- Subjijncts. 
 guiflied one from another, and ranked under dif- 
 ferent Names - t yet, agreeing in fome common 
 
 Properties,
 
 ( 33 ) 
 
 Properties, which taken together make up the 
 Notion of Body, are thence all conceived to par 
 take of this general Nature, and to differ only 
 as different Modifications of the fame Subftance. 
 Whatever confifts of folid extended Parts, is 
 called Matter ; and as all the various Species of 
 Body, however diftinguifhed from one another 
 by their feveral Properties, have yet this in 
 common, that they are made up of fuch folid 
 feparable Parts, hence they fall naturally under 
 the general Denomination of material Beings, 
 and are not conceived to differ but in their 
 Form. Thus Gold, Antimony, Wood, &c. 
 alike partake of the Notion of Bodyj they are 
 all equally material Subftances, and have no 
 other Difference but what arifes from the dif- 
 ferent Structure and Conformation, C3?t\ of 
 Parts, as we have fhewn above. But Spirit is 
 fomething altogether diftinft from Body, nay, 
 and commonly placed in Oppofition to it j for 
 which Reafon, the Beings of this Clafs are 
 called immaterial; a Word that implies not any 
 Thing of their Nature, but merely denotes its 
 Contrariety to that of Matter. 
 
 XI. BODY and Spirit, therefore, 
 Then may le Differ not as Species of the /fame 
 
 many vartcus 
 
 SptdetofSub- Subftance, but are really diftincc 
 
 ft tboj"tba?c d <,mt Kinds of Subftances, and ferve as 
 within tit general Heads under which to rank 
 
 all
 
 ( 39 ) 
 
 all the particular Beings that fall R eac i f tttr 
 within the Compafs of our Know- Faculties. 
 ledge. For we having no Ways of Perception 
 but Senfe and Confcioufnefs, can have no No- 
 tices of Things, but as derived from thefe two 
 Inlets. By our Senfes we are informed of the 
 Exiftence of folid extended Subftances, and Re- 
 flection tells us that there are thinking confci- 
 ous ones. Beyond thefe our Conceptions reach 
 not ; and therefore, though there may be many 
 other Kinds as different from them as they are 
 from one another, yet having no Faculties fuited 
 to them, they are as remote from our Know- 
 ledge, as Light and Colours from the Appre- 
 henfion of a Man born blind. I believe it will 
 hardly be doubted but the Subftance of the Cre- 
 ator differs more from that of his Creatures, than 
 any two created Subftances can from one an- 
 other ; and therefore when we call God a Spirit, 
 we ought not rafhly to prefume that he is fo in the 
 fame Senfe in which the human Soul is a Spirit. 
 The Word is indeed ufed by us, to denote in 
 general all thinking intelligent Subftances, in 
 which Senfe God is very fitly called a Spirit. 
 But it were the Height of Folly to imagine, be- 
 caufe this Name is applied as well to the Mind 
 of Man as the Creator, that therefore they par- 
 take of one common Nature, and differ only as 
 different Modifications of the fame Subftance. 
 
 This
 
 ( 40 ) 
 
 This I mention here, to check the Preemption 
 of the human Mind, always forward to conclude 
 that every Thing comes within its Reach, and 
 to deny Exiflence to whatever exceeds the Com- 
 prehenfion of its fcanty and limited Powers. 
 Beings of a fuperior Clafs may enjoy many 
 "Ways of Perception unknown to us, from 
 which they receive Notices as different from 
 thofe in our Minds, as the Ideas we apply 
 to Spirit are from the Ideas we apply to Body. 
 Solid and thinking Beings are, it is true, the 
 only Ideas of Subftance that ifre are able to 
 frame j but this is no more an Argument againft 
 the Exiftence of other Kinds, than the Want of 
 the Ideas of Light and Colours in a blind Man 
 would be a good Argument againft the Reality 
 or Poflibility of fuch Perceptions. 
 
 XII. BEFORE I difmifs this Sub- 
 
 Difftrttcc in . . , 
 
 the Manner jeer, it may not be improper to take 
 
 I^StrSl notice of a remarkable Difference 
 ff initial Sub- as to the Manner of our conceiving 
 corporeal and fpiritual Subftances. 
 Thofe of the firft Kind convey themfelves into 
 the Mind by Impreflions made upon the Organs 
 of Senfe ; and as thefe Impreflions are different in 
 different Bodies, the Ideas they produce muft of 
 courfe vary in Proportion. Thus we get Percep- 
 tions of diftincl Powers and Properties, and range 
 Bodies into daffes, according as we find them to 
 
 agree
 
 agree or difagree in thefe their obfervable Quali- 
 ties. But it is not fo in our Notion of Spirits ; 
 for having no Conception of their Powers and 
 Operations but by what we feel and experience 
 within ourfelves, we cannot afcribe to them 
 Properties or Ways of Knowledge, diftinct from 
 thofe fuggefted to us by our own Confcioufnefs. 
 And hence it is, that though we readily own 
 there may be various Ranks of fpiritual Beings, 
 yet we are not to imagine them divided from 
 one another by any Diverfity of Powers and 
 Operations, but merely by poflelTing the fame 
 Powers, C5"c. in a higher or lower Degree. It is 
 not however repugnant to Reafori, that they 
 fhould be diftinguifhed by their feveral Properties 
 in like Manner as fenfible Things are by the dif- 
 ferent Qualities obfervable in them ; but Proper- 
 ties of intellectual Natures, diftincl: from thofe 
 of our own Minds, being altogether remote 
 from our Conception, cannot ferve us as a 
 Means whereby to diftinguifli their different 
 Orders. We are therefore neceflitated to con- 
 ceive of them in a Manner fuited to our Way of 
 Knowledge; and when we would rank them into 
 Species, according to the Degrees of Superiority 
 they are imagined to poffefs in the Scale of Be- 
 ing, we afcribe to them what we find moft ex- 
 cellent in ourfelves, as Knowledge, Thinking, 
 Forefight, &c. ; and thofe in different Meafures, 
 
 propor-
 
 ( 42 ) 
 
 proportioned to the Station peculiar to each Rank 
 or Species. But that this is a very imperfect Way 
 of diftinguifhing the various Orders of intellec- 
 tual Beings, will not, I think, need many Words 
 to make appear j efpecially if we confider, that 
 the Manner of communicating their Thoughts, 
 without the Intervention of bodily Organs, is a. 
 Thing to us altogether incomprehenfible, and 
 necefiarily leads us to fuppofe that they have 
 Ways of Perception and Knowledge which our 
 Faculties cannot give us any Notice of. 
 
 XIII. BUT I fhall not purfue 
 
 Tot Boundi (if 
 
 Know/edge in thefe Reflections farther ; what has 
 'sitttilry b ecn k^ fufficing to give us fomc 
 nwu.; jj tt ] e Infight into the Extent and 
 Capacity of our own Minds j to convince us 
 that our prefent State will not admit of a perfect 
 and adequate Comprehenfion of Things ; and to 
 let us fee that there may be other Ways or" 
 Knowledge, beyond the Reach of the Faculties 
 we now enjoy ; which yet, in fucceeding Stages 
 of our Exiftence, we may arrive at, when being 
 freed from the prefent cumberfome Load of the 
 Body, we fhall mount up to Stations of greater 
 Eminence, and advance by a perpetual Series of 
 Approaches towards Him, who is the Standard 
 of Perfection and Happinefs, 
 
 CHAP.
 
 ( 43 ) 
 
 CHAP. iv. 
 
 "Of Ideas framed by the Mind. 
 
 1. TTITHERTO we have con- Jn p am \ ns 
 JLA fidered only fuch Combina- fX comfit* 
 
 r / 1*1 Utai, the 
 
 lions of our ample Ideas as have a Mmd iiiobolly 
 real Union in Nature, and are fug- ^y"^' 
 gefted to the Mind by Things them- i**tary Choice. 
 felves varioufly affecting our Perception : it is 
 -now time to take a View of the other Clafs of 
 our complex Notions j I mean thofe arbitrary 
 Collections of different Ideas, which we on 
 many Occafions bring together by that Power 
 which we find in ourfelves, of uniting, com- 
 paring, and diverfifying our Notices of Things. 
 In the Reception of fimple Ideas, and even in 
 thofe of Subftances, the Underftanding is wholly 
 paffive, and the Perceptions produced correfpond 
 to the Impreffions made upon it. When we fee 
 a Houfe, or a Tree, they necefTarily appear each 
 under its proper Form j nor is it in our Power 
 to receive from thefe Objects other Ideas than 
 what they are fitted to produce. But in this fe- 
 cond Clafs of complex Conceptions, the Mind 
 acts voluntarily and of Choice ; it combines only 
 fuch Ideas as are fuppofed beft to fuit its prefent 
 
 Purpofe 5
 
 ( 44 > 
 
 Purpofe ; and alters or changes thefe Combina- 
 tions, by inferring fomc, and throwing out others, 
 according as the Circumftances of Things re- 
 quire their being viewed in different Lights. 
 Now as this is by far the moft comprehenlive 
 Branch of our Ideas, and includes thofe that moft 
 frequently occur in the Search and Purfuit of 
 Knowledge, I fhall endeavour to treat of them 
 in the exadteft Order and Method ; and for that 
 Purpofe range them under feveral Heads, accord- 
 ing to the different A&s of the Mind exerted in 
 framing and putting them together. 
 
 II. THESE A els may in the gene- 
 
 1 brtt ft-veral , , ., 
 
 Aditxtrttd ral be all reduced to three, i. Com- 
 tytbtMind pofaw}, w hen we join many fimple 
 
 t* framing It I * J J J 
 
 arbitrary. Ideas together, and coniider them, 
 ', as one Piclure or Reprefentation. 
 Such are our Ideas of Beauty, Gra- 
 titude, a Furlong, ^<r. And here let it be< ob- 
 ferved, that the Mind fometimes confines itfelf 
 to the various Confideration of the fame Idea, 
 and, by enlarging it in different Degrees, exhi- 
 bits it under a Diverfity of Forms. Thus by 
 adding Units together, in diftinct feparate Col- 
 lections, we come by all the feveral Combina- 
 tions of Numbers, as a Dozen, a Score, a 
 Million. At other Times we unite Perceptions 
 of different Kinds; in which Cafe the Compofition 
 is more manifeft, and the Idea itfelf becomes of 
 
 courfc
 
 ( 45 ) 
 
 courfe more complicated. Harmony, for in- 
 fiance, is a compound Idea, made up of many 
 different Sounds united; all which the Mufician 
 muft have, and put together in his Mind, before 
 the Ear can be entertained with the actual Per- 
 formance. Now although the Act of the Mind 
 K in fome meafure exerted in the framing of all 
 our complex Notions, yet as many of them in- 
 clude certain limited and particular Confidera- 
 tions, arifing from other Operations of the Mind 
 employed about them, it is neceflary to take ac- 
 count of thefe Acts alfo, if we would conceive 
 clearly the Manner in which the feveral Species 
 of our compound Ideas are formed. 
 
 III. 2. The next Operation there- 
 fore of the Mind, about its Ideas, is . 
 AbjlraftiGn^ when we feparate from any of our 
 Conceptions all thofe Circumftances that render 
 it particular, or the Reprefentative of a fingle 
 determinate Object ; by which Means, inftead 
 of {landing for an Individual, it is made to denote 
 a whole Rank or Clafs of Things. Thus upon 
 feeing, for inftance, a Square, or Circle, we 
 leave out the Confideration of their Bulk,' and 
 every Thing elfe peculiar to them, as they im- 
 mediately affect our Sight, retaining only the 
 Notion of their Figure and Shape. In this Man- 
 ner we get our general Ideas ; for fuch naked 
 Appearances, (eparated from the Circumftances 
 
 of
 
 of Time, Place, &c. ferve the Mind as Standards 
 by which to rank and denominate particular Ob- 
 jects. When therefore we meet with a Figure 
 anfwering to that Shape and Form we had laid 
 up in our UndeHtandings, it is immediately re- 
 ferred by the Mind to this Pattern, and called by 
 its Name, which by this Means becomes proper 
 to the whole Species. Thus a Square, or Circle, 
 are univerfal Terms, common to all Figures of 
 that particular Shape, and alike applicable to 
 them wherever they exift ; in like Manner as 
 the Ideas themfelves are general^ and Reprefen- 
 tatives of all of the Kind. 
 
 IV. 3. THE third and laft A& of 
 fiffn. Coff!fa ~ the Mind about its Ideas, is the com- 
 paring them one with another, when 
 we carry our Confideration of Things beyond the 
 Objects themfelves, and examine their Refpects 
 and Correfpondences in Reference to other 
 Things which the Mind brings into View at 
 the fame Time. It is thus we get all our Ideas of 
 Relations, as of Greater, Lefs, Older, Younger, 
 Father, Son, and innumerable others. This 
 threefold View of our Ideas, as either compound- 
 ed of many others put together, or made univer- 
 fal by the Abftra&ion of the Mind, or as repre- 
 fcnting the various Relations and Habitudes of 
 Things, will give us an Opportunity of obferv- 
 ing whatever is mofl curious and ufefu] in this 
 1 1 fun-
 
 ( 47 ) 
 
 fundamental Branch of Knowledge, and of ex- 
 plaining the Manner and Procedure of the Un- 
 derftanding in enlarging its Views, and multi- 
 plying the Objects of Perception. That we may 
 therefore conceive of this Matter with the 
 greater Order and Clearnefs, we fhall make each 
 of thefe feveral Ideas the Subject of a diftinct 
 Section. 
 
 SECT. I. 
 
 Of Compound Ideas. 
 I, "T T T E begin therefore with 
 
 VV L r TJ v u CcmpoanJ 
 
 V V tnofe Ideas which may jj ea , corfJereJ 
 be properly termed compound, as be- b r ere " ere! y at 
 
 r r j t L-omoiTiatiOKt 
 
 ing derived from that Power the if the Undir- 
 Mind has of uniting many Concep- * "' 
 tions into one. Though this Clafs comprehends, 
 in fome Sort, all our complex Notions, yet they 
 are at prefent confidered merely as they are Com- 
 binations of the Understanding, and with a View 
 to thofe particular Ideas out of which they are 
 framed. Here, as was already obferved, the 
 Mind fometimes proceeds by enlarging and di- 
 verfifying the fame Idea ; at other Times it brings 
 together Ideas of different Kinds ; and in both 
 Ways finds infinite Scope and Variety. But that 
 we may follow the natural Procedure of the In- 
 tellect, and trace it in its Advances from fimple 
 
 to
 
 to more complicated Acts, we fhall firft take a 
 View of it as employed about one and the fame 
 Idea, where perhaps we may meet with fuch In- 
 ftances of Addrefs, Management, and Contri- 
 vance, as will appear perfectly aftonifhing to one 
 who has never fet himfelf ferioufly to confider the 
 Manner and Conduct of his own Mind. 
 . . II. The moft obvious and fimple 
 
 TOriz'tnai and Idea we have, is that of Unity or 
 
 Foundation of /-\ T> j v .. . ^r ir 
 
 milevr ideai ^ ne ' "J adding it to itfelf continu- 
 jNumbtr. a iiy j anc i retaining the feveral Col- 
 lections in our Minds, we come by all the diffe- 
 rent Combinations of Numbers, in which we rea- 
 dily perceive an endlefs Diverfity. All thefe 
 Ideas are neverthelefs evidently diftinct among 
 themfelves, the Addition of a fmgle Unit con- 
 ftituting a Number as clearly different from that 
 immediately before it, as any two the moft re- 
 mote Ideas are.from one another. But that the 
 Underftanding may not. lofe itfelf in the Con- 
 fideration of thofe infinite Combinations of 
 which Unity is capable, it proceeds by regular 
 Steps ; and beginning with the original Idea it- 
 felf, purfues it through all its Varieties, as they 
 are formed by the repeated continual Addition of 
 Unit after Unit. Thus Numbers are made to 
 follow one another in an orderly Progrefljon, 
 and the feveral fucceffive Collections are diftin- 
 guifhed by particular Names, 
 
 III, AND
 
 ( 49 ) 
 
 III. And here we may take Notice rte att p ut 
 of a wonderful Artifice, made ufe cp*f-t\on 
 
 r ... of the Namet 
 
 of by the Mind, to facilitate and e f Numbers, * 
 help it forward in its Conceptions. jS* t9 
 For as the Advance from Number to tint. 
 Number is endlefs, were they all to be diftin- 
 guifhed by different Denominations that had no 
 Connection or Dependence one upon another, 
 the Multitude of them muft foon overcharge the 
 Memory, and render it impoflible for us to go 
 any great Way in the Progrefs of Numbering, 
 For this Reafon it is fo contrived, that the 
 Change of Names is reftrained to a few of the 
 firft Combinations, all the reft that follow being 
 marked by a Repetition of the fame Terms, va- 
 rioufly compounded and linked together. Thus 
 thirteen is ten and three, fourteen ten and four, 
 and fo on to twenty^ or two tens, when we begin 
 again with one, two, ffr. until we advance to 
 thirty, or three tens. In this Manner the Progref- 
 fion continues j and when we arrive at ten tens, 
 to prevent Confufion by a too frequent Repetition 
 of the fame Word, that Sum is diftinguifhed by 
 the Name of a Hundred. Again, ten hundred is 
 called a Thoufand, at which Period the Computa- 
 tion begins anew, running thro' all the former 
 Combinations, as ten thoufand, a hundred thou- 
 fand, ten hundred thoufand; which laft Collec- 
 tion, for the Reafons mentioned above, has the 
 D Name
 
 ( ,50 ) 
 
 Name of a Million appropriated to it. With this 
 Million we can- begin as before, until it is re- 
 peated a Million of Times j when, if we change 
 the Denomination to Billions^ and advance in 
 the fame Manner through Trillions, ^uartillions^ 
 the Series may be carried on, without Confufion, 
 to any Length we pleafe. 
 
 IV. THIS artful Combination of 
 Ad ontoftbe N arn es, to mark the gradual Increafe 
 
 priitciptil i\3- 
 
 fon that our o f Numbers, is perhaps one of the 
 
 Ideal of Kum- n T\ r r i 
 
 ten are jo re- greatelt Refinements or the human 
 *2'fy W- ' Underftanding, and particularly de- 
 ferves our Admiration for the Man- 
 ner of the Compofition; the feveral Denomina- 
 tions being fo contrived, as to diftinguifh exactly 
 the Stages of the Progreflion, and point out their 
 Diftance from the Beginning of the Series. By 
 this Means it happens, that our Ideas of Num- 
 bers are of all others, the moft accurate and dif- 
 tincr,; nor does the Multitude of Units aflembled 
 together, in the leaft puzzle or confound the 
 Underftanding. It is indeed amazing that the 
 Mind of Man, fo limited and narrow in its Views, 
 fhould yet here feem to fhake off its natural 
 Weaknefs, and difcover a Capacity of managing 
 with Eafe the. moft bulky and formidable Collec- 
 tions. If we errquire particularly into theReafon 
 of this, we fhall find it wholly owing to the Ad- 
 drefs of the Mind in thus diftinguifhing Numbers 
 
 '
 
 by different Names, according to the natural Or- 
 der of Progreffion. For as thofe Names are made 
 to grow one out of another, they may be aptly 
 compared to .a Chain, all whofe Parts are linked 
 together by an obvious and vifible Connexion. 
 Hence it comes to pafs, that when we fix our 
 Thoughts upon any Number, however great and 
 feemingly unmanageable; yet, if it isonce deter- 
 mined to a particular Name, we find it eafy to run 
 back through all the Stages of the Progreflion, 
 even till we arrive at Unity itfelf. By this Means 
 we fee, with a fingle Glance of our Minds, not 
 only the two Extremes of the Number under 
 Confideration, but alfo the feveral intermediate 
 Parts, as they are united to make up the Whole. 
 
 V. Now it is to this clear and 
 accurate View of the interjacent At '^v Mf 
 
 J us to a cler 
 
 ideas, that we owe our fo diftmct Pcrtepthnof 
 Perception of the various Com'bi- '%?? 
 nations of Numbers. And indeed 
 we may obferve, in the general, that all our Ideas 
 of Quantity, efpecially when they grow to be. 
 very large, are no-otherwife afcertained than by 
 that Perception we have of the intervening Parts, 
 lying, if I may fo fay, between the Extremes. 
 When we look at any Object considerably dif- 
 tant from us, if we have a clear View of the in- 
 terjacent Lands and Houfes, we are able to de- 
 termine pretty nearly of its Remotenefs but if, 
 without fuch a Knowledge of the intervening 
 Da Spaces,
 
 ( 5* ) 
 
 Spaces, we ihould pretend to judge of the Dif- 
 tance of Objects, as when we fee the Spire of a 
 Steeple behind a Wall, or beyond a Mountain, 
 every one's Experience is a Proof how liable we 
 are, in thefe Cafes, to be deceived. Juft fo it is in 
 judging of Duration. When we carry back our 
 Thoughts to any paft Period of our Lives, with- 
 out Confideration of the Number of Years or 
 Months, we find that our Idea of the Time 
 elapfed grows more diftinft, in proportion as 
 we become fenfible of the intermediate Parts of 
 our Exiftence. At firft we are apt to judge the 
 Diftance extremely fliort j but when we fet our- 
 felves to confider our feveral fuccefllve Thoughts 
 and Actions, the Idea of the Duration grows 
 upon us, and continues to increafe as the Atten- 
 tion of the Mind brings new Periods of Life into 
 View. 
 
 VI. HENCE it will be eafy to 
 Without conceive how much the Mind is 
 
 Names, tot . , . 
 
 cannot makt helped forward in its Perception of 
 '" Number, by that ready Comprehen- 
 fion of all the feveral Stages in a 
 Progrefllon, which peculiarly belongs to Ideas of 
 this Clafs. But this, as I have before intimated, 
 Vic derive from the orderly Series and Connection 
 of Names j infbmuch that where they ceafe, the 
 Computation of Numbers alfo ceafes with them, 
 We can have no Idea of any Sum, without a 
 Knowledge of all the Terms that go before, ac- 
 cording
 
 ( 53 ) 
 
 cording to the natural Order in which they fol- 
 low one another ; fo that he who cannot, in a 
 regular Way, count to ninety-nine, will never, 
 while that Incapacity continues, be able to form 
 the Idea of a Hundred j becaufe the Chain that 
 holds the Parts together, is to him wholly unfer- 
 viceable, nor can he reprefent to his Mind the 
 feveral interjacent Combinations, without which 
 it is impoifible in this Cafe to arrive at a diftinl 
 Perception r 
 
 VII. I HAVE infifted the more 
 largely upon this, not only becaufe 
 it is by Number that we meafure all A** 
 
 (tiffing our 
 
 other Things, as Duration, Exten- //<* C B - 
 fion, Motion, &c. but alfo becaufe '*"'"" 
 it lets us into the moft natural View of the Con- 
 duel and Procedure of the Underftanding, and 
 makes us fenfible of the great Art and Addrefs 
 that is neceflary in the claflrng our very complex 
 Conceptions. He that can fo put together the 
 component Parts of an Idea, as that they fliall 
 lie obvious to the Notice of the Mind, and pre- 
 fent themfelves, when Occafion requires, in a 
 juft and orderly Connection, will not find it very 
 difficult to obtain clear and accurate Percep- 
 tions, in moft of thofe Subjects about which our 
 Thoughts are converfant. For the great Art of 
 Knowledge lies in managing with Skill the 
 Capacity of the Intellect, and contriving fuch 
 Helps as, if they ftrengthen not its natural Pow- 
 D 3 ers,
 
 ( 54 ) 
 
 ers, may yet expofe them to no unneceflary Fa- 
 tigue, by entangling and perplexing them with 
 Confiderations remote from the Bufmefs in 
 hand. When Ideas become very complex, and 
 by the Multiplicity of their Parts grow too un- 
 wieldy to be dealt with in the Lump, we muft 
 cafe the View of the Mind, by taking them to 
 Pieces, and fetting before it the feveral Portions 
 feparately, one after another. By this leifurely 
 Survey we are enabled to take in the whole ; and 
 if we can draw ic into fuch an orderly Combina- 
 tion, as will naturally lead the Attention, Step 
 by Step, in any fucceeding Confideration of the 
 fame Idea, we fhall ever have it at Command, 
 and with a fingle Glance of Thought -be able 
 to run over all its Parts. I have therefore ex- . 
 plained here, at fome Length, the Conduct of 
 the Mind in numbering ; it feeming to me the 
 beft Model in this Kind, whether we confider 
 the many Advantages derived from fuch an order- 
 ly Difpofition of our Ideas, or the great Art and 
 Skill difplayed in binding thefe Ideas together. 
 This alfo is farther remarkable, in the Confide- 
 ration of Number, that from it chiefly we de- 
 rive the Notion we have of Infinity ; it being 
 apparent that, in adding Number to Number, 
 there is no End ; the Poflibility of doubling, or 
 increafmg our Stock in any Degree, remaining , 
 as obvious to the Understanding, after a great and 
 
 continued
 
 ( 55 ) 
 
 continued Run of Progreflions, as when it firft 
 began, the Computation. 
 
 VII. IF we now turn our 
 
 Thoughts towards Space and Dura- **/j 
 
 tion^ here too we (hall find that we hr, of great 
 
 r i i i i r UJ* '" "/" 
 
 very feldom arrive at clear and oil- cert aimr.g our 
 
 tinft Ideas of either, but when we #' 
 
 and Duration, 
 
 introduce the Confideration of Num- 
 btr. The more obvious and limited Portions, it 
 is true, eafily flide into the Mind, in the na- 
 tural Way of Perception ; but it was the Necef- 
 fity of comparing thefe together, that put us up- 
 on the Contrivance of certain ftated Meafures, 
 by which precifely to determine the Quantity in 
 each. Thus Inches, Feet, Yards, Miles, 2^ 
 afcertain our Ideas of Extenfion ; as Minutes, 
 Hours, Days, Years, &c. meafure the Progrefs 
 of Duration. The lefler -Parts, as lyittg moft 
 open to the Notice of the Underftanding, and 
 beino; more on a level with its Powers, 'are re- 
 
 C? * 
 
 tained with tolerable Exa&nefs ; and the larger 
 Portions, when the Number of Repetitions of 
 which they are made up is known, are thereby 
 alfo reduced into clear and determinate Concep- 
 tions. A Foot, and Yard, are Meafures eafi'y 
 - comprehended by the Mind j nor do we find any 
 Difficulty in conceiving a Mile, when we con- 
 fider it as equal to a certain Number of Yards. If 
 we are ftill for increafing the Standard, we may 
 take the Semidiameter of the Earth, and fuppof- 
 
 D 4 in S
 
 ( 56 ) 
 
 ing it equal to 8000 Miles, make ufe of it as a 
 Meafure by which to afcertain the Diftance of 
 the Sun or fixed Stars. Juft fo it is in Dura- 
 tion ; from Hours we. rife to Days, Months, and 
 Years.} by thefe repeated, and added together, 
 we meafure Time paft, or can run forward at 
 pleafure into Futurity, and that without any 
 Confufion or Perplexity. 
 
 IX. IT is however to Number 
 
 Without it , 
 
 tbty ere apt alone that we owe this Dmincmefs 
 todwntrat, of p crc ep t ion, inafmuch as Space 
 
 into a confujfa 
 
 ad irregular and Time, coiifidered apart from 
 the regular and orderly Repetition 
 of Miles or Years, leave no determinate Impref- 
 fions in the Mind, by which to know and dif- 
 tinguifh their feveral Portions. Ideas of either, 
 thus taken in at a Venture, are a confufed and 
 irregular Heap, efpecially where we endeavour 
 to enlarge and magnify our Views, and give full 
 Play to the Powers of the Intellect. Something 
 indeed the Mind conceives, vaft and mighty, but 
 nothing that is precife, accurate, and juft. But 
 when it begins to confider thefe Ideas as made 
 up of Parts, and fixing upon fuch as are propor- 
 tioned to its Reach, fets itfelf to examine how 
 often they are repeated to make up the Whole, 
 the Perceptions of the Underftanding put on a 
 new Form, and difcover their exacl Bounds and 
 Limits. 
 
 X. AND
 
 ( 57 ) 
 
 X. AND thus, as before in Num- . , 
 
 7 Infinity an 
 
 ber, fo here in Extenfion and Du- 
 
 ration, the Mind begins with fimple 
 and obvious Notices, advancing by human Mind. 
 Degrees to more enlarged and intricate Concep- 
 tions. A Day, or a Furlong, are of eafy Appre- 
 henfion to the Underftanding, and by their Sub- 
 divifions into ftill lefler Spaces exhibit them- 
 felves diftinly in all their Parts. With thefe 
 varioufly repeated, we travel through Space and 
 Time ; fo that being able to reduce all our Ideas 
 of this Clafs, however mighty and enlarged, to 
 the clear and determinate Perceptions of Num- 
 ber, we can conduct our Thoughts without Per- 
 plexity, and never find ourfelves puzzled, but 
 when, prefuming too much on our own Strength, 
 we launch into Speculations that ftretch beyond 
 the Powers of the human Intellect. Number 
 may be compared to a Line, that fetting out 
 from Unity, runs on in a continued Increafe of 
 Length, without a Poffibility of ever arriving at 
 its ultimate Period. So far as we purfue it incur 
 Thoughts, and trace its regular Advances, fo 
 far our Ideas are accurate andjuft. But when 
 we let loofe our Underftandings after a bound- 
 lefs Remainder, and would fathom the Depth of 
 Infinity, we find ourfelves loft amidft the Great- 
 nefs of our own Conceptions. Some Notions it 
 is true we have, but fuch as, exceeding the Di- 
 D 5 menfions
 
 -menfions of the Mind, lie involved in Darknefs 
 and Obfcurity ; and being deftitute of Order, 
 Method, and Connexion, afford no Founda- 
 tion whereon to build any juft and accurate 
 Conclufion. 
 
 XI. AND this perhaps may be 
 Ntwr^n. the R eafon why many mo dern Phi- 
 
 Jen tea in itt * * 
 
 full Dimm- lofophers, in their Difcourfes con- 
 
 /.'-.', bat / y T r* i 
 
 an endiefi and ceming Infinity, have run into ap- 
 wrgrnoiig parent Contradidions ; becaufe, en- 
 countering with an Object too large 
 for the Survey of the Understanding, they found 
 themfelves furrounded with inextricable Diffi- 
 'culties, which their fcanty and defective Ideas 
 were by no means able to diffipate or remove. 
 The Truth of it is, finite Ideas alone are propor- 
 tioned to a finite Understanding; and although 
 we are not wholly without a Notion of the Infi- 
 nity of Number, yet it is not fuch a one as com- 
 prehends and exhaufts its Object, or exhibits it 
 to the Mind in its full Size and Dimenfions. 
 We only fee the Idea, as capable of an endlefs 
 Increafe, but cannot by any Effort of Thought 
 take in the whole Profpect; and indeed it is 
 properly that Part of it which lies beyond the 
 Reach of our Perception, and flill remains to 
 be taken into the Account, to which we give 
 the Name of Iftfinity, 
 
 XII. THIS
 
 ( 59 ) 
 
 XII. THIS Idea of the Infinity of Durat! 
 Number, impsrfecl: as it may feem, -whether con, 
 
 .... , i i i filtered as paS 
 
 is neverthelefs that by which the 6r to come r t * 
 Mind afcends to the Conception of ^""^f 1 > 
 
 ivbcnce our 
 
 Eternity and Immenfity. For when IdeaofEttr- 
 we confider Duration, either as paft " tty " 
 
 * i 
 
 or to come, we find nothing to ftop the Progrefs 
 of our Thoughts, in the Repetition of Years, or 
 Millions of Years : the farther we proceed, the 
 more the Idea grows upon us ; and when we 
 have wearied ourfelves with vain Efforts, we 
 muft own at laft that we can no more arrive 
 at the End of Duration, than at the End of Num- 
 ber. It is true, the feveral Generations of MeR 
 rife and difappear in very quick Succeffions ; 
 Earth itfelf may decay ; and thofe bright Lumi- 
 naries that adorn the Firmament of Heaven, be 
 extinguifhed. But the Courfe of Time will not 
 be thereby difturbed j that flows uniform and 
 invariable, nor is bounded by the Period of their 
 Exiftence, This double View of Duration, as 
 having already revolved thro' numberlefs Ages, 
 and yet (till advancing into Futurity in an end- 
 lefs Progreflion, properly conftitutes our Idea 
 of Eternity. We fpeak indeed of an Eternity 
 paft, and an Eternity to come, but both thefe 
 are bounded at one Extreme : the former ter- 
 minates in the prefent Moment, and therefore 
 has an End ; the latter fets out from the fame 
 Period, and therefore has a Beginning; but, 
 D 6 4 taken
 
 taken together, they form a Line both ways in- 
 finitely extended, and which reprefents Eterni- 
 ty in its full Dimenfions. 
 
 Tt>eldt of XIII. As, in the Confideration of 
 Time, we fix upon the prefent Mo- 
 
 r 
 
 n-vtd from the . 
 
 thn ment, regarding it as the middle 
 
 i Point which divides the whole 
 
 Sidn ofut. Line of Duration into two equal 
 Parts j fo, in the Confideration of Space, that 
 particular Place in which we exift is looked 
 upon as a Kind of Center to the whole Expan- 
 fion. From thence we let loofe our Thoughts on 
 every Side above, below, around and find we 
 can travel on, in the Repetition of Miles, and 
 Millions of Miles, without ever arriving at the 
 End of the Progreffion. It is not difficult, indeed 
 to carry our Conceptions to the utmoft Bounds 
 of the Univerfe ; at leaft fo far as it falls with- 
 in our Notice. But then the Imagination refts 
 not here j it fees immeafurable Spaces beyond, 
 capable of receiving new Worlds, which it can 
 purfue, as rifing one above another in an end- 
 ]efs Succeffion. This Confideration of Space 
 ever growing on all Sides of us, and yet never 
 to be exhaufted, is that which gives us the Idea 
 of Immenfity, which is in fa& nothing elfe 
 but the Infinity of Number, applied to certain 
 Portions of Extenfion, as Miles, or Leagues, 
 &c. and thefe conceived as extended every Way 
 
 around
 
 ( fri 7 
 
 around us, in infinite and innumerable right 
 Lines. 
 
 XIV. HITHERTO we have con- 
 fidered the Mind as employed about 
 one and the fame Idea, enlarging fr** Union 
 
 rc . . . . T? of Perception* 
 
 and diverhfymg it in various i< orms. of different 
 We have feen it rifing from the moft Kindi ' 
 fimple and obvious Notices to the Conception' 
 of Infinity itfelf j and taken a View of it in all 
 the different Stages of its Improvement. Let us 
 now proceed to the more complicated A6t of 
 Compofition, when the Mind brings feveral Ideas 
 ef different Kinds together, and voluntarily 
 combines them into one complex Conception. 
 Such, for inftance, is our Idea of a Tune^ as com- 
 prehending a Variety of Notes, with many dif- 
 ferent Modulations of Sound. And here it is ta 
 be obferved, that tho' the complex Idea may be- 
 excited in us, by hearing the Air itfelf ftruck off 
 upon a proper inftrument j yet,- confidered origi- 
 nally, it ftill belongs to this Clafs of Percep- 
 tions, which are diftinguifhed as the arbitrary 
 Collections of the Mind. It was the Mufician, 
 or Compofer, that combined the feveral Notes,, 
 and determined the Order in which they were to 
 follow one another j nor had that peculiar Com- 
 pofition of Sounds any real Union in Nature, 
 before they were thus brought together in his 
 Mind. Of the fame Nature are mofl of our 
 Ideas of human A&ions ; for tho' many of them 
 
 come
 
 ( 62 ) 
 
 come to our Notice by feeing the A&ion^ them*, 
 felves, or hearing them defcribed by others, as 
 Dtftilling) Carving, Treafon, &c. yet it is plain 
 that they muft have been projected and contriv- 
 ed in the Mind of Man before they had a real 
 Exiftence. 
 ,. . ... , XV. Ir is here that the Under- 
 
 Hoto the Mind 
 
 it determined {landing has the greateft Scope, and 
 'tbtfeComto- k nc ' s mo ^ Employment for its active 
 nations. Powers : nor indeed is it pofllble 
 
 to fet any Bounds to the Ideas of this Clafs j 
 the Combinations already made being almoft in- 
 numerable, and thofe, yet in the Power of the 
 Mind affording an endlefs Diverfity. It may not 
 however be amifs to confider how we condudl 
 ourfelves amidft fo great a Variety, and by what 
 Rules we proceed in making thofe Combina- 
 tions to which we have affixed particular Names, 
 while others, perhaps, no lefs obvious, are ne- 
 gledted. The Idea of Killing, for inftance, joined 
 to that of a Father, makes a diftincl: Species of 
 Action, known by the Name of Parricide. It was 
 doubtlefs as obvious to diftinguifli between the 
 killing of an old Man and a Child, which yet w 
 find is not done j both thefe Adlions being compre- 
 hended under the general Name of Murder. By 
 what Views therefore does the Mind regulate thefe 
 its Combinations ? Why is it determined to one 
 Collection of Ideas rather than another ? This 
 
 cannot
 
 ( 63 ) 
 
 cannot be well underftood, without obferving^ 
 that it is the End of Language to communicate 
 our Thoughts one to another. Words are the 
 Signs of our Ideas, and ferve to exprefs the Con- 
 ceptions of the Mind. NOW it is apparent that 
 fuch Conceptions as are moft apt to occur in 
 the Commerce of Life, would be firft diftin- 
 guifhed by particular Names ; the frequent Oc- 
 cafion Men have of mentioning, thefe among 
 themfelves, rendering this abfolutely neceflary. 
 But as many of thefe Conceptions are Collec- 
 tions of different fimple Ideas, hence we are 
 infenfibly led to fuch peculiar Combinations, 
 as are moft ferviceable to Purpofes of mutual 
 Intercourfe and Communication. 
 XVI. LET us fuppofe, in the firft 
 
 !- c o si Ideal of bu- 
 
 JSegmnings of bociety, a Company man Am* 
 of Leeiflators met together, in order *f ttn f '"** 
 
 before the 
 
 to confult of proper Regulations ^fiiom them- 
 for the Government of the Commu- ^"* IX '^' 
 nity. If they are. Men of Prudence and Fore- 
 fight, they will naturally obferve many new Oc- 
 currences likely to arife from- this Coalition of 
 Mankind, and their living together in Crowds. 
 Perhaps the Age in which they live has not 
 produced an Inftance of one Man's killing an- 
 other ; yet from the Knov/ledge of their own 
 Frame, and their Power of doing Hurt, they 
 conceive this as a pofiible Cafe, and are willing 
 to provide againft it. Thus all the Ideas that 
 
 enter
 
 enter into the 'Complex one of Murder, arc 
 brought together and united into one Concep- 
 tion, before the Action itfelf really exifts. It 
 is not however thought neceflary to take into 
 Confideration the Age of the Ferfon ; the chief 
 Thing in View being to prevent the putting an 
 End to another's Life unjuftly, whether old or 
 young ; and therefore the Penalty equally af- 
 fects both Cafes. But when they come to con- 
 fider the Relation in which the Perfon killed 
 may ftand to the Murderer, here there appears 
 a manifeft Difference ; as it adds to the Crime 
 when committed upon a Benefactor, and ren- 
 ders it particularly heinous in the Cafe of a 
 Father. This laft, therefore, is made to con- 
 flitute a diftinct Species of Adtion, and has a 
 peculiar Punifhment allotted to it. Thus we 
 fee how Men, according to their different Man- 
 ner of Life, and the Relations they ftand in to 
 one another, are naturally led to form feveral 
 Collections of fimple Ideas, preferably to others, 
 as forefeeing they may have frequent Occafion 
 to take Notice of fuch precife Combinations. 
 And becaufe it would be tedious in Converfa- 
 tion, every time thefe complex Notions occur j 
 to enumerate all the Ideas of which they con- 
 fift j therefore, for the- Sake of Eafe and Dif- 
 patch, they give them particular Names, and 
 thereby render the Cornpofitions fixed and per- 
 uianenU- 
 
 XVII..
 
 ( 65 ) 
 
 XVII. THAT it is in this Man- ~, 
 
 The NcceJJity 
 
 ner we come by our complex Ideas, of mutual in- 
 
 i i i i- tfcourft. and 
 
 which multiply upon us according Mensparti- 
 
 as the Exigencies of Society require, cular 
 
 _ r . * f i i rw -f i Life, a great 
 
 or our Purfuits, Method or Lire, and Source ofcom- 
 
 difFerent Aims, throw Occafions in 
 our Way of combining fuch and fuch Percep- 
 tions together, might be eafily made appear by 
 a fhort View of the Combinations themfelves. 
 Human Ac-lions, as occurring moft frequently, 
 and affording large Matter of Converfation, De- 
 bate, and Enquiry among Men, have been very 
 nicely modified, and diftinguiftied into Clafles, 
 according to the feveral Circumftances moft 
 likely to attend them. In like manner the Arts 
 and Sciences, in proportion as they are culti- 
 vated, leading us into many compound Views 
 of Things, which otherwife would never offer 
 themfelves to the Confideration of the Mind ; 
 the complex Ideas of this Sort, with the Names 
 by which they are exprefled, are, we find, the 
 Work of fuch particular Nations^ where thefe 
 Arts and Sciences have chiefly flouriflied. The, 
 Greekiy for inftance, excelled in Learning and 
 polite Knowledge ; hence many of the Terms 
 belonging to Rhetorick, Poetry, Philofophy,. 
 Phyfick, &V. come originally from their Lan- 
 guage. Modern Fortification has received its 
 greateft Improvements among the French j and, 
 
 accordingly
 
 ( 66 ) 
 
 accordingly the Ideas and Terms of the Art arc 
 moftly derived from Writers of that Nation. In 
 Italy^ Architecture, Mufick, and Painting, have 
 been the great Exercife of the Men of Genius ; 
 it is therefore among them that we find the fe- 
 veral complex Notions belonging to thefe Parts 
 of Study, as well as the Names by which they are 
 exprefledj nor can we difcourfe accurately and 
 minutely of the above-mentioned Arts, without 
 having recourfe to the Language of that Cli- 
 mate. And if we dcfcend into the particular 
 Callings and Profeffions of Men, they have all 
 their peculiar Collections of Ideas, diftinguifhed 
 by their feveral Names, and hardly known but 
 to fuch as are converfant in that Manner of Life. 
 Thus Calcination^ Cobobation y Filtration, &c. are 
 Words ftanding for complex Ideas frequently 
 framed in the Minds of Chymifts, and therefore 
 familiar to Men of that Employment. Yet as 
 thefe, and fuch like Combinations, feldom oc- 
 cur in common Life, the Generality of Man- 
 kind, we fee, are in a great Meafure unac- 
 quainted with them. 
 
 Htr.ie d\ffertnt XVIII. I MIGHT purfue thefe 
 
 pM&lZ'Z/t- Speculations farther, and fhcw how 
 rent centner, the feveral Fafhions, Cuftoms, and 
 
 and Words in . 
 
 ene Larguage Manners or one Natjon, leading 
 
 35T* them to form man y com P lex N - 
 
 in anoibtr. tions. which come not fo naturally 
 
 in
 
 ( 6; ) 
 
 in the Way of another ; different Sets of Ideas 
 prevail in different Countries, and of courfe have 
 Names appropriated to them in one Language, 
 to which there are no Words that anfwer in an- 
 other. The Procedure and Forms of our Courts 
 of Juftice have introduced many Terms into 
 the Englijh Law, which ftand for Collections of 
 Ideas framed among no other People. Nor 
 tvould it be pofiible to render thefe Terms by 
 any fingle Words of another Language; becaufe, 
 where the Ideas themfelves prevail not, there are 
 no Names provided to exprefs them. In this 
 Cafe, therefore, it becomes necefTary to ufe Cir- 
 cumlocutions, and enumerate the feveral Ideas 
 comprehended in the Collection, if we would 
 fo exprefs ourfelves as to be underftood in the 
 Language of other Nations. Nay, even among 
 the fame People, the Change of Cuftoms and 
 Opinions frequently brings new Sets of Ideas,' 
 which of courfe muft be diftinguifhed by parti- 
 cular Names ; while, at the fame Time, the No- 
 tions of former Ages grow into Difufe, and the 
 Words anfwering them are wholly laid afide, or 
 employed in a Signification different from what 
 they had before. 
 
 XIX. THUS Languages are in a m WJ tbe 
 perpetual Flux, and by Degrees vary Caufe that 
 
 r \ r i i T^ Lanvuav'.i 
 
 fo much from their original Frame, are in * fer >. 
 as to become unintelligible even to f etual flu *' 
 the Defcendants of thofe who fpeak them. If 
 
 we
 
 ( 68 ) 
 
 we run back into the Ages of Chivalry in Eng- 
 land* when Tilts and Tournaments were in 
 Fafhion, how many complex Ideas, peculiar 
 to that Mode of Life, fhall we find familiar 
 among the Men of thofe Times, which are now 
 little known or attended to \ On the contrary, 
 the Improvements in Arts and Sciences that 
 have fmce taken place, have led us into innu- 
 merable Views of Things to which our Fore- 
 fathers were perfect Strangers. But I fhall not 
 pufh thefe Reflections any farther, believing that 
 what has been faid will be fufficient to fhew 
 the Origin and Progrefs of our compound Ideas, 
 and how the Mind is directed in the Choice of 
 the Combinations it makes. We therefore pro- 
 ceed to the Confideration of abftract Ideas t 
 which make the Subject of the following Sec- 
 tion. 
 
 SECT. II. 
 
 Of dbftraft or Univerfal Ideas. 
 
 I. T TAV1NG difpatched what 
 
 General Ideal I i ... , f ., 
 
 firmed by tbc JL JL was neceflary to be laid, 
 " 1 "^ concerning our compound Ideas, 
 confidered merely as they are Com- 
 binations of the Underftanding, it is now Time 
 to explain how we come by our general No- 
 tions, which ferve to reprefent to us a Multitude 
 
 of
 
 ( 69 ) 
 
 of Individuals, and are the Standards by which 
 we rank Things into Sorts. And this, as we 
 have before intimated, is done by the Abftrac- 
 tion of the Mind ; which Aft may be extended 
 to all our Ideas, whether fimple, compound, or 
 of Subftances. If, for inftance, we fix our 
 Attention on any particular Colour, as Scarlet, 
 we can leave out the Confideration of all prefent 
 Circumftances, as the Subject in which it in- 
 heres, the Time and Place of feeing it, fcff. and 
 retaining only the Impreflion itfelf, make it a 
 Reprefentative of that Quality or Appearance, 
 wherever we chance to meet with it. It is thus 
 that abftract and univerfal Ideas are framed ; for 
 the Mind regarding only the Scarlet Colour, 
 which one Day it obferves perhaps in a Piece of 
 Cloth, another in a Picture, and a third in the 
 Rainbow ; the Appearance is conceived to be 
 the fame in all thefe Objects, and therefore is 
 called by the fame Name. 
 
 II. BUT to enter a little more AiitbePtr- 
 clofely into this Matter, and fhew r^'V^' 
 
 J U nderflandtng 
 
 that thefe our general Conceptions particular, 
 are the mere Creatures of the Understanding, it 
 may not be amifs to take Notice, that all our 
 Perceptions of Things, whether we derive them 
 from Senfation or Reflection, are of their own 
 Nature particular, and reprefent to us fingle 
 determinate Objects. When we fee a Horfe, for 
 
 inftance.
 
 ( 70 ) 
 
 inftance, in the Fields, our Idea is that of an In- 
 dividual. If we hear a Sound, it is fomething 
 particular, and different from what we hear at 
 any other Time. Every Perception of the Mind 
 is diftinct from every other Perception ; nay, 
 and every Idea brought into View by the Ima- 
 gination, as when we frame the Image of a 
 Lion landing before us, is iiill Angular, and 
 reprefents a fingle Object. 
 
 . Ill, BUT when we come to take 
 tbt'sftcitire- a View of thefe feveral Particulars, 
 prtftntiiubat we re adily obferve among; fome of 
 
 H common to ' ' 
 
 d:fer<nt jndl- them a Refcmblancej and framing 
 to ourfelves an Idea of thofe Things,- 
 in which any of them are found to agree, we 
 thereby get a general Notion, applicable to 
 many Individuals. Thus Horfes are found to 
 refemble one another in Shape, Vcice, and 
 Structure of Parts. The Idea which takes in 
 only the Particulars of this Refemblance, ex- 
 cluding what is peculiar to each fingle Animal, 
 becomes of courfe common to all Cic- ures of 
 that Kind, and is therefore the Reprefemative of 
 a whole Clafs of Beings. Accordingly jhe Name 
 of that general Idea is given to every Animal 
 in which that Shape, Voice, and Structure is 
 found j for the Word Horfe, implying only 
 thefe Particulars, muft belong to al] Creatures 
 wherein they exift. This is the firft Step or 
 
 Gradation
 
 'Gradation in the forming of abftra& Notions, 
 when the Mind confines itfelf to the Confide- 
 ration of individuals, and frames an Idea that 
 comprehends fuch only under it. The Rank 
 or Clafs of Things anfwering to this Idea, is 
 called Species in the Language of the Schools. 
 So a Horfe is a certain Species of Animals, an 
 Oak is a Species of Trees, and a Square is a Specif s 
 of four-fided Figures. 
 
 IV. WHEN we have thus learnt 
 
 1 T i i i o i "' Idea of 
 
 to rank Individuals into sorts and the Genus re- 
 Claffes, according to the Refem- ?' '/""' vbat 
 
 is common tt 
 
 blance found among them, the Mind fwerel Spe- 
 proceeds next to confider the Species 
 themfelves, and often in thefe too obferves a 
 certain Likenefs. Whereupon, throwing out all 
 thofe Particulars wherein the feveral Species 
 are found to difagree, and retaining only fuch 
 as are common to them all, we thereby frame a 
 itill more general Idea, comprehending under it 
 a Variety of different Species. Thus a Sparrow, 
 a Hawk, an Eagle, &c. are diftincl Specks of 
 Birds, which have each their peculiar Shape and 
 Make. They neverthelefs referable one another, 
 in being covered with Feathers, and provided 
 with Wings that bear them through the Air. 
 Out of thefe Particulars we form a new Idea, 
 including all the common Properties of the fea- 
 thered Kind j and appropriating to it the Name 
 4 Bird,
 
 ( 7* ) 
 
 Bird, mark by that Word another Clafs of 
 Things, of a higher Order than any of the 
 former. This fuperior Divifion, which extends 
 to feveral Species at once, is called in the Schools 
 the Genus, and is the fecond Step the Mind takes 
 in advancing to univerfal Notions. 
 
 V. AND thus have I given a fhort, 
 
 n, Mind may 
 
 advance by but 1 hope intelligible Account, of 
 Jri^lf "-" the Bufmefs of Genera and Species, 
 /ing from Par- about which fo much has been faid 
 
 titulars to Ge- . . . . . 
 
 rt.'s. in the Wntmgsof Logicians. Species, 
 
 in Stridtnefs and Propriety of Speech, is fuch a 
 Rank or Clafs of Things, as comprehends under 
 it only individuals ; Genus advances ftill higher, 
 and takes in a Variety of diftinft Species. It is 
 however to be obferved, that the Mind, in rifmg 
 from Particulars to Generals, does not confine 
 itfelf to one or two Gradations, but may carry 
 its Views through the whole Extent of Things, 
 until at length it arrive at an Idea embracing the 
 univerfal Compafs of Nature. For when we 
 have ranked Things into Sorts, and reduced thefe 
 again to the higher Order or Genus, thefe Genera 
 are ftill found to refemble one another in fome 
 Particulars j which being collected into one Idea, 
 form a new and more comprehenfive Divifion of 
 Things. Thus Bird is a Genus, embracing all 
 the Varieties of the feathered Kind. Fijb im- 
 plies the feveral Species of living Creatures 
 
 which
 
 ( 73 y 
 
 which inhabit the Waters. >yad)-uptd and Infcft 
 are alfo univerfal Ideas, that take in many infe- 
 rior Diftributions and Clafles. Yet all thefe dif- 
 ferent Orders of Being, have this in common ; 
 that they are provided with organical Bodies, 
 fitted for the Purpofes of Life and fpontaneous 
 Motion. An Idea therefore comprehending only 
 thefe laft Particulars, will equally belong to all 
 the Divifions before enumerated, and the Word 
 Animal^ by which it is exprefled, becomes a ge- 
 neral Name for the feveral Creatures endued with 
 Life, Senfe, and fpontaneous Motion. If we are 
 for carrying our Views ftill farther, and framing 
 a yet more univerfal Notion, we can caft our 
 Eyes upon both the animate and inanimate Parts 
 of Nature j wherein we find this mutual Cor* 
 refpondence, that they exift, and continue in 
 Being. This laft Idea therefore of Being in ge- 
 neral, comprehends under it all the Varieties of 
 Things, and may be univerfally applied to what- 
 ever has either Life or Exiftence ; fo that in re~ 
 fpe& of' the prefent Frame of Nature, it is the 
 higheft and moft univerfal Idea we have. 
 VI. IN this Series of Notions, 
 
 . - , i rx Whence many 
 
 nnng one above another in the Ue- i^ttrmtdiM 
 gree of Univerfality ; that Divifion, 
 which comprehends under it feveral Genus 
 Genera, is called in the Schools the lowtjl S * ec!es ' 
 higher Genus ; which Denomination continues, 
 until we arrive at the laft Advance of the Under. 
 ihnding,
 
 ( 74 ) 
 
 (landing, when being come to the moft general 
 of all Ideas, that admits not of a fuperior, it is 
 diftinguifhed by the Name of the Genus genera- 
 lijjin.um. In like manner, the feveral Genera com- 
 prehended under a higher Genus^ are in refpecl of 
 it confidered as Species ; and as thefe two laft 
 have Species under them, the inferior Divifions 
 are for Diftinclion's fake termed lower Species. 
 Thus the Progreflion continues, and when we 
 come to the loweft Subdivifion of all, compre- 
 hending only Individuals, which, as I have before 
 intimated, conftitures the proper Species, this 
 the Schools denominate the Species fpecialijjima. 
 All that lie between it and the higheft Dittribu- 
 tion of things, are the intermediate Genera and 
 Species which are termed each in their 7'urn, 
 Gtints gtntralfUS) or Species fpecialior, according as 
 we confider them in the afcending or defcending 
 Scale of our Ideas ; or, to fpeak in the Language 
 of Logicians, according to their Afcent or De- 
 fcent in Linea pradicamentali. I Ihould not have 
 entered fo far into thefe verbal Difquifitions, had 
 not the Terms here explained, been fuch as fre- 
 quently occur in the Writings of Philofophers ; 
 infomuch that without fome Knowledge of them, 
 we muft often be at a Lofs, in the Profecu- 
 tion of thefe Studies. Befides, it is both cu- 
 rious and ufeful, to fee the gradual Progrefs of 
 the Mind, in its Advances from particular to ge- 
 neral Conceptions ; to obferve it ranging its 
 
 Ideas
 
 ( 75 ) 
 
 Ideas into Clafles, and eftablifllinga juft and re^- 
 gular Subordination in its Views and Notices of 
 Things. This is the flior teft Way to Knowledge, 
 and affords the beft Means of preferring the 
 Order and due Connexion of our Thoughts, fo 
 as to make them fubfervient to the Increafe of 
 Science, For when we fee how Things com^ 
 prehend, or are comprehended in one another, 
 we are able to difcover the mutual Dependence 
 of all the feveral Branches of Knowledge, which 
 leads us into the true and natural Method of 
 conducting our Understandings in the Search 
 of Truth. 
 
 VII. FROM what has been faid it 
 is evident, that general Ideas are JjSfiJf 
 the Creatures and Inventions of the eftbtUndtr- 
 Underftanding. Nature, it is true, 
 in the Production of Things, makes many of 
 them alike j but it is the Mind alone, that col- 
 lefts the Particulars in which they agree, into 
 one Idea, arid fets it up as a Reprefentative of 
 many Individuals. And now I think we may ven- 
 ture upon that much agitated Queflion, Where 
 do the Genera and Species of Things exift ? To 
 which I anfwer, in the Mind. Univtrfality be- 
 longs not to Things themfelves, it being appa- 
 rent, that they are all particular in their Exif- 
 tence. However, as they often have many Pro- 
 perties in common, the Underftanding, by uni- 
 ting thefe into one Conception, obtains a ge- 
 E 2 neral
 
 ( 7* ) 
 
 ireral Idea, under which it ranks all the feveral 
 Objedls wherein thefe Properties are found. 
 So far indeed we muft allow, that the particular 
 Combination of Properties, which conftitutes 
 the Genus or Species, exifts in all the Indivi- 
 duals referred to that Genus or Species; but 
 then it is in Conjunction with other Properties, 
 by which thefe Individuals are diftinguiflied 
 from one another. Thus the Collection of fim- 
 ple Ideas, fignified by the Word Bird, is to be 
 found for Inftance in a Hawk> or any other fingle 
 Animal, to which we apply that general Name j 
 but the Notion itfelf, abftracled from all the 
 Particulars to which it belongs, has evidently 
 no Exiftence out of the Underftanding. There 
 is not a Being in Nature that can be called a 
 Bird in general, or that does not neceflarily im- 
 ply, in the very Conception of it, feveral fmiple 
 Ideas, befides thofe marked by that Word. For 
 the Name in this Cafe fignifies no more than an 
 Animal covered with Feathers, and provided with 
 Wings, without Regard either to Shape, Bulk, 
 or the particular Time and Place of its Exiftence. 
 Thefe laft Confiderations however are infbpara- 
 ble from the Reality of Things, and therefore 
 Hiuft be added to the general Idea, before we can 
 conceive any Thing conformable to it a&ualljr 
 brought into Being. 
 
 VIII. HENCE
 
 ( 77 1 
 
 VIII. HENCE we fee at once, c a */yw*- 
 what fort of an Exigence general part they ex\Jf 
 
 tnly in tot 
 
 Natures have. Confidered apart, and Mind, im in 
 by themfelves, they are wholly the JgSS 
 Workmanfhip of the Underftand- Idtas \ntbe 
 
 ... i T ' i T Individual* 
 
 ing, and derive their Being and Re- comprehended 
 ality from it j but viewed in con- UKdlrtbem ' 
 jun&ion with other Ideas that co-exift with them 
 in the feveral Objects of Nature, they are to be 
 found in the Individuals to which they refer j and 
 therefore according to this way of Conception, 
 may be faid to have an Exiftence in them. Thus 
 fo long as the Ideas anfwering to the Words Man 
 or Tree, continue general and undetermined, they 
 have no real Objects anfwering them in Nature ; 
 nor can the Collections of fimple Ideas, marked 
 by thefe Names, while all others are fuppofed ex- 
 cluded, exift any where out of the Underftand- 
 ing. Neverthelefs, as all the fimple Ideas in- 
 cluded in the general Notioa of Man, are to be 
 found in every particular Man j and all thofe im- 
 plied in the Notion of a Tree, in every particular 
 Tree; hence the general Nature of Man, exifts 
 in every individual Man, as does the general Na- 
 ture of a Tree, in every individual Tree. 
 
 IX. ONE Thing ftill remains to Difference f 
 be obferved, with regard to thefe our UwMfi- 
 
 atred at con*- 
 
 general Ideas ; that though many of pound and as 
 them are evidently Combinations of univt ^ ah 
 different fimple Ideas, and according to that 
 E 3 Way
 
 ( 7* ) 
 
 Way of confidering them, are included in the 
 firft Divifion of our complex Conceptions, 
 thofe namely framed by the Compofitiqn of the 
 Mind j yet we are carefully to diftinguifli be- 
 tween an Idea as it is compound, and as it is uni- 
 yerfal. In the firft Cafe, the Mind chiefly con- 
 fiders the feveral Ideas that are combined toge- 
 ther; or, in other Words, all the Attributes, Qua- 
 lities, or Parts, that are contained in any Idea. 
 Thus the Idea of a Bird, includes Life, Senfe, 
 fpontaneous Motion, a Covering of Feathers, 
 Wings, &(. none of which can be left out with- 
 out deflroying the very Nature of the Idea, and 
 making it fomething quite different from what it 
 was before. This Way of confidering Things 
 according to the Number of their Parts and Pro- 
 perties, is called by Logicians the Comprehenfton 
 of an Idea. But the Univerfality of our Notions 
 implies quite another Turn of Thinking; in as 
 much as it fixes the Regard of the Mind, upon 
 the Subjects to which our Ideas extend, or the 
 Individuals and Species comprehended under 
 them. In this Senfe the Ideas anfwering to the 
 Word Bird, takes in the feveral Species of the fea- 
 thered Creation, the Hawk, the Eagle, Sparrnv, 
 Lark, and innumerable others, to all which it 
 may with equal Propriety be applied. And here 
 it is remarkable, that the Idea lofes nothing of 
 its Force or Comprehenfion, by being reftricled to 
 a particular Kind. When I fay the Bird of Jove, 
 
 though
 
 ( 79 ) 
 
 though in this Cafe the Idea is reftrained to the 
 Eagle alone, it (till remains as diftindt, and in- 
 cludes as many fimple Ideas in its Compofition, 
 as when before it was extended to all the diffe- 
 rent Tribes of feathered Animals. 
 
 X. WE fee therefore that our The Compre- 
 compound Ideas, may continue the 
 fame in refpect of their Attributes, 
 or the Number of Parts, and yet vary confidera- 
 bly in the Degree of Univerfality. The gene- 
 ral Idea of Man is the fame, whether applied 
 to the whole human Race, or thofe of any parti- 
 cular Nation. When I affirm, for Inftance, of 
 Mankind in general, that their Knowledge falls 
 fhort of Perfection, and afterwards make the like 
 Obfervation of the Men of the prefent Age ; in 
 both Cafes, the Word Man ftands for one and 
 the fame Collection of fimple Ideas ; but in re- 
 fpect of the Individuals to which it is applied, 
 there is a great and manifeft Difference. That 
 is, the Term, Man, denotes one invariable com- 
 pound Idea ; which notwithftanding, confider- 
 ed as a general Notion, may be contracted or 
 enlarged at Pleafure. And as in the former Cafe 
 the feveral Parts of the compound Idea is called 
 its Comprehenfion ; fo in the latter, the Indivi* 
 duals to which the univerfal Idea is applied, is 
 called its Extenfion. I might add many more 
 Obfervations on this Subject, but choofe rather 
 4 to
 
 to ftop here, having faid enough to explain the 
 Difference between compound and abftradl 
 Ideas, and (hew the Reafon of my ranging them 
 under diiiin& Heads. 
 
 SECT. III. 
 
 Of our Ideas of Relations* 
 
 I. T COME now to the third and 
 
 JJtai of Rt- 
 
 latiom txct,d- JL laft Divifion of thofe Ideas 
 which I confider as the Creatures 
 and Workmanfhip of the Underftanding ; fuch 
 namely as arife, from the comparing of Things 
 one with another. For the Mind in its Views, 
 is not tied to fingle Obje&s ; but can examine 
 their References and Refpe&s, in regard to 
 others, brought under Confideration at the 
 fame time. And when it does fo, and thence 
 derives new Notices of Things, the Ideas thus 
 got are called Relations, and make, I am apt 
 to think, the largeft Clafs of all our Percep- 
 tions. For every fingle Object will admit of 
 almoft innumerable Comparifons with others, 
 and in this Senfe may become a very plentiful 
 Source of Ideas to the Underftanding. Thus if 
 We compare one Thing with another in refpeft 
 
 of
 
 of Bulky we get the Ideas of greater, lefs, or 
 Equality; if in refpe& of Time, of older and 
 younger; and fo for other Relations, which we 
 can purfue at pleafure, almoft without End j 
 whence it is eafy to conceive, how very exten* 
 live this Tribe of our Perceptions muil be. 
 
 II. I SHALL not pretend to trace 
 out thefe Ideas particularly, nor in- 
 deed fo much as to enumerate thei r to particular 
 
 f 1 r\- -r t_ v. Cemparifons 
 
 ieveral Divmons j it being enough iy t be 
 
 to obferve, that here, as well as in 
 
 ctes of Life. 
 
 the other kinds of our complex 
 Ideas, we bound ourfelves for the moft part to 
 fuch Comparifons, as the Exigencies of Society, 
 the Wants of Life, and the different Profeffions 
 of Men, render necefiary j and are more or lefs 
 accurate in tracing out the Relations of Things, 
 according to the Degree of Importance they ap- 
 pear to have in thefe Refpe&s. The Relations 
 of Men one to another, arifing either from the 
 Ties of Blood, their feveral Ranks and Places 
 in the Community, or a mutual Intercourfe of 
 good Offices, being of great Weight and Con- 
 cern in the Commerce of Life, have in a parti- 
 cular Manner engaged our Attention, and are 
 therefore very minutely defcribed. For the fame 
 Reafon, Men have found it neceflary, to deter- 
 mine as exactly as poflible, the various Depen- 
 dence of Things, as their Happinefs is nearly 
 5 conne&ed
 
 ( 8* ) 
 
 conne&ed with this Knowledge. When we 
 confider Objects merely in refpect of Exiftence, 
 as either giving or receiving it, we come by 
 the Ideas of Caufe and EffeR ': Nor need I men- 
 tion, how much the Welfare of Mankind de- 
 pends upon an extenfive View of Things, as 
 theyftand connected in this Relation ; it being 
 evident, that the feveral Schemes and Purpofes 
 of Life, are all conduced upon a previous Sup- 
 pofition, that certain known Caufes, will have 
 their ufual regular Effects, and fuch and fuch 
 Actions, be attended with fuch and fuch Confe- 
 quences. 
 
 III. BUT there are other Rela- 
 
 felations of . r i i i i /* i L/-I 
 
 Creator and tlOHS of thlS kllld, belldeS thole that 
 
 Creature, &e. re gard merely Exiftence ; as when 
 we alfo take into the Account, the additional 
 Gifts of a Capacity for Happinefs, and the 
 Means of attaining it j which conftitutes the Re- 
 lation of Creator and - Creature* in the more 
 folemn Acceptation of thefe Words. Again, 
 when we confider the great Author of our Be- 
 ing, not only as the Creator of the Univerfe, but 
 alfo as preferving and holding it together, and 
 prefiding over the prefent Frame of Things with 
 uncontrouled Dominion; he then appears un- 
 der the Notion of a moral Governor^ to whom 
 we are accountable for our Actions, and the 
 Ufe we make of thofe Powers and Faculties we 
 
 derive
 
 ( 83 ) 
 
 derive from him. Now as it is of the higheft 
 Confequence for Men, not to be unacquainted 
 with thefe, and fuch like Relations ; hence we 
 find, that the wifeft Nations, and fuch as beft 
 underftood the true Application of the Powers of 
 the Mind, have always made it their chief Study 
 to regulate and afcertain thefe Ideas, and trace 
 them in all their Confequences. And thus we 
 may in fome meafure perceive, how the Mind 
 proceeds in comparing its Ideas together, and 
 by what Views it is chiefly governed, in fram- 
 ing the complex Notions of this Clafs, by which 
 it reprefents the various Habitudes of Things. 
 I fhall only add upon this Subjeft, thefe two 
 Obfervations. 
 
 IV. FIRST, that our Ideas of 
 Relations, are for the moft part very SMW 
 clear and diftincl. For the compar- cle < tr **& A/- 
 ing of things together, being a vo- 
 luntary A& of the Mind, we cannot but fuppofe 
 that it muft be acquainted with its own Views in 
 the Comparifon ; and of courfe have a clear 
 Conception of the Foundation of that Relation,, 
 if fets itfelf to enquire into. Thus the Relation 
 of Caufe and Effect, implying only that one 
 thing produces, or is produced by another, 
 which Notions are always diftin&ly fettled in 
 the Underftanding before it goes about to make- 
 the Comparifon j it is evident, that the Idea re- 
 E 6 prefenting
 
 preferring this mutual Refpecfc of Obje&s, will 
 be nolefs clear, than are the Notions themfelves 
 upon which the Relation is founded. And 
 what is ftill more remarkable of the Ideas of 
 this Clafs ; they ceafe not to be diftindt, even 
 where the Subjects compared are but very imper- 
 fectly known. For I can well enough conceive 
 that one thing has produced another, and that 
 therefore they ftand related as Caufe and Effect, 
 though my Ideas of the things themfelves may 
 perhaps be very obfcure, and come far fhort of 
 xeprefenting their real Nature and Properties. I 
 doubt not but it will be readily owned, that our 
 Idea of the Univerfe, confidered as comprehend- 
 ing the whole Frame of created Things, is very 
 inadequate ; and I think it is ftill more apparent, 
 that our Notion of the Supreme Being comes 
 not up to the Excellence and Perfection of his 
 Nature. Yet we very well underftand what is 
 meant, by calling God the Author of the World ; 
 and though we comprehend not the Manner of 
 his producing it, find no Difficulty in framing 
 the Ideas, the relative Words Creator and Crea- 
 ture ftand for. 
 
 V. I HAVE yet another Obferva- 
 
 Jdeas cfRe!a- . . . . . 
 
 Hens among tlOtt tO make Upon thlS bubjeCT ; 
 
 the mtf im. and j t j s that Qur J deas of Re j a _ 
 
 fottant Con- 
 
 <ct>thi / the tions are among the moft impor- 
 tant Conceptions of the Under- 
 
 ftanding,
 
 ( 85 ) 
 
 landing, and afford the largeft Field for the 
 Exercife and Improvement of human Know- 
 ledge. Moft of our Enquiries regard relative 
 Ideas, and are fet on foot with a View to invef- 
 tigate the mutual Habitudes of Things. The 
 Mathematician has taken Quantity for his Pro- 
 vince, and teaches us how to compare Magnitudes 
 of different Figures and Dimenfions, in order to 
 judge with Certainty of their relative proper- 
 ties. The Philofopher attaches himfelf to the 
 Chain of Caufes and Effe&s, and endeavours to 
 trace out the various Dependence of Things 
 confidered in this Light. In fine, whither do 
 all our Refearches tend, but by means of cer- 
 tain known Properties and Relations, to find 
 out others that ftand fome how connected with 
 them ? As for the Importance of thefe Concep- 
 tions, no one can call that in queftion, who 
 reflects j that from our Relations to our Creator 
 and one another, arife all the Duties of Morality 
 and Religion j and that the Correfpondence of 
 the feveral Objects of Nature, to the Organs of 
 the Body, and Faculties of the Mind, is that 
 by which alone we can judge, of what will 
 procure us Happinefs or Mifery. Whence it is 
 evident, that without an exact Knowledge of 
 thefe Relations, we muft wander on in Life 
 with great Uncertainty, and may often plunge 
 into Calamities and Misfortunes, by thofe very 
 
 Purfuits,
 
 ( 86 ) 
 
 Purfuits, from which we expected nothing but 
 Joy and Pleafure. 
 
 VI. THUS have I gone through 
 
 Recapitulation. . , i T\- -r e TJ 
 
 the leveral JJwuons of our Ideas* 
 which I have endeavoured to reprefent in fuch 
 a Manner as their vaft Extent may moft eafily 
 appear, and the Conduct of the Mind in framing 
 them be diftinctly apprehended. I might eafily 
 run into other Diftinctions, by confidering them 
 as clear or olfcure 9 adequate or inadequate, true 
 orfalfe. But the Limits of this Tract will not 
 allow my entering more fully into the Subject, 
 and I think it the lefs needful, becaufe the very 
 Names are'almoft fufficient to convey a Notion 
 of thefe feveral Kinds of Ideas into the Mind. 
 But as the Divifion explained above feems to be 
 of great Importance, towards fettling in the 
 Underftanding a juft View of the Progrefs of 
 human Knowledge, and the Steps by which it 
 advances from one Degree of Improvement to 
 another, I fhall here run over it again in as few 
 Words as poffible, that the whole Procefs may 
 been feen at once. Our Ideas are all derived into 
 the Underftanding, either by Senfation or Re- 
 flection. This however is obfervable, that one 
 and the fame Object often excites a Variety of 
 Perceptions at once, which are neverthelefs rea- 
 dily diftinguifhed by the Mind, and appear each 
 under a Form peculiar to itfelf. Thefe confti- 
 
 tute
 
 tute our primary and original Notices, and are 
 eafily known from all others, in as much as they 
 are intirely void of Plurality, and cannot be di- 
 vided into two or more different Ideas. They 
 are alfo the Materials out of which the others 
 are formed, and are therefore by Way of Dif- 
 tindion called fimple Ideas. But the Mind, 
 though it has no Power over thefe, either to 
 fafhion or deftroy them, can yet combine them 
 in an infinite Number of Ways ; and from their 
 various Combinations refult all our complex 
 Ideas, which are of two principal Kinds. Firft, 
 fuch as are derived from without, and reprefent 
 thofe Combinations of fimple Ideas, that have a 
 real Exiftence in Nature. Of this Sort are all 
 our Ideas of Subftances. Secondly, the Con- 
 ceptions formed by the Mind itfelf, arbitrarily 
 uniting and putting together its Ideas. And as 
 this makes by far the largeft Clafs, and compre- 
 hends all thofe Ideas which may be properly 
 termed our own, as being the real Workmanfhip 
 of the Underftanding ; fo they fall very naturally 
 under three diftinc~l Heads. For either the Mind 
 combines feveral fimple Ideas together, in order 
 to form them into one Conception, in which the 
 Number and Quality of the Ideas united, are 
 principally confidered ; and thus it is we come 
 by all our compound Notions : or it fixes upon 
 any of its Ideas, whether fimple, compound, or 
 
 of
 
 ( 88 ) 
 
 of Subftances, and leaving out the Circumftanees 
 of Time, Place, real Exiftence, and whatever 
 renders it particular, confiders the Appearance 
 alone, and makes that a Reprefentative of all of 
 the Kind; whence our abjlraft and univerfal 
 Ideas are derived : or, laftly, it compares Things- 
 one with another, examines their mutual Con- 
 nections, and thereby furnifhes itfelf with a new 
 Set of Notions, known by the Name of Relations, 
 which, as has been already remarked, make by 
 no means the leaft important Clafs of our Per- 
 ceptions. This Divifion of our Ideas, as it feems 
 to be the moft natural, and truly to reprefent the 
 Manner in which they are introduced into the 
 Mind, fo I believe it will be found to compre- 
 hend them in all their Varieties. I fhall there- 
 fore now proceed to offer fome Obfervations- 
 upon Language, as being the great Inftrument, 
 by which we are enabled to make our Ideas and 
 Perceptions known to others. 
 
 CHAP. V. 
 
 Of Words conjidered as the Signs of our Ideas. 
 
 Word* fumijb I. "\ T 7"E have fcen how the Miner 
 tb.Mt.mcf yy comestobefirftfurnifhed 
 
 recording our 
 
 ewn Thoughts, with Ideas, and by what Methods 
 it contrives to diverfify and enlarge its Stock 5, 
 
 let
 
 ( 89 ) 
 
 let us now confider the Means of making 
 known our Thoughts to others, that we may 
 not only underfland how Knowledge is ac- 
 quired, but alfo in what Manner it may be com- 
 municated with the greateil Certainty and Ad- 
 vantage. For our Ideas, though manifold and 
 various, are neverthelefs all within our own 
 Breafts, invifible to others, nor can of them- 
 felves be made appear. But God defigning us 
 for Society, and to have a Fellowfhip with thofe 
 of our Kind, has provided us with Organs fitted 
 to frame articulate Sounds, and given us alfo a 
 Capacity of ufing thofe Sounds, as Signs of in- 
 ternal Conceptions. Hence fpring Words and 
 Languages ; for having once pitched upon any 
 Sound to ftand as the Mark of an Idea in the 
 Mind, Cuftom, by Degrees eftablifhes fuch a 
 Connection between them, that the Appearance 
 of the Idea in the Underftanding always brings 
 to our Remembrance the Sound or Name by 
 which it is exprefled j as in like manner the 
 hearing of the Sound never fails to excite the 
 Idea for which it is made to ftand. And thus 
 it is eafy to conceive, how a Man may record 
 his own Thoughts, and bring them again into 
 View, in any fucceeding Period of Life. For 
 this Connection being once fettled, as the fame 
 Sounds will always ferve to excite the fame Ideas ; 
 if he can but contrive to regifter his Words, in 
 the Order and Difpofition in which the prefent 
 
 Train
 
 ( 90 ) 
 
 Train of his Thoughts prefents them to has 
 Imagination ; it is evident he will be able to re- 
 call thefe Thoughts at Pleafure, and that too in 
 the very Manner of their firft Appearance. Ac- 
 cordingly we find, that the Inventions of Writ- 
 ing and Painting, by enabling us to fix and per- 
 petuate fuch perifhable things as Sounds, have 
 alfo furnifhed us with the Means of giving a 
 kind of Permanency to the Tranfaclions of the 
 Mind, infomuch that they may be in the fame 
 Manner fubjecled to our Review, as any the 
 other abiding Objects of Nature. 
 
 II. BUT befides the Ability of re- 
 
 And of tbt .. ,_,, 
 
 vutuai Cim- cording our own Thoughts, there is 
 wiumcaticn of tn i s f art her Advantage in the Ufe of 
 
 Kncivlcdgt to. ii 11 
 
 jrom om Ma external oigns, that they enable us 
 to another. to communicate our Sentiments to 
 others, and alfo receive Information of what 
 pafles in their Breafts. For any Number of 
 Men, having agreed to eftablifh the fame Sounds 
 as Signs of the fame Ideas, it is apparent that 
 the Repetition of thefe Sounds muft excite the 
 like Perceptions in each, and create a perfect 
 Correfpondence of Thoughts. When, for in- 
 flance, any Train of Ideas fucceed one another 
 in my Mind, if the Names by which I am wont 
 to exprefs them, have been annexed by thofe 
 with whom I converfe, to the very fame Set of 
 Ideas, nothing is more evident than that by re- 
 peating thofe Names according to the Tenor of 
 
 rn/
 
 my prefent Conceptions, I fhall raife in their 
 Minds the fame Courfe of Thought as has taken 
 Pofleffion of my own. Hence, by barely attend- 
 ing to what pafles within themfelves, they will 
 alfo become acquainted with the Ideas in my 
 Underftandie'g, and have them in a manner laid 
 before their View. So that we here clearly per- 
 ceive, how a Man may communicate his Senti- 
 ments, Knowledge, and Difcoveries to others, 
 if the Language in which he converfes, be ex- 
 tenfive enough to mark all the Ideas and Tranf- 
 a&ions of his Mind. But as this is not always 
 the Cafe, and Men are often obliged to invent 
 Terms of their own, to exprefs new Views and 
 Conceptions of Things j it may be afked, how in 
 thefe Circumftances we can become acquainted 
 with the Thoughts of another, when he makes 
 ufe of Words to which we have never annexed 
 any Ideas, and that of courfe can raife no Per- 
 ceptions in our Minds. Now in order to unveil 
 this Myftery, and give fome little Infight into the 
 Foundation, Growth, and Improvement of Lan- 
 guage, the following Obfervations'will, I am apt 
 to think, be found of confiderable Moment. 
 III. FIRST, that no Word can be 
 
 A /r i r<- c T i !! Simple Ideal 
 
 to any Man the Sign of an Idea, till can i, ot b eca9 . 
 that Idea comes to have a real Ex- v '!' d . ',"'" tb * 
 
 Mind by 
 
 iftence in his Mind. For Names #Wi, or * 
 being only fo far intelligible, as they e J crt f tu 
 denote known internal Conceptions, where they 
 
 have
 
 ( 92 ) 
 
 have none fuch to anfwer them, there they are 
 plainly Sounds without Signification, and of 
 courfe convey no Inftruclion or Knowledge, 
 But no fooner are the Ideas to which they be- 
 long raifed in the Underftanding, than finding 
 it eafy to connect them with the eftablifhed 
 Names, we can join in any Agreement of this 
 Kind made by others, and thereby enjoy the 
 Benefit of their Difcoveries. The firft thing 
 therefore to be confidered is, how thefe Ideas 
 may be conveyed into the Mind ; that being 
 there, we may learn to connect them with their 
 appropriated Sounds, -and fo become capable 
 of underftanding others, when they make ufe 
 of thefe Sounds in laying open and communU 
 eating their Thoughts. Now to comprehend 
 this diftin&ly, it will be neceflary to call to 
 mind, the before-mentioned Divifion of our 
 Ideas into fimple and complex. And firft, as 
 for our fimple Ideas, it has been already ob- 
 ferved, that they can find no Admiflion into 
 the Mind, but by the two original Fountains 
 of Knowledge, Senfation and Reflexion. If 
 therefore any of thefe have as yet no Being in 
 the Underftanding it is impoflible by Words 
 or a Defcription to excite them there. A Man 
 who had never felt the Impreflion of Heat^ 
 could not be brought to comprehend that Sen- 
 fation, by any thing we might fay to explain it. 
 If we would really produce the Idea in him, it 
 
 nuift
 
 ( 93 ) 
 
 tnuft be by applying the proper Object to his 
 Senies, and bringing him within the Influence 
 of a hot Body. When this is done, and Expe- 
 rience has taught him the Perception to which 
 Men have annexed the Name Heat, it then be- 
 comes to him the Sign of that Idea, and he 
 thenceforth underftands the Meaning of a Term, 
 which before, all the Words in the World 
 would not have been fufficient to convey into 
 his Mind. The Cafe is the fame in refpect of 
 Light and Colours. A Man born blind, and 
 thereby deprived of the only Conveyance for 
 the Ideas of this Clafs, can never be brought 
 to underftand the Names by which they are ex- 
 prefled. The Reafon is plain : they ftand for 
 Ideas that have no Exiftence in his Mind ; and 
 as the Organ appropriated to their Reception is 
 wanting, all other Contrivances are vain, nor 
 can they by any Force of Defcription be raifed 
 in his Imagination. But it is quite otherwise 
 in our complex Notions. For thefe being no 
 more than certain Combinations of fimple Ideas 
 put together in various Forms j if the original 
 Ideas out of which thefe Collections are made, 
 have already got Admiffion into the Underftand- 
 ing, and the Names ferving to exprefs them arc 
 known ; it will be eafy, by enumerating the 
 leveral Ideas concerned in the Compofition, and 
 marking the Order and Manner in which they 
 
 arc
 
 ( 94 ) 
 
 are united, to raife any complex Conception in 
 the Mind. Thus the Idea anfwering to the 
 Word Rainbow, may be readily excited in the 
 Imagination of another, who has never feen the 
 Appearance itfelf, by barely defcribing the Fi- 
 gure, Largenefs, Pofition, and Order of Co- 
 lours ; if we fuppofe thefe feveral fimple Ideas, 
 with their Names, fufficiently known to him. 
 <rb< Namn ,f IV ' AND this naturally leads me 
 com/ilex Idtat to a fecond Obfervation upon this 
 
 definaklt, tbofe -,..,-. . . TTT , n , 
 
 of fmpu idea* Subject, namely : that Words itand- 
 *"" ing for complex Ideas are all defin- 
 
 able, but thofe by which we denote fimple Ideas 
 are not. For the Perceptions of this latter Clafs, 
 having no other Entrance into the Mind, than 
 by Senfation or Reflection j can only be got by 
 Experience from the feveral Objects of Nature, 
 proper to produce thofe Perceptions in us. 
 Words indeed may very well ferve to remind us 
 of them, if they have already found Admiflion 
 into the Underftanding, and their Connection 
 with the eftablifhed Names is known j but they 
 can never give them their original Being and 
 Exiftence there. And hence it is, that when 
 any one aflcs the Meaning of a Word denoting 
 a fimple Idea, we pretend not to explain it to 
 him by a Definition, well knowing that to be 
 impoflible ; but fuppofing him already acquaint- 
 ed with the Idea, and only ignorant of the Name 
 12 b/
 
 .. ( 95 ) 
 
 by which it is called, we either mention it to him 
 by fome other Name, with which we prefume he 
 knows its Connexion, or appeal to the Object 
 where the Idea itfelf is found. Thus, was any 
 one to afk the Meaning of the Word white, we 
 fliould tell him it flood for the fame Idea as ] 
 a/bus in Latln^ or blanc in French j or if we 
 thought him a Stranger to thefe Languages, 
 might appeal to an Object producing the Idea, 
 by faying it denoted the Colour we obferve in 
 Snow or Milk. But this is by no Means a Defi- 
 nition of the Word, exciting a new Idea in his 
 Underftanding ; but merely a Contrivance to 
 remind him of a known Idea, and teach him its 
 Connection with the eftablifhed Name. For if 
 the Idea after which he enquires, has never yet ] 
 been raifed in his Mind ; as fuppofe one who had 
 feen no other colours than black and white, fhould 
 afk the Meaning of the Wordfcar/et j it is eafy 
 to perceive, that it would be no more poflible 
 to make him comprehend it by Words or a De- 
 finition, than to difcourfe the fame Perception 
 into the Imagination of a Man born blind. The 
 only Method in this Cafe is, to prefent fome 
 Object, by looking at which the Perception it- 
 felf many be excited, and thus he will learn both 
 the Name and the Idea together. 
 
 V. SHOULD any one's Curiofity Exf>eriettfeattJ 
 now prompt him to enquire, how it 0&***t* 
 
 comes]
 
 ( 96 ) 
 
 comes to pafs, that Men ao;ree in their 
 
 ;T;::;V Names f the fim P le "> f ^s 
 
 fimpit Ideai. they cannot view the Perceptions in 
 one another's Minds, nor make known thefe 
 Perceptions by Words to others ; I anfwer, that 
 the Effect here mentioned is produced by Expe- 
 rience and Obfervation. Thus finding, for in- 
 france, that the Name Heatj is annexed to that 
 Impreffion which Men feel when they approach 
 the Fire, I make it alfo the Sign of the Idea ex- 
 cited in me by fuch an Approach, nor have any 
 doubt but it denotes the fame Perception in my 
 Mind as in theirs. For we are naturally led to 
 imagine, that the fame Objects operate alike upon 
 the Organs of the human Body, and produce an 
 Uniformity of Senfations. No Man fancies, 
 that the Idea raifed in him by the Tafte of 
 Stigar^ and which he calls Sweetnefs y differs 
 from that excited in another by the like Means ; 
 or that Wormwood^ to whofe Relifh he has 
 given the Epithet Bitter , produces in others 
 the Senfation which he denotes by the Word 
 Sweet. Prefuming therefore upon this Confor- 
 mity of Perceptions, when they arife from the 
 fame Objects, we eafily agree as to the Names 
 of our fimple Ideas j and if at any time, by a 
 more narrow Scrutiny into Things, new Ideas of 
 this Clafs come in our Way, which we choofe to 
 exprefs by Terms of our own Invention j thefe 
 x Names
 
 ( 97 ) 
 
 Names are explained not by a Definition, but 
 by referring to the Obje&s, whence the Ideas 
 themfelves may be obtained. 
 
 VI. BEING in this Manner ftr- 
 nifhed with Ample Ideas, and the ***. 
 Names by which they are exprefled, />/'* idea by 
 the Meaning of Terms that frand w f/-/c^"ri- ' 
 for complex Ideas is eafily got ; be- vaac '* Na " 
 
 J ture. 
 
 caufe the Ideas themfelves anfwer- 
 ing to thefe Terms, may 'be conveyed into the 
 Mind by Definitions. For our complex Notions, 
 as was already obferved, are only certain Combi- 
 nations of fimple Ideas. . When therefore thefe 
 are enumerated, and the Manner in which they 
 are united into one Conception explained, no- 
 thing more .is wanting to raife that Conception 
 in the Understanding ; and thus the Term de- 
 noting it comes of courfe to be underftood. And 
 here it is worth while to refledl a little upon the 
 wife Contrivance of Nature, in thus furnifhing 
 us with the very apteft means of communicating 
 our Thoughts. For were it not fo ordered, that 
 we could thus convey our complex Ideas from 
 one to another by Definitions, it would in many 
 Cafes be impoflible to make them known at all. 
 This is apparent in thofe Ideas which are the 
 proper Work of the Mind. For as they exift 
 only in the Underftanding, and have no real 
 Objects in Nature, in Conformity to which they 
 F arc
 
 ( 98 ) 
 
 are framed ; if we could not make them known 
 by a Defcription, they muft lie for ever hid 
 within our own Breafts, and be confined to the 
 narrow Acquaintance of a fingle Mind. All the 
 fine Scenes, that rife from time to time in the 
 Poet's Fancy, and by his lively Painting, give 
 fuch Entertainment to his Readers } were he de- 
 ftitute of this Faculty, of laying them open to 
 the View of others by Words and Defcriptions ; 
 could not extend their Influence beyond his own 
 Imagination, or give Joy to any but the original 
 Inventor. 
 
 VII. THERE is this farther Ad- 
 of gnat vantage in the Ability we enjoy, of 
 
 il to- . J '*_ 
 
 rds the Im- communicating our complex No- 
 tions b 7 Definitions ; that as thefe 
 make by far the Jargefl Clafs of our 
 Ideas, and moft frequently occur in the Progrefs 
 and Improvement of Knowledge ; fo they are by 
 this means imparted with the greateft Readinefs, 
 than which nothing could tend more to the In- 
 creafe and fpreading of Science. For a Definition 
 is foon perufed, and if the Terms of it are well 
 underftood, the Idea itfelf finds an eafy Admif- 
 iion into the Mind. Whereas in fimple Percep- 
 tions, where we are referred to the Objecls pro- 
 ducing them, if thefe cannot be come at, as is 
 fometimes the Cafe, the Names by which they 
 are exprefled muft remain empty Sounds. But 
 new Ideas of this Clafs occurring very rarely in 
 
 the
 
 ( 99 ) 
 
 the Sciences, they feldom create any great Ob- 
 ftru&ion ; it is otherwife with our complex No- 
 tions, for every Step we take, leading us into 
 new Combinations and Views of Things, it be- 
 comes neceffary to explain thefe to others, before 
 they can be made acquainted with our Difcove- 
 ries. And as the manner of Definitions is eafy, 
 requiring no Apparatus but that of Words, which 
 are always ready, and at hand j hence we can 
 with the lefs Difficulty, remove fuch Obftacles, 
 as might arife from Terms of our own Inven- 
 tion, when they are made to ftand for new com- 
 plex Ideas, fuggefled to the Mind by fome pre- 
 fent Train of thinking. And thus at laft we are 
 let into the Myftery hinted at in the Beginning of 
 this Chapter, viz. how we may become ac- 
 quainted with the Thoughts of another, when 
 he makes ufe of Words to which we have as yet 
 joined no Ideas. The Anfwer is obvious, from 
 what has been already faid. If the Terms de- 
 note fimple Perceptions, he muft refer us to thofe 
 Objedls of Nature, whence the Perceptions them- 
 felves are to be obtained ; but if they ftand for 
 complex Ideas, their Meaning may be explained 
 by a Definition. As for the Names of fimple 
 Ideas, I fhall here dtfmifs them ; it being fufficient 
 to take Notice, that our Knowledge this Way 
 can be extended only by Experience and Obfer- 
 vation. But the Theory of Definitions making a 
 F 2 material
 
 material Part of Logiclc, and being indeed of 
 great Importance towards the Improvement of 
 human Knowledge, it will be necefiary to lay it 
 a little more open to the View of the Reader. 
 
 VIII. COMPLEX Ideas are, as has 
 Kirn and Re- Deen already faid, no other than fim- 
 foiution ef our pl e Ideas put together in various 
 
 Cample* Ideal. r> LI 
 
 Forms. i>ut then it is to be ob- 
 ferved, that in making thefe Collections, the Mind 
 is not always tied down to the immediate View 
 of the fimple Perceptions out of which they are 
 framed. For if we fuppofe the Underftanding 
 already furnifhed with a confiderable Stock of 
 compound Notions, thefe again maybe made the 
 conftituent Parts of others ftill more compound- 
 ed, infomuch that the new Idea thence arifing 
 may be termed a Combination of complex Con- 
 ceptions. Thus the Idea annexed to the Word 
 Animal^ includes many Perceptions under it, as 
 Life, Scnfe, fpontaneous Motion, C5"r. In like 
 manner, by the Term rational, we denote a Va- 
 riety of fimple Ideas. If now combining thefe 
 two Conceptions together, we form the ftill more 
 complex Notion of a rational Animal j the Idea 
 thus got is truly a Collection of compound NQ- 
 tices. In a Word, the fame Thing happens here 
 as in Numbers, which we may confider not only 
 as various Collections of Units, thefe being in- 
 deed their original -and conftituent Parts 5 but alfo 
 
 as
 
 C ioi J 
 
 as fometimes compofed of other lefler Numbers, 
 which all put together make up the refpeftive 
 Sums. Now in tracing any very large Number, 
 when for the Eafe of the Mind we confider it at 
 firft as compofed of various others ftill lefTer : if 
 we next take thefe lefler Parts to Pieces, and pur- 
 fue them continually until we arrive at the Units 
 out of which they are compofed j we thereby to- 
 tally unravel the Collection, and being able to 
 pufh our Refearches no farther, reft fatisfied in 
 the View thus offered to the Underftanding. Juft 
 fo it is in the Examination of our complex Ideas. 
 For when any very compounded Notion comes 
 under the Infpeclion of the Mind in order to be 
 traced to its firft Principles ; we begin with re- 
 fblving it into other Ideas lefs complicated ; and 
 taking thefe again to Pieces one by one, ftill go 
 on with the Search, until we have broken the 
 whole into our firft and fimple Perceptions, be- 
 yond which the Purfuit cannot poflibly be carried. 
 And this is the Reafon why I have all along 
 called our fimple Ideas the Foundation and 
 Ground-work of human Knowledge j becaufe in 
 unravelling the Conceptions of the Mind, we find 
 ourfelves at length bounded by thefe Ideas, which 
 are indeed the laft Refort of the Underftanding. 
 
 IX. FROM what has been faid it rte Namn f 
 will be eafy to conceive, how in de- /"/"' J' / " 
 
 may be cenji- 
 
 fining a Term, ftanding for any very dtred at tbt 
 F 3 complex
 
 complex Idea, other Terms may be 
 
 EitnttHtirj . . 
 
 P*n*fLan- introduced, that alfo denote com- 
 
 pound Ideas, though of an inferior 
 Glafs. For the firft Idea being refolvable into 
 others lefs complicated ; the Definition which 
 enumerates thefe component Ideas muft confift 
 of the Names by which they are exprefied. And 
 if it fo happen, that the Ideas of this fecond 
 Clafs are alfo unknown, their Terms too ought 
 to be ftill farther defined. In this manner may a 
 Series of Definitions be carried on until we ar- 
 rive at the Names of fimple Ideas, which not 
 being definable, the Analyfis muft neceffarily 
 ceafe. And thus we fee, that as our fimple Ideas 
 are the Materials and Foundation of Know-. 
 ledge, fo the Names of fimple Ideas may be 
 confidered as the Elementary Parts of Language, 
 beyond which we cannot trace the Meaning and 
 Signification of Words. When we come to 
 them, we fuppofe the Ideas they ftand for alrea- 
 dy known ; or if they are not, Experience alone 
 muft be confulted, and not Definitions or Ex- 
 plications. And here it is well worth our No- 
 tice, that as the Names of thefe our original 
 Conceptions, conftitute the primary and funda- 
 mental Articles of Speech, upon which the 
 whole Superftru&ure of human Language is 
 built, fo they are of all others the lead doubtful 
 and uncertain in their Signification. Becaufe 
 
 {landing
 
 landing each for one fimple Perception, not pre- 
 carioufly excited in the Mind, but the Effect of 
 certain Powers in Things, fitted to produce that 
 Senfation in us ; there is no Danger of Error or 
 Miftake. He that once knows Sweetnefs to be 
 the Name of the Tafte received from Sugar, 
 Wlntenefs of the Colour in Snow or Milk, and 
 Heat of the Senfation produced by approaching 
 the Fire, will not be apt to mifapply thofe Words, 
 or annex them to Perceptions of a different Kind. 
 And as the Names of complex Ideas may all be 
 refolved into thefe primitive Terms, it is apparent 
 that we are fufficiently provided with the Means 
 of communicating our Thoughts one to another j 
 and that the Miftakes fo frequently complained of 
 on this Head, are wholly owing to ourfelves, in 
 not fufficiently defining the Terms we ufe, or 
 perhaps not connecting them with clear and de- 
 terminate Ideas. 
 
 CHAP. VI. 
 
 i i 
 
 Of Definition, and itsfeveral Kinds. 
 
 I. TTAVING laid thefe Foun- The Variety of 
 
 rl dations, {hewn what Words 2JL 
 are, and what are not definable, tbt -various 
 
 i in* r r t AtpllCttltn 
 
 and taught the Manner or relolv- tfw ar dt. 
 ing our Notions, as well as Language itfelf, 
 F 4 into
 
 into its firfl and original Principles ; we now 
 proceed to explain a little more particularly the 
 Nature of a Definition, and the feveral Kinds 
 made ufe of according to the different Views 
 Men have in communicating their Thoughts one 
 to another. Definitions are intended to make 
 known the Meaning of Words franding for com- 
 plex Ideas j and were we always careful to form 
 thofe Ideas exactly in our Minds, and copy our 
 Definitions from that Appearance, much of the 
 Confufton and Obfcurity complained of in Lan- 
 guages might be prevented. But unhappily for 
 us, we are by no means ileady in the Application 
 of Names, referring them fometimes to one 
 thing, fometimes to another ; which often creates 
 great uncertainty in their Signification, and 
 pbliges us to give a different Turn to our Defini- 
 tions, according to the different Reference of 
 the Terms defined. In order therefore to render 
 this whole Matter as clear and obvious as poffi- 
 ble, we fhall firft confider to what it is that 
 Names, in the Ufe of Language, are moft com- 
 monly applied ; and then from the Variety of 
 this Application, endeavour to account for the 
 feveral Methods of defining, mentioned in the 
 Writings of Logicians. 
 
 II. WORDS then have manifeftly a 
 
 Words have * 
 
 a threefold threefold Reference. Firft and more 
 wr "</" immediately, they denote the Ideas 
 tijt ffetbtrs, j n ^e Mind of him who ufes them ; 
 
 and
 
 ( 105 ) 
 
 and this is their true and proper Sig- 
 
 . , f . and tie real 
 
 mhcation. When a Man Ipeaks, it Being cf 
 is that he may be underftood j and the '*""' 
 Words he employs to convey his Thoughts, are 
 fuch as by Ufe he has learnt to connect with the 
 Ideas then prefent to his Mind. But becaufe 
 thofe with whom we converfe, are alfo fuppofed 
 to know the Meaning of the Terms we ufe, 
 hence Secondly, we confider our Words as 
 Signs likewife of the Ideas in their Minds ; and 
 this is the Foundation of what is called Propriety 
 in Language, when Men take Care to affix 
 fuch Notions to their Words, as are commonly 
 applied to them by thofe of moft Underftanding 
 in the Country where they live. The Third and 
 laft Reference of Words is to Things them- 
 felves, For many of our Ideas are taken from the 
 feveral Objects of Nature, wherewith we are fur- 
 rounded ; and being confidered as Copies of 
 Things really exifting, the Words by which 
 they are exprefled, are often transferred from, 
 the Ideas themfelves, _to fignify thofe Obje&s 
 which they are fuppofed to reprefent. Thus the 
 Word Sun y not only denotes the Idea excited 
 in the Mind by that Sound, but is alfo frequent- 
 ly made to ftand for the luminous Body itfelf, 
 which inhabits the Center of this our Planetary 
 Syftem. Now according to this threefold Ap- 
 plication of Names, their Definitions, and the 
 Manner of explaining them, muft be various ; 
 FS for
 
 { 106 ) 
 
 for it is one Thing to unfold the Ideas in a Man's 
 own Mind, another to defer! be them as they 
 are fuppofed to make their Appearance in the 
 Minds of others ; and laftly, it is fomething 
 ftill different, to draw Images or Pictures, that 
 fhall carry in them a Conformity to the Being and 
 Reality of Things. But we fhall treat of each 
 in Order. 
 
 III. FIRST then, when we con- 
 
 Defnitiant of rj _ , c . f T 
 
 tke Name "der Words, as bignte of the Ideas in 
 teach only tbt t h e Mind of him who ufes them : a 
 
 Connefttcn of 
 
 ear Wordt and Definition is nothing elfe, but fuch v' 
 SSSflZlm an Explication of the Meaning of 
 trtry. ar) y Term, as that the complex Idea 
 
 annexed to it by the Speaker, may be excited in 
 the Underftanding of him with whom he con- 
 verfes. And this is plainly no more than teach- 
 ing the Connection of our Words and Ideas, that 
 others may underftand the Senfe of our Expref- 
 fions, and know diftin&ly what Notions we affix 
 to the Terms we ufe. When we fay, for in- 
 ftance, that by the Word Square we mean a Fi- 
 gure bounded by four equal Sides, joined toge- 
 ther at right Angles ; what is this but a Decla- 
 ration, that the Idea of a quadrilateral, equila- 
 teral, rectangular Figure, is that which in Dif- 
 courfe or Writing we connect with the Term 
 Square? This is that Kind of Definition, which 
 Logicians call the Definition of the Name ; be- 
 caufe it difcovers the Meaning of the Words or 
 
 Names
 
 Names we make ufe of, by fhewing the Ideas for 
 which they ftand. Now as Sounds are of them- 
 felves indifferent to fignify any Ideas, hence it 
 is plain, that the Definitions of Names are arbi- 
 trary, every Man having a Liberty to affix what 
 Notions he pleafes to his Words. But the Con- 
 venience of Communication making it neceflary 
 for Men fpeaking the fame Language to agree as 
 nearly as pofllble in the Signification of Sounds, 
 a Conformity has accordingly been ftudied. 
 Neverthelefs we find that Differences will from 
 time to time creep in, which muft create great 
 Confufion in Men's Difcourfes and Reafonings, 
 if they are not careful to define their Terms, that 
 their Signification may be kept fixed and fteady, 
 and lie always open to the View of the Mind. 
 The Writings of the Mathematicians are a cleaf 
 Proof, how much the Advancement of human 
 Knowledge depends upon a right Ufe of Defini- 
 tions. For as by means of them they every where 
 preferve the fame determined Signification to 
 their Words, hence there is little Difpute as to 
 the Meaning of their Expreffions, almoft all 
 Men understanding them in the fame Senfe. 
 And thus it happens, that fuch as apply their 
 Thoughts this Way, having perfectly the fame 
 Views of Things, readily comprehend the Dif- 
 coveries already made, and are thereby enabled 
 with joint Labour, and an exa<l Conformity of- 
 E 6 Notions,,
 
 Notions, to carry on the Improvement of this 
 Branch of Knowledge. And if Men in other 
 Parts of Learning, were alike careful to fix the 
 Meaning of their Terms, the Progrefs of Science 
 muft be greatly furthered, and all thofe verbal 
 Difputes, that now fo much interrupt the Courfe 
 of our Improvement, might be prevented. 
 
 IV. THIS then ought to be our 
 
 Definition of 
 
 the Name not firft Care, when we enter upon a 
 ? J i*Dt- Defign of illuftrating any particular 
 fnitiotis. Branch of Study ; to afcertain ouv 
 
 Ideas, and mark the Names by which they are 
 exprefled. And altho' Definitions of Words are 
 indeed arbitrary, (for a Man may affix what Ideas 
 he pleafes to his Terms, nor can any one conteft 
 this Liberty with him,) yet it will be proper to 
 conform as near as poffible to common Accepta- 
 tion, that thereby our Thoughts may find a 
 more eafy and ready Entrance into the Minds 
 /. of others. If it fhould now be afked, what are 
 the Rules of a good Definition; I anfwer, that as 
 in Definitions of the Name, we aim at no more 
 than teaching the Connection of Words and 
 Ideas ; every Contrivance, by which we are 
 enabled to excite the Idea annexed to any Word 
 in the Mind of another, will ferve the Purpofe 
 of a Definition. Now the Ideas we join with 
 our Words are of two kinds : either fuch as ^e 
 have reafon to believe are already in the Minds
 
 of others, though perhaps they know not the 
 Names by which they are called ; or fuch as 
 being new and of our own Formation, can be 
 no otherwife made known than by a Defcription. 
 In the firft Cafe, there is no Neceflity for lay- 
 ing open the Idea itfelf, becaufe being already 
 known, any Contrivance to remind us of it is 
 fufficient. When we fay, for inftance, that a 
 Clock is an Inftrument by which pve meafure the 
 Hours of the Day j it is plain, that the Idea an- 
 fwering to the Word Clock, is not here unfold- 
 ed ; but we being before-hand fuppofed to have 
 an Idea of this Inftrument, are only taught by 
 what Name it is called. Now in this Senfe, 
 the Names of even flmple Ideas may be defined. 
 For by faying that tWite is the Colour we ob- 
 ferve in Snow or Milk, Heat the Senfation pro- 
 duced by approaching the Fire, we fufficiently 
 make known what Ideas we connect with the 
 Terms IFhite and Heat, which is the true Pur- 
 pofe of a Definition of the Name. Hence it ap- 
 pears, that many of thofe Explanations of 
 Words, which Logicians call Definitions of 
 the Name, are not Definitions in a true and pro- 
 per Senfe, that is, fuch Defcriptions of Ideas, 
 as would ferve to excite them in the Mind of 
 another, even fuppofing him before wholly un- 
 acquainted with them, but merely Contrivances 
 to remind us of known Ideas, and teach us the 
 Names by which they are called. 
 
 V. BUT
 
 ( iro ) 
 
 , V ' BlJT where the 
 
 ttey coincide with our Words, are new and of 
 fnitita If t'be our own Formation, there they are 
 Wing. to be laid open by a Defcription.. 
 
 Becaufe being fuppofed unknown to others, we 
 xnuft firft raife them in their Minds, before they 
 ean learn to conned them with any particular 
 Names. And here it is, that the Definition of 
 the Name coincides with what Logicians call the 
 Definition of the. Thing^ as in either Cafe we pro- 
 ceed by unfolding the Idea itfelf for which the 
 Term defined tands.. And indeed this alone is 
 what conftitutes a Definition in. the true and 
 proper Senfe of the Word, as will appear more 
 fully afterwards, when we come to confider the 
 Terms we ufe, as referred to the real Objects 
 of Nature. We fhall therefore poftpone this 
 Confideration of the Definition of the Name, 
 till we come to treat of the Definition of the 
 Thing, when it will more naturally fall, in our 
 way. It may not however be amifs to obferve, 
 that when we fay the Definitions of the Name 
 are arbitrary, we mean not that the Defcriptions 
 of Ideas are fo too. For every Idea having a 
 peculiar Appearance of its own, by which it is- 
 diftinguifhed from all others, nothing is more 
 evident, than that the Defcription muft be fuch 
 as to exhibit that precife Conception. But then 
 the Connection of any Idea, with the Name by 
 which, it is exprefied, being, as we have faid,- 
 
 wholly.
 
 ( III ) . - 
 
 wholly arbitrary, the confidering the Defcrlp- 
 tion of that Idea as the Definition of that par- 
 ticular Name muft be fo to. So that although 
 Definitions confidered as Defcriptions of our 
 Ideas, are fteady and invariable, yet the Applica- 
 tion of them to particular Sounds, (which is all 
 that we underftand by the Definition of the 
 Name) is wholly a Work of our own free Choice*. 
 VI. BUT Secondly, befides con- Definition of 
 
 rt' txr j i cv c Wordt accord- 
 
 fidenng Words as the Signs of our ing t!>lhe(om , 
 own Ideas, we are alfo very apt on mon u f e f 
 
 Language not 
 
 many Uccahons, to refer them to arbitrary. 
 the Ideas in the Minds of other Men. Now to 
 define a Term in this View, is to inveftigate its 
 Meaning or Acceptation, according to the com- 
 mon Ufe of Speech. Here then it is plain that 
 Definitions are not arbitrary. For although in. 
 regarding Words as the Marks of our own Ideas,,, 
 we may give them what Meaning we pleafe ; yet 
 when we confider them in reference to the 
 Thoughts of others, they have a fixed and fteady 
 Signification j namely,, that which Cuftom and? 
 the Propriety of Language has afligned them. 
 The Words Ability ;and Genius, may by. any Man 
 be made to ftand for one and the fame Idea in his 
 own Mind, and if he takes care to advertife us 
 of this, he is at liberty to ufe them promifcuoufly. 
 But if the common Courfe of Language hath 
 confined the Word Genius to exprefs the natural. 
 Strength and Talents of the Mind, and the 
 
 Word
 
 C 
 
 Word Ability to denote thofe which are acquired, 
 whoever pretends to explain the proper Accep- 
 tation of thefe Terms, is bound to take notice 
 of this Difference. As Propriety of Speech 
 makes our Language intelligible, and gives our 
 Thoughts a ready Entrance into the Minds of 
 others, it well deferves our Application and Care. 
 The beft way to acquire it is from the Writings 
 and Difcourfes of thofe who feem to have had the 
 cleareft Notions, and to have applied their Terms 
 \vith the exateft Choice and Fitnefs. 
 
 , VII. WE come now to the third 
 
 Definition! of 
 
 the Thing re- and laft Species of Definition, that 
 M namely, which confiders Words as 
 
 referred to Things themfelves. And 
 here it is plain we are not at liberty to feign and 
 fafhion our Explications at pleafure, but being 
 tied down to the real Objects of Nature, muil 
 ftudy a Conformity to Things themfelves. When 
 we define for inftance the Sun y confidered as that 
 Being who poflefTes the Center of our Syftem, 
 and diffufes Heat and Light to the Planets around 
 him ; it is not enough that we give an Account 
 of the Idea, anfwering to that Word in our Minds. 
 We muft further take care, that the Idea itfelf 
 carries in it a real. Conformity to the Object it is 
 fuppofed to reprefent. And hence it is, that all 
 Definitions of this kind, when juftly made, are 
 in reality Pictures or Reprefentations, taken from 
 * the
 
 the Being and Exiftence of Things. For they arc 
 intended to exprefs their Nature and Properties, 
 fo as to diftinguifh them from all others, and 
 exhibit them clearly to the View of the Mind. 
 'Tis for this Reafon that Logicians call them De- 
 finitions of Things^ becaufe they are fuppofed to 
 refer, not fo much to the Ideas in the Under- 
 ft and ing, as to the Things themfelves repre- 
 fented by thofe Ideas. 
 
 VIII. AND this alfo lets us into 
 
 Ground tftbf 
 
 the (jround of that Diftmction fo Dijtmaion 
 univerfally received, between Defini- b %""*l f 
 tions of the Name and of the Thing, the Name and 
 The firft are arbitrary, and not lia- f tbe<rbin &- 
 ble to Debate or Contradiction. The fecond are 
 Propofitions capable of Proof and Illuftration, 
 and which may therefore be contefted. The Rea- 
 fon is obvious. Definitions of the Name ferve 
 only to mark what Ideas we connect with our 
 Words. And as Sounds are of themfelves in- 
 different to fignify any Ideas, we are intirely at 
 liberty to affix to them what Notions we pleafe. 
 But it is otherwife in the Definition of the Thing. 
 For here our Words ferving to denote particular 
 Beings in Nature, cannot be the Signs of any 
 Ideas at pleafure, but of fuch only as carry in 
 them a Conformity to the feveral Objects to 
 which the Words refer. A Man may ufe the 
 Term Square to exprefs that Idea, which others 
 
 denote
 
 denote by the Word Triangle, and define it ac- 
 cordingly. In this Cafe indeed he recedes from 
 the common Forms of Speech, but his Definition 
 cannot be charged with Falfehood, He tells us 
 that by a Square he means a three-fided Figure, 
 and who can difpute the Truth of this, if he 
 really all along ufes the Word in that Senfe ? I 
 would only obferve, that by changing thus the 
 Meaning of Words, we cHhnge not Things 
 themfelves, or their Relations and Habitudes one 
 towards another. Thefe are at all Times the 
 fame and invariable, nor have any Dependence 
 upon the Fancy and Caprice of Men. It is 
 true the Properties of the Triangle may after 
 this Definition, be affirmed of the Square ; but 
 as in either Cafe, the Idea to which thefe Proper- 
 ties belong, is the fame, the Propofitions only 
 expreifing our Judgments, and not our Judg- 
 ments themfelves, fuffer a feeming Variation. 
 jffrevhut IX. BUT where Words are made 
 
 Convtetion it- to denote particular Objects, previ- 
 
 tvicen Namu r . . 
 
 tnd Things, ous to any Definitions given, there- 
 Tit'ray "EX-'' arbitrary Explications cannot have 
 fixations, place. For in this Cafe* we are not 
 put upon explaining what Ideas we conned with- 
 eur Words, but a Connection being already fup- 
 pofed between the Name and the Thing fignified^ 
 our Bufinefs is to unfold that Idea by which the 
 Object itfelf is moft clearly aad diftin<31y repre-v 
 
 8
 
 fented. Thus the Word Gold denotes that Me- 
 tal which is of higheft Value among Men, and 
 goes fartheft in the way of Commerce. This - 
 Connection being once fettled, we are no longer 
 left to arbitrary Definitions, but muft defcribe it 
 by fuch Properties as are really to be found in it, 
 and will beft ferve to diftinguifh it when it comes 
 in our Way ; as by faying it is a SubftanceyelloiV) 
 very heavy, malleable ^ fufible^ &c. 
 
 X. FROM what has been faid it j^ Matlt- 
 appears. that in the Language of ">*t>cat Dtfi- 
 
 rr DO nttiont bavt 
 
 Logicians, Definitions of the Thing bun accounted 
 refpeft only Subflances and Beings 
 that have a real Exiftence in Nature, 
 ferving to defcribe them by their Properties 
 and Attributes. And this I doubt not is the 
 Reafon, that the Definitions of the Mathema- 
 ticians are not confidered as Definitions of the 
 Thing, but of the Name j becaufe the Ideas 
 therein defcribed, are the mere Creatures of the 
 Underftanding, and not fuppofed to be copied 
 from Patterns exifting without us. A Circle, a 
 Triangle, a Square, &c. fuch as Mathematicians 
 conceive them, are no where to be found in Na- 
 ture that we know of. Hence it might juftly be 
 accounted abfurd, to call our Definitions of thefe^ 
 Definitions of the Thing, when they ferve not to 
 defcribe any real Objects of Nature, but merely 
 to unfold the Conceptions of the Mind. And 
 
 yet
 
 ( 1x6 ) 
 
 yet if we look into the Matter narrowly, we 
 fhall find that the Rules followed in thefe 1> fi- 
 nitions are preciftly the fame with thofe which 
 Logicians have laid down for the Definition of 
 the Thing. All the feveral Species of Figures 
 are defcribed by their Properties, fome of which 
 are common to different Ranks, others peculiar 
 to the Tribe defined. The common Properties 
 conftitute what Logicians call the Genus, and 
 thofe that are peculiar the Difference. Now the 
 Genus and Difference make up the Logical Defini- 
 tion of the Thing, as will be more clearly under- 
 flood from what follows. 
 
 XI. I AM therefore apt to think, 
 t h at Mathematical Definitions, as 
 on of they are of the fame general Form 
 with tne Definitions of Subftances, 
 ot to be ac- anc ] f u bje6t to the fame Rules, have 
 
 teunttder- . J 
 
 titrary. been improperly conndered as mere 
 
 Definitions of the Name, in which we are left 
 wholly to arbitrary Explications. For however 
 we may change the Name of one Figure for ano- 
 ther in Difcourfe or Writing, ufmg the Term 
 Square to denote a Triangle, or the Word Triangle 
 to exprefs a Square^ it is certain the Ideas them- 
 felves are invariable, and no lefs capable of be- 
 ing diftinguifhed by their Properties, than the 
 feveral Species of Subftances. Thus if we fup- 
 
 pofe
 
 pofe the Word Square to denote that Species of 
 Figures, whofe Sides feverally fubtend Quadrants 
 of a circumfcribed Circle, we ihali find ourfelves 
 equally fhut out from arbitrary Explications, as 
 in the Definition of the Names of Subftances. 
 For as this happens in no Figures but thofe 
 which are bounded by four equal Sides joined 
 together at right Angles ; it follows evidently, 
 that the true and proper Definition of a Square^ 
 is that which exhibits the precife Idea here men- 
 tioned, and no other, to the Mind. And thus 
 it appears, that the common Divifion of Defini- 
 tions, into thofe of the Name and Thing, is not 
 fuificiendy calculated to give us right Apprehen- 
 fions, as to what is and what is not arbitrary in 
 the Explication of Words. It may not therefore 
 be improper, if we here endeavour to clear up 
 this Matter a little, and free it from thofe Ob- 
 fcurities in which it has hitherto been involved. 
 To this end we fhall premife the following Ob** 
 fervations. 
 
 XII. i. FIRST, that whatever Lo- 
 
 . . i T^ DtSnttttns 
 
 gicians may pretend about the De- pnperijjptek- 
 
 finition of the Thing, it is yet cer- '"* ."^ rt ~ 
 
 . S ar " **"*' 
 
 tain that none of our Definitions, but merely oar 
 
 when purfued to their Source, regard 
 immediately Things themfelves, but merely the 
 Ideas in our own Minds. This I doubt not will 
 appear a Paradox to many, who will be apt to 
 
 enquire,
 
 ( II* ) 
 
 enquire, whether the Definition of Gold, be not 
 taken from that Metal, independent of the vari- 
 ous Conceptions of Men about it. To this I 
 anfwer, that indeed in framing our Idea of Gold, 
 we regard chiefly the Thing itfelf, uniting in 
 our Conception fuch Properties as are moft con- 
 fpicuous, and ferve beft to diftinguifh it from 
 other Metals, to which it may bear any Refem- 
 blance. But as it is by this Idea alone that Gold 
 is known to us, fo in defcribing it to others, we 
 aim at nothing more than to transfer the fame 
 Conception into their Minds. Now this can no- 
 otherwife be done, but by enumerating the feve- 
 ral Properties out of which our own complex 
 Notion is formed. And indeed it were in the 
 higheft Degree abfurd to imagine, that Men in 
 explaining Things to others, fliould make ufe 
 of any Marks or Characters but thole by which 
 they are known to themfelves. Hence it comes 
 to pafs, that all our Definitions, are in Fact no- 
 thing elfe but Tranfcripts of the Ideas in our 
 Minds. Where thefe are imperfect, the Defi- 
 nitions muft be fo too ; where they are juft and 
 adequate, the Copies taken from them, if drawn 
 out with Accuracy and Care, cannot fail to ex- 
 hibit the Object defcribed. And this will very 
 well ferve to account for that great Diverfity of 
 Definitions we often meet with, even of one 
 and the fame Object. Becaufe Men, in Con- 
 
 fequence
 
 fequence of their different Purfuits and Appli- 
 cations, falling often into different Views of 
 Things, muft needs vary no lefs in their Defi- 
 nitions than in the Ideas themfelves from which 
 thefe Definitions are copied. He whofe Obfer- 
 vation goes no farther than the more obvious 
 Qualities of Gold, will content himfelf with 
 defcribing it by its Colour, Weight and per- 
 haps Malleability and Fufibility. On the other 
 hand a Goldfmith, having enquired farther into 
 the Nature of that Metal, and finding feveral 
 other Properties that equally belong to it, will 
 be apt to take thefe alfo into his complex Idea, 
 and accordingly introduce them in a Definition, 
 Hence his Defcription will add to the former, 
 Fixednefs, and Solubility in Aqua Regia, &c. 
 And fo in Proportion, as Men's various Purfuits 
 lead them into a more accurate Examination 
 of things, their Explications will take a different 
 Turn, fuitable to the Ideas they have framed 
 within themfelves. 
 
 XIII. 2. THIS then being evi- D ; fllnalon be _ 
 dent, that our Definitions refpeft not tween the Dt ' 
 
 _,. . i. / i i i T i fait ion of the 
 
 1 hings themlelves, but the Ideas in tJameand 
 our own Minds; I would in the next Tb ^ t f' 7 '/'* 
 
 and to be rt- 
 
 Place obferve, that the Diftin&ion of jeHed. 
 them into thofe of the Name and Thing, is al- 
 together ufelefs, and tends rather to miflead us 
 than give right Apprehenfions of the Subject in 
 hand. For thus Men are apt to fancy, that many 
 
 of
 
 ( 120 ) 
 
 of their Definitions are expreffive of the real Ef- 
 fence of Things, whereas they are in truth no 
 more than Tranfcripts of their own Ideas. And 
 as it fometimes falls out that thefe Ideas are not 
 collected with fufficient Care, from the Objects 
 they reprefent j we find by Experience, that a 
 miftaken Idea never fails to occafion a Miftake 
 alfo in the Definition. But this could not happen 
 were our Definitions copied from Things them- 
 felves : becaufe their Eflences being immutable 
 and always the fame, the Definition would in 
 this Cafe ferve to correct the Idea, and might be 
 confidered as a Standard, by which to judge 
 whether the Idea was rightly framed. I deny 
 not that Words are often transferred from our 
 Ideas to fignify the Objects which thefe Ideas re- 
 prefent ; as when we talk of the Sun, the Earth, 
 Men, and other Animals. But then let it be ob- 
 ferved, that as thefe Objects are only known to 
 us by the Ideas of them in our Minds ; fo in de- 
 fcribing them to others, all we aim at is, diftindtly 
 to lay open our Conceptions about them. Hence 
 it appears, that what Logicians call a Definition of 
 the Thing, is in Truth no more than an unfold- 
 ing of the Idea, by which that Thing is repre- 
 fented to the Underftanding. But now in Ma- 
 thematical Definitions, and indeed all others 
 whatfoever, this alfo is our whole Aim and Intent, 
 to exhibit and lay open thofe Ideas, of which the 
 Words we ufe art the Signs. And thus it hap- 
 pen*,
 
 ( III ) 
 
 pens, that in innumerable Inftances, what Lo- 
 gicians call the Definition of the Name, is yet 
 found to coincide with, and 'proceed by the very 
 fame Rules, as the Definition of the Thing j which 
 clearly demonftrates the Neceflity of banifhing 
 this frivolous Diftin&ion, and eftablifhing fome 
 precife and determinate Notion, expreffive of the 
 true Nature of a Definition, and comprehending 
 it in its full Extent. 
 
 XIV. NOR will this appear fo dif- Definitions in 
 ficult a Tafk. if we call to mind that f Ca f' s D *' 
 
 Jcnpttons of 
 
 Words are in all Cafes the Signs of cur ideas. 
 our Ideas, and no otherwife fignify Things, than 
 as theyftand for thofe Ideas by which Things are 
 reprefented to the Underftanding. By defining 
 our Words therefore we can mean no more, than 
 the laying open to the View of others the Ideas 
 of which thefe Words are the Signs. For thus it 
 is that the Meaning of our Expreffions come to 
 be known, and that we find ourfelves capable 
 of transferring our Thoughts and Conceptions 
 into the Minds of thofe with, whom we converfe. 
 Where Words are referred to Things themfelves, 
 there we explain the Ideas by which thefe things 
 are reprefented ; where they denote Conceptions 
 framed by the Mind, there we lay open thefe Con- 
 ceptions, and endeavour to exhibit them accord- 
 ing to their real Appearance within our own 
 Breads. But in both Cafes it is our own Ideas, 
 G it
 
 it is the Perceptions of our own Minds, either 
 
 as taken from things without, or framed by the 
 
 Understanding itfelf, that we explicate and un- 
 
 fold. 
 
 Wot arbitrary, XV. AND thus we have at length 
 
 ? t'"V"~ fettled the true and genuine Notion 
 
 fned to the 
 
 of a Definition, comprehending all 
 
 At- lts Varieties, from whatever Science 
 /. taken, or to whatever Object ex- 
 
 tended. For from what we have faid it evidently 
 follows, that a Definition is the unfolding, of fame 
 Conception of the Mind^ anfwering to the Word or 
 I'erm made ufe of as the Sign of it. Now as in ex- 
 hibiting any Idea to another, it is necefTary that 
 the Defcription be fuch as may excite that precife 
 Idea in his Mind ; hence it is plain, that Defi- 
 nitions properly fpeaking are not arbitrary, but 
 confined to the reprefenting of certain determi- 
 nate fettled Notions, fuch namely as are annex- 
 ed by the Speaker or Writer to the Words he 
 ufes. As neverthelefs it is univerfally allowed, 
 that the Signification of Words is perfectly vo- 
 luntary, and not the Effect of any natural and 
 neceflary Connection, between them and the 
 Ideas for which they frand, fome may perhaps 
 wonder why Definitions are not fo too. In order 
 therefore to unravel this Difficulty, and fhew 
 diftinclly what is, and what is not arbitrary in 
 Speech, we muft carefully diftinguifli between 
 
 the.
 
 ( "3 ) 
 
 the Connexion of our Words and Ideas, and 
 the unfolding of the Ideas themfelves. 
 
 XVI. FIRST, as to the Connec- ri>e Cwr- 
 tion of our Words and Ideas, this it '1 *"'"* 
 
 ' fvordi and 
 
 is plain is a purely arbitrary Inftitu- idt&t, a pcr- 
 tion, When for inftance we have in fatyEpa*' 
 our Minds, the Idea of any particu- bnjhmtnt. 
 lar Species of Metals, the calling it by the Name 
 Gold, is an Effect of the voluntary Choice of Mea 
 fpealdng the fame Language, and not of any pe- 
 culiar Aptnefs in that Sound to exprefs that Idea. 
 Other Nations we find make ufe of different 
 Sounds, and with the fame Effect. Thus Aurum 
 denotes that Idea in Lattn^ and Or in French, 
 And even the Word Gold itfelf, would have as 
 well ferved to exprefs the Idea of that Metal 
 which we call Silver, had Cuftom in the Begin- 
 ning fo eftablifned it. 
 
 XVII. BUT although we are thus 
 
 ...... fbt Defcr'ip. 
 
 mtirely at liberty, in connecting any tiom of Idcst 
 Idea with any Sound, yet it is quite '."' fy *?' 
 
 1 * J bounded to toe 
 
 otherwife in unfolding the Ideas Rtprefentation 
 themfelves. For every Idea, having 3^r 
 a precife Appearance of its own, by *> " wb ' tcb &V 
 
 . , . . ,.. . n i arediflin- 
 
 Which it is diitinguiihed from every gwjbed among 
 other Idea ; it is manifeft, that in them f elv "- 
 laying it open to others, we muft ftudy fuch a 
 Defcription, as (hall exhibit that peculiar Ap- 
 pearance. When we have formed to ourfelves 
 the Idea of a Figure bounded by four equal Sidej 
 G 2 joined
 
 C 
 
 joined together at right Angles, we are at liberty 
 to exprefs that Idea by any Sound, and may call 
 it either a Square or a Triangle. But whichever 
 of thefe Names we ufe, fo long as the Idea is the 
 fame, the Defcription by which we would fig- 
 nify it to another, muft be fo too. 1 et it be 
 called Square or Triangle^ it is ftill a Figure hav- 
 ing four equal Sides, and all its Angles right 
 ones. Hence we clearly fee, what is, and what 
 is not arbitrary in the Ufe of Words. The 
 eftablifliing any Sound, as the Mark of fome 
 determinate Idea in the Mind, is the Effect of 
 free Choice, and a voluntary Combination 
 among Men. And as different Nations make ufe 
 of different Sounds, to denote the fame Ideas, 
 hence proceeds all that Variety of Languages 
 which we meet with in the World. But when 
 a Connection between our Ideas and Words is 
 once fettled, the unfolding of the Idea anfwering 
 to any Word, which properly conftitutes a 
 Definition, is by no means an arbitrary thing. 
 For here, as I have already obferved, we are 
 bound to exhibit that precife Conception, which 
 cither the Ufe of Language or our own particular 
 Choice, hath annexed to the Term we ufe. 
 Caufcs of tit XVIII. AND thus it appears that 
 
 Obfcurity that -r\ r r j i -rx /- . 
 
 tat hitherto Definitions, confidered as Defcnp- 
 ptrpkxtdtbi t j ons of jd eas j n tne j^ind, are fteady 
 
 Ibetry of De- ,...,, * 
 
 fnitioti, and invariable, being bounded to 
 the Reprefentation of thofe precife Ideas. But 
 
 then
 
 then in the Application of Definitions to particu- 
 lar Names, we are altogether left to our own free 
 Choice. Becaufe as the connecting of any Idea 
 with any Sound, is a perfectly arbitrary Inftitu- 
 tion ; the applying the Defcription of that Idea, 
 to that Sound, muft be fo too. When therefore 
 Logicians tell us, that the Definition of the 
 Name is arbitrary, they mean no more than this; 
 that as different Ideas may be connected with 
 any Term, according to the good Pleafure of him, 
 that ufes it, in like manner may different De- 
 fcriptions be applied to that Term, fuitable to 
 the Ideas fo connected. But this Connection 
 being fettled, and the Term confidered as the 
 Sign of fome fixed Idea in the Understanding, 
 we are no longer left to arbitrary Explications, 
 but muft ftudy fuch a Defcription as correfponds 
 ^with that precife Idea. Now this alone, accord- 
 ing to what has been before laid down, ought to 
 be accounted a Definition. What I am apt to 
 think has occafioned no fmall Confufion in this 
 Matter, is j that many Explanations of Words, 
 where no Idea is unfolded, but merely the Con- 
 nection between fome Word and Idea afiertedj, 
 have yet been dignified with the Name of Defi- 
 nitions. Thus in the Inftance before given, when 
 we fay that a Clock is an Instrument by which we 
 meafure Time: this is by fome called a Definition, 
 And yet it is plain, that we are beforehand fup- 
 pofed to have an Idea of this Inftrument, and 
 G 3 only
 
 ( 1*6 } 
 
 nly taught that the Word Clock^ ferves in com- 
 mon Language to denote that Idea. By this Rule 
 all Explications of Words in our Dictionaries 
 will be Definitions, nay, as was already ob- 
 ferved, the Names of even fimple Ideas may be 
 thus defined. White we may fay is the Colour 
 we obferve in Snow or Milk, Heat the Senfation 
 produced by approaching the Fire, and fo in 
 innumerable other Inftances. But thefe, and 
 all others of the like kind, are by no means De- 
 finitions, exciting new Ideas in the Underftand- 
 ing, but merely Contrivances to remind us of 
 known Ideas, and teach their Connection with 
 the eftablifhed Names. It is neverthelefs worth 
 our Notice, that what Logicians call Definitions 
 of the Name, extend properly no farther than 
 ihefe Explanations, ferving to mark the Con-r 
 ne6lion of our Ideas and Words ; and are there- 
 fore juftly accounted arbitrary, inafmuch as the 
 Connections themfelves are altogether fo. 
 Complex ideal XI X. BUT now in Definitions 
 kne capable p rO perly fo called, we firft confider 
 
 / that Kind * J 
 
 / Description the Term we ufe, as the bign of 
 
 * me i nwar d Conception, either an- 
 Dtfinition. nexed to it by Cuftom, or our own 
 free Choice j and then the Bufinefs of the Defi- 
 nition is to unfold and explicate that Idea. As 
 therefore the whole Art lies, in giving juft and 
 true Copies of our Ideas ; a Definition is then 
 faid to be perfect, when it ferves diftinclly to ex- 
 
 cite
 
 ( "7 ) 
 
 cite the Idea described in the Mind of another, 
 even fuppofing him before wholly unacquainted 
 with it. This Point fettled, let us next enquire 
 into what thofe Ideas are, which are capable of 
 being thus unfolded. And in the firft Place it 
 is evident, that all our fimple Ideas are necefla- 
 rily excluded. We have feen already, that Ex- 
 perience alone is to be confulted here, infomuch 
 that if either the Objects whence they are de- 
 rived come not in our Way, or the Avenues ap- 
 pointed by Nature for their Reception are want- 
 ing, no Defcription is fuificient to convey them 
 into the Mind. But where the Underftanding 
 is already fupplied with thefe original and pri- 
 mitive Conceptions, as they may be united to- 
 gether in an Infinity of different Forms; fo may 
 all their feveral Combinations be diftinclly laid 
 open by enumerating the fimplc Ideas concerned 
 in the various Collections, and tracing the Order 
 and Manner in which they are linked one to ano- 
 ther. Now thefe Combinations of fimple No- 
 tices conftitute what we call our complex 
 Notions j whence it is evident that complex 
 Ideas, and thofe alone, admit of that kind of 
 Defcription, which goes by the Name of a 
 Definition. 
 
 G 4 XX. THE
 
 ( 128 ) 
 
 XX. THE Bufmefs of Definitions 
 e Z' y . now I think pretty plain. They 
 be fid to be are> as we have feen, Pi&ures or 
 
 fully unfolded. 
 
 Representations of our Ideas ; and 
 as thefe Reprefentations are then only poflible, 
 when the Ideas themfolves are complex ; it is 
 obvious to remark, that Definitions cannot have 
 place, but where we make ufe of Terms, {land- 
 ing for fuch complex Ideas. But perhaps the 
 Reader may ftill expedt, that we fhould enter a 
 little more particularly into the Nature of a De- 
 finition, defcribe its Parts, and Ihew by what 
 Rules it ought to proceed, in order to the Attain- 
 ment of its proper End. To give therefore what 
 Satisfaction we are able upon this Point, we muft 
 again call to mind, that the Defign of a Defi- 
 nition is, fo to unfold the Idea anfwering to any 
 Term, as that it may be clearly and diftindly 
 transferred into the Mind of another. But now 
 our complex Ideas, which alone are capable of 
 this kind of Defcription, being, as we have faid, 
 nothing more than different Combinations of 
 fimple Ideas ; we then know and comprehend 
 them perfedl y> when we know the feveral fimple 
 Ideas of which they confift, and can fo put 
 them together in our Minds, as is neceflary to- 
 wards the framing of that peculiar Connection, 
 which gives every Idea its diftinct and proper 
 Appearance, 
 
 XXI. Two
 
 ( '29 ) 
 
 XXI. Two Things are therefore Two 
 
 i . T\ c. *. 17" n. required in a 
 
 required in every Definition, tirft, D y e jf nltilH . 
 that all the original Ideas, out of tnumeratt tbe 
 
 . Ideas, and 
 
 which the complex one is formed, explain the 
 be diftinflly enumerated. Second, g 
 ly, that the Order and Manner of nation. 
 combining them into one Conception, be clearly 
 explained. Where a Definition has thefe Re- 
 quifites, nothing is wanting to its Perfection ; 
 becaufe every one who reads it, and underftands 
 the Terms, feeing at once what Ideas he is to 
 join together, and alfo in what Manner, can at 
 pleafure form in his own Mind the complex 
 Conception anfwering to the Term defined. 
 .Let us, for inftance, fuppofe the Word Square, 
 to ftand for that Idea, by which we reprefent to 
 ourfelves a Figure, whofe Sides fubtend Qua- 
 drants of a circumfcribed Circle. The Parts of 
 this Idea, are the Sides bounding the Figure. 
 Thefe muft be four in Number, and all equal 
 among themfelves, becaufe they are each to 
 fubtend a fourth Part of the fame Circle. But 
 befides thefe component Parts, we muft alfo take 
 Notice of the Manner of putting them together,, 
 .if we would exhibit the precife Idea, for which 
 the Word Square here ftands. For four equal 
 right Lines, any how joined, will not fubtend 
 Quadrants of a circumfcribed Circle. A Figure 
 with this Property, muft have its Sides (landing 
 G 5 alfo
 
 alfo at right Angles. Taking in therefore this 
 laft Confideration, refpefting the Manner of 
 combining the Parts, the Idea is fully defcribed, 
 and the Definition thereby rendered complete* 
 .For a Figure bounded by four equal Sides, join- 
 ed together at right Angles, has the Property 
 required ; and is moreover the only right-lined 
 Figure to which that Property belongs. 
 
 XXII. AND now I imagine it will 
 
 J/ow tut are 
 
 topioceidto be obvious to every one, in what 
 *J?6yrtr Manner we ought to proceed, in 
 Definitions. order to arrive at juft and adequate 
 Definitions. Firft, we are to take an exacl View 
 of the Idea to be defcribed, trace it to its origi- 
 nal Principles, and mark the feveral fun pie Per- 
 ceptions that enter into the Compofition of it. 
 Secondly, we are to confider the particular Man- 
 ner in which thefe elementary Ideas are com- 
 bined, in order to the forming of that precife 
 Conception, for which the Term we make ufe 
 of ftands. When this is done, and the Idea 
 wholly unravelled, we have nothing more to 
 do than fairly tranfcribe the Appearance it makes 
 to our own Minds. Such a Defcription, by dif- 
 tin&ly exhibiting the Order and Number of our 
 primitive Conceptions, cannot fail to excite at 
 the fame Time, in the Mind of every one that 
 reads it, the complex Idea refulting from them ; 
 and therefore attains the true and proper End of 
 a Definition. 
 
 CHAP.
 
 CHAP. VII. 
 
 Of the Compofition and Refolution cf our 
 Ideas y and the Rules of Definition thence 
 arifing. 
 
 I. rpHE Rule laid down in the t ttnptu ^ 
 A foregoing Chapter, is ge- ig our Ideas 
 
 i i- 11 /vi i /~i / *v e proceed by 
 
 neral, extending to all poflible Cafes j a f u ccefflve 
 and is indeed that to which alone Gradation. 
 we can have recourfe where any Doubt or Diffi- 
 culty arifes. It is not however neceflary, that 
 we fhould pra&ife k in every particular Inftance. 
 Many of our Ideas are extremely complicated, 
 infomuch that to enumerate all the fimple Per- 
 ceptions out of which they are formed, would 
 be a very troublefome and tedious Work. For 
 this Reafon, Logicians have eftabliflied certain 
 compendious Rules of defining, of which it 
 may not be amifs here to give fome Account. 
 But in order to the better underftanding of what 
 follows, it will be neceflary to obferve, that 
 there is a certain Gradation in the Compofition 
 of our Ideas. The Mind of Man is very limited 
 in its Views, and cannot take in a great Num- 
 ber of Obje&s at once. We are therefore fain to 
 proceed by Steps, and make our firft Advances 
 fubfervient to thofe which follow. Thus in 
 forming our complex Notions, we begin at firft 
 G6 \vith
 
 with but a few fimple Ideas, fuch as we can 
 manage with Eafe, and unite them together into 
 one Conception. When we are provided with a 
 fufficient Stock of thefe, and have by Habit and 
 Ufe rendered them familiar to our Minds, they 
 become the component Parts of other Ideas ftill 
 more complicated, and form what we may call 
 a fecond Order of compound Notions. This 
 Procefs, as is evident, may be continued to any 
 degree of Compofition we pleafe, mounting from 
 one Stage to another, and enlarging the Num- 
 ber of Combinations. 
 
 II. BUT now in a Series of this 
 
 Hence Ideai of , > 
 
 this C'afs lift kind, whoever would acquaint him- 
 
 3KtSi felf p erfeai y with the Iaft and hi s h - 
 
 *>ance gradu- eft Order of Ideas, finds it much the 
 
 flfy through n ... . .- . . . 
 
 Wtbtjtvtral moft expeditious Method, to pro- 
 Crden. cee j gradually through all the inter- 
 
 mediate Steps. For was he to take any very com- 
 pounded Idea to pieces, and without regard to 
 the feveral Clafles of fimple Perceptions, that 
 have already been formed into diflinft Combina- 
 tions, break in at once into its original Princi- 
 ples, the Number would be fo great as perfe&ly 
 to confound the Imagination, and overcome the 
 utmoft Reach and Capacity of the Mind. When 
 \ve fee a prodigious Multitude of Men, jumbled 
 together in Crowds, without Order, or any re- 
 gular Pofition, we find it impoflible to arrive at 
 an exaft Knowledge of their Number. But if 
 
 they
 
 they are formed into feparate Battalions, and fa 
 ftationed as to fall within the leifurely Survey of 
 the Eye ; by viewing them fucceflively, and in 
 Order, we come to an eafy and certain Deter- 
 mination. It is the fame in our complex Ideas* 
 When the original Perceptions, out of which 
 they are framed, are very numerous, it is not 
 enough that we take a View of them in loofe 
 and fcattered Bodies. We muft form them into 
 diftinct Clafies, and unite thefe Clafles in a juft 
 and orderly Manner, before we can arrive at a 
 true Knowledge of the compound Notices re- 
 fulling from them. 
 
 III. THIS gradual Progrefs of the 
 
 .. , . j -KT Our Defa!tioHI 
 
 Mind to its compound Notions, ought to kiep 
 through a Variety of intermediate *** 
 
 * Ideat, and ob~ 
 
 Steps, plainly points out the manner ferveoiike 
 of conducting the Definitions by 
 which thefe Notions are conveyed into the Minds 
 of others. For as the Series begins with fimple- 
 and eafy Combinations, and advances through a 
 Succefiion of different Orders, rifing one above 
 another in the Degree of Compofition - 3 it is evi- 
 dent that in a Train of Definitions expreiTIng 
 thefe Ideas, a like Gradation is to be obferved. 
 Thus the complex Ideas of the lovveft Order, 
 can no otherwife be defcribed, than by enume- 
 rating the fimple Ideas cut of which they are 
 made, and explaining the manner of their Union, 
 But then in the fecond, or any fucceeding Or- 
 der j
 
 ( 134 ) 
 
 der; as they are formed out of thofe gradual Com- 
 binations, that conftitute the inferior Clafles, it 
 is not neceiTary in defcribing them, to mention 
 one by one, all the fimple Ideas of which they 
 confift. They may be more diftinftly and briefly 
 unfolded, by enumerating the compound Ideas 
 of a lower Order, from whofe Union they re- 
 fult, and which are all fuppofed to be alVeady 
 known, in Confequence of previous Definitions. 
 Here then it is, that the Logical Method of de- 
 fining takes Place ; which that we may the 
 better underftand, I fhall explain fomewhat more 
 particularly, the feveral Steps and Gradations of 
 the Mind, in compounding its Ideas, and thence 
 deduce that peculiar Form of a Definition, which 
 Logicians have thought fit to eftabliih. 
 
 IV. ALL the Ideas we receive, 
 from the feveral Obeds of Nature 
 
 Mid proceed* t h at furround us, reprefent diftinft 
 
 jromfarticular 
 
 togenual Individuals. Thefe Individuals, 
 ideas ' when compared together, are found 
 
 in certain Particulars to refemble. Hence, by 
 collecting the refembling Particulars into one 
 Conception, we form the Notion of a Species. 
 And here let it be obferved, that this laft Idea 
 is lefs complicated than that by which we re- 
 prefent any of the particular Objects contained 
 under it. For the Idea of the Species excludes 
 the Peculiarities of the feveral Individuals, and 
 retains only fuch Properties as are common to 
 
 them
 
 ( '35 ) 
 
 them all. Again, by comparing feveral Species 
 together, and obferving their Refemblance, we 
 form the Idea of the Genus ; where in the fame 
 Manner as before, the Compofition is lefiened, 
 becaufe we leave out what is peculiar to the fe- 
 veral Species compared, and retain only the par- 
 ticulars wherein they agree. It is eafy to con- 
 ceive the Mind, proceeding thus from one Step 
 to another, and advancing through its feveral 
 Clafles of general Notions, until at laft it comes 
 to the higheft Genus of all, denoted by the 
 Word Being, where the bare Idea of Exiftence 
 is only concerned. 
 
 V. IN this Procedure we fee the 7te (^ niltft 
 Mind unravelling a complex Idea oftbtMindm 
 
 i . ... _ ,. r> i c impeundinrits 
 
 and tracing it in the afcending scale, ideas, as it ad- 
 from greater to lefs Degrees of Com- ? c " th '' ' tbe 
 
 ~ t aiferentOrdtn 
 
 poution, until it terminates in one / Perception. 
 fimple Perception. If now we take the Series 
 the contrary Way, and beginning with the laft 
 or higheft Genus, carry our View downwards, 
 thro' all the inferior Genera and Species, quite 
 to the Individuals j we fhall thereby arrive at a 
 diftinit Apprehenfion of the Conduct of the 
 Underftanding in compounding its Ideas. For 
 in the feveral Clafles of our Perceptions, the 
 higheft in the Scale, is for the moft Part made 
 up of but a few fimple Ideas, fuch as the Mind 
 can take in and furvey with Eafe. This firft 
 
 general
 
 ( 136 ) 
 
 general Notion, when branched out into the 
 different Subdivisions contained under it, has 
 in every one of them fomething peculiar, by 
 which they are diftinguifhed among themfelves ; 
 infomuch that in defcending from the Genus 
 to the Species, we always fuperadd fome new 
 Idea, and thereby increafe the Degree of Com- 
 pofition. Thus the Idea denoted by the Word 
 Figure^ is of a very general Nature, and com- 
 pofed of but few fimple Perceptions, as implying 
 no more than Space every where bounded. But 
 if we defcend farther, and confider the Boun- 
 daries of this Space, as that they may be either 
 Lines or Surfaces, we fall into the feveral Spe- 
 cies of Figure. For where the Space is bounded 
 by one or more Surfaces, we give it the Name 
 of zfolid Figure ; but where the Boundaries are- 
 .Lines, it is called a plain Figure, 
 f be Idea of ^I I N this View of Things it is 
 the Sfteiei evident, that the Species is formed by 
 
 formed by fa- * f ' 
 
 ft,add\r,g tie fuperadding a new Idea to the Genus. 
 Here for Jnftance, the Genus is 
 circumfcribcd Space. If now to ! 
 this we fuperadd the Idea of a Circumfcription 
 ty Line, we frame the Notion of that Species of 
 Figures which are called plain ; but if we con- 
 ceive the Circumfcription to be by Surfaces, 
 we have the Species of fo/id Figures. This fuper- 
 added Idea is called ti\e fpecifick Difference, not 
 3 only
 
 ( 137 ) 
 
 nly as It ferves to divide the Species from the 
 Genus, but becaufe being different in all the fe- 
 veral Subdiviflons, we thereby alfo diftinguifh 
 the Species one from another. And as it is like- 
 wife that Conception, which by being joined to 
 the general Idea, compleats the Notion of the 
 Species', hence it is plain that the Genus and 
 Specifick Difference are to be confidered as the 
 proper and conftituent Parts of the Species. If 
 we trace the Progrefs of the Mind ftill farther, 
 and obferve it advancing thro' the inferior Spe- 
 cies, we (hall find its manner of proceeding to 
 be always the fame. For every lower Species 
 is formed by fuperadding fome new Idea to the 
 Species next above it; infomuch that in this 
 . defcending Scale of our Perceptions, the Under- 
 ftanding pafles thro' different Orders of complex 
 Notions, which become more and more com- 
 plicated at every Step it takes. Let us refume 
 here, for inftance, the Species of plain Figures. 
 They imply no more than Space bounded by 
 Lines. But if we take in an additional Confi- 
 deration of the Nature of thefe Lines, as whe-. 
 ther they are Right or Curves, we fall into the 
 Subdivifions of plain Figure, diftinguilhed by 
 the Names Reftilinear, Curvilinear? and Mlx- 
 tilinear. 
 
 VII. AND here we are to obferve, And in ail the 
 that tho' plain Figures when con- '"f tri9r s f e ~ 
 
 cut by fupsr- 
 
 fidcred as one of thofe Branches that adding the 
 
 come.
 
 ( 13* ) 
 
 come under the Notion of Figure in 
 Sfttifiek Dif- 
 
 fertnce to the general, take the Name of a bpe- 
 *urefl CM,. cies . yet CO mpared with the ClafTes 
 of Curvilinear, Re&ilinear, and Mixtilinear, 
 into which they themfelves may be divided, they 
 really become a Genus, of which the before- 
 mentioned Subdivifions conftitute the feveral 
 Species. Thefe Species, in the fame manner as 
 in the Cafe of plain and folid Figures, confift 
 of the Genus and fpecifick Difference as their 
 conftituent Parts. For in the Curvilinear Kind, 
 the Curvity of the Lines bounding the Figure, 
 makes what is called \hefpecifick Difference ; to 
 whicn if we join the Genus, which here is plain 
 Figure, or Space circumfcribed by Lines, we 
 have all that is necefTary towards completing 
 the Notion of the Species. We are only to take 
 Notice, that this laft Subdivifion, having two 
 Genera above it, viz. plain Figure, and Figure 
 in general ; the Genus joined with the fpecifick 
 Difference, in order to conftitute the Species of 
 Curvilinear*, is that which lies neareft to the 
 faid Species. It is the Notion of plain Figure, 
 and not of Figure in general', that joined with 
 the Idea of Curvity, makes up the complex Con- 
 ception of Curve-lined Figures. For in this de- 
 fcending Scale of our Ideas ; Figure in general^ 
 plain Figures^ Curve-lined Figures^ the two firft 
 are confidered as Genera in refpeit of the third ; 
 and the fecond in order, or that which (lands 
 
 next
 
 ( '39 ) 
 
 next to the third, is called the ntareft Genus. 
 But now as it is this fecond Idea, which joined 
 with the Notion of Curvity, forms the Species of 
 Curve-lined Figures ; it is plain, that the third 
 or laft Idea in the Series, is made up of the 
 nearejl Genus cindfpectfici Difference. This Rule 
 holds invariably, however far the Series is con- 
 tinued ; becaufe in a Train of Ideas thus fuc- 
 ceeding one another, all that precede the laft 
 are conildered as fo many Genera in refpecl: of 
 that laft, and the laft itfelf is always formed, 
 by fuperadding the fpecifick Difference to the 
 Genus next it. 
 
 VIII. HERE then we -have an ne idea of 
 univerfal Defcription, applicable to "* J H ^ td al 
 
 r compofcd of 
 
 all our Ideas of whatever kind, from the 
 
 the higheft Genus to the loweft 
 Species. For taking them in order / 
 downwards from the faid general Idea, they 
 every where confift of the Genus proximum y and 
 Differentia fpecifica^ as Logicians love to exprefs 
 themfelves. But when we come to the loweft 
 Species of all, comprehending under it only In- 
 dividuals, the fuperadded Idea, by which thefe 
 Individuals are diftinguifhed one from another, 
 no longer takes the name of the fpecifick Dif- 
 ference. For here it ferves not to denote dif- 
 tindt Species, but merely a Variecy of Indivi- 
 duals, each of which having a particular exif- 
 tence of its own, is therefore numerically dif- 
 
 feren
 
 ( '40 ) 
 
 ferent from every other of the fame Kind. And 
 hence it is, that in this laft Cafe, Logicians 
 chcofe to call the fuperadded Idea by the Name 
 of the numerical Difference ; infomuch that as 
 the Idea of a Species, is made up of the nearejl 
 Genus zndfpecijjcfc Difference^ fo the Idea of an 
 Individual, confifts of the loweji Species and - 
 merick Difference. Thus the Circle is a Species 
 of Curve-lined Figures, and what we call the 
 loivejl Species^ as comprehending under it only 
 Individuals. Circles in particular are diftin- 
 guiftied from one another by the Length and 
 Pofition of their Diameters. The Length there- 
 fore and Pofition of the Diameter of a Circle, 
 is what Logicians call the numerical Difference ; 
 becaufe thefe being given, the Circle itfelf may 
 be defcribed, and an Individual thereby con- 
 flicted. 
 
 IX. AND thus we have endea- 
 
 Definitttni t , i i n 
 
 follow out voured to trace, in the belt manner 
 e are a bj e t h e p rO ff re f s o f tne 
 
 Train, and 
 
 faf, tbro" the Mind in compounding its Ideas. 
 "if ^ begins we fee with the moft gene- 
 tur compound ra ] Notions, which confifting of but 
 a few fimple Notices, are eafily 
 combined and brought together into one Con- 
 ception. Thence it proceeds to the Species 
 comprehended under this general Idea, and 
 thefe are formed by joining together the Genus- 
 and fpecif.ck Difference, And as it often hap- 
 
 pens,
 
 Jpens, that thefe Species may be flill further 
 fubdivided, and run on in a long Series of con- 
 tinued Gradations, producing various Orders 
 of compound Perceptions j fo all thefe feveral 
 Orders are regularly and fucceffively formed, 
 fey annexing in every Step, the fpecifick Diffe- 
 rence to the mareji Genus, When by this Me- 
 thod of Procedure, we are come to the lowed 
 Order of all j by joining the Species and numerick 
 Difference^ we frame the Ideas of Individuals. 
 And here the Series neceflarily terminates, be- 
 caufe it is impofiible any farther to bound or 
 limit our Conceptions. This View of the Com- 
 pofition of our Ideas, reprefenting their confti- 
 tuent Parts in every Step of the Progrefllon, na- 
 turally points out the true and genuine Form of 
 a Definition, For as Definitions are no more 
 than Defcriptions of the Ideas for which the 
 Terms defined ftand ; and as Ideas are then de- 
 fcribed, when we enumerate diftinftly and in 
 Order, the Parts of which they confift j it is 
 plain, that by making our Definitions follow 
 one another, according to the natural Train of 
 our Conceptions, they will be fubjecl: to the 
 fame Rules, and keep pace with the Ideas they 
 defcribe. 
 
 X. As therefore the firft Order of rtt Formcfa 
 cur compound Notions, or the Ideas Dfiinon 
 
 . n . i i i n /- > a '' '^' farioui 
 
 that conititute the nigheit Lrenera, Orders of Con- 
 in, the different Scales of Perception, /"' 
 
 arc
 
 are formed, by uniting together a certain Nunr- 
 ber of finiple Notices j fo the Terms expreffing 
 thefe Genera, are defined by enumerating the/tmple 
 Nttices fo combined. And as the Species com- 
 prehended under any Genus, or the complex 
 Ideas of the fecond Order, arife from fuper- 
 adding the fpecifick Difference, to the faid ge- 
 neral Idea ; fo the Definition of the Names of 
 the Species is abfolved, in a Detail of the Ideas 
 ef the fpecifick Difference, connefted with the Term 
 of the Genus. For the Genus having been before 
 defined, the Term by which it is exprefled 
 (lands for a known Idea, and may therefore be 
 introduced into all fubfequent Definitions, in 
 the fame manner as the Names of fimple Per- 
 ceptions. It will now I think be fufficiently 
 obvious, that the Definitions of all the fuc- 
 ceeding Orders of compound Notions, will 
 every where confift of the Term of the nearejl 
 Genus joined with an Enumeration of the Ideas 
 that conftitute the fpecijlck Difference ; and that 
 the Definition of Individuals, unites the Name of 
 the lowejl Species, with the Terms by which we ex~ 
 prefs the Ideas of the numerick Difference. 
 Tie Logical XI. Here then we have the true 
 
 ofde- anc i proper Form of a Definition, in 
 
 f mug perf eft . 
 
 in its Kind. all the various Orders of Concep- 
 tion. This is that Method of Defining, which 
 is commonly called Logical, and which we fee is 
 perfect in its kind, inafmuch as it prefects a full 
 
 and
 
 ( 143 ) 
 
 *md adequate Defcription of the Idea, for whick 
 the Term defined ftands. There are ftill two 
 Things worthy of Obfervation, before we take 
 leave of this Subject. Firft, that the very Frame 
 and Contexture of thefe Definitions, points out 
 the Order in which they ought to follow one 
 another. For as the Name of the Genus is ad- 
 mitted into a Defcription, only in confequence 
 of its having been before defined ; it is evident, 
 that we muft pafs gradually through all the 
 different Orders of Conception. Accordingly, 
 Logicians lay it down as a Rule, that we are 
 to begin always with the higheft Genus, and 
 carry on the Series of Definitions regularly, 
 thro' all the intermediate Genera and Species, 
 quite down to the Individuals. By this means 
 our Defcriptions keep pace with our Ideas, and 
 pafs through the fame fucceflive Gradations ; 
 infomuch, that the Perufal of them muft excite 
 thofe Ideas in the Underftanding of another, 
 in the very Order and Manner in which they 
 are put -together by the Mind, in its uniform 
 Advances from fimple to the moft complicated 
 Notions. Now this is the true and proper End 
 of Defining, and indeed the higheft Perfection 
 of that Art. 
 
 XII. THERE is yet another . , ^ 
 
 f And applicable 
 
 Thing to be obferved on this Head, to all Words 
 
 ^.u . *.\- T> wbatfoevir, 
 
 namely; that the Form here pre- capable of a 
 /crjbed, is applicable to all Words De fi n t9 ' 
 
 2 whatfo-
 
 "whatfoever, capable of a Definition. For as 
 every Term we ufe, muft denote fome Idea, 
 either general or particular ; and as all our 
 complex Notions, relating to both thefe Clafles 
 of Perception, from the higheft Genus quite 
 down to the Individuals, come within the Rules 
 of Defcription here given j it is evident, that 
 this particular Manner of unfolding an Idea, 
 may be extended to all the pofiible complex 
 Conceptions we can connect with our Words. 
 By the Rules therefore of this Method, Defini- 
 tions may be applied to all Terms {landing 
 for complex Ideas ; and as thefe, by what we 
 have fliewn at large in the two foregoing Chap- 
 ters, are the only definable Articles of Speech ; 
 it neceflarily follows, that the Directions here 
 given are univerfal, extend to all particular In- 
 itances, and are alike applicable in all Lan- 
 guages. And thus at length, we have not only 
 deduced that peculiar Form of a Definition, 
 which obtains among Logicians, but fliewn it 
 -alfo to be perfect in its kind, and to take in the 
 whole Compafs of Language. 
 
 THE
 
 ( I4S ) 
 
 THE 
 
 ELEMENTS 
 
 O f 
 
 LOGIC K. 
 
 BOOK II. 
 
 Of JUDGMENT 0r INTUITION. 
 
 CHAP. I. 
 
 Of the Grounds of human Judgment. 
 
 w: 
 
 ed with Ideas, its next Step fpeffi tie Re- 
 
 ., TIT TJ- i j .1 lations he- 
 
 rn the Way to Knowledge is, the lvleen our 
 
 comparing thefe Ideas together, in Idtai v>he ' t 
 
 thy are \m- 
 
 order to judge of their Agreement mediately per- 
 orDifagreement. In this joint View ttlvabl <' 
 of our Ideas, if the Relation is fuch, as to be 
 immediately difcoverable by the bare Infpe&ion 
 of the Mind j the Judgments thence obtained are 
 H called
 
 called intuitive, from a Word that denotes to look 
 at: for in this Cafe, a mere Attention to the 
 Ideas compared, fuffices to let us fee, how far 
 they are connected or disjoined. Thus, that the 
 Whole is greater than any of its Parts, is an intui- 
 tive Judgment, nothing more being required to 
 convince us of its Truth, than an Attention 
 to the Ideas of 'Whole and Part. And this too is 
 the Reafon, why we call the Ac} of the Mind 
 forming thefe Judgments, Intuition ; as it is in- 
 deed no more than an immediate Perception of 
 the Agreement or Difagreement of any two 
 Ideas. 
 
 Ixperunce ^* ^ UT nere lt IS tO ^ e bfcrved, 
 
 anj Ttjiimony tna t our Knowledge of this kind.re- 
 
 tbt Ground of _ . T . i i_ T 
 
 Judging at to fpects only our Ideas, and the Rela- 
 faRs. tions between them, and therefore 
 
 can ferve only as a Foundation to fuch Reafon- 
 ings, as arc employed in inveftigating thefe Rela- 
 tions. Now it fo happens, that many of our 
 Judgments are converfant about Fa&s, and the 
 real Exiftence of Things which cannot be traced 
 by the bare Contemplation of our Ideas. It does 
 not follow, becaufe I have the Idea of a Circle in 
 my Mind, that therefore a Figure anfwering to 
 that Idea, has a real Exiftence in Nature. I can 
 form to myfelf the Notion of a Centaur, or golden 
 Mountain, but never imagine on that account, 
 that either of them exift. What then are the 
 Grounds of our Judgment in relation to Fah ? 
 
 I anfwer,
 
 ( '47 ) 
 
 I anfwer, thefe two : Experience and Tejlimony. 
 By Experience we are informed of the Exiftence 
 of the feveial Objects which furround us and 
 operate upon our Senfes. Tejlimony is of a wider 
 Extent, and reaches not only to Objects beyond 
 the prefent Sphere of our Obfervation, but alfo 
 to Facts and Tranfactions, which being now 
 paft, and having no longer any Exiftence, could 
 not without this Conveyance, have fallen under 
 our Cognizance. 
 
 III. HERE then we have three ^^ Foun _ 
 Foundations of human Judgment, dathnt /- 
 from which the whole Syftem of our w?,,",'Vizf~ 
 
 Knowledge may with Eafe and Ad- l ; 
 
 \ T" the Ground of 
 
 vantage be deduced, run Intuition, f 
 
 which refpefts our Ideas themfelves, 
 and their Relations, and is the Foundation of 
 that Species of Reafoning, which we call.De- 
 monflration. For whatever is deduced from our 
 intuitive Perceptions, by a clear and connected 
 Series of Proofs, is faid to be demonftrated, and 
 produces abfolute Certainty in the Mind. Hence 
 the Knowledge obtained in this manner, is what 
 we properly term Science ; becaufe in every Step 
 of the Procedure, it carries its own Evidence 
 along with it, and leaves no room for Doubt or 
 Hefitation. And what is highly worthy of No- 
 tice; as the Truths of this Clafs exprefs the Re- 
 lations between our Ideas, and the fame Rela- 
 tions muft ever and invariably fubfift between the 
 H 2 fame
 
 fame Ideas, our Deductions in the way of Sci- 
 ence, conftitute what we call eternal, necefTary, 
 and immutable Truths. If it be true that the 
 Whole is equal to all its Parts, it muft be fo un- 
 changeably ; becaufe the Relations of Equality 
 being attached to the Ideas themfelves, muft ever 
 intervene where the fame Ideas are compared. 
 Of this Nature are all the Truths of natural Re- 
 ligion, Morality and Mathematics j and in ge- 
 neral whatever may be gathered from the bare 
 View and Confideration of our Ideas. 
 
 a. Exptrinc, IV ' THE fecond Ground of hu- 
 rt; Ground of man' Judgment is Experience : from 
 
 far Know- 
 ledge of ibe which we infer the Exiftence of thofe 
 
 S^inia'f Ob J eas that Around us, and fall 
 SoJiet. under the immediate Notice of our 
 
 Senfes. When we fee the Sun, or caft our Eyes 
 towards a Building, we not only have Ideas of 
 thefe Objects within ourfelves, but afcribe to 
 them a real Exiftence out of the Mind. It is alfo 
 by the Information of the Senfes that we judge 
 of the Qualities of Bodies j as when we fay that 
 Snow is white, Fire hot, or Steel hard. For as 
 we are wholly unacquainted with the internal 
 Structure and Conftitution of the Bodies that 
 produce thefe Senfations in us, nay, and are un- 
 able to trace any Connection between that Struc- 
 ture and the Senfations themfelves, it is evident, 
 that we build our Judgments altogether upon 
 Obfcrvation, afcribing to Bodies fuch Qualities 
 
 as
 
 ( H9 ) 
 
 as are anfwerable to the Perceptions they excite 
 in us. But this is not the only Advantage de- 
 rived from Experience, for to that too are we 
 indebted for all our Knowledge regarding the 
 Co-exiftence of fenfible Qualities in Objects, 
 and the Operations of Bodies one upon another. 
 Ivory, for inftance, is hard and elaftic ; this 
 we know by Experience, and indeed by that 
 alone. For being altogether Strangers to the 
 true Nature both of Elafticity and Hardnefs, 
 we cannot by the bare Contemplation of our 
 Ideas determine how far the one neceflarily 
 implies the other, or whether there may not be 
 a Repugnance between them. But when we 
 obferve them to exift both in the fame Objecl, 
 we are then aflureu from Experience, that they 
 iire not incompatible j and when we alfo find, 
 that a Stone is hard and not elaftic, and that 
 Air though elaftieis not hard, we alfo conclude 
 upon the fame Foundation, that the Ideas are 
 not neceflarily conjoined, but may exift fepa- 
 rately in different Objects. In like manner with 
 regard to the Operations of Bodies one upon 
 another, it is evident that our Knowledge this 
 Way is all derived from Obfervation. Aqua Re- 
 gia diflblves Gold, as has been found by frequent 
 Trial, nor is there any other Way of arriving at 
 the Difcovery. Naturalifts may tell us if they 
 pleafe, that the Parts of dqua Regia are of a 
 H 3 Texture
 
 Texture apt to infmuate between the Corpufcles 
 of Gold, and thereby loofen and (hake them 
 afunder. If this is a true Account of the Matter, 
 I believe it will notwithftanding be allowed, that 
 our Conje&ure in regard to the Conformation 
 of thefe Bodies is deduced from the Experiment, 
 and not the Experiment from the Conjecture. It 
 was not from any previous Knowledge of the in- 
 timate Structure of Aqua Regla and Gold^ and the 
 Aptnefs of their Parts to a<3: or be acted upon, 
 that we came by the Conclufion above mentioned. 
 The internal Cohftitution of Bodies is in a man- 
 ner wholly unknown to us ; and could we even 
 furmount this Difficulty, yet as the Separation of 
 the Parts of Gold implies fomething like an ac- 
 tive Force in the Menflruum^ and we are unable 
 to conceive how it comes to be poflefled of this 
 Activity; the Effect muft be owned to be alto- 
 gether beyond our Comprehenfion. But when 
 repeated Trials had once confirmed it, infomuch 
 that it was admitted as an eftabliflied Truth in 
 Natural Knowledge, it was then eafy for Men 
 to fpin out Theories of their own Invention, and 
 contrive fuch a Structure of Parts both for Gold 
 and Aqua Regia, as would beft ferve to explain 
 the Phenomenon, upon the Principles of that 
 Syftem of Philofophy they had adopted. I might 
 eafily (hew from innumerable other Inftances, 
 how much our Knowledge of the mutual Ac- 
 tion
 
 tion of Bodies depends, upon Obfervation. The 
 Bite of a Viper will kill. Plants are fome falu- 
 tary, others noxious. Fire diflblves one Body, 
 and hardens another. Thefe are Truths gene- 
 rally known, nor is it lefs evident, that we owe 
 their Difcovery wholly to Experience. 
 V. AND hence it is eafy to ac- ., 
 
 rr py many 
 
 count for what to fome Writers has /<// /- 
 
 n i i tioni owe their 
 
 appeared a very great Paradox j that Birtb ta 
 many of the moft important Inven- Chance. 
 tions in human Life have taken their Rife from 
 Chance, and inftead of coming out of the Schools 
 of Philofophers, are for the moft part afcribed 
 to Men of no Figure in the Commonwealth of 
 Learning. Sowing, Planting, the Ufe of the 
 Compafs, and fuch like, are not Deductions of 
 human Reafon, but Difcoveries which owe their 
 Birth to Obfervation and Trial. No wonder 
 therefore, if thefe Inventions derived their Be- 
 ginning from fuch as being engaged in the ac- 
 tive and bufy Scenes of Life, were more in the 
 Way of thofe Experiments which lead to Difco- 
 veries of this Nature. And here, as the parti- 
 cular Callings and Profeflions of Men, and oft- 
 times Chance, has a great Afcendant, it need not 
 feem ftrange, if fome of the moft ufeful Arts in 
 Society appear to haye had an Original purely 
 cafual. 
 
 H 4 VI. FROM
 
 ( 152 ) 
 
 VI. FROM what has been faid it 
 
 Natural . . . 
 
 is evident, that as Intuition is the 
 
 Foundation of what we call fdenti- 
 wbicb it reft fi ca l Knowledge, fo is Experience 
 
 *f>tly termed J f , 
 
 Exferimentai or natural. V or this laft being 
 PMoftbj. who]ly taken up wjth the objeds 
 
 of Senfe, or thofe Bodies that conftitute the natu- 
 ral World : and their Properties, as far as we can 
 difcover them, being to be traced only by a long 
 and painful Series of Obfervations ; it is appa- 
 rent, that in order to improve this Branch of 
 Knowledge, we muft betake ourfelves to the 
 Method of Trial and Experiment. Accordingly 
 we find, that while this was neglected, little 
 Advance was made in the Philofophy of Nature ; 
 whereas a contrary Proceeding has inriched the 
 prefent Age with many valuable Difcoveries j 
 infomuch that Natural Knowledge, in Allufion 
 to the Foundation on which it {rands, has been 
 very aptly called Experimental Philofophy. 
 Tbotigb much VII. BUT though Experience is 
 
 / -rr 
 
 we ma term l ^ e ' mrnet ^' ate 
 
 depends an Foundation of Natural Knowledge, 
 
 Ttflimeny, yet r _ t T- 
 
 Exferiirceii yet with refpect to particular rer- 
 tbi ultimate fo j ts i n fl uence j s ver y narrow 
 
 Foundation of 
 
 it. and confined. The Bodies that fur- 
 
 round us are numerous, many of them lie at a 
 great Diftance, and fome quite beyond our 
 Reach. Life too is fhort, and fo crouded with 
 
 Cares,
 
 ( '53 ) 
 
 Cares, that but little Time is left for any fingle 
 Man to employ himfelf in unfolding the Myf- 
 teries of Nature. Hence it is necefTary to ad- 
 mit many Things upon the Teftimony of others, 
 which by this means becomes 'the Foundation 
 of a great Part of our Knowledge of Body. No 
 Man doubts of the Power of Aqua Regia to dif- 
 folve Gold, though perhaps he never himfelf 
 made the Experiment. In thefe therefore, and 
 fuch like Cafes, we judge of the Facts and Ope- 
 rations of Nature, upon the mere Ground of 
 Teftimony. However, as we can always have 
 recourfe to Experience where any Doubt or 
 Scruple arifes, this is juftly confideredas the true 
 Foundation of Natural Philofophy ; being indeed 
 the ultimate Support upon which our Aflent refts, 
 and whereto we appeal, when the higheft Degree 
 of Evidence is required. 
 
 VJII. BUT there are many Facts 3 . r t fti m y, 
 that will not allow of an Appeal to t ^.^ rot " l , d / 
 
 r Hijtoncal 
 
 the Senfes, and in this Cafe Tefti- Knowledge. 
 mony is the true and only Foundation of our 
 Judgments. AH human Actions-, of whatever 
 Kind, when considered as already part, are of tht* 
 Nature here defcribed ; becaufe having now no 
 longer any Exiftence, both the Facts themfelves,. 
 and the Circumftances attending them, can be 
 known only from the Relations of fuch as had 
 fufficient Opportunities of arriving at the Truth. 
 Tejtimony therefore is juftly accounted a third 
 H 5 Ground
 
 ( '54 ) 
 
 Ground of human Judgment; and as from the 
 other two we have deduced fdentijical and natural 
 Knowledge, fo may we from this derive htftori- 
 cal- t by which I would be underftood to mean, 
 not merely a Knowledge of the civil Tranfadions 
 of States and Kingdoms, but of all Fac"ls whatfo- 
 ever, where Teftimony is the ultimate Founda- 
 tion of our Belief. 
 
 IX. BEFORE I conclude this Chap- 
 
 Tbeficor.d . 
 
 of ter, it will be neccflary to obferve ; 
 
 the Mind, that tho , the fecond Operation o f t h e 
 
 commonly ex- 
 
 tended btyond Mind, properly fpeaking, extends 
 not beyond intuitive Perceptions, 
 yet Logicians have not confined themfelves to fo 
 flri& a View of it j but calling it by the Name 
 Judgment, thereby denote all Ah of the Mind, 
 where only two- Ideas are compared, without the 
 immediate Interpofition of a third. For when the 
 Mind joins or feparates two Ideas tho' perhaps 
 this is done in confequence of a Train of pre- 
 vious Reafoning, yet if the Underftanding pro- 
 ceeds upon eftablifhed Notions, without attend- 
 ing to that Train of Reafoning, its Determina- 
 tions are ilill confidered as A&s of Judgment. 
 Thus, that God created the Univerfe, that Men are 
 accountable for their Attions^ are frequently men- 
 tioned by Logicians, as Inftances of the Mind 
 judging. And yet it is apparent, that thefe Judg- 
 ments are by no means of the Kind we call in- 
 g tuitive j
 
 C 155 ) 
 
 tuitive ; nay, that it requires much Exercife of 
 the Reafoning Faculty, before a Man can trace 
 their Connection with the Perceptions of that 
 Name. I could in the fame manner eafily fliew, 
 that even our Judgments of Experience and Tef- 
 timony, when purfued to their Source, derive all 
 their Power of Perfuafion, from being linked 
 with intuitive Truths. But I fhall wave this 
 Enquiry for the prefent, as being of a Nature 
 too fubtile for a Work of this kind. The Re- 
 mark itfelf however was needful, as well to illuf- 
 trate the proper Diftin&ion between the Powers 
 of the Underibnding, as to explain the Reafon, 
 why in this Part of Logick, we extend the fe- 
 cond Operation of the Mind beyond thofe Li- 
 mits, that in Striclnefs of Speech belong to it. 
 Let us now proceed to confider a Jittle more par- 
 ticularly the Nature and Variety of thefe our 
 Judgments. 
 
 CHAP. I 
 
 Of Affirmative and Negative 
 
 I. "\ T 7" H I L E the comparing 
 
 VV ofourldeasisconfidered S 
 merely as an AcT: of the Mind, af- f a Pnpofi- 
 
 f . ,. , .... tion explaintd* 
 
 fembhng them together, and joining 
 
 H6 or
 
 ( 156 ) 
 
 or disjoining them according to the Refult of its 
 Perceptions, we call it Judgment ; but when our 
 Judgments are put into Words, they then bear 
 the N ame of Proportions. A Proportion there- 
 fore is a Sentence expreffing fome Judgment of 
 the Mind, whereby two or more Ideas are affirm- 
 ed to agree or difagree. Now as our Judgments 
 include at leaft two Ideas, one of which is affirm- 
 ed or denied of the other, fo muft a Proportion 
 have Terms anfwering to thefe Ideas. The 
 Idea of which we affirm or deny, and of courfe 
 the Term exprefling that Idea, is called the Sub- 
 jeff of the Propofition. The Idea affirmed or 
 denied, as alfo the Term anfwering it, is called 
 the Predicate. Thus in the Propofition, God is 
 omnipotent: God is the Subject, it being of him 
 that we affirm Omnipotence j and omnipotent is 
 the Predicate, becaufe we affirm the Idea, ex- 
 preffed by that Word, to belong to God. 
 
 , H- BUT as in Propofltiom, Ideas 
 arc either joined or disjoined ; it is 
 not enough to have Terms expreffing thofe Ideas, 
 unlefs we have alfo fome Words to denote their 
 Agreement or Difagreement. That Word in 
 a Propofition, which connects two Ideas together, 
 is called the Copula; and if a negative Particle be 
 annexed, we thereby underftand that the Ideas 
 are disjoined. The Subftantive Verb is common- 
 ly made ufe of for the Copula, as in the above- 
 men-
 
 ( 157 ) 
 
 mentioned Propofition God is omnipotent ; where 
 it reprefents the Copula, and fignifies the Agree- 
 meht of the Ideas of God and Omnipotence* But 
 if we mean to feparate two Ideas j then, befides 
 the Subftantive Verb, we muft alfo life fome 
 Particle of Negation, to exprefs this Repug- 
 nance. The Propofition, Man is not perfect ; 
 may ferve as an Example of this kind, where 
 the Notion of Perfeflion, being removed from 
 the Idea of Man, the negative Particle not is in- 
 ferted after the Copula, to fignify the Difagree- 
 ment between the Subjedl and Predicate. 
 
 III. EVERY Propofition necefla- 
 rily confifts of thefe three Parts, fgg^, 
 but then it is alike needful that pn/ed by a 
 they be all feverally exprefled in 
 Words ; becaufe the Copula is often included 
 in the Term of the Predicate, as when we fay, 
 be Jtts ; which imports the fame as he is fitting. 
 In the Latin Language, a fingle Word has often 
 the Force of a whole Sentence. Thus ambulat 
 is the fame, as tile eft ambulans ; amo, as ego fum 
 amans ; and fo in innumerable other Inftances ; 
 by which it appears, that we are not fo much 
 to regard the Number of Words in a Sentence, 
 as the Ideas they reprefent, and the Manner in 
 which they are put together. For whenever 
 two Ideas are joined or disjoined in an Expref- 
 fion, though of but a fingle Word, it is evi- 
 dent that we have a Subject, Predicate, and 
 
 Copula,
 
 ( 158 ) 
 
 Copula, and of confequence a complete Pro- 
 pofition. 
 
 IV. WHEN the Mind joins two 
 
 jQfK' motive T , 1 1 ,. or 
 
 *d negttnii Ideas, we call it an affirmative 
 Propojitttnt. Judgment j when it feparates them, 
 a negative j and as any two Ideas compared to- 
 gether, muft necefTarily either agree or not 
 agree, it is evident, that all our Judgments fall 
 under thefe two Divifions. Hence, likewife, 
 the Propofitions expreffing thefe Judgments, 
 are all either affirmative or negative. An af- 
 firmative Proportion connects the Predicate 
 with the Subject, as a Stone is heavy ; a nega- 
 tive Propofition feparates them, as God is not 
 the Author of Evil. Affirmation therefore is the 
 fame as joining two Ideas together, and this 
 is done by means of the Copula. Negation on 
 the contrary marks a Repugnance between the 
 Ideas compared, in which Cafe a negative Par- 
 ticle muft be called in, to fhew that the Con- 
 nection included in the Copula does not tak 
 place. 
 
 Wben the ne- V. AND hence we fee the Reafon 
 J??" of the Rule commonly laid down 
 Idtai. by Logicians ; that in all negative 
 Propofitions, the Negation ought to affect the 
 Copula. For as the Copula, when placed by 
 itfelf, between the Subject and the Predicate, 
 manifestly binds them together j it is evident, 
 that in order to render a Proportion ne- 
 gative,
 
 ( 159 ) 
 
 gative, the Particle of Negation muft enter it in 
 fuch Manner, as to deftroy this Union. In a 
 Word, then only are two Ideas disjoined in a 
 Propofition, when the negative Particle may be 
 fo referred to the Copula, as to break the Affir- 
 mation included in if, and undo that Connec- 
 tion it would otherwife eftablifh. When we fay, 
 for Inftance, No Man is per f eft ; take away the 
 Negation, and the Copula of itfelf plainly unites 
 the Ideas in the Propofition. But as this is the 
 very Reverfe of what is intended, a negative 
 Mark is added, to fhew that this Union does 
 not here take place. The Negation, therefore, 
 by deftroying the Effect of the Copula, changes 
 the very Nature of the Propofition, infomuch 
 that inftead of binding two Ideas together, it de- 
 notes their Separation. On the contrary, in 
 this Sentence ; The Man who departs not from an 
 upright Behaviour, is beloved of God : the Predi- 
 cate, beloved of God) is evidently affirmed of the 
 Subject, an upright Man, fo that notwithftand- 
 ing the negative Particle, the Propofition is ftill 
 affirmative. The Reafon is plain j the Nega- 
 tion here affects not the Copula, but making 
 properly a Part of the Subject, ferves with other 
 Terms in the Sentence, to form one complex 
 Idea, of which the Predicate, beloved of God, is 
 directly affirmed. This perhaps to fome may 
 appear a mere Logical Refinement, contrived to 
 
 juftify
 
 ( 160 ) 
 
 juftify the Scholaftic Rule for diflinguifliing be- 
 tween affirmative and negative Propofidons. 
 But if it be confidered, that this Diftinftion is 
 of great Importance in Reafoning, and cannot 
 in many Cafes be made with Certainty but by 
 means of this Criterion here given, the Reader 
 will fee fufficient Reafon for my taking fo much 
 Pains to iiluftrate it. 
 
 Hw * Co fu ia VI - PERHAPS it may ftill appear 
 tomes to be a Myftery, how a Copula can be faid 
 
 Part of a nt- , r> e r r 
 
 gative Pnpo- to be a rart of a negative Propou- 
 J lMn ' tion, whofe proper Bufinefs it is to 
 
 disjoin Ideas. This Difficulty however will 
 vanifh, if we call to mind, that every Judgment 
 implies a direct Affirmation, and that this Affir- 
 mation alone makes the true Copula in a Propo- 
 fition. But as our Affirmations are of two kinds, 
 viz. either of Agreement or of Difagreement, 
 between the Ideas compared; hence there is alfo 
 a twofold Expreffion of our Judgments. In the 
 Cafe of Agreement, the Copula alone fuffices, 
 becaufe it is the proper Mark whereby we de- 
 note an Identity or Conjunction of Ideas. But 
 where Perceptions difagree, there we muft call 
 in a negative Particle ; and this gives us to un- 
 derftand that the Affirmation implied in the 
 Copiua, is not of any Connection between the 
 Subject and Predicate, but of their mutual Op- 
 pofition and Repugnance. 
 
 CHAP.
 
 CHAP. III. 
 
 Of Univerfal and Particular Proportions. 
 
 I. / I AH E next confiderable Divi- u; v ^ og O f 
 JL fion of Propofitions, is into P't>f"'"> KI 
 
 i /~\ T i ""* iint-vtrjal 
 
 univerfal and particular. Our Ideas, and fanicu- 
 according to what has been already lar ' 
 obferved in the firft Part, are all fingular as they 
 enter the Mind, and reprefent individual Ob- 
 jects. But as by Abftra&ion we can render 
 them univerfal, fo as to comprehend a whole 
 Clafs of Things, and fometimes feveral Clafles 
 at once ; hence the Terms expreffing thefe 
 Ideas muft be in like manner univerfal. If 
 therefore we fuppofe any general Term to be- 
 come the Subject of a Propofition, it is evident, 
 that whatever is affirmed of the abftrat Idea 
 belonging to that Term, may be affirmed of all 
 the Individuals to which that Idea extends. 
 Thus when we fay, Men are mortal } we confi- 
 der Mortality, not as confined to one or any 
 Number of particular Men, but as what may 
 be affirmed without Reftriction of the whole 
 Species By this means the Propofition becomes 
 as general as the Idea which makes the Subject 
 of it, and indeed derives its Univerfality intirely 
 from that Idea, being more or lefs fo, according 
 as this may be extended to more or fewer Indi- 
 viduals.
 
 viduals. But it is further to be obfcrved of" thefo 
 general Terms, that they fometimes enter a Pro- 
 pofition in their full Latitude, as in the Ex- 
 ample given above; and fometimes appear with 
 a Mark of Limitation. In this laft Cafe we are 
 given to underftand, that the Predicate agrees 
 not to the whole univerfal Idea, but only to a 
 Part of it ; as in the Propofition, Some Men art 
 wife: for here Wifdom is not affirmed of every 
 particular Man, but reftrained to a few of the 
 human Species. 
 
 II. Now from this different Ap- 
 
 Propofitiont 
 
 vniverfai pearance of the general Idea, that 
 J t fihfc'^,"b'- conftitutes the Subject of any Judg- 
 es a Mark of m ent, arifes the Divifion of Propo- 
 
 Xe/lriflieH. 
 
 fitions into univerfal and particular, 
 An univerfal Propofition is that, wherein the 
 Subjedl is Ibme general Term, taken in its full 
 Latitude, infomuch that the Predicate agrees to 
 all the Individuals comprehended under it, if it 
 denotes a proper Species ; and to all the feveral 
 Species and their Individuals, if it marks an Idea 
 of a higher Order. The Words, a//, every y 
 no, none, &c. are the proper Signs of this Uni- 
 verfality j and as they feldom fail to accompany 
 general Truths, fo they are the moft obvious 
 Criterion whereby to diflinguifh them. All Ani- 
 mals have a Power of beginning Motion. This is 
 an univerfal Propofition ; as we know from the 
 Word all t prefixed to the Subject Animal, which 
 
 denotes
 
 ( 163 ) 
 
 denotes that it muft be taken in its full Extent. 
 Hence the Power of beginning Motion may be 
 affirmed of all the feveral Species of Animals; as 
 of Birds, Quadrupeds, Infe&s, Fifties, &c. and 
 of all the Individuals of which thefe different 
 dalles confift, as of this Hawk, that Horfe, and 
 fo for others. 
 
 III. A particular Propofition has Propofitknt 
 in like manner fome general Term t ar ' icul f r 
 
 ivbtrefome 
 
 for its Subject, but with a Mark of uaiverfai Sub- 
 
 -r 111 i t i f ff appeart 
 
 Limitation added, to denote, that \ hk a Mark 
 the Predicate agrees only to fome of f Limitation. 
 the Individuals comprehended under a Species, 
 or to one or more of the Species belonging to 
 any Gennc, and not to the whole univerfal Idea. 
 Thus, Some Stones are heavier than Iron ; Some 
 Men have an uncommon Share of Prudence. In the 
 laft of thefe Propofitions, the Subje&fome Men t 
 implies only a certain Number of Individuals, 
 comprehended under a fmgle Species. In the 
 former, where the Subject is a Genus, that ex- 
 tends to a great Variety of diftincl Chfks,fome 
 Stones may not only imply any Number of par- 
 ticular Stones, but alfo feveral whole Species 
 of Stones ; inafmuch as there may be not a few, 
 with the Property there defcribed. Hence we 
 fee, that a Propofition does not ceafe to be par- 
 ticular, by the Predicate's agreeing to a whole 
 Species, unlefs that Species, fmgly and dif- 
 tinflly corifidered, makes alfo the Subject of 
 
 which
 
 which we affirm or deny. For if it belongs to 
 feme Genus, that has other Species under it, 
 to which the Predicate does not agree ; it is plain, 
 that where this Genus is that of which we affirm 
 or deny, the Predicate agreeing only to a Part of 
 it, and not to the whole general Idea, conilitutes 
 the Propofition particular. 
 dfurtindin- IV. HERE then we have a fure 
 f.lnkhCrit*. and infallible Mark, whereby to dif- 
 
 nwwbertby to ' 
 
 dtfir.guift) be- tinguifti between univerfal and par- 
 
 fWt n un'f'tr- > T r TITL i. 
 
 fat^ndfartku- ticular Propoutions. Where the 
 l Prtftftitns. Predicate agrees to all the Indivi- 
 duals comprehended under the Notion of the 
 Subject, there the Propofition is univerfal j where 
 it belongs only to lome of them, or to fome of 
 the Species of the general Idea, there the Pro- 
 pofitioii is particular. This Criterion is of eafy 
 Application, and much fafer than to depend upon 
 the common Signs of <?//, every, forne^ none t 
 &c. becaufe thtfe being different in different 
 Languages, and often varying in their Signifi- 
 cation, are very apt in many Cafes to miflcad 
 the Judgment. Thus if we fay, All the Soldiers 
 when drawn up^ formed a Square of a hundred 
 Men a Side : it is evident, that the Predicate 
 cannot be affirmed of the feveral Individuals, 
 but of the whole collective Idea of the Subject ; 
 whence by the Rule given above, the Propofition 
 is not univerfal. It is true, Logicians lay down 
 many Obfei vations, to enable us to diftinguifti 
 
 aright
 
 aright on this Head ; but if the Criterion here 
 given be duly attended to, it will be of more real 
 Service to us than an hundred Rules. For it is 
 infallible, and may be applied with Eafe j whereas 
 the Directions which we meet with in Treatifes 
 of Logick, being drawn for the moft Part from 
 the Analogy of Language, and common Forms 
 of Speech, are not only burdenfome to the Me- 
 mory, but often very doubtful and uncertain in 
 their Application. 
 
 V. THERE is ftill one Species of singular Pro. 
 Proportions that remains to be de- ftf'' ** - 
 
 tamed under 
 
 Icnbed ; and which the more deferves the Head of 
 our Notice, as it is not yet agreed a- Particulars. 
 mong Logicians, to which of the two Clafles 
 mentioned above, they ought to be referred. I 
 mean fingular Propositions j or thofe where the 
 Subject is an Individual. Of this Nature are the 
 following : Sir Ifaac Newton was the Inventor of 
 Fluxions j This Book contains many ufeful Truths, 
 What occafions fome Difficulty, as to the proper 
 Rank of thefe Propofitions, is ; that the Subject 
 being taken according to the whole of its Exten- 
 fion, they fometimes have the fame Effect in Rea- 
 foning, as Univerfals. But if it be confidered, 
 that they are in Truth the moft limited kind of 
 particular Propofitions, and that no Proportion, 
 can with any Propriety be called univerfal, but 
 where the Subject is fome univerfal Idea ; we 
 ihall not be long in determining to which Clafs 
 
 they
 
 ( 166 ) 
 
 they ought to be referred. When we fay, Some 
 Books contain ufeful Truths ; the Propofition is 
 particular, becaufe the general Term appears 
 with a Mark of Reftri&ion. If therefore we fay, 
 This Book contains ufeful Truths ; it is evident 
 that the Propofition muft be ftill more particu- 
 lar, as the Limitation implied in the Word this, 
 isof_a more confined Nature, than in the for- 
 mer Cafe. I know there are Inftances, where 
 fmgular Propofitions have the fame Effect in 
 Reafoning, as Univerfals; yet is not this, by 
 reafon of any proper Univerfality, belonging to 
 them ; but becaufe the Conclufion in fuch Cafes 
 being always fmgular, may be proved by a mid- 
 dle Term which is alfo fmgular ; as I could ea- 
 fily demonftrate, were this a proper Place for 
 entering into a Difcuffion of that Nature. 
 
 Tb, fourfold VI - WE fee therefore, that all 
 DivifioH of Propofitions are either affirmative or 
 
 Proto/itlens. . ....... 
 
 negative ; nor is it lels evident, that 
 in both Cafes, they may be universal or particular. 
 Hence arifes that celebrated fourfold Divifion 
 of them, into univerfal Affirmative^ and univer- 
 fal Negative ; particular Affirmative^ and parti' 
 cular Negative; which comprehends indeed all 
 their Varieties. The Ufe of this Method of dif- 
 tinguifhing them will appear more fully after- 
 wards, when we come to treat of Reafoning and 
 Syllogifm. 
 
 CHAP.
 
 CHAP. IV. 
 
 Of Abjolute and Conditional Proportions. 
 I. nr^H E Objects about which we 
 
 J _ f DijtinSion f 
 
 JL are chiefly converfant in this Qua/iiits into 
 World, are all of a Nature liable to * 
 
 Change. What may be affirmed of 
 them at one time, cannot often at another; and 
 it makes no fmall Part of our Knowledge to dif- 
 tinguifh rightly thefe Variations, and' trace the 
 Reafons upon which they depend. For it is ob- 
 fervable, that amidft all the Viciflitudes of Na- 
 ture, fome things remain conftant and inva- 
 riable ; nor are even the Changes to which we 
 fee others liable, effected, but in confequence of 
 uniform and fteady Laws, which when known, 
 are fufficient to direct us in our Judgments about 
 them. Hence Philofophers, in diftinguifhing the 
 Objects of our Perception into various ClafTes, 
 have been very careful to note, that fome Pro- 
 perties belong effentially to the general Idea, fo 
 as not to be feparable from it but by deftroying 
 its very Nature ; while others are only acciden- 
 tal, and may be affirmed or denied of it, in dif- 
 ferent Circumftances. Thus, Solidity, a yellow 
 Colour, and great Weight, are confidered as 
 eflential Qualities of Gold j but whether it fhall 
 exift as an uniform conjoined Mafs, is not alike 
 
 necefTary.
 
 ( 168 ) 
 
 jiece/Tary. We fee that by a proper Menftruum, 
 it may be reduced to a fine Powder ; and that 
 intenfe Heat will bring it into a State of Fufion. 
 II. Now from this Diverfity in 
 
 Hence a tor.Ji- * 
 
 dtrabu Diver- the feveral Qualities of Things, 
 ar ^ es a confiderablc Difference as 
 to the Manner of our judging about 
 them. For in the firft Place, all fuch Proper- 
 ties, as are infeparable from Obje&s, when 
 confidercd as belonging to any Genus or Spe- 
 cies, are affirmed abfofutely and without Re- 
 ferve of that general Idea. Thus we fay ; Gold 
 ts very weighty ; A Stone is hard', Animals have 
 a Power of Self-Motion. But in the Cafe of 
 mutable or accidental Qualities, as they depend 
 upon fome other Confideration, diftincl: from 
 the general Idea j that alfo muft be taken into 
 the Account, in order to form an accurate Judg- 
 ment. Should we affirm, for inftance, of fome 
 Stones, that they are very fufceptible of a rolling 
 Motion; the Propofition, while it remains in this 
 general Form, cannot with any Advantage be 
 introduced into our Reafonings. An Aptnefs 
 to receive that Mode of Motion flows from the 
 Figure of the Stone j which, as it may vary in- 
 finitely, our Judgment then only becomes ap- 
 plicable and determinate, when the particular 
 Figure of which Volubility is a Confequence, 
 is alfo taken into the Account. Let us then bring 
 
 in
 
 C ^9 ) 
 
 in this other Confideration, and the Proportion 
 will run as follows : Stones of afpherical Form are 
 eafily put into a rolling Motion. Here we fee the 
 Condition upon which the Predicate is affirmed, 
 and therefore know in what particular Cafes the 
 Propofition may be applied. 
 
 III. THIS Confideration of Pro- jv b - icb g - tvet 
 pofitions, refpe&ing the Manner in "/" " ihe '** 
 
 * . . Dtvijkn f 
 
 which the Predicate is affirmed of the Profofnions 
 
 SubjeS, gives rife to the Divifion of % %% 
 them into abfolute and conditional, / 
 Abfolute Propofitions are thofe, wherein we affirm 
 fome Property infeparable from the Idea of the 
 Subject, and which therefore belongs to it in all 
 poflible Cafes ; as, God is infinitely wife : Virtue 
 tends to the ultimate Happinefs of Man. But where 
 the Predicate is not neceflarily connected with 
 the Idea of the Subject, unlefs upon fome Con- 
 fideration diftint from that Idea, there the Pro- 
 pofition is called conditional. The Reafon of the 
 Name is- taken from the Suppofition annexed, 
 v/hich is of the Nature of a Condition, and may 
 be exprefled as fuch. Thus ; If a Stone is expofcd 
 to the Rays of the Su>i 9 it ivill contrail fome Degree 
 sf Heat. If a River runs in a very declining Chan- 
 nel-t its Rapidity will conflantly increafe. 
 
 IV. THERE is not any thing of 
 
 greater Importance in Philofophy, 2jJJ' g f ir " 
 than a due Attention to this Divi- tbit Divijion^ 
 
 r ,. ,, r . f r at it rendtrt 
 
 iion or Propofitions. If we are care- 
 
 I ful
 
 Proponent ful never to affirm Things abfolute- 
 dtttiminatt. ]y ? k u t -where the Ideas are infcpa^ 
 rably conjoined ; and if in our other Judgments, 
 we diftin&ly mark the Conditions, which deter- 
 mine the Predicate to belong to the Subject ; 
 we fhall be the lefs liable to miftake, in applying 
 general Truths to the particular Concerns of 
 human Life. It is owing to the exact Obfervance 
 of this Rule, that Mathematicians have been fo 
 happy in their Difcovcrics ; and that what they 
 demonstrate of Magnitude in general, may be ap- 
 plied with Eafe in all obvious Occurrences. 
 
 V. THE Truth of it is, particu- 
 ^ Propofitions are then known to be 
 Particulars tt true, when we can trace their Con- 
 nection with Unive; fuls ; and it is ac- 
 cordingly the great Bufmefs of Science, to find 
 out general Truths, that may be applied with 
 Safety in all obvious Infhnces. Now the great 
 Advantage arifing from determining with Care 
 the Conditions upon which one Idea may be 
 affirmed or denied of another, is this ; that there- 
 by particular Propofitions really become univer- 
 fal, may be introduced with Certainty into our 
 Reafonings, and ferve as Standards to conduct 
 and regulate our Judgments. To illuftrate this 
 by a familiar Inftance : If we fay, Some Water 
 aJts very forcibly > the Propofition is particular: 
 and as the Conditions on which this forcible 
 Action depends are not mentioned, it is as yet 
 
 uncertain
 
 C 171 ) 
 
 uncertain in what Cafes it may be applied. Let 
 us then fupply thefe Conditions, and the'Propo- 
 fition will run thus : Water conveyed infufficient 
 Quantity along a Jleep Defcent afts very forcibly. 
 Here we have an univerfal Judgment, inafmuch 
 as the Predicate forcible Aftion^ may be afcribed to 
 all Water under the Circumftances mentioned. 
 Nor is it lefs evident, that the Propofition in 
 this new Form, is of eafy Application ; and in 
 fact we find, that Men do apply it in Inftances 
 where the forcible Action of Water is required j 
 as in Corn-Mills, and many other Works of Art. 
 Thus we fee, in what manner we are to proceed, 
 in order to arrive at univerfal Truths, which is 
 the great End and Aim of Science. And indeed, 
 would Men take the fame Care, duly to exprefs 
 the Conditions on which they affirm and deny, 
 as Mathematicians do, in thofe Theorems which 
 they term hypothetical, I doubt not, but we 
 might be able to deduce many Truths, in other 
 Parts of Philofophy, with no lefs Clearnefs, 
 Force, and Perfpicuity, than has hitherto been 
 thought peculiar to the Science of Quantity. 
 
 I 2 CHAP.
 
 CHAP. V. 
 
 Of Simple and Compound Propofitions. 
 
 I. "FTlTHERTO we have treated 
 
 p'r^poKt'tani J^ JL of Propofitions, where only 
 
 ititofimpu two Ideas are compared together. 
 
 and compound. f . , 
 
 Thefe are in the general called fwi~ 
 pie ; becaufe having but one Subject and one Pre- 
 dicate, they are the Effect of a fimple Judgment 
 that admits of no Subdivifion. But if it fo hap- 
 pens, that feveral Ideas offer themfelves to our 
 Thoughts at once, whereby we are led to affirm 
 the fame thing of different Objects, or different 
 things of the fame Object ; the Propofitions cx- 
 prefling thefe Judgments are called co?npound : 
 becaufe they may be refolved into as many 
 others as there are Subjects or Predicates in 
 the whole complex Determination of the Mind. 
 Thus : God is infinitely wife, and infinitely power- 
 ful Here there are two Predicates, infinite Wtf- 
 dom and infinite Powar^ both affirmed of the fame 
 Subject ; and accordingly, the Propofition may 
 be refolved into two others, affirming thefe Pre- 
 dicates feverally. In like manner in the Propo- 
 fition, Neither Kings nor People are exempt from 
 Death ; the Predicate is denied of both Subjects, 
 and may therefore be feparated from them, in 
 diftinct Propofitions. Nor is it kfs evident, that 
 
 if
 
 ( '73 ) 
 
 if a complex Judgment confifts of feveral Sub- 
 jects and Predicates, it may be refolved into as 
 many fimple Propofitions as are the Number 
 of different Ideas compared together. Riches, 
 and Honours are apt to elate the Mind and increafs 
 the Number of our Defires. In this Judgment 
 there are two Subjects and two Predicates, and 
 it is at the fame time apparent, that it may be 
 refolved into four difrincl: Propofitions. Riches 
 are apt to elate the Mind. Riches are apt to increafe 
 the Number of our Defires. And fo of Honours. 
 II. LOGICIANS have divided thefe n e proptr 
 compound Propofitions into a great Nottonc f* 
 
 rr /-, rr compound Pro*. 
 
 many different Clafies ; but in my fofr,on afrtr- 
 Opinion, not with a due Regard """"* 
 to their proper Definition. Thus Conditional*} 
 Caufals, Relatives, &c. are mentioned as fo many 
 diftinct Species of this Kind, though in fact they 
 are no more than fimple Propofitions. To give 
 an Inftanceofa Conditional : If a Stone is expofed 
 to the Rays of the Sun, it will contraft fome Degree 
 of Hfat. Here we have but one Subject and one" 
 Predicate ; for the complex Expreflion, A Stone 
 expofed to the Rays of ths Sun, conftitutes the 
 proper Subject of this Propofition, and is no 
 more than one determinate Idea. The fame 
 Thing happens in Caufals. Rehoboam was ;;- 
 happy, b<caiife h? followed evil Counfel. I deny not 
 that there is here an Appearance of two Propo- 
 I 3 fitions
 
 ( 174 ) 
 
 fitions arifmg from the Complexity of the Ex- 
 preflion j but when we come to confidcr the 
 Matter more nearly, it is evident that we have 
 but a fingle Subject and Predicate. The Purfuit 
 cf evil Counftl brought Mifery upon Rehoboam. 
 It is not enough therefore to render aPropofition 
 compound, that the Subject and Predicate are 
 complex Notions, requiring fometimes a whole 
 Sentence to exprefs them : for in this Cafe, the 
 Comparifon is {till confined to two Ideas, and 
 conftitutes what we call a fimple Judgment. 
 But where there are feveral Subjects or Predi- 
 cates, or both, as the Affirmation or Negation 
 nuiy be alike extended to them all, the Propo- 
 fition expreffing fuch a Judgment is truly a 
 Collection of as many fimple ones as there arc 
 different Ideas compared. Confining ourfelves 
 therefore, to this more ftricT: and juft Notion of 
 compound Propofitions, they are all reducible to* 
 two Kinds, viz. Copulatives and Disjunctives. 
 Compound III. A Copulative Propofition is, 
 
 P e - t l f fc"p u . where the Subjefls and Predicates 
 la:ivt, ' are fo linked together, that they may 
 be all feverally affirmed or denied one of another, 
 Of this Nature are the Examples of compound 
 Propofitions given above. Riches and Honours are 
 apt to elate the Mlnd^ and inircafe the Number of 
 our Deftres. Neither Kings nor People are exempt 
 from Death. In the firfl of thefe, the two Predi- 
 cates
 
 catcs may be affirmed feverally of each Subject, 
 whence we have four diftincSl Propofitions. The 
 other furnifhes an Example of the Negative Kind, 
 where the fame Predicate being disjoined from 
 both Subjects, may be alfo denied of them in 
 Separate Propofitions. 
 
 IV. THE other Species of com- Or phjunc- 
 pound Propofitions are thofe called ''*" 
 Disjunctives ; in which, comparing feveral Pre- 
 dickies with the fame Subject, we affirm that one 
 of them necefTarily belongs to it, but leave the 
 particular Predicate undetermined. If any one, 
 for example, fays : This World either exijh ofit- 
 felf-> or is the Work of fame all-wife and powerful 
 Caufe ; it is evident that one of the two Predi- 
 cates mud belong to the World ; but as the Pro- 
 pofition determines not which, it is therefore of 
 the kind we call Disjunctive. Such too are the 
 following : The Sun either moves round the Earth , 
 or is the Center about which the Earth revolves. 
 Friendjhip finds Men equal^ or makes them fo. It 
 is the Nature of all Propofitions of this Clafs, 
 fuppofmg them to be exact in Point of Form ; 
 that u.;on determining the particular Predicate, 
 the'relt are of courfe to be removed ; or if all 
 the Predicates but one are removed, 'that one 
 ncceflarily takes place. Thus in the Example 
 given above ; if we allow the World to be the 
 Work of fome wife and powerful Caufe, we o/ 
 courfe. deny it to be felf-exiftent, or if we deny 
 1 4 it
 
 It to be felf-exifienr, we muft neceflarily adnut 
 that it was produced by fome wife and jwwerful 
 Caufe. Now this particular Manner of linking 
 the Predicates together, fo that the eftablifhing 
 one difplaces all the reft ; or the excluding all 
 but one neceflarily eftablifhes that one ; cannot 
 otherwife be effected than by means of disjunc- 
 tive Particles. And hence it is that Propofitions 
 of this Clafs take their Names from thefe Par- 
 ticles, which make fo neceflary a Part of them, 
 and indeed conftitute their very Nature, con- 
 fidered as a diftindl Species. But I (hall referve 
 what farther might be faid on this Head till 
 I come to treat of Reafoning, where the great 
 Ufe and Importance of disjunctive Propofitions 
 will better appear. 
 
 CHAP. VI. 
 
 Of the Divifion of 'Propofitions into Self- 
 evident and Dcwonftrable. 
 
 oftbit I. A S we are foon to enter 
 /A. upon the third Part of 
 Logick, which treats of Reafoning, and as the 
 Art of Reafoning lies in deducing Propofitions 
 whofe Truth does not immediately appear, from 
 others more known j it will be proper before we 
 
 proceed
 
 proceed any farther, to examine a little the dif- 
 ferent Degrees of Evidence that accompany our 
 Judgments ; that we may be the better able to 
 diftinguifh, in what Cafes we ought to have re- 
 courfe to Reafoning, and what thofe Propofi- 
 tions are, upon which, as a fure and unerring 
 Foundation, we may venture to build the Truth 
 of others. 
 
 II. WHEN any Propofition is of- Prtfojilhat 
 fered to the View of the Mind, if the divided into 
 
 T- v- i tr J (elf -evident 
 
 Terms in which it is expreiled are J a ^ d emon - 
 underftood ; upon comparing the ft rable - 
 Ideas together, the Agreement or Difagreement 
 afTerted is either immediately perceived, or found 
 to lie beyond the prefent Reach of the Under- 
 ftanding. In the firft Cafe the PropofiUon is faid 
 to be felf- evident, and admits not of any Proof, 
 becaufe a bare Attention to the Ideas themfelves 
 produces full Conviction and Certainty ; nor is 
 it pofllble to call in any thing more evident, by 
 way of Confirmation. But where the Connec- 
 tion or Repugnance comes not fo readily under 
 the Infpeclion of the Mind, there we muft have 
 recourfe to Reafoning ; and if by a clear Series 
 of Proofs we can make out the Truth propofed, 
 infomuch that Self-evidence fhall accompany 
 every Step of the Procedure, we are then able 
 to demonftrate what we affert, and the Propo- 
 fition itfdf is faid to be demwjlrable* When we 
 I 5 affirm,
 
 affirm, for inftance, that it is itnpojfible for the 
 fame thing to be and not to be ; whoever under- 
 frands the Terms made ufe of, perceives at firft 
 Glance the Truth of what is aflerted ; nor can 
 he by any Efforts bring himfdf to believe the 
 contrary. The Propofition therefore \sfelf- evi- 
 dent^ and fuch, that it is impoffible by Reafon- 
 ing to make it plainer ; becaufe there is no Truth 
 more obvious, or better known, from which as 
 a Confcquence it may be deduced. , But if we 
 fay, This World had a Beginning ; the Afiertion 
 is indeed equally true, but (bines not forth with 
 the fame Degree of Evidence. We find great 
 Difficulty in conceiving how the World could 
 be made out of nothing ; and are not brought to 
 a free and full Confenr, until by Reafoning we 
 arrive at a clear View of the Abfurdity involved 
 in the contrary Suppofition. Hence this Propofi- 
 tion is of the kind we call demonjlrable, inafmuch 
 as its Truth is not immediately perceived by the 
 Mind, but yet may be made appear by means of 
 others more known and obvious, whence it fol- 
 lows as an unavoidable Confequence. 
 
 , , ,. III. FROM what has been faid it 
 
 N by ttefecor.a 
 
 Operation of appears, that Reafoning is employ - 
 'corfJdivboiiy ed only about demonftrable Propo- 
 10 ir.sui:i;n. fitions, and that our intuitive and 
 felf-evident Perceptions, are the ultimate Foun- 
 dation on which it refts, And now we fee 
 
 clearly
 
 ( 179 ) 
 
 clearly the Reafon, why in the Diftinclion of 
 the Powers of the Underftanding, as explained 
 in the Introduction to this Treatife, the feconcl 
 Operation of the Mind was confined wholly to 
 intuitive A6h. Our firft Step in the Way to 
 Knowledge, is to furnifh ourfdves with Ideas. 
 \Vhen thefe are obtained, we next fet ourfelves 
 to compare them together, in order to judge 
 of their Agreement or Difagreement. If the 
 Relations we are in queft of lie immediately 
 open to the View of the Mind, the Judgments 
 expreffing them are felf-evident ; and the At 
 of the Mind forming thefe Judgments is what 
 we call Intuition. But if upon comparing our 
 Ideas together, we cannot readily and at once 
 trace their Relation, it then becomes necefl'ary 
 to employ Search and Examination, and call 
 in the AfTiftance of felf-evident Truths, which 
 is what we properly term Reafoning. Every 
 Judgment therefore that is not intuitive, being 
 gained by an Exercife of the Reafoning Faculty, 
 neceffarily belongs to the third Operation of the 
 Mind, and ought to be referred to it in a juft 
 Divifion of the Powers of the Underftanding. 
 And indeed it is with this View chiefly, that we 
 have diftinguifhed Pronofitions into felf-evident 
 and demonftrable. Under the firil Head are 
 comprehended all our intuitive Judgments, that 
 is, all belonging to the fecond Operation of the 
 I 6 Mind.
 
 Mind. Demonftrable Proportions are the pro- 
 per Province of the Reafoning Faculty, and 
 conftitute by far the moft confiderable Part of 
 human Knowledge. Indeed Renfon extends alfo 
 to Matters of Experience and Tcftimony, where 
 the Proofs adduced are not of the kind called 
 Demonftration. But I am here only confider- 
 ing the Powers of the Mind as employed in 
 tracing the Relations between its own Ideas, in 
 which View of Things every true Propofition is 
 cemonftrable ; tho' very often we find ourfelves 
 incapable of difcovering and applying thofe in- 
 termediate Ideas upon which the Demonftration 
 depends. 
 
 IV. DEMONSTRABLE Propofi- 
 r'{'tiTttyrft tions therefore, belonging properly 
 Printifht of to t h e t hj r a Operation of the Mind, 
 I {hall for the prefent difmifs them, 
 and return to the Confederation of felf-evident 
 Truths. Thefe, as I have already obferved, 
 furnifh the firft Principles of Reafoning ; and 
 it is certain, that if in our Refeaiches, we em- 
 ploy only fuch Principles as have this Charac- 
 ter of Self-evidence, and apply them according 
 to the Rules to be afterwards explained, we 
 fhall be in no Danger of Error, in advancing 
 from one Difeovery to another. For this I may 
 appeal to the Writings of the Mathematicians, 
 
 which
 
 which being conducted by the exprefs Model 
 here mentioned, are an inconteftible Proof of the 
 Firmnefs and Stability of human Knowledge, 
 when built upon fo fure a Foundation. For 
 not only have the Propofitions of this Science 
 flood the Teft of Ages, but are found attended 
 with that invincible Evidence, as forces the 
 Affent of all who duly confider the Proofs upon 
 which they are eftablifhed. Since then Mathe- 
 maticians are univerfally allowed to have hit 
 upon the right Method of arriving at Truths ; 
 fince they have been the happieft in the Choice, 
 as well as Application of their Principles ; it 
 may not be amifs to explain here the Divifion 
 they have given of felf-evident Propofitions j 
 that by treading in their Steps, we may learn 
 fomething of that Juftnefs and Solidity of 
 Reafoning for which they are fo defervedly 
 efteemed. 
 
 V. FIRST then it is to be ob- 
 
 Dtpnitions a 
 
 ferved, that they have been very great Help to 
 careful in afcertaining their Ideas, %". %' 
 and fixing the Signification of their Knowledge. 
 Terms. For this Purpofe they begin with De- 
 finitions, in which the Meaning of their Words 
 is fo diftin&ly explained, that they cannot fail 
 to excite in the Mind of an attentive Reader 
 the very fame Ideas as are annexed to them by 
 the Writer. And indeed I am apt to think 
 
 that
 
 ( 182 ) 
 
 that the Clearnefs and irrefiftible Evidence of 
 Mathematical Knowledge, is owing to nothing 
 fo much as this Care in laying the Foundation. 
 Where the Relation between any two Ideas is 
 accurately and juftly traced, it will not be dif- 
 ficult for anothfcr to comprehend that Relation, 
 if in fetting himfelf to difcover it, he brings the 
 very fame Ideas into Comparifon. But if, on 
 the contrary, he affixes to his Words Ideas dif- 
 ferent from thofe that were in the Mind of him 
 who firft advanced the Demonftration ; it is evi- 
 dent, that as the fame Ideas are not compared, 
 the fame Relation cannot fubfift, infomuch that 
 a Propofition will be rejected as falfe, which, 
 had the Terms been rightly underftood, muft 
 have appeared unexceptionably true. A Square, 
 for inftance, is a Figure bounded by four equal 
 right Lines, joined together at right Angles. 
 Here the Nature of the Angles makes no lefs a 
 Part of the Idea, than the Equality of the Sides ; 
 and many Properties demonftrated of the Square 
 flow from its being a rectangular Figure. If 
 therefore we fuppofe a Man who has formed a 
 partial Notion of a Square, comprehending only 
 the Equality of its Sides, without regard to the 
 Angles, reading feme Demonftration that im- 
 plies alfo this latter Confideration ; it is plain 
 he would rejec~t it as not univerfally true, inaf- 
 inuch as it could not be applied where the Sides 
 
 were
 
 were joined together at unequal Angles. For 
 this laft Figure anfwering (till to his Idea of 
 a Square, would be yet found without the 
 Property afligned to it in the Propofition. But 
 if he comes afterwards to correct his Notion, 
 and render his Idea complete, he will then rea- 
 dily own the Truth and Juftnefs of the De- 
 monft ration. 
 
 VI. WE fee therefore, that no- Matbtmai , 
 thing contributes fo much to the "** ty bs- 
 
 T i f-< r i "" ; ' n S to'nb 
 
 Improvement and Certainty of hu- them, frocure 
 
 man Knowledge, as the having de- a ready R e - 
 
 _ ctpnn to the 
 
 terminate Ideas, and keeping them Truths tbty 
 
 {ready and invariable in all our ad " vance - 
 Difcourfes and Reafonings about them. And 
 on this Account it is, that Mathematicians, as 
 was before obferved, always begin by defining 
 their Terms, and diftin&ly unfolding the No- 
 tions they are intended to exprefs. Hence fuch 
 as apply themfelves to thefe Studies, having 
 exactly the fame Views of Things, and bring- 
 ing always the very fame Ideas into Comparifon, 
 readily difcern the Relations between them, 
 when clearly and diftin&ly reprefented. Nor 
 is there any more natural and obvious Reafon 
 for the univerfal Reception given to Mathema- 
 tical Truths, and for that Harmony and Cor- 
 refpondence of Sentiments which makes the 
 diftinguifliing Character of the Literati of this 
 Clafs. 
 
 VII. WHE*
 
 ntepaiii/bini VI1 - W HEN they have taken this 
 tf Principles fi r fl. step, and made known the 
 
 tbt ftcond Step * 
 
 in Matbem'iti- Ideas whole Relations they intend 
 te) their next 
 
 lay down fome felf-evident 1 ruths, which may 
 ferve as a Foundation for their future Reafon- 
 ings. And here indeed they proceed with re- 
 markable Circumfpection, admitting no Prin- 
 ciples but what flow immediately from their 
 Definitions, and neceflarily force themfelves 
 upon a Mind in any Degree attentive to its 
 ? Perceptions. Thus a Circle is a Figure formed 
 by a Right Line, moving round fome fixed 
 Point in the fame Plane. The fixed Point round 
 which the Line is /uppofed to move, and where 
 one of its Extremities terminates, is called the 
 Center of the Circle. The other Extremity, 
 which is conceived to be carried round, until 
 it returns to the Point whence it firft fet out, 
 defer ibes a Curve running into itfelf, and termed 
 the Circumference. All Right Lines drawn from 
 the Center to the Circumference are called 
 Radii. From thefe Definitions compared, Geo- 
 metricians derive this felf-evident Truth, that 
 the Radii of the fame Circle are all equal one to 
 another. I call it felf-evident, becaufe nothing 
 more is required, to lay it open to the imme- 
 diate Perception of the Mind, than an Attention 
 to the Ideas compared. For from the very Ge- 
 nefis of a Circle it is plain, that the Circum- 
 
 ference
 
 icrence is every where diftant from the Center, 
 by the exadr. Length of the defcribing Line ; 
 and that the feveral Radii are in Truth nothing 
 more, than one and the fame Line varioufly 
 pofited within the Figure. This fhort Defcrip- 
 tion will, I hope, ferve to give fome little In- 
 fight into the Manner of deducing Mathemati- 
 cal Principles, as well as into the Nature of that 
 Evidence which accompanies them. 
 
 VIII. AND now I proceed to ob- 
 
 f L ^ 11 r> r Propofitient 
 
 ferve, that in all Proportions we d ^\ d j edini9 
 either affirm or deny fome Property St e ' ulat ' me 
 
 r i TI i /T i Vi i andpra&ical. 
 
 of the Idea that conftitutes the Sub- 
 ject of our Judgment, or we maintain that 
 fomething may be done or effected. The firil 
 Sort are called fyeculatlve Proportions, as in 
 the Example mentioned above, the Radii of the 
 fame Circle are all equal one to another. The 
 others are called practical, for a Reafon too ob- 
 vious to be mentioned ; thus, that a Right Line 
 may be drawn from one Point to another, is a prac- 
 tical Propofition ; inafmuch as it exprefles that 
 fomething may be done. 
 
 IX. FROM this twofold Confi- 
 
 . c T, r . /- , Hence Mai be- 
 
 deration of Propofitions anfes the ma ,; C a, Pri- 
 twofold Divifion of Mathematical "ff" <<&'- 
 
 guijeta into 
 
 Principles, into Axioms and Pojiu- Axioms and 
 lates. By an Axiom they umlerftand 
 any felf- evident fpcculative Truth : as, that the 
 Whole is greater than its Parts: That Things equal 
 
 to
 
 f 186 ) 
 
 to one ar.d the fdir.eThing, are equal to one another. 
 But a felf-evident practical Propofition is what 
 they cajl a Pojhdate. Such are thofc of Euclid - t 
 that a finiie Right Line may be continued direEily 
 forwards : That a Circle may be dcfcribed about 
 any Center with any Dijiance. And here we arc 
 to obferve, that as in an Axlom^ the Agreement 
 or Difagreement between the Subject and Pre- 
 dicate muft come under the immediate Infpec- 
 tion of the Mind ; fo in a Pojlitlate, not only 
 the Poffibility of the Thing afterted mud be 
 evident at firft View, but alfo the Manner in 
 which it may be effected. But where this Man- 
 ner is not of itfelf apparent, the Propofition 
 comes under the Notion of the demonftrable 
 kind, and is treated as fuch by the Geometrical 
 Writers. Thus, to draw a Right Line from ont 
 Point to another ; is afiumed by Euclid as a Pof- 
 tu'ate, becaufe the manner of doing it is fo ob- 
 vious. as to require no previous Teaching. 
 But then it is not equally evident, how we are 
 to conjlrucl an equilateral Triangle. For this 
 Reafon he advances it as a demonftrable Pro- 
 pofition, lays dowji Rules for the exact Per- 
 formance, and at the fame time proves that if 
 thcfe Rules are followed, the Figure will be 
 juftly defcribed. 
 
 A'-.d tetr.in- X. THIS naturally leads me to 
 
 ^onlnt^"' talce notice > tll2t zsfdf -evident Truth, 
 
 1'beortmi and arc diilin^uiflied into different kinds, 
 
 Prothms. .. 
 
 5 according
 
 according as they are fpcculative or practical ; 
 (a is it alfo with dcmonjlrable Propofitions. A 
 demonftrable fpeculative Proportion, is by Ma- 
 thematicians called a Theorem. Such is the fa- 
 mous 4jth Proposition of the firft Book of the 
 Elements, known by the Name of the Pythagorick 
 Theorem, from its fuppofed Inventor Pythagoras, 
 "viz. That In every Right-angled Triangle, the 
 Square defcribed upon the Side fubtending the Right 
 /ingle, is equal to both the Squares defcribed upon 
 the Sides containing the Right Jingle. On the 
 other hand, a demonftrable practical Propofi- 
 tion is called a Problem ; as where Euclid teaches 
 us to defcribe a Square upon a given Right Line. 
 XI. SINCE I am upon this Sub- 
 
 1 Lorollanes an 
 
 jeer, it may not be amifs to add, obihutDe- 
 that befides the four Kinds of Pro- JSSfeT 
 pofitions already mentioned, Mathe- P r ^"'> 
 maticians have alfo a fifth, known by the Name 
 of Corollaries. Thefe are ufually fubjoined to 
 Theorems^ or Problems, and differ from them only 
 in this ; that they flow from what is there de- 
 monftrated, in fo obvious a Manner as to dif- 
 cover their Dependence upon the Proportion 
 whence they are deduced, almoft as foon as 
 propofed. Thus Euclid having demonftrated, 
 that in every Right-lined Triangle, all the three 
 Singles taken together are equal to two Right Angles ; 
 adds by way of Corollary, that all the three
 
 C 188 ) 
 
 Angles of any one Triangle taken together , are equal 
 to all the three Angles cf any other Triangle taken 
 together : which is evident at firil Sight ; be- 
 caufe in all Cafes they are equal to two right 
 ones, and Things equal to one and the fume 
 thing, are equal to one another. 
 
 XII. THE laft Thing I (hall take 
 
 Scbclia ftrvi . i r r>- e i 
 
 the Purport notice or in the Practice or the 
 f Annotate Mathematicians, is what they call 
 
 tr a Cunment, 
 
 their Scholia. They are indifferently 
 annexed to Definitions, Proportions, or Corol- 
 laries ; and anfwer the fame Purpofes as Anno- 
 tations upon a Claffic Author. For in them 
 Occafion is taken, to explain whatever may 
 appear intricate and obfcure in a Train of Rea- 
 foning ; to anfwer Objections ; to teach the 
 Application and Ufes of Propofitions j to lay 
 open the Original and Hiftory of the feveral Dif- 
 coveries made in the Science ; and in a Word, 
 to acquaint us with all fuch Particulars as de- 
 ferve to be known, whether confidered as Points 
 of Curiofity or Profit. 
 
 XIII. THUS we have taken a 
 
 Tb:iMtthodof _ ,,. c i r >i 
 
 the Matbt.na- ihort View of the io much cele- 
 ticitnt unrvtr. brated Method of the Mathemati- 
 
 /tf/, and a furt 
 
 Guide to Ctr- cians ; which to any one who con- 
 fiders it with a proper Attention, 
 mud needs appear univerfal, and equally appli- 
 cable in other Sciences. They begin with De- 
 finitions.
 
 ( 1 89 ) 
 
 finitions. From thefe they deduce their Axioms 
 and Poftulates, which ferve as Principles of 
 Reafoning j and having thus laid a firm Foun- 
 dation, advance to Theorems and Problems, 
 eftablifliing all by the ftri&eft Rules of Demon- 
 ftration. The Corollaries flow naturally and 
 of themfelves. And if any Particulars are ftill 
 wanting to illuftrate a Subject, or complete the 
 Reader's Information j thefe, that the Series of 
 Reafoning may not be interrupted or broken, 
 are generally thrown into Scholia. In a Syftem 
 of Knowledge fo uniform and well connected, 
 no wonder if we meet with Certainty ; and if 
 thofe Clouds and DarknefTes, that deface other 
 Parts of human Science, and bring Difcredit 
 even upon Reafon itfelf, are here fcattered and 
 difappear. 
 
 XIV. BUT I fhall for the prefent , ,, ... 
 
 aelf-e-viifent 
 
 wave thefe Reflections, which every Trmbi km-io* 
 Reader of Underftanding is able to /J, u^ij. 
 make of himfelf, and return to the ab!t Co<ftion 
 
 /", r . r r ic i n bet-Wten the 
 
 Confideration of felf-evident Propo- Sutj.-a and 
 fitions. It will doubtlefs be expeft- *'*<*<' 
 ed, after what has been here faid of them, that 
 I fhould eftablifh fome Criteria^ or Marks, by 
 which they may be diftinguifhed. But 1 frankly 
 own my Inability in this RefpecT:, as not being 
 able to conceive any Thing in them more obvi- 
 ous and ftriking, than that Self-evidence which 
 
 . constitutes
 
 ) -: 
 
 conftitutes their very Nature. All I have there- 
 fore to obferve on this Head is, that we ouo-ht 
 
 * O 
 
 to make it our firft Care, to obtain clear and de- 
 terminate Ideas. When afterwards we come 
 to compare thefe together, if we perceive be- 
 tween any of them a neceffary and unavoidable 
 Connection, infomuch that it is impoffible to 
 conceive them exifting afunder, without deftroy- 
 ing the very Ideas compared; we may then 
 conclude, that the Proportion expre/fing this 
 Relation is a Principle, and of the Kind we 
 call felf-evident. In the Example mentioned 
 above, The Radii of the fame Circle are all equal 
 between themfehcs, this intuitive Evidence fhines 
 forth in the cleared Manner ; it being impoflible 
 for any one who attends to his own Ideas, not 
 to perceive the Equality here aflerted. For as 
 the Circumference is every where diftant from 
 the Center by the exact Length of the defcrib- 
 ing Line ; the Radii drawn from the Center to 
 the Circumference, being feverally equal to this 
 one Line, muft needs alfo be equal among them- 
 felves. If we fuppofe the Radii unequal, we at 
 the fame Time fuppofe the Circumference more 
 diftant from the Center in fome Places than 
 in others ; from which Suppofition, as it would 
 exhibit a Figure quite different from a Circle, 
 we fee there is no feparating the Predicate from 
 the Subject in this Proportion, without deflroy- 
 
 in<r
 
 ing the Idea in relation to which the Compa- 
 rifon was made. The fame Thing will be found 
 to hold in all our other intuitive Perceptions, 
 infomuch that we may eftablifh this as an uni- 
 verfal Criterion, whereby to judge of and dif- 
 tinguifh them. I would not, however, be un- 
 derftood to mean, as if this ready View of the 
 unavoidable Connection between fome Ideas 
 was any Thing really different from Self-evidence. 
 It is indeed nothing more than the Notion of 
 Self-evidence a little unfolded, and as it were 
 laid open to the Infpe<5tion of the Mind. In- 
 tuitive Judgments need no other diftinguifhing 
 Marks, than that Brightnefs which furrounds 
 them ; in like Manner as Light difcovers itfelf 
 by its own Prefence, and the Splendor it uni- 
 verfally diffufes. But I have faid enough of 
 felf-evident Propofitions, and fhall therefore now 
 proceed to thofe of the demonftrable kind ; 
 which being gained in confequence of Reafon- 
 ing, naturally leads us to the third Part of Logick, 
 where this Operation of the Underftanding is 
 explained, 
 
 THE
 
 ( 19* ) 
 
 THE 
 
 ELEMENTS 
 
 O F 
 
 L O G I C K. 
 
 BOOK III. 
 Of REASONING. 
 
 CHAP. I. 
 
 Of Reafoning in general, and the Parts 
 of which it confifts. 
 
 Remote R,Ia . "* \\ T^ haVC ^ een h W the 
 
 "?7 dl ' c *"", V V proceeds in furnifhin? it- 
 
 ed by mrans of 
 
 ir.:ermtdiau felf with Ideas, and framing intuitive 
 Perceptions. Let us next enquire 
 into the manner of difcovering thofe more remote 
 Relations, which lying at a Diftance from the 
 Underflanding, are not to be traced but by means 
 of a higher Exercife of its Powers. It often hap- 
 
 pens
 
 C 193 ) 
 
 pens In comparing Ideas together, that their 
 Agreement or Difagreement cannot be difcerned 
 at firft View, efpecially if they are of fuch a Na- 
 ture, as not to admit of an exa& Application one 
 to another. When, for inftance, we compare two 
 Figures of a different Make, in order to judge of 
 their Equality or Inequality, it is plain, that by 
 barely confidering the Figures themfelves, we 
 cannot arrive at an exact Determination ; be- 
 caufe by reafon of their difagreeing Forms, it is 
 impoffible fo to put them together, as that their 
 feveral Parts ftiall mutually coincide. Here then 
 it becomes neceflary to look out for fome third 
 Idea, that will admit of fuch an Application as 
 the prefent Cafe requires ; wherein if we fuc- 
 ceed, all Difficulties vanifh, and the Relation 
 we are in queft of may be traced with Eafe. Thus 
 right-lined Figures are all reducible to Squares, 
 by means of which we can meafure their Areas, 
 and determine exactly their Agreement or Dif- 
 agreement in Point of Magnitude. 
 
 II. IF now it be afked, how any Tbh Manntr 
 third Idea can ferve to difcover a Re- jf "T""'"* j' 
 
 I rule termid 
 
 lation between two others : I an- Rtafoning. 
 fwer, by being compared feverally with thefe 
 others ; for fuch a Comparifon enables us to fee 
 how far the Ideas with which this third is com- 
 pared, are connected or disjoined between them- 
 felves. In the Example mentioned above of two 
 right-lined Figures^ if we compare each of them 
 K. \r!th
 
 ( 194 ) 
 
 wjth fome Square whofe Area is known, and 
 find the one exactly equal to it, and the other 
 lefs by a Square-Inch, we immediately conclude 
 that the Area of the firft Figure is a Square Inch 
 greater than that of the fecond. This manner 
 of determining the Relation between any two 
 Ideas, by the Invention of fome third with which 
 they may be compared, is that which we call 
 Reasoning t and indeed the chief Inftrument, by 
 which we pulh on our Difcoveries, and enlarge 
 our Knowledge. The great Art lies, in finding 
 out fuch intermediate Ideas, as when compared 
 with the others in the Queftion, will furnifh evi- 
 dent and known Truths, becaufe, as will after- 
 wards appear, it is only by means of them, that 
 we arrive at the Knowledge of what is hidden 
 and remote. 
 
 III. FROM what has been faid it 
 
 7 be Partf 
 
 'that eonfiitute appears, that every Act of Reafon^ 
 f fie -' j ing neceflarily includes three dif- / 
 
 J\QJGnit]g Afid O J 
 
 a Syllogijm. tinct Judgments j two, wherein the 
 Ideas, whofe Relation we want to difcover, are 
 feverally compared with the middle Idea, and 
 a third, wherein they are themfelves connected 
 or disjoined according to the Refult of that Com- 
 parifon. Now as in the fecond Part of Logick, 
 our Judgments when put into Words were cal- 
 led Propofitions, fo here in the third Part, the 
 Expreflions of our Reafonings are termed Syllo- 
 gifms. And hence it follows, that as every Act 
 
 of
 
 ( 195 ) 
 
 of Reafoning implies three feveral Judgments, 
 fo every Syllogifm muft include three diftinft 
 Propofitions. When a Reafoning is thus put 
 into Words, and appears in Form of a Syllogifm, 
 the intermediate Idea made ufe of to difcover 
 the Agreement or Difagreement we fearch for, 
 is called the middle Term ; and the two Ideas 
 themfelves, with which this third is compared, 
 go by the Name of the Extremes. 
 
 IV. BUT as thefe things are beft T ,. 
 
 , Inftanct, Matt 
 
 illuftrated by Examples ; let us, for and Actount- 
 inftance, fet ourfelves to enquire, 
 whether Men are accountable for their Actions. As 
 the Relation between the Ideas of Man and Ac- 
 count ablenefs comes not within the immediate 
 View of the Mind, our firft Care muft be, to find 
 out fome third Idea, that will enable us the 
 more eafily to difcover and trace it. A very 
 imall Meafure of Reflection is fufficient to in- 
 form us, that no Creature can be accountable 
 for his Actions, unlefs we fuppofe him capable 
 of diftinguifhing the good from the bad ; that 
 is, unlefs we fuppofe him poflefled of Reafon. 
 Nor is this alone fufficient. For what would 
 it avail him to know good from bad Actions, if 
 he had no Freedom of Choice, nor could avoid 
 the one, and purfue the other ? Hence it be- 
 comes neceflary to take in both Confederations 
 in the prefent Cafe. It is at the fame Time equally 
 apparent, that wherever there is this Ability of 
 K 2 diitinguilhing
 
 ( 196 ) 
 
 diftittguifhing good from bad A&ions, and pur- 
 fuing the one and avoiding the other, there alfo 
 a Creature is accountable. We have then got a 
 third Idea, with which Accountablenefi is infepa- 
 r ably connected, viz, Reafon and Liberty; which 
 are here to be confidered as making up one com- 
 plex Conception. Let us now take this middle 
 Idea, and compare it with the other Term in 
 the Queftion, viz. Man^ and we all know by 
 Experience that it may be affirmed of him. Hav- 
 ing thus by means of the intermediate Idea form- 
 ed two feveral Judgments, viz. that Man is pof- 
 fejjed of Reafon and Liberty ; and that Reafun and 
 Liberty imply Acccuntablenefs ; a third obvioufly 
 and neceffarily follows, viz. that Man is accoun- 
 table for his dtfions. Here then we have a com- 
 plete At of Reafoning, in which, according to 
 what has been already obferved, there are three 
 diftindt Judgments j two that may be ftiled pre- 
 vious, inafmuch as they lead to the other, and 
 arife from comparing the middle Idea with 
 the two Ideas in the Queflion : the third is a Con- 
 fequence of thefe previous Acts, and flows from 
 combining the extreme Ideas between them- 
 felves. If now we put this Reafoning into Words, 
 it exhibits what Logicians term a Syllogifm, 
 and when propofed in due Form, runs thus : 
 
 Every Creature pojj'ej/ed of Reafon and Liberty is 
 accountable for his Aftions. 
 
 Man is a Creature poj/ejftd of Reafin and Liberty. 
 
 There-
 
 ( 197 ) 
 
 Therefore Man is accountable for his. 
 V. IN this Syllogifm we may ob- Premife^ 
 ierve, that there are three fcveral JjjJjJ" 1 
 Propofitions, exprefling the three miiidieTtrm. 
 Judgments implied in the Act of Reafoning, and 
 fo difpofed, as to reprefent diftin&ly what pafles 
 within the Mind, in tracing the more diftant Re- 
 lations of its Ideas. The two firft Propofitions 
 anfwer the two previous Judgments in Reafon- 
 ing, and are called the Premifes^ becaufe they are 
 placed before the other. The third is termed the 
 Conclufiori) as being gained in confequence of 
 what was afTerted in the Premifes. We are alfo 
 to remember, that the Terms exprefling the 
 two Ideas whofe Relation we enquire after, as 
 here Man and Accountablenefs^ are in general cal- 
 led the Extremes', and that the intermediate Idea, 
 by means of which the Relation is traced, viz. 
 A Creature pojjejjed of Reafon and Liberty , takes 
 the Name of the middle Term. Hence it follows, 
 that by the Premifes of a Syllogifm, we are al- 
 ways to underftand the two Propofitions, where 
 the middle Term is feverally compared with Ex- 
 tremes ; for thefe conftitute the previous Judg- 
 ments, whence the Truth we are in queft of 
 is by Reafoning deduced. The Condujion is that 
 other Propofition, in which the Extremes them- 
 felves are joined or feparated, agreeably to what 
 appears upon the above Comparifon. All this 
 is evidently feen in the foregoing Syllogifm, 
 K 3 where
 
 where the two firft Propositions which reprefcnt 
 the Premifes, and the third' that makes the Con- 
 clufion, are exactly agreeable to the Definitions 
 here given. 
 ,. , VI. BEFORE we take leave of 
 
 Major and 
 
 Mimr Term, this Article, it will be farther nccef- 
 Mwr "pro- f" ar y to obferve, that as th Conclu- 
 fo/itio*. f lon i s mac ] e * U p O f the extreme 
 
 Terms of the Syllogifm, fo that Extreme, which 
 ferves as the Predicate of the Conclufion, goes 
 by the Name of the Majir Term : the other Ex- 
 treme, which makes the Subject in the fame 
 Propofition, is called the Minor Term. From 
 this Diftinction of the Extremes, arifes alfo a 
 Diftindtion between the Premifes where thefe 
 Extremes are feverally compared with the mid- 
 dle Term. That Propofition which compares 
 the greater Extreme, or the Predicate of the Con- 
 clufion, with the middle Term, is called the 
 Major Propofition : the other, wherein the fame 
 middle Term is compared with the Subject of the 
 Conclufion, or lefler Extreme, is called the Mi- 
 nor Propofition. All this is obvious from the Syl- 
 logifm already given, where the Conclufion is 
 Man is accountable for his rfttwns.. For here the 
 Predicate Accountable for his Acliom, being con- 
 nected with the middle Term in the firft of the 
 two Premifes ; Every Creature pojjeffed of Reafon 
 *nd Liberty is accountable for his Aft'ions^ gives 
 what we call the Major Propofition. In the fe- 
 
 cond
 
 ( 199 ) 
 
 cond of the Premifes ; Man is a Creature psjfijf- 
 ed of Reafon and Liberty ', we find the lefler Ex- 
 treme, or Subject of the Cpnclufion, viz. fifarr, 
 connected with the fame middle Term, whence 
 it is known to be the Minor Proportion, I (hall 
 only add, that when a Syllogifm is propofed in 
 due Form, the Major Proportion is always placed 
 firft, the Minor next, and the Concluiion lair, ac- 
 cording as we have done in that offered above. 
 VII. HAVING thus cleared the ~ ; 
 
 Judgment and 
 
 Way, by explaining iuch Terms, as Propa/itien, 
 
 IM i L r c Reifaniaf and 
 
 we are likely to have occafion for fyfoif t Jip. 
 in the Progrefs of this Treatife ; it tUgntpa. 
 may not be amifs to obferve, that tho' we have; 
 carefully diftinguimed between the Aft of Reafon- 
 ing) and a Syllogifm, which is no more than the 
 Expreffion of it, yet common Language is not 
 fo critical on this Head ; the Term Reafoning be- 
 ing promifcuoufly ufed to fignify, either the 
 Judgments of the Mind as they follow one an- 
 other in Train, or the Propofitions exprefling 
 thefe Judgments. Nor need we wonder that it 
 is fo, inafmuch as our Ideas, and the Terms ap- 
 propriated to them, are fo connected by Habit and 
 Ufe, that our Thoughts fall as it were fpontane- 
 oufly into Language, as faft as they arife in the 
 Mind j fo that even in our Reafonings within 
 ourfelves, we are not able wholly to laid afide 
 Words. But notwithftanding this ftricT: Con- 
 nection between mental and verbal Reafoning, if 
 K 4 1 may
 
 ( 200 ) 
 
 I may be allowed that Expreflion, J thought' it 
 needful here to diftinguifh them, in order to 
 give a juft Idea of the manner of deducing on* 
 Truth from another. While the Mind keeps 
 the Ideas of Things in view, and combines its 
 Judgments according to the real Evidence at- 
 tending them, there is no great Danger of Mif- 
 take in our Reafonings, becaufe we carry our 
 Conclufions no farther than the Clearnefs of our 
 Perceptions warrants us. But where we make 
 ufe of Words, the Cafe is often dtherwife ; no- 
 thing being more common than to let them pals 
 y/ithout attending to the Ideas they reprefent 5 
 infomuch that we frequently combine Expreflions 
 which upon Examination appear to have no de- 
 terminate Meaning. Hence it greatly imports 
 us to diftinguifh between Reafoning and Syllo- 
 gifm j and to take care that the one be in all 
 Cafes th true and juft Reprefentation of the 
 other. However, as I am unwilling to recede 
 too far from the common forms of Speech, or 
 to multiply Diftin&ions without Necefiity, I 
 fhall henceforward confider Propofitions as re- 
 prefenting the real Judgments of the Mind, and 
 Syllogifms as the true Copies of our Reafonings ; 
 which indeed they ought always to be, and un- 
 doubtedly always will be, to Men who think 
 juftly, and are defirous of arriving at Truth. 
 Upon this Suppofition there will be no Danger 
 in ufing the Words Judgment and Propofnion 
 
 promifcuoufly ;
 
 ( 201 ) 
 
 promifcuoufly ; or in confidering Reafoning as 
 either a Combination of various Judgments, or 
 of the Proportions exprefiing them; becaufe 
 being the exacT: Copies one of another, the 
 Refult will be in all Cafes the fame. Nor is it 
 a fmalt Advantage that we can thus conform 
 to common Speech, without confounding our 
 Ideas, or running into Ambiguity. By this 
 means we bring ourfelves upon a Level with 
 other Men, readily apprehend the Meaning of 
 their ExprefTions, and can with Eafe convey 
 our own Notions and Sentiments into their 
 Minds. 
 
 VIII. THESE things premifed, 
 
 u u D r l**fiKle 
 
 we may in the general define Reafon- An of Rea- 
 
 ing, to be an Al or Operation of the ^f mujl 
 Mind^ deducing fame unknown Pro- ^ intuit ivt 
 
 r . V , Trutbt. 
 
 p^itton^ from other previous ones that 
 ate evident and known. Tbefe previous Propo- 
 fitrons, in a fimple Act of Reafoning, are only 
 two in Number j #nd it is always required that 
 they be of themfelves apparent to the Under- 
 ftanding, infomuch that we a/lent to and per- 
 ceive the Truth of them as foon as propofed. In 
 the Syllogifm given above, the Premifes are 
 fuppofed to be felf-evident Truths, otherwife 
 the Conclufion could not be inferred by a fingle 
 Acl of Reafoning. If, for inftance, in the Ma- 
 jor, Every Creature pojjejjed of Reafon and Liber- 
 ty is accountable for his Ati'ion^ the Connection 
 K 5 between
 
 ( 202 ) 
 
 between the Subject and Predicate could nof 
 be perceived by a bare Attention to the Ideas 
 themfelves ; it is evident, that this Propofition 
 would no lefs require a Proof, than the Conclu- 
 fion deduced from it. In this Cafe a new mid- 
 dle Term muft be fought for, to trace the Con- 
 nection here fuppofed ; and this of courfe fur- 
 nifhes another Syllogifm, by which having efta- 
 blifhed the Propofition in queftion, we are then, 
 and not before, at liberty to ufe it in any fuc- 
 ceeding Train of Reafoning. And fhould it fo 
 happen that in this fecond Eflay, there was ftill 
 fome previous Propofition whofe Turn did not 
 appear at firft Sight; we muft then have recourfe 
 to a third Syllogifm, in order to lay open that 
 Truth to the Mind ; becaufe fo long as the Pre- 
 mifes remain uncertain, the Conclufion built 
 upon them muft be fo too. When by conduct- 
 ing our Thoughts in this Manner, we at laft 
 arrive at fome Syllogifm, where the previous 
 Propofitions are intuitive Truths; the Mind 
 then refts in full Security, as perceiving that the 
 feveral Conclufions it has pafled through, ftand 
 upon the immoveable Foundation of Self-evi- 
 dence, and when traced to their Source termi- 
 nate in it. 
 
 Rfafon'mg in IX. WE fee therefore, that in or- 
 t k, tigbtfl der to infer a Conclufion by a fingle 
 
 Extrcije oj tt, 1 
 
 tr.ty a Coma- A&of Reafoning, the Premifesmuft 
 
 be 
 
 1O
 
 be intuitive Proportions. Where tension f 
 they are not, previous Syllogifms are $%#* 
 required, in which Cafe Reafoning becomes a 
 complicated Acl, taking in a Variety of fuccefllve 
 Steps. This frequently happens in tracing the 
 more remote Relations of our Ideas, where many 
 middle Terms being called in, the Conclufion 
 cannot be made out, but in confequence of a 
 Series of Syllogifms following one another in 
 Train. But although in this Concatenation of 
 Propofitions, thofe that form the Premifes of 
 the laft Syllogifm, are often considerably re- 
 moved from Self-evidence j yet if we trace the 
 Reafoning backwards, we fhall find them the 
 Conclufions of previous Syllogifms, whofe 
 Premifes approach nearer and nearer to In- 
 tuition, in proportion as we advance, and 
 are found at laft to terminate in it. And if 
 after having thus unravelled a Demonftration, 
 we take it the contrary way j and obferve 
 how the Mind, fetting out with intuitive Per- 
 ceptions, couples them together to form a 
 Conclufion j how by introducing this Conclu- 
 fion into another Syllogifm, it ftill advances 
 one Step farther ; and fo proceeds, making 
 every new Difcovery fubfervient to its future 
 Progrefs ; we fhall then perceive clearly, that 
 Reafoning, in the higheft Exercife of that Fa- 
 culty, is no more than an orderly Combina- 
 tion of thofe fimple Acts, which we have al- 
 K 6 ready
 
 ( 204 ) 
 
 ready fo fully explained. The great Art lies, in 
 fo adj ufting our Syllogifms one to another, that 
 the Proportions feverally made ufe of as Premifes, 
 may be manifeft Confluences of what goes be- 
 fore. For as by this means, every Conclufion is 
 deduced from known and eftablifhed Truths, the 
 *ery laft in the Series, how far foever we carry it, 
 will have no lefs Certainty attending it, than the 
 original intuitive Perceptions themfelves, in which 
 the wkole Chain of Syllogifms takes its Rife. 
 
 we fee that 
 
 '*''*" c<r - beginning with firft Principles, rifes 
 
 tatnty in tvery fc 
 
 ftepoftte gradually from one Judgment to 
 Progrtfo*. another> and connecls them in fuch 
 Manner, that every Stage of the Progreflion 
 brings intuitive Certainty along with it. And 
 now at length we may clearly underftand the 
 Definition given above of this diftinguifhing 
 Faculty of the human Mind. Reafon we have 
 faid is the Ability of deducing unknown Truths 
 from Principles or Propofitions that are already 
 known. This evidently appears by the fore- 
 going Account, where we fee, that no Propo- 
 fition is admitted into a Syllogifm, to ferve as 
 one of the previous Judgments on which the 
 Conclufion refts, unlefs it is itfelf a known and 
 eftablifhed Truth, whofe Connection with felf- 
 evident Principles has been already traced. 
 Stlf-eviJent ^CI. THERE is yet another Obfer- 
 fmtbt, tbt yation which naturally offers itfelf, 
 
 in
 
 in confequence of the above Detail ; ultimate 
 viz. that all the Knowledge acquired ^-"^ 
 by Reafoning, how far foever we Certainty, 
 carry our Difcoveries, is ftill built upon our intui- 
 tive Perceptions. Towards the End of the laft 
 Part we divided Proportions into felf-evident 
 and demonftrable, and reprefented thofe of the 
 felf-evident Kind, as the Foundation on which 
 the whole Superftru&ure of human Science 
 refted. This Do&rine is now abundantly con- 
 firmed by what has been delivered in the prefent 
 Chapter. We have found that every Difcovery 
 of human Reafon, is the Confequence of a Train 
 of Syllogifms, which when traced to their 
 Source, always terminate in felf-evident Per* 
 ceptions. When the Mind arrives at thefe pri- 
 mitive Truths, it purfues not its Enquiries far- 
 ther, as well knowing, that no Evidence can 
 exceed that which flows from an immediate 
 View of the Agreement or Difagreement be- 
 tween its Ideas. And hence- it is, that in unra- 
 velling any Part of Knowledge, in order to 
 come at the Foundation on which it ftands ; 
 intuitive Truths are always the laft Refort 
 of the Underftanding, beyond which it aims 
 not to advance, but poflefles its Notions in 
 perfect Security, as having now reached the 
 very Spring and Fountain of all Science and 
 Certainty. 
 
 CHAP-
 
 ( 206 ) 
 
 CHAP. II. 
 
 Of the fever al Kinds of Reafcningj and fir ft 
 of that ly which we determine the Genera 
 and Species of things. 
 
 ig I. *\ TT 7"E have endeavoured in the 
 t^o. yy f ore g i n g Chapter to give 
 
 as diftinft a Notion as poffible of Reafoning, 
 and of the Manner in which it is conduced. 
 Let us now enquire a little into the Difcoverics 
 made by this Faculty, and what thofe Ends are, 
 which we have principally in View in the Ex- 
 crcife of it. All the Aims of human Reafon 
 may in the general be reduced to thefe two : 
 I. To rank Things under thofe univerfal Ideas 
 to which they truly belong ; and 2. To afcribc 
 to them their leveral Attributes and Properties 
 in confequence of that Diftribution. 
 The frji Kind H. FIRST, then I fay, that one 
 regards tie great Aim of human Reafon is, to 
 
 Centra and 
 
 Species of determine the Genera and Species 
 Thing,. of Things. We have feen in the 
 
 firft Part of this Treatife, how the Mind pro- 
 ceeds in framing general Ideas. We have alfo 
 feen in the fecond Part, how by Means of thefe 
 general Ideas, we come by univerfal Propofi- 
 tions. Now as in thefe univerfal Proportions, 
 we affirm fome Property of a Genus or Species, 
 
 it
 
 ( 207 ) 
 
 it is plain, that we cannot apply this Property 
 to particular Objects, till we have firft deter- 
 mined, whether they are comprehended under 
 that general Idea, of which the Property is af- 
 firmed. Thus there are certain Properties be- 
 longing to all even Numbers, which neverthelefs 
 cannot be applied to any particular Number, 
 until we have firft difcovered it to be of the Spe- 
 cies exprefled by that general Name. Hence 
 Reafoning begins with referring Things to their 
 feveral Divifions and ClafTes in the Scale of our 
 Ideas 3 and as thefe Divifions are all diftinguifhed 
 by peculiar Names, we hereby learn to apply the 
 Terms exprefung general Conceptions, to fuch 
 particular Objects, as come under our immediate 
 Obfervation. 
 
 III. Now in order to arrive at ne Stefl ly 
 
 thefe Conclufions, by which the 
 
 . rive at Can- 
 
 feveral Objects of Perception are ciufons of tint 
 brought under general Names, two Sort ' 
 Things are manifeftly neceflary. Firft, that we 
 take a View of the Idea itfelf denoted by that ge- 
 neral Name, and carefully attend to the diftin- 
 guifhing Marks which ferve to characterize it. 
 Secondly, that we compare this Idea with the 
 Obje6l under Confideration, obferving diligently 
 wherein they agree or differ. If the Idea is found 
 to correfpond with the particular Object, we 
 then without Hefitation apply the general N^me; 
 but if no fuch Correfpondence intervenes, the 
 
 Conclu-
 
 ( 208 ) 
 
 Onclufion muft neceflarily take a contrary 
 Turn. Let us, for Inftance, take the Number 
 Eighty and confider by what fteps we are led to 
 pronounce it an even Number. Firft then we call 
 to mind the Idea fignified by the Expreflion an 
 even Number, viz. that it is a Number diviftble 
 into two equal Parts. We then compare this Idea 
 with the Number Eight^ and finding them ma- 
 nifeftly to agree, fee at once the Neceflity of ad- 
 mitting the Conclufion. Thefe feveral Judg- 
 ments therefore, transferred into Language, and 
 reduced to the Form of a Syllogifm, appear thus : 
 
 Every Number that may be divided Into two 
 tqual Parti Is an EVEN Number. 
 
 The Number EIGHT may be divided Into two 
 equal Parts. 
 
 Therefore the Number "EiGHT is an EVEN 
 Number. 
 
 IV. I HAVE made Choice of this 
 
 Theft Sups al- 
 
 iio&yifaiio-uitd, Example, not fo much for the Sake 
 L/MW**" of the Conclufion, which is obvious 
 always attend enough, and might have been ob- 
 tained without all that Parade of 
 Words j but chiefly becaufe it is of eafy Compre- 
 henfion, and ferves at the fame time diftinctly to 
 exhibit the Form of Reafoning by which the 
 Underftanding conduces itfelf in all Inftances 
 of this Kind. And here it may be obferved, that 
 where the general Idea, to which particular Ob- 
 jects are referred, is very familiar to the Mind, 
 
 and
 
 ( 209 ) 
 
 and frequently in View; this Reference, and 
 the Application of the general Name, feem to 
 be made without any Apparatus of Reafoning. 
 When we fee a Horfe in the Fields, or a Dog 
 in the Street, we readily apply the Name of the 
 Species ; Habit, and a familiar Acquaintance 
 with the general Idea, fuggefting it inflantane- 
 oufly to the Mind. We are not however to ima- 
 gine on this Account, that the Underftanding 
 departs from the ufual Rules of juft Thinking. 
 A frequent Repetition of Acts begets a Habit; 
 and Habits are attended with a certain Prompt- 
 nefs of Execution, that prevents our obferving 
 the feveral Steps and Gradations by which any 
 Courfe of A3ion is accomplifhed. But in other 
 Inftances, where we judge not by pre-contra&ed 
 Habits, as when the general Idea is very com- 
 plex, or lefs familiar to the Mind; we always 
 proceed according to the Form of Reafoning 
 eflablifhed above. A Goldfmith, for Inftance, 
 who is in doubt as to any Piece of Metal, whe- 
 ther it be of the Species called Gold; fir ft exa- 
 mines its Properties, and then comparing them 
 with the general Idea fignified by that Name, 
 if he finds a perfect Correfpondence, no longer 
 hefitates under what Clafs of Metals to rank it. 
 Now what is this, but following Step by Step 
 thofe Rules of Reafoning, which we have be- 
 fore laid down as the Standards, by which to 
 
 regulate
 
 ( 210 ) 
 
 regulate our Thoughts in all Conclufions of this 
 kind? 
 
 Tbtgrtat Im- V. NOR let it be imagined, that 
 r""btf- tb " our Refearches here, becaufe in Ap- 
 R<ajomng. pearance bounded to the impofmg of 
 general Names upon particular Objedts, art 
 therefore trivial and of little Confequence. 
 Some of the moft confiderable Debates among 
 Mankind, and fuch too as nearly regard their 
 Lives, Ifltereft, and Happinefs, turn wholly upon 
 this Article. Is it not the chief Employment 
 of our feveral Courts of Judicature, to deter- 
 mine in particular Inftances, what is Law, Juf- 
 tice, and Equity? Of what Importance is it in 
 many Cafes, to decide aright, whether an Action 
 fliall be termed Murder or Manflaughter? We 
 fee that no lefs than the Lives and Fortunes of 
 Men depend often upon thefe Decifions. The 
 Reafon is plain. Actions when once referred to 
 a general Idea, draw after them all that may 
 be affirmed of that Idea ; infomuch that the de- 
 termining the Species of Actions, is all one with 
 determining what Proportion of Praife or Dif- 
 praife, Commendation or Blame, &c. ought to 
 follow them. For as it is allowed that Murder 
 deferves Death, by bringing any particular Ac- 
 tion under the Head of Murder, we of courfe 
 decide the Punifhment due to it. 
 
 VI. BUT
 
 ( 211 ) 
 
 VI. BUT the great Importance Andtbcexaa 
 f this Branch of Reafoning, and 0'fw" f 
 
 L XT n~ n " fttffid h 
 
 the Neceffity of Care and Circum- M^b^.afi- 
 fpech'on, in referring particular Ob- '"""' 
 jecls to general Ideas, is ftill farther evident from 
 the Practice of the Mathematicians. Every one 
 who has read Euclid knows, that he frequently 
 requires us to draw Lines thro' certain Points, 
 and according to fuch and fuch Directions. 
 The Figures thence. refulting are often Squares, 
 Parallelograms, or Rectangles. Yet Euclid ne- 
 ver fuppofes this from their bare Appearance, 
 but always demonftrates it upon the ftridteft 
 Principles of Geometry. Nor is the Method he 
 takes in any thing different from that defcribed 
 above. Thus, for Inftance, having defined a 
 Square to be a Figure bounded by four equal 
 Sides, joined together at right Angles - 3 when 
 fuch a Figure arifes in any Conftruciion previous 
 to the Demonftration of a Proportion, he yet 
 never calls it by that Name, until he has fhewn 
 that the Sides are equal, and all its Angles right 
 ones. Now this is apparently the fame Form of 
 Reafoning we have before exhibited, in proving 
 Eight to be an even Number ; as will be evident 
 to any one who reduces it into a regular Syl- 
 logifm. I (hall only add v that when Euclid has 
 thus determined the Species of any Figure, he. 
 is then, and not before, at Liberty to afcribe to 
 it all the Properties already demonftrated of that 
 
 Figure,
 
 ( 212 ) 
 
 Figure, and thereby render it fubfervient to the 
 future Courfe of his Reaftming. 
 
 VII. HAVING thus fufficiently 
 
 Fixed and in- * 
 
 explained the Rules by which we 
 a re to conduct ourielves, in ranking 
 particular Obiccls under general 
 
 tbii Part of J 
 
 Ideas, and fticwn their Conformity 
 
 a " d ^ the Plaice and Manner of the 
 Mathematicians ; it remains only to 
 obferve, that the true Way of rendering this Part 
 of Knowledge both eafy and certain, is ; by ha- 
 bituating ourfelves to clear and determinate 
 Ideas, and keeping them fteadily annexed to 
 their refpedlive Names. For as all our Aim is, 
 to apply general Words aright; if thefe Words 
 fland for invariable Ideas, that are perfectly 
 known to the Mind, and can be readily diftin- 
 guiflied upon Occafion, there will be little 
 Danger of Miftake or Error in our Reafonings. 
 Let us fuppofe that by examining any Object, 
 and carrying our Attention fucceflively from 
 one Part to another, we have acquainted our- 
 felves with the feveral Particulars obfervable in 
 it. If among thefe we find fuch as conflitute 
 fome general Idea, framed and fettled before- 
 hand by the Understanding, and diftinguifhed 
 by a particular Name j the Refemblance thus 
 known and perceived, neceflarily determines 
 the Species of the Object, and thereby gives 
 ft a Right to the Name by which that Species
 
 is called. Thus four equal Sides, joined toge- 
 ther at right Angles, 'make up the Notion of 
 a Square. As this is a fixed and invariable Idea, 
 without which the general Name cannot be 
 applied, we never call any particular Figure a 
 Square, until it appears to have thefe feverai 
 Conditions j and contrarily, wherever a Figure 
 i-s found with thefe Conditions, it neceflarily 
 takes the Name of a Square. The fame will be 
 found to hold in all our other Reafonings of this 
 Kind ; where nothing can create any Difficulty 
 but the Want of fettled Ideas. If for inftance 
 we have not determined within ourfelves, the pie- 
 cife Notion denoted by the Word Manjlaugh- 
 ter ; it will be impoflible for us to decide, whe- 
 ther any particular Action ought to bear that 
 Name: becaufe however nicely we examine the 
 Action itfelf, yet being Strangers to the general 
 Idea with which it is to be compared, we are 
 utterly unable to judge of their Agreement or 
 Difagreement. But if we take Care to remove 
 this Obftacle, and diftinclly trace the two Ideas 
 under Confideration, all Difficulties vanifti, and 
 the Refolution becomes both eafy and certain. 
 VIII. THUS we fee of what Im- gyfueb a 
 portance it is, towards the Improve- Co ^ dui t Cer- 
 
 7 fainty and Di- 
 
 ment and Certainty of human 
 Knowledge, that we accuftom our-
 
 f 214 ) 
 
 traduced ht felves to clear and determinate Ideas, 
 
 ether Parti of 
 
 Knowledge at and a fteady Application of Words. 
 tbtmaticks. Nor is this fo eafy a Tafk as fome may 
 perhaps be apt to imagine ; it requiring both a 
 comprehenfive Understanding, and great Com- 
 mand of Attention, to fettle the precife Bounds 
 of our Ideas, when they grow to be very com- 
 plex, and include a Multitude of Particulars. 
 Nay, and after thefe Limits are duly fixed, there 
 is a certain Quicknefs of Thought and Extent 
 of Mind required, towards keeping the feveral 
 Parts in View, that in comparing our Ideas one 
 .with another, none of them may be overlooked. 
 .Yet ought not thefe Difficulties to difcourage us', 
 tho' great they are not unfurmountable, and the 
 Advantages ajifing from Succefs will amply re- 
 compenfe our Toil, The Certainty and eafjr 
 Application of Mathematical Knowledge is 
 \vholly owing to the exa& Obfervance of this 
 Rule. And I am apt to imagine, that if we were 
 to employ the fame Care about all our other 
 Ideas, as Mathematicians have done about thofe 
 of Number and Magnitude, by forming them 
 into exact Combinations, and diftinguifhing 
 thefe Combinations by particular Names, in or- 
 der to keep them fteady and invariable ; we 
 fhould foon have it in our Power to introduce 
 Certainty and Demonftration into other Parts of 
 human Knowledge. 
 
 CHAP,
 
 CHAP. III. 
 
 Of Reafoning) as it regards the Powers and 
 Properties of Things, and the Relations of 
 our general Ideas. 
 
 "T T T 
 
 VV 
 
 I. 
 
 great End which Men 
 have in View in their Reafonings, regard* tt 
 
 , i i-r i r Sciences* and 
 
 namely ; the difcovenng and af- as k concerm 
 cribing to Things their feveral Attri- com>non L 'f e ' 
 butes and Properties. And here it will be necef- 
 fary to diftinguifh between Reafoning, as it re- 
 gards the Sciences, and as it concerns common 
 Life. In the Sciences, our Reafon is employed 
 chiefly about univerfal Truths, it being by them 
 alone that the Bounds of human Knowledge are 
 enlarged. Hence the Divifion of Things into 
 various Clafles, called otherwife Genera and 
 Species. For thefe univerfal Ideas, being fet up 
 as the Reprefentatives of many particular Things, 
 whatever is affirmed of them, may be alfo affirm- 
 ed of all the Individuals to which they belong. 
 Murder for Inftance is a general Idea, reprefent- 
 ing a certain Species of human Actions. Reafon 
 tells us, that the Puniftiment due to it is Death. 
 Hence every particular Action coming under the 
 Notion of Murder, has the Punifhment of Death 
 
 allotted
 
 allotted to it. Here then we apply the general 
 Truth to fome obvious Inftance, and this is what 
 properly conftitutes the Reafoning of common 
 Life. For Men, in their ordinary Tranfadtions 
 and Intercourfe one with another, have for the 
 moft part to do only with particular Objects. 
 Our Friends and Relations, their Characters and 
 Behaviours, the Conftitution of the feveral Bodies 
 that furround us, and the Ufes to which they 
 may be applied, are what chiefly engage our At- 
 tention. In all thefe we reafon about particular 
 Things ; and the whole Refult of our Reafonin:; 
 is, the applying the general Truths of the Sci- 
 ences to the ordinary Tranfadtions of human 
 Life. When we fee a Viper, we avoid it. 
 Wherever we have Occafion for the forcible -Ac- 
 tion of Water, to move a Body that makes con- 
 fiderable Refinance, we take care to convey it in 
 fuch a Manner, that it (hall fall upon the Object 
 with Impetuofity. Now all this happens, in 
 confcquence of our familiar and ready Applica- 
 tion of thefe two general Truths : Ibe Bite of a 
 Viper is mortal : Water falling upon a Body with 
 Impetuofity t affs very forcibly towards fetting It in 
 Motion. In like Manner, if we fet ourfelves to 
 confider any particular Character, in order to 
 determine the Share of Praife or Difpraife that 
 belongs to it, our great Concern is, to afcertain 
 exactly the Proportion of Virtue and Vice. The 
 
 Reafon
 
 Reafon is obvious. A juft Determination in all 
 Cafes of this kind depends intirely upon an Ap- 
 plication of thefe general Maxims of Morality : 
 Virtuous Allans deferve Praife : Vicious A ft ions 
 deferve Blame. 
 
 II.- HENCE it appears, that Rea- rte Steps by 
 foning, as it regards common Life. wA/fAw^ra- 
 
 J teed in the Rea- 
 
 is no more than the afcribing the fining of - 
 general Properties of Things to thofe "'" L ' fc ' 
 feveral Objects with which we are immediately 
 concerned, according as they are found to be of 
 that particular Divifion or Clafs to which the 
 Properties belong. The Steps then by which 
 we proceed are manifeftly thefe. Firft we refer 
 the Object under Confideration to fome general 
 Idea or Clafs of Things. We then recollect the 
 feveral Attributes of that general Idea. And, 
 laftly, afcribe all thofe Attributes to the prefent 
 Object. Thus irt confidering the Character of 
 Sempronius, if we find it to be of the Kind called 
 Virtuous ; when we at the fame Time reflect, that 
 a virtuous Character is deferving of Efteem, it 
 naturally and obvioufly follows, that Sempronius 
 is fo too. Thefe Thoughts put into a Syllogifm y 
 in order to exhibit the Form of Reafoning here 
 required, run thus : 
 
 Every virtuous Man is worthy of EJleem. 
 SEMPRONIUS is a virtuous Man: 
 Thtrefort SEMPRONIUS is worthy of EJleem. 
 
 L III. BY
 
 III. BY this Syllosrifm it appear*, 
 
 tffiM . , f ' ' y ,. f 
 
 - that before we affirm any Thing of a 
 jtT ' particular Objeft, that Object muft 
 jirancbei of be referred to fome general Idea. 
 
 Reafoninv one r , c 
 
 ufmanoibtr. Sempromusis pronounced worthy of 
 Efteem, only in Confequence of his 
 being a virtuous Man, or coming under that ge- 
 neral Notion. Hence we fee the neceflary Con- 
 nection of the various Parts of Reafoning, and 
 the Dependence they have one upon another. 
 The determining the Genera and Species of 
 Things is, as we have faid, one Exercife of hu- 
 man Reafon ; and here we find that this Exer- 
 cife is the firft in Order, and previous to the 
 other, which confifts in afcribing to them their 
 Powers, Properties, and Relations. But when we 
 have taken this previous Step, and brought par- 
 ticular Objects under general Names ; as the Pro- 
 perties we afcribe to them are no other than thole 
 of the general Idea, it is plain, that in order to a 
 fuccefsful Progrefs in this Part of Knowledge, 
 we muft thoroughly .acquaint ourfelves with the 
 feveral Relations and Attributes of thefe our ge- 
 neral Ideas. When this is done, the other Part 
 will be eafy, and require fcarce any Labour of 
 Thought, as being no more than an Application 
 of the general Form of Reafoning reprefented in 
 the foregoing Syllogifm. Now as we have already 
 fufficiently (hewn, how we are to proceed in de- 
 termining
 
 tertnining the Genera and Species of Things, 
 which as we have faid is the previous Step to this 
 fecond Branch of human Knowledge; all that 
 is farther wanting to a due Explanation of it is, 
 to offer fome Confiderations, as to the Manner ' 
 of inveftigating the general Relations of our 
 Ideas. This is the higheft Exercife of the Pow- 
 ers of the Underftanding, and that by means 
 whereof, we arrive at the Difcovery of univerfal 
 Truths ; infomuch that our Deductions in this 
 Way conftitute that particular Species of Rea- 
 foning which we have before faid regards princi- 
 pally the Sciences, 
 
 IV. BUT that we may conduct 
 our Thoughts with fome Order and required t* 
 Method, we fliall begin with obferv- makf "S ^ 
 
 Reajoncr. 
 
 ing, that the Relations of our gene- 
 ral Ideas are of two Kinds. Either fuch as im- 
 mediately difcover themfelves, upon comparing 
 the Ideas one with another ; or fuch, as being 
 more remote and diftant, require Art.and Con- 
 trivance to bring them into View. The Rela- 
 tions of the firft Kind, furnifh us with intuitive 
 and felf-evident Truths : thofe of the fecond are 
 traced by Reafoning, and a due Application of 
 intermediate Ideas, It is of this laft Kind that 
 we are to fpeak here, having difpatched what 
 was neceflary with regard to the other in the 
 fecond Part. As therefore in tracing the more 
 diftant Relations of\ Things, we muil always 
 L 2 have
 
 ( 220 ) 
 
 have recourfe to intervening Ideas, and are more 
 or lefs fuccefsful in our Refearches, according to 
 our Acquaintance with thefe Ideas, and Abi- 
 lity of applying them ; it is evident, that to 
 make a good Rcafoner, two Things are princi- 
 pally required. Fir/t, an extenfive Knowledge 
 of thofe intermediate Ideas by means of which 
 Things may be compared one with another. Sc- 
 fondly^ the Skill and Talent of applying them 
 happily, in all particular Inftances that come 
 under Confideration. 
 
 F,rfl, an ex- V. FIRST I fay, that in order to 
 JEJrJjJJ: our fuccefsful Progrefs in Reafoning, 
 median Ideas, we muft have an extenfive Know- 
 ledge of thofe intermediate Ideas, by means of 
 which Things may be compared one with ano- 
 ther. For as it is not every Idea that will an- 
 fwer the Purpofe of our Enquiries, but fuch only 
 as are peculiarly related to the Objects about 
 which we reafon, fo as by a Comparifon with 
 them, to furnifh evident and known Truths j 
 nothing is more apparent, than that the greater 
 Variety of Conceptions we can call into View, 
 the more likely we are to find fome among them 
 that will help us to the Truths here required. 
 And indeed it is found to hold in Experience, 
 that in Proportion as we enlarge our View of 
 Things, and grow acquainted with a Multitude 
 of different Objects, the Reafoning Faculty ga- 
 thers Strength. For by extending our Sphere 
 
 of
 
 of Knowledge, the Mind acquires a certain 
 Force and Penetration, as being accuflomed 
 to examine the feveral Appearances of its Ideas, 
 and obferve what Light they caft one upon ano- 
 ther. 
 
 VI. AND this I take to be the Rea- TO txceli* 
 fon, that in order to excel remark- a ^ a " b O f 
 ably in any one Branch of Learning, Learning we 
 
 _. in wft bt i 
 
 it is neceflary.to have at leait a gene- nera iac- 
 
 ral Acquaintance with the whole f " 
 
 ,~\ n TM ' 
 
 Circle of Arts and Sciences. The c\,deofArtt 
 Truth of it is, all the various Divl- " /5f '- 
 fions of human Knowledge are very nearly re- 
 lated among thcmfelves, and in innumerable Tn- 
 ftances ferve to illuitrate and fet off each other, 
 And altho' it is not to be denied, that by an ob- 
 ftinate Application to one Branch of Study, a 
 Man may make considerable Progrefs, and ac- 
 quire fo me Degree of Eminence in it; yet his 
 Views will be always narrow and contracted, 
 and he will want that rnafterly Difcernment 
 which not only enables us to purfue our Difco- 
 veries with Eafe, but alfo in laying them open to 
 others, to fpread a certain Brightnefs around 
 them. I would not however here be underftood 
 to mean, that a general Knowledge alone is fuf- 
 ficient for all the Purpofes of Reafoning. I only 
 recommend it as proper to give the Mind a cer- 
 tain Sagacity and Quicknefs, and qualify it for 
 L 3 judging
 
 ( 222 ) 
 
 judging aright in the ordinary Occurrences of 
 Life. But when our Reafoning regards a parti- 
 cular Science, it is farther necefTary that we 
 more nearly acquaint ourfelves with whatever 
 relates to that Science. A general Knowledge 
 is a good Preparation, and enables us to proceed 
 with Eafe and Expedition in whatever Branch 
 of Learning we apply to. But then in the mi- 
 nute and intricate Queftions of any Science, we 
 are by no means qualified to reafon with Advan- 
 tage, until we have perfectly mattered the Science 
 to which they belong- ft being hence chiefly 
 tf>?.t -^e are furnifhed with thofe intermediate 
 Ideas, which lead to a juft and fuccefsful Solu- 
 tion. 
 
 WbyMubt- VII. AND here, as it comes fo 
 matieians naturally in my Way, I cannot 
 
 (onetimes an- __ . .~, 
 
 fv>e r rot the avoid taking Notice of an Obferva- 
 
 Expttfation t ; on ^t is frequently to be met 
 
 tbetr great * 
 
 Learning with, and feems to carry in it at 
 firft Sight fomething very ftrange 
 and unaccountable. It is in fliort this, that 
 Mathematician^ even fuch as are allowed to ex- 
 cel in their own Profeffion, and to have difco^ 
 vered themfelves perfect Matters in the Art of 
 Reafoning, have not yet been always happy in 
 treating upon other Subjects ; but rather fallen 
 fhort, not only of what might naturally have 
 been expe&ed from them, but of many Writers 
 much kfs exercifed in the Rules of Argumen- 
 
 tation.
 
 ( 223 ) 
 
 tation. This will not appear fo very extraor- 
 dinary, if we reflect on what has been hinted 
 above. Maihtmaticks is an engaging Study, and 
 Men who apply themfelves that Way, fo wholly 
 plunge into it, that they are for the mod part 
 but little acquainted with other Branches of 
 Knowledge. When therefore they quit their 
 favourite Subject, and enter upon others that 
 are in a manner new and ftrange to them, no 
 wonder if they find their Invention at a Stand. 
 Becaufe however perfect they may be in the Art 
 of Reafoning, yet wanting here thofe interme- 
 diate Ideas which are neceflary to furnifli out 
 a due Train of Proportions, all their Skill and 
 Ability fails them. For a bare Knowledge of *( 
 the Rules is not fufficbnt. We muft farther 
 have Materials whereunto to apply them. And 
 when thefe are once obtained, then it is that an 
 able Reafoner difcovers his Superiority, by the 
 juft Choice he makes, and a certain mafterly 
 Difpofition, that in every Step of the Procedure 
 carries Evidence and Conviction along with it. 
 And hence it is, that fuch Mathematicians as 
 have of late Years applied themfelves to other 
 Sciences, and not contented with a fuperficial 
 Knowledge, endeavoured to reach their inmoft 
 Recefies ; fuch Mathematicians, I fay, have by 
 mere Strength of Mind,, and a happy Applica- 
 tion of Geometrical Reafoning, carried their Dif- 
 coveries far beyond what was heretofore judged 
 LA the
 
 ( 224 ) 
 
 the utmoft Limits of human Knowledge. This 
 is a Truth abundantly known to all who arc 
 acquainted with the late wonderful Improve-* 
 ments in Natural Philofophy. 
 
 Secondly, ttt VIIl.IcoME now to the fccond 
 
 */// 4>W/- 
 
 i*g intermediate 1 hing required, in order to a fuccefs- 
 
 f^X? ful Pro f efs in Reafoning, namely ; 
 IrfaKctt. the Skill and Talent of applying 
 
 intermediate Ideas happily in all particular In- 
 llances that come under Confideration. And 
 here I {hall not take up much Time in laying 
 down Rules and Precepts, becaufe I am apt to 
 think they would do but little Service. Ufe and 
 Zxercife are the beft Inftru&ors in the prefent 
 Cafe: and whatever Logicians may boaft, of 
 being able to form perfect Reafoners by Book 
 and Rule, yet we find by Experience, that the 
 Study of their Precepts does not always add any 
 great Degree of Strength to the Underftanding. 
 In fliort, 'tis the Habit alone of Reafoning that 
 makes a Reafoner. And therefore the true Way 
 to acquire this Talent is, by being much con- 
 verfant in thofe Sciences where the Art of 
 Reafoning is allowed to reign in the greateft 
 Perfection. Hence it was that the Ancients, 
 who fo well understood the Manner of forming 
 the Mind, always began with Matbematicks as 
 the Foundation of their Philofophical Studies. 
 Here the Underftanding is by Degrees habituat- 
 ed to Truth, contrails infenfibly a certain Fond- 
 
 efs
 
 ( s ) 
 
 nefs for it, ad karns never to yield its AfTent to 
 any Propofition but where the Evidence is fuf- 
 ficient to produce full Conviction* For this 
 Reafon Plato has called Mathematical Demon- 
 firations the Catharticks or Purgatives of the Soul, 
 as being the proper Means to cleanfe it from 
 Error, and reftore that natural Exercife of its 
 Faculties in which juft Thinking confifts. And 
 indeed I believe it will be readily allowed, that 
 no Science furnifhes fo many Inftances of a happy 
 Choice of intermediate Ideas, and a dexterous 
 Application of them, for the Difcovery of Truth 
 and Enlargement of Knowledge. 
 
 IX. IF therefore we would form The Study of 
 
 .... T T i / T / Mathematical 
 
 our Minds to a Habit of Keafoning Dtmonftra- 
 clofelv and in train,, we cannot take '''"' fg r * a t 
 
 f . ' Avail t* tbtt 
 
 any more certain Method, than the refpee-. 
 cxercifing ourfelves in Mathematical 
 Demonftrations, fo as to contract a kind of Fa- 
 miliarity with them, " Not that we look upon 
 " it as neceflary, (to ufe the Words of the great 
 " Mr. Locke) that all Men fhould be deep 
 " Mathematicians, but that, having got the 
 " Way of Reafoning which that Study necefla- 
 " rily brings the Mind to, they may be able to 
 " transfer it to other Parts of Knowledge, as 
 ** they fhall have Occafion. For in all forts of 
 '* Reafoning, every fingle Argument fhould 
 " be managed as a Mathematical Demonftra- 
 ** tion, the Connection and Dependence of 
 L 5 ? Idea*
 
 ( 226 ) 
 
 " Ideas fhould be followed, till the Mind is 
 " brought to the Source on which it bottoms, 
 " and can trace the Coherence through the 
 " whole Train of Proofs. It is in the general 
 " obfervable, that the Faculties of our Souls are 
 " improved and made ufeful to us juft after the 
 " fame manner as our Bodies are. Would you 
 " have a Man write or paint, dance or fence 
 " well, or perform any other manual Operation, 
 " dexteroufly and with Eafe ? Let him have ever 
 " fo much Vigour and Activity, Supplenefs and 
 *' Addrefs naturally, yet nobody expects this 
 " from him unlefs he has been ufed to it, and 
 " has employed Time and Pains in fafliioning 
 ** and forming his Hand, or outward Parts, to 
 thefe Motions. Juft fo it is in the Mind ; 
 " would you have a Man reafon well, you mud 
 " ufe him to it betimes, exercife his Mind in 
 " obferving the Connection of Ideas, and fol- 
 " lowing them in train. Nothing does this 
 " better than Mathematicks ; which therefore 
 '* I think fhould be taught all thofe, who have 
 ** the Time and Opportunity, not fo much 
 " to make them Mathematicians, as to make 
 *' them reafonable Creatures ; for though we 
 " all call ourfelves fo, becaufe we are born to 
 * it, if we pleafe ; yet we may truly fay, Na- 
 " ture gives us but the Seeds of it. We are born 
 " to be, if we pleafe, rational Creatures ; but 
 * 'tis Ufe and Exercife only that makes us fo, 
 
 "and
 
 f 227 ) 
 
 * and we are indeed fo, no farther than Induftry, ^ 
 " and Application has carried us." Conduft of 
 the Under/landing* 
 
 X. BUT although the Study of ^ ta if of 
 Mathematicks be of all others the >'* J*"* 8 ? 
 
 en other Ou0- 
 
 moir. ufeful to form the Mind and jeffi, as are 
 
 i T> 1-/1. r T u L diftlnguifhed- 
 
 give it an early Relifh of Truth, yet j / tre j ttg[b 
 Gus:ht not other Parts of Philofophy a d J^S* 
 
 T? L ir fteajni'ig. 
 
 to be neglected, tor there alfo we 
 meet with many Opportunities of exercifing the 
 Powers of the Underftandingj and the Variety 
 of Subjects naturally leads- us to obferve all thofe 
 different Turns of Thinking that are peculiarly 
 adapted to the feveral Ideas we examine,, and the- 
 Truths we fearch, after. A Mind thus trained, 
 acquires a certain Maftery over its own 
 Thoughts, infomuch that it can range and mo- 
 del them at pleafure,. and call fuch into View 
 as befl fuit its prefent Defigns. Now in this, 
 the whole Art of Reafoning confifts, from a 
 mong a great Variety of different Ideas to fingle- 
 out thofe that are moft proper for the BufinefSf 
 in hand r and to lay them together in fuch Or-r 
 der, that from plain and eafy Beginnings, byr 
 gentle Degrees, and a continual Train of evi-: 
 dent Truths, we may be infenftbly led. on to 
 fuch Difcoveries, as at our firft fetting out ap- 
 peared beyond the Reach of the human Under 
 ftanding. For this purpofe, befides the Study 
 L 6 oS
 
 ( "8 ) 
 
 of Mathematicks before recommended, we ought 
 to apply ourfelves diligently to the reading of 
 fuch Authors as have diftinguilhed themfelves 
 for Strength of Reafoning, and a juft and ac- 
 curate Manner of Thinking. For it is obferv- 
 able, that a Mind exercifed and feafoned to Truth 
 feldom refts fatisfied in a bare Contempla- 
 tion of the Arguments offered by others, but 
 will be frequently eflaying its own Strength, and 
 purfuing its Difcoveries upon the Plan it is moft 
 accuftomed to. Thus we infenfibly contract a 
 Habit of tracing Truth from one Stage to ano- 
 ther, and of inveftigating thofe general Rela- 
 tions and Properties which we afterwards af- 
 cribe to particular Things, according as we find 
 them comprehended under the abftracl: Ideas to 
 which the Properties belong. And thus having 
 particularly fhewn how we are to diftribute the 
 feveral Objects of Nature under general Ideas^ 
 what Properties we are to afcribe to them in 
 confequence of that Diftribution, and how to- 
 trace and inveftigate the Properties themfelves j 
 I think I have fufficiently explained all that is 
 neceflary towards a due Conception of Reafon- 
 ing, and {hall therefore here conclude this 
 Chapter. 
 
 CHAP.
 
 CHAP. IV. 
 
 Of the Forms of Syllogifmt. 
 
 H 1 
 
 tented ourfelves with age- g mtt 
 neral Notion of Syllogifms, and of 
 the Parts of which they confift. It is now time 
 to enter a little more particularly into the Sub- 
 ject, to examine their various Forms, and to lay 
 open the Rules of Argumentation proper to each. 
 In the Syllogifms mentioned in the foregoing 
 Chapters, we may obferve that the middle Term 
 is the Subject of the Major Propofition, and the 
 Predicate of the Minor. This Difpofition, tho' 
 the moft natural and obvious, is not however 
 neceflary ; it frequently happening, that the 
 middle Term is the Subject in both the Premifes, 
 or the Predicate in both ; and fometimes di- 
 rectly contrary to its Difpofition in the forego- 
 ing Chapters, the Predicate in the Major, and 
 the Subject in the Minor. Hence the Diftindtion 
 of Syllogifms into various kinds, called Figures 
 by Logicians. For Figure, according to their 
 Ufe of the Word, is nothing elfe but the Order 
 and Difpofition of the middle Term in any Syl- 
 logifm. And as this Difpofition is we fee four- 
 fold, fo the Figures of Syllogifms thence arifing 
 are four in Number. When the middle Term
 
 C 
 
 Is the Subject of the Major Proportion, and the 
 Predicate of the Minor, we have what is called 
 thej?r/? Figure. If on the other hand, it is the 
 Predicate of both the Premifes, the Syllogifm is 
 faid to be in tbe fecond Figure. Again, in the 
 third FigurejFmj middle Term is the fubjeft of 
 the two Premifes. And laftly, by making it the 
 Predicate of the Major, and Subject of the Minor, 
 we obtain Syllogifms in the fourth Figure. 
 
 of U- BUT befides this fourfold Dif- 
 tinction of Syllogifrns, there is alfo 
 a farther Subdivifion of them in every Figure, 
 arifing from the n<antity and Quality as they are 
 called of the Propofitions. By Quantity we mean 
 the Confederation of Propofitions as univerfal or 
 particular, by ghiality as affirmative or negative. 
 Now as in all the feveral Difpofitions of the mid- 
 dle Term, the Propofitions of which a Syllogifm 
 confifts may be either univerfal or particular, 
 affirmative or negative; the due Determination 
 of thefe, and fo putting them together as the 
 Laws of Argumentation require, conftitute what 
 Logicians call the Moods of Syllogifms. Of 
 thefe Moods there are a determinate Number to 
 every Figure, including all the poflible Ways in 
 which Propofitions differing in Quantity or Dua- 
 lity can be -combined, according to any Difpofi- 
 tion of the middle Term, in order to arrive at a 
 juft Conclufion. The Shortnefs of the prefent 
 
 Work
 
 Work will not allow of entering into a more 
 particular Defcription of thefe feveral Diftinc- 
 tions and Divifions. I fhall therefore content 
 myfelf, with referring the Reader to the Port- 
 Royal Art of thinking^ where he will find the 
 Moods and Figures of Syllogifms diftinctly ex- 
 plained, and the Rules proper to each very neatly 
 demonstrated. 
 
 III. THE Divifion of Syllogifms Foundation of 
 according to Mood and Figure, re- laAH" " 
 
 fpefts thofe efpecially, which are 
 known by the Name of plain fimple Syllogifms j 
 that is, which are bounded to three Proportions, 
 all fimple, and where the Extremes and middle 
 Term is connected, according to the Rules laid 
 down above. But as the Mind is not tied down 
 to any one precife Form of Reafoning, but fome- 
 times makes ufe of more, fometimes of fewer 
 Premifes, and often takes in compound and con- 
 ditional Proportions, it may not be amifs to take 
 notice of the different Forms derived from this 
 Source, and explain the Rules by which the 
 Mind conducts itfelf in the ufe of them. 
 
 IV. WHEN in any Syllogifm, the Conditional ' 
 Major is a conditional Propofition, Syikg\fmi. 
 the Syllogifm itfelf is .termed Conditional. Thus: 
 
 If there is a God^ he ought to be wor flipped.. 
 
 But there is a God: 
 
 Therefore he ought to be worflipped. 

 
 ( 232 } 
 
 In this Example, the Major or firft Propofifion, 
 is we fee conditional, and therefore the Syllo- 
 gifm itfelf is alfo of the kind called by that 
 Name. And here we are to obferve, that all 
 conditional Propofitions are made up of two 
 diftincl Parts; one expreffing the Condition- 
 upon which the Predicate agrees or difagrees 
 with the Subject:, as in this now before us, if 
 there is a God; the other joining or disjoining 
 the faid Predicate and Subject, as here, he ought 
 to be worjhipped. The firft of thefe Parts, or that 
 wlv'-h implies the Condition, is called the An~ 
 tecedent; the fecond r where we j.oin or disjoia 
 the Predicate and Subject,, has the Name of 
 the Confequent. 
 
 V. THESE Things explained, we 
 are farther to obferve; that in all 
 Proportions of thia kind, fuppofmg 
 them to be exact in point of Form, the Relation 
 between the Antecedent and Confequent muft 
 ever be true and real ; that is, the Antecedent 
 muft always contain fome certain and genuine 
 Condition,, which neceflarily implies the Con- 
 fequent : for otherwife, the Propofition itfelf 
 witt be falfe, and therefore ought not to be ad- 
 mitted into our Reafonings. Hence it follows, 
 that when any conditional Propofition is aflumed, 
 if we admit the Antecedent of that Propofition, 
 we muft at the feme time neceiTarily admit the 
 
 Confe-
 
 ( 233 ) 
 
 Confequent ; but if we reject the Confequent, 
 we are in like manner bound to rejecl alfo the 
 Antecedent. For as the Antecedent always ex- 
 prefles fome Condition which neceflarily im- 
 plies the Truth of the Confequent ; by admit- 
 ting the Antecedent we allow of that Condition, 
 and therefore ought alfo to admit the Confe- 
 quent. In like manner if it appears that the 
 Confequent ought to be rejected, the Antece- 
 dent evidently muft be fo too; becaufe as we 
 juft now demonftrated, the admitting of the An- 
 tecedent would neceflarily imply the Admiflion 
 alfo of the Confequent. 
 
 VI. FROM what has been faid it , 
 
 The fwo 
 
 appears, that there are two Ways of Af/>di of 
 arguing in hypothetical Syllogifms, *Jg 
 which lead to a certain and un- 
 avoidable Conclufion. For as the Major is 
 always a conditional Propofition, confiding of 
 an Antecedent and a Confequent j if the Minor 
 admits the Antecedent, it is plain that the Con- 
 clufion muft admit the Confequent. This is 
 - called arguing from the Admiflion of the Ante- 
 cedent to the Admiflion of the Confequent, and 
 onftitutes that Mood or Species of hypothetical 
 Syllogifms, which is diftinguiflied in the Schools 
 by the Name of the Modus ponens, inafmuch as 
 by it the whole conditional Propofition, both 
 Antecedent and Confequent, is eftablifhed. 
 Thus:
 
 If God is infinitely wife, and afis with perfitf 
 
 Freedom, he does nothing but what is beji. 
 But God is infinitely wife, and afls with per- 
 
 fefl Freedom : 
 
 Therefore he does nothing but what is be/I. 
 Here we fee the Antecedent or firft Part of 
 the conditional Propofition is eftablifhed in the 
 Minor, and the Confequent or fecond Part in 
 the Conclusion ; whence the Syllogifm itfelf is 
 an Example of the Modus ponens. But if now 
 we on the contrary fuppofe, that the Minor re- 
 jects the Confequent, then it is apparent, that 
 the Conclufion muft alfo rejedl: the Antecedent. 
 In this Cafe we are faid to argue from the Re- 
 moval of the Confequent, to the Removal of 
 the Antecedent, and the particular Mood or 
 Species of Syllogifms thence arifing is called by 
 Logicians the Modus tollens j becaufe in it, both 
 Antecedent and Confequent are rejected or taken 
 away, as appears by the following Example : 
 If Gcd were not a Being of infinite Goodnefs r 
 neither would he canfult the Happinefs of 
 his Creatures, 
 But God does confuh the Happinefs of his 
 
 Creatures : 
 
 Therefore he is a Being of infinite Goodnefe. 
 Delude VII. THESE two Species take in 
 
 the whole Cbfs of ""M" 1 Syl- 
 logifms, and include all the poflible 
 Ways of arguing that lead to a legitimate Con- 
 clufion j
 
 ( 235 ) 
 
 clulion ; becaufe we cannot here proceed by a 
 contrary Procefs of Reaibning, that is, from 
 the Removal of the Antecedent to the Removal 
 of the Confequenr, or from the eftablifhing of 
 the Confequent to the eftablifhing of the Ante- 
 cedent. For altho* the Antecedent always ex- 
 prefles fome real Condition, which once ad- 
 mitted neceflarily implies the Confequent, yet it 
 does not follow that there is therefore no other 
 Condition ; and if fo, then after removing the 
 Antecedent, the Confequent may fti)l hold, be- 
 caufe of fome other Determination that infers it. 
 When we fay : If a Stone is expo fed fome time tit 
 the Rays of the Sun> it will contra ff a certain De- 
 gree of Heat j the Propofition is certainly true, 
 and admitting the Antecedent, we muft alfo ad- 
 mit the Confequent. But as there are other 
 Ways by which a Stone may gather Heat, it 
 will not follow, from the ceafing of the befope- 
 mentioned Condition, that therefore the Confe- 
 quent cannot take place. In other Words, we 
 cannot argue, But the Stone has not been expo fed 
 to the Rays of the Sun ; therefore neither has it ar.y 
 Degree of Heat ; inafmuch as there are a great 
 many other Ways by which Heat might have 
 been communicated to it. And if we cannot 
 argue from the Removal of the Antecedent to 
 the Removal of the Confequent, no more can 
 we from the Admiffion of the Confequent to the 
 
 Admiffion
 
 Admiflion of the Antecedent. Becaufe as the 
 Confequent may flow from a great Variety of 
 different Suppofitions, the allowing of it does 
 not determine the precife Suppofition, but only 
 that fome one of them muft take place. Thus 
 in the foregoing Propofttion, If a Stone is ex- 
 pofed fome time to the Rays of the Sun, it will con- 
 tra fi a certain Degree of Heat : Admitting the 
 Confequent, viz. that it has contrasted a certain 
 Degree of Heat, we are not therefore bound to 
 admit the Antecedent, that it has been fome time 
 expofed to the Rays of the Sun j becaufe there are 
 many other Caufes whence that Heat may have 
 proceeded. Thefe two ways of arguing there- 
 fore hold not in conditional Syllogifms. Indeed, 
 where the Antecedent exprefles the only Condi- 
 tion on which the Confequent takes place, there 
 they may be applied with Safety ; becaufe where- 
 ever that Condition is not, we are fure that 
 neither can the Confequent be, and fo may ar- 
 gue from the Removal of the one to the Removal 
 of the other ; as on the contrary, wherever the 
 Confequent holds, it is certain that the Condi- 
 tion muft alfo take place; which ihews, that 
 by eftablifhing the Confequent, we at the fame 
 time efbblifii the Antecedent. But as it is a 
 very particular Cafe, and that happens but fcl- 
 dom, it cannot be extended into a general Rule, 
 and therefore affords not any fteady and univer- 
 
 fal
 
 ( 237 ) 
 
 fal Ground of Reafoning upon the two foregoing 
 Suppositions. 
 
 VIII. As from the Major's being 
 
 ... . n ,, . J . . Tbt M.nr.tr 
 
 a conditional Propohtion, we obtain O f arguing in 
 the Species of conditional Syllo- 
 
 . . ... 
 
 gifms ; fo where it is a disjunctive 
 Proportion, the Syllogifm to which it belongs is 
 called disjunctive, as in the following Example : 
 
 The World is either f elf- exijlent, or the Work 
 of fame finite ^ or of fame infinite Being. 
 
 But it is not felf-exijlent, nor the Work of a 
 finite Being : 
 
 Therefore it is the Work of an infinite Being. 
 Now a disjunctive Proportion is that where 
 of feveral Predicates we affirm one neceflarily 
 to belong to the Subject, to the Exclufion of 
 all the reft, but leave that particular one unde- 
 termined. Hence it follows, that as foon as 
 we determine the particular Predicate, all the 
 reft are of courfe to be rejected; or if we rejecl 
 all the Predicates but one, that one neceflarily 
 takes place. When therefore in a disjunctive 
 Syllogifm, the feveral Predicates are enumerated 
 in the Major ; if the Minor eftablifhes any one 
 of thefe Predicates, the Conclufion ought to 
 remove all the reft j or if in the Minor, all the 
 Predicates but one are removed, the Conclufion 
 muft necefTarily eftablifh that one. Thus in 
 the disjunctive Syllogifm given above, the 
 Major affirms one of three Predicates to belong 
 
 to
 
 to the Earth, viz. Self-exiftence, or that it is 
 the Work of a finite, or that it is the Work of an 
 infinite Being. Two of thefe Predicates are re- 
 moved in the Minor , viz. Self-exijlence, and 
 the Work of a finite Being. Hence the Conclu- 
 fion neceflarily afcribes to it the third Predicate, 
 and affirms that it is the Work of an infinite Being. 
 If now we give the Syllogiihi another Turn, 
 infomuch that the Minor may eftablifli one of 
 the Predicates, by affirming the Earth to be 
 the Production of an infinite Being ; then the 
 Conclufion muft remove the other two, afTert- 
 ing it to be neither felf-exijlent^ nor the Work of 
 a finite Being. Thefe are the Forms of Reafon- 
 ing in this Species of Syllogifms, the Juftnefs 
 of which appears at firft Sight ; and that there 
 can be no other, is evident from the very Nature 
 of a disjunctive Propofition. 
 ImperfcEi or I^f. * N tne feveral Kinds of Syl- 
 logifms hitherto mentioned, we 
 may obferve, that the Parts are 
 complete ; that is, the three Propofitions of 
 which they confift are reprefented in Form. 
 But it often happens, that fome one of the Pre- 
 mifes is not only an evident Truth, but alfo fa- 
 miliar and in the Minds of all Men ; in which 
 Cafe it is ufually omitted, whereby we have an 
 imperfect Syllogifm, that feems to be made up of 
 only two Propofitions. Should we, for inftance, 
 argue in this manner : 
 
 Every
 
 ( 239 ) 
 
 Every Man is mortal ; 
 
 Therefore -every King is mortal ; 
 the Syllogifm appears to be imperfect, as confifr- 
 ing but of two Propofitions. Yet it is really 
 complete, only the Minor [Every King is a Man] 
 is omitted, and left to the Reader to fupply, as 
 being a Proportion fo familiar and evident, that 
 it cannot efcape him. 
 
 X. THESE feemingly imperfect 
 
 p 11 -r ~ 11 j r- 7 Entbymtmct. 
 
 byllognms are called knthymemes, 
 and occur very frequently in Reafoning, efpe- 
 cially where it makes a Part of common. Con- 
 verfation. Nay, there is a particular Elegance 
 in them, becaufe not difplaying the Argument 
 in all its Parts, they leave fomewhat to the 
 Exercife and Invention of the Mind. By this 
 means we are put upon exerting ourfelves, and 
 feem to (hare in the Difcovery of what is pro- 
 pofed to us. Now this is the great Secret of 
 fine Writing, fo to frame and put together our 
 Thoughts, as to give full Play to the Reader's 
 Imagination, and draw him infenfibly into our 
 very Views and Courfe of Reafoning. This 
 gives a Pleafure not unlike to that which the 
 Author himfelf feels in compofmg. It befides 
 fhortens Difcourfe, and adds a certain Force 
 and Livelinefs to our Arguments, when the 
 Words in which they are conveyed, favour the 
 natural Quicknefs of the Mind in its Opera- 
 tions, 
 8
 
 lions, and a fingle Expreflion is left to exhibit a 
 whole Train of Thoughts. 
 
 XI. BUT there is another Spe- 
 
 Ground of , 
 
 Reajtning in cies of Reafonmg with two Propo- 
 immeaiatt fitions, which feems to be complete 
 
 Conftfutncei. 
 
 in itfelf, and where we admit the 
 Conclufion, without fuppofing any tacit or fup- 
 prefled Judgment in the Mind, from which it 
 follows fyllogiflically. This happens between 
 Propofitions where the Connexion is fuch, that 
 the Admifiion of the one, neceflarily, and at 
 the firft fight, implies the Admiflion alfo of the 
 other. For if it fo falls out, that the Propofi- 
 tion on which the other depends is felf-evident, 
 we content ourfelves with barely affirming it, 
 and infer that other by a direcl: Conclufion. 
 Thus by admitting an univerfal Propofition, we 
 are forced alfo to admit of all the particular Pro- 
 pofitions comprehended under it, this being the 
 very Condition that conftitutes a Propofition 
 univerfal. If then that univerfal Propofition 
 chances to be felf-evident, the particular ones 
 follow of courfe, without any farther Train of 
 Reafoning. Whoever allows, for inftance, that 
 Things equal to one and the fame Thing are equal 
 to one another^ muft at the fame time allow, that 
 two Triangle j, each equal to a Square wbofe Side 
 is three Inches^ are alfo equal between thernfelves* 
 This Argument therefore, 
 
 Things
 
 Things equal to one and the fame Tiring^ are 
 
 equal to one another j 
 Therefore thofe two Triangles, each equal to the 
 
 Square of a Line of three Inches , are equal 
 
 between themfelves j 
 
 is complete in its Kind, and contains all that is 
 neceflary towards a juft and legitimate Conclu- 
 fion. For the firft or univerfal Propofition is 
 felf-evident, and therefore requires no farther 
 Proof. And as the Truth of the Particular is 
 infeparably connected with that of the Univer- 
 fal, it follows from it by an obvious and una- 
 voidable Confequence. 
 
 XII. Now in all Cafes of this Alindutittt 
 kind where Proportions are deduc- to fjlhgifm* 
 
 ofjomt one 
 
 ed one from another, on account of Form or ether. 
 a known and evident Connection, we are faid 
 to reafoa by immediate Confequence. Such a Co- 
 herence of Propofitions, manifeft at firft fight, 
 and forcing itfelf upon the Mind, frequently 
 occurs in Reafoning. Logicians have explained 
 at fome length, the feveral Suppofitions upon 
 which it takes place, and allow of all immediate 
 Conferences that follow in Conformity to them. 
 It is however obfervable, that thefe Arguments, 
 though feemingly complete, becaufe the Con- 
 clufion follows necelTarily from the fingle Pro- 
 pofition that goes before, may yet be confidered 
 as real Enthymemes, whofe Major, which is a 
 conditional Propofition, is wanting. The Syl- 
 M logifm
 
 loglfm but juft mentioned, when reprefented ac- 
 cording to this View, will run as follows : 
 
 If Things equal to one and the fame Tiring are 
 
 equal to one another ; thefe two Triangles, 
 
 each equal to a Square whofe Side is three 
 
 Inches, are alfo equal between themfelves. 
 
 But Things equal to one and the fame Thing, 
 
 are equal to one another ; 
 Therefore alfo thefe Triangles, &c. are equal 
 
 between themfelves. 
 
 This Obfervation will be found to hold in all 
 immediate Confequences whatfoever, infomuch that 
 they are in fa& no more than Enthymemes of hy- 
 pothetical Syllogifms. But then it is particular 
 to them, that the Ground on which the Conclu- 
 fion refts, namely, its Coherence with the Minor, 
 is of itfelf apparent, and feen immediately to flow 
 from the Rules and Reafons of Logick. As 
 it is therefore intirely unneceflary to exprefs a 
 felf-evident Connection, the Major, whofe Office 
 that is, is conftantly omitted} nay, and feems 
 fo very little needful to enforce the Conclufion, 
 as to be accounted commonly no Part of the Ar- 
 gument at all. It muft indeed be owned, that 
 the foregoing immediate Consequence might have 
 been reduced to zfimple, as well as an hypothetical 
 Syllogifm. This will be evident to any one who 
 gives himfelf the Trouble to make the Experi- 
 ment. But it is not my Defign to enter farther 
 
 into
 
 ( 243 ) 
 
 into thefe Niceties, what has been faid fufficing 
 to fhew, that all Arguments confiding of but 
 two Propofitions are real Entbymemes, and redu- 
 cible to complete Syllogtfms of fome one Form 
 or other. As therefore the Ground on which 
 the Conclufion refts, muft needs be always the 
 fame with that of the Syllogifms to which they be- 
 long, we have here an univerfal Criterion, whereby 
 at all times to afcertain the Juftnefs and Validity 
 of our Reafonings in this Way. 
 XIII. The next Species of Rea- 
 
 A Sontes of 
 foning we (hall take notice of here 5 plain fimpic 
 
 is what is commonly known by the 3 'S'J ms 
 Name of a Sorites. This is a Way of arguing, 
 in which a great Number of Propofitions are for 
 linked together, that the Predicate of one be- 
 comes continually the Subject of the next follow- 
 ing, until at laft a Conclufion is formed, by 
 bringing together the Subject of the firft Propo- 
 fition and the Predicate of the laft. Of this kind 
 is the following Argument : 
 God is omnipotent. 
 
 An omnipotent Being can do every thing pojjlble. 
 He that can do every thing pojfible, can da 
 
 whatever involves not a Contradiction : 
 Therefore Goo' can do whatever Involves not a 
 
 Contradiction. 
 
 This particular Combination of Propofitions 
 
 may be continued to any Length we pleafe, 
 
 M z with-
 
 > ( 244 )' 
 
 without in the leaft weakening the Ground up- 
 on which the Conclufion refts. The Rcafon is, 
 becaufe the Sorites itfelf may be refolved into as 
 many fimple Syllogifms as there are middle 
 Terms in it j where this is found univerfally to 
 hold, that when fuch a Refolution is made, and 
 the Syllogifms are placed in train, the Conclu- 
 fion of the laft in the Series is alfo the Conclu- 
 fion of the Sorites. This kind of Argument there- 
 fore, as it ferves to unite feveral Syllogifms into 
 one, muft ftand upon the fame Foundation with 
 the Syllogifms of which it confilrs, and is in- 
 deed, properly fpeaking, no other than a com- 
 pendious Way of Reafoning fyllogiftically. Any 
 one may be fatisfied of this at Pleafure, if he but 
 takes the Trouble of refolving the foregoing 
 Sorites into two diftindt Syllogifms. For he 
 will there find, that he arrives at the fame Con- 
 clufion, and that too by the very fame Train of 
 thinking, but with abundantly more Words, 
 and the Addition of two fuperfluous Propofi- 
 tions. 
 . c . e XIV. WHAT is here faid of 
 
 A Sorttei of 
 
 hypothetical plain fimple Propofitions, may be 
 well applied to thofe that are con- 
 ditional ; that is, any Number of them may be 
 fo joined together in a Series, that the Con- 
 fcquent of one, fhall become continually the 
 Antecedent of the next following j in which 
 Cafe, by eftablifliing the Antecedent of the firit 
 
 8 Fro-
 
 ( 245 ) 
 
 Propofition, we eftablifh the Confequent of the 
 laft, or by removing the laft Confequent, remove 
 alfo the firft Antecedent. This Way of Rea- 
 foning is exemplified in the following Argu- 
 ment : 
 
 If we love any Per fan, all Emotions of Hatred 
 
 towards him ceafe. 
 
 If all Emotions of Hatred towards a Perfott 
 ceafe j ^ve cannot rejoice in his Misfortunes* 
 If we rejoice not in his Misfortunes, we cer- 
 tainly wijb him no Injury, 
 llwefore if we love a^ P erf on, we wijh him 
 
 no Injury. 
 
 It is evident that this Sorites, as well as the laft, 
 may be refolved into a Series of diftincl Syllo- 
 gifms, with this only Difference, that here the 
 Syllogifms are all conditional. But as the Con- 
 clufion of the laft Syllogifm in the Series is the 
 fame with the Concluflon of the Sorites, it is 
 plain, that this alfo is a compendious Way of 
 Reafoning, whofe Evidence arifes from the Evi- 
 dence of the feveral fingle Syllogifms into which 
 it may be refolved. 
 
 XV. I COME now to that kind of ,, _ . _ 
 
 The Ground of 
 
 Argument which Logicians call In- Reafoning by 
 
 . . . / L i_ TT Indufiioit* 
 
 duftion ; m order to the right Un- 
 derftanding of which, it will be neceflary to ob- 
 ferve, that our general Ideas are for the moft 
 part capable of various Subdivifions. Thus the 
 Idea of the loweft Species may be fubdivided 
 M into
 
 into its feveral Individuals ; the Idea of any 
 Genus, into the different Species it compre- 
 hends; and fo of the reft. If then we fuppofc 
 this Diftribution to be duly made, and fo as to 
 take in the whole Extent of the Idea to which 
 it belongs; then it is plain, that all the Sub- 
 divifions or Parts of any Idea taken together 
 conftitute that whole Idea. Thus the feveral 
 Individuals of any Species taken together con- 
 ftitute the whole Species, and all the various 
 Species comprehended under any Genus, make 
 up the v/hole Genus. This being allowed, it is 
 apparent, that whatfoever may be affirmed of all 
 the feveral Subdivifions and ClafTes of any Idea, 
 ought to be affirmed of the whole general Idea to 
 which thefe Subdivifions belong. What may 
 be affirmed of all the Individuals of any Species, 
 may be affirmed of the whole Species ; and what 
 may be affirmed of all trie Species of any Genus, 
 may alfo be affirmed of the whole Genus ; be- 
 caufe all the Individuals taken together, are the 
 fame with the Species, and all the Species taken 
 together, the fame with the Genus. 
 
 XVI. THIS Way of arguing 
 
 The Form and . . r . r .. 
 
 Sirufiurt of where we infer umverially concern- 
 t* ?$"*' in? any Idea, what we had before 
 
 ty laaufiiin. z> J 
 
 affirmed or denied feparately, of all 
 its feveral Subdivifions and Parts, is called Rea- 
 foning by Induction. Thus if we fuppofe the 
 whole Tribe of Animals, fubdivided into Men, 
 
 Beafts,
 
 ( 247 ) 
 
 Eeafts, Birds, Infe&s, and Fifties, and then- rea- 
 fon concerning them after this Manner : AH 
 Mtn Jiave a Power of beginning Motion ; all Beafts, 
 Birds, and Infefis, have a Power of beginning Mo- 
 tion j all Fijhes have a Power of 'beginning Motion ; 
 therefore all Animals have a Power of beginning 
 Motion : The Argument is an Induttion. When 
 the Subdivisions are juft, fo as to take in the 
 whole general Idea, and the Enumeration is 
 perfect, that is, extends to all and every of the 
 inferior Clafles or Parts ; there the Induction is 
 complete, and the manner of Reafoning by In- 
 duftion is apparently concluilve. 
 
 XVII. THE laft Species of Syl- Tit Ground 
 logifms I fhall take notice of in this t y?~ 
 Chapter, is that commonly diftin- Dilemma. 
 guilhed by the Name of a Dilemma. A Dilemma 
 is an Argument by which we endeavour to 
 prove the Abfurdity or Falfehood of fome Afler- 
 tion. In order to this we aflame a conditional 
 Propofition; the Antecedent of which is the Af- 
 fertion to be difproved and the Confequent a 
 disjunctive Propofition, enumerating all the pof- 
 fible Suppofitions upon which that AfFertion can 
 take place. If then it appears, that all thefe fe- 
 veral Suppofitions ought to be rejected, it is 
 plain, that the Antecedent, or Aflertion, itfelf, 
 muft be fo too. When therefore fuch a Pro- 
 pofition as that before-mentioned, is made the 
 Major of any Syllogifm ; if the Minor rejedts all 
 M 4 the
 
 the Suppofitions contained in the Conicquent, ft 
 follows neceflarily, that the Conclufion ought to 
 reje<5l the Antecedent, which, as we have faid, is 
 the very Aflertion to be difproved. This parti- 
 c,ular Way of arguing, is that which Logicians 
 call a Dilemma', and from the Account here given 
 of it, it appears, that we may in general define 
 it, to be an hypothetical SyllogifM, where the Con- 
 fequent of the Major is a disjunctive Propofition^ 
 which is -wholly taken away or removed in the Mi- 
 nor. Of this kind is the following : 
 
 JfGod did not create the World perf eft in its 
 kind) it miift either proceed from want of 
 Inclination, or from want of Power. 
 But it could not proceed either from want of 
 
 Inclination^ or from want of Power. 
 Therefore he created the World per feel in its, 
 kind. Or, which is the fame thing : 'Tis 
 abfurd tefay that he did not create the World 
 perfe.ft in its kind. 
 
 Jn ua ; ve ,fai XVHK The Nature then of a. 
 Dilemma is univerfally this. The 
 
 * 
 
 cflt. . _ 
 
 Major is a conditional rropoluion,. 
 whofe Confequent contains all the feveral Sup- 
 pofitions upon which the Antecedent can take 
 place. As therefore thefe Suppofitions are whol- 
 ly removed into the Minor y it is evident that 
 the Antecedent muft be fo too ; infomuch that 
 we here always argue from the Removal of the 
 Confequent to the Removal of the Antecedent.. 
 
 That
 
 ( 249 J 
 
 That is, a Dilemma is an Argument, in the trio* 
 dus tollens of hypothetical Syllogifms, as Logici- 
 ans love to (peak. Hence it is plain, that if the 
 Antecedent of the Major is an affirmative Propo- 
 fitiori, the Conclufion of the Dilemma will be 
 negative ; but if it is a negative Propofition, the 
 Conclufion will be affirmative. I cannot dif- 
 mifs this Subject without obferving, that as 
 there is fomething very curious and entertaining 
 in the Structure of a Dilemma, fo is it a Manner 
 of Reafoning that occurs frequently in mathema- 
 tical Demonstrations. Nothing is more com- 
 mon with Euclid^ when about to mew the Equa- 
 lity of two given Figures, or which is the fame 
 thing, to prove the Abfurdity of aflerting them 
 unequal ; nothing, 1 fay, is more common 
 with him than to afiume, that if the one is not 
 equal to the other, it mujl be either greater or lefs : 
 and having deftroyed both thefe Suppofitions, 
 upon which alone the Aflertion can ftand, he 
 thence very naturally infers, that the Aflertion 
 itfelf is falfe. Now this is precifely the Reafon- 
 ing of a Dilemma, and in every Step coincides; 
 with the Frame and Compofition of that Argu- 
 ment, as we have defcribed it above* 
 
 M $ CHAP,
 
 C 250 ) 
 
 CHAP. V. 
 Of DEMONSTRATION. 
 
 of Reafowg I. T J AV I N G difpatched what 
 
 by a Cincate- """ 
 
 T J 
 
 """ 
 
 JL JL 
 
 - / rr 
 
 ration of Sy i- JL JL fecmcd necefiacy to be laid 
 
 gifms, we now proceed to fuppiy their Ufe and 
 Application in Reafoning. We have feen, that 
 in all the different Appearances they put on, we 
 ftill arrive at a juft and legitimate Conclufion : 
 Now it often happens, that the Conclufion of 
 one Syllogifm becomes a previous Propofition 
 in another, by which means great Numbers of 
 them are fometimes linked together in a Series, 
 and Truths are made to follow one another in 
 Train. And as in fuch a Concatenation of Syl- 
 logifms, all the various Ways of Reafoning that 
 are truly conclufive, may be with Safety intro- 
 duced ; hence it is- plain, that in deducing any 
 Truth from its firft Principles, efpecially when 
 it lies at a confiderable Diftance from them, we 
 are at Liberty to combine all the feveral kinds of 
 Arguments above explained, according as they 
 are found beft to fuit the End and Purpofe of our 
 Inquiries. When a Propofition is thus, by means 
 of SyllogifmSj collected from others more evident 
 
 and
 
 and known, it is faid to be proved j fo that we may 
 in the general define the Proof of a Propofition y 
 to be a Syllogifm,. or Series of Syllogifms, col- 
 Jecling that Propofition from known and evident 
 Truths. But more particularly, if the Syllo- 
 gifms of which the Proof confifts, admit of no 
 Premifes but Definitions, felf-evident Truths, 
 and Propofitions already eftablifhed, then is the 
 Argument fo conftituted called a Demon/oration j 
 whereby it appears, that Demonftrations are ul- 
 timately founded on Definitions and felf-evident 
 Propofitions. 
 
 II. BUT as a D'emonftration oft- Ms 3 tt, g if Kf 
 times confifts of a long Chain of wtarjuver 
 
 T r u 11 i. TTT reducible to 
 
 Proofs, where all the various Ways tbefrft Fi~ 
 of arguing have place, and where the gure ' 
 Ground of Evidence muft of courfe be different irr 
 different Parts, agreeably to the Form of the Ar- 
 gument made ufe of; it may not perhaps be un- 
 acceptable, if we here endeavour to reduce the 
 Evidence of Demonftration. to one fimple Prin- 
 ciple, whence, as a (lire and unalterable Foun- 
 dation, the Certainty of it may in all Cafes be 
 derived. In order to this we muft obferve, that 
 all Syllogifms whatfoever, whether compound, 
 multiform, or defective, are reducible to plain 
 fimple Syllogifins in fome one of the four Fi- 
 gures. But this is not all. Syllogifms of the firft 
 Figure in particular admit of all poffible Con- 
 clufions; that is, any Propofition whatfoever, 
 M 6 whether
 
 c *5 y 
 
 whether an univerfal Affirmative, or univerfaV 
 Negative, a particular Affirmative or particu- 
 lar Negative, which fourfold Divifion, as we 
 have already demonftrated in the fecond Part, 
 embraces all their Varieties ; any one, I fay, 
 of thefe may be inferred, by virtue of fome Syl- 
 logifm in the firft Figure. By this means it 
 happens that the Syllogifms of all the other Fi- 
 gures are reducible alfo to Syllogifms of the firft 
 Figure, and may be confidered as ftanding en the 
 fame Foundation with them. We cannot here 
 demonftrate and explain the Manner of this Re- 
 duclion, becaufe it would too much fwell the 
 Bulk of this Treatife. It is enough to take no- 
 tice, that the Thing is univerfally known and 
 allowed among Logicians, to whofe Writings 
 we refer fuch as defire farther Satisfaction in this 
 Matter. This then being laid down, it is plain, 
 that any Demonftration whatfoever may be con- 
 fidered as compofed of a Series of Syllogifms, all 
 in the firft Figure. For fince all the Syllogifms, 
 that enter the Demonftration, are reduced to- 
 Syllogifms of fome one of the four Figures, and 
 fince the Syllogifms of all the other Figures are 
 farther reducible to Syllogifms of the firft Fi- 
 gure, it is evident, that the whole Demonftra- 
 tion may be refolved into a Series of thefe laft 
 Syllogifms. Let us now if pofllble difcover the 
 Ground upon which the Conclufion refts, in 
 Syllogifras of the firft Figure j becaufe by fo do-
 
 ( 253 ) % 
 
 ing, we fhall come at an univerfal Principle of 
 Certainty, whence the Evidence of all Demon- 
 ftrations in all their Parts may be ultimately de- 
 rived. 
 
 III. THE Rules then of the firft TbiGrcur.dof 
 Figure are briefly thefe. The mid- ffijffil* 
 die Term is the Subject of the Major gurt. 
 Propofition, and the Predicate of the Minor. 
 The Major is always an univerfal Propofition, 
 and the Minor always affirmative. Let us now 
 fee what Effect thefe Rules will have in Reafon- 
 ing. The Major is an univerfal Propofition, 
 of which the middle Term is the Subject, and 
 the Predicate of the Conclufion the Predicate. 
 Hence it appears, that in the Major^ the Pre- 
 dicate of the Conclufion is always affirmed or de- 
 nied univerfally of the middle Term. Again, the 
 Minor is an affirmative Propofition, whereof 
 the Subjeft of the Conclufion is the Subject, and 
 the middle Term the Predicate. Here then the 
 middle Term is affirmed of the Subjeft of the Con- 
 clufion: that is, the SubjeSl of the Conclufion is 
 affirmed to be comprehended under, or to make 
 a Part of the middle Term. . Thus then we fee 
 what is done in the Premifes of a Syllogifm of 
 the firft Figure. The Predicate of the Conclu- 
 fion is univerfally affirmed or denied of fome 
 Idea. The Subjett of the Conclufion is affirmed 
 to be, or to make a Part of that Idea. Hence 
 it naturally and unavoidably follows, that the 
 
 Predicate
 
 ( 254 ) 
 
 Prtdicate of the Conclufion ought to be affirmed 07 
 denied of the Subject. To illuftrate this by an 
 Example, we (hall refume one of the Syllogifms 
 of the firft Chapter : 
 
 Every Creature poj/ejfed of Reafcn and Liberty 
 is accountable for his Actions. 
 
 Man is a Creature poffejfed of Reafon and 
 Liberty : 
 
 Therefore Man is accountable for his Actions. 
 Here in the firft Proportion, the Predicate of 
 the Conclufion Accountablenefs is affirmed of all 
 Creatures that have Reafon and Liberty* Again, 
 in the fecond Propofition, Man y the Subject of 
 the Conclufion, is affirmed to be, or to make 
 a Part of this Clafs of Creatures. Hence the 
 Conclufion neceflarily and unavoidably follows, 
 viz. that Man is accountable for his Actions. I 
 fay this follows neceiTarily and unavoidably. 
 Becaufe if Reafon and Liberty be that which 
 conftitutes a Creature accountable^ and Man has 
 Reafon and Liberty, it is plain he has that 
 which conftitutes him accountable. In like man- 
 ner, where the Major is a negative Propofition, 
 or denies the Predicate of the Conclufion univerfally 
 of the middle Term, as the Minor always afTerts 
 the SubjecJ of the Conclujion to be or make a Part 
 of that middle Term, it is no lefs evident, that 
 the Predicate of the Conclufon ought in this Cafe 
 to be denied of the Subject. So that the Ground 
 of Reafoning in all Syllogifms of the firft Fi- 
 gure
 
 gurc is manifeftly this: JPTjatever may le af- 
 firmed univerfally of any Idea, may be affirmed of 
 (very or any Number of Particulars comprehended, 
 under that Idea. And again : Whatever may be 
 denied univerfally of any fdea, may be in like Man- 
 ner denied of every or any Number of its Indivi- 
 duals. Thefe two Propofitions are called by 
 Logicians the Diflum de omni, and Dictum de 
 nullo, and are indeed the great Principles of 
 fyllogiftick Reafoning j inafmuch as all Con- 
 clufions whatfoever, either reft immediately 
 upon them, or upon Propofitions deduced from 
 them. But what adds greatly to their Value is, 
 that they are really felf-evidertt Truths, and 
 fuch as we cannot gain fay, without running 
 into an exprefs Con trad idlion. To affirm, for 
 Inftance, that No man is perfefl, and yet argue 
 that Some Men are perfeft ; or to fay that All 
 Men are mortal, and yet that Some Men are not 
 mortal^ is to aflfert a Thing to be and not to be 
 at the fame Time. 
 
 IV. AND now I think we are fuf- Dtmonflranan 
 
 r. . , . . i ff. an infallible 
 
 hciently authorized to affirm, that Guide toTmb 
 in all Syllogifms of the firft Figure, *<*&' tainty. 
 if the Premifes are true, the Conclufton muft needs 
 be true. If it be true that the Predicate of the 
 Conclufion, whether affirmative or negative, a- 
 grees univerfally to fome Idea, and if it be alfo 
 true, that the Subjeft of the Conclufion is a Part 
 of or comprehended under that Idea, then it 
 
 neceiTarily
 
 neceflarily follows, that the Predicate of the Cert- 
 clttfjon agrees alfo to the Subjeft. For to afTert 
 the contrary, would be to run counter to fome 
 one of the two Principles before eftablifhed ; 
 that is, it would be to maintain an evident Con- 
 tradiction. And thus we are come at laft to 
 the Point we have been all along endeavouring 
 to eftablifh, namely ; that every Proportion 
 which can be demonflrated is neceflarily true. 
 For as every Demonftration may be refolved into 
 a Series of Syllogifms all in the firft Figure, and 
 as in any one of thefe Syllogifms, if the Pre- 
 mifes are true, the Conclufion muft needs be fo 
 too : it evidently follows, that if all the feveral 
 Premifes are true, all the feveral Conclufions 
 are fo, and confequently the Conclufion alfo of 
 the laft Syllogifm, which is always the Propo- 
 fition to be demonftrated. Now that all the 
 Premifes of a Demonftration are true, will ea- 
 fily appear, from 'the very Nature and Definition 
 of that Form of Reafoning. A Demonftration, 
 as we have faid, is a Series of Syllogifms, all 
 whofe Premifes are either Definitions, felf-evi- 
 dent Truths, or Propofitions already eftablifhed. 
 Definitions are identical Propofitions, wherein 
 we connect the Defcription of an Idea with 
 the Name by which we choofe to have that 
 Idea called ; and therefore as to their Truth 
 there can be no Difpute. Self-evident Propo- 
 fitions appear true of themfelves, and leave no 
 
 Doubt
 
 Doubt or Uncertainty in the Mind. Propofitioris 
 before eftablifhed, are no other than Conclu- 
 fions, gained by one or more Steps from Defini- 
 tions and felf-evident Principles j that is, from 
 true Premifes, and therefore muft needs be true. 
 Whence all the previous Proportions of a De- 
 inonftration, being we fee manifeftly true, the 
 laft Conclufion, or Propofition to be demon- 
 ftrated, muft be fo too. So that Demonftration 
 not only leads to certain Truth, but we have 
 here a clear View of the Ground and Founda- 
 tion of that Certainty. For as in demonftrating 
 we may be faid to do nothing more than com- 
 bine a Series of Syllogifms together, all refting 
 on the fame Bottom j it is plain, that one uni- 
 form Ground of Certainty runs thro' the whole, 
 and that the Conclufions are every where built 
 upon fome one of the two Principles before 
 eftablifhed as the Foundation of all our Rea- 
 foning. Thefe two Principles are eafily re- 
 duced into one, and may be exprefied thus: 
 Whatever Predicate, whether affirmative or nega- 
 tive, agrees univ erf ally to any Idea, the fame muft 
 needs agree to every or any Number of Individuals, 
 comprehended under that Idea. And thus at 
 length we" have, according to our firft Defign, 
 reduced the Certainty of Demonftration to one 
 fimple and univerfal Principle, which carries 
 Us own Evidence along with it, and which is 
 
 indeed
 
 ( 258 ) 
 
 indeed the ultimate Foundation of all fyllogiftick 
 Reasoning. 
 
 ibt Ru/et of V. DEMONSTRATION therefore, 
 ajufficiemC^. feeing as an infallible Guide to 
 terienfor the Truth, and ftanding on fo fure and 
 
 dljlln^uljhing - 
 
 bttioetnTruib unalterable a Bans, we may now 
 *dF a i]tbo,d. venture to a fT ert , w hat I doubt not 
 
 will appear a Paradox to many ; namely, that 
 the Rules of Logiclc furnifh a fufficient Criterion 
 for the diftinguifhing between Truth and Falfe- 
 hood. For fmce every Proportion that can be 
 demonftrated, is neceflarily true, he is able to 
 diftinguifh Truth from Falfehood, who can with 
 Certainty judge when a Propofition is duly 
 demonftrated. Now a Demonftration is, as we 
 have faid, nothing more than a Concatenation 
 of Syllogifms, all whofe Premifes are Defini- 
 tions, felf-evident Truths, or Propofitions pre- 
 vioufly eftablifhed. To judge therefore of the 
 Validity of a Demonftration, we muft be able 
 to diftinguifh whether the Definitions that en- 
 ter it are genuine, and truly defcriptive of the 
 Ideas they are meant to exhibit : whether the 
 Propofitions alTumed without Proof as intuitive 
 Truths, have really that Self-evidence to which 
 they lay claim : whether the Syllogifms are 
 drawn up in due Form, and agreeable to the 
 Laws of Argumentation : in fine, whether they 
 are combined together in a juft and orderly
 
 ( 259 ) 
 
 Manner, fo that no demonftrable Propositions 
 ferve any where as Premifes unlefs they are 
 Conclufions of previous Syllogifms. Now it 
 is the Bufmefs of Logick, in explaining the 
 /everal Operations of the Mind, fully to inftruct 
 us in all thefe Points. It teaches the Nature 
 and End of Definitions, and lays down the 
 Rules by which they ought to be framed. It 
 unfolds the feveral Species of Propofitions, and 
 diftinguifhes the felf-evident from the demon- 
 ftrable. It delineates slfo the different Forms 
 of Syllogtfms, and explains the Laws of Argu- 
 mentation proper to each. In fine, it defcribes 
 the Manner of combining Syllogifms fo as that 
 they may form a Train of Reafoning, and lead 
 to the fucceflive Difcovery of Truth. The 
 Precepts of Logick therefore, as they enable us 
 to judge with Certainty, when a Propofition is 
 duly demonftrated, furnifh a fure Criterion for 
 the diftinguifhing between Truth and Falfe- 
 hood. 
 
 VI. BUT perhaps .it may be ob- . , 
 
 / And extending 
 
 iected, that Demonftration is a thing to all Cafes 
 
 i i where a cer- 
 
 very rare and uncommon, as being tain Know . 
 the Prerogative of but a few Sci- '<* '/Truth 
 
 * , f , . is attainable. 
 
 ences, and therefore the Criterion 
 here given can be of no great Ufe. I anfwer, 
 that wherever by the bare Contemplation of our 
 Ideas, Truth is difcoverable, there alfo De- 
 monftration may be obtained. Now that I think 
 
 is
 
 ( 260 } 
 
 is an abundantly fufficient Criterion, which en- 
 ables us to judge with Certainty, in all Cafes 
 where the Knowledge of Truth comes within 
 our Reach ; for with Difcoveries that lie be- 
 yond the Limits of the human Mind we have 
 properly no Bufmefs nor Concernment. When 
 a Proportion is demonftrated, we are certain of 
 its Truth. When, on the contrary, our Ideas 
 are fuch as have no vifible Connection nor 
 Repugnance, and therefore furnifh not the pro- 
 per Means of tracing their Agreement or Dif- 
 agreement, there we are fure that Knowledge, 
 Scientifical Knowledge I mean, is not attain- 
 able. But where there is fome Foundation of 
 Reafoning, which yet amounts not to the full 
 Evidence of Demonftration, there the Precepts 
 of Logick, by teaching us to determine aright 
 of the Degree of Proof, and of what is ftill 
 wanting to render it full and complete, enable 
 us to make a due Eftimate of the Meafures of 
 Probability, and to proportion our Aflent to 
 the Grounds on which the Proportion flands. 
 And this is all we can pofftbly arrive at, or 
 even fo much as hope for, in the Exercife of 
 Faculties fo imperfect and limited as ours. For 
 it were the Height of Folly to expect a Criterion 
 that fhould enable us to diftinguiih Truth from 
 Falfehood, in Cafes where a certain Knowledge 
 of Truth is not attainable. 
 
 VII. WE
 
 VII. WE have now done with ne ^^; Bf . 
 what regards the Ground and Evi- tun of DC- 
 
 -IT. monjtratloit 
 
 dence of Demonftration ; but be- into- d\na 
 fore we conclude this Chapter, it aad '*>"*> 
 may not be improper to take Notice of the Dif- 
 tin&ion of it into direfl and Indirect. A direft 
 Demonjlratlon is, when beginning with Defini- 
 tions, felf-evident Propofitions, or known and 
 allowed Truths, we form a Train of Syllogifms, 
 and combine them in an orderly Manner, con- 
 tinuing the Series thro' a Variety of fuccefilve 
 Steps, until at laft we arrive at a Syllogifm, 
 whofe Conclufion is the Propofition to be de- 
 monftrated. Proofs of this kind leave no Doubt 
 or Uncertainty behind them, becaufe all the fe- 
 veral Premifes being true, the Conclufions muft 
 be fo too, and of courfe the very laft Conclufion, 
 or Propofition to be proved. I mail not there- 
 fore any farther enlarge upon this Method of 
 demonftrating ; having I hope fufKciently ex- 
 plained it in the foregoing Part of this Chapter, 
 and fhewn wherein the Force and Validity of it 
 lies. The other Species of Demonftration is 
 the indiref?) or, as it is fometimes called, the 
 dpological. The Manner of proceeding here 
 is, by afluming a Propofition which direclly 
 contradids that we mean to demonftrate, and 
 thence by a continued Train of Reafoning, in 
 the Way of a direct Demonftration, deducing 
 
 fome
 
 ( 262 ) 
 
 fome Abfurdity or manifelt Untruth. For here- 
 upon we conclude that the Propofition a/Turned 
 was falfe, and thence again by an immediate 
 Confequence, that the Propofition to be demon- 
 ftrated is true. Thus Euclid in his third Book 
 being to demonftrate, that Circles which touch one 
 another inwardly have not the fame Center ; aflumcs 
 the direct contrary to this, viz. that they have 
 the fame Center; and hence by an evident Train 
 of Reafoning proves, that a Part is tqual to the 
 JPliole. The Suppofition therefore leading to 
 the Abfurdity he concludes to be falfe, viz. that 
 Circles touching one another inwardly have the fame 
 Center^ and thence again immediately infers, 
 that they have not the fame Center. 
 GriundofRea- VIII. Now becaufe this Manner 
 J?!i?" of Demonftration is accounted by 
 ^rations. fome not altogether fo clear and fa- 
 tisfa&ory, nor to come up to that full Degree 
 of Evidence, which we meet with in the diredl 
 Way of Proof; I fhall therefore endeavour here 
 to give a particular Illuftration of it, and to (hew 
 that it equally with the other leads to Truth and 
 Certainty. In order to this we muft obferve, 
 that two Propofitions are faid to be contradictory 
 one of another, when that which is aflerted to 
 be in the one, is aflerted not to be in the other. 
 Thus the Propofitions : Circles that touch one an- 
 ether inwardly have the fame Center ; and Circles 
 
 that
 
 that touch one another inwardly have not the fame 
 Center : are Contradiflories ; becaufe the fecond 
 aflerts the direct contrary of what is aflerted in 
 the firft. Now in all contradictory Propofiti- 
 ons this holds univerfally, that one of them is 
 neceflarily true, and the other neceflarily falfe. 
 For if it be true, that Circles which touch one 
 another inwardly have not the fame Center, it 
 is unavoidably falfe that they have the fame 
 Center, On the other hand, if it be falfe that 
 they have the fame Center, it is neceflarily true 
 that they have not the fame Center. Since there- 
 fore, it is impoflible for them to be both true or 
 both falfe at the fame time, it unavoidably fol- 
 lows, that one is neceflarily true, and the other 
 neceflarily falfe. This then being allowed, which 
 is indeed felf-evident, if any two contradictory 
 Propofitions are afTumed, and one of them can 
 by a clear Tram of Reafoning be demonftrated 
 to be falfe, it neceflarily follows that the other 
 is true. For as the one is necefTarily true, and 
 the other neceflarily falfe, when we come to dif- 
 cover which is the falfe Propofition, we thereby 
 alfo know the other to be true. 
 
 IX. Now this is precifely the Indinsi Di- 
 
 _ _ _ . .. _. _. n ntonftrationt a 
 
 Manner of an indirect Demonltra- j ure Guide to 
 tion, as is evident from the Account Certa '""y' 
 given of it above. For there we aflume a Pro- 
 pofition which directly contradicts that we. mean 
 to demonftrate, and having by a continued Se- 
 ries
 
 ries of Proofs fhewn it to be falfe, thence infer 
 that its Contradictory, or the Propofition to 
 be demonftrated, is true. As therefore this laft 
 Conclufion is certain and unavoidable, let us 
 next inquire, after what Manner we come to 
 be fatisfied of the Falfehood of the afTumed 
 Propofition, that fo no pofiible Doubt may re- 
 main, as to the Force and Validity of Demon- 
 ftrations of this kind. The Manner then is 
 plainly this. Beginning with the afTumed Pro- 
 pofition, we by the Help of Definitions, felf- 
 evident Truths, or Propofitions already efta- 
 blifhed, continue a Series of Reafoning, in the 
 Way of a direct Demonftration, until at length 
 we arrive at fome Abfurdity or known Falfe- 
 hood. Thus Euclid, in the Example before 
 mentioned, from the Suppofition that Circles 
 touching one another inwardly have the fame 
 Center, deduces that a Part is equal to the 
 Whole. Since therefore by a due and orderly 
 Procefs of Reafoning, we come at laft to a falfe 
 Conclufion, it is manifeft that all the Pre- 
 mifes cannot be true. For were all the Pre- 
 mifes true, the laft Conclufion muft be fo too, 
 * by what has been before demonftrated. Now 
 as to all the other Premifes made ufe of in the 
 Courfe of Reafoning, they are manifeft and 
 known Truths -by Suppofition, as being either 
 Definitions, felf-evident Propofitions, or Truths 
 eftablifhed. The aflumcd Propofitign is that 
 
 on!/
 
 only as to which any Doubt or Uncertainty 
 remains. That alone therefore can be falfe, and 
 indeed from what has been already {hewn, mud 
 unavoidably be fo. And thus we fee, that in 
 indirect Demonstrations, two contradictory Pro- 
 positions being laid down, one of which is de- 
 monflrated to be falfe, the other, which is al- 
 ways the Propofition to be proved, muft necefla- 
 rily be true j fo that here, as well as in the direct 
 Way of Proof, we arrive at a clear and fatif- 
 factory Knowledge of Truth. 
 
 X. THIS is univerfally the Me- Apartau'ar 
 thod of Reafoning in all Apological c l/</'^'- 
 
 i O N red D:msn- 
 
 or indirect Demonftrations j but flranen. 
 there is one particular Cafe, which has fome- 
 thing fo fingular and curious in it, that well de- 
 ferves to be mentioned byitfelf; more efpecially, 
 as the Ground on which the Conclufion refts 
 will require fome farther Illuftration. It is in 
 fliort this : that if any Propofition is alTumed, 
 from which in a direct Train of Reafonins: we 
 
 O 
 
 can deduce its Contradictory, the Propofition 
 fo afTumed is falfe, and the contradictory one 
 true. For if we fuppofe the afTumed Propofi- 
 tion to be true, then, fince all the other Prcmifes 
 that enter the Demonftration are alfo true, we 
 fhall have a Series of Reafoning, confining 
 wholly of true Premifes ; whence the la ft Con- 
 clwfion, or Contradictory of the aiTumed Pro- 
 N
 
 ( 266 ) 
 
 pofition, muft be true likewife. So that by this 
 Means we fhould have two contradictory Pro- 
 pofitions both true at the fame Time, which is 
 manifeftly impoflible. The afTumed Propofition 
 therefore whence this Abfurdity flows, muft ne- 
 cefiarily be falfe, and confequently its Contra- 
 dictory, which is here the Proportion deduced 
 from it, muft be true. If then any Propofition 
 is propofed to be demonftrated, and we ajjume 
 the ContradiRory of that Propofition, and thence 
 directly infer the Propofition to be demonftrated, 
 by this very Means we know that the Propofition 
 fo inferred is true. For fince from an aiTumed 
 Propofition we have deduced its Contradictory, 
 we are thereby certain that the afiumed Propofi- 
 tion is faifej and if fo, then its Contradictory, or 
 that deduced from it, which in this Cafe is the 
 fame with the Propofition to be demonftrated, 
 muft be true. 
 
 XI. THAT this is not a mere 
 
 A due Kntto- , . i r n TT* 
 
 ledge of the empty Speculation, void of all Ufe 
 ?*fii> of an( j Application in Practice, is evi- 
 
 Logick indtf- 
 
 fcfaiiy re- dent from the Conduct of the Ma- 
 I'rPI/'r*"" ' thematicians, who have adopted this 
 judges cfDe- Manner of Reafoning, and given it 
 
 tncr/lraiien. . 
 
 a Place among their Uemonitra- 
 tions. We have a curious Inftance of it in the 
 twelfth Propofition of the ninth Book of the 
 Elements. Euclid there propofes to demon- 
 
 ftrate,
 
 ftrate, that in any Series of Numbers, rlfingfrofn 
 Unity in Geometrical PrsgreJJlon^ all the Prims 
 Numbers that meafnre the lajl Term In the Series* 
 will alfo meafure the next after Unity. In order 
 to this he afiumes the Contradictory of the 
 Propofition to be demonftrated, namely; that 
 fame prime Number measuring the lajl Term In the 
 Series^ does not meafure the next after Unity , and 
 thence by a continued Train of Reafoning proves, 
 that it actually does meafure it. Hereupon he 
 concludes the aflumed Propofition to be falfe, 
 and that which is deduced from it, or its Contra- 
 dictory, which is the very Propofition he pro- 
 pofed to demonftrate, to be true. Now that 
 this is a juft and conclufive Way of Reafoning^ 
 is abundantly manifeft, from what we have fo 
 clearly eftablifhed above. I would only here 
 obferve, how neceiTary fome Knowledge of the 
 Rules of Logick is, to enable us to judge of the 
 Force, Juftnefs, and Validity of Demonftrations; 
 fince fuch may fometimes occur, where the 
 Truth of the Propofition demonstrated will nei- 
 ther be owned nor perceived, unlefs we know 
 before-hand, by means of Logick, that a Con- 
 clufion fo deduced, is neceflarily true and valid, 
 For though it be readily allowed, that by tho- 
 mere Strength of our natural Faculties, we can at 
 once difcern, that of two contradictory Propo- 
 fitions, the one is neceflarily true, and the other 
 N 2 neceflarily
 
 ( 268 ) 
 
 irecefiarily falfe : yet when they are fo linked to- 
 gether in a Demonftration, as that the one ferves 
 as a previous Propofition, whence the other is 
 deduced; it does not fo immediately appear, 
 without fome Knowledge of the Principles of 
 Logick, why that alone which is collected by 
 Reafoning, ought to be embraced as true, and 
 the other whence it is collected to be rejected 
 as falfe. 
 
 XII. HAVING thus I hope fuf- 
 
 And of itfilf r , , -it y, 
 
 f*jftent to nciently evinced the Certainty of 
 guard a- Demonftration in all its Branches, 
 
 gatr.jt En or 
 
 **df*ift and ihewn the Rules by which we 
 ought to proceed, in order to arrive 
 at a juft Conclufion, according to the various 
 Ways of arguing made ufe of; I hold it need- 
 lefs to enter upon a particular Confideration 
 of thofe feveral Species of falfe Reafoning 
 which Logicians diftinguifh by the Name of 
 Syphifms. He that thoroughly underflands the 
 Form and Structure of a good Argument, will 
 of himfelf readily difcern every Deviation from 
 it. And although Sophifms have been divided 
 into many Clafles, which are all called by found- 
 ing Names, that therefore carry in them much 
 Appearance of Learning ; yet are the Errors 
 themfelves fo very palpable and obvious, that I 
 Ihould think it loft Labour to write for a Man 
 capable of being milled by them. Here there- 
 fore
 
 fore we choofe to conclude this third Part of Lo- 
 gicic, and {hall in the next Book give fome Ac- 
 count of Method^ which though infeparable from 
 Reafoning is neverthelefs always confidered by 
 Logicians as a diftindl Operation of the Mind j 
 becaufe its Influence is not confined to the mere 
 Exercife of the Reafoning Faculty, but extends 
 in fome Degree to all the Tranfaclions of the 
 Underftanding, 
 
 N a THE
 
 THE 
 
 ELEMENTS 
 
 O F 
 
 L O G I C K. 
 
 BOOK IV. 
 
 CHAP. I. 
 
 Of Method in general, and the Divificn of if 
 info Analytick and Synthetick. 
 
 Ti-t UuJtr- I. "T "V T E have now done with 
 
 Ji ending feme- VV , r /l f^. 
 
 nm,s tmfhytd T T the three iuft Opera- 
 
 "?."" '"&"- tionsof the Mind, v/hofe Office it 
 
 fitter h noio 
 
 Truths. is to fearch after Truth, and enlarge 
 
 the Bounds of human Knowledge. There is 
 yet a fourth, which regards the Difpofal and 
 Arrangement of our Thoughts, when we endea- 
 vour fo to put them together, that their mutual 
 
 Connection
 
 Connection and Dependence maybe dearly feen^ 
 This is what Logicians call Method, and place 
 always the laft in Order in explaining the 
 Powers of the Underftanding ; becaufe it necef- 
 farily fuppofes a previous Exercife of our other 
 Faculties, and fome Progrefs made in Know- 
 ledge, before we can exert it in any extenfive 
 Degree. It often happens in the Purfuit 'of 
 Truth, that unexpected Discoveries prcfent them- 
 felves to the Mind, and thofe too relating to Sub- 
 jects very remote from that about which we are 
 at prefent employed. Even the Subjects them- 
 felves of our Enquiry, are not always chofen 
 with a due Regard to Order, and their Depen- 
 dence one upon another. Chance, our particu- 
 lar Way of Life, or fome prefent and preffing 
 Views, often prompt us to a Variety of Re- 
 iearches, that have but little Connection in the 
 Nature of Things. When therefore a Man ac- 
 cuftomed to much Thinking comes, after any 
 eonfiderable Interval of Time, to take a Survey 
 of his intellectual Acquifitions, he feldom finds 
 Reafon to be fatisfied with that Order and Dif- 
 pofuion, according to which, they made their 
 Entrance into his Underftanding. They are 
 there difperfed and fcattered, without Subordi- 
 nation, or anyjuft and regular Coherence j info- 
 much that the Subferviency of one Truth to the 
 Difcovery of another does not fo readily appear 
 N 4 to*
 
 o the Mind. Hence Jie is convinced of the Nc- 
 ceffity of diftiibuting them into various Clafles, 
 .uid combining into an uniform Syftem whatever 
 relates to one and the fame Subject. Now this is 
 the true and proper Bulinefs of Method ; to af- 
 certain the various Divifions of human Know- 
 ledge, and fo to adjuft and connect the Parts in 
 every. Branch, that they may feem to grow one 
 out of another, and form a regular Body of Sci- 
 ence, rifing from firft Principles, and proceeding* 1 
 by an orderly Concatenation of Truths. 
 
 Sometimes in JI. IN this View of Things It IS 
 
 tr?.^ard> and p\ a ' ir} that we muft be before-hand 
 
 UlJfWtry uf 
 
 flct at are well acquainted with the Truths we 
 are to combine together : othcrwife 
 how could we difcern their feveral Connec- 
 tions and Relations, "or fo difpofe of them as their 
 mutual Dependence may require ? But now it 
 often happens, the Underftanding is employed, 
 not in the Arrangement and Competition of 
 known Truths, but in the Search and Difcovery 
 of fuch as are unknown. And here the Manner 
 of proceeding is very different, inafmuch as we 
 ailemble at once our whole Stock of Knowledge 
 relating to any Subject, and after a general Sur- 
 vjy of Things, begin with examining them fe- 
 parately and by Parts. Hence it comes to pafs, 
 that whereas at our firit fetting out, we were ac- 
 quainted only with fome of the grand Strokes 
 
 and
 
 and Outlines, if I may fo fay of Truth, by thus 
 purfuing her through her feveral Windings and 
 Recefles, gradually difcover thofe more inward 
 and finer Touches, whence (he derives all her 
 Strength, Symmetry, and Beauty. And here it 
 is that when by a narrow Scrutiny into Thing?, 
 we have unravelled any Part of Knowledge, and 
 traced it to its firft and original Principles, info- 
 much that the whole Frame and Contexture of it 
 lies open to the View of the Mind ; here I fay it 
 is, that taking it the contrary Way, and begin- 
 ning with thefe Principles, we can fo adjuft and 
 put together the Parts, as the Order and Me- 
 thod of Science requires. 
 
 III. BUT as thefe Things are beft 
 
 n , , ... n 11 T- JUuflrated hy 
 
 underftood when illuftrated by Lx- the Similitude 
 amples y efpecially if they are obvi- c / " Watcb ' 
 ous, and taken from common Life; let us fup- 
 pofe any Machine, for inftance a Watch, pre- 
 fented to us, whofe Structure and Compofition 
 we are as yet unacquainted with, but want if 
 poflible to difcover. The Manner of proceeding 
 in this Cafe is, by taking the Whole to Pieces, 
 and examining the Parts feparately one aftec 
 another. When by fuch a Scrutiny we have 
 thoroughly informed ourfelves of the Frame and 
 Contexture of each, we then compare them to- 
 gether, in order to judge of their mutual Action 
 and Influence, By this means we gradually 
 N 5 trace
 
 ( 274 ) 
 
 trace out the inward Make and Connpofition of , 
 the Whole, and come at length to difcern, how 
 Parts of fuch a Form, and fo put together as we 
 found, in unravelling and taking them afunder, 
 conftitute that particular Machine called a 
 Watch, and contribute to all the fcveral Motions 
 and Phenomena obfervable in it. This Difco- 
 very being made, we can take Things the con- 
 trary Way, and beginning with the Parts, fo dif- 
 pofe and connect them, as their feveral Ufes and 
 Structures require, until at length we arrive at 
 the Whole itfelf, from the unravelling of which 
 thefe Parts refulted. 
 
 Ground f tie IV. AND as it is in tracing and 
 S$M*"* examining the Works of Art, fo it 
 Makedi. is in a great Meafure in unfolding 
 any Part of human Knowledge. For the Rela- 
 tions and mutual Habitudes of Thing?, do not 
 always immediately appear, upon comparing 
 them one with another. Hence we have re- 
 courfe to intermediate Ideas, and by Means of 
 them are furnifhed with thofe previous Propofi- 
 tions that lead to the Conclufion we are in queft 
 of. And if it fo happen, that the previous Pro- 
 pofitions themfelves are not fufficiently evident, 
 we endeavour by new middle Terms to afcertain 
 their Truth, ftill tracing Things backward in a 
 continued Series, until at length we arrive at fome 
 Syllogifm, where the Premifes are firft and felf- 
 
 evident
 
 ( 275 
 
 evident Principles. This done, we become per-- 
 fe&ly fatisfied as to the Truth of all the Con- 
 elufions we have pafled through, inafmuch as- 
 they are now feen to frand upon the firm and im- 
 moveable Foundation of our intuitive Percep-- 
 tions. And as we arrived at this Certainty, by 
 tracing Things backward to the original Prin- 
 ciples whence they flow, fo may we at any Time 
 renew it by a direct contrary Procefs, if begin- 
 ning with thefe Principles, we carry the Train 
 of our Thoughts forward, until they lead us by 
 a connected Chain of Proofs to the very laft Con- 
 clufion of the Series. 
 
 V. HENCE it appears,, that in Dwjion cf 
 
 i- r r i *. ' ^.L Me bad into 
 
 difpofmg and putting together our j aafytick ar , d 
 Thoughts, either for our own Ufe, Sytbetick. 
 that the Difcoveries we have made may at all 
 Times lie open to the Review of the Mind ; or 
 where we mean to communicate and unfold thefe 
 Difcoveries to others, there are two Ways of 
 proceeding equally within our Choice. For we 
 may fo propole the Truths relating to any Part 
 of Knowledge, as they prefented themfelves to 
 the Mind in the Manner of Inveftigation, 
 carrying on the Series of Proofs in a reverfe 
 Order, until they at laft terminate in firft Prin- 
 ciples : or beginning with thefe Principles we 
 may take the contrary Way, and from them de-. 
 duce,. by a direct Train of Reafoning, all the 
 N 6 feveral
 
 feveral Proportions we want to efhiblifh. This 
 Diverfity in the Manner of arranging our 
 Thoughts gives rife to the twofold Divifion of 
 Method eftablifhed among Logicians. For Me- 
 thod, according to their Ufe of the Word, is no- 
 thing elfe but the Order and Difpofltion of our 
 Thoughts relating to any Subject. When Truths 
 are fo propofed and put together, as they were 
 or might have been difcovered, this is called 
 the Analytic Method, or the Method of Refolutwn \. 
 imfmuch as it traces Things backward to their 
 Source, and refolves Knowledge into its firft and- 
 original Principle. When on the other Hand they, 
 are deduced from thefe Principles, and. connected 
 according to t-heir mutual. Dependence,, infomuch 
 that the Truths fidl in Order tend always to the 
 Demonftration of thofe that follow, this confti- 
 tutes what we call the Sy.nthetick Method^ or Me- 
 thod of Ccmpofition. For here we proceed by ga- 
 thering together the feveral fcattered Parts of 
 Knowledge, and combining them into one Whole 
 or Syftem, in fuch Manner, that the Underftand-" 
 ing is enabled diftinclly to follow Truth through 
 all her different Stages and Gradations* 
 Called otber- VI. THERE is this farther to be 
 
 10 iii i be Me- XT f i t r 
 
 iko.i efiwen- taken Notice or, in relation to theie 
 i-T^'r* two Species of Method: that the 
 
 Method of 
 
 Kntr.ce. firft has alib obtained the Name of 
 
 the Method of Invention^ becaufc it cbfcrves the 
 
 Ordet
 
 ( 277 ) 
 
 Order in which our Thoughts fucceed one an- 
 other in the Invention or Difcovery of Truth. 
 The other again is often denominated the Me- 
 thod of Doctrine or Injlruftion, i-nafmuch as in 
 laying our Thoughts before others, we generally 
 choofe to proceed in the Synthetici Manner, de- 
 ducing them from their nrft Principles. For 
 we are to obferve, that although there is great 
 Pleafure in purfuing Truth in the Method of 
 Inveftigation, becaufe it places us in the Con- 
 dition of the Inventor, and {hews the particular 
 Train and Procefs of Thinking by which he 
 arrived at his Difcoveries j yet it is not fo well 
 accommodated to the Purpofes of Evidence and 
 Conviction. For at our firft fetting out, we are 
 commonly unable to divine where the Analyfis 
 will lead us j infomuch that our Refearches are 
 for fome Time little better than a mere groping 
 in the Dark. And even after Light begins to 
 break in upon us, we are ftill obliged to many 
 Reviews, and a frequent Comparifon of the fe- 
 veral Steps of the Inveftigation among them- 
 felves. Nay, when we have unravelled the 
 Whole, and reached the very Foundation on 
 which our Difcoveries ftand, all our Certainty 
 in regard to their Truth will be found in a 
 great Meafure to arife from that Connexion we 
 are now able to difcern between them and firft 
 Principles, taken in the Order of Competition. 
 But iu the Synthetick Manner of difpofing our 
 
 Thoughts,
 
 Thoughts, the Cafe is quite different. For as we 
 here begin with intuitive Truths, and advance 
 by regular Deductions from them, every Step of 
 the Procedure brings Evidence and Conviction 
 along with it ; fo that in our Progrefs from one 
 Part of Knowledge to another, we have always 
 a clear Perception of the Ground on which our 
 AfTent refts. In communicating therefore our 
 Difcoveries to others, this Method is apparently 
 to be chofen, as it wonderfully improves and 
 enlightens the Underiranding, and leads to an. 
 immediate Perception of Truth, And hence it 
 is, that in the following Pages, we choofe to 
 diftinguifh it by the Name of the Method of Sc i- 
 ence ; not only as in the Ufe of it we arrive at 
 Science and Certainty, but becaufe it is in Fail 
 the Method, in which all thofe Parts of human 
 Knowledge that properly bear the Name of 
 Sciences are and ought to be delivered. But we 
 now proceed to explain thefc two Kinds of Me- 
 thod more particularly. 
 
 CHAP. II, 
 
 Of the Method of Invention. 
 Origin of the 1. T)Y the Method of Invention we 
 
 underftand fuch a Difpofition 
 
 and Jniernom 
 
 f human Lifr. and Arrangement of our Thoughts, 
 as follows the natural Procedure of the Under- 
 
 Handing,
 
 ( 279 ) 
 
 ftanding, and prefents them in the Order in 
 which they fucceed one another in the Invefti- 
 gation and Difcovery of Truth. Now it is 
 plain, that to handle a Subject fuccefsfully ac- 
 cording to this Method, we have no more to 
 do than obferve the feveral Steps and Advances 
 of our Minds, and fairly copy them out to the 
 View of others. And indeed it will be found 
 to hold in general, with regard to all the active 
 Parts of human Life, efpecially when reduced 
 to that which is in the Schools termed an Art j 
 that the Rules by which we conduct ourfelves 
 are no other than a Series of Obfervations drawn 
 from the Attention of the Mind to what pafles, 
 while we exercife our Faculties in that particu- 
 lar Way. For when we fet about any Inven- 
 tion or Difcovery, we are always pufhed on by 
 fome inward Principle, Difpofition, or Aptitude 
 fhall I call it, which we experience in ourfelves, 
 and which makes us believe, that the Thing we 
 are in queft of is not altogether beyond our 
 Reach. We therefore begin with efTaying our 
 Strength, and are fometimes fuccefsful, though 
 perhaps more frequently not. But as the Mind, 
 when earneftly bent upon any Purfuit, is not 
 eafily difcouraged by a few Difappointments, 
 we are only fet upon renewing our Endeavours, 
 and by an obftinate Perfeverance, and repeated 
 Trials, often arrive at the Difcovery of what 
 we have in View. Now it is natural for a Man 
 
 of
 
 of a curious and inquifitive Turn, after having 
 mattered any Part of Knowledge with great La- 
 bour and Difficulty, to fet himfelf to examine 
 how he happened to rnifcarry in his firft At- 
 tempts, and by what particular Method of Pro- 
 cedure he at length came to be fuccefsful. By 
 this Means we difcover on the one Hand, thofe 
 Rocks and Shelves which ftand moft in our Way, 
 and are apt to difturb and check our Progrefs j 
 and on the other, that more fure and certain 
 Courfe, which if we continue in fteadily, will 
 bring us to the Attainment of what we are in 
 Purfuit of. Hence fpring ail the Arts and In- 
 ventions of human Life, which, as we have 
 already faid, are founded upon a Series of Rules 
 and Obfcrvations, pointing out the true and 
 genuine Manner of arriving at any Attainment. 
 When the Mind refts fatisfied in a baie Con- 
 templation of the Rules,, and the Reafons on 
 which they are founded, this Kind of Know- 
 ledge is called Speculative. But if we proceed 
 farther, and endeavour to apply thefe Rules to 
 Practice, fo as to acquire a Habit of exerting 
 them on all proper Occafions, we are then faid to 
 be poflefled of the Art itfelf. 
 
 II. FROM what has been faid it 
 
 WlyintrcatiKg 
 
 f the Method appears, that in order diltinctly tQ 
 l L l e 'figw explain the Method of Invention,. 
 fine Account if we mutt take a View of the Under- 
 
 tbe Art iijtlf. n . 
 
 funding as employed in the Search 
 
 and
 
 and Inveftigation of Truth. For by duly at- 
 tending to its Procedure and Advances, we fhall 
 not only difcover the Rules by which it con- 
 duels itfelf, but be enabled alfo to trace out 
 the feveral Helps and Contrivances it makes 
 ufe of, for the more fpeedy and effectual At- 
 tainment of its Ends. And when thefe Parti- 
 culars are once known, it, will not be difficult 
 for us, in laying open our Difcoveries to others, 
 to combine our Thoughts agreeably to the Me- 
 thod here required. Becaufe having fixed and 
 afcertained the Rules of it, and being perfectly 
 acquainted with the Conduct and Manner -of 
 the Mind, we need only take a Review of the 
 feveral Truths as they fucceed one another in 
 the Series of Inveftigation, fet them in order 
 before us, and fairly tranfcribe the Appearance 
 they make to the Underftanding. Hence it is 
 that Logicians, in treating of the Method of 
 Invention, have not merely confined themfelves 
 to the laying down of Directions for the Dif- 
 pofal and Arrangement of our Thoughts ; but 
 have rather explained the Art itfelf, and efta- 
 blifhed thofe Rules by which the Mind ought to 
 proceed in the Exercife of its inventive Powers. 
 For they rightly judged, that if thefe were once 
 thoroughly underftood, the ether could no 
 longer remain unknown. By this Means it 
 happens that the Method of Invention is' become 
 
 another
 
 C 
 
 another Expreffion for the Art of 'Invention, and 
 very often denotes the Conduct and Procedure 
 of the Underftanding in the Search of Truth. 
 And as fome Knowledge of the Principles of 
 the Art, is in a Manner abfolutely necefTary 
 towards a true Conception of the Rules by 
 which we ought to govern and difpofe our 
 Thoughts in treating Subjects after this Me- 
 thod ; we fliall therefore follow the Example 
 of other Logicians, and endeavour to give fome 
 fhort Account of the Bufinefs of Invention, and 
 of thofe feveral Helps and Contrivances by 
 which the Mind is enabled to facilitate and en- 
 large its Difcoveries. 
 
 III. IT has been already obferved,, 
 
 A'.ttarion and n i 
 
 e. cemtrtbtnjj-ve that when the Mind employs itfelf 
 U^nJi.g ; the s h of unknown Truths, 
 
 toe tnparatary 
 
 i^uaijcatiint it begins with aflembling at once its 
 
 t Ini/tntitn. , . -, . _ , r , , , . 
 
 whole Stock or Knowledge relating 
 to the SubjecT:, and after a general Survey of 
 Things, fets about examining them feparately 
 and by Parts. Now as in this feparate Exami- 
 nation, the Number of Parts continually in- 
 ereafe upon us j and as it is farther necefliiry r 
 that we fuivey them on all Sides, compare them 
 one. with another, and accurately trace their 
 mutual Habitudes and Refpecls ; it is from 
 hence apparent, that in the Exercife of Inven- 
 tion, two Things arc of principal Confideration.. 
 
 Firft,
 
 Firft, an enlarged and comprehenfive Under- 
 ftanding, able to take in the great Multitude 
 of Particulars that frequently come under our 
 Notice. Secondly, a ftrong Habit of Atten- 
 tion, that lets nothing remarkable flip its View, 
 and diftinguifhes carefully all thofe Circum- 
 ftances which tend to the illuftrating and clear- 
 ing the Subject we are upon. Thefe are the 
 great and preparatory Qualifications, without 
 which it were in vain to hope that any confi- 
 derable Advance could be made in enlarging 
 the Bounds of human Knowledge. Nor ought 
 we to efteem it a fmall Advantage, that they 
 are in fome Meafure in our own Power, and 
 may, by a proper Cultivation, be improved and 
 ftrengthened to a Degree almoft beyond Belief. 
 We find by Experience, that the Study of Ma- 
 thematicks in particular is greatly ferviceable to 
 this End. Habits we all know grow ftronger 
 by Exercife, and as in this Science there is a 
 perpetual Call upon our Attention, it by De- 
 grees becomes natural to us, fo as that we can 
 preferve it fteady and uniform, through long and 
 intricate Calculations, and that with little or 
 no Fatigue to the Underftanding. But a yet 
 more wonderful Advantage arifing from the 
 Culture of the Mathematicks is this, that hereby 
 we in fome Meafure extend the Dimenfions of 
 the human Mind, enlarge its Compafs of Per- 
 ception, and accuftom it to wide and compre- 
 henfive
 
 henfive Views of Things. For whereas at our 
 firft fetting out, we often find it extremely dif- 
 ficult to matter a fhort and eafy Demonftration, 
 and trace the Connection of its feveral Parts j 
 yet as we advance in the Science, the Under- 
 ftanding is feen gradually to dilate, and ftretch 
 itfelf to a greater Size ; infomuch that a long 
 and intricate Series of Reafoning is often taken 
 in with fcarce any Labour of Thought j and not 
 only fo, but we can in fome Cafes, with a fingle 
 Glance of our Minds, run through an entire 
 Syftem of Truths, and extend our View at once 
 to all the feveral Links that unite and hold them, 
 together. 
 
 IV. WHEN we are furnifhed 
 
 j judicious 
 
 Choice of inter' with thefe two preparatory Quali- 
 tfZt fications, the next Requifite to the 
 Rtquiftte in Difcovery of Truth is, a judicious 
 
 tbll Art. ,, . T 
 
 Choice or intermediate Ideas. We 
 have feen in the third Part of this Treatife, that 
 many of our Ideas are of fuch a Nature as not to 
 difcover their feveral Habitudes and Relations by 
 any immediate Comparifon one with another. 
 In this Cafe we mufl have Recourfe to inter- 
 mediate Ideas ; and the great Art lies in finding 
 out fuch as have an obvious and perceivable 
 Connection with the Ideas whofe Relations we 
 enquire after. For thus it is that we are fur- 
 nifhed with known and evident Truths, to 
 ferve as Premifes for the Difcovery of fuch as 
 
 are
 
 are unknown. And indeed the whole Bufmefs 
 of Invention feems in a great Meafure to lie in 
 the due Afiemblage and Difpofition of thefe 
 preliminary Truths. For they not only lead 
 us Step by Step to the Difcovery we are in 
 queft of, but are fo abfolutely neceflary in the 
 Cafe, that without them it were in vain to at- 
 tempt it ; nothing being more certain than that 
 unknown Propofitions can no otherwife be 
 traced but by means of fome Connection they 
 have with fuch as are known. Nay, Reafon 
 itfelf, which is indeed the Art of Knowledge, 
 and the Faculty by which we pufh on our Dif- 
 coveries ; yet by the very Definition of it im- 
 plies no more, than an Ability of deducing un- 
 known Truths from Principles or Propofitions 
 that are already known. Now although this 
 happy Choice of intermediate Ideas, fo as to 
 furnifh a due Train of previous Propofitions, 
 that fhall lead us fuccefnvely from one Difco- 
 very to another, depends in fome Meafure upon 
 a natural Sagacity and Quicknefs of Mind ; it 
 is yet certain from Experience, that even here 
 much may be effe&ed by a ftubborn 'Applica- 
 tion and Induftry. In order to this it is in the 
 firft place neceflary that we have an extenfive 
 Knowledge of Things, and fome general Ac- 
 quaintance with the whole Circle of Arts and 
 Sciences. Wide and extended Views add great 
 Force and Penetration to the Mind, and enlarge 
 
 its
 
 its Capacity of judging. And if to this we join 
 in the fecond place a more particular and inti- 
 mate. Study of whatever relates to the Subject 
 about which our Enquiries are employed, we 
 feem to bid fair for Succefs in our Attempts. 
 For thus we are provided with an ample Va- 
 riety out of which to choofe our intermediate 
 Ideas, and are therefore more likely to difcover 
 fome among them that will furnifli out the pre- 
 vious Propofitions neceflary in any Train of 
 Reafoning. 
 
 Sigaciyaada V. IT is not indeed to be denied, 
 3*'t>""Js "f that when we have even got all our 
 
 Undtr Handing 
 
 greatly pro- Materials about us, much ftill de- 
 
 ' muted by tbt , TV 
 
 Study of pends upon a certain Dexterity and 
 Algebra. Addrefs, in fingling out the moft 
 proper, and applying them fkilfully for the Dif- 
 covery of Truth. This is that Talent which 
 is known by the Name of Sagacity, and com- 
 monly fuppofed to be altogether the Gift of Na- 
 ture. But yet I think it is beyond Difpute, 
 that Practice, Experience, and a watchful At- 
 tention to the Procedure of our own Minds 
 while employed in the Exercife of Reafoning, are 
 even here of very great Avail. It is a Truth 
 well known to thofe who have made any confi- 
 derable Progrefs in the Study of Algebra, that 
 an Addrefs and Skill in managing intricate 
 Queftions may be very often obtained, by a 
 careful Imitation of the beft Models. For 
 
 although
 
 although when we firft fet out about the Solu- 
 tion of Equations, we are puzzled at every 
 Step, and think we can never enough admire 
 the Sagacity of thofe who prefent us with ele- 
 gant Models in that Way ; yet by Degrees we 
 ourfelves arrive at a great Maftery, not only in 
 devifing proper Equations, and coupling them 
 artfully together, fo as from the more compli- 
 cated to derive others that are fimple j but alfo 
 in contriving ufeful Subftitutions, to free our 
 Calculations from Fractions, and thofe Intrica- 
 cies that arife from Surds and irrational Quan- 
 tities. Nor is it a fmall Pleafure attending the 
 Profecution of this Study, that we thus difcern 
 the growing Strength of our own Minds, and 
 fee ourfelves approaching nearer and nearer to 
 that Sagacity and Quicknefs of Understanding 
 which we fee fo much admired in others, and 
 were at firft apt to conclude altogether beyond 
 our Reach. 
 
 VI. WE have now confidered 
 
 i r T r- T Where Art 
 
 thofe Requifites to Invention, that andManagt- 
 have their Foundation in the natu- ment a . re rt ~ 
 
 quired in the 
 
 ral Talents of the Mind: an en- Bufmijtof 
 
 i i i i r TT i Invention. 
 
 larged and comprehennve Under- 
 ftanding, a ftrong Habit of Attention, a Saga- 
 city and Quieknefs in difcerning and applying 
 intermediate Ideas. Let us next take a View 
 of fuch other Helps as more immediately de- 
 pend upon Art and Management, and fliew 
 9 the
 
 C 
 
 the Addrefs of the Mind, in contriving Means 
 to facilitate its Difcoveries, and free it from all 
 unneceflary Fatigue and Labour. For we are 
 to obferve, that tho' the Capacity of the Intel- 
 lect may be greatly enlarged by Ufe and Excr- 
 cife, yet ftill our Views are confined within cer- 
 tain Bounds, beyond which a finite Underftand- 
 ing cannot reach. And as it often happens in 
 the Inveftigation of Truth, efpecially where it 
 lies at a confiderable Diftance from firft Prm- 
 ciples, that the Number of Connections and 
 Relations are fo great, as not to be taken in at 
 once by the moft improved Underftanding ; it is 
 therefore one great Branch of the Art of In- 
 vention, to take Account of thefe Relations as 
 they come into View, and difpofe of them in 
 fuch Manner, that they always lie open to the 
 Infpec~tion of the Mind, when difpofed to turn 
 its Attention that Way. By this Means, with- 
 out perplexing ourfelves with too many Confi- 
 derations at once, we have yet thefe Relations 
 at Command, when neceflary to be taken notice 
 of in the Profecution of our Difcoveries : and 
 the Underftanding thus free and difengaged, can 
 bend its Powers more intenfely towards that par- 
 ticular Part of the Invefligatien it is at prefent 
 concerned with. Now in this, according to 
 my Apprehenfion, lies the great Art of human 
 Knowledge ; to manage with Skill the Capacity 
 of the Intellect, and contrive fuch Helps, as may 
 
 bring
 
 bring the mo{l wide and extended Objects within 
 the Compafs of its natural Powers. When 
 therefore the Multitude of Relations increafe 
 very faft upon us, and grow too unwieldy to be 
 dealt with in the Lump, we muft combine them 
 in different Claries, and fo difpofe of the feveral 
 Parts, as that they may at all times lie open to 
 the leifurely Survey of the Mind. By this means 
 we avoid Perplexity and Confufion, and are en- 
 abled to conduit our Refearches, without being 
 puzzled with that infinite Crowd of Particulars, 
 that frequently fall under our Notice in long and 
 difficult Investigations. For by carrying our 
 Attention fucceffively from one Part to another, 
 we can upon occafion take in the whole ; and 
 knowing alfo the Order and Difpofition of the 
 Parts, may have recourfe to any of them at plea- 
 fure, when its Aid becomes neceflary in the 
 Courfe of our Enquiries. 
 
 VII. FIRST then I fay, that an An Br/ t er t y 
 orderly Combination of things, and Difpoftuncf 
 
 J great L'fe in 
 
 clafTing them together with Art and acting ob~ 
 Addrefs, brings great and otherwife ^t&^tf 
 unmanageable Objects, upon a Level the Under- 
 with the Powers of the Mind. We ^ Ir ' g " 
 have feen in the firft Part of this Treatife how by 
 taking Numbers in a Progreflive Series, and ac- 
 cording to an uniform Law of Compofition, the 
 moft bulky and formidable Collections are com- 
 O prehended
 
 C 290 } 
 
 prehended with Eafc, and leave diftinct Impref- 
 iions in the Underftanding. For the feveral 
 Stages of the Progreflion ferve as fo many Steps 
 to the Mind, by which it afcends gradually to 
 the higheft Combinations ; and as it can carry 
 its Views from one to another with great Eafe 
 and Expedition, it is thence enabled to run over 
 all the Parts feparately, and thereby rife to a juft 
 Conception of the Whole. The fame thing hap- 
 pens in all our ether complex Notions, efpecially 
 when they grow very large and complicated ; 
 for then it is that we become fenfible of the Ne- 
 ceifity of eftablifhing a certain Order and Gra- 
 dation in the Manner of combining the Parts. 
 This has been already explained at fome Length, 
 in the Chapter of the Compofition and Refolu- 
 tion of our Ideas ; where we have traced the gra- 
 dual Progrefs of the Mind through all the dif- 
 ferent Orders of Perception, and fhewn, that 
 the moft expeditious Way of arriving at a juft 
 Knowledge of the more compounded Notices of 
 the Underftanding, is by advancing regularly 
 through all the intermediate Steps. Hence it is 
 eafy to perceive what Advantages muft arife 
 from a like Conduct, in regard to thofe feveral 
 Relations and Connections, upon which the In- 
 veftigation of Truth depends. For as by this 
 means we are enabled to bring them all within 
 the Reach of the Mind, they can each in their 
 Turns be made ufe of upon Occafion, and fur- 
 
 nifh
 
 nifti their Afliftance towards the Difcovery of 
 what we are in queft of. Now this is' of princi- 
 pal Confideration in the Bufinefs of Invention, 
 to have our Thoughts fo much under Command^ 
 that in comparing Things together, in order to 
 difcover the Refult of their mutual Connecti- 
 ons and Dependence, all the feveral Lights that 
 tend to the clearing the Subject we are upon, 
 may lie diftindtly open to the Underftanding> 
 fo as- nothing material fhall efcape its View: 
 becaufe an Overfight of this kind in fumming 
 up the Account, muft not only greatly retard 
 its Advances, but in many Cafes check its Pro- 
 grefs altogether. 
 
 VIII. BUT fecondly, another Ad- Antinen- 
 vantase arifing from this orderly ttbl g ui '" 
 
 ' proceed gra- 
 
 Difpofition is, that hereby we free dually and 
 the Mind from all unnecefTary Fa- e lvveftig*i- 
 tigue, and leave it to fix its A.tten- thn efTrutb. 
 tion upon any Part feparately, without perplex- 
 ing itfelf -with the Confideration o the Whole. 
 Unknown Truths, as we have already obferved, 
 are only to be traced by means of the Relation 
 between them and others that are known. When 
 therefore thefe Relations become very numerous, 
 it muft needs greatly diftracl the Mind, were it 
 to have its Attention continually upon the 
 Stretch after fuch a Multitude of Particulars at 
 once. But now, by the Method of clafling and 
 O 2 ordering
 
 ordering our Perceptions above explained, this 
 Inconvenience is wholly prevented. For a juft 
 Diftribution of things, as it afcertains diftincl- 
 ]y the Place of each, enables us to call any of 
 them into View at Pleafure, when the prefent 
 Confideration of it becomes neceflary. Hence 
 the Mind, proceeding gradually through the fe- 
 veral Relations of its Ideas, and marking the 
 Refults of them at every Step, can always pro- 
 portion its Enquiries to its Strength ; and con- 
 fining itfelf to fuch a Number of Objects as it 
 can take in and manage with Eafe, fees more 
 diftin&ly all the Confequences that arife from 
 comparing them one with another. When 
 therefore it comes afterwards to take a Review of 
 thefe its feveral Advances, as by this means the 
 Amount of every Step of the Invefligation is fair- 
 Jy laid open to its Infpetion, by adjufting and 
 putting thefe together in due Order and Method, 
 it is enabled at laft to difcern the Refult of the 
 Whole. And thus as before in the Compofition 
 of our Ideas, fo likewife here in the Search and 
 Difcovery of Truth, we are fain to proceed gra- 
 dually, and by a Series of fucceflive Stages. For 
 thefe are fo many refting Places to the Mind, 
 whence to look about it, furvey the Conclufions 
 it has already gained, and fee what Helps they 
 afford, towards the obtaining of others which it 
 muft flill pafs through before it reaches the End 
 of the Inveftigation, Hence it often happens, 
 
 that
 
 ( 2 93 ) 
 
 that very remote and diftant Truths, which lie 
 far beyond the Reach of any fmgle Effort of the 
 Mind, are yet by this progreflive Method fuc- 
 cefsfully brought to light, and that too with lefs 
 Fatigue to the Underftanding than could at firft 
 have well been imagined. For although the 
 whole Procefs, taken together, is frequently much 
 too large to come within the View of the Mind 
 at once ; and therefore confidered in that Light 
 may be faid truly to exceed its Grafp ; yet the 
 fcveral Steps of the Inveftigation by ihemfelves 
 are often e&fy and manageable enough ; fo tha: 
 by proceeding gradually from one to another, 
 and thoroughly mattering the Parts as we advance^ 
 we carry on our Refearches with wondrous Dif- 
 patch, and are at length conducted to that very 
 Truth, with a View to the Difcovery of which 
 the Inquifition itfelf was fet on foot. 
 
 IX. BUT -now perhaps it may not jy ge i, ra ar j 
 be improper, if we endeavour to slritbmetick 
 illuftrate thefe Obfervations by an .w%botk> A t\ 
 Example, and fet ourfelves to trace /'"' 
 the Conduct and Manner of the A'lind, when- 
 employed in the Exercife of Invention. There 
 are two great Branches of the Mathematicks pe- 
 culiarly fitted to furnifli us with Models in this 
 Way. Arltbmetlck I mean, and Algebra. Algebra 
 is univerfally known to be the very Art and Prin- 
 ciple of Invention ; and in Arithmetick too, we 
 O 3 are
 
 ( 294 ) 
 
 are frequently put upon the finding out of un- 
 known Numbers, by Means of their Relations 
 and Connections with others that are known : as 
 where it is required to find a Number equal to 
 this Sum of two others, or the Product of two 
 others. I choofe to borrow my Examples chiefly 
 irom this laft Science, both becaufe they will be 
 more within the Reach of thofe for whom this 
 Treatife is principally defigned ; as likewife, be- 
 caufe Arithmetick furnifhes the beft Models of 
 a happy Sagacity and Management, in clafling 
 and regulating our Perceptions. So that here 
 more than in any other Branch of human Know- 
 ledge, we fhall have an Opportunity of obferv- 
 ing, how much an orderly Difpofition of Things 
 tecc!s to the Eafe and Succefs of our Enquiries, 
 by leaving us to canvafs the Parts feparately, and 
 thereby rife to a gradual Conception of the Whole 
 without entangling ourfelves with too many Con- 
 fiderations at once, in any (ingle Step of the In- 
 veftigation. For it will indeed be found, that 
 a Dexterity and Addrefs in the Ufe of this laft 
 Advantage ferves to facilitate and promote our 
 Difcoveries, almoft beyond Imagination or Be- 
 lief. 
 
 M'tbod X. W E have already explained 
 7 the Manner of reducing Numbers 
 . i nto Clafles and of diftinguifliing 
 thefe Clafles by their fcveral Names. And now 
 we are farther to obferve, that the prefent Me- 
 thod
 
 ( 295 ) 
 
 thod of Notation is fo contrived, as exaftly to 
 fall in with this Form of numbering- For as in 
 the Names of Numbers, we rife from Units to 
 Tens, from Tens to Hundreds, from Hundreds to 
 Thoufands, &c> fo likewife in their Notation, 
 the fame Figures, in different Places, fignify 
 thefe feveral Combinations. Thus 2 in the firft 
 Place on the right Hand denotes two Units, in 
 the fecond Place it expreffes fo many Tens, in 
 the third Hundreds, in the fourth Thoufands. 
 By this means it happens, that when a Number 
 is written down in Figures, as every Figure in 
 it exprefles fome diftincl Combination, and all 
 thefe Combinations together make up the total- 
 Sum j fo may the feveral Figures be confidtred 
 as the conftituent Parts of the number. Thus 
 the Number 2436, is evidently by the very No- 
 tation diftinguifhed into four Parts, marked by 
 the four Figures that ferve to exprefs it. For 
 the firft denotes two Thoufand, the fecond four 
 Hundred, the third Thirty or three Tens, and the 
 fourth Six. Thefe feveral Parts, tho' they here 
 appear in a conjoined Form r may yet be alfo 
 exprefled feparately thus, 2000, 400, 30, and 6, 
 and the Amount is exadtly the fame. 
 
 XI. THJS then being the Cafe, if *r be Helps 
 it is required to find a Number equal thence derived 
 
 * _ to-wardt an 
 
 to the Sum of two others given; our tafy Addition 
 Buiinefc is,, to examine feparately ****"* 
 O 4 thefe
 
 ( 296 ) 
 
 ftefe given Numbers, and if they appear too large 
 and bulky to be dealt with by a fingle Effort of 
 Thought, then, fmce the very Notation diftin- 
 guifhes them into different Parts, we 'muft con- 
 tent ourfelves with confidering the Parts afunder, 
 and finding their Sums one after another. For 
 fmce the whole is equal to all its Parts, if we find 
 the Sums of the feveral Parts of which any two 
 Numbers confift, we certainly find the total Sum 
 of the two Numbers. And therefore, thefe dif- 
 ferent Sums, united and put together, according 
 to the eftablifhed Rules of Notation, will be the 
 very Number we are in queft of. Let it be pro- 
 pofed, for inftance, to find a Number equal to 
 the Sum of thefe two: 2436, and 4352. As the 
 finding of this by a fingle Effort of Thought 
 would be too violent an Exercife for the Mind, 
 I confider the Figures reprefenting thefe Num- 
 bers as the Parts of which they confift, and there- 
 fore fet myfelf to difcover their Sums one after 
 another. Thus 2, the firft Figure on the right 
 Hand of the one, added to 6, the firft Figure on 
 the right hand of the other, makes 8, which is 
 therefore the Sum of thefe two Parts. Again, 
 the Sum of 5 and 3, the two Figures or Parts in 
 the fecond Place, is like wife 8. But now as Fi- 
 gures in the fecond Place, denote not fimple Units, 
 but Tens ; hence it is plain, that 5 and 3 here, 
 fignify five Tens and three Tens, or 50 and 30, 
 whofe Sum therefore muft be eight Tcns t or 80. 
 
 And
 
 ( 297 ) 
 
 And here again I call to mind, that having al- 
 ready obtained one Figure of the Sum, if I place 
 that now found immediately after it, it will 
 thereby {land alfo in the fecond Place, and fo 
 really exprefs, as it ought to do, eight Tens, or 
 80. And thus it is happily contrived, that tho' 
 in the Addition of the Tens, I confider the Fi- 
 gures compofing them as denoting only fimple 
 Units, which makes the Operation eafier and 
 lefs perplexed ; yet by the Place their Sum ob- 
 tains in the Number found, it exprefles the real 
 Amount of the Parts added, taken in their full 
 and complete Values. The fame Thing happens 
 in fumming the Hundreds and Thoufands ; that is, 
 though the Figures exprefling thefe Combina- 
 tions, are added together as fimple Units ; yet 
 their Sums, {landing in the third and fourth Places 
 of the Number found, thereby really denote the 
 Hundreds and Thoufands, and fo reprefent the 
 true Value of the Parts added. 
 
 XII. HERE then we have a mani- Btcaufe in tkt- 
 feft Proof of the great Advantages /"*"'*?'. 
 
 O by lukicb it it 
 
 derived from an artful Method of carried en, the 
 
 , ff. T> . -i-^ , Mind is put 
 
 claliing our Perceptions. Jb or as the ,., /,-/, * 
 Numbers themfelves are by this Fati ae - 
 Means diftinguifhed into different Parts, which 
 brings them more readily within the Compafs of 
 the. Underftanding; fo by taking thefe Parts fe- 
 "O 5 parately,
 
 parately, the Operations about Numbers are ren- 
 dered very eafy and fimple. And indeed it is par- 
 ticularly worthy our Notice, and tho' in adding 
 two very large Numbers together, the whole Pro- 
 cefs is of fufficient Length; yet the feveral Steps 
 "by which it is conducted, are managed with in- 
 credible Difpatch, and fcarce any Fatigue to the 
 Mind. This is apparent in the Example given 
 above, where we fee, that in every Advance from 
 one Part to another, nothing more is required 
 than to add together the two Figures in the like 
 Places of the Numbers to be fummed. But what 
 is yet more wonderful, tho r in the Progrefs of a 
 long Operation, the Figures rife in their V r alue as 
 we advance, and grow to fignify Thoitfands, Mil- 
 lions. Billions, &c. yet fo happily, a re they contriv- 
 ed for exprefling the different Parts of Numbers, 
 that in every Step of the. Procedure we confider 
 them as denoting only fimple Units, all other 
 Deficiencies being made up, by the Places their 
 Sums obtain in the total Amount. And thus it is- 
 fo ordered in this admirable Form of Notation, 
 that however large the Numbers are that come 
 under Examination, they are neverthelefs ma- 
 naged with the fame Eafe as the moft fimple and 
 obvious Collections j becaufe in the feveral Ope- 
 rations about them, the Mind is neither tied down? 
 to the View of too many Parts at once, nor en- 
 tangled
 
 (' 299 ) 
 
 tangled with any Confiderations regarding the 
 Bulk and Compofition of thofe Parts. 
 
 XIII. AND if thefe Advantages rbis farter 
 are fo very manifeft in the firft and w/-^ p 
 
 on Example 
 
 jfimpleft Rules of Arithmeticlc, much in Multiple 
 more do they difcover themfelves in- ca " on ' 
 thofe that are intricate and complex. Let a Man 
 endeavour' in his Thoughts to find the Product 
 of two Numbers, each confiding of twenty or 
 thirty Places, and that without confidering the 
 Parts feparately ; I believe he will foon be fenfi- 
 ble, that it is a Difcovery far beyond the Limits 
 of the human Mind. But now in the progreffive 
 Method above explained, nothing is more fimple 
 and eafy. For if we take the firtt Figure on the 
 right Hand of the one Number, and by it multiply 
 every Figure of the other feparately ; thefe feve- 
 ral Produces, connected according to the eftablifli- 
 ed Laws of Notation, muft truly reprefent the to- 
 tal Product of this other, by that Part of the mul- 
 tiplying Number. Let us fuppofe, for Inftance,, 
 the Figure in the Unit's Place of the Multiplier to . 
 be 2, and the three laft Places of the Multiplicand 
 to be 432. Then, 2 multiplying 2 produces 4, 
 which therefore is the firft Part of the Product. 
 Again, 2 multiplying 3 produces 6. But now 3 
 ftanding in the fecond Place of the Multiplicand, 
 denotes in its real Value three Tens, or 30, which 
 therefore taken twice, amounts to fix Tens or 60. 
 O 6 And
 
 ( 30 ) 
 
 And accordingly the Figure 6, coming after 4 al- 
 ready found, is thereby thrown into the fecond 
 Place of the Product, and fo truly exprefies 60, 
 its full and adequate Value. The fame thing hap- 
 pens in multiplying 4, which {landing in the Place 
 of Hundreds, its Product by 2 is 800. But this 
 very Sum the Figure 8, produced from 2 and 4, 
 really denotes in the total Product. Becaufe 
 coming after 64, the two Parts already found, it 
 is thereby determined to the third Place, where 
 it of Courfe exprefles fo many Hundreds. This 
 Procefs, as is evident, may be continued to any 
 length we pleafe ; and it is remarkable that in 
 like Manner as in Addition, tho' the Value of 
 the Figures in the Multiplicand continually rifes 
 upon us, yet we all along proceed with them as 
 firnple Units; becaufe the Places of the feveral 
 Produces in the total Amount, reprefent the juft 
 Refult of multiplying the Figures together, ac- 
 cording to their true and adequate Value. 
 
 XIV. HAVING thus obtained the 
 
 Of the Diji>o- 
 
 ftionoftte Product by the firft Figure of the 
 
 (iveral Pro- . - , . .. ' - . . 
 
 duSi in order Multiplier, we next take that in the 
 to Addition, fecond Place, and proceed with it in 
 the fame Manner. This fecond Operation gives 
 us the Effect of that Figure, confidered as a fim- 
 ple Digit. But as it flood in the fecond Place, 
 and therefore really denoted fo many Tent 9 hence 
 it is plain that the Product now gained muft be 
 
 yet
 
 ( 3 01 ) 
 
 yet multiplied by Ten, in order to exprefs the 
 true Product fought. This is accordingly done 
 in the Operation, by placing the firft Figure of 
 this fecond Product under the fecond Figure 
 of the firft Product. For this, when they come 
 to be added together, has the fame Effect as 
 annexing a Cypher, or multiplying by Ten, as 
 every one knows who is in the leaft acquainted 
 with the Rules of Arithmetick. In like Man- 
 ner, when we multiply by the Figure in the 
 third Place, as this new Product is placed ftill 
 one Figure backwards, we do in effect annex 
 two Cyphers to it, or multiply it by a Hundred. 
 And this we ought certainly to do ; becaufe 
 having confidered the multiplying Figure as 
 denoting only fimple Units, when it really ex- 
 preffed fo many Hundreds, the firft Operation 
 gives no more than the hundredth Part of the 
 true Product. The Cafe is the fame in multiply- 
 ing by the fourth or fifth Figures, becaufe the 
 Products ftill running backwards, we thereby in 
 effect annex as many Cyphers to them as brings 
 them up feverally to their refpective adequate 
 Value. By this means it happens, that though 
 the Figures of the Multiplier in every Advance, 
 denote ftill higher and higher Combinations, 
 yet we all along proceed with them as fimple 
 Digits ; the Difpofition of the feveral Products 
 in order to Addition making up for all the 
 Deficiencies that arife from this Way of confi- 
 
 dering
 
 ( 302 ) 
 
 dering them. When in this Method of Pro-- 
 cedure, we have obtained the Product of the 
 Multiplicand into all the different Parts of the 
 Multiplier, by adding thefe Produces together 
 we obtain alfo the total Product of the two 
 Numbers. For fince the whole is equal to all 
 its Parts, nothing is more evident, than that 
 the Product of any one Number into another, 
 muft be equal to its Product into all the Parts 
 of that other : and therefore the fevera! partial 
 Produces united into one Sum, cannot but truly* 
 reprefent the real Product fought. 
 Arithmetical XV. THUS we fee, that in Quef- 
 operation*, l>y t j ons o f Multiplication, thoueh the 
 
 being carried 
 
 tin in a pro- whole Proccfs is fometimes fuffici- 
 S$ .rf ently long and tedious, yet the fe- 
 eafy and in- yeral Steps by which it is carried 
 
 telliglblc. . . _^ 
 
 on are all very level to the rowers 
 of the Underftanding. For from the Account 
 given above it appears, that nothing more is re- 
 quired in any of them than barely to multiply 
 one Digit by another. But now this eafy Rule 
 ef Operation is wholly derived from the before- 
 mentioned Addrefs in clafling our Perceptions. 
 For to this it is owing, that the Numbers under 
 Consideration are diftinguifhed into Parts, and 
 that the feveral Parts are alfo clearly repre- 
 fented to the Mind in the very Form of Nota- 
 .tion. Now as thefe Parts have an invariable 
 Relation one to another, and advance in their 
 
 Value
 
 Value by an uniform Law of Progrefiion ; the 
 Underftanding by means of fuch a Link can 
 eafily hold them together, and carry its Views 
 from Stage to Stage without Perplexity or Con- 
 fufion. Hence it happens, that however large 
 and mighty the Numbers are, fo as far to ex- 
 ceed the immediate Grafp of the Mindj yet by 
 running gradually through the feveral Combi- 
 nations of which they are made up, we at 
 length comprehend them in their full Extent, 
 And becaufe it would be impoflible for the Un- 
 derftanding to multiply very large Numbers one 
 into another, by a fimple Effort of Thought; 
 therefore here alfo it confiders the Parts fepa- 
 rately, and, taking them in an orderly Series, 
 advances by a Variety of fucceffive Steps. It 
 is true indeed in the Progrefs of the Operation, 
 the feveral Figures rife in their Value r but this 
 Confideration enters not the Work itfelf. For 
 there, as we have already feen, though the 
 Characters are taken as denoting only fimple 
 Units, yet the Order and Difpofition of the 
 partial Produces, exhibits each according to its 
 real Amount. Hence in every Step, we have 
 only to multiply one Digit by another, which as 
 it is attended with fcarce any Difficulty, the 
 whole Procefs is carried on with wondrous Dif- 
 patch. And thus by a Series of eafy Opera- 
 tions, we at length rife to Difcoveries, which 
 in any other Method of Procedure, would have 
 
 been
 
 been found altogether beyond the Reach of tlie 
 
 Mind. 
 
 I'te Art of XVI. SINCE therefore by a due 
 
 ehffiif our and orc j cr ] y Difpofition of our Ideas, 
 
 Perception 
 
 the great we can bring the moft wide and ex- 
 hft'umMtof tended Objeds upon a Level with 
 In-vtntion. the Powers of the Underftanding : 
 and fince by this alfo we abridge the Fatigue 
 and Labour of the Mind, and enable it to carry 
 on its Refearches in a progrelTive Method, with- 
 out which Contrivance, almoft all the more re- 
 mote and diftant Truths of the Sciences muft 
 have lain for ever hid from our knowledge ; I 
 think we may venture to affirm, that the Art 
 of regulating and clailing our Perceptions is 
 the great Mean and Inftrument of Invention. 
 It is for this Reafon that I have endeavoured 
 in fo particular a Manner to illuftrate it from 
 Examples in Numbers; becaufe we have here 
 not only a perfect Model of the Art itfelf, but 
 fee alfo in the cleared manner, what Helps it 
 furnifhes towards a ready Comprehenfion of 
 Objects, and a mafterly Inveftigation of Truth. 
 Nor let any one find fault, as if we had infifted 
 rather too long upon Matters that are obvious 
 and known to all. For I am apt to think, 
 that though very few are Strangers to the re- 
 ceived Method of Notation, and the common 
 Rules of Operation in Arithmetick ; yet it is 
 not every one that fets himfelf to confider the 
 
 Addrefs
 
 ( 305 ) 
 
 Addrefs and Sagacity that may be feen in the 
 Contrivance of them, or to unravel thofe Prin- 
 ciples of Investigation, which we have here fo 
 clearly deduced from them. And this I take to 
 be the Reafon, that we fometimes meet with 
 Inftances of Men, who tho' thoroughly verfed 
 in the Art of Invention, with regard to fome 
 particular Branches of Knowledge; yet if taken 
 out of their ufual Track, find themfelves im- 
 mediately at a Stand, as if wholly bereft of 
 Genius and Penetration. With fuch men In- 
 vention is a mere Habit, carried on in a Man- 
 ner purely mechanical, without any Know- 
 ledge of the Grounds and Reafons upon which 
 the feveral Rules of Invefligation are founded. 
 Hence they are unfurnifhed with thofe general 
 Obfervations, which may be alike ufefully ap- 
 plied in all Sciences, with only fome little necef- 
 fary Variations, fuited to the Nature of the Sub- 
 ject we are upon. And indeed I know of no 
 furer Way to arrive at a fruitful and ready In- 
 vention, than by attending carefully to the Pro- 
 cedure of our own Minds, in the Exercife of 
 this dirtinguifhed Faculty ; becaufe from the 
 particular Rules relating to any one Branch, we 
 are often enabled to derive fuch general Remarks, 
 as tend to lay open the very Foundation and 
 Principles of the Art itfeif. 
 
 XVII. IF
 
 Tie Manner of XVII. IF HOW VVC tUOl OUr 
 
 *?"*?? " Thoughts from Aritbmetick to Alge- 
 
 tee Rejolution 
 
 J Algebraic bra? here alfo we fhall find, that the 
 great Art of Invention lies, in fo re- 
 gulating and difpofmg our Notices of Things, 
 that we may be enabled to proceed gradually 
 in the Search of Truth. For it is the principal 
 Aim of this Science, by exhibiting the feveral 
 Relations of Things in a kind of fym,bolical 
 Language, fo to reprefent them to the Ima- 
 gination, as that we may carry our Attention 
 from one to another, in any Order we pleafe. 
 Hence, however numerous thofe Relations are, 
 yet by taking only fuch a Number of them into 
 Confederation at once, as is fuited to the Reach 
 and Capacity of the Underftanding, we avoid 
 Perplexity and Confufion in our Refearches, 
 and never put our Faculties too much upon 
 the Stretch, fo as to lofe ourfelves amidft the 
 Multiplicity of our own Thoughts. As there- 
 fore in Arithmetlcki we rife to a juft Conception 
 of the greateft Numbers, by confidering them as 
 made up of various progrefllve Combinations ;. 
 fo likcwife in Algebra, thofe manifold Relations 
 that often intervene, between known and un- 
 known Quantities, are clearly reprefented to 
 the Mind, by throwing them into a Series of 
 diflincl Equations. And as the moft difficult 
 Queftions relating to Numbers are managed 
 
 with
 
 ( 307 ) 
 
 with Eafe, becaufe we can take the Parts or 
 Figures feparately, and proceed with them one 
 after another ; fo alfo the moft intricate Prob- 
 lems of Algebra are in like Manner readily un- 
 folded, by examining the feveral Equations 
 apart, and unravelling them according to cer- 
 tain eftablifhed Rules of Operation. And here 
 it is well worth our Notice, that in very com- 
 plicated Problems, producing a great Number 
 of different Equations, it for the moft part fo 
 happens, that every one of them includes a Va- 
 riety of unknown Quantities. When therefo/6 
 we come to folve them feparately, as it would 
 too much diftracT: and entangle the Mind, to en- 
 gage in the Purfuit of fo many different Ob- 
 jects at once; our firft Bufmefs is, by artfully 
 coupling the feveral Equations together, or by 
 the various Ways of Multiplication, Subtrac- 
 tion, Addition, and Subflitution, to derive 
 others from them more fimple, until at length 
 by fuch a gradual Procefs we arrive at fome 
 new Equation, with only one unknown Quan- 
 tity. This done, we fet ourfelves to confider 
 the Equation laft found, and having now to do 
 with an Object fuited to the Strength and Ca- 
 pacity of the Mind, eafily by the eftabliflied 
 Rules of the Art, difcover the Quantity fought. 
 In this Manner we proceed with all the feveral 
 unknown Quantities one after another, and 
 having by a Series of difrincT: Operations traced 
 
 them
 
 them fcparately, the Queftion is thereby com- 
 pletely refolved. 
 
 Ofibofeotbtr XVIII. HENCE it appears, that 
 jrtijicmvtocb the Bufmefs of Invention, as prac- 
 
 may be conji- ' 
 
 dired a, f u hfi. tifed in Algebra, depends entirely 
 iZ"t' upn the Art of abridging our 
 Thoughts, reducing the Number 
 of Particulars taken under Conllderation at once 
 to the feweft pofllble, and eftablifliing that pro- 
 greflive Method of Inveftigation, which we have 
 already fo fully explained from Examples in 
 Arithmetick. I might eafily fhew that the 
 fame Obfervation holds equally in other Sci- 
 ences ; but having already exceeded the Bounds 
 I at firft prefcribed to myfelf in this Chapter, 
 fhall only add, that befides the grand Inftru- 
 ments of Knowledge already mentioned, there 
 are innumerable other Artifices, arifing out of 
 the particular Nature of the Subjefl we are 
 upon, and which may be confidered as fuhfi- 
 diary Helps to Invention. Thus in Geometry, 
 many Demonstrations of Problems and Theo- 
 rems are wholly derived from the Conftruction 
 of the Figure made u.fe of, and the drawing of 
 Lines from one Point to another. In like man- 
 ner in Algebra, the devifing of proper Equa- 
 tions from the Conditions of the Queftion pro- 
 pofed, and contriving neat ExprefTions for the 
 unknown Quantities, contribute not a little t<a 
 the eafy Solution of Problems, And when we 
 
 have
 
 fiave even carried on the Inveftigation to fome 
 fingle Equation with only one unknown Quan-- 
 tity ; as that unknown Quantity may be vari- 
 oufly perplexed and entangled with others that 
 are known, fo as to require a Multiplicity of 
 different Operations, before it can be difen- 
 gaged, which often involves us in long and 
 intricate Calculations, and brings Surds and 
 irrational Quantities in our Way; Algebraifts, 
 to prevent in fome Meafure thefe Inconveni- 
 ences, and fhorten as much as poflible the 
 Procefs, have fallen upon feveral Methods of 
 Subftitution, which are of great Service in 
 very complicated Queftions. But thefe and 
 fuch like Artifices of Invention, cannot be ex- 
 plained at length in this fhort EfTay. It is 
 enough to have given the Reader a Hint of them, 
 and put him in the Way of unravelling them, 
 himfelf, when he comes to apply his Thoughts 
 to thofe particular Branches of Knowledge where 
 they are feverally made ufe of. 
 
 XIX. THERE is one Thing how- Of tie great 
 
 , . , , jidvantavef 
 
 ever, that in a particular manner de- arifingf^m a 
 ferves to be taken Notice of, before b ?W ^ ot<t ' 
 
 ' tion or Ex- 
 
 we difmifs this Subject j and that is, prcffion of our 
 the great Advantages that may re- 
 dound to Science, by a happy Notation or Ex- 
 preflion of our Thoughts. It is owing entirely 
 to this, and the Method of denoting the feveral 
 Combinations of Numbers by Figures ftanding 
 
 in
 
 in different Places, that the moft complicated 
 Operations in Arithmetick are managed with fo 
 much Eafe and Difpatch. Nor is it lefs appa- 
 rent, that the Difcovcries made by Algebra, are 
 wholly to be imputed to that fymbolical Lan- 
 guage made ufe of in it. For by this means we 
 are enabled to reprefent the Relations of Things 
 in the Form of Equations, and by varioufly 
 proceeding with thefe Equations, to trace out 
 Step by Step the feveral Particulars we are in 
 queft of. Add to all this, that by fuch a No- 
 tation, the Eyes and Imagination are alfo made 
 fubfervient to the Difcovery of Truth. For 
 the Thoughts of the Mind rife up and difap- 
 pear, .according as we fet ourfelves to call them 
 into View; and therefore, without any particu- 
 lar Method of fixing and afcertaining them as 
 they occur, the retrieving them again when out 
 of Sight, would often be no lefs painful than the 
 very firft Exercife of deducing them one from 
 another. When therefore in the Purfuit of 
 Truth we carry our Attention forward from 
 one Part of the Inveftigation to another, as ne- 
 verthelefs we have frequent Occafion to look 
 back upon the Difcoveries already pafled through, 
 could thefe be no otherwife brought into View, 
 than by the fame Courfe of thinking in which 
 they were firft traced, fo many different Atten- 
 tions at once muft needs greatly diftraft the 
 Mind, and be attended with infinite Trouble 
 
 and
 
 and Fatigue. But now, the Method of fixing 
 and afcertaining our Thoughts by a happy and 
 well-chofen Notation, entirely removes all thefe 
 Obftacles. For thus, when we have Occafion 
 to run to any former Difcoveries, as Care is 
 taken all along to delineate them in proper 
 Characters, we need only caft our Eye upon 
 that Part of the Procefs where they ftand ex- 
 prefled, which will lay them at once open to 
 the Mind in their true and genuine Form. By 
 this means we can at any Time take a quick 
 and ready Survey of our Progrefs, and running 
 over the feveral Conclufions already gained, 
 fee more diftin&ly what Helps they furnifh to- 
 wards the obtaining of thofe others we are ftill 
 in Purfuit of. Nay further, as the Amount of 
 every Step of the Inveftigation h'es fairly before 
 us, by comparing them varioufly among them- 
 felves, and adjufting them one to another, we 
 come at length to difcern the Refult of the whole, 
 and are enabled to form our feveral Difcoveries 
 into an uniform and well-connected Syftem of 
 Truths, which is the great End and Aim of all 
 our Enquiries. 
 
 XX. UPON the whole then it ap- 
 
 , ... Recapitulation, 
 
 pears, that in order to proceed fuc- 
 cefsfully in the Exercife of Invention, we muft 
 endeavour as much as poffible to enlarge the 
 Capacity of the Mind, by accuftoming it to 
 wide and comprehenfive Views of Things : 
 
 9 that
 
 that we mud habituate ourfelves to a ftrong 
 and unfhaken Attention, which carefully dif- 
 tinguifhes all the Circumftances that come in 
 our Way, and lets nothing material flip its 
 Notice : In fine, that we muft furnifh ourfelves 
 with an ample Variety of intermediate Ideas, 
 and be much in the Exercife of fingling them 
 out and applying them for the Difcovery of 
 Truth. Thefe preparatory Qualifications ob- 
 tained, what depends upon Art lies chiefly in 
 the Manner of combining our Perceptions, 
 and clafling them together with Addrefs, fo as 
 to eftablifli a prcgreflive Method of Inveftiga- 
 tion. And here it is of great Importance, to 
 contrive a proper Notation or Expreflion of 
 our Thoughts, fuch as may exhibit them ac- 
 cording to their real Appearance in the Mind, 
 and diftinHy reprefent their feveral Divifions, 
 Clafles, and Relations. This is clearly feen in 
 the Manner of computing by Figures in Arith- 
 metick, but more particularly in that fymbo- 
 lical Language, which hath been hitherto fo fuc- 
 cefsfully applied in unravelling of Algebraical 
 Problems. Thus furnifhed, we may at any time 
 fet about the Inveftigation of Truth ; and if 
 we take Care to note down the feveral Steps of 
 the Procefs, as the Mind advances from one 
 Difcovery to another, fuch an Arrangement or 
 Difpofition of our Thoughts conftitutes what 
 is called the Method of Invention. For thus it is 
 
 plain,
 
 ( 3'3 ) 
 
 plain that we follow the natural Procedure of 
 the Underftanding, and make the Truths we 
 have unravelled to fucceed one another, accord- 
 ing to the Order in which they prefent them- 
 felves to the Mind, while employed in tracing 
 and finding them out. And here again it well 
 deferves our Notice, that as by this means the 
 whole Inveftigation lies diftindlly before us ; fo 
 by comparing the feveral Steps of it among them- 
 felves, and obferving the Relation they bear one 
 to another, we are enabled to form our Difco- 
 veries into a regular Sylrem of Knowledge, where 
 the Truths advanced are duly linked together, 
 and deduced in an orderly Series from firft Prin- 
 ciples. This other Manner of combining our 
 Thoughts, is diftinguifhed by the Name of the 
 Method of Science, which therefore now offers 
 itfelf to be explained, and is accordingly the 
 Subject of the enfuing Chapter. 
 
 CHAP. lit- 
 
 Of fbe Method cf Science. 
 
 I. TN order to give the jufter Idea 
 JL of the Rules peculiar to this 
 
 n i i-n. - 
 
 Species of Method, and eitabhin pi,tu* of our 
 
 them upon their proper Foundation, 3 
 
 it will be neceflary to begin with fet- v*tbang 
 
 tling the Meaning of the Word Sci~ ffatl>re ' 
 
 P
 
 tncf, and {hewing to what Parts of human Know- 
 ledge that Term may be mod fitly applied. We 
 have already obferved in the firft Chapter of the 
 fecond Book, that there are three feveral Ways 
 of coming at the Knowledge of Truth. Firft, 
 by contemplating the Ideas in our own Minds. 
 Secondly, by the Information of the Senfes. 
 Thirdly, by the Teftimony of others. When 
 we fet ourfelves to confider the Ideas in our own 
 Minds, we varioufly compare them together, in 
 order to judge of their Agreement or Difagree- 
 nient. Now as all the Truths deduced in this 
 Way, flow from certain Connections and Rela- 
 tions, difcerned between the Ideas themfelves; 
 and as when the fame Ideas are brought into 
 Compari-fon, the fame Relations muft ever and 
 invariably fubfift between them; hence it is 
 plain, that the Knowledge acquired by the Con- 
 templation of our Ideas, is of a neceflary and 
 unchangeable Nature. But farther, as thefe 
 Relations between our Ideas, are not only fup- 
 pofed to be real in themfelves, but alfo to be 
 feen and difcerned by the Mindj and as when 
 we clearly perceive a Connection or Repugnance 
 between any two Ideas, we cannot avoid judg- 
 ing them to agree or difagree accordingly ; it evi- 
 dently follows, that our Knowledge of this Kind is 
 attended with abfolute Certainty and Conviction, 
 jnfpmuch that it is impoffible for us to withhold 
 
 .our
 
 our Affent, or entertain any Doubt as to the Rea- 
 lity of Truths fo ofFered to the Underftanding. 
 The Relation of Equality between the whole 
 and all its Parts is apparent to every one who 
 has formed to himfelf a diftindl Notion of what 
 the Words IPhole and Fart ftand for. No Man, 
 therefore, who has thefe two Ideas in his Mind, 
 can poffibly doubt of the Truth of this Propofi- 
 tion, that the Whole is equal to all its Parts. For 
 this would be only endeavouring to perfuade him- 
 felf, that that was not, which he plainly and un- 
 avoidably perceives to be. So that in all Cafes 
 where we difcern a Relation between any of our 
 Ideas, whether immediately by comparing them, 
 one with another, or by means of intermediate 
 Ideas, that lay it open diftin&Jy to the Under- 
 ftanding; the Knowledge thence arifmg is cer- 
 tain and infallible. I fay infallible ; becaufe we 
 not only perceive and own the Truth of Propofi- 
 tions fo ofFered to the Mind, but having at the 
 fame time a clear View of the Ground on which 
 our Aflent refts, are intirely fatisfied within our- 
 felves, that we cannot polfibiy be deceived in 
 this Perception. 
 
 II. THIS fecond Way of coming A fanning 
 at Knowledge is by the means of the f ; om tbt In ~ 
 
 } formation of 
 
 Senfes. From them we receive Infor- '<&< Stnjet, te- 
 
 c L T -/L c r^i r g" s undoubttd 
 
 mation or the t-xiftence of Objects jjuranc*, but 
 without us, of the Union and Con- '* < ^ / V < "? // 
 
 .._ PoJJibility of 
 
 junction cf different Qualities in the tdrgdtteivtj. 
 P 2 fame
 
 fame Subject, and of the Operations of Bodies one 
 upon another. Thus our Eyes tell us, that there 
 is in the Univerfe fuch a Body as we call the Sun, 
 our Sight and. Touch, that Light and Heat, or at 
 leaft the Power of exciting thofe Perceptions in 
 us, co-exift in that Body ; and laftly, by the fame 
 Sight we alfo learn, that Fire has the Power of 
 difiblving Metals, or of reducing Wood to Char- 
 coal and Alhes. ButTiow with regard to this 
 Kind of Knowledge we are to obferve, that tho* 
 when the Organs of the Body are rightly difpofed 
 and operate in a natural Way, we never doubt 
 the Teftimony of our Senfes, but form moft of 
 the Schemes of Life upon their Information ; yet 
 are not the Truths of this Clafs attended with 
 that abfolute and infallible AfTurance, which 
 belongs to thofe derived from the Contemplation 
 of our own Ideas. We find that the Senfes 
 frequently reprefent Objects as really exifting, 
 which yet have no Being but in our own Ima- 
 ginations ; as in Dreams, Phrenfies, and the 
 Deliriums of a Fever. A Diforder too in the 
 Organs, makes us often afcribe Qualities to Bo- 
 dies, intirely different from thofe they appear 
 to poilefs at other Times. Thus a Man in the 
 Jaundice fhall fancy every Object prefented to 
 him yellow; and in bodily Diftempers, where 
 the Tafte is greatly vitiated, what naturally 
 produces the Idea of Sweetnefs, is fometimes 
 attended with a quite contrary Senfation. It 
 
 is
 
 i-s true, thefe Irregularities neither ought,- nor 
 indeed do they with confiderate men in any 
 ways tend, to discredit the Teftimony of Ex- 
 perience. He that, awake, in his Senfes, and 
 fatisfied that his Organs operated duly, fhould 
 take it into his Head to doubt whether Fire 
 would burn, or Arfenick poifon him, and there- 
 fore rafhly venture upon thefe Objects, would 
 foon be convinced of his Error, in a Way not 
 much to his liking. As neverthelefs the fenfes 
 do fometimes impofe upon us,, there is no abfo- 
 lute and infallible Security that they may not 
 at others j therefore the AfTurance they produce, 
 though reafonable, fatisfying, and diffidently 
 well founded to determine us in the feveral Ac- 
 tions and Occurrences of Life, is yet of fuch a 
 Nature, as not necefiarily to exclude all Poifi- 
 bility of being deceived. Hence fome Men o 
 fo far as to maintain, that we ought to diftruft 
 our Senfes altogether : nay, whole Seels among 
 the Ancients, becaufe of this bare Poflibility, 
 which really extends no farther than to Matters 
 of Experience and Tejlimony^ yet eftabliihed it as 
 a Principle, that we ought to doubt of every 
 thing. Nor are there wanting Philofophers 
 among the Moderns, who upon the fame Grounds 
 deny the Exifteace of Bodies, and afcribe the 
 Perceptions excited in us, not to the Action of 
 external Matter, but to certain eftablifhed Laws 
 in Nature, which operate upon us in fuch Man- 
 P 3 er
 
 rcr as to produce all thofe fevcral Effects that 
 Teem to flow from the real Prefence of Obje&s 
 varioufly affecting our Perception. It is not my 
 Dehgn here to enter into a particular Difcuflion 
 of thefe Matters: all I aim at is to (hew, that 
 the Teftimony of the Senfes, though fufficient 
 to convince fober and reafonable Men, yet does 
 not fo unavoidably extort our Aflent, as to leave 
 no room for Sufpicion or Diftruft. 
 Aif . un(led III. THE third and lad Way of 
 UIM Teflon*- coming at Truth is, by the Report 
 
 ry, tfajliil , _, -.. r i T 1 !.- 
 
 rrt rfu : certain and Teftimony of others. This re- 
 x a t u rt >t bouk gan ] s c hiefly paft Facts and Tranf- 
 
 in mar.y Ctjei J * 
 
 embraced actions, which having no longer any 
 
 without Wa- -i- . rt i i. i 
 
 iitnnv or >./- ^xiltence, cannot be brought witnm 
 tru ft* the prcfent Sphere of our Obferva^ 
 
 tion. For as thefe could never have fallen under 
 our CogniAunce, but by the Relations of fuch as 
 had fufficient Opportunities of being informed ; 
 it is hence apparent, that all our Knowledge of 
 this Kind. is wholly founded upon the Convey- 
 ance of Tertimony. But now, although this 
 in many Cafes is a fufficient Ground of Aflenr, 
 fo as to produce a ready Belief in the Mind, 
 yet is it liable to ftill greater Objections than 
 even the Reports of Experience. Our Senfes, it 
 is true, on fome Occafions , deceive us, and 
 therefore they may pofiibly on others. But this 
 bare Poflibility creates little or no Diftruft j be- 
 caufe there are fixed Rules of judging, when 
 
 they
 
 they operate according to Nature, and when they 
 are prevented or given up to Caprice. It is other- 
 wife in Matters of mere human Testimony. For 
 there, befides the Suppolition that the Perfons 
 themfelves may have been deceived, there is a 
 farther Poflibility, that they may have confpired* 
 to impofe upon others by a falfe Relation. This 
 Confideration has the greater Weight, as we 
 frequently meet with fuch Inftances of Difm- 
 genuity among Men, and know it to be their 
 Intereft in fome particular Cafes, to diflemble 
 and mifreprefent the Truth. It would never- 
 thelefs be the Height of Folly, to reject all hu- 
 man Teftimony without Diftinclion, becaufe' 
 of this bare Poflibility. Who can doubt whe- 
 ther there ever were in the World fuch Conque- 
 rors as Alexander and Julius Cafar ? There is 
 no abfolute Contradiction indeed in fuppoftng, 
 that Hiftorians may have confpired to deceive 
 us. But fuch an univerfal Concurrence to a 
 Falfehood, without one contradicting Voice, ts- 
 fo extremely improbable, and fo very unlike 
 what ufually happens in the World, that a wifer 
 Man could as foon perfuade himfelf to believe 
 the grofleft Abfurdity, as to admit of a Suppo- 
 fition fo remote from every Appearance of Truth. 
 Hence the Fars of Hiftory, when well attefred, 
 :\TQ readily embraced by the Mind j and though 
 the Evidence attending them be not fuch 
 as produces a neceflary and infallible AfTurance, 
 P4 it
 
 ( 320 ) 
 
 it h yet abundantly fufficicnt to juftify our Be- 
 lief, and leave thofe without Excufe, who upon 
 the bare Ground of Pofiibility, are for reje&ing 
 JntireJy the Conveyance of Teftimony. 
 <, . IV. UPON the whole then it ap- 
 
 A*'!tnctt>ciongi 
 
 intfrtiyro that pears,that abfolute Certainty, fuch as 
 }S attended with unavoidable Afient, 
 
 which it de- anc l excludes all Pdflibility of being 
 
 rivtdjrtm tbe . ... . r , , . , 
 
 Conumpiaticn deceived, is to be found only in the 
 
 Contemplation of our own Ideas. In 
 Matters of Experience and Teftimony, Men we 
 lee may frame Pretences for Sufpicion and Dif- 
 iruft : but in that Part of Knowledge which re- 
 gards the Relations of our Ideas, none fuch can 
 have place. For as all thefe feveral Relations are 
 either immediately difcerned by the Mind, or 
 traced by means of immediate Ideas, where Self- 
 Evidence is fuppofed to accompany -every Step 
 of the Procedure, it is abfolutely impofiible for 
 a Man to perfuade himfelf that that is not, 
 which he plainly and neceflarily perceives to be. 
 Now it is to Knowledge attended with this laft 
 Kind of Evidence alone, that in Stri&nefs and 
 Propriety of Speech we attribute the Name of 
 Science. For Science implies Perception and Dif- 
 cernment, what we ourfelves fee and cannot 
 avoid feeing ; and therefore has place only in 
 Matters of abfolute Certainty, where the Truths 
 advanced are either intuitive Propofitions, or 
 
 deduced
 
 ( 321 ) . 
 
 deduced from them in a Way of ftricl Demon- 
 ftration. And as this kind of Certainty is no 
 where to be found, but in inveftigating the Re- 
 lations of our Ideas ; hence it is plain, that Science, 
 properly fpeaking, regards wholly the firft Branch 
 of human Knowledge; that which we have faid 
 is derived from a Contemplation of the Ideas in 
 our own Minds. 
 
 V. BUT here I expect it will be -, 
 
 Our Kvoio- 
 
 afked, if Science and Demonjlration l<dgecftbe 
 belong only to the Confideration of Ifobj^it'not 
 our own Ideas, what Kind of Know- ia ' u "' ve ' 
 ledge it is that we have relating to Bodies, their 
 Powers, Properties, and Operations one upon 
 another ? To this I anfwer, that we have already 
 diitinguifhed it by the Name of Natural or Ex- 
 perimental, But that we may fee more diftintly 
 wherein the Difference between Scientifical and 
 Natural Knowledge lies, it may not be improper 
 to add the following Obfervations. When we 
 caft our Eyes towards the Sun, we immediately 
 conclude, that there exifts an Object: without us, 
 correfponding to the Idea in our Minds. We 
 are however to take Notice, that this Conclufion 
 does not arife from any necefTary and unavoid- 
 able Connexion difcerned, between the Appear- 
 ance of the Idea in the Mind, and the real Ex- 
 iftence of the Object without us. We all know 
 by Experience, that Ideas may be excited, and 
 P 5
 
 ( 3" ) 
 
 that too by a feeming Operation of Obje&s upon 
 our Senfes, when there are in Fact no fuch Ob- 
 jects exifting j as in Dreams, and the Deliriums 
 of a Fever. Upon what then is the before- 
 mentioned Conclufion properly grounded ? Why 
 evidently upon this : that as we are fatisfied our 
 Organs operate duly, and know that every Ef- 
 fect muft have a Caufe, nothing is more natural 
 than to fuppofe, that where an Idea is excited in 
 the Mind, fome Object exifts correfponding to 
 the Idea, which is the Caufe of that Appear- 
 ance. But as this Conclufion, by what we have 
 feen, is not necefiary and unavoidable, hence 
 there is no Intuition in the Cafe, but merely a 
 probable Conjecture, or reafonable Preemption, 
 grounded upon an intuitive Truth. 
 
 VI. AGAIN, when a Piece of 
 
 Absolute Ccr- ... 
 
 tamy in na- Gold is difiolved in jfquci Regia, we 
 and own the Effed pro- 
 
 toivbat falls (juced, but cannot be faid in Stridl- 
 
 tinder tur im~ . 
 
 mediate A'o- ^ e fs and Propriety ofbpeech, to have 
 *'" any Perception or Difcernment of it. 
 
 The Reafon is, becaufe being unacquainted with 
 the intimate Nature both of dqua Regia and 
 Gold, we cannot, from the Ideas of them in our 
 Minds, deduce why the one operates upon the 
 other in that particular Manner. Hence it is, 
 that our Knowledge of the Fats and Operations 
 of Nature extends not with Certainty beyond 
 
 the
 
 C 3*3 ) 
 
 tire prefcnt Inftance, or what falls under our imv 
 mediate Notice j fo that in all our Refearches re- 
 lating to them, we muft proceed in the Way of 
 Trial and Experiment, there being here no gene* 
 ral or univerfal Truths, whereon to found fcien* 
 tifical Deductions. Becaufe the Solution of Gold 
 in Aqua Regla holds in one Experiment, we 
 cannot thence infallibly conclude that it will 
 hold in another. For not knowing upon what 
 it is, in either of thefe Bodies, that the Effect here 
 mentioned depends, we have no abfolute Cer- 
 tainty in any new Experiment we propofe to 
 make, that the Objects to be applied one to ano- 
 ther have that precife Texture and Conftitu- 
 tion from which this Solution refults. Chemifts 
 know by Experience, that Bodies which go by 
 the fame Name, and have the fame outward Ap- 
 pearance, are not always however exactly alike 
 in their Powers and Operations. In vain do they 
 often fearch for thofe Properties in one Piece of 
 Antimony, which on former Occafions they may 
 have found in another; and by this means, to 
 their no fmall Mortification, find themfelves fre- 
 quently difappointed, in very coftly and promif- 
 ing Experiments, Nor have we any exprefs 
 and pofitive AfTurance, that the very Bodies with 
 which we have formerly made Experiments, 
 continue fo exactly the fame, as to afford the 
 like Appearances in any fucceeding Trial. A 
 P 6 thoufand
 
 ( 324 ) 
 
 thoufand Changes happen every Moment in the 
 natural World, without our having the leaft 
 Knowledge or Perception of them. An Altera- 
 tion in our Atmofphere, the Approach or Recefs 
 of the Sun, his Declination toward the North 
 or South, not only vary the outward Face of 
 Things, but occafion many Changes in the hu- 
 man Conftitution itfelf, which we yet perceive 
 jiot when they happen ; nor fhould ever be fen- 
 lible of, but by the Effects and Confequences re- 
 lulting from them. And whether Alterations 
 analogous to thefe may not fometimes be pro- 
 duced in the Frame and Texture of many Bodies 
 that furround us, is what we cannot with Cer- 
 tainty determine. Hence, from an Experiment's 
 lucceeding in one Inftance, we cannot infallibly 
 argue that it will fucceed in another, even with 
 the fame Body. The Thing may indeed be pro- 
 bable, and that in the higheft Degree ; but as 
 there is ftill a Poffibility that fome Change may 
 have happened to the Body, unknown to us, 
 there can be no abfolute Certainty in the Cafe. 
 VJI. HAD we fuch an intimate 
 
 WbatKindtf A . . , , c ... 
 
 Kno-wUdgc of Acquaintance with the Structure 
 Body -wnld both of dqua Regia and Gold, as to 
 
 dejtr-vttbe t i 7 -,-r 
 
 Ka*e of Set- be able thence to diicern why the 
 
 one fo operates upon the other as 
 
 to occafion its Diflblution j infomuch that from 
 
 the Ideas of them in our own Minds we could 
 
 clearly
 
 ( 3*5 ) 
 
 clearly deduce, that Bodies of fuch a Make ap- 
 plied one to another, rhuft neceflarily produce 
 the EffecT: here mentioned ; our Knowledge 
 would then be fcientifical, and ftand upon the 
 Foundation either of Intuition or Dcmonjlration^ 
 according as the Perception was immediate, or 
 attained by means of intervening Ideas. In this 
 Cafe therefore, having two ftandard Ideas in 
 our Minds, whofe Relations we perfectly well 
 know ; wherever we found Objects conform- 
 able to thefe Ideas, we could then pronounce 
 with Certainty, that the Application of them 
 one to another would be attended with the 
 above Effect : becaufe whatever is true in Idea, 
 is unavoidably fo alfo in Reality of Things, 
 where Things exift anfwerable to thefe Ideas. 
 If it be true in Idea, that a Parallelogram is 
 the double of a Triangle, ftanding upon the 
 fame Bafe, and between the fame Parallels j the 
 fame will be true of every real Triangle and 
 Parallelogram, that exift with the Conditions 
 here mentioned. We are likewife to obferve, 
 that the Changes to which Bodies are daily 
 liable, could produce no Confufion or Perplexity 
 in natural Knowledge, did it ftand upon the 
 Foundation here mentioned. For in fuch a 
 Cafe, the Powers and Properties of Obje&s be- 
 ing deduced from the Ideas of them in our own 
 Minds, would no otherwife be applied to Things 
 really exifting, than as thefe Things are found 
 
 perfectly
 
 perfectly conformable to our Ideas. When' 
 therefore an Alteration happened in any Body, 
 as it would by this means differ from that ftand- 
 ard Idea whence its former Properties were 
 feen to flow, we muft of courfe be fenfible, 
 that fome fuitable Change would follow in the 
 Properties themfelves, and that its Powers and 
 Operations in regard of other Bodies would 
 not be in all refpects the fame. 
 
 VIIL B UT what is MI more re- 
 
 or.iyFtur.da- markable ; we fhould upon this 
 
 tlon of return! . 
 
 buppohtion be able to determine 
 
 the mutual Action and Influence of Bodies,. 
 without having Recourfe to Trial or Experi- 
 ment. Had we, for inftance, a perfect Know- 
 ledge of the intimate Nature and Compofition 
 of an animal Body, and of that particular Poifon 
 that is infufed into it by the Bite of a Viper, 
 fo as clearly and diftindtly to difcern how they 
 are adapted one to another ; we might thence 
 fcientifically deduce, without the Help of Ex- 
 periments, that the Bite of a Viper would fo 
 unhinge the human Fabrick, and produce fuch 
 Ferments and Combuftions in it, as muft ne- 
 ceflarily be followed by a total Extinction of all 
 the vital Functions, and leave that admirable 
 Machine a mere lifelefs Lump. But as fuch 
 perfect and adequate Ideas of Objects, and their 
 mutual Habitudes one to another, are plainly 
 beyond the Reach of our prefent Faculties j it 
 
 were
 
 ( 327 ) 
 
 were vain for us to think of improving natural 
 Knowledge by abftract Reafoning or fcienti- 
 fical Dedu&ions. Experience is here the true 
 and proper Foundation of our Judgments, nor 
 can we by any other means arrive at a Difco- 
 very of the feveral Powers and Properties of Bo- 
 dies. How long might a Man contemplate the 
 Nature of Hemlock, examine the Stru&ure of 
 its Parts in a Microfcope, and torture and ana- 
 lyfe it by all the Procefles of Chemiftry, be- 
 fore he could pronounce with Certainty the 
 Effect: it will have upon a human Body ? One 
 fingle Experiment lays that open in an Inftant, 
 which all the Wit and Invention of Men would 
 never of themfelves have been able to trace. 
 The fame holds in all the other Parts of natural 
 Philofophy. Our Difcoverks relating to Elec- 
 tricity, the Powers and Properties of the Load- 
 ftone, the Force of Gunpowder, &Y. were not 
 gained by Reafoning, or the Confideration of 
 our abftracl: Ideas, but by means of Experi- 
 ments made with the Bodies themfelves. Hence 
 it happened, that while the Philofophy of Ari- 
 ftotle prevailed in the Schools, which dealt much 
 in Metaphyfical Notions, occult Qualities, Sym- 
 pathies, Antipathies, and fuch like Words with- 
 out Meaning; the Knowledge of Nature was 
 at a Stand : becaufe Men pretended to argue 
 abftra&edly about Things of which they had 
 no perfect and adequate Ideas, whereon to 
 
 ground
 
 ( 3*8 ) 
 
 ground fuch a Method of Reafoning. But 
 now in the prefent Age, that we have returned 
 to the Way of Trial and Experiment, which 
 is indeed the only true Foundation of natural 
 Philofophy ; great Advances have already been 
 made, and the Profpedt of ftill greater lies be- 
 fore us. 
 
 D,ff<r<n fe k. IX * AND thus at len S th we ma 7 
 t-wetn fciend- fufficiently underftand wherein the 
 
 ral Know-"' P r P er DifFereiice lies, between fci- 
 leJge. entifical and natural Knowledge. 
 
 In Matters of Science we argue from the Ideas 
 in our own Minds, and the Connections and 
 Relations they liave one to another. And as 
 when thefe Relations are fet clearly and plainly 
 before us, we cannot avoid perceiving and 
 owning them, hence all the Truths of this 
 Clafs produce abfolute Certainty in the Mind, 
 and are attended with a neceflary and unavoid- 
 able Aflent. It is oiherwife in the Cafe of 
 natural Knowledge. Intuition and inward Per- 
 ception have here no Place. We difcern not 
 the Powers and Properties of thofe Objects that 
 furround us, by any View and Comparifon of 
 the Ideas of them one with another, but merely 
 by Experience, and the Impreflions they make 
 on the Senfes. But now the Reports of Senfe 
 happening in fome Inftances to deceive us, we 
 have no infallible Aflurance that they may not 
 in others j which weakens not a little the Evi- 
 dence
 
 ( 3*9 ) 
 
 dence attending this Kind of Knowledge, and 
 leaves room for fufpicion and Diftruft. Nay, 
 what is yet more confiderable, as we have no 
 perfect and adequate Ideas of Bodies, repre- 
 fenting their inward Conftitution, or laying 
 open the Foundation upon which their Quali- 
 ties depend, we can form no univerfal Propo- 
 fitions about them, applicable with Certainty 
 in all particular Inftances. Fire, we fay, dif- 
 folves Metals. This, though exprefled inde- 
 finitely, is however only a particular Truth, 
 nor can be extended with abfolute Aflurance, 
 beyond the feveral Trials made. The Reafon 
 is, that being ignorant of the inward Frame and 
 Compofition both of Fire and Metals ; when 
 Objects are offered to us under that Name, we 
 have therefore no pofitive Certainty that they 
 are of the very Make and Texture requifite to 
 the Succefs of the Experiment. The Thing 
 may indeed be probable in the higheft Degree, 
 but for want of ftandard and fettled Ideas, we 
 can never arrive at a clear and abfolute Per- 
 ception in the Cafe. 
 
 X. As neverthelefs it is certain n e Manntr 
 that many general conclufions in f RiJ J ol " n S 
 
 in natural 
 
 natural Philofophy are embraced Knoictedgt. 
 without Doubt or Hefitation ; nay, that we 
 form moft of the Schemes and Purfuits of Life 
 upon that Foundation ; it will naturally be afked 
 here, how come we by this Affurance ? I anfwer, 
 
 not
 
 not fcientificalty, and in the way ef (trier. De- 
 monrtration, but by Analogy, and an Induction, 
 f Experiments. We diftinguifh Fire, for in- 
 france, by fuch of its Qualities as lie more im- 
 mediately open to the Notice of the Senfes ; 
 among which Light and Heat are the moft con- 
 fiderable. Examining Bill farther into its Na- 
 ture, we find it likewife pofTefied of the Power 
 of diffblving Metals. But this new Property 
 not having any neceflary Connection that we 
 can trace, with thofe other Qualities by which 
 Fire is diflinguifhed, we cannot therefore argue 
 with Certainty, that wherever Light and Heat, 
 fcff. are, the Power of difiblving Metals co-exifts 
 with them. 'Tis not till after we have tried the 
 Thing in a Variety of Experiments, and found 
 it always to hold, that we begin to prefume 
 there may be really fome fuch Connection, tho* 
 our Views are too fhort and imperfect to difco- 
 vcr it. Hence we are led to frame a general 
 Conclufion, arguing from what has already 
 happened, to what will happen again in the 
 like Cafes; infomuch that where we meet with 
 all the other Properties of Fire in any Body, we 
 have not the leaft Doubt but that upon Trial,- 
 the Power above-mentioned will be found to 
 belong to it alfo. This is called Reafoning by 
 Analogy^ and it is, as we fee, founded intirely 
 upon Induction, and Experiments made with 
 particular Objects j the more precife and accu- 
 rate
 
 rate our Ideas of thefe Objects are, and tb* 
 greater the Variety of Experiments upon which 
 \ve build our Reafoning, the more certain and 
 undoubted will the Conclufions be. 'Tis in 
 this Manner we arrive at all the general Truths 
 of natural Knowledge : as that the Bite of cer- 
 tain Animals is mortal j that a Needle touched 
 by a Loadftone points to the North ; that Gra- 
 vity belongs univerfally to all Bodies j and in- 
 numerable others, which though not capable 
 of ftricl: Demonftration, are neverthelefs as 
 readily embraced upon the Foundation of Ana- 
 logy, as the moft obvious and intuitive Judg- 
 ments j nay, and become fixed and fteady Prin- 
 ciples of Action in all the Aims and Purfuits of 
 Life. 
 
 XI. AND here again it is parti- jj ow evtn 
 cularly remarkable, that having af- >''""// 
 
 Riafoiiiig may 
 
 certained the general Properties of be imroduetd 
 Things by Analogy, if we proceed 
 next to eltablifh thefe as Poftulata in Philofophy, 
 we can upon this Foundation build ftrit and 
 mathematical Demonftrations, and thereby in- 
 troduce fcicntifeal Reafoning into natural Know- 
 ledge. In this Manner Sir Ifaac Newton^ having 
 determined the Laws of Gravity by a Variety 
 of Experiments, and laying it down as a Prin- 
 ciple, that it operates according to thofe Laws 
 thro' the whole Syftem of Nature j has thence, 
 
 in
 
 ( 33* ) 
 
 in a Way of ftrit Dcmonftration, deduced the 
 whole Theory of the heavenly Motions. For 
 granting once this Pojlulatum^ that Gravity be- 
 longs univerfaliy to all Bodies, and that it acts 
 according to their folid Content, decreafing 
 with the Difrance in a given Ratio ; what Sir 
 Jfaac has determined in regard to the Planetary 
 Motions, follows from the bare Confideration 
 of our own Ideas j that is, neceffarily and fci~ 
 entifically. Thus likewife in Optics, if we lay 
 it down as a Principle, that Light is propagated 
 on all Sides in right Lines, and that the Rays 
 of it are reflected and refracted according to 
 certain fixed invariable Laws, all which is 
 known to be true by Experience j we can upon 
 this Foundation eftablifh mathematically the 
 Theory of Vifion. The fame happens in Me- 
 chanicksy Hydrojlaiicks^ Pneumatuks^ &c. where 
 from Pojlulata afcertained by Experience, the 
 whole Theory relating to thefe Branches of 
 Knowledge follows in a Way of ftrift Demon- 
 ftration. And this I take to be the Reafon 
 why many Parts of natural Philofophy are ho- 
 noured with the name of Sciences. Not that 
 they are ultimately founded upon Intuition j. 
 but that the feveral Principles peculiar to them 
 being aflumed upon the Foundation of Experi- 
 ence, the Theory deduced from thefe Principles 
 is eftabhfhed \>y fcientifical Reafoning. 
 
 XII. COULD
 
 ( 333 ) 
 
 XII. COULD we indeed difcerti 
 any neceflary Connection between P" 
 
 ' _. the ultimate 
 
 Gravity and the known eiiential Ground of t,ur 
 Qualities of Matter, infomuch that A -^ nt ' 
 it was infeparabie from the very Idea of it ; the 
 whole Theory of the Planetary Motions would 
 then be ftri&ly and properly fcientificoL For 
 feeing, from the Notion of Gravity, we can 
 demonftratively determine the Laws that Bo- 
 dies will obferve in their Revolutions, in any 
 known Circumftances ; if the Circumftances 
 relating to any Syftem of Bodies can be traced, 
 and Gravity is fuppofed eflential to them, we 
 can then, from the bare Confideration of our 
 own Ideas, deduce all their Motions and Phse~ 
 nomena. Now this is precifely what Sir Jfaac 
 has done in regard to our Planetary Syftem. He 
 has determined the Circumftances of the Bodies 
 that compofe it, in refpeft of Situation, Dif- 
 tance, Magnitude, &c. all which being fup- 
 pofed, if they are efientially actuated by Gra- 
 vity, their feveral Revolutions and Appearances 
 muft be equally eflential. But as the Principle 
 of Gravitation cannot be accounted for by the 
 known Qualities of Matter, neither can this 
 Theory be immediately deduced from the Idea 
 of : Body ; and therefore, tho' our Reafoning 
 in this Part of Philofophy be truly fcientifical, 
 yet as the Principle upon which that Reafoning 
 is grounded, is derived from Experience, the 
 
 Theory
 
 ( 334 ) 
 
 Theory itfelf muft needs ultimately reft upon the 
 fame Foundation. And thus even the Doctrine 
 of the Planetary Motions, though feemingly 
 eftablifhed by mathematical Reafoning, falls yer, 
 in Stridtnefs and Propriety of Speech, under the 
 r' Head of natural Knowledge. For in this pre- 
 cifely confifts the Difference between Science, 
 and what we call the Philofophy of Nature; that 
 the one is grounded ultimately on Intuition, the 
 other on Experience. As the Obfervation here 
 made holds alike in all the other Branches of na- 
 tural Philofophy, into which fcientifical Reafon- 
 ing has been introduced ; it is hence apparent, 
 that they are not Sciences^ in the ftrict and proper 
 Senfe of the Word, but only by a certain Latitude 
 of ExprelTion common enough in all Languages. 
 What we have therefore faid above relating to 
 the Impoflibility of improving natural Know- 
 ledge by fcientifical Deductions, is not con- 
 tradicted by any thing advanced in this Section. 
 We there meant Deductions grounded ultimately 
 on Intuition, and derived from a Confideration of 
 the abftract Ideas of Objects in our own Minds ; 
 not fuch as flow from Pojlulata aflumed upon 
 the Foundation of Experience. For thefe laft, 
 as we have already obferved, are not truly and 
 properly fcientifical, but have obtained that Name 
 merely on account of the Way of Reafoning in 
 which they are collected from the faid Pojlu- 
 lata* 
 
 XIII. IF
 
 ( 335 ) 
 
 XIII. IF then abfolute and in- ri>e Mantitr 
 -fallible Certainty is not to be ob- tf* e . a f. 
 
 in Hijiortcal 
 
 tained in Natural Knowledge, much Knowledge. 
 lefs can we expert it in Hiftorical. For here 
 Teftimony is the only Ground of Afienr, and 
 therefore the Polfibility of our being deceived, 
 is ftill greater than in the Cafe of Experience. 
 Not only he who reports the FacT: may himfelf - ! 
 have formed a wrong Judgment j but-could we 
 even get over this Scruple, there is ftill Room 
 to fufpeft, that he may aim at impofing upon 
 us by a falfe Narration. In this Cafe therefore 
 it is plain, there can be no Intuition or inward 
 Perception of Truth, no ftricl: and abfolute De- 
 monftration, and confequently no Science. There 
 is however a Way of Reafoning even here, that 
 begets an intire Acquiefcence, and leads us to 
 embrace without wavering, the Fads and Re- 
 ports of Hiftory. If, for Inftance, it appears, - 
 that the Hiftorian was a Man of Veracity ; if 
 he was a competent Judge of what he relates ; 
 if he had fufficient Opportunities of being in- 
 formed j if the Book that bears his Name was 
 really writ by him ; if it had been handed down 
 to us uncorrupted ; in fine, if what he relates 
 is probable in itfelf, falls in naturally with the 
 other Events of that Age, and is attefted by 
 contemporary Writers : By thefe and fuch like 
 Arguments, founded partly on Criticifm, part- 
 ly on probable Conjcdure, we judge of paft 
 
 Tranf-
 
 ( 336 ) 
 
 Tranfa&ions ; and though they are not capable 
 of fc ientijical Proof, yet in many Cafes we ar- 
 rive at an undoubted Aflurance of them. For 
 as it is abfurd to demand mathematical Demon- 
 ftration in Matters of P'a&, becaufe they admit 
 not of that Kind of Evidence ; it is no lefs fo to 
 doubt of their Reality, when they are proved by 
 the beft Arguments their Nature and Quality 
 will bear. 
 
 Scrpticifa* XIV. AND thus we fee, in the 
 
 neet/arify feveral Divifions of human Know- 
 
 txeiaaea frcm 
 
 Matttrt of ledge, both what is the Ground of 
 Scuna. Judging, and the Manner of Rea- 
 
 foning, peculiar to each. In Scientifical Know- 
 ledge, which regards wholly the abftradl Ideas 
 of the Mind, and thofe Relations and Con- 
 nections they have one with another ; our 
 Judgments are grounded on Intuition^ and the 
 Manner of Reafoning is by Demonftratlon. In 
 Natural Knowledge, refpecting Objects that 
 exift without us, their Powers, Properties, 
 and mutual Operations j we judge on the Foun- 
 dation of Experience^ and reafon by Induftion 
 and Analogy. Laftly, in, Hijlorical Knowledge^ 
 which is chiefly converfant about paft Fads 
 and Tranfa&ions ; Teflimony is the Ground of 
 Judgment, and the Way of Reafoning is by 
 Criticifm and probable Conjefture. And now I 
 think we are able effectually to overthrow that 
 abfurd Kind of Scepticifm maintained by fome 
 9 of
 
 ( 337 ) 
 
 of the Ancients, which brings all Propofitiona 
 upon a. Level, and reprefents them as equally 
 uncertain. What gave the firft Rife to this 
 Doctrine was, the Caprice of certain Philo- 
 fophers, who obferving that the Reports of 
 Senfe and Teftimony were in fome Inftances 
 deceitful, took thence Occafion to fuppofe that 
 they might be fo likewife in others, and there- 
 upon eftablifhed it as a Principle, that we 
 ought to doubt of eyery Thing. But even with 
 refptd to this Doubting we are to obferve, that 
 it can in Fact extend no farther than to Matters 
 of Experience and Tejlimony^ being totally and ne- 
 ceiTarily excluded from Scientifical Knowledge. 
 When Ideas make their Appearance in the Un- 
 der'tanding, it is impoffible for us to doubt of 
 their being there. And when the Relations of 
 any of our Ideas are clearly and diftinclly dif- 
 cerned by the Mind, either immediately, which 
 is Intuition, or by Means of intervening Ideas, 
 which is Demon/lration ; it would be in vain 
 for us to endeavour to perfuade ourfelves that 
 that is not, which we plainly and unavoidably 
 perceive to be. In this Cafe therefore we can- 
 not withhold our AiTent ; Truth forces its Way- 
 over all Oppofition, and breaks in w?th fo much 
 Light upon the Mind, as t9 beget abfolute and 
 infallible Certainty. 
 
 Q, XV. IK*
 
 ( 338 ) 
 
 And tt be ad- ' I N D E D n Natural and 
 
 mitted -with Hiftorical Knowledge Scepticifm 
 
 Caution in i_ T>I L / 
 
 Matten of m *Y " ave "J a ce ; bccaufe, as we 
 Experience have faid, there is a Poflibility of 
 
 anJTiflimony. . . . . 
 
 our being deceived, .but then it is 
 to be obferved, that a bare Poflibility is a very 
 weak Ground whereon to bottom any Philo- 
 fophical Tenet. It is poflible that Great Britain 
 may be fwallowed up by the Sea before To-mor- 
 row ; but I believe no Man is on 'this Account 
 inclined to think that it will be fo. It is pof- 
 fible the whole human Race may be extinguifhed 
 the next Inftant ; yet this Poflibility creates no 
 Apprehenfion that the Thing itfelf will really 
 happen. In a Word, we ought to judge of 
 Things by the Proofs brought to fupport them, 
 not by bare abftrad: Poflibilities ; and when we 
 have all the Evidence they are capable of, that 
 alone is fufficient to convince, tho' perhaps the 
 contrary cannot be fhewn to imply a Contra- 
 diction. Will any wife and confidcrate Man 
 doubt whether there be fuch a Place as America^ 
 becaufe we cannot prove by any neceflary Argu- 
 ment, that it is abfolutely impoffible all the Re- 
 lations concerning it fhould be falfe ? Strict and 
 rigorous Demonftrations belong not to Hiftory, 
 or the Philofophy of Nature. The Way of Rea- 
 foning in thefe Branches of Knowledge is by 
 Arguments drawn from Experience and Tefti- 
 mony. And when the Truth of any Propofition 
 
 is
 
 ( 339 ) 
 
 is in this Manner fufficiently afcertained, info- 
 much that it appears with all the Evidence it is 
 capable of, and we have as great Reafon to be- 
 lieve that it is, as we could pofllbly have, fup* 
 pofing it were, is not this upon the Matter as 
 fatisfa&ory as a Demonftration ? It muft be 
 owned indeed, there is no inward Perception in 
 the Cafe, and therefore our Aflent cannot be faid 
 to be neceflary and unavoidable. Men may in. 
 thefe Matters be Scepticks if they pleafe j and if 
 they are refolved upon it, it is in vain to contend 
 with Qbftinacy and Perverfenefs. I cannot how- 
 ever but obferve, that if they will really aft up to 
 their own Principles, and treat all Things in 
 good earneft as uncertain, that admit not of ftri& 
 fcientifical Proof, their Conduit muft be the 
 very Madnefs of Folly. No Man can demon- 
 ftrate mathematically, that Poifon has not been 
 conveyed into his Meat or Drink. And if he 
 will be fo very cautious as not to tafte of either, 
 till he has reached this Degree of Certainty, I 
 know no other Remedy for him, but that in 
 great Gravity and Wifdom he muft die for Fear 
 of Death. The Truth of it is, the moft zealous 
 Patrons of Scepticifm^ after all their pretended 
 Doubts and Scruples, find it yet convenient to 
 behave in the feveral Occurrences of Life, as if 
 they gave entire Credit to the Reports of Senfe 
 and Teftimony. They will no more venture up- 
 on a Dofe of Arfenic, or rufh into the Midft of a 
 Q.2 glowing
 
 ( 340 ) 
 
 glowing Furnace, than if they verily believed 
 Death would be the Confequence. And though 
 in this it muft be owned they act difcreetly, yet 
 have we hence at the fame Time a very convincing 
 Argument of the Abfurdity of thofe Notions they 
 affect to entertain. In Reality, can any Thing be 
 more ridiculous, than to give into a Scheme of 
 Thinking, which we find ourfelves neceflitated 
 to contradict in almoft every Occurrence of Life? 
 Opinions are not to be taken up out of Caprice 
 and Fancy, but to ferve as Principles of Action, 
 and ftanding Rules of Behaviour. When they 
 anfwer not this main Purpofe, they are unavail- 
 ing and fruitlefs, and an obftinate Adherence to 
 them, in Spite of the repeated Admonitions of 
 Experience, juftly deferves to be branded for 
 Folly. We f&all not therefore attempt to multi- 
 ply Arguments in a Matter fo obvious, it fuffi- 
 ciently anfwering our prefent Purpofe to have 
 fhown, that Doubting and Uncertainty have 
 no Place in fcientifical Knowledge, and that 
 even in Matters of Hiftory, and the Facts of 
 Nature, an undiftinguifhing Scepticifm would 
 be in the higheft Degree abfurd. 
 Sctcnct apfii- XVI. BUT here perhaps it will 
 
 cable to the b ftgj Wh ]j th j mighty N ojfe 
 CoKcerns of ' J 91 
 
 human Life, about Science, when even according 
 to the prefent Account, it feems to be fo very 
 capricious and arbitrary a Thing ? For feeing 
 it is wholly confined to the Confideration of our 
 
 Ideas,
 
 ( 34i ) 
 
 Ideas, and we are at Liberty to frame and combine 
 thofe Ideas at Pleafure, this indeed opens a Way 
 to Caftles in the Air of our own building, to 
 many chimerical and fanciful Syftems, which 
 Men of warm and lively Imaginations love to 
 entertain themfelves with, but promifes little 
 of that Knowledge which is worth a wife Man's 
 Regard, and refpe&s the great Ends and Pur- 
 pofes of Life. Where is the Advantage of barely 
 contemplating our Ideas, and tracing their fe- 
 veral Habitudes and Relations, when it is in 
 Truth the Reality of Things that we are chiefly 
 concerned to know, and thofe Refpeds they 
 bear to us and one another ? To this I anfwer : 
 that if indeed our Ideas no way regarded Things 
 themfelves, the Knowledge acquired by their 
 Means would be of very little Confequence t. 
 human Life. But fince, as we have already ob- 
 ferved, whatever is true in Idea, is unavoidably 
 fo alfo in the Reality of Things, where Things 
 exift anfwerable to thefe Ideas ; it is apparent, 
 that by copying our Ideas with Care from the 
 real Objects of Nature, and framing them in 
 a Conformity to thofe Conjunctures and Cir- 
 cumftances in which we are moil likely to be 
 concerned, a Way is laid open to Difcoveries of 
 the greateft Importance to Mankind. For in 
 this Cafe, our feveral Reafonings and Conclw- 
 fions, holding no lefs of the Objects themfelves, 
 Q.3 than
 
 ( 342 ) 
 
 than of the Ideas by which they are reprefented, 
 may be therefore applied with Certainty to thefe 
 Objects, as often as they fall under our Notice. 
 Thus Mathematicians, having formed to them- 
 felves Ideas of Cones, Cylinders, Sphere^, 
 Prifms, ffr. varioufiy compare them together, 
 examine their feveral Properties, and lay down 
 Rules by which to calculate their relative Bulk 
 and Dimenfions. But now as Bodies anfwering 
 ia Figure to thefe Ideas come frequently under 
 pur Obfervation, we have by this Means an Op- 
 portunity of applying Mathematical Knowledge 
 to the common Concerns of Life ; and by deter- 
 mining precifely the Quantity of Extenfion in 
 each Body, can the better judge how far they 
 will anfwer the Purpofes we have in View. 
 The fame Thing happens in Politicks and Mora- 
 lity. If we form to ourfelves Ideas of fuch Com- 
 munities, Connexions, Actions, and Conjunc- 
 tures, as do or may fubfift among Mankind ; all 
 our Reafonings and Conclusions will then refpecl 
 real Life, and ferve as fteady Maxims of Behavi- 
 our in the feveral Circumftances to which it is 
 liable. It is not therefore enough that we fet 
 about the Confideration of any Ideas at Random ; 
 we muft further take Care that thofe Ideas truly 
 regard Things themfelves : for altho' Knowledge 
 is always certain, when derived from the Con- 
 templation of our own Ideas, yet is it then only 
 ufeful and worthy aur Rega.rd a when it refpe&s 
 
 Ideas
 
 ( 343 ) 
 
 Ideas taken from the real Objects of Nature, and 
 ftridly related to the Concerns of human Life. 
 XVII. HAVING thus fhown that <n,,; M/^W 
 there is fuch a Thing as Science, fixed J Science be- 
 ad afcertained the Bounds of it, and pertaining our 
 explained its great Ufe and Impor- &'<*' 
 tance in the Affairs of Mankind j it now remains 
 that we lay down the Rules of Method peculiar 
 to this Branch of Knowledge, and give fome Ac- 
 count of the Manner in which that Certainty 
 and Conviction which are infeparable from it, 
 may be moft naturally and effectually produced. 
 Science, as we have faid, regards wholly the ab- 
 ftradt Ideas of the Mind, and the Relations they 
 have one to another. The great Secret there- 
 fore of attaining it lies, in fo managing and con- 
 ducting our Thoughts, as that thefe feveral Re- 
 lations may be laid open to the View of the Un- 
 derftanding;, and become the necefTary and un- 
 avoidable Objects of our Perception. In order 
 to this we muft make it our firft Care, diftin&ly 
 to frame and fettle the Ideas about which our 
 Enquiries are to be employed. For as the Re- 
 lations fubfifting between them can no otherwife 
 be difcerned, than by comparing them one with 
 another ; and as this Comparifon neceflarily fup- 
 pofes that the Ideas themfelves are actually in 
 the Mind, and at that very Time under our im- 
 mediate InfpeCtion ; it plainly follows, that all 
 Science muft begin with fixing and afcertain- 
 0.4 ing
 
 ( 344 ) 
 
 ing thofe Ideas. Now our Ideas, as has been 
 already obferved in the firft Book, come all very 
 naturally within the Divifion of Simple and Com- 
 plex. Simple Ideas are excited by a&ual Im- 
 preflions made upon the Undci (landing j and as 
 they exift under one uniform Appearance, with- 
 out Variety or Compofition, are in no Danger of 
 being miftaken, or confounded one with another. 
 It is otherwife in our Complex Conceptions. For 
 thefe confifting of many fimple Ideas joined to- 
 gether, great Care muft be taken, that we ac- 
 quaint ourfelves with the true Number combin- 
 ed, and the Order and Manner of their Connec- 
 tion. By this Means alone are thefe our moft 
 intricate Notices kept diftin& and invariable, in- 
 fomuch that in all our feveral Views of them, 
 they ever have the fame Appearance, and exhi- 
 bit the fame Habitudes and Refpe&s. Here there- 
 fore, properly fpeaking, the Art of Knowledge 
 begins. Fpr altho' we find it eafy enough to 
 bound and fettle our Ideas, where they confift 
 of but few limple Perceptions ; yet when they 
 grow to be very complicated, it often requires 
 great Addrefs and Management to throw them 
 imo fuch Views as may prevent that Confufion 
 which is apt to arife from the joint Confidera- 
 tion of a Multiplicity of different Objects. 
 Hence that Gradation in the Compofition of our 
 Ideas, which we have explained at large in the 
 laft Chapter of the firft Book. For as they are 
 
 by
 
 ( 345 ) 
 
 by this Means formed into different Orders, and 
 thefe Orders arife continually one out of ano- 
 ther j the Underftanding, by taking them in a 
 juft Succeflion, gradually mounts to the higheft 
 Conceptions, and can at any Time, with incredi- 
 ble Eafe and Expedition bring all their Parts dif- 
 tinclily into View. To know therefore the full 
 Value of this Contrivance, we muft attentively 
 confider the ftridl Connection that obtains be- 
 tween the feveral ClafTes of our Perceptions 
 
 * - 
 
 when difpofed in fuch a Series. Every Succeeding 
 Order is formed out of thofe Combinations that 
 conftitute the Rank next below it. And as irk 
 advancing from one Degree to another, we are 
 always to proportion the Number of Notices 
 united, to the Strength and Capacity of the 
 Mind ; it is apparent that by fuch a Procedure 
 the Ideas will be thoroughly afcertained in every 
 Step, and however large and bulky, lie yet fairly 
 within our Grafp. This obvioufly accounts for 
 that wonderful Clearnefs of Apprehenlion, which 
 we often experience within ourfelves, even in 
 regard to the moft complicated Conceptions. 
 For though the Multitude of Parts in many 
 Cafes be great, I may fay beyond Belief, yet 
 as they have been all previously formed into fe- 
 parate Clafles, and the Clafles themfelves dif- 
 tindly fettled in the Undemanding } we find 
 it eafy, by fuch a Series of Steps, to rife to any 
 Idea how complex foever, and with a fingle 
 Q. 5 Glance
 
 Glance of Thought embrace it in its full Ex- 
 tent. 
 
 Andcimmu- XVIlI. BtJT it is not enough 
 I^Melns of 1 l ^ at we barely f rm Ideas in our own 
 Dtfia'niont. Minds: We muft alfo contrive a 
 Way to render them ftable and permanent, that 
 when they difappear upon calling off our Atten- 
 tion, we may know how to retrieve them again 
 with Certainty. This is beft done by Words and 
 Descriptions, which ferve not only to fubje& 
 them to our own Review, but alfo to lay them 
 open to the Perception of others. And indeed 
 as one of the main Ends of reducing Knowledge 
 into the Form of a Science is, the eafy and ad* 
 vantageous Communication of Truth 5 it ought 
 always to be our firft Care, when we fet about 
 unfolding our Difcoveries, to exhibit the feveral 
 Conceptions to which they relate, in a juft and 
 accurate Series of Definitions. For till we have 
 diftinctly transferred our Ideas into the Under* 
 Handings of thofe to whom we addrefs ourfelves, 
 and taught their Connection with the appro* 
 priated Sounds, all our Reafonings will evidently 
 be without Efieft. If Men comprehend not the 
 true Import of our Words, and are therefore 
 led by them to bring wrong Ideas into Compa- 
 rifon, they can never fure fee Connections and 
 Habitudes that really fubfift not. But if on 
 the contrary the Terms we ufe exci-te thofe very 
 Perceptions in others, which they denote in 
 2 our
 
 ( 347 ) 
 
 our own Minds ; then, as the feveral Relations 
 pointed out will lie fairly open to View, they 
 muft needs be difcerned with great Readinefs 
 and Eafe, and ftamp the Character of Certainty 
 upon all our Deductions. 
 
 XIX. THUS we fee, that the Me- rt,e Names ef 
 thod of Science begins with unfolding fiP' e Idta * 
 
 J torjliture the 
 
 our Ideas, and communicating them original and 
 by Means of Definitions. And here f e ^ s '^ y Lan . 
 it is of great Importance to obferve, <* 
 that there muft be in all Languages, certain Ori- 
 ginal and Elementary Names, whence our De- 
 fcriptions take their firft Rife, and beyond which 
 we cannot trace the Meaning and Signification 
 of Sounds. For fince our very Definitions are 
 made up of Words, if we fuppofe not fuch pri- 
 mitive and fundamental Terms, into which they 
 all refolve themfelves, and where they at laft ne- 
 ceffarily terminate, it is evident there would be 
 no End of explaining. Now it is peculiar to our 
 fimple Ideas, that they cannot be originally ex- 
 cited by Words, but muft always make their 
 firft Entrance into the Underftanding by the ac- 
 tual Operation of Objedls upon it. When there- 
 fore, in a Series of Definitions, we arrive at the 
 Names of thefe Ideas, 'tis plain we can pufli 
 our Defcriptions no farther, but are neceffitated 
 to fuppofe, that the Perceptions themfelves have 
 already found Admifiion into the Mind. If they 
 Q.6 have
 
 have ftot, Definitions avail nothing ; nor can 
 they any other Way be imprefTed upon us, than 
 by betaking ourfelves to the feveral Objes in 
 which the Power of producing them refides. 
 Hence it appears, that the primary Articles of 
 Speech, into which the Whole of Language may 
 be ultimately refolved, are no other than the 
 Names of fimple Ideas. Thefe we fee admit not 
 Definitions. It is by Experience and Obferva- 
 tion that we grow acquainted with their Mean- 
 ing, and furnifh ourfelves with the Perceptions 
 they ferve to denote. For finding that thofe in 
 whofe Society we live, make ufe of certain ar- 
 ticulate Sounds, to mark the various Impreffions 
 of Objects, we too annex thefe Sounds to the 
 fame Impreffions, and thus come to underftand 
 the Import of their Words. This Way of Know- 
 ledge takes Place, in regard to all our fimplq 
 Ideas j but in many of thofe that are complex, 
 as they are the mere Creatures of the Underftand- 
 ing, and exift no-where out of the Mind, there 
 are of Courfe no real Objects without us, whence 
 they may be originally obtained. If therefore 
 they could not be communicated by Defcrip- 
 tions, we fhould be left wholly without the 
 Means of transferring them into the Minds of 
 others. But happily it fo falls out, that all 
 complex Conceptions whatfoever may be dif- 
 tindily exhibited in Definitions. For as they 
 are no more than different Combinations of fim- 
 
 pie
 
 ( 349 ) 
 
 pie Ideas, if thefe fimple Ideas have already got 
 Admiffion into the Understanding, and the 
 Names ferving to exprefs them are known ; it 
 will be eafy, by defcribing the Order, Number, 
 and peculiar Connection of the Notices com- 
 bined, to raife in the Mind of another the com- 
 plex Notion refulting from them. 
 
 XX. SINCE then it is by fimple A K 
 Ideas and their Names, that we un- 
 fold all the other Conceptions of the pojed in band- 
 Mind ; it manifestly follows, that in 
 handling any Subje&feienti/ically, we 
 muft always fuppofe thofe to whom we addrefs 
 ourfelves previoufly furnifhed by Experience 
 with thefe firft Principles and Elements of 
 Knowledge. Nor is this by any Means an un- 
 reafonable Pojlulatum : Becaufe the fimple Ideas 
 that relate to the Sciences, being few in Num- 
 ber* and coming very often in our Way, it is 
 hardly poffible we fhould be unacquainted with 
 them, or not have frequently heard their Names 
 in Converfe with others. What principally de- 
 mands our Care is, to apply thofe Names aright, 
 and according to the ftri& Ufe and Propriety of 
 the Language in which we write. 'Tis feldom 
 allowable to change the Signification of Words, 
 efpecially thofe by which we denote fimple Ideas. 
 If however fuch a Liberty fhould at any Time be 
 found neceflary, we may ftill make ourfelves 
 
 underftood,
 
 ( 350 ) 
 
 underftood, by mentioning the Idea under its 
 common Name, and fignifying its Connexion 
 with the newly-appropriated Sound. Indeed it 
 fcmetimes happens, that new and unufual Ideas 
 of this Kind are to be taken under Confideration, 
 which we muft therefore exprefs by Terms of 
 our own Invention. In this Cafe, as the Ideas 
 themfelves cannot be laid open by Definitions, 
 we refer to the feveral Obje&s whence they may 
 be obtained ; which though it excites not the 
 Perceptions immediately, yet fufficiently an- 
 fwers our Purpofe, by putting Men in a Way 
 of being furnifhed with them at Pleafure. 
 
 XXI. THIS Foundation being 
 
 The Order and , . . . f ^ . . r 
 
 CoMeflhnof J ai " the Communication of our 
 eurDefni'iom. com pl e x Conceptions by Definitions 
 becomes both eafy and certain. For fince the 
 Ideas themfelves are formed into different Or- 
 ders, and thefe Orders arife continually one out 
 of another ; nothing more is required on our 
 Part, than to obferve a like Method and Grada- 
 tion in our Defcriptions. As therefore the firft 
 Order of our compound -Notions is formed 
 immediately from fimple Ideas ; fo the Terms 
 appropriated to this Order muft be defined by 
 the Names of thefe Ideas. And as the fecond 
 and all the fucceeding Orders arife continually 
 cut of thofe Combinations that conftitute the 
 Clafles next below them, fo the Definitions 
 
 correfponding
 
 / ( 351 } 
 
 correfponding to thefe different Orders gra- 
 dually take in the Terms by which the feveral 
 inferior Divifions are regularly and fucceflively 
 exprefled. In fuch a Series of Oefcriptions, it 
 is evident at firft Sight, that nothing can be ob- 
 fcure and unintelligible. For as it begins with 
 the Names of fimple Ideas, whofe Meaning is 
 fuppofed to be known; and as in every Order 
 of Definitions, fuch Terms only occur, as have 
 been previously explained in the preceding Dif- 
 tributions j by advancing regularly from one 
 to another, we gradually furnifh ourfelves with 
 whatever is neceflary towards a diftincl: Con- 
 ception of all that is laid before us. Nor is it 
 a fmall Advantage attending this Difpofltion, 
 that the feveral Ideas defcribed are hereby ex- 
 ciied in the Underftanding, in the very Order 
 and Manner in which they are framed by a 
 Mind advancing uniformly from fimple to the 
 mod complicated Notions. Hence we fee dif- 
 tin&ly the various Dependence of Things, ami 
 being put into that very Train of Thinking 
 which leads dire&ly to Science and Certainty, 
 are drawn infenfibly to intereft ourfelves in the 
 Purfuit ; infomuch' that while in Fail we do 
 no more than follow a Guide and Conductor, 
 we can yet hardly forbear fancying ourfelves 
 engaged in the actual Exercife of deducing 
 one Part of Knowledge from another. 
 
 XXII. WHEN
 
 ( 352 ) 
 
 Of tke tmrne- XXII. WHEN W6 have tllUS fixed 
 
 JUH andin- and afcertained our Ideas, and dif- 
 
 tvitive Refa- /-> i > M i i r\ f 
 
 tiot bttnttn tinctly exhibited them in Denm- 
 tur ides,. tions, we then enter upon the im- 
 portant Tafk of tracing their feveral Habitudes 
 and Relations. In order to this we fet about 
 comparing them among themfelves, and viewing 
 them in all the Variety of Lights, by which we 
 can hope to arrive at a Difcovery of their mu- 
 tual Agreement or Difagreement. And here it 
 happens, that fome Relations forwardly offer 
 themfelves to the Notice of the Underiranding,. 
 and become the neceflary Objects of Perception, 
 upon the very firft Application of our Ideas one 
 to another, Thofe are therefore immediately 
 owned, and conflitute our primary and intuitive 
 Judgments, being attended with the higheft De- 
 gree of Evidence, and producing abfolute Cer- 
 tainty in the Mind. But in many Cafes, the 
 Connection or Repugnance between our Ideas, 
 even when true and real, comes not yet within 
 our immediate View, but requires Search and 
 Examination to difcover it. On this Occafion, 
 we have Recourfe to intermediate Notices, and 
 if by Means of them we can mufter up a Train 
 of evident and known Truths, which, difpofed 
 in a regular Series of Argumentation, lead at 
 laft to a Conclufion expreffing the Relations we 
 are in Queft of, the Proof thence arifing is called 
 Demonflration. Now as the Conviction attend- 
 ing
 
 ( 353 ) 
 
 ing Demonftration is no lefs neceflary and un- 
 avoidable than that which proceeds from, In- 
 tuition ; it evidently follows, that whether the 
 Relations between our Ideas are injtnediately 
 difcerned by the Mind, or whether they are 
 traced by Means of intervening Perceptions, in 
 either Cafe we arrive at Science and Certainty. 
 This however is particularly to be obferved, 
 that the more remote and diftant Refpels, be- 
 ing deduced from fuch as are obvious and felf- 
 evident, the Propofitions expreffing thefe laft 
 demand our firft Notice, and ought to be previ- 
 oufly eftablifhed, before we enter upon higher 
 Inveftigations. When therefore, in the Method 
 ff Science, we have finifhed the Bufinefs of De- 
 finitions; it muft be our next Care, diftin&ly 
 to unfold in Propofitions, thofe immediate and 
 intuitive Relations, which are neceflarily feen 
 and owned by the Mind, upon the very firft 
 comparing of our Ideas one with another. Thefe 
 Propofitions have obtained the Name of firft 
 Principles^ becaufe occurring firjl in the Order 
 of Knowledge, and being manifeft of themfelves, 
 they fuppofe not any prior Truths in the Mind, 
 whence they may be evidenced and explained. 
 It is not needful to enlarge here upon the Ne- 
 ceflity of Circumfpeclion and Care, in fettling 
 thefe primitive and fundamental Perceptions. 
 For fmce the whole Superftruclure of our Know- 
 ledge refts ultimately upon them, it is evident at 
 
 firft
 
 ( 354 ) 
 
 firft Sight, that a Miftake in this Cafe muft at 
 once overturn and annihilate all our future 
 Reafonings. But having already explained the 
 Nature of thefe Propofitions in the fecond Book, 
 unfolded the Notion of Self-Evidence, and 
 taught the 'Manner of diftinguifhng between 
 the Truths of this Clafs, and thofe that are 
 demonftrable j \ve fhall for the prefent wave 
 any farther Confideration of this Subject, re- 
 ferring the Reader to what is there advanced, 
 if he defires fuller Information. 
 
 XXIII. THE firft and more im- 
 mediate Relations of our Ideas be- 
 jng thus pointed out, our next Bu- 
 
 in dimonfirat- _ . . . _ . - , 
 
 finefs is, to mveltigate fuch as are 
 
 r '* 0!e **4 remote and diftant. And here it is 
 
 aijtant, 
 
 that we have Occafion for inter- 
 mediate Notices, and a fkilful Application of 
 intuitive Truths. But tho' felf-evident Pro- 
 pofitions be the ultimate Foundation of our 
 Reafoning, we are not on that Account to ima- 
 gine, that the Art of improving Knowledge 
 Jies in aflembling at Random a large and com- 
 prehenfive Stock of thefe. Even General Prin- 
 ciples^ confidered by themfelves, avail but little 
 towards the Inveftigation of Truth. They are 
 indeed ufeful as Media of Certainty, by pre- 
 ferving the Evidence of our Reafonings diftincr, 
 which never fail to convince, if, being purfued 
 to their Source, they are found to refolve them- 
 
 felves
 
 ( 355 ) 
 
 felves into, and ultimately terminate in thefe 
 Principles. But when we fet about the In- 
 creafe and Enlargement of Science, far other 
 Helps are required. For here the whole Secret 
 confifts, in devtfing and fingling out fuch in- 
 termediate Ideas, as being compared with thofe 
 others whofe Relations we enquire after, may 
 furnifh out a -Train of obvious and known 
 Truths, ferving diftinctly to inveftigate the faid 
 Relations. Euclid, in the firft Book of the Ele- 
 ments, has demonftrated, that the three inward 
 Angles of a Triangle taken together, are equal t& 
 two Right Angles. The Reafoning by which he 
 eftablifhes that Proportion, refolves itfelf into 
 this general Principle : Things equal to one and 
 the fame Thing, are equal to vne another. Will 
 any one however pretend to fay, that a bare 
 Confideration of the Principle itfelf led him to 
 that Difcovery ? The mereft Novice in Ma- 
 thematicks would upon this Suppofition be 
 equally qualified for the Bufmefs of Invention, 
 with one that had made the greateft Progrefs; 
 inafmuch as thefe general Principles of the 
 Science are commonly alike known to both. 
 But the Truth of it is, Euclid having found 
 out Angles, to which the three Angles of a 
 Triangle, and two Right Angles, being com- 
 pared, were found feverally equal ; thereby af- 
 certained the Propofition in Queftion, by (hewing 
 it to terminate in the above Axiom, tho' perhaps 
 
 the
 
 ( 356 ) 
 
 the Axiom itfelf was never once thought of dur- 
 ing the whole Courfe of the Inveftigation. 
 
 */*,'* XXIV - AND here jt ma x not bc 
 
 rejoivabie into improper to obferve, that tho' it be 
 
 generalTrutbi) r 1 T> r 
 
 nftt \mmtdi- ufttsu in Kealoning, when we arrive 
 oteiyupcn at any p art icular felf-evident Pro- 
 
 f articular r 
 
 j<if-e-v,j>r<t pontion, to refer to the general 
 rofofitHns. Axiom under which it is compre- 
 hended : yet is not this done out of abfolute 
 Neceffity, or for the Sake of any additional 
 Confirmation. All intuitive Truths, whether 
 general or particular, {landing upon the fame 
 Foundation of immediate Perception, are ne- 
 ceflarily embraced for their own Sake, and re- 
 quire no mutual Illuftration one from another. 
 When therefore we have found, that the three 
 Angles of a Triangle, and two Right Angles, 
 are feverally equal to the Angles formed by one 
 Right Line {landing upon another, we thence 
 immediately difcern their Equality between 
 themfelves, independent of the general Axiom 
 into which this Truth maybe refolved. Nor do 
 we in Reality refer to that Axiom, by Way of 
 Evidence and Proof; but merely to {how the 
 Coincidence cf the Example under Notice, with 
 a previoufly eftabliflied general Principle. The 
 fame Thing happens in all other Demonftrations 
 whatfoever, which terminating thus in particu- 
 lar felf-evident Truths, are therefore of them- 
 felves fufficient to Certainty, and acquire not 
 
 any
 
 ( 357 ) 
 
 new Force by being ultimately referred to 
 general Maxims. This I mention here, to ob- 
 viate a common Prejudice, whence many are led 
 to imagine, that particular intuitive Propofitions 
 derive their Evidence from thofe that are general, 
 as being neceflarily included in them. But fince 
 they both ftand upon the fame Foundation of 
 Certainty, and are admitted in confequence of 
 immediate Perception, they have therefore an 
 equal Claim to Self-Evidence, and cannot be 
 made plainer by any mutual Appeal. 
 
 XXV. As however it is ufual in Particular 
 the Method of Science to lay down J< l f- ""<*">* 
 
 rropofitiont 
 
 certain general Principles by Way fo called here, 
 of Foundation for our future Rea- $gJr" 
 fonings ; fome will perhaps object, Principle*. 
 that this feems to be a needlefs Precaution, fince 
 Demonftrations may fubfift without them, and 
 commonly terminate in particular felf-evident 
 Truths, peculiarly connected with the Subject 
 under Confideration. In order therefore to give 
 a diftindl Idea of the true Defign of this previous 
 Step, we fliall begin with obferving, that by 
 the particular Propofitions in which Demonftra- 
 tions terminate, muft not be underftood fuch as 
 are fo according to the ftridl Definition of the 
 Word, or in Oppofition to Univerfals ; but only 
 confined and limited Truths, when compared 
 with others that are more general. Thus the 
 Propofition, Circles equal to one and the fame 
 
 Circle,
 
 ( 358 ) 
 
 Circle, are equal between thernfefoes, is in Strict ~ 
 nefs and Propriety of Speech univerfal, becaufe 
 the Subject is taken in its full Extent, and the 
 Predicate agrees to all the Individuals compre- 
 hended under it. We here notwithftanding 
 confider it as only a particular Truth, becaufe 
 it is of a very limited Nature, when compared 
 with the general Axiom mentioned above j 
 Things equal to one and the fame Thing , are equal 
 to one another. For this not only extends to all 
 the various Species of Figures, but takes in 
 every Object without Exception, that comes 
 under the Denomination of Quantity. 
 GwralPrin. XXVI. THIS Point fettled, it 
 dples few will eafily appear, that the Method 
 
 fir ft to contra ft c .~ i T. i 
 
 tte Bottom of r premihng general Principles in 
 ur Reaftaiag. t h e Sciences anfwers thefe two 
 great and valuable Purpofes. Fir ft ^ to contract 
 the Bottom of our Reafoning, and bring it within 
 fuch Bounds as are fufficiently accommodated 
 to the Capacity of the Mind. For Demon- 
 flrations being carried on by Means of inter- 
 mediate Ideas, which muft always have fome 
 peculiar Connection with the Matter in Hand, 
 the particular felf-evident Propofitions in which 
 they terminate are almoft as various as the Sub- 
 jects to which they relate. Thus in invefti- 
 gating the Equality of different Objects, whe- 
 ther Angles, Triangles, Circles, Squares, &c, 
 the intuitive Truths on which the Proofs reft 
 
 always
 
 ( 359 ) 
 
 always regard the particular Species, and may 
 be therefore multiplied in infinitum^ as well as 
 the Species themfelves. But now it is remark- 
 able that all thefe feveral Truths, numerous as 
 they may appear, are yet reducible to this one 
 general Principle already mentioned ; Things 
 equal to one and the fame Thing, are equal to one 
 another. The fame Obfervation will be found 
 to hold in other Parts of human Knowledge ; 
 infomuch that tho' the particular Truths on 
 which we bottom our Reafonings are really 
 innumerable j yet may they be all without Ex- 
 ception refolved into a very few general Max- 
 ims, and thereby brought readily within the 
 Compafs ^of the Underftanding. When there- 
 fore we begin with premifing thefe general 
 Truths, and as we advance in Science, take 
 Care univerfally to refolve our Demonftrations 
 into them ; this muft needs add a wonderful 
 Clearnefs and Perfpicuity to our Reafonings, 
 and by eftablifhing them upon a Foundation 
 previoufly admitted, and of whofe Strength and 
 Firmnefs we are abundantly fatisfied, give them 
 that irrefiitible Force and Influence, which 
 ferves to produce abfolute Certainty. Nor can 
 we poflibly imagine any Thing more elegant 
 and beautiful, than thus to behold Knowledge- 
 rifing from a firm and fathomable Root, bear- 
 ing its Head aloft, and fpreading forth into in- 
 numerable Branches of Science, j which though 
 
 variously
 
 varioufly implicated and entangled, and ftretch- 
 ing to a vaft Extent, yet by their Union in 
 one common Stock, derive thence fo fure and 
 ftable a Support, that all the Aflaults of Cavil 
 and Scepticifm are not able to deftroy or loofen 
 their Connection. 
 
 XXVII. BUT Secondly, another 
 
 Secoad/y, to . . 
 
 afcenoin the Purpolc lerved by general Principles 
 
 Jijhcfs of it j that t| b] I h ] f jp 
 
 with mare 
 
 Fofe, and left tigue and Labour, and lefs Hazard 
 
 Hazard of r \/r-r r r ' r- i 
 
 Mi/carriage. ' Milcarriage, to latisfy ourlelves 
 as to the Juftnefs of thofe Reafon- 
 ings by which Science is eftablifhed. For fince 
 Demonftrations, when purfued to their Source, 
 terminate always in particular intuitive Truths, 
 which are therefore the ultimate Foundation of 
 Certainty ; it greatly imports us to beware, 
 that we receive not any Propofitions under 
 this Name, until we have diftin&ly fettled them 
 in our own Minds, and attained a full and clear 
 Perception of that Self-Evidence, on account 
 of which they are admitted without Proof. 
 But now thefe Propofitions being many in 
 Number, and differing according to the Nature 
 of the Subject about which our Refearches are 
 employed ; it muft greatly perplex and re-tard 
 our Reafonings, were we to check ourfelves 
 every Time they occur, in order to examine 
 them by the Rules of firft Principles. Nor is 
 it a Matter of flight Confideration, that in the 
 
 Heat
 
 Heat and Hurry of demonftrating, while the 
 Mind is advancing eagerly from one Difcovery 
 to another, we fhould be often tempted to pafs 
 them over haftily, and without that Attention 
 their Importance requires ; which muft expofe 
 us to many Errors and Miftakes. Thtfe In- 
 conveniences are effe&ually prevented by the 
 Method of premifing general Truths : becaufe 
 upon referring particular Propofitions to them ; 
 as the Connection is obvious at firft Sight, and 
 cannot poflibly efcape our Notice, the Evidence 
 is difcerned to be the very fame with that of the 
 Principles to which they belong. And thus by 
 a bare Reference, without the Trouble of parti- 
 cular Examinations, the Grounds of Reafoning 
 are afcertained, and our Demon%ations found 
 ultimately to reft on Maxims pjevioufly cfta- 
 blifhed. 
 
 XXVIII. HAVING explained the oftbtMaa* 
 Ufe of general Principles, fhewn r>f j linking 
 them to be the great Medea of Cer- topthr^i* 
 tainty, and found, that in order to " dtrt <>' bt 
 
 1 L T> I i- forming of It- 
 
 enlarge the isounds of science, we gititate De- 
 rnuft have recourfe to intermediate >7 ""'/ r3 "' < ""- 
 Ideas, as by Means of them we are furnifhed with 
 the feveral previous Truths, of which Reafoning 
 confifts ; it now remains that we enquire in 
 what Manner thefe Truths are to be difpofed 
 and liaked together, towards the forming of juft 
 and legitimate DemonJIrationt. We have feen 
 R already
 
 already in the preceding Book, that Syllogifms 
 drawn up according to the Rules there eftablifh- 
 ed, lead to a certain and infallible Conclufion. 
 If therefore evident and allowed Truths are dif- 
 pofed in a Syllogijtic Order, fo as to offer a regu- 
 lar Conclufion, that Conclufion is neceflarily 
 true and valid. And fince in every genuine Syl- 
 logifm, if the Premifes are true, the Conclufion 
 muft needs be true ; it manifeftly follows, that 
 the Conclufion already gained, being now a 
 known and eftabliflied Truth, may be admitted 
 as one of the Premifes of any fucceeding Syllo- 
 gifm, and thereby contribute towards the ob- 
 taining a new Conclufion. In this Manner may 
 Fyllogifms follow one another in Train, and lead 
 to a fucceffive Difcovery of Truth ; Care being 
 always taken, that the Premifes in every Step 
 are either felf-evident Propofitions, or Conclu- 
 fions previoufly eftablifhed. And indeed the whole 
 Art of demonfirating lies in this due and orderly 
 Combination of our Syllogifms. For as by this 
 means all the feveral Premifes made ufe of are 
 manifefUy true, all the feveral Conclufions muft 
 be fo too, and confcquently the very Jaft Con- 
 clufion of the Scries, which is therefore faid to 
 be dcmonjlrated. The fame Order is to be ob- 
 ferved in the Difpofition of the Dcmonftrations 
 themfelves. That is, thofe Propofitions are al- 
 W.ys firft to be demonftrated, which furnifli 
 Principles of Reafoning in others ; it being 
 
 upon
 
 ( 3*3 ) 
 
 upon the Certainty of the Principles made Ufe 
 of, that the Certainty of the Truths deduced 
 from them depends. And fince even the dif- 
 ferent Branches and Divifions of Science have 
 a near Connection among themfelves, info- 
 much that the Knowledge of one is often pre- 
 fuppofed in another ; great Care muft be taken 
 to adjuft the feveral Parts with an Eye to this 
 Dependence, that thofe may always come firft 
 in Order, whence the Poftulata of Demonftra- 
 tion in others are borrowed. 
 
 XXIX. IN this Way /of putting why tit Me.- 
 together our Thoughts, it is evident tb . od . bt . re '*~ 
 
 b plained is ;all- 
 
 at firft Sight, that however far we e d the M<tt>ad 
 carry our Refearches, Science and of Sci " !Cl ' 
 Certainty will ftill attend us. But what is par- 
 ticularly elegant and happy in the Method now 
 explained, we hereby fee Knowledge rifing 
 out of its firft Elements, and difcern difti nelly 
 how thofe Elements are combined and inter- 
 woven, in order to the erecting a goodly Struc- 
 ture of Truth. Experience furnifhes us with 
 fimple Ideas and their Names, which are the 
 primary Materials of Thinking and Communi- 
 cation. Definitions teach how to unite and 
 bind thefe Ideas together, fo as to form them 
 into complex Notions of various Orders and 
 Degrees. The general Principles premifed in 
 Science exhibit to the Underftanding fuch in- 
 tuitive and fundamental Truths as exprefs the 
 
 immediate
 
 immediate Relations between our Ideas, and con- 
 ftitute the ultimate Ground of Certainty. De~ 
 tnonjlratlons link known and eftablifhed Truths 
 together in fuch Manner, that they neceflarily 
 lead to others which are unknown and remote. 
 In fine, the duly adjufting the feveral Branches 
 of Science, and the Demonftrations in every 
 Branch, lays Knowledge fo open to the Mind, 
 that we fee the Parts of it growing one out of 
 another, and embrace them with full Convic- 
 tion and Affurance. Thus are we gradually led 
 from fimple Ideas, through all the Windings and 
 Labyrinths of Truth, until we at length reach 
 the higheft and moft exalted Difcoveries of hu- 
 man Reafon. It is true the Method here laid 
 down hath hitherto been obferved ftri&ly only 
 among Mathematicians ; and is therefore by 
 many thought to be peculiar to Number and 
 Magnitude. But it appears evidently from what 
 we have faid above, that it may be equally ap- 
 plied in all fuch other Parts of Knowledge as re- 
 gard the abftract Ideas cf the Mind, and the 
 Relations fubfiiVmg between them. And fmce, 
 wherever it is applied, it neceflarily begets Science 
 and Certainty, we have hence chofen to denomi- 
 nate it the Method of kcience> the better to inti- 
 mate its true Nature and Extent. 
 
 FINIS.
 
 
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