UC-NRLF 
 
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 GIFT OF 
 
 Dr.tHA^ T^v 
 
ELEMENTS' . - 
 
 OF ' f4 C< ,<U<)^ 
 
 L O G I C. 
 
 IN 
 
 BOOK I. 
 
 ■ the original of our ideas, 
 their various divisions, and 
 the manner in which they 
 pontribott to the increase 
 of knowledge ; with a phi- 
 losophical account of the 
 rise, ] i d nature of 
 
 human language. 
 
 BOOK II. 
 
 fthe grounds of human judg- 
 ment, the doctrine of pro- 
 ions, their use in rea- 
 soning, & division* into self 
 evident and demonstrable. 
 
 book nr. 
 
 Of reasoning and demonstra- 
 tion, with their application 
 tothe investigation of know- 
 ledge, and the common af- 
 fairs of life. 
 
 book iv. 
 
 Of the methods of invention, 
 and science, where the se- 
 veral degrees of evidence 
 are examined, the notion of 
 certainty is fixed and stated, 
 and the parts of knowledge 
 in which it may be attain- 
 ed, demonstrated at large. 
 
 DESIGNED PARTICULARLY FOR 
 
 Young Gentlemen at the University; 
 
 tfD TO PREPARE THE WAY TO THE STUDY OF 
 PHILOSOPHY AND THE MATHEMATICS. 
 
 BY WILLIAM DUNCAN, 
 
 a 
 
 Professor of Philosophy in Marishal College y Aberdeen^ 
 
 Doctrina sed vim promovet insitam ; 
 Rectique cultus pectora roborant Hok, 
 
 NEW-YORK : 
 
 PHINTED BY L. NICHOLS, & C©. 
 FOR RyERT DUrCKIXCK* BOOKSELLER. 
 
\o* 
 
 &1 
 
 0> 
 
T© THE 
 
 RIGHT HONORABLE 
 
 STEPHEN POYNTZ ; Esq. 
 
 SIR, 
 
 IF I take this opportunity of publishing to the 
 world the efteem I have for a character to which 
 learning is fo greatly indebted, I hope you will not 
 think yourfelf injured by fuch a declaration from a 
 man that honors you, and who looks upon the liber- 
 ty of putting the following work under your patron- 
 age, as one of the happy incidents of his life. 
 
 From, the fir ft moment I formed the defign of it, 
 I had it in my thoughts to acldrefs it to you ; and 
 indeed what could be more natural, tl^an that I 
 (hould be ambitious of infcribing a treai the 
 
 elements of philofophy, to one, who has 10 emi- 
 nently diftinguifhed himfelf by his extenfive know- 
 ledge in that, as well as all the other branches of 
 human learning ? 
 
 Your great abilities in every kind, have deferv- 
 edly recommended you to the notice of your king 
 and country, and occasioned your being courted and 
 importuned to accept of thofe high offices of ftate, 
 which others purfue with fo much eagernefs, and 
 find it often difficult to obtain, by all the arts and 
 endeavors of ambition. Nor have your talents bee a 
 confined to the view of your country alone. Fo- 
 reign nations have feen and admired you, and ftill 
 fpeak with the greateft applaufes of your wife and 
 able conduft, when it was your province to a£t as 
 a Britifh minifter abroad. 
 
4 DEDICATION. 
 
 But the qualities of a great flatefman are not 
 thofe alone by which you have rendered yourfelf il- 
 luftvious. The virtues of private life no lefs actu- 
 ate and adorn your whole behavior, and add a new 
 dignity to the high ftation to which your merit has 
 raifed you. Affability, complacency of manners, 
 and, above all, an extenfive humanity and benevo- 
 lence, which takes pleafure'in doing good, are dis- 
 tinguishing parts of your character, and have con- 
 tributed no lefs than your other extraordinary en- 
 dowments, to that univerfal acknowledgement which 
 is paid you by your country. 
 
 ' Tjiat 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 hear- 
 ty prayer of, 
 
 Six, 
 
 Tquv most obliged) and most obedient 
 
 Humble Servant, 
 
 Z8X. Duncan, 
 
 %% m 
 
C 5 ] 
 
 3[ntromictton. 
 
 Sec. l,.„Importance of the Knowledge of Ourseh:o* 
 
 OF all the human sciences, that concerning man is 
 certainly the most worthy of man, and the most 
 necessary part of knowledge. We find ourselves in this 
 •world surrounded with a variety of objects : we have 
 powers and faculties fitted to deal with them, and arc 
 happy or miserable in proportion as we know how to 
 frame a right judgment of things, and shape our actions 
 agreeably to the circumstances in which we are placed. 
 No study, therefore, is more important than that which 
 introduces us to the knowledge of ourselves. Hereby 
 we become acquainted with rhe extent and capacity of 
 the human mind ; and learning to distinguish what ob- 
 jects it is suited to, and in what manner it must proceed 
 in order to compass its ends, we arrive by degrees, at 
 that justness and truth of understanding, which is the 
 great perfection of a rational being. 
 Sec. II.... Different gradations of Perfection in Things* 
 
 If we look attentively into things, and survey th 
 in their full extent, we see them rising one above ano- 
 ther in various degrees of eminence. Among the ina- 
 nimate parts of matter, some exhibit nothing worthy 
 our attention : their parts seem as it were jumbled 
 together by mere chance % nor can we discover any beau- 
 ty, order, or regularity in their composition. In others, 
 •we discern the finest arrangement, and a certain ele- 
 gance of contexture, that makes us afRxto tlnm a no- 
 tion of worth and excellence. Thus metals, and pre- 
 cious stones, are conceived as far surpassing those un- 
 formed masses of earth, that lie every where exposed 
 to view. If we trace nature onward, and pursue her 
 through the vegetable and animal kingdoms, we find 
 her still multiplying her perfections, and rising, by a 
 just gradation, from mere mechanism to perception, 
 and from perception, in all its various degrees, to rea- 
 son and understanding. 
 
 Sec. 111. ...Usefulness of Culture, and particularly of 
 the Study of Logic. 
 
 But though reason be the boundary by which man is 
 A 3 
 
vi INTRODUCTION, 
 
 distinguished from the other creatures that surround him, 
 yet we are far from finding it the same in all. Nor is this 
 inequality to be wholly ascribed to the original make 
 of men's minds, or the difference of their natural en- 
 dowments. For if we look abroad into the several na- 
 tions of the world, some are over-run with ignorance and 
 barbarity ; others flourish in learning and the sciences ; 
 and what is yet more remarkable, the same people have 
 indifferent ages, been distinguished by these very op- 
 posite characters. It is therefore by culture, and a due 
 application of the powers of our minds, that we increase 
 their capacity, and carry human reason to perfection. 
 "Where this method is followed, knowledge and strength 
 of understanding never fail to ensue ; where it is neg- 
 lected, we remain ignorant of our own worth ; and 
 those latent qualities of the soul, by which she is fitted 
 to survey this vast fabric of the world, to scan the hea- 
 vens, and search jnto the causes of things, He buried in 
 darkness and obscurity. No part of knowledge, there- 
 fore, yields a fairer prospect of improvement, than 
 that which takes account of the understanding, exa- 
 mines its powers and faculties, and shews, the ways by 
 -which it comes to attain its various notions of things. 
 This is properly the design of Logic, which may be just- 
 ly stiled the history of the human mind, inasmuch as it 
 traces the progress of our knowledge, from our first 
 and simple perceptions, through all their different com- 
 binations, and all those numerous deductions that result 
 from variously comparing them one with another. It is 
 thus that we are let into the natural frame and contex- 
 ture of our own minds, and learn in what manner we 
 ought to conduct our thoughts, in order to arrive at 
 truth, and avoid error. We see how to build one dis- 
 covery upon another, and, by preserving the chain of 
 reasonings uniform and unbroken, to pursue the rela- 
 tions of things through all their labyrinths and wind- 
 ings, and at length exhibit them to the view of the soul, 
 ytith all the advantages of light and conviction. 
 
 Sec. IV. ...Operations of the Mind, 
 
 But as the understanding, in advancing from one 
 
INTRODUCTION. vii 
 
 part of knowledge to another, proeeeds by a just gra- 
 dation, and exerts various acts, according to the diifer- 
 ent progress it has made, logicians have been careful 
 to note these several steps, and have distinguished them 
 in their writings by the name of the operations of the 
 mind. These they make four in number, and agreeably 
 to that have divided the whole system of logic into four 
 parts, in winch these acts are severally explained, 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 distinction of the powers 
 of the understanding, let us take a short view of the 
 mind, and the manner of its progress, according to the 
 experience we have of it in ourselves, and see whi- 
 ther the chain of our own thoughts will without con- 
 straint lead us. 
 
 Sec. V '.*.• Perception* 
 
 First, then, we find ourselves surrounded with a va- 
 riety of objects, which, acting differently on our senses, 
 convey distinct impressions into the mind, and thereby 
 rouse the attention and notice of the understanding. 
 By reflecting, too, on what passes within us, we become 
 sensible o£ the operations of our own minds, and at- 
 tend to them as a new set of impressions. But in all this 
 there is only bare consciousness. The mind, without 
 proceeding any farther, takes notice of the impressions 
 that are made upon it, and views things in order as 
 they present themselves one after another. This atten- 
 tion of the understanding to the objects acting upon it, 
 whereby it becomes sensible of the impressions ther 
 make, is called, by logicians, perception ; and the no- 
 tices themselves, as they exist in the mind, and are 
 there treasured up to be the materials of thinking and 
 knowledge, are distinguished by the name of ideas* 
 
 Sec. VI... •Judgment. 
 
 But the mind does not always rest satisfied in the 
 
 bare view and contemplation of its ideas. It is of a 
 
 more active and busy nature, and likes to be assembling 
 
 them together, and comparing them one with another. 
 
viii INTRODUCTION. 
 
 In this complicated view of things, it readily discerns, 
 that some agree and others disagree, and joins or sepa- 
 rates them according to this perception. Thus, upon 
 comparing the idea of two added to two, with the idea 
 of four, we, at first glance,'' perceive their agreement, 
 and thereupon pronounce that two and two are equal 
 to four. Again, that white is not black, that five is less 
 than seven, are truths to which we immediately assent, 
 as soon as we compare those ideas together. This is the 
 first and simplest act of the min^l, in determining the 
 relation of things, whe$, by a bare attention to its 
 own ideas, comparing any two of them together, it 
 can at once see how far they are connected or disjoin- 
 ed. The knowledge thence derived is called intuitive, 
 as requiring no pains or examination; and the act of 
 the mind assembling its ideas together, and joining or 
 disjoining them, according to the result of its fiercep* 
 tions, is what logicians term judgment. 
 
 Sec. V 'II.... Reasoning, 
 
 Intuition affords the highest degree of certainty; it 
 breaks in with an irresistible light upon the undemand- 
 ing, and leaves no room for doubt or hesitation.. Could 
 we in all cases, by thus putting two ideas together,, 
 discern immediately their agreement or disagreement, 
 we should be exempt from error, and all its fatal con- 
 sequences. But it so happens, that many of our ideas 
 are of such a nature, that they cannot be thus examined 
 in concert, or by any immediate application one to 
 another ; and then it becomes necessary to find out some 
 other ideas that will admit of this application, that by 
 means of them we may discover the agreement or dis- 
 agreement we search for. Thus the mind wanting to 
 know the agreement or disagreement in extent between 
 two enclosed fields, which it cannot so put together as 
 to discover their equality or inequality by an immedi- 
 ate comparison, casts about for some intermediate idea, 
 which, by being applied first to the one, and then to 
 the pther, will discover the relation it is in quest of. 
 Accordingly it assumes some stated length, as a yard, &c» 
 and measuring the fields one after the other, comes by 
 
INTRODUCTION. i* 
 
 that means to the knowledge*of the agreement or dis- 
 agreement in question. Tjie intervening ideas made use 
 of on these occasions, are called proofs ; and the exer- 
 cise of the mind in finding them out, and applying 
 them for the discovery of the truths it is in search of, is 
 ■what we term reasoning. And here let it be observed, 
 that the knowledge gained by reasoning is a deduction 
 from our intuitive perceptions, and ultimately founded 
 on them. Thus in the case before mentioned, having 
 found by measuring, that one of the fields makes three- 
 score square yards, -fnd the other only fifty-five, we 
 thence conclude, that the firft field is larger than the 
 second. Here the two first perceptions are plainly in- 
 tuitive, and gained by an' immediate application of the 
 measure of a yard to the two fields, one after another; 
 The conclusion, though it produces no less certain 
 knowledge, yet differs from the others in this, that it 
 is not obtained by an immediate comparison of the 
 ideas contained in it, one with another, bu4 is a deduc- 
 tion from the two preceding judgments, in which the 
 ideas are severally compared with a third, and their 
 relation thereby discovered. We see, therefore, that 
 reasoning is a much more complicated act of the 
 mind than simple judgment, and necessarily presup- 
 poses it, as being ultimately founded on the percep- 
 tions thence gained, and implying the various compa- 
 risons of them one with another. This is the great 
 exercise of the human faculties, and the chief instru- 
 ment by which we push on our discoveries, and enlarge 
 our knowledge. A quickness of mind to find out in- " 
 termediate ideas, and apply them skilfully in determin- 
 ing the relations of things, is one of the principal dis- 
 tinctions among men, and that which give some so re- 
 markable a superiority over others, that we are apt to 
 look upon them as creatures of another species. 
 
 Sec. VUL...Method. 
 
 Thus far we have traced the progress of the mind in 
 thinking, and seen it rising by natural and easy steps 
 from its first and simple perceptions, to the exercise 
 •f its highest and most distinguishing faculty. Let us 
 
x INTRODUCTION. 
 
 now view it in another light, as enriched with know- 
 ledge, and stored with a variety of discoveries, acquired 
 by a due application of its natural powers. It is obvi- 
 ous to consider it in these circumstances, as taking a 
 general survey of its whole stock of intellectual ac- 
 quisitions, disposing them under certain heads and 
 classes, and tying them together, according to those 
 connexions and dependencies it discerns between them* 
 It often happens, in carrying on our enquiries from 
 subject to subject, that we stumble upon unexpected 
 truths, and are encountered by discoveries- which our 
 present train of thinking gave no prospect of bring- 
 ing in our way. A man of clear apprehension, and 
 distinct reason, who, after due search and examina- 
 tion, has mastered any part of knowledge, and even 
 made important discoveries in it, beyond what he at 
 first expected, will not suffer his thoughts to lie jum- 
 bled together in the same confused manner as chance 
 offered them; he will be for combining them into a re- 
 gular system, where their mutual dependence may be 
 easily traced, and the parts seem to grow one out of 
 another. This is that operation of the mind, known 
 by the name of disposition or method, and comes in the 
 last in order, according to the division of the logicians, 
 as presupposing some tolerable measure of knowledge, 
 before it can have an opportunity of exerting itself in 
 any extensive degree. 
 
 Sec. IX.... Percept ion and Judgment terms of a very 
 extensive signification. 
 
 We see, then, that this fourfold distinction of the 
 powers of the mind, in perception, judgment, reason- 
 ing, and disposition, as well as the order in which they 
 are placed, have a real foundation in nature, and a rise 
 from the method and procedure of our own thoughts. 
 It is true, there are many other actions and modifica- 
 tions of the understanding, besides those above men- 
 tioned, as believing, doubting, assenting, Sec. but these 
 are all implied in the act of reasoning, in the like man- 
 ner, as comprehending, abstracting, remembering, may 
 be referred to tbe first operation of the mind, or per- 
 
INTRODUCTION. » 
 
 Caption. This will appear more fully in the sequel, 
 ivhen we come to handle the several parts of logic sepa- 
 rately : at present we shall content ourselves with this 
 general account of things ; only it seems necessary to 
 observe, that perception and judgment, in the propriety 
 of the English tongue, have a much more extensive 
 signification than logicians commonly allow them. We 
 not only perceive the ideas in our, own minds, but we 
 are said also to perceive their agreement or disagree- 
 ment ; and hence arise the common phrases of intuitive 
 perceptions, perceptions of truth, and of the justness 
 of arguments or proofs; where it is manifest, that the 
 word is applied not only to our judgments, but also to 
 our reasonings. In a word, whatever comes under 
 the view of the mind, so as to be distinctly represented 
 and taken notice of, whether an idea, proposition, 
 chain of reasoning, or the order and connexion of 
 things, is thereby rendered an object of perception, 
 and gives employment to this first and most simple of 
 our faculties. In like manner, the vr oi&, judgment, is 
 seldom, in common discourse, confined to obvious and 
 self-evident truths. It rather signifies those conjectures 
 and guesses that we form, in cases which admit not of 
 undoubted certainty, and where we are left to deter- 
 mine by comparing the various probabilities of thing?. 
 Thus a man of sagacity and penetration, who sees far 
 into the humours and passions of mankind, and seldom 
 mistakes in the opinions he frames of characters and 
 actions, is said to judge well, or think judiciously. For 
 these reasons, it might not be improper to change the 
 common names of die two first operations of the mind, 
 calling the one simjyle apprehension^ and the other ihtuU 
 tion ; which two words seem better to express their na- 
 ture, and the manner in which they are conversant 
 about their several objects. This accuracy of distin- 
 guishing, where there is any the least difference, is in 
 a peculiar manner necessary in a treatise of logic, as it 
 is the professed design of that science, to teach us how 
 to form., clear and distinct notions of things, and there- 
 by avoid being misled by their similitude or rcsem* 
 blance. 
 
*ii INTRODUCTION. 
 
 See* ¥L. t »*Logic divided into Four Parts: Its Useful" 
 ness and Excellency* 
 Having thus given a general idea of the four opera- 
 tions of the mind, and traced their connection and de- 
 pendence upon one another, I would next observe, that 
 in consequence of this division of the powers of the un- 
 derstanding, logic is also divided into four parts, which 
 treat severally of these acts, and give rules and direc- 
 tions for their due conduct and regulation. The ope- 
 rations themselves we have from nature.; but how to 
 exert tbem justly, and employ them with advantage 
 in the search of truth, is a knowledge that may be ac- 
 quired by study and observation. It is certain, that we 
 meet with false reasonings as well as just. Some men 
 are distinguished by an accuracy of thinking, and a 
 happy talent of unravelling and throwing light upon 
 the most obscure and intricate subjects. Others con- 
 found the easiest speculations ; their understandings 
 seem to be formed awry, and they are incapable of ei- 
 ther conceiving clearly themselves, or making their 
 thoughts intelligible to others. If then we set ourselves 
 carefully to observe what it is that makes the one suc- 
 ceed so well, and how the others come to miscarry, 
 these remarks will furnish us with an art of the highest 
 use and excellency in the conduct of life. Now this is 
 the precise business of logic — to explain the nature of 
 the li'iman mind, and the proper manner of conducting 
 its several powers, in order to the attainment of truth, 
 and knowledge. It lays open those errors and mistakes 
 we are apt through inattention to run into, and teach- 
 es us how to distinguish between truth, and what car- 
 ries only the appearance. of it. By this means, we grow 
 acquainted with the nature and force of the under- 
 standing, see what things lie within its reach, where 
 we may attain certainty and demonstration, and when 
 we must be contented with bare probability. xhese 
 considerations sufficiently evince the usefulness and 
 benefit of this science, which ought to be established as 
 the foundation and ground-work of all our other know- 
 ledge, if we really wish to succeed in our enquiries. 
 But we shall now proceed to treat of its parts separate- 
 ly, according to the division given of them above. 
 
E LEMENTS OF LOG IC. 
 
 OF SIMPLE APPREHENSION, 
 OR PERCEPTION, 
 
 C&ap. I. 
 
 t)F THE ORIGINAL OF OUR IDEAS* 
 
 ooooooooooooooooo 
 
 Sec, I Simple Apprehension and Ideas, 
 
 THE first thinf^ we observe, when we take a vietfr 
 of what passes within us, is, that we are capable 
 of receiving impressions from a variety of objects ; that 
 distinct notices are thereby conveyed into the under- 
 standing ; and-that we are conscious of their being 
 there. This attention of the mind to the objects acting 
 upon it, is what we c:di simple apprehension, and is, in 
 fact, the mind itself taking a view of things, as repre- 
 sented to it by its own consciousness. It is by this 
 means that we come to be furnished with all those 
 ideas about which our thoughts are employed. For be-* 
 ing sensible of the impressions made upon us, aiul at- 
 tending to the perceptions they bring, we can renew 
 them again upon occasion, even when the objects that 
 first produced them are removed* Now, our ideas are 
 nothing else but these renewed representations 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 seem to have a kind of existence in it. It 
 is true, we can upon "many occasions combine our ideas 
 variousiy together, and thereby form to ourselves re- 
 presentations of tilings that never had an existence in 
 nature, as when we fancy a centaur, or a golden moun- 
 tain ; but it is Still certain, that the original ideas, 
 ktattfe °f which these are made, are such as have been 
 ^28kveyed into the xniiid bv -some former impressions, - 
 
 B 
 
14 DTJNCAN' : S ELEMENTS 
 
 Ir remains therefore to enquire how we come 'by our. 
 first' notions and perception's of things. Whence doe3 
 the understanding derive these original impressions and 
 characters, which it can combine in so many differens 
 ways, and represent to itself under such infinite varie- 
 ties ? To this I answer, that if we attend carefully to 
 Tvhat 'passes in our minds, we shall observe two inlets of 
 knowledge, from whence, as from two fountains, the un- 
 derstanding is supplied with all the materials of think- 
 ing. 
 
 Sec. II... *All our original Ideas derived either from 
 Sensation, 
 Rrst, outward objects, acting upon otir senses, 
 rouse in us a variety of perceptions, according, to the 
 different manner in which they affect us. It is thus, 
 that we acquire ideas of light and darkness, heat and 
 cold, sweet and bitter, and all those other impressions 
 which we term sensible qualities. This great source 
 and inlet of knowledge is commonly distinguished by 
 the name of sensation, as comprehending all the noticed 
 conveyed into the mind 3 by impulses made upon the 
 organs of sense* 
 
 See. III.. ..Or Reflection* 
 But these ideas, numerous as they are, are wholly 
 derived to us from without : there is therefore yeff 
 another source of impressions, arising from the mind's 
 attention to its own acts, when, turning in Wards upoh- 
 itself, it takes a view of the perceptions that are lodg- 
 ed there, and the various ways in which it employs it- 
 self about them. For the ideas furnished by the senses, 
 give the mind an opportunity of exerting its several 
 powers ; and as all our thoughts, under whatever 
 form they appear, are attended with consciousness, 
 lience the impressions they leave, when we come to turn 
 the eye of the soul upon them, enrich the understanding 
 "With a new set of perceptions, no less distinct than those 
 conveyed in by the senses. Thus it is that we get ideas 
 of thinking, doubting, believing, willing) <kc. which 
 are the different acts and workings of our minds, repre- 
 sented to us by our own consciousness. This second 
 source of ideas is called reflection, and evidently ptesup* 
 
OF LOGIC. 15 
 
 poses sensation ; as the impressions it furnishes are only 
 q£ the various powers of the understanding, employed 
 about perceptions already in the mind. 
 
 Sect. IV Rise and Progress of Human Knowledge* 
 
 These considerations, if we duly attend to them, will 
 'give us a clear and distinct view of the natural proce- 
 dure of the human intellect, in its advances to know- 
 ledge. We can have no perception of the operations 
 of our own minds, until they are exerted ; nor can they 
 be exerted before the understanding is furnished with, 
 ideas about which to employ them : and as these ideas, 
 that give the first employment to our faculties, are evi- 
 dently the perceptions of sense, it is plain, that all our 
 knowledge must begin here. This, then, is the first 
 capacity of the human mind, that it is fitted to receive* 
 the impressions made upon it by outward objects affect- 
 ing the senses; which impressions, thus derived into 
 the understanding, and there lodged, for the view of the 
 soul, employ it in various acts of perceiving, remember- 
 ing, considering, Sec. all which are attended with am 
 internal feeling and consciousness. And this leads us 
 to the second step the mind takes in its ^progress to- 
 wards knowledge, viz. that it can, by its own consci- 
 ousness, represent to itself these its several workings 
 and operations, and thereby furnish the understanding 
 with a new stock of ideas. From these simple begin- 
 nings, all our discoveries take their rise: for the mind, 
 thus provided with its original characters and notices of 
 things, has a power of combining, modifying, and ex- 
 amining them in an infinite variety of lights, by which 
 means it is-eiiabled to enlarge the objects of its percep- 
 tion, and finds itself possessed of an inexhaustible stock 
 of material-!. It is in the various comparison of these 
 ideas, according to such combinations of them as seem 
 best to suit its ends, that the understanding exerts it- 
 self in the arts of judging and reasoning, by which the 
 capacious mind cf man pushes on its views of things, 
 adds discovery to discovery, and often extends its 
 thoughts beyond the utmost bounds of the universe. 
 Thus we see, as it were, at one glance, the whole pro- 
 gress of the soul, from the very hrst dawnings of per- 
 
16 DUNCAN'S ELEMENTS 
 
 ception, till it reaches the perfection of human know- 
 ledge ; nor shall we, among all its vast stock of disco- 
 veries, or that infinite variety of conceptions whereof 
 they consist, be able to find one original idea which is 
 not derived from sensation or reflection, or one com- 
 plex idea which is not. made up of those original ones. 
 Sec. V. Division of our Ideas into Simple and Complex* 
 Having thus shown how the mind comes- to be first 
 furnished with ideas, we shall next proceed to the 
 consideration of the ideas themselves, and endeavour 
 to give such an account of them, as will best serve to? 
 explain their several appearances, and the manner in 
 which they are formed. It is evident, from what has 
 been said above, that they all fall naturally under 
 these two heads : first, those original impressions that 
 are conveyed into the mind by sensation and reflection,' 
 and which exist there, simple, uniform, and without 
 any shadow of variety. Secondly^ those more complex 
 notions of things, that result from the various com- 
 binations of our simple ideas, whether they are con- 
 ceived to exist of themselves, in any particular subject, 
 or are united and joined together by the mind enlarg- 
 ing its conceptions of things, and pursuing the ends 
 and purposes of knowledge. These two classes com- 
 prehend our whole stock of ideas ; and, when consi- 
 dered separately, in that order wherein they most* na- 
 turally seem to offer themselves to our thoughts, will, 
 I hope, give such a view of the conduct and manner 
 of the mind, as may contribute not a little to intro- 
 duce us to an acquaintance with ourselves, and make 
 us sensible pf the capacity and extent of the human 
 intellect. We proceed, therefore, to a more particular 
 account of this division of our ideas. 
 
 Cjmp. n. 
 
 Of SIM PLE IDEAS. 
 
 Sec. I..,.. Simple Ideas what, 
 
 THE first class of our ideas are those which I dis- 
 tinguish by the. name of simple perception ; be- 
 
OF LOGIC. 17 
 
 cause they exist in the mind under one uniform appear- 
 ance without variety or composition. For though ex- 
 ternal objects convey at once into the understanding* 
 many different ideas, all united together, and making 
 as it were one whole : yet the impressions themselves are 
 evidently distinct, and are conceived by the mind, each 
 under a form peculiar to itself. Thus the ideas of co- 
 lour, extension, and motion, may be taken in at one and 
 the same time, from the same body ; yet these three 
 perceptions are. as distinct in themselves, as if they all 
 proceeded from different objects, or were exhibited to 
 our notice at diifereni times. We are therefore care- 
 fully to distinguish between our simple and primitive 
 conceptions, and those different combinations of them, 
 which are ofcen suggested to the mind by single ob- 
 jects acting upon it. The first constitute our original 
 notices of things, and are not distinguishable into dif- 
 ferent ideas, bur enter by the senses simple and unmix- 
 ed. They are ajso the materials, out of which all the 
 others, how complex and complicated soever, are form- 
 ed ; and therefore ought deservedly to be looked on as 
 the foundation and groundwork of our knowledge. 
 
 Sec. II Simple Ideas of Sensation* 
 
 Now if we take a survey of these ideas, and their 
 several divisions and classes, we shall find them all sug- 
 gested to us, either by our senses, or the attention of 
 the mind to what passes within itself. Thus our no- 
 tices of the different qualities cf bodies, are all of the 
 kind we call simple ideas, and may be reduced to five ge- 
 neral heads, according to the several organs which are 
 affected by them. Colours, Sec. and sounds, are con- 
 veyed in by the eyes and ears ; tastes and smells by the 
 nose and palate ; and heat, cold, solidity, Sec. by the 
 touch. Besides these, there are others' which maxe im- 
 pressions on several cf our senses, as extension, figure, 
 rest, and motion, Sec. the ideas of which we receive 
 into our minds both by seeing and feeling. 
 
 Sec. 111,.,,, Simple. Ideas of Reflexion, fcrV. 
 If we next turn cur view upon what passes within 
 ourselves, we shall find another set of simple ideas ari- 
 B 2 
 
18 DUNCAN'S ELEMENTS 
 
 sing from our consciousness of the acts and operations 
 of our own minds. Perception or thinking, and voli- 
 tion or willing, are what every man experiences in him- 
 self, and cannot avoid being sensible of. I shall, only 
 observe further, that besides all the above-mentioned 
 perceptions, there are others that come into our minds 
 by all t^ie ways of sensation and reflexion ; such are the 
 ideas of pleasure and gain, power, existence, unity, suc- 
 cession, &x. which are' derived into our understandings 
 both by the action of objects without us, and the con- 
 sciousness of what we feel within. It is true some of 
 these ideas, as of extension and duration, cannot be con- 
 ceived altogether without parts, nevertheless, they are 
 justly ranked among our simple ideas; because their 
 parts "being all of the same kind, and without the mix- 
 ture of any other idea, neither of them can be resolved 
 into two distinct and separate conceptions. Thus they 
 still answer the definition given above, of being one 
 uniform appearance in the mind, with variety or plural- 
 ity. But to prevent confounding our simple ideas of 
 space and duration, with those complex modes of them 
 marked out by tne several measures commonly in use, 
 as yards, miles, days, years, &x. it may perhaps be most 
 proper to consider the least portions of either whereof 
 we can form a clear and distinct perception, as the sim- 
 ple ideas-of that kind out of which all their other modes 
 and combinations are formed. Such an instant, or 
 point, may be conceived to be the same in respect of 
 duration or space, as unity is in respect of number ; 
 and will serve best to show, how by a continued addi- 
 tion or repetition, our more enlarged and complex ideas 
 are made up. 
 
 Sec. IV... .Simple Ideas have no Admission but by the 
 proper Inlets of Nature. 
 Having thus given a general view of our simple 
 ideas, I have still two observations to make concerning 
 them. The first is, that they are such as can only be 
 conveyed into the mind by the proper channels and 
 •avenues provided by nature ; insomuch that if we are 
 destitute of any of those inlets, by which the impres- 
 sions that produce tjiem are want to be admitted, all the 
 
OF LOGIC. 1S> 
 
 ideas thence arising are absolutely lost to us ; nor can 
 we, by any quickness 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 notion or conception of sounds. 
 Hence it appears, that these our simple ideas are just 
 such as nature has furnished them, and have no depen- 
 dence on our will ; we can neither destroy them when 
 in the understanding, nor fashion or invent any nevr 
 one, not taken in by the ordinary means of perception. 
 So that we here see the utmost bounds of human 
 knowledge, which, however mighty and enlarged, can- 
 -not exceed the limits of those our simple original ideas, 
 and their various combinations. 
 
 Sec. V.... They furnish ample Materials of Knowledge* 
 
 And this leads me to the second observation I pro- 
 posed to make, which is, that though the mind cannot, 
 in multiplying its conceptions of things, advance one 
 step beyond the materials furnished it by sense and 
 consciousness ; yet as it has a power of combining, 
 modifying, and enlarging them, in all the different 
 ways in which they can be put together, it therefore 
 finds itself in possession of an inexhaustible treasure 
 of ideas, sufficient to employ it to the full extent of all 
 its powers, and furnish matter for all those various 
 opinions, fancies, and views of things, that make up 
 the subject of its thoughts and contemplations. Let 
 us but reflect upon the single idea of unity or one, and 
 observe what a variety of combinations are formed, by 
 continually adding it to itself; insomuch that the'un- 
 derstanding finds no stop or boundary, in its progress 
 from number to number. In what an infinity of dif- 
 ferent lights may extension alone be considered ! what 
 limits can be set to that endless diversity of figures, 
 which it is in the power of the imagination to fashion 
 and represent to itself? if to these we add those num- 
 berless other combinations that' result from variously 
 compounding and comparing the rest of our simple 
 ideas, we shall have little reason to complain of being 
 limited to a scanty measure of knowledge, or that the 
 
£0 DUNCAN'S ELEMENTS 
 
 exercise of the human faculties is confined within nar- 
 row bounds. But having traced the progress of the 
 mind thro' its original and simple ideas, until it begins 
 to enlarge its conceptions by uniting and tying them 
 together ; it is now time to take a survey of it as thus 
 employed in multiplying its views, that we may see by 
 what steps it advances from one degree of improve- 
 ment to another, and how it contrives to manage that 
 infinite stock of materials it finds itself possessed of. 
 
 Sec. VI.... The Division of complex Ideas into those &f 
 real Existence, and those framed by the Mind, 
 
 Whoever attentively considers his own thoughts, 
 and takes a view of the several complicated ideas that 
 from time to time offer themselves to his understand- 
 ing ; will readily observe, that many of them are 
 such as have been derived from without, and suggest- 
 ed by different objects affecting his perception ; others, 
 again, are formed by the mind itself variously combi- 
 ning its simple ideas, as seems best to answer those ends 
 and purposes it has for the present in view. Of the 
 first kind are all our ideas of substance?, as of a man, a 
 horse, a stone, gold. Of the second arc those arbitrary 
 collections of things, which we on many occasions put 
 together, either for their usefulness in the commerce of 
 life, or to further the pursuit of knowledge : such are 
 our ideas of stated lengths, whether of duration or 
 space ; as hours, months, miles, leagues, &x. which 
 divisions are apparently the creatures of the mind, in- 
 asmuch as we often find them different in different 
 countries ; a sure sign that they are taken from no 
 certain and invariable standard in nature. Many of 
 our ideas of human actions may be also referred to 
 this head ; as treason, incest, manslaughter, &c. which 
 complex notions we do not always derive from an actual 
 'view of what these words describe, but often from com- 
 bining the circumstances of them in our minds,' or, 
 which is the most usual way, by hearing their names 
 explained, and the ideas they stand for enumerated. 
 These two classes comprehend all our complex con- 
 ceptions, it being impossible to conceive any that are 
 
OF LOGIC. 21 
 
 not cither suggested to the understanding "*by some 
 real existences, or formed by the mind itself arbitrarily 
 uniting and compounding its ideas. We shall treat of 
 each in order. 
 
 C&ap. in. 
 
 
 
 OF OUR IDEAS OF SUBSTANCES. 
 
 Sec. I.... Ideas of Substances y Collections of Simple 
 IdeaSy held together by some unknown support, 
 
 THE first head of complex ideas mentioned in the 
 foregoing chapter, is that of substances^ -which I 
 choose to handle before the other ; because, as will af- 
 terwards appear, the notices derived from this source 
 very much help us in forming those arbitrary collec- 
 tions, which make up the second division. For in many 
 ef. them we take our hints from the reality of things, 
 and combine ideas that actually exist together, though 
 often with an exclusion of others, as will be explained 
 when we come to treat of abstract and universal notions. 
 It has been already observed, that the impressions con- 
 veyed into the understanding from external objects, con- 
 sist for the most part of many different ideas joined to- 
 gether, which all unite to make up one whole. These 
 collections of various ideas, thus co-existing in the same 
 common subject, and held together. by some unknown 
 bond of union, have been distinguished by the name of . 
 substances, a word which implies their subsisting of 
 themselves, without dependence (at least as far as our 
 knowledge reaches) on any other created beings. Such 
 are the ideas we have of gold, iron, water, a man, Sec. 
 For if we fix upon any one of these, for instance, gold, 
 the notion under which we represent it to ourselves is 
 that of a body yellow, very weighty, hard* fusible, mal- 
 leable, &c. where we may observe, that the several pro- 
 perties that go to^the composition of gold, are repre- 
 sented to us by clear and evident perceptions ; the 
 union too of these properties, and their thereby consti- 
 tuting a distinct species of body, is clearly apprehends 
 
22 DUNCAN'S ELEMENTS 
 
 ed by the mind : but when we would push our enqui- 
 ries farther, and know wherein this union consists, 
 what holds the properties together, and gives them 
 their self-subsistence, here we find ourselves at a loss. 
 However, as we cannot conceive qualities, without at 
 the same time supposing some subject in which they 
 adhere, hence we are naturally led tc form the notion 
 of a support, which, serving- as a foundation for the co- 
 existence and union of the different properties of things, 
 gives them that separate, and independent existence 
 under which they are represented to our conception. 
 This support we denote by the name, substance; and as 
 it is an idea applicable to all the different combinations 
 of qualities that exist any where by themselves, they are 
 accordingly all called substances. Thus a house, a bow!| 
 a stone, kc. having each their -distinguishing properties, 
 and being conceived to exist independent one of ano- 
 ther, the idea of substance belongs alike to them all. 
 
 Sec. II....7Yzs Division of Modes into Essential and 
 
 Accident ah 
 • In substances ^therefore there are two things to be 
 considered : .first, the general notion of self-subsist- 
 ence, which, as 2 have said, belongs equally to them all ; 
 and then the several qualities, or properties, by which 
 the different kinds and individuals are distinguished 
 one from another. These qualities are otherwise cal- 
 Jed modes, and have been distinguished into essential 
 and accidental, according as they are perceived to be 
 
 I separable, or inseparable from the subject to which they 
 
 ! belong. Extension and solidity are essential modes of 
 a stone ; because it cannot be conceived without them ; 
 but roundness is only an accidental mode ; as a stone 
 
 I may exist under any shape or figure,' and yet still re- 
 
 I tain its nature and other properties. 
 
 j Sec. III....77it* Notion of Self-Subsistence inseparable 
 
 from Substances. 
 
 I might run farther into these divisions and subdivi- 
 
 \ s-ions, in which logicians have been very fertile ; but 
 
 as they tend little to the advancement of real know- 
 
 t ledge, and serve rather to fill the .memory with words. 
 
OF LOGIC. 23 
 
 and their significations, than furnish clear amd distinct 
 apprehensions of things, 1 -hall nojt trouble the reader 
 with them, It is more material to observe, that the 
 change of properties in any substance, iho' it oft-times 
 changes the nature of that substance, that is, its spe- 
 cies or kind ; yet it never destroys the general notion 
 of self-existence, but leaves that equally clear and ap- 
 plicable, as before any such alteration happened. Wood, 
 by tfeft application of fire is turned into charcoal ; but 
 charcoal, however different from "wood is still -.a sub- 
 stance. In like manner, wax may be converted into 
 flame arid smoke ; a human body will moulder into 
 dust : yet these alterations destroy not their being or - 
 existence ;' they are still substances as before, tho' un- 
 der a different form and appearance. In the several ex- 
 periments made by chemits, bodies undergo many 
 'changes, and put on successivelv a great variety of dif- 
 ferent shapes, and yet, by the skill and address of the 
 operator, they are often brought back to their first 
 and primitive form. \Vhat alteration can we suppose 
 the fire, or the application of any other body, to make, 
 unless on the configuration, texture, or cohesion of the 
 minute parts ? when these are changed, the body is 
 proportionably changed ; when they return to then 
 original state, the body likewise puts on its first and 
 natural appearance. 
 
 Sec* IV....'Founda!!o i of the different Species of Corpo- 
 real Substances. 
 
 All that is essential to matter^ therefore, is the cohe- 
 sion of solid extended parts : but as these parts are ca- 
 pable of innumerable configurations — as their texture 
 may be very various, and the internal constitution 
 thence arising be of consequence extremely different in 
 different bodies — we may from these considerations 
 conceive pretty clearly the source and foundation of all 
 the different species of corporeal substances. Nor is 
 this a notion taken up at random, or one of those chi- 
 merical fancies in philosophy, derived rather from a 
 warmth and liveliness of imagination, than observa- 
 tions drawn from things themselves. Do we not daily 
 
24 DUNCAN'S ELEMENTS 
 
 see our food, by the changes it-undergoes in the differ- 
 ent avenues of the body, converted first into blood, and 
 thence employed in nourishing, building up, and ..en* 
 larging, the several parts of that wonderful fabric ? 
 Rain, descending from the clouds, and mixing with the 
 mold or earth of a garden, becomes aliment for trees of 
 various kinds, puts on a diversity of forms, according to 
 the different channels and conveyances through which 
 it passes ; and at last,, after innumerable changes and 
 transmutations, sprouts forth in leaves, opens in budsj 
 or is converted into the substance of the tree itself. 
 Can we conceive any greater difference between the 
 component parts of gold, and those of stone, than be- 
 tween the moistened particles of garden mold, and those 
 new forms and figures under which they appear, after 
 they have been thus fashioned by nature for the pur- 
 poses of growth and nourishment ? 
 
 Sec. Vm»Essence of Substances nothing but the inter* 
 nal structure end constitution ; 
 
 If this be duly attended to, it will not appear won- 
 derful to assert, that the variety of material substances 
 arises wholly from the different configuration, size, tex- 
 ture, and motion of the minute parts. As these happen 
 ■to.be variously combined, and knit together, under dif- 
 ferent forms, bodies put on a diversity of appearances, 
 and convey into the mind by the senses all those sever- 
 al impressions, by which they are distinguished one 
 from another. This internal constitution or structure 
 of parts from which the several properties that dis- 
 tinguish any substance flow, is caflcd the essence of 
 that substance, and is, in fact, unknown to us, any 
 farther, than by the perceivable impressions it makes 
 upon the organs of sense. Gold, as, has been said, is a 
 body yellow, vtry weighty, hard, fusible, malleable, 
 &.C. That inward structure, and conformation ftf its 
 minute particles, by which they are so closely linked 
 together, and irom which the properties above men- 
 tioned are conceived to flow, is called its essence ; and 
 the properties themselves. are the perceivable marks that 
 make it known to us ; and distinguish it from all o';her 
 
OF LOGIC. 25 
 
 substances ; for our senses are not acute enough to 
 reach its inward texture and constitution. The parts 
 themselves, as well as their arrangement, lie far be- 
 yond the utmost penetration of human sight, even 
 when assisted by microscopes, and all the other con- 
 trivances of art. 
 
 £ec. VI Is wholly unknown to us end serves to dis- 
 tinguish the Species ; 
 
 Thus, as to the essence or internal constitution of 
 gold, we are wholly in the dark ; but many of the pro- 
 perties deriyed from this essence, make obvious and. 
 distinct impressions, as the weight, hardness, and yel- 
 low colour, Sec. These properties combined together, 
 and conceived as co-existing in the same common sub- 
 ject, make up our complex idea of gold. The same 
 may be said of all the other species of corporeal sub- 
 stances, as lead, glass, water, &c. our ideas of them 
 being nothing else but a collection of the ordinary qua- 
 lities observed in them. 
 
 Sec. VII....7"<?Z it is rightly presumed to be distinct 
 in all the several kinds. 
 
 This, hawever, ought to be observed, that though 
 the essence or inward structure of bodies is altogether 
 unknown to us, yet we rightly judge, that in all the 
 several species, the essences are distinct. For each spe- 
 cies being a collection of properties, which, taken to- 
 gether, are different from thooe of every other species, 
 the conformation of par£s, on which these properties 
 depend, must in like manner be different ; and this, as 
 we have said, constitutes the essence. Iron and glass 
 are evidently distinct kinds of body ; their perceivable 
 qualities have little or nothing common ; and there- 
 fore the inward structure or constitution from which 
 these qualities flow, cannot be the same in both. But 
 after all, this is the only thing we can with certainty 
 affirm concerning these essences, which lying so wholly 
 in the dark, we shall do well to lay them aside in our 
 reasonings about things, and adhere to those more in- 
 telligible and settled ideas acquired by joining toge- 
 ther their various properties and powers. For thus 
 jonly is true knowledge promoted, when we argue from 
 C 
 
26 DUNCAN'S ELEMENTS 
 
 known qualities, and not from a supposed internal con-^ 
 stitution, which, however real in itself, yet comes not 
 within the reach of our faculties, and therefore can 
 n$ver be a ground to us for any discoveries or im- 
 provements. 
 
 Sec, VIII.. ..By what steps we arrive at the Notions 
 of Immaterial Substances ; 
 Material substance, as I have said, includes the idea 
 of solid, cohering, extended parts, and is divided into 
 different classes according to the different^ impressions 
 made upon the organs of sense. But, besides these 
 sensible ideas received from without, we also experience 
 in ourselves thinking and volition. These actions have 
 no connection with the known properties of body; nay, 
 they seem plainly inconsistent with some of its most 
 essential qualities. For the mind not only discovers 
 no relation between thinking, and the motion or ar- 
 rangement of parts ; but it also perceives, that consci- 
 ousness, a simple individual act, can never proceed from 
 a compounded substance, capable of being divided in- 
 to many. Let us suppose, for instance, a system of 
 matter endowed with thought ; then either all the 
 parts, of which this system is composed, must think, 
 which would make it not one, but a multitude of dis- 
 tinct conscious beings ; or its power of thinking must 
 arise from the connection of the parts one with another, 
 their motion and disposition, Sec, which, all taken to- 
 gether, contribute to the production of thought. But 
 it is evident, that the motion of parts, and manner of 
 combining them, can produce nothing but an artful 
 structure, and various modes of motion. All machines 
 of human composition, as watches, clocks, Sec. howe- 
 ver artfully their parts are set together, however com- 
 plicated their structure— -though we conceive innume- 
 rable different motions, variously conjoined, and run- 
 ning one into another with an endless diversity, yet 
 never produce any thing but figure and motion. If a 
 clock tells the hour and minute of the day, it is only 
 by the motion of the different hands, pointing succes- 
 sively at the figures marked on the hour-plate for that 
 purpose, We never imagine this to be the effect of 
 
OF LOGIC. 2? 
 
 thought or intelligence ; nor conceive :t possible, by 
 any* refinement of structure, so to improve the compo- 
 sition, as that it shall become capable of knowledge and 
 consciousness. The reason is plain : thought is some- 
 thing altogether different from motion and figure ; - 
 there is not the least connection between them ; and 
 therefore it can never be supposed to result from them* 
 Sec. IX....^A/c/t we otherwise call Spirits* 
 
 This then being evident, that intelligence cannot 
 arise from an union or combination of unintelligible 
 parts ; if we suppose it to belong to any system of mat- 
 ter, we must necessarily attribute it to all the parts, 
 of which that system is composed ; whereby, instead of 
 one, we shall, as was before observed, have a multi* 
 tude of distinct conscious beings. And because mat* 
 ter, how far soever we pursue the minuteness of its 
 parts, is still capable of repeated divisions, even to in* 
 inky ; it is plain, that this absurdity will follow us, 
 through all the suppositions that make thought inhe* 
 rent in a material substance. Finding, therefore, con* 
 sciousness incompatible with the cohesion of solid se* 
 parable parts we are necessarily led to place it in some 
 other substance, of a distinct nature and properties, 
 which we call spirit. 
 
 Sec. X..,.Body and Spirit distinct Substances. 
 
 And here it is carefully to be observed, that the se- 
 veral species of corporeal substances, though distin- 
 guished one from another, and ranked under different 
 names ; yet, agreeing in some common properties, 
 which, taken together, make up the notion of body, 
 are thence all conceived to partake of this general na- 
 ture, and to differ only as different modifications of 
 the same substance. Whatever consists of solid ex- 
 tended parts, is called matter ; and as all the various 
 specie-s of body, however distinguished from one ano- 
 ther by their several properties, have yet this in com- 
 mon, that they are made up of such solid separable 
 parts, hence they fall naturally under the general de- 
 nomination of material beings, and are not conceived 
 to differ, but in their form. 1 bus gold, antimony,- wood,. 
 &c. alike partake of the notion of body $ they are aH 
 
28 DUNCAN'S ELEMENTS 
 
 equally material substances, and have no other differ* 
 ence, but what arises from the different structure and 
 conformation, Sec. of parts, as we have shewn above. 
 But spirit is something altogether distinct from body, 
 nay, and commonly placed in opposition to it ; for 
 -which reason, the beings of this class are called imma- 
 terial ; a word that implies not any thing of their na- 
 ture, but merely denotes its contrariety to that of matter. 
 Sec. XI. Thtrt may be many various Species of Sub - 
 
 stances, besides those that come within the reach of 
 
 our Faculties, 
 
 Body and spirit, therefore, differ not as species of the 
 same substance, but ar.e really distinct kinds of sub- 
 stances, and serve as general heads under which to 
 rank all the particular beings that fall within the com- 
 pass of our knowledge. For we having no ways of per- 
 ception but sense and consciousness, can have no no- 
 tices of things, but as derived from these two inlets. 
 By our senses we are informed of the existence of so- 
 lid extended substances ; and reflection tells us, that 
 there are thinking conscious ones. Beyond these our 
 conceptions reach not ; and therefore, though there may 
 be many other kinds, as different from them as they are 
 from cne another, yet having no faculties suited to 
 them, they are as remote from our knowledge, as light 
 and colours from the apprehension of a man born blind. 
 Ibelievexit will hardly be doubted but the substance 
 of the Creator differs more from that of his creatures, 
 than any two created substances can from one ano- 
 ther ; and therefore when we call God a spirit, wc 
 ought not rashly to presume, that he is so in the same 
 sense in which the human soul is a spirit. The word 
 is, indeed, used by us, to denote in general all thinking 
 intelligent substances, in which sense God is very fitly 
 called a spirit. But it were the height of folly to ima- 
 gine, because this name is applied as well to the mind 
 of man as the Creator, that therefore they partake of 
 one common nature, and differ only as different modi- 
 fications of the same substances This I mention here, 
 to check the presumption of the human mind, always 
 forward to conclude, that every thing cornea withim 
 
OF LOGIC. 29 
 
 Its reach, and to deny existence to whatever exceeds 
 the comprehension of its scanty and limited powers. 
 Beings of a superior class may enjoy many ways of per- 
 fection unknown to us, from which they receive no- 
 tices as diffe ent from those in our minds, as the ideas 
 we apply to pirit are from the ideas we apply to body* 
 Solid and thinking beings are, it is true, the only ideas 
 of substance that we are able to frame ; but this is no 
 more an argument against the existence of other kinds, 
 than the want of the ideas of light and colours in a 
 blind man would be a good argument against the reali- 
 ty or possibility of such perceptions. 
 See, XII. ...Difference in the manner of conceiving 
 Corporeal and Spiritual Substances* - 
 Before I dismiss this subject, it may not be improper 
 to take notice of a remarkable difference as to the man- 
 ner of our conceiving corporeal and spiritual substan- 
 ces. Those of the first kind convey themselves into 
 the mind by impressions made upon the organs of sense ; 
 and as these impressions are different in different bodies, 
 the ideas they produce must^of course vary in propor- 
 tion. Thus we get preceptions of distinct powers and 
 properties, and range bodies into classes, according as 
 we find them to agree or disagree in these their obser- 
 vable qualities. But it is not so in our notion of spi- 
 rits ; for having no conception of their powers and 
 operations but by what we feel and experience within 
 ourselves, we camiot ascribe to them properties or ways 
 - of knowledge, distinct from those suggested to us by 
 our own consciousness. And hence it is, that though 
 we readily own there may be ^various ranks of spiritual 
 beings, yet we are not to imagine them divided from 
 one another by any diversity of powers and operations, 
 but merely by possessing the same powers, &c. in a 
 higher orlower degree. It is not, however, repugnant 
 to reason, that they should be distinguished by their se- 
 veral properties in like manner as sensible things are 
 by the different qualities observable in them ; but pro- 
 perties of intellectual natures, distinct from those of our 
 own minds, being altogether remote from our concep- 
 tion, cannot serve as a means whereby to distinguish 
 C % 
 
30 DUNCAN'S ELEMENTS 
 
 their different orders. We are, therefore, necessitated 
 to conceive of them in a manner suited to our way of 
 knowledge ; and when we would rank them into spe- 
 cies, according to the degrees of superiority they are? 
 imagined to possess in the scale of being, we ascribe to 
 them what we find most excellent in ourselves, as know- 
 ledge, thinking, foresight, &c. and those in different 
 measures proportioned to the station peculiar te each 
 rank or species. But that this is a very imperfect way 
 of distinguishing the various orders of intellectual be* 
 ings, will not, I think, need many words to make it ap- 
 pear ; especially if we consider, that the manner of 
 communicating their thoughts, without the interven- 
 tion of bodily organs, is a thing to us altogether in- 
 comprehensible, and necessarily leads us to suppose, 
 that they have ways of perception and knowledge 
 which our faculties cannot. give us any notice of. 
 
 Sec. XIII.... The bounds of Knowledge in our present 
 state very narrow. 
 But I shall not pursue these reflexions farther ; what 
 Las been said sufficing to give us some little insight into 
 the extent and capacity of our own minds ; to convince 
 us that our present state will not admit of a perfect and 
 adequate comprehension of things; and to let us see, 
 that there may be other ways of knowledge, beyond the 
 reach of the faculties we now enjoy ; which yet, in suc- 
 ceeding stages of our existence, we may arrive at, when, 
 being freed from the present cumbersome load of the 
 body? we shall mount up to stations of greater eminence, 
 and advance by a perpetual series of approaches towards 
 him, who is the standard of perfection and happiness. 
 
 Cfmp. iv. 
 
 OF IDEAS FRAMED BY THE MIND. 
 
 Sec. I..../n framing many complex Ideas, the Mind is 
 wholly active, and proceeds by a voluntary choice* 
 
 HITHERTO we have considered only such combi- 
 nations of our simple ideas as have a real union 
 
OF LOGIC. t€ 
 
 in nature, and are suggested to the mind by things - 
 themselves variously affecting our perception : it is now*> 
 time to take a view of the other cias3 of. our complex 
 notions ; I mean those arbitrary collections of different 
 ideas, which we on many occasions bring together by 
 that power which we fifid in ourselves, of uniting, com- 
 paring, and diversifying our notices of things. In the 
 reception of simple ideas, and even in those of substan- 
 ces, the understanding is wholly passive, and the per- 
 ception* produced correspond to the impressions made 
 upon it. When we see a house, or a tree, they neces- 
 sarily appear each under its proper form; nor is it in 
 our power to receive from these objects other ideas than 
 what they are fitted to produce. But in this second 
 class of complex conceptions, the mind acts voluntari- 
 ly and of choice ; it combines only such ideas as are 
 supposed best to suit its present purpose; and alters or 
 changes- these combinations, by inserting some, and 
 throwing out others, according as the circumstances of' 
 things require their being viewed in different lights. 
 Now as this is by far the most comprehensive branch of 
 our ideas, and includes those that most frequently occur 
 in the search and pursuit of knowledge, I shall endea- 
 vour to treat them in the exactest order and method; 
 and for that purpose range them under several heads, 
 according to the different acts of the mind exerted in 
 framing and putting them together. 
 
 Sec. II.... Three several Acts exerted by the Mind in 
 framing its arbitrary Ideas, viz. Composition ; 
 
 These acts may in the general all be reduced to three* 
 1, Composition, when we join many simple ideas toge- 
 ther, and consider them as one picture or representa- 
 tion. Such are our ideas of beauty, gratitude, a fur- 
 long, Sic. And here let it be observed, that the mind 
 sometimes confines itself to the various consideration of 
 the same idea, and, by enlarging it in different degrees, 
 , exhibits it under a diversity of forms. Thus by adding 
 units together, in distinct separate collections, we 
 come by the several combinations of numbers, as a 
 dozen> a score, a million. At other times we unite 
 
9* DUNCAN'S ELEMENTS 
 
 perceptions of different kinds; in which case the com- 
 position is more manifest, and the idea itself becomes of 
 course more complicated. Harmony, for instance, is a 
 compound .idea, made up of many different sounds 
 united; all which the musician must have, and put to- 
 gether in his mindjjbefore the ear can be entertained 
 ■with the actual performance. Now although the act of 
 the mind is in some measure exerted in the framing of 
 all our complex notions, yet as many of them include 
 certain limited and particular considerations, arising 
 from other operations of the mind employed about 
 them, it is necessary to take account of these acts also, 
 if we would conceive clearly the manner in which the 
 *everal species of our compound ideas are formed. 
 Sec. \\1..*. Abstraction* 
 
 2. The next operation therefore of, the mind, about its 
 ideas, is abstraction, when we separate from any of our 
 conceptions all those circumstances that render it parti- 
 cular, or the representative of a single determinate 
 object ; by which means, instead of standing for an in- 
 dividual, it is made" to denote a whole rank or class of 
 things. Thus upon seeing, for instance, a square or 
 circle, we leave out the consideration of their bulk, 
 and everything else peculiar to them, as they imme- 
 diately affect our sight, retaining only the notion of 
 their figure and shape. In this manner we get our^-e- 
 nerat ideas ; for such naked ' appearances, separated 
 from the circumstances of time place, &c. serve the 
 mind as standards by which to rank and denominate 
 particular objects. When therefore me meet with a 
 figure answering to that shape and form we had laid 
 up in oui\understandings, Itis immediately referred 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 universal terms, 
 common to all figures of that particular shape,, and 
 alike applicable to them wherever they exist ; in like 
 manner as the ideas themselves are general, and repre- 
 sentatives of all the kind. £ 
 Sec. TV..,.And Comparison, 
 
 3« The third and last act of the mind about its ideas', 
 
_GF LOGIC. 38 
 
 is the comparing them one with another, when we carry 
 our consideration of things beyond the objects them- 
 selves, and examine their respects and correspondences 
 in reference to other things which the mind brings 
 into view at the same time. It is thus we get all our 
 ideas of relations, as of greater, less, older, younger, 
 father, son, and innumerable others. This threefold 
 view of our ideas, as either compounded of many others 
 put together, or made universal by the abstraction of 
 the mind, or as representing the various relations and 
 habitudes of things, will give us an opportunity of ob- 
 serving whatever is most curious and useful in this 
 fundamental branch of knowledge, and of explaining 
 the manner and procedure of the understanding in en- 
 larging its views, and multiplying the objects of per- 
 ception. That we may therefore conceive of this 
 matter with the greater order and clearness, we shall 
 make each of these several ideas the subject of a dis- 
 tinct article. 
 
 ART. I. 
 
 OF COMPOUND IDEAS. 
 
 Sec. I. •••Compound Ideas considered here merely etg 
 Combinations of the Understanding, 
 
 WE begin therefore with those ideas which maf 
 be properly termed compound, as being derived 
 from that power the mind has of uniting many concep- v 
 tions into one. Though this class comprehends, in some 
 sort, all our complex notions, yet they are at present 
 considered merely as they are combinations of the un- 
 derstanding, and with a view to those particular ideas 
 out of which they are framed. Here, as was already- 
 observed, the mind sometimes proceeds by enlarging 
 and diversifying the same idea ; at other times it brings 
 together ideas of different kinds ; and in both ways 
 finds infinite scope and variety. But that we may fol- 
 low the natural procedure of the intellect, and trace it 
 in its advances from simple to more complicated acts> 
 Hf« shall first take a view of it as employed about ©*• 
 
34 DUNCAN'S ELEMENTS 
 
 and the same idea, where perhaps we may m«et witk 
 such instances of address, management, and contri- 
 vance, as will appear perfectly astonishing to one who 
 has-never set himself seriously to consider the manner 
 and conduct tff his own mind. 
 
 Sec. Il„. .Unity the Original and Foundation of all our 
 Ideas of Number* 
 The most obvious and simple idea we have, is that of 
 Unity or one. By adding it to itself continually, and 
 retaining the several collections in our minds, we come 
 by all the different combinations of numbers, in which 
 we readily perceive an endless diversity. All these 
 ideas are nevertheless evidently distinct among them- 
 selves, the addition of a single unit constituting a 
 number a§ clearly different from that immediately be- 
 fore it-, as any two the most remote ideas are from one 
 ano/cher. But that the understanding may not lose it- 
 self in the consideration of those infinite combinations 
 of which unity is capable, it proceeds by regular steps ; 
 and beginning with the. original idea itself, pursues it 
 through all its varieties, as they are formed by the re- 
 peated continual addition of unit after unit. Thus 
 numbers, a re made to follow one another in an orderly 
 progression, and the several successive collections are 
 distinguished by particular names. 
 
 Sec. III....77i<? artful composition of the names of 
 
 Numbers a great help to our conceptions ; 
 And here we may take notice cf a wonderful artifice 
 made use of by the. mind, to facilitate and help it for- 
 ward in its conceptions. For as the advance from num- 
 ber to number is endless, were they all to be distinguish- 
 ed by different denominations that had no connexion or 
 dependence one upon another, the multitude of them, 
 must, soon overcharge the memory, and render it impos- 
 sible for us to go any great way in the progress of num- 
 bering. For this reason it is so contrived, that the 
 change of names is restrained to a few of the first com- 
 binations, all the rest that follow being marked by a 
 repetition of the same terms, variously compounded and 
 linked together. Thus thirteen is ten and three, four- 
 
OF LOGIC. 35 
 
 teen, ten and four, and so on to twenty, or two tens, 
 when we begin again with one, two,~&cc. until we ad- 
 vance to thirty, or three tens. In this manner the 
 progression continues ! and when we arrive at ten tens, 
 ■to prevent confusion by a two frequent repetition of 
 the same word, that sum is distinguished by the name 
 of a hundred. Again, ten hundred is called a thousand, 
 at which period the computation begins anew, running 
 through all the former combinations, as ten thousand, 
 a hundred thousand, ten hundred thousand ; which last 
 collection, for the reasons mentioned above, has the 
 name of a million appropriated to it. With this mil- 
 lion, we can begin as before, until it is repeated a mil- 
 lion of times ; when, if we change the denomination 
 to billions, and advance in the same manner through 
 trillions, quartillians, the series may be carried on with- 
 out confusion, to any length wc please. 
 
 Sec. IV.. ..And of the principal Reasons that our Ideas 
 of Numbers are so remarkably distinct. 
 
 This artful combination of names" to mark the gra- 
 dual increase of numbers, is perhaps one of the greatest 
 refinements of the human understanding, and particu- 
 larly deserves our admiration for the manner of the 
 composition ; the several denominations being so con- 
 trived as to distinguish exactly the stages of the pro- 
 gression, and point out the distance from the begin- 
 ning of the series. By this means it happens, that our 
 ideas of numbers are of all others the most accurate 
 and distinct ; nor does the multitude of units assem- 
 bled together, in the least puzzle or confound the un- 
 derstanding. It is indeed amazing, that the mind of 
 man, so limited and narrow in its views, should yet 
 here seem to shake off its natural weakness, and disco- 
 ver a capacity of managing with ease the most bulky 
 and formidable collections. If we enquire particular- 
 ly into the reason of this, we shall find it wholly owing 
 to the address of the mind in thus distinguishing num- 
 bers by different names, according to the natural or- 
 der of progression. For as those names are made to 
 grow one ou£ of another, they may be aptly compared 
 
36 DUNCAN'S ELEMENTS 
 
 to a chain, all whose parts are linked together by an 
 obvious and visible connexion. Hence it comes to pass, 
 that when we fix our thoughts upon any number, how- 
 ever great and seemingly unmanageable ; yet, if it is 
 once determined to a particular name, we find it easy 
 to run back through all the stages of the progression, 
 even till we arrive at unity itself. By this means we 
 see, with a single glance of our minds, not only the two 
 extremes of the number under consideration, but also 
 the several intermediate parts, as they are united to 
 make up the whole. 
 
 Sec V.t..^ they kelp us to a clear Perception of the in* 
 terjacent Parts. 
 
 Now it is to this clear and accurate view of the in- 
 terjacent ideas, that we owe our so distinct perception 
 of the various combinations of numbers. And indeed we 
 may observe, in the general, that all our ideas of quan- 
 tity, especially when they grow to be very large, are 
 no otherwise ascertained than by that perception we 
 have of the intervening parts, lying, if I may so say, 
 between the extremes. When we look at any object 
 Considerably distant from us, if we have a clear view 
 of the interjacent lands anH houses, we are able to de- 
 termine pretty nearly of its remoteness ; but if, with- 
 out such a knowledge of the intervening spaces, we 
 should pretend to judge of the distance of objects, as 
 when we see the spire of a steeple behind a wall, or be- 
 yond a mountain, every one's experience is a proof how 
 liable we are, in these cases, to be deceived. Just so it 
 is in judging of duration. When we carry back our 
 thoughts to any past period of our lives, without con- 
 sideration of the number of years or months, we find 
 that our idea of the time elapsed grows more distinct, 
 in proportion as we become sensible of the intermedi- 
 ate parts of our existence. At first we are apt to judge 
 the distance extremely short; but when we set our- 
 selves to consider our several successive thoughts and 
 actions, the idea of the duration grows upon us, and 
 continues to increase as the attention of the mind bring* 
 new periods of life into view. 
 
OF LOGIC. zr 
 
 Sec. VI.,*JVithout names, nue cannot make any pro* 
 gress in Numbering* 
 
 Hence it will be easy to conceive how much the mini 
 is helped forward in its perception of number, by that 
 ready comprehension of all the several'stages in a pro- 
 gression. Which peculiarly belongs to ideas of this class. 
 But this, as I have before intimated, we derive from the 
 orderly series and connexion of names, insomuch that 
 where they cease, the computation of numbers also ceases 
 with them. We can have no idea of any sum, without 
 a knowledge of all. the terms that go before, according 
 to the natural order in which they follow one another ; 
 so that he who cannot, in a regular way, count to nine- 
 ty-nine, will never, while that incapacity continues, be 
 able to form the idea of a hundred; because the chain 
 that holds the parts together, is to him wholly unser- 
 viceable, nor can he represent to his mind the several 
 interjacent combinations, without which it is impossi- 
 ble in this case to arrive at a distinct perception. 
 
 Sec. VII.... The great advantages of Address in Class- 
 ing our complex Conceptions. 
 I have insisted the more largely upon this, not only 
 because it is by number that we measure all other 
 things, as duration, extension, motion, &x. but also 
 because it lets us into the most natural view of the con- 
 duct and procedure of the understanding, and makes u$ 
 sensible of the great art and address that is necessary in 
 the classing our very complex conceptions. He that can 
 so put together the component parts of an idea, as that 
 they shall lie obvious to the notice of the mind, and pre- 
 sent themselves, when occasion requires, in a just and 
 orderly connexion, will not find it very difficult to obtain 
 clear and accurate perceptions, in most of those sub- 
 jects about which our thoughts are conversant. For the 
 great art of knowledge lies in managing with skill the 
 capacity of the intellect, and contriving such helps as, 
 if they strengthen not its natural powers, may yet ex- 
 pose them to no unnecessary fatigue, by entangling and 
 perplexing them with considerations remote from the 
 business in hand* When ideas become very complex, 
 
 n 
 
38 DUNCAN'S ELEMENTS 
 
 and by the multiplicity of their parts grow too unwieldy 
 to be dealt with in the lump, we must ease the view of 
 the mind, by taking them to pieces, and setting before 
 it the several portions separately, one after another. 
 By this leisurely survey we are enabled to take in the 
 whole ; and if we can draw it into such an orderly com- 
 bination, as will naturally lead the attention, step by 
 step, in any succeeding consideration of the same idea, 
 we shall ever have it at command, and with a single 
 glance of thought be able to run over all its parts. I 
 have therefore explained here, at some length, the con- 
 duct of the mind in. numbering; it seeming to me the 
 best model in this kind, whether we consider the many 
 advantages derived from such an orderly disposition of 
 our ideas, or the great art and skill displayed in binding 
 these ideas together. This also is farther remarkable, 
 in the consideration of number, that from it chiefly we 
 derive the notion we have of infinity ; it being appar- 
 ent, that, in adding number to number, there is no 
 end ; the possibility of doubling or increasing our stock 
 in any degree, remaining as obvious to the understand- 
 ing, after a great and continued run of progressions, 
 as when it first began the computation. 
 
 Sec. VIII..., The Consideration of Number, of great Use 
 in ascertaining our Ideas of Space and Duration, 
 
 If we now turn our thoughts towards space and du- 
 ration, here too we shall find that \ve very seldom ar- 
 rive at clear and distinct ideas of either, but when we 
 introduce the consideration of number. The more ob- 
 vious and limited portions, it is true, easily slide into 
 the mind, in the natural way of perception ; but it 
 was the necessity of comparing these together, that 
 pu.t us upon the contrivance of certain stated measures 
 by which precisely to determine the quantity in each. 
 Thus, inches, feet, yards, miles, &c. ascertain our ideas 
 of extension ; as minutes, hours, days, years, &c. mea- 
 sure the progress of duration. The lesser parts, as ly- 
 ing most open to the notice of the understanding, and 
 being more on a level with its powers, are retained. 
 yfhk tolerabk exactness j and the larger portion^ 
 
OF LOGIC. 39 
 
 when the number of repetitions of which they are 
 made up is known, are thereby also reduced into clear 
 and determinate conceptions. A foot, and yard, are 
 measures easily comprehended by the mind ; nor do Ave 
 find any difficulty in conceiving a mile, when we consi- 
 der it as equal to a certain number of yards. If we arc 
 still for increasing the standard, we may take the se- 
 midiameter of the earth, and supposing it equal to 
 8b00 miles, make use of it as a measure by which to 
 ascertain the distance of the sun or fixed stars. Just so 
 it is in duration ; from hours we rise to days, months, 
 and years ; by these, repeated, and added together, 
 we measure time past, or can run forward at pleasure 
 into futurity, and that without any confusion or per* 
 plexity. 
 
 Sec. lX*...J7ithout they are apt to degenerate into a 
 confused and irregular Heap. 
 It is however to number alone that we owe this dis- 
 tinctness of perception, inasmuch as space and time, 
 considered apart from the regular and orderly repeti- 
 tion of miles or years, leave no determinate impres- 
 sions in the mind, by which to know and distinguish 
 their several portions. Ideas of either, thus taken in 
 tt a venture, are a confused and irregular heap, especi- 
 ally where we endeavour to enlarge and magnify our 
 views, and give full play to the powers of our intel- 
 lect. Something indeed the mind conceives, vast and 
 mighty, but nothing that is precise, accurate, and just. 
 But when it begins to consider these ideas as made up 
 cf parts, and fixing upon such as are proportioned to 
 its reach, sets itself to examine how often they are re- 
 peated to make up the whole, the perceptions of the un- 
 derstanding put on a new form, and discover their ex- 
 act bounds and limits. 
 
 Sec. %»:J[nfiMtj an Object too mightj for the Survey of 
 , the human Mind, 
 
 And thus, as before in number, so here in extension 
 and duration, the mind begins with simple and obvious 
 notices, advancing by degrees to more enlarged and 
 intricate conceptions. A day, or a furlong, are of easy 
 
40 DUNCAN'S ELEMENTS 
 
 apprehension to the understanding, and by their subdi- 
 visions into still lesser spaces, exhibit themselves dis- 
 tinctly in all their parts. With these variously re- 
 peated, we travel through space and time ; so that be- 
 ing able to reduce all our ideas of this class, however 
 mighty and enlarged, to the clear and determinate per- 
 ceptions of number, we can conduct our thoughts with- 
 out perplexity, and never find ourselves puzzled, but 
 when, presuming too much on our own strength, we 
 launch into speculations, that stretch beyond the pow- 
 ers of the human intellect. Number may be compared 
 to a line, that, setting out from unity, runs on in a con- 
 tinued increase of length, without a possibility of ever 
 arriving at its ultimate period. So far as we pursue it 
 in our thoughts, and trace its regular advances, so far 
 our ideas are accurate and just. But when we let loose 
 our understandings, after a boundless remainder, and 
 would fathom the depth of infinity, "we find ourselves 
 fpst amidst the greatness of our own conceptions* 
 Some notions, it is true, we have, but such as, exceed- 
 ing the dimensions of the mind, lie involved in dark- 
 ness and obscurity ; and being destitute of order, me- 
 thod, and connexion, afford no foundation whereon to 
 build any just and accurate conclusion. 
 
 Sec. ~KI...» Never represented in its full Dim ens ions ^but 
 bj an endless and ever growing Idea. 
 
 And this perhaps may be the reason why many mo- 
 dern philosophers, in their discourses concerning infi- 
 nity, have run into apparent contradictions ; because, 
 encountering an object too large for the survey of the 
 understanding, they found themselves surrounded with 
 inextricable difficulties, which their scanty and defec- 
 tive ideas were by no means able to dissipate or remove. 
 The truth of it is, finite ideas alone are proportioned 
 to a finite understanding ; and although we sire not 
 wholly without a notion of the infinity of number, 
 yet it is not such a one a3 comprehends and exhausts 
 its object, or exhibits it to the mind in its full size 
 and dimensions. We only see the idea, as capable of 
 an endless increase; but cannot by any effort of thought 
 
OF LOGIC. 41 
 
 take in the whole prospect ; and indeed it is properly 
 that part of it which lies beyond the reach of our per- 
 ception, and still remains to be taken into the account, 
 to which we give the name of infinity. 
 
 Sec. Xll...»Duration^nvhet?ier considered as pest or 
 to come, Boundless, whence our Idea of Eternity. 
 This idea of the infinity of number, imperfect as it 
 may seem, is nevertheless that by which the mind as- 
 cends to the conception of eternity and immensity. For 
 when we consider duration, either as past or to come, 
 we find nothing to stop the progress 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 ourselves with vain efforts, 
 we must own at last that we can no more arrive at the 
 end of duration, than at the end of number. It is 
 true, .the several generations of men rise and disappear 
 in very quick successions ; earth itself may decay ; and 
 those bright luminaries that adorn the firmament of 
 heaven, be extinguished. But the course of time will 
 not be thereby disturbed ; that flows uniform and in- 
 variable, nor is bounded by the period of their exist- 
 ence. This double view of duration, as having already 
 revolved through numberless ages, and yet still ad- 
 vancing into futurity in an endless progression, pro- 
 perly constitutes our ideas of eternity. We speak in- 
 deed of an eternity past, an eternity to come, but 
 both these are bounded at one extreme : the former 
 terminates in the present moment, and therefore has an 
 end : the latter sets out from the same period, and 
 therefore has a beginning; but, taken together, they 
 form a line both ways infinitely extended, and which 
 represents eternity in its full dimensions. 
 
 Sec. XIII. ... The Idea of Immensity derived from the 
 Consideration of Space ever growing on all side- of us. 
 As, in the consideration of time, we fix upon the 
 present moment, regarding it as the middle point which 
 divides the whole line of duration into two equaj pa-ts ; 
 so, in the consideration of space, th.u particuhi. place 
 in which we exist is looked upon as a kind erf centre to 
 D 2 
 
42 DUNCAN'S ELEMENTS 
 
 the whole expansion. From thence we let loose our 
 thoughts on every side — above, below, around — and find 
 we can travel on, in the repetition of miles, and mil- 
 lions of miles, without ever arriving at the end of the 
 progression. It is not difficult, indeed, to carry our 
 conceptions to the utmost bounds of the universe ; at 
 least so far as it falls within our notice. But then the 
 imagination rests not here ; it sees immeasurable spaces 
 beyond, capable of receiving new worlds, which it can 
 pursue, as rising one above another in an endless suc- 
 cession. This consideration of space ever growing on 
 all sides of us, and yet never to be exhausted, is that 
 which gives us the idea of immensity ; which is in fact 
 nothing else but the infinity of number, applied to cer- 
 tain portions of extension, as miles, or leagues, &c. 
 and these conceived as extended every way around us, 
 in infinite and innumerable right lines. 
 
 Sec. XIV. Compound Ideas resulting from the Union 
 of Perceptions of different Kinds. 
 
 Hitherto we have considered the mind as employed 
 rrbout one and the same idea, enlarging and diversify- 
 ing it in various forms. We have seen it rising from 
 the most simple and obvious notices to the conception 
 of infinity itself ; and taken a view of it in all the dif- 
 ferent stages of its improvement. Let us now proceed 
 to the more complicated act of composition, when the 
 mind br'mgs several ideas of different kinds together, 
 and voluntarily combines them into one complex con- 
 ception. Such for instance, is our idea of a tune, as 
 comprehending a variety of notes, with many differ- 
 ent modulations of sound. And here it is to be observ- 
 ed, that though the complex idea may be excited in us, 
 by hearing the air itself struck off upon a proper in- 
 strument ; yet, considered originally, it still belongs 
 to this class of perceptions, which are distinguished as 
 the arbitrary collections of the mind. It was the mu- 
 sician, 01* composer, that combined the several notes, 
 and determined the order in which they were to follow 
 one another ; nor had that peculiar composition of 
 sounds any real union in nature, before they were thus 
 
OF LOGIC. 43 
 
 brought together in his mind. Of the same nature are 
 most of our ideas of human actions ; for though many 
 of them come to our notice by seeing the actions them- 
 selves, or hearing them described by others, as distil- 
 ling, carvings treason, 8cc. yet it is plain that they 
 must have been projected and contrived in the mind of 
 man before they had a real existence. 
 Sec. XV..../fi?w the Mind is determined in making 
 these Combinations. 
 It is here that the understanding has the greatest 
 ficope, and finds most employment for its active powers : 
 nor indeed i^ it possible to set any bounds to the ideas 
 of this class ; the combinations already made being al- 
 most innumerable, and those yet in the power of the 
 mind affording an endless diversity. It may not, how- 
 ever, be amiss to consider how we conduct ourselveg 
 amidst so great a variety, and by what rules we pro- 
 ceed in making those combinations to which we have 
 affixed particular names, while others, perhaps, no less 
 obvious, are neglected. The idea of killing, for in- 
 stance, joined to that of a father, makes a distinct spe- 
 cies of action, known by the name of parricide. It was 
 doubtless as obvious to distinguish between the killing 
 of an old man and a child, which yet we find is not done ; 
 both these actions being comprehended under the ge- 
 neral na ro^fl f murder. By what views therefore does the 
 mind re^pfte its combinations? Why is it determined 
 to one collection of ideas rather than another? This 
 cannot be well understood, without observing, that it 
 is the end of language to communicate our thoughts 
 one to another. Words are the signs of our ideas, and 
 serve to express the conceptions of the mind. Now it is 
 apparent, that such conceptions as are most apt to occur 
 in the commerce of life, would be first distinguished by 
 particular names ; the frequent occasion men have, of 
 mentioning these among themselves, rendering this ab- 
 solutely necessary. But as many of these conceptions 
 are collections of different simple ideas, hence we are 
 insensibly led to sucli peculiar combinations, as are 
 most serviceable to purposes of mutual intercourse and 
 communication. 
 
44 DUNCAN'S ELEMENTS 
 
 Sec XV I... 'Ideas of Human Actions often formed, £<*- 
 fore the Actions themselves exist* 
 
 Let us suppose, in the first beginnings of society, 
 a company of legislators met together, in order to con- 
 sult on proper regulations for the government of the 
 community. If they are men of prudence and foresight, 
 they will naturally observe many new occurrences, 
 likely to arise from this coalition of mankind, and 
 their living together in crowds. Perhaps the age in 
 which they live, has not produced an instance of one 
 man's killing ^another ; yet from the knowledge of 
 their own frame, and their power of doing hurt, they 
 conceive this as a possible case, and are wiliing to pro- 
 vide against it. Thus all the ideas that enter into the 
 complex one of murder, are brought together, and 
 united into one conception, before the action itself 
 really exists. It is not, however, thought necessary to 
 take into consideration the age of the person ; the 
 chief thing in view being to prevent the putting an 
 end to another's life unjustly, whether old or young ; 
 and therefore the penalty equally effects both cases. 
 But when they come to consider the relation in which 
 the person killed may stand to the murderer, here 
 there appears a manifest difference ; as it adds to the 
 crime, when committed upon a benefactofl^ and ren- 
 ders it particularly heinous in the case ofa father. 
 This last, therefore, is made to constitute a distinct spe- 
 cies of action, and lias a peculiar punishment allotted 
 to it. Thus we see how men, according to their dif- 
 ferent manner of life, and the relations they stand in 
 to one another, are naturally led to form several col- 
 lections of simple ideas, preferably to others, as fore- 
 seeing they may have frequent occasion to take notice 
 of such precise combinations. And because it would 
 be tedious in conversation, every time these complex 
 notions occur, to enumerate all the ideas of which 
 they consist ; therefore, for the sake of ease and dis- 
 patch, they give them particular names, and thereby 
 render the compositions fixed and permanent. 
 
OF LOGIC. 4$ 
 
 Sec. XVII.... Tta necessity of Mutual Intercourse^ 
 and Men's particular Aims in Life, a great Source 
 of Complex Ideas. 
 
 That it is in this manner we come by our complex 
 ideas, which multiply upon us according as the exi- 
 gencies of society require, or our pursuits, method of 
 life, and different aims x throw occasions in our way, 
 of combining such and such perceptions together, 
 might be easily made appear, by a short view of the 
 combinations themselves. Human, actions, as occur- 
 ring most frequently, and affording large matter of 
 conversation, debate, and enquiry among men, have 
 been very nicely modified, and distinguished into 
 classes, according to the several circumstances most 
 likely to attend them. In like manner, the arts and 
 sciences, in proportion as they are cultivated, leading 
 us into many compound views of things, which other- 
 wise would never offer themselves to the considera- 
 tion of the mind ; the complex ideas of this sort, 
 with the names by which they are expressed, are, we 
 find, the work of such particular nations, where these 
 arts and sciences have chiefly flourished. The Greeks, 
 for instance, excelled in learning and polite know- 
 ledge ; hence many of the terms belonging to rhetoric, 
 poetry, philosophy, physic, See. come originally from 
 their language. Modern fortification has received its 
 greatest improvements among the French; and ac- 
 cordingly the ideas and terms of the art are mostly der:-. 
 ved from writers of that nation. In Italy, architec- 
 ture, music, and painting, have been the great exer- 
 cise of the men of genius ; it is therefore .among them 
 that we find the several complex notions belonging te 
 these parts of study, as well as the names by which 
 they are expressed ; nor can we discourse accurately 
 and minutely of the above-mentioned arts, without 
 having recourse to the language of that climate. And 
 if we descend into the^particular callings and profes- 
 sions of men, they have all their peculiar collections of 
 ideas, distinguished by their several names, and hardly 
 known but to such as are conversant in that manner of 
 
46 DUNCAN'S ELEMENTS 
 
 life. Thus calcination, coliobation, filtration, £cc.-?.re 
 ■Words standing for complex ideas frequently framed in 
 the minds of chymists, and therefore familiar to men of 
 that employment. Yet as these, and such like com- 
 binations, seldom occur in common life, the generality 
 of mankind, we see, are in a great measure unacquaint- 
 ed with them. 
 
 Sec. XVIII. ...Hence different Sets of theni prevail in 
 different Countries : and Words in one Language have 
 none to ansxver them in another. 
 
 I might pursue these speculations farther, and shew 
 how the several fashions, customs, and manners of one 
 nation, leading them to form many complex notions 
 "which come not so naturally in the way of another ; 
 different sets of ideas prevail in different countries, 
 and of course have names appropriated to them in 
 the language, to which there are no words that an- 
 swer in another. The procedure and forms cf our 
 courts of justice have introduced many terms into the 
 English law, which stand for collections of ideas framed 
 among no other people. Nor would it be possible to ren- 
 der these terms by any single words of another lan- 
 guage ; because, where ideas themselves prevail not, 
 there are no names provided to express them. In this 
 case, therefore, it becomes necessary to use circumlo- 
 cutions, and enumeraie the several ideas comprehended 
 in the collection, if we would so express ourselves, as 
 to be understood in the language of other nations. 
 Kay, even among the same people, the change of cus- 
 toms and opinions frequently brings new sets of ideas, 
 "which, of course, must be distinguished by particular 
 names ; while, at the same time, the notions of former 
 ages grow into disuse, and the words answering them 
 are wholly laid aside, or employed in a signification dif- 
 ferent from what they had before. 
 
 See. XIX....77i/.r, too, the cause that Languages 
 are in a perpetual Jlux. 
 Thus languages are in a perpetual flux, and by de- 
 grees vary so much from their original frame, as to be- 
 come unintelligible even to the descendants of those 
 
OF LOGIC. 47 
 
 who speak them. If we run back into the ages of chi* 
 valry in England, when tilts and tournaments were in 
 fashion, how many complex ideas, peculiar to that mode 
 of life, shall we find familiar among the men of those 
 times, which are now little known or attended to? On 
 the contrary, the improvements in arts and sciences 
 that have since taken place, have hd us into innumerab- 
 le views of things, to which our fore-fathers were per- 
 fect strangers. But I shall not push these reflections any 
 farther, believing that what has been said will be suffi- 
 cient to show the origin and progress of our compound 
 ideas, and how the mind is directed in the choice of the 
 combinations it makes. We therefore proceed to the 
 consideration of abstract ideas, which make the sub- 
 ject of the following article. 
 
 ART. II. 
 
 OF ABSTRACT OR UNIVERSAL IDEAS. 
 
 Sec. L.^Gencral Ideas formed by the Abstraction of 
 the Mind. 
 
 HAVING dispatched what was necessary to be said 
 concerning our compound ideas, considered mere- 
 ly as they are combinations of the understanding, it is 
 now time to explain how we come by our general no- 
 tions which serve to represent to us a multitude of in- 
 dividuals and are the standards by which we rank things 
 into sorts. And this, as we have before intimated, is 
 done by the abstraction of the mind; which act may- 
 be extended to all our ideas, whether simple, compound, 
 or of substances. Ifj for instance, we fix our attention 
 on any particular colour, as scarlet, we can leave out 
 the consideration of all present circumstances, as the 
 subject in which it inheres, the time and place of seeing 
 it, Sec. and retaining only the impression itself, make^ 
 it a representative cf that quality or appearance, where - 
 ever we chance to meet with it. It is thus that abstract 
 and universal ideas are framed ; for the mind regarding 
 fciiiy the scarlet colour, which one day it observes per- 
 
48 DUNCAN'S ELEMENTS 
 
 haps in a piece of cloth, another in a picture, and a 
 third in the rainbow; the appearance is conceived to 
 be the same in all these objects, and therefore is called 
 by the same name. 
 
 Sec, II.... A 11 the Perceptions of the Understanding 
 particular* 
 But to enter a little more closely into this matter, and 
 show that these our general conceptions are the mere 
 creatures of the understanding, it may not be amiss to 
 take notice, that all our perceptions of things, whether 
 we derive them from sensation or reflexion, are of their 
 own nature particular^ and represent to us single, de- 
 terminate objects. When we see a horse, for instance, 
 in the fields, our idea is that of an individual. If we 
 hear a sound, it is something particular, and different 
 from what we hear at any other time. Every percep- 
 tion of the mind is distinct from every other perception; 
 nay, and every idea brought into view by the imagina- 
 tion, as when we frame the image of a lion standing 
 before us, is still singular, and represents a single object. 
 
 Sec. IIL«««77t? Idea of the Species represents what is 
 common to different individuals* 
 But when we come to take a view of these several 
 particulars, we readily observe among some of them 
 a resemblance ; and framing to ourselves an idea of 
 those things in Which any of them are found to agree, 
 we thereby get a general notion, applicable to many 
 individuals. Thus horses are found to resemble one 
 another in shape, voice, and structure of parts. The 
 idea, which takes in only the particulars of this resem- 
 blance, excluding what is peculiar to each single ani- 
 mal, becomes of course common to all creatures of 
 that kind, and is therefore the representative of a 
 whole class of beings. Accordingly the name of that 
 general idea is given to every animal in which that 
 shape, voice, and structure is found; for the word 
 horse, implying only these particulars, must belong to 
 all creatures wherein they exist. This is the first step 
 or gradation in the forming of abstract notions, when 
 tfee mind confines itself textile consideration of indiyi* 
 
OF LOGIC. 49 
 
 duals, and frames an idea that comprehends such only 
 under it. The rank or class of things answering to 
 this idea, is called species in the language of the 
 schools. So a horse is a certain species of animals, an 
 oak is a species of trees, and a square is a species of 
 four-sided figures. 
 
 Sec. IV.... The Idea of the Genus represents what us 
 common to several Species. 
 When we have thu3 learned to rank individuals into 
 sorts and classes, according to the resemblance found 
 among them, the mind proceeds next to consider the 
 species themselves, and often in these too observes a 
 certain likeness. Whereupon, throwing out all those 
 particulars wherein the several species are found to 
 disagree, and retaining only such as are common to 
 them all, we thereby frame a still more general idea, 
 comprehending under it a variety of different species. 
 Thus a sparrow, a hawk, and eagle, &c. are distinct 
 species of birds, which have each their peculiar shape 
 and make. They nevertheless resemble one another, 
 in being covered with feathers, and provided with wings 
 that bear them through the air. Out of these parti- 
 culars we form a new idea, including all the common 
 properties of the feathered kind ; and appropriating to 
 it the name of bird, mark by that word another class of 
 things, of a higher order than any of the former. This 
 superior division, which extends to several species at 
 once, is called in the schools the genus, and is the second 
 step the mind takes in advancing to universal notions. 
 
 Sec. V.. ..The Mind may advance by manifold Grada- 
 tions, in rising from Particulars' to Generals. 
 And thus have I given a short, but I hope intelligi- 
 ble account, of the business of genera and species, about 
 which so much has bee» said in the writings of logici- 
 ans. Species, \n strictness and propriety of speech, is 
 such a rank or class of things, as comprehends under 
 it only individuals : genus advances still higher, and 
 takes in a variety of distinct species. It is, however, to 
 be observed, that the mind in rising from particulars 
 .to generals, dees not confine itself to cue or two gra- 
 
 E 
 
30 DUNCAN'S ELEMENTS 
 
 dations, but may carry its views through the whole 
 extent ©f things, until at length it arrive at an idea 
 embracing the universal compass of nature. For when 
 ■we have ranked things into sorts, and reduced these 
 again to the higher order or ge?ius, these genera are 
 still found to resemble one another in some particu- 
 lars, which being collected into one idea, form a new 
 and more comprehensive division of things. Thus 
 Urd is a genus, embracing all the varieties of the fea- 
 thered kind. Fish implies the several species of living 
 creatures which inhabit the waters. Quadruped and 
 insect are also universal ideas, that take in many infe- 
 rior distributions and classes. Yet all these different 
 orders of being, have this in common, that they are 
 provided with organical bodies, fitted for the purposes 
 of life and spontaneous motion. An idea, therefore, 
 comprehending only these last particulars, will equally 
 belong to all the divisions before enumerated ; and the 
 ■word animal^ by which it is expressed, becomes a gene- 
 ral name for the several creatures endued with life, 
 sense, and spontaneous motion. If we are for carry- 
 ing our views still farther, and framing a yet more uni- 
 versal notion, we can cast our eyes upon both the ani- 
 mate and inanimate parts of nature ; wherein we find 
 this mutual correspondence, that they exist, and con- 
 tinue in being. This last idea, therefore, of being in 
 general, comprehends under it all the varieties of 
 things, and may be universally applied to whatever 
 has either life or existence ; so that in respect of the 
 present frame of nature, it is tjie highest and most uni- 
 versal idea we have. 
 
 Sec* VI... .Whence many intermediate Steps betnveenthc 
 highest Genus and lowest Species. 
 
 In this series of notions, rising one above another, 
 in the degree of universality ; that division, which 
 comprehends under its several genera, is called in the 
 schools the higher genus ; which denomination conti- 
 nues, until wc arrive at the last advance of the under- 
 standing, when, being come to the most general of all 
 ideas, that admits not of a superior, it is distinguished 
 
OF LOGIC, 51 
 
 fey the name of the genus generalissimum* In like man- 
 ner the several genera, comprehended under a higher 
 genus, are, in respect of it, considered as species ; and 
 as these two last have species under them, the inferior 
 divisions are, for distinction's sake, termed lower spe- 
 ties. Thus the progression continues, and when we 
 come to the lowest subdivision of all, comprehending 
 only individuals, which, as I have before intimated, 
 constitutes the proper species, this the schools denomi- 
 nate the species specialissima. All that lie between 
 it and the highest distribution of things, are the inter- 
 mediate genera and species, which are termed, each in 
 their turn, genus gener alius, or species specialior, ac- 
 cording as we consider them in the ascending or de- 
 scending scale of our ideas ; or, to speak in the lan- 
 guage of logicians, according to their ascent or descent 
 in linea prtdicamentali. 1 should net have entered so 
 far into these verbal disquisitions, had not the terms 
 here explained, been such as frequently occur in the 
 writings of philosophers ; insomuch that without some 
 knowledge of them we must often be at a loss, in the 
 prosecution of these studies. Besides, it is both curious 
 and useful, to see the gradual progress of the mind, in 
 its advances from particular to general conceptions— 
 to observe it ranging its ideas into classes, and esta- 
 blishing a just and regular subordination in its views 
 and notices of things. This is the shortest way to 
 knowledge, and affords the best means of preserving the 
 order and due connexion of our thoughts, so as to 
 make them subservient to the increase of science. For 
 when we see how things comprehend, ' or are compre- 
 hended in, one another, we are able to discover the mu- 
 tual dependence of all the several branches of know- 
 ledge which leads us into the true and natural method of 
 conducting our understandings in the search of truth. 
 Sec. VU....G<7i<?ra/ Ideas the Creatures of the Under* 
 standing. 
 From what has been said, it is evident, that gene- 
 ral ideas' are the creatures and inventions oi the under- 
 standing. Nature, it is true, in the production of 
 things, makes many of them alike ; but it is the mind 
 
52 DUNCAN'S ELEMENTS 
 
 alone, that collects the particulars in which they agree ? 
 into one idea, and sets it up as a representative of ma- 
 ny individuals. And now 1 think we may venture upon 
 that much-agitated question, where do the genera and 
 species of things exist ? To which I answer, in the 
 mind. Universality belongs not to things themselves, it 
 being apparent, that they are all particular in their ex- 
 istence. However, as they often have many properties 
 in common, the understanding, by uniting these into 
 one conception, obtains a general idea, under which it 
 Tanks all the several objects wherein these properties 
 are found. So far indeed we must allow, that the par- 
 ticular combination of properties, which constitutes the 
 genus or species, exists in all the individuals referred to 
 that genus or species ; but then it is in conjunction with 
 other properties, by which these individuals are distin- 
 guished from one other. Thus the collection of simple 
 ideas, signified by the word bird, is to be found, for in- 
 stance, in a hawk, or any other single animal, to which 
 we apply that general name: but the notion itself, ab- 
 stracted from all the particulars to which it belongs, 
 has evidently no existence out of the understanding. 
 There is not a being in nature that can be called a bird 
 in general, or that does not necessarily imply, in the 
 very conception of it, several simple ideas, besides those 
 marked by that word. For the name, in this case, sig- 
 nifies 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"existence. 
 These last considerations, however, are inseparable 
 from the reality of things, and therefore must be added 
 to the general idea, before we can conceive any thing 
 conformable to it actually brought into being. 
 Sec. VIII... .Considered apart, they exist only in the 
 Mind, but in conjunction with other Ideas in the in- 
 dividuals comprehended under them. 
 Hence we see at once, what sort of an existence ge- 
 neral natures have. Considered apart, and by them- 
 selves, they are wholly the workmanship of the under- 
 standing, and derive their being and reality from it ; 
 but viewed in conjunction with other ideas that co-exist 
 
OF LOGIC. 53 
 
 with them in the several objects of nature, they are to 
 be found in the individuals to which they refer ; and 
 therefore, according to this way of conception, may be 
 said to have an existence in them. Thus, so long as 
 the ideas answering to the words man or tree, continue 
 general and undetermined, they have no real objects' 
 answering them in nature ; nor can the collections o£ 
 simple ideas, marked by these names, while all others 
 are supposed excluded, exist any where out of the un- 
 derstanding. Nevertheless, as all the simple ideas, in- 
 cluded in the general notion of man, are to be found in 
 every particular man — and all those implied in the no- 
 tion of a t recy in every particular tree — hence the general 
 nature of man, exists in every individual man, as does 
 the general nature of a tree, in every individual tree. 
 Sec. IX. ... Difference of Ideas considered as compound 
 and as universal. 
 One thing still remains to be observed, with regard 
 to these our general ideas ; that, though many of therm 
 are evidently combinations of different simple ideas, and 
 according to that way of considering them, are includ- 
 ed in the first division of our complex conceptions, those, 
 namely, framed by the composition of the mind ; yet 
 we are carefully to distinguish between an idea, as it is 
 compound, and as it is universal. In the first case, the 
 mind chiefly considers the several ideas that are com- 
 bined together; or, in other words, all the attributes, 
 qualities, or parts, that are contained in any idea. Thus 
 the idea of a bird, includes life, sense, spontaneous mo- 
 tion, a covering of feathers, wings. &x. none of which 
 can be left out without destroying the very nature o£ 
 the idea, and making it something quite different from 
 what it was before. This way of considering things 
 according to the number of their parts and properties, 
 is called by logicians the comprehension of an idea. But 
 the universality of our notions implies quite another 
 turn of thinking, in as much as it fixes the regard of 
 the mind, upon the subject to which our ideas extend, 
 or the individuals and species comprehended under them. 
 In this sense, the idea answering to the word bird, takes 
 in the several species of the feathered creation, the/raw^ 
 K 9 
 
54 DUNCAN'S ELEMENTS 
 
 the eagle, sparrow, lark, and innumerable others, to all 
 which it may with equal propriety be applied. And 
 here it is remarkable, that the idea loses nothing of its 
 force or comprehension, by being restricted to a parti- 
 cular kind. When I say the bird of Jove, though in 
 this case the idea is restrained to the eagle alone, it still 
 remains as distinct, and includes as many simple ideas 
 in its composition, as when, before, it was extended to 
 all the different tribes of feathered animals. 
 Sec. X... The comprehension and extension of our Ideas* 
 We see, therefore, that our compound ideas may 
 continue t»he same in respect of their attributes, or the 
 number of parts, and yet vary considerably in the degree 
 of universality. The general idea of man is the same, 
 whether applied to the whole human race, or those of 
 any particular nation. When I affirm, for instance, of 
 mankind in general, that their knowledge falls short of 
 perfection, and afterwards make the like observation of 
 the men of the present age ; in both cases, the word 
 fnan stands for one and the same collection of simple 
 ideas; but in respect of the individuals to which it is 
 applied, there is a great and manifest difference. That 
 is, the term, man, denotes one invariable compound 
 idea; which, notwithstanding, considered as a general 
 notion, may be contracted or enlarged at pleasure. 
 And as in the former case, the several parts of the' com- 
 pound idea are called its comprehension ; so in the lat- 
 ter, the individuals, to which the universal idea is ap- 
 plied, are called its extension. I might add many more 
 observations on this subject, but choose rather to stop 
 here, having said enough to explain the difference be- 
 tween compound and abstract ideas, and show the rea- 
 son of my ranging them under distinct heads. 
 
 ART. III. 
 
 OF OUR IDEAS OF RELATIONS. 
 
 Sec. I.,., Ideas of Relations exceeding numerous, 
 [ GOME now to the third and last division of those 
 L ideas, which I consider as the creatures and work- 
 
OF LOGIC. 55 
 
 manship of the understanding ; such, namely, as arise 
 from the comparing of things one with another. For 
 the mind, in its views, is not tied to single objects ; but 
 can examine their references and respects, in regard to 
 others, brought under consideration at the same time. 
 And when it docs so, and thence derives new notices of 
 things, the ideas thus got are called relations, and make, 
 I am apt to think, the largest class of all our percep- 
 tions. For every single object will admit of almost in- 
 numerable comparisons with others, and in this sense 
 may become a very plentiful source of ideas to the un- 
 derstanding. Thus, if we compare one thing with ano- 
 ther, in respect of bulk, we get the ideas of greater, less, 
 or equality ; if in respect of time, of older and younger $ 
 and so for other relations, which we can pursue at plea- 
 sure, almost without end ; whence it is easy to conceive, 
 how very extensive this tribe of our perceptions must be. 
 Sec. II. ...Men chiefly determined to particular Com" 
 parisons by 4 he Wants and Exigencies of Life. 
 I shall not pretend to trace out these ideas particu- 
 larly, nor indeed so much as to enumerate their several 
 divisions ; it being enough to observe, that here, as 
 well as in the other kinds of our complex ideas, we 
 bound ourselves, for the most part, to such comparisons, 
 as the exigencies of society, the wants of life, and the 
 different professions of men, render necessary ; and are 
 more or less accurate in tracing out the relations of 
 things, according to the degree of importance they 
 appear to have in these respects. The relations of 
 men one to another, arising either from the ties of blood, 
 their several ranks and places in the community, or a 
 mutual intercouse of good offices, being of great weight 
 and concern in the commerce of life, have in a particu- 
 lar manner engaged our attention, and are therefore 
 very minutely described. For the same reason, men 
 have found it necessary, to determine, as exactly as 
 possible, the various dependence of things, as their 
 happiness is nearly connected with this knowledge. 
 When we consider objects merely in respect cf exist- 
 ence, as either giving or receiving it, we come by the 
 ideas of cause and effect ; nor need 1 mention how muck 
 
56 DUNCAN'S ELEMENTS 
 
 the welfare of mankind depends on an extensive view 
 of things, as they stand connected in this relation ; it 
 being evident, that the several schemes and purposes of 
 life, are all conducted upon a previous supposition, that 
 certain known causes will have their usual regular ef- 
 fects, and such and such actions be attended with such 
 and such consequences. 
 Sec. Ill,*; Relations of Creator and Creature^ Istcm 
 But there are other relations of this kind, besides 
 those that regard merely existence ; as when we also 
 take into the account the additional gifts of a capa- 
 city for happiness, and the means of attaining it ; 
 which constitutes the relation of Creator and creature*) 
 in the more solemn acceptation of these words. Again, 
 when we consider the great Author of our being, not 
 only as the Creator of the universe, but also as pre- 
 serving and holding it together, and presiding over the 
 present frame of things with uncontrouled dominion \ 
 he then appears under the notion of a moral G 'over -nor , 
 to whom we are accountable for our actions, and the 
 use we make of those powers and faculties we derive 
 from him. Now as it is of the highest consequence 
 for men, not to be unacquainted with these, and such 
 like relations ; hence we find, that the wisest nations, 
 and such as best understood the true application of the 
 powers of the mind, have always made it their chief 
 study to regulate and ascertain these ideas, and trace 
 them in all their consequences. And thus we may, in 
 some measure, perceive, how the mind proceeds in 
 comparing its ideas together, and by what views it is 
 chiefly governed, in framing the complex notions of this 
 class, by which it represents the various habitudes of 
 things, I shall only add upon this subject, these two 
 observations. 
 
 Sec. IV...0«r Ideas of relations very clear and distinct* 
 First, that our ideas of relations, are for the most 
 part very clear and distinct. For the comparing of 
 things together, being a voluntary act of the mind, 
 we cannot but suppose that it must be acquainted with 
 its own views in the comparison ; and of course have 
 a clear conception of the foundation of that relation, 
 
OF LOGIC. sr 
 
 it sets itself to enquire into. Thus the relation of 
 cause and effect, implying only that one thing produ- 
 ces, or is produced by another, which notions are al- 
 ways distinctly settled in the understanding before it 
 goes about to make the comparison ; it is evident, 
 that the idea representing this mutual respect of ob- 
 jects, -will be no less clear, than are the notions them- 
 selves upon which the relation is founded. And what 
 is still more remarkable of the ideas of this class ; 
 they cease not to be distinct, even where the subjects 
 compared are but very imperfectly known. For 1 can 
 well enough conceive, that one thing has produced 
 another, and that therefore they stand related as cause 
 and effect, though my ideas of the things themselves 
 may perhaps be very obscure, and come far short of 
 representing their real nature and properties. I doubt 
 not but it will be readily owned, that our idea of the 
 universe, considered as comprehending the whole 
 frame of created things, is very inadequate ; and I 
 think it is still more apparent, that our notion of the 
 Supreme Being comes not up to the excellence and 
 perfection of his nature. Yet we very well -understand 
 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 creature stand for. 
 
 Sec. V,. ..Ideas of Relations among the most important 
 Conceptions of the Mind* 
 
 I have yet another observation to make upon this 
 subject ; and it is, that our ideas of relations are among 
 the most important conceptions of the understanding, 
 and afford the largest field for the exercise and im- 
 provement of human knowledge. Moat of our en- 
 quiries regard relative ideas, and are set on foot with 
 a view to investigate the mutual habitudes of things. 
 The mathematician has taken quantity for his province, 
 and teaches us how to compare magnitudes of differ- 
 ent figures and dimensions, in order to judge with 
 certainty of their relative properties. The philosopher 
 attaches himself to the chain of causes and effects, and 
 
58 DUNCAN'S ELEMENTS 
 
 endeavours to trace out the various dependence of 
 things considered in this li$$it. In fine, whither do 
 all our researches tend, But by means of certain 
 known properties and relations, to find out others that 
 stand some how connected with them ? As for the 
 importance of these conceptions, no one can call that 
 in question, who reflects ; that from our relations to 
 our Creator and one another, arise all the duties of 
 morality and religion, and that the correspondence of 
 the several 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 happiness 
 or misery. Whence it is evident, that without an 
 exact knowledge of these relations, we must wander 
 on in life with great uncertainty, and may often plunge 
 into calamities and misfortunes, by those very pur- 
 suits from which we expected nothing but joy and 
 pleasure. 
 
 Sec. VI... •Recapitulation. 
 
 Thus have I gone through the several divisions of 
 our iaeas, which I have endeavoured to represent in 
 such a manner as their vast extent may most easily ap- 
 pear, and the conduct of the mind in framing them 
 be distinctly apprehended. I might easily run into 
 other distinctions, by considering them as clear or 
 obscure, adequate or inadequate, true or false. But 
 the limits of this tract will not allow my entering 
 more fully into the subject, and I think it the less 
 needful, because the very names are almost sufricieat 
 to convey a noticn of these several kinds of ideas into 
 the mind. But as the division explained above seems 
 to be of great importance, towards settling in the un- 
 derstanding a just view of the progress of human know- 
 ledge, and the steps by which it advances from one 
 degree of improvement to another, I shall here run 
 over it again in as few words as possible, that the 
 whole process may be seen at once. Our ideas are all 
 derived into the understanding, either by sensation or 
 reflexion. This, however, is observable, that one and 
 the same object often excites a variety of perceptions 
 
OF LOGIC, 3$ 
 
 at once, which are nevertheless readily distinguish- 
 ed by the mind, and appear each under a farm pe« 
 culiar to itself. These constitute our primary and 
 original notices, and are easily known from all others, 
 in as much as they are entirely void of plurality, and 
 cannot be divided into two or more different ideas. 
 They are also the materials out of which the others 
 are formed, and are therefore, by way of distinction, 
 called simple ideas. But the mind, though it has no 
 power over these, either to fashion or destroy them, 
 can yet combine them in an infinite number of ways ; 
 and from their various combinations result all our 
 complex ideas, which are of two principal kinds. First, 
 such as are derived from without, and represent those 
 combinations of simple ideas, that have a real existence 
 in nature. Of this sort are all our ideas of substances. 
 Secondly, the conceptions formed by the mind itself, 
 arbitrarily uniting and putting together its ideas. And 
 as this makes by far the largest class, and comprehend* 
 all those ideas which may be properly termed our own, 
 as being the real workmanship of the understanding ; so 
 they fall very naturally under three distinct heads. For 
 either the mind combines several simple ideas together, 
 in order to form them into one conception, in which 
 the number and quality cf the ideas united, are prin- 
 cipally considered ; and thus it is we come by all our 
 compound notions : or it fixes upon any of its ideas, 
 whether simple, compounder of substances ; and, leav- 
 ing out the circumstances of time, place, real exist- 
 ence, and whatever renders it particular, considers the 
 appearance alone, and makes that a representative of 
 all of the kind ; whence our abstract and universal 
 ideas are derived : or lastly, it compares things one 
 with another, examines their mutual connexions, and 
 thereby furnishes itself with a new set of notions, 
 known by the name of relations, which, as has been al- 
 ready remarked, make by no means the least important 
 class of our perceptions. This division of our ideas, 
 as it seems to be the most natural, and truly to repre- 
 sent the manner in which they are introduced into the 
 «iind ; so 1 believe it will be found to comprehend them 
 
60 DUNCAN'S ELEMENTS 
 
 in all their varieties. I shall therefore now proceed to 
 offer some observations upon language, as being the 
 great instrument, by which we are enabled to make our 
 ideas and perceptions known to others* 
 
 Cfjap, V. 
 
 OF WORDS, CONSIDERED AS THE 
 SIGNS OF OUR IDEAS. 
 
 Sec. I Words furnish the Means of recording our 
 
 own 'Thoughts* 
 
 WE have seen how the mind comes to be first 
 furnished with ideas, and by what methods it 
 contrives to diversify and enlarge its stock : let us now 
 consider the means of making known our thoughts to 
 others, that we may not only understand how know- 
 ledge is acquired, but also in what manner it may be 
 communicated with the greatest certainty and advan- 
 tage. For our ideas, though manifold and various, are 
 nevertheless, all within our own breasts, invisible to 
 others, nor can of themselves be made appear. But 
 God designing us for society, and to have a fellowship 
 with those of our kind, has provided us with organs fit- 
 ted to frame articulate sounds, and given us also a ca- 
 pacity of using those sounds as signs of internal con- 
 ceptions. Hence ppring words and languages ; for 
 having once pitched upon any sound, to stand as the 
 mark of an idea in the mind, custom^ by degrees, estab- 
 lishes such a connexion between them, that the appear- 
 ance of the idea in the understanding always brings 
 to our remembrance the sound or name by which it is 
 expressed ; as, in like manner, the hearing of the sound 
 newer fails to excite the idea for which it is made to 
 stand. And thus it is easy to conceive, how a man 
 may record his own thoughts, and bring them again 
 into view, in any succeeding period of life. For this 
 connexion being once settled, as the same sounds will 
 always serve to excite the same ideas - 9 if he can but 
 
OF LOGIC. 61 
 
 contrive to register his words, in the order and dispo- 
 sition in which the present train of his thoughts pre- 
 sents them to his imagination ; it is evident he will be 
 able to recall these thoughts at pleasure, and that too 
 in the very manner of their first appearance. Accord- 
 ingly we find, that the inventions of writing and paint- 
 ing, by enabling us to fix and perpetuate such perish- 
 able things as sounds, have also furnished us with the 
 means, of giving a kind of permanency to the transac- 
 tions of the mind, insomuch that they may be in the # 
 same manner subjected to our review, as any the other 
 abiding objects of nature. 
 
 Sec. II*. ., And of the mutual Communication of Know* 
 ledge from one Man te another. 
 
 But besides the ability of recording our own thoughts 
 there is this farther advantage in the use of external 
 signs, that they enable us to communicate our senti- 
 ments to others, and also receive information of what 
 passes in their breasts. For any number of men, hav- 
 ing agreed to establish the same sounds as signs of the 
 same ideas, it is apparent, that the repetition of these 
 sounds must excite the like perceptions in each, and 
 create a perfect correspondence of thoughts. When 
 for instance, any train of ideas succeed one another in 
 my mind, if the names, by which I am wont to express 
 them, have been annexed by those with whom I con- 
 verse, to the very same set of ideas,. nothing is more 
 evident, than that by repeating those names, according 
 to the tenor of my present conceptions, I shall raise in 
 their minds the same course of thought as has taken 
 possession of my own. Hence, by barely attending to 
 what passes within themselves, they wiH also become 
 acquainted with the ideas in my own understanding, 
 and have them in a manner laid before their view. 
 So that we here clearly perceive, how a man may com- 
 municate his sentiments, knowledge, and discoveries 
 to others, if the .language \n which he converses, be 
 extensive enough to mark all the ideas and transactions 
 of his mind. But as this is not always the case, and 
 »en are often obliged to invent tenns of their own ? to 
 F 
 
62 DUNCAN'S ELEMENTS 
 
 express new views and conceptions of thing ; it may be 
 asked, how, in these circumstances, we can become ac- 
 quainted with the thoughts of another, when he makes 
 use of words to which we have never annexed any ideas, 
 and which of course, can raise no perceptions in our 
 minds? Now, in order*to unveil this mystery, and give 
 some little insight into the foundation, growth, and 
 improvement of language, the following observations 
 will lam apt to think, be found of considerable moment. 
 
 Sec. III... •Simple Ideas cannot be conveyed into the 
 Mind by Words, or a Description ; 
 
 Tii*st, that no word can be to any man the sign of an 
 idea,"~till that idea comes to have a real exigence in his 
 mind. For names being only so far intelligible, as 
 they denote known internal conceptions, where they 
 have none such to answer them, there they are plainly 
 sounds without signification, and of course convey no 
 instruction or knowledge. But no sooner are the ideas 
 to which they belong raised in the understanding, than, 
 finding it easy to connect them with the established 
 names, we can join in any agreement of this kind made 
 by others, and thereby enjoy the benefit made by their 
 discoveries. The first thing, therefore, to be consider- 
 ed, is, how these ideas may be conveyed into the mind ; 
 that, being there, we may learn to connect them with 
 their appropriated sounds, and -so become capable of 
 understanding others, when they make use of these 
 sounds-ili laying open, and communicating their tho'ts. 
 Now to comprehend this distinctly it will be necessa- 
 ry to call to mind, the before-mentioned divi-sion of 
 our ideas into simple and^ complex. And first, as for 
 our simple ideas, it has been already observed, that 
 they can find no admission into the mind, but by two 
 original fountains of knowledge, sensation and reflex- 
 ion. If therefore any of these have as yet no being 
 in the understanding, it is impossible by words, or a 
 description, to excite them there. A man, who had 
 never felt the impression of heat, could not be brought 
 to comprehend that sensation, by any thing we might 
 say to explain it. If we would really produce the ide* 
 
OF LOGIC. 63 
 
 in him, it must be by applying the proper object to his 
 senses, and bringing him within the inflrv.nce, t>f-a,-h«>t 
 body. When this is done, and experience has taught 
 him the perception to traiefe men hive m.iexel the 
 name, keif* it then becomes to him the sign of that' 
 idea ; and he thenceforth understands the meaning of 
 *. term, which, before, all the words in the world would 
 not have been sufficient to convey into his mind. The 
 .case is the same in respect of light and colours. A man 
 born blind, .and thereby deprived of the only convey- 
 ance for the ideas of this class, can never be brought 
 to understand the names by. which they are expressed. 
 The reason is plain ; they stand for ideas that have no 
 existence m his mind ; and as the organ appropriated to 
 their reception is wanting, all other contrivances are 
 vain, nor can they, by any force of description, be rais- 
 ed in his imagination. But it is quite otherwise in our 
 complex notions. For these being no more than cer- 
 tain combinations of simple ideas put together in va- 
 rious forms — if the original ideas, out of which these 
 collections are made, have already got admission into 
 the understanding, and the names serving to express 
 them are known — it will be easy, by enumerating the 
 several ideas concerned in the composition, and mark- 
 ing the order and manner in which they are united, 
 to raise any complex conception in the mind. Thus 
 the idea answering to the word rainbow^ may be readi- 
 ly excited in the imagination of another, who has ne- 
 ver seen the appearance itself, by barely describing the 
 figure, largeness, position, and order of colours; if we 
 £.tppose these several simple ideas, with their names, 
 sufficiently known to him. 
 
 Sec. IV. ...The Nature of Complex Ideas Definable^ 
 these of Simple Ideas not. 
 
 And this_ naturally leads me to a second observation, 
 upon this s.ubject, namely: that words standing for 
 complex ideas are all definable'; but these, by'which 
 we denote simple ideas, are not. For the perceptions 
 of this latter class, having no other entrance into the 
 mind, than by sensation or reflexion ; can only be ac- 
 
64 DUNCAN'S ELEMENTS 
 
 quired by experience from the several objects of nature* 
 pops*- to prtDfl^-ce those perceptions in us. Words, 
 indeed, may very well serve to remind us of them, if 
 they have already found admission into the undetstand- 
 ing, and their connexion with the established names is 
 known ; but they can never give them their original 
 being and existence there. And hence it is, that when 
 anyone asks the meaning of a word denoting a simple 
 idea, we pretend not to explain it to him by a defini- 
 tion, well knowing that to be impossible ; but suppos- 
 ing him already acquainted with the idea, and only 
 ignorant of the name by which it is called, we either 
 mention it to him by some other name, with which we 
 presume he knows its connexion, or appeal to the ob- 
 ject where the idea itself is found.. Thus^ was any one 
 to ask the meaning of the word white, we should tell 
 him it stood for the idea as albus, in Latin, or blanc, in 
 French; or, if we thought him a stranger to these lan- 
 guages, might appeal to an object producing the idea, 
 by saying, it denotedthe colour we observe in snoiv or 
 milk. But this is by no means a definition of the word, 
 exiting a new idea in his understanding ; but merely a 
 contrivance to remind him of a known idea, and teach 
 him its connexion with the established name. For if 
 the idea after which he enquires, has never yet been 
 raised in his mind- — as suppose one, who had seen no 
 other colours than black andw/nJe, should ask the mean- 
 ing of the word scarlet — it is easy to perceive, that it 
 would be no more possible to make him comprehend it by 
 words, or a definition, than to inculcate the same per- 
 ception into the imagination of a man born blind. 
 The only method in this case, is, to present some ob- 
 ject, by looking at which the perception itself may be 
 excited ; and thus he will learn both the name and the 
 idea together. 
 
 Sec. V .... Experience and Observation bring Men to ail 
 Agreement in the Names of Simple Ideas. 
 
 Should any one's curiosity now prompt him to enquire* 
 how it comes to pass, that men agree in their names of 
 the simple ideas, seeing they cannot view the percep- 
 
OF LOGIC. 6* 
 
 tiotis in one another's minds, nor make known these 
 perceptions by words to others ; I answer, that the ef- 
 fect here mentioned is produced by experience and ob- 
 servation. Thus, finding, for instance, that the name, 
 heat) is annexed to that impression which men feel 
 when they approach the fire, I make it also the sign of 
 the idea excited in me by; such an approach, nor have 
 any doubt, but it denotes the same perception in my 
 mind as in their's. For we are naturally led to ima- 
 gine, that the same objects operate alike upon the or- 
 gans of the human body, and produce an uniformity of 
 sensations. No man fancies, that the idea raised in 
 him by the taste of sugar, and which he calls sweet- 
 ness, differs from that excited in another by the like 
 means ; or that wormwood, to whose relish he has given 
 the ep'nhetbitter, produces in others the sensation which 
 he denotes by the Word sweet. Presuming, therefore, 
 upon this conformity of perceptions, when they arise 
 from the same objects, we easily agree as to the names 
 of our simple ideas ; a*nd if at any time, by a more 
 narrow scrutiny into things, new ideas of this class 
 come in our way, which we choose to express by terms 
 of our own invention ; these names are explained not 
 by a definition, but by referring to the objects, whence 
 the ideas themselves maybe obtained. 
 
 Sec. VI.„,The Conveyance of Complex Ideas by Defi- 
 nitions, a wise Contrivance in Nature ; 
 
 Being in this manner furnished with simple ideas, 
 and the names by which they are expressed, the meaning 
 of terms that stand for complex ideas is easily attain- 
 ed ; because the ideas themselves answering to these 
 terms, may be conveyed into the mind by definitions. 
 For our complex notions, as was already observed, are 
 only certain combinations of simple ideas. When, 
 therefore, these are enumerated, and the manner in 
 which they are united into one conception explained, 
 nothing more is wanting to* raise that conception in the 
 understanding; and thus the term denoting it comes 
 of course to be understood. And here it is worth while, 
 to reflect a little upon the wise contrivance of nature, 
 
 f £ 
 
65 DUNCAN'S ELEMENTS 
 
 in thus furnishing us with the very aptest means of 
 communicating our thoughts. For were it not so or- 
 dered, that we could thus convey our complex ideas 
 from one to another by definitions, it would in many 
 cases be impossible to make them known at all. This 
 is apparent in those ideas Which are the proper work 
 of the mind. For as they exist only in the understand- 
 ing, and have no real objects in nature, in conformity 
 to which they are framed, — if we could -not make them 
 known by a description, they must lie forever hidden 
 within our own breasts, and be confined to the narrow 
 acquaintance of a single mind. All the fine scenes, that 
 rise from time to time in the poet's fancy, and, by his 
 lively painting, give such entertainment to his readers 
 — were he destitute of this faculty, of laying them 
 open to the view of others by words and descriptions, 
 — -could not extend their influence beyond his own 
 imagination, or give joy to any but the original 
 inventor. 
 
 Sec. VII,, ..And of great avail towards the Improve- 
 ment of Knowledge, 
 
 There is this farther advantage in the ability we en- 
 joy, of communicating our complex notions by defini- 
 tions ; that as these make by far the largest class of our 
 ideas, and most frequently occur in the progress and 
 improvement of knowledge ; so they are by this means 
 imparted with the greatest readiness, than which no- 
 thing could tend more to the increase and spreading of 
 science. For a definity is soon perused, and if the 
 terms of it are well understood, the idea itself finds an 
 easy admission into the mind. Whereas in simple 
 perceptions, where we are referred to the objects pro- 
 ducing them, if these cannot be come at, as is some- 
 times the case, the names, by which they are expressed 
 must remain empty sounds. But new ideas of this 
 class occurring very rarely in the sciences, • they sel- 
 dom create any great obstruction. It is otherwise with 
 our complex notions ; for every step we take, leading 
 us into new combinations and views of things, it be- 
 comes necessary to explain these to others, before they 
 
of logic. er 
 
 can be made acquainted with our discoveries. And as 
 the manner of definitions, is easy, requiring no appara- 
 tus but that of words, which are always ready, and at 
 hand ; hence we can, with the less difficulty, remove 
 such .obstacles, as might arise from terms of our own 
 invention, when they are made to stand for new com- 
 plex ideas, suggested to the mind by some present train 
 of thinking. And thus at last we are let into the mys- 
 tery hinted at in the beginning of this chapter, <viz» 
 how we may become acquainted with the thoughts of 
 another, when he makes use of words to which we have 
 as yet joined no ideas. The answer is obvious, from 
 what has been already said. If the terms denote simple 
 perceptions, he must refer us to those objects of nature, 
 whence the perceptions themselves are to be obtained ; 
 bat if they stand for complex ideas, their meaning may 
 be explained by a definition. As for the names of sim- 
 ple ideas, I shall here dismiss them ; it being sufficient 
 to take notice, that our knowledge this way can be ex- 
 tended only by experience and observation. But the 
 theory of definitions making a material part of logic, 
 and being indeed of great importance towards the im- 
 provement of human knowledge, it will be necessary 
 to lay it a little more open to the view of the reader. 
 
 Sec. VIII;... The Composition and Resolution of our 
 Complex Ideas* 
 
 Complex ideas are, as h?s been already said, no other 
 than simple ideas put together in various forms. But 
 then it is to be observed, that in making these collec- 
 tions, the mind is not always tied down to the immedi- 
 ate view of the simple perceptions out of which they are 
 framed. For if we suppose the understanding already 
 "furnished with a considerable stock of compound no- 
 tions, these again may be made the constituent parts of 
 others still more compounded, insomuch that the new 
 idea thence arising may be termed a combination of 
 complex conceptions. Thijs the idea annexed to the 
 word animal, includes many perceptions under it, as 
 life, sense, spontaneous motion, &c. In the like man- 
 ner by the term rational, we denote a variety of simple 
 
68 DUNCAN'S ELEMENTS 
 
 ideas. If now combining these two conceptions toge- 
 ther, we form the still more complex notion of a ration- 
 al animal; the idea thus got is truly a collection of 
 compound notices. In a word, the same thing happens 
 here as in numbers, which we may consider not only 
 as various collections of units, these being indeed their 
 original and constituent parts; but also as sometimes 
 composed of other lesser numbers, which, all put toge- 
 ther, make up the respective sums. Now in tracing 
 any very large number, when, for the ease of the mind, 
 we consider it at first as composed of various others still 
 less — if we next take, these less parts, to pieces, and 
 pursue them continually, until we arrive at the units 
 out of which they are composed ; we thereby totally 
 unravel the collection, and being able to push our re- 
 searches no farther, rest satisfied in the view thus offered 
 to the understanding. Just so it is in the examination 
 of our complex ideas. For when any very compounded 
 notion comes under the inspection of the mind, in or- 
 der to be traced to its first principles — we begin with 
 resolving it into other ideas less complicate'd; and taking 
 these again to pieces, one by one, still go on with the 
 search, until we have broken the whole into our first 
 and simple perceptions, beyond which the pursuit can- 
 not possibly be carried. And this is the reason why I 
 have all along called our simple ideas the foundation 
 and groundwork of human knowledge ; because, in 
 unravelling the conceptions of the mind, we find our- 
 selves at length bounded by these ideas, which are in- 
 deed the last resort of the understanding. 
 
 Sec. IX....77ze Names of Simple Ideas-may be consider- 
 ed as the Elementary Parts Gf Language. 
 
 From what has been said,it will be easy to conceive 
 how, in defining a term, standing for any very complex 
 idea, other terms may be introduced, that also denote 
 compound ideas, though of an inferior class. For the 
 first idea being resolvable into others less complicated ; 
 the definition, which enumerates these component ideas, 
 must consist of the names by which they are expressed. 
 And if it so happen, that the ideas of this second class 
 
OF LOGIC. 65 
 
 are also unknown, their terms, too, ought to be still far* 
 ther defined. In this manner may a series of definitions 
 be carried on, until we arrive at the names of simple 
 ideas, which not being definable, the analysis must ne- 
 cessarily cease. And thus we see, that as our simple 
 . ideas are the materials and foundation of knowledge, so 
 the names of simple ideas may be considered as the ele- 
 mentary parts of language, beyond which we cannot 
 trace the meaning and signification of words. When 
 we come to them, we suppose the ideas they stand for 
 already known ; or, if they are riot, experience alone 
 must^be consulted', and not definitions or explications. 
 And here it is well worth our notice, that as the names 
 of these our original conceptions, constitute the prima- 
 tive and fnndamental articles of speech, upon which 
 the whole superstructure of human language is built, 
 so they are, of all others, the least doubtful and uncer- 
 tain in their signification. Because, standing each for 
 one simple perception, not precariously excited in the 
 mind, but the effect of certain powers in things, fitted 
 to produce that sensation in us; there is no danger of 
 error or mistake. He that once knows sweetness to be 
 the name of the taste received from sugar, whiteness 
 of the colour in snow or milk, and heat of the sensation 
 produced by approaching the fire, will not be apt to 
 misapply those words, or annex them to perceptions of 
 a different kind. And as the names of complex ideas 
 may all be resolved into these primitive terms, it is ap- 
 parent, that we are sufficiently provided with the means 
 of communicating our thoughts one to another ; and 
 that the mistakes so frequently complained of on this 
 head, are wholly owing to ourselves, in not sufficiently 
 defining the terms we use, or perhaps not connecting 
 them with clear and determinate ideas. 
 
70 DUNCAN'S ELEMENTS 
 
 Cfcap. VI. 
 
 OF DEFINITION, AND ITS SEVERAL 
 KINDS. 
 
 Sec, I*,.. The Variety of Definitions proceeds from the 
 various Application of Words* 
 
 HAVING laid these foundations, shown what 
 words are, and what are not definable, and taught 
 . the manner of resolving our notions, as well as lan- 
 guage itself, into its first and original principles ; we 
 now proceed to explain a little more particularly the 
 nature of a definition, and the several kinds made use 
 of, according to the different views, men have in com- 
 municating their thoughts one to another. Definitions 
 are intended to make known the meaning of words 
 standing for complex ideas ; and were we always care- 
 ful to form those ideas exactly in our minds, and copy 
 our definitions from that appearance, much of the con- 
 fu ion and obscurity complained of in languages might 
 be prevented. But, unhappily for us, we are by no 
 means steady in the application of names, referring 
 them sometimes to one thing, sometimes to another ; 
 ■■which often creates great uncertainty in their signifi- 
 cation, and obljges us to give a different turn to our de- 
 viations, according to the different reference of the 
 terms defined. In order, therefore, to render this 
 whole matter as clear and obvious as possible, we shall 
 first consider to what it is that names, in the use of 
 language, are most commonly applied ; and then from 
 the variety of this application, endeavour to account 
 for the several methods of defining, mentioned in the 
 writings of logicians. 
 
 Sec. 1L ...Words have a threefold Reference ; to our 
 own Ideas, those of others, and the real being vf things. 
 Words then have manifestly a threefold reference. 
 First, and more immediately, they denote the ideas in 
 the mind of him who uses them; and this is their true 
 and proper signification. When a man speaks, it is 
 
OF LOGIC. 71 
 
 that he may be understood ; and the words he em- 
 ploys to convey his thoughts, are such as hy use he has 
 learned to connect with the ideas then present to his 
 mind. But because those with whom we converse, arc 
 also supposed-to know the meaning of the terms we 
 use, hence, secondly, we consider our words as signs, 
 likewise, of the ideas in their n.inds ; and this is the 
 foundation of what is called propriety in language, 
 when men take care to afrixsuch notions to their words, 
 as are commonly applied to them by those of most un- 
 derstanding in l;he country where they live. The third 
 and last reference of woi;ds is to things themselves. 
 For many of our ideas are taken from the several ob- 
 jects of nature, wherewith we arc surrounded ; and. 
 being considered as copies of things really existing, 
 the words, by which they are expressed, are often trans- 
 ferred frcm the ideas themselves, to signify those ob- 
 jects which they are supposed to represent. Thus the 
 word, sun, not only denotes the idea excited in the 
 1 by that sound, but is also frequently made to 
 stand for the luminous body itself, which inhabits the 
 centre of this our planetary system. Now, according 
 this threefold application -of names, their- definitions, 
 and the manner of explaining them, must be various ; 
 for it is one thing to unfold the ideas in a man's 
 own mind, another to describe them, as they are sup- 
 posed to make their appearance in the minds of others ; 
 and lastly, it is something still different, to draw 
 images or pictures, that shall carry in them a conform- 
 ity to the being and reality of things. But we shall 
 treat of each in order. 
 
 Sec. III,.*. Definitions of the Name teach only the Con- 
 nexion of our Words and Ideas, and are therefore 
 arbitrary. 
 
 First, then, when we consider words, as signs of the 
 ideas in the mind of him who uses them ; a definition 
 is nothing else, but such an explication of the meaning 
 of any- term, as that the complex idea annexed to it by 
 the speaker, may be excited in the understanding of 
 him with whom he converses, And this is plainly uq 
 
72 DUNCAN'S ELEMENTS 
 
 Hi ore than teaching the connexion, of our words and 
 ideas, that others may understand the sense of our ex- 
 pressions, and know distinctly what notions we affix to 
 the terms we use. When we say, for instance, that 
 by the word square we mean a. figure bounded by four 
 equal sides, joined together at right angles ; what is 
 this but a declaration, that the - idea of a quadrilateral, 
 equilateral, rectangular figure, is that which in dis- 
 course or writing we connect with the term square ? 
 This is that kind of definition, which logicians call 
 the definition of the name ; because it discovers the 
 meaning of the words or names we make use of, by 
 showing the ideas for which they stand. Now, as sounds 
 are of themselves indifferent to signify any ideas, 
 hence it is plain, that the definitions of names are arbi- 
 trary, every man having a liberty to affix what notions 
 he pleases to his words. But the convenience of com- 
 munication making it necessary for men speaking the 
 same language to agree as nearly as possible in the sig- 
 nification of sounds, a conformity has accordingly been 
 studied. Nevertheless, we find that differences will 
 from time to time creep in, which must create great 
 confusion in men's discourses and reasonings, if they 
 are not careful to define their terms, that their signifi- 
 cation may be kept fixed and steady, and lie always 
 open to the view of the mind* The writings of the 
 mathematicians are a clear proof, how much the ad- 
 vancement of human knowledge depends upon a right 
 use of definitions. For as by means of them they 
 every where preserve the same determined significa- 
 tion to their words, hence there is little dispute as to 
 the meaning of their expressions, almost all men un- 
 derstanding them in the same sense. And thus it hap- 
 pens, that such as apply their thoughts this way, hav- 
 ing perfectly the same views of things, readily compre- 
 hend the discoveries already made, and are thereby ena- 
 bled with joint labour, and an exact conformity of no- 
 tions, 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 progress of science must be greatly furthered, and 
 
OF LOGIC. 73 
 
 all those verbal disputes, that now so much interrupt 
 the course of our improvement, might be prevented. 
 
 Sec. IV. ...Definitions of the Name not always true 
 and real Definitions ; 
 
 This then ought to be our first care, when we enter 
 upon a design of illustrating any particular branch of 
 study; to ascertain our ideas, and mark the names by 
 which they are expressed. And although definitions of 
 words are indeed arbitrary, (for a man may affix what 
 ideas he pleases to his terms, nor can any one contest 
 this liberty with him,) yet it will be proper to conform, 
 as near as possible, to common acceptation, that there- 
 by our thoughts may find a more easy and ready en- 
 trance into the minds of others. If it should now be 
 asked, what are the rules of a good definition; I an- 
 swer, that as in definitions of the name, we aim at no 
 more than teaching the connexion 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 serve the purpose of a definition. Now the ideas 
 we join with our words are of two kinds: either such 
 as we have reason to believe are already in the minds of 
 others, though perhaps they know not the names by 
 which they are called ; or such as, being new and of our 
 own formation, can be no otherwise made known than 
 by a description. In the first case, there is no necessi- 
 ty for laying open the idea itself, because being already 
 known, any contrivance to remind us of it is sufficient. 
 When we say for instance, that a clt ck is an instrument^ 
 by which we measure the hours of the day ; it is plain, 
 that the idea answering to the word clock, is not here 
 unfolded ; but we being before-hand supposed to have 
 an idea of this instrument, are only taught by what 
 name it is called. Now in this sense, the names of 
 even simple ideas may be defined. For, by saying that 
 ivhite is the colour we observe in snow or milk, heat 
 the sensation produced by approaching the fire, we suf- 
 ficiently make known what ideas we connect with the 
 terms, white and heat, which is the true purpose of a 
 definition of the name. Hence it appears, that many 
 
74 DUNCAN'S ELEMENTS 
 
 of those explanations of words, which logicians call de- 
 finitions of the name, are not definitions in a true and 
 proper sense, that is, such descriptions of ideas, as 
 •would serve to excite them in the mind of another, even 
 supposing him before wholly unacquainted with them, 
 but merely contrivances to remind us of known ideas, 
 and teach us the names by which they are called. 
 Sec, Y,,,,But only when they Coincide with the Defi- 
 nition of the Thing, 
 But where the ideas we join with our words, are new 
 and of our own formation, there they are to be laid open 
 by a description, because, being supposed unknown to 
 others, we must first raise them in their minds, before 
 they can learn to connect 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 case we proceed by unfolding the 
 idea itself for which the term defined stands. And 
 indeed this alone is what constitutes a definition, in 
 the true and proper sense of the word, as will appear 
 more fully afterwards, when we come to consider the 
 terms we use, as referred to the real objects of nature. 
 We shall therefore postpone this consideration of the 
 definition of the name, till we come to treat of the de- 
 finition of the thing, when it will more naturally fall 
 in our way. It may not, however, be amiss to observe, 
 that when we say the definitions of the name are arbi- 
 trary, we mean not that the descriptions of ideas are 
 so too. For every idea having a peculiar appearance 
 of its own, by which it is distinguished from all others, 
 nothing is more evident, than that the description must 
 be such as to exhibit that precise conception. But 
 then the connexion of any idea, with the name by 
 which it is expressed, being, as we have said, wholly 
 arbitrary, the considering the description of that idea 
 as the definition of that particular name rqust be so too. 
 So that although definitions, considered as descriptions 
 of our ideas, are steady and invariable, yet the appli- 
 cation of them to particular sounds, (which is ail that 
 we understand by the definition of the name) is wholly 
 a work Qf our own free choice. 
 
OF LOGIC. YS 
 
 Sec. VI.... Definition of IVords according to the com* 
 mon use of Language nut Arbitrary. 
 
 But secondly, besides considering words as the signs 
 of our own ideas, we arc also very apt, on many occa- 
 sions, to refer them to the ideas in the minds of other 
 men. Now, to define a term, in this view, is to inves- 
 tigate its meaning or acceptation, according to the 
 common use of speech. Here then it is plain, that de- 
 finitions are not arbitrary. For although in regarding 
 words as the marks of our own ideas,, we may give them 
 what meaning we please; yet when we consider them 
 in reference to the thoughts of others, they have a fix- 
 ed and steady signification ; namely, that which custom 
 and the propriety of languagAas assigned them. The 
 words, ability and genius, may, by any man, be made? 
 to stand for one and the same idea in his own mind, 
 and if he takes care to advertise us of this, he is at IU 
 berty to use them promiscuously. But if the common 
 course of language hath confined the word genius to 
 express the natural strength and talents of the mind, 
 and the word ability to denote those which are acquir- 
 ed, whoever pretends to explain the proper acceptation 
 of these terms, is bound to take notice of this differ-* 
 ence. As propriety of speech makes our language in- 
 telligible, and gives our thoughts a ready entrance into 
 the minds of others, it well deserves our application and 
 care. The best way to acquire it is from the writ- 
 ings and discourses of those who seem to have had the 
 clearest notions, and to have applied their terms with 
 the exactest choice and fitness. 
 
 Sec. V "II.. ..Definitions of the Thing refer to the real 
 Objects of Nature. 
 We come now to the third and last species of defini- 
 tion, that namely, which considers words as referred to 
 things themselves. And here it is plain, we are not at 
 liberty to feign and fashion our explications at pleasure, 
 but being tied down to the real objects of nature must 
 study a conformity to things themselves. When we 
 define, for instance, the sun, considered as that being 
 who possesses the centre of our system, and diffuses 
 
76 DUNCAN'S ELEMENTS 
 
 heat and light to the planets around him ; it is not 
 enough that we give an -account of the idea, answer- 
 ing to that word in our minds. We must further 
 take care, that the idea itself carries in it a real-con- 
 formity to the object it is supposed to represent. And 
 hence it is, that all definitions of this kind, when just- 
 ly made, are in- reality pictures or representations, ta- 
 ken from the being and existence of things. For they - 
 are intended to express their nature and properties so 
 as to distinguish them from all others, and exhibit 
 them clearly to the view of the mind. *Tis for this 
 reason- that logicians call them definitions of things,, 
 because they are supposed to refer, not so much to the 
 ideas in the understanding, as to the things themselves 
 represented by those ideas. 
 
 Sec. VIII... .Ground of the distinction between the de- 
 finition of the Name and of the Thing. 
 
 And this also lets us into the ground of that distinc- 
 tion so universally received between definitions of the 
 name and of, the thing. The first are arbitrary, and 
 not liable to debate or contradiction. The second are 
 propositions, capable of proof and illustration, and 
 which may therefore be contested. The reason is ob- 
 vious. Definitions of the name serve only to mark what 
 ideas we connect with our words. And as sounds are 
 of themselves indifferent to signify any ideas, we are en- 
 tirely at liberty to affix to them what notions we please. 
 But it is otherwise in the definition of the thing. For 
 here our words, serving to denote particular beings in 
 nature, cannot be' the signs of any ideas at pleasure, but 
 of such only as carry in them a conformity to the sever- 
 al objects to which the words refer. A man may use 
 the term, square, to express that idea, which others de- 
 note by the word, triangle, and define it accordingly* 
 In this case, indeed, he recedes from the common forms 
 of speech, but his definition cannot be charged with 
 falsehood. Fie tells us that by a square he means a 
 three-sided figure ; and who can dispute the truth of 
 this, if he really all along uses the word in that sense ? 
 I would only observe, that by changing thus the mea^ 
 
OF LOGIC. 77 
 
 ing of words, we change not things themselves, or their 
 relations and habitudes one towards another. These 
 are at all times the same and invariable, nor have any de- 
 pendence 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 case, the idea 
 to which these properties belong, is the same, the pro- 
 positions only expressing our judgments, and not our 
 judgments themselves, suffer a seeming variation. 
 
 Sec. IX. *;A previous connexion between Names and 
 Things, cuts off all Arbitrary Explications. 
 But where words are made to denote particular ob- 
 jects, previous to any definitions given, there arbitrary- 
 explications cannot have place. For in this case, we 
 are not put upon explaining what ideas we connect with 
 our words, but a connexion being already supposed be- 
 tween the name and the thing signified, our "business 
 is to unfold that idea by which the object itself is most 
 clearly and distinctly represented. Thus the word gold 
 denotes that metal which is of highest value among men, 
 and goes farthest in the way of commerce. This con- 
 nexion being once settled, we are no longer left to ar- 
 bitrary definitions, but must describe it by such proper- 
 ties as are really to be fou.nd in it, and will best serve to 
 distinguish it when it comes in our way ; as by saying it 
 is a substance yellow, very heavy, malleable, fusible, Sec. 
 
 Sec. X...jr/jv Mathematical Definit ions have been ac- 
 counted mere Dejinitions of the Name ; 
 From what has been said, it appears, that in the lan- 
 guage of logicians, definitions of the thing respect only 
 substances and beings that have a real existence m na- 
 ture, serving to describe them by their properties and 
 attributes. And this, I doubt not, is the reason, that 
 the definitions of the mathematicians are not consider*- 
 ed as definitions of the thing, but of the name ; because 
 the ideas therein described, are the mere creatures of 
 the understanding, and not supposed to be copied from 
 patterns existing without us. A circle, a triangle, a 
 square, &c. such as mathematicians conceive them, are 
 no where to be found in nature, that we know of* 
 
73 DUNCAN'S ELEMENTS 
 
 Hence it might justly be accounted absurd, to call our 
 definitions of these, definitions of the thing, when they 
 serve not to describe" any real objects of nature, but 
 merely to unfold the conceptions of the mind. And 
 yet if we look into the matter narrowly, we shall find, 
 that the rules followed in these definitions are precisely 
 the same with those which logicians have laid down 
 for the definition of the thing. All the several species 
 of figures are described by their properties, some of 
 • which are common to different ranks, others peculiar 
 to the tribe defined. The common properties consti- 
 tute what logicians call the genus, and those that are 
 peculiar, the difference. Now the genus and differ- 
 ence make up the logical definition of the thing, as will 
 be more clearly understood from what follows* 
 
 Sec. XI. When yet they coincide with the logical defi* 
 nition of the thing, and therefor* ought not to be ac- 
 counted arbitrary* 
 
 I am therefore, apt to think, that mathematical 
 definitions, as they are of the same general with the 
 definitions of substances, and subject to the same rules, 
 have been improperly considered as mere definitions of 
 the name, m which we are left wholly to arbitrary 
 explications. For however we may change the name 
 of one figure for another in discourse or writing, using 
 the term square to denote a triangle, or the word tri- 
 angle to express a square, it is certain the ideas them- 
 selves are invariable, and no less capable of being 
 distinguished by their properties, than the several spe- 
 cies of substances. Thus if we suppose the word 
 square to denote that species of figures, whose sides 
 severally subtend quadrants of a circumscribed circle, 
 we shall find ourselves equally shut out from arbitrary 
 explications, as in the definition of the names of sub- 
 stances. For as this happens in no figures but those 
 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 precise idea here mentioned, and no other, to the 
 mind, And thus it appears, that the common drvisicn 
 
OF LOGIC, n 
 
 of definitions, into those of the name and thing, is not 
 sufficiently calculated to give us right apprehensions, 
 as to what is and what is not arbitrary in the explica- 
 tion of words. It may not, therefore, be improper, if 
 we here endeavour to clear up this matter a little, and 
 free it from those obscurities in which it has hitherto 
 been involved. To this end we shall premise the foL 
 lowing observations. 
 
 Sec. XII... . Definitions, property speaking, never regard 
 Things, but merely our own Ideas. 
 
 1. First, that whatever logicians may pretend about 
 the definition of the thing, it is yet certain, that none 
 of our definitions, when pursued to their source, regard 
 immediately things themselves, but merely the ideas 
 in our own minds. This, I doubt not, will appear a 
 paradox to many, who will be apt to enquire, whether 
 the definition of gold, be not taken from that metal, 
 independent of the various conceptions of men about 
 it. To this I answer, that indeed in framing our idea 
 of gold, we regard chiefly the thing itself, uniting in 
 our conception such properties as are most conspicuous, 
 and serve best to distinguish it from other metals, to 
 which it may bear any resemblance. But as it is by this 
 idea alone that gold is known to us, so in describing it 
 to others, we aim at nothing more than to transfer the 
 same conception into their minds. Now this can no 
 otherwise be done, but by enumerating the several pro- 
 perties of which our own complex notion is formed. 
 And indeed it were in the highest degree absurd to ima- 
 gine, that men in explaining things to others, should 
 make use of any marks or characters but those by which 
 they are known to themselves. Hence it comes to pass, 
 that all our definitions are in fact nothing else but tran- 
 scripts of the ideas in our minds. Where these are im- 
 perfect, the definitions must be so too ; where they are 
 just and adequate, the copies taken from them, if drawn 
 out with accuracy and care, cannot fail to exhibit the 
 ©bject described. And this will very well serve to ac- 
 count for that great diversity of definitions we often 
 inect with, even of one and the same object. Because 
 
80 DUNCAN'S ELEMENTS 
 
 men, in consequence of their different pursuits and ap- 
 plications, falling often into different views of things, 
 must needs vary no less in their definitions, than in the 
 ideas themselves from which these definitions are copi- 
 ed. He, whose observation goes no farther than the 
 more obvieus qualities of gold, will content himself 
 with describing it by its colour, weight, and perhaps 
 malleability and fusibility. On the other hand, a 
 goldsmith, having enquired farther into the nature 
 ef that metal, and finding several other properties that 
 equally belongs to it, will be apt to take these also into 
 his complex idea, and accordingly introduce them in a 
 definition. Hence his description will add to the form- 
 er, fixedness, and solubility in aqua regia, Sec. And so 
 in proportion, as men's various pursuits lead them into 
 a more accurate examination of things, their explica- 
 tions will take a different turn, suitable to the ideas 
 they have framed within themselves. 
 Sec. XIII..... Distinction between the Definition of the 
 name and thing useless, and to be rejected. 
 2. This then being evident, that our definitions re- 
 spect not things themselves, but the ideas in our own 
 minds ; I would in the next place observe, that the dis- 
 tinction of them into those of the name and thing, is 
 altogether useless, and tends rather to mislead us than 
 give right apprehensions of the subject in hand. For 
 thus men are apt to fancy, that many of their defini- 
 tions are expressive of the real essence of things, where- 
 as they are in truth no more than transcripts of their 
 own ideas. And'as it sometimes falls out, that these 
 ideas; are not collected with sufficient care, from the 
 objects they represent ; we find, by experience, that a 
 mistaken idea never fails to occasion a mistake also in 
 the definition. But this could not happen, were our 
 definitions copied from things themselves : because their 
 essences being immutable and always the same, the defi- 
 nition would in thi? case sejve to correct the idea, and 
 might be considered 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 signify the 
 objects which these ideas represent j as whea we talk 
 
OF LOGIC, 81 
 
 of the sun, the earth, men, and other animals. But 
 then let it be observed, that as these objects are only 
 known to us, by the ideas of them in our minds ; so, in 
 describing them to others, all we aim at is, distinctly, 
 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 unfolding of the 
 idea, by which that thing is represented to the under- 
 standing. But now in mathematical definitions, and in- 
 deed all others whatsoever, this also is our whole aim and 
 intent, to exhibit and lay open those ideas, of which 
 the words we use are the signs. And thus it happens, 
 that in innumerable instances, what logicians call the 
 definition of the name, is yet found to coincide with 
 and proceed by the very same rules, as the definition of 
 the thing; which clearly demonstrates the necessity of 
 banishing this frivolous distinction, and establishing 
 some precise and determinate notion, expressive of the 
 true nature of a definition, and comprehending it in its 
 full extent 
 
 Sec. XIV Definitions in all cases descriptions of 
 
 our Ideas. 
 
 Nor will this appear so difficult a task, if we call to 
 mind, that words are in all cases the signs of our ideas* 
 and no otherwise signify things, than as they stand 
 for those ideas by which things are represented to the 
 understanding. By defining our words, therefore, we 
 can mean no more, than the laying open to the view 
 of others, the ideas of which these words are the signs» 
 For thus it is, that the meaning of our expressions 
 comes to be known, and that we find ourselves capable 
 of tran?£erring our thoughts and conceptions into the 
 minds of those with whom we converse. Where words 
 are referred to things themselves, there we explain the 
 ideas by which these things are represented ; where 
 they denote conceptions framed by the mind, there we 
 lay open these conceptions, and endeavour to exhibit 
 them according to their real appearance within our 
 own breasts. But in both cases, it is our own ideas, 
 it is the perceptions of our own minds, either as taken 
 
B2 DUNCAN'S ELEMENTS 
 
 from things without, or framed by the understanding 
 itself, that we explicate an4 unfold. 
 
 Sec. XV Not arbitrary , as being confined to ths 
 
 Representation of certain determinate Notions* 
 And thus we have at length settled the true and ge- 
 nuine notion of a definition, comprehending all its va- 
 rieties, from whatever science taken, or to whatever 
 object extended. For from what we have said, it evi- 
 dently follows, that a definition is the unfolding cf 
 some conception of the mind, answering to the word cr 
 term made use of as the sign of it. Now, as in exhi- 
 biting any idea to another, it is necessary that the de- 
 scription be such as may excite that precise idea in 
 his mind ; hence it is plain, that definitions, proper- 
 ly speaking, are not arbitrary, but confined to the re- 
 presenting of certain determinate settled notions, such, 
 namely, as are annexed by the speaker or writer to 
 the words he uses. As, nevertheless, it is universally- 
 allowed, that the signification of words is perfectly vo- 
 luntary, and not the effect of any natural and necessary 
 connexion between them and the ideas for which ihey 
 stand, some may perhaps wonder why definitions are 
 not so too. In order, therefore, to unravel this diffi- 
 culty, and show distinctly what is, and what is not ar- 
 bitrary in speech w r e must carefully distinguish be- 
 tween the connexion of our words and ideas, and the 
 unfolding of the ideas themselves. 
 
 Sec. XVI The Connexion between Words andldeas f 
 
 a perfectly voluntary Establishment* 
 First, as to the connexion of our words and ideas, 
 this, it is plain, is a purely arbitrary institution. When 
 for instance, we have in our minds, the icea of any 
 particular species of metals, the calling it by the name 
 goldy is an effect of the voluntary choice of men speak- 
 ing t,he same language, and not of any peculiar apt- 
 ness in that sound ,to express that idea. Other nations, 
 we find make use of different sounds, and .with the 
 same effect. Thus aurum denotes that idea in Latin, 
 and or in French. And even the word gold itself, 
 would have as well served to express the idea of that 
 
OF LOGIC. 83 
 
 metal which we call silver, had custom in the begin- 
 ning so established it. 
 
 Sec. XVII..... TAj? Descriptions of Ideas not so, but 
 bounded to the Representation of that precise xip- 
 pearance by which they are distinguished among 
 themselves. 
 
 But although we are thus entirely at liberty, in 
 connecting any idea with any sound, yet it is quite 
 otherwise in unfolding the ideas themselves. For eve- 
 ry idea, having a precise appearance of its own, by 
 •which it is distinguished from every other idea ; it is 
 manifest, that in laying it open to others, we must 
 study such a description, as shall exhibit that peculiar 
 appearance. When we have formed to ourselves the 
 idea of a figure bounded by four equal sides, joined to- 
 gether at right angles, we are at liberty to express that 
 idea by any sound, and may call it either a square or a 
 triangle. But which ever of these names we use, so 
 long as the idea is the same, the description, by which 
 we would signify it to another, must be so too. Let 
 it be called square or triangle, it is still a figure hav- 
 ing four equal sides, and all its angles right ones. 
 Hence we clearly see, what is, and what is not arbitary 
 in the use of words. The establishing any sound, as 
 the mark of some determinate idea in the mind, is the 
 effect of free choice, and a voluntary combination a- 
 mong men. And as different nations make use of 
 different sounds, to denote the same ideas, hence pro- 
 ceeds all that variety of languages which we meet with 
 in the world. But when a connexion between our 
 ideas and words is once settled, the unfolding of the 
 idea answering to any word, which properly consti- 
 tutes a definition, is by no means an arbitrary thing. 
 For here,_as I have already observed, we are bound to 
 exhibit that precise conception, which either the u%% 
 of language or our own particular choice, hath annex- 
 ed to the term we use. 
 
84 DUNCAN'S ELEMENTS 
 
 Sec. XVIII Causes of the Obscurity that has hither* 
 
 to perplexed the Iheory of Definitions, 
 
 And thus it appears, that definitions, considered as 
 descriptions of ideas in the mind, are steady and inva- 
 riable, being bounded to the representation of those 
 precise ideas. But then in the application of definitions 
 to particular names, we are altogether left to our own 
 free choice. Because as the connecting of any idea 
 with any sound, is a perfectly arbitrary institution ; 
 the applying the description of that idea, to that 
 sound, must be so 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 
 pleasure of him that uses it, in like manner may differ- 
 ent descriptions be applied to that term, suitable to 
 the ideas so connected. But this connection being set- 
 tled, and the term considered as the sign of some fixed 
 idea in the understanding, we are no longer left to ar^ 
 bitrary explications, but must study such a descript- 
 ion as corresponds with that precise idea. Now this 
 alone, according to what has been before laid down, 
 ought to be accounted a definition. What, I am apt 
 to think, has occasioned no small, confusion in this 
 matter is, that many explanations of words, where no 
 idea is unfolded, but merely the connexion between 
 some word and idea asserted, have yet been dignified 
 with the name of definitions. Thus, in -the instance 
 before given, when we say that a clock is an instru- 
 ment by which we measure time ; this is by some called 
 a definition. And yet it is plain, that vve are before*, 
 hand supposed to have an idea of this instrument, and 
 only taught that the word, clocks serves in common 
 language to denote that idea. By this rule all expli- 
 cations of words in our dictionaries will be definitions ; 
 nay, as was already observed, the names of even sim- 
 ple ideas may be thus defined. White, we may say, is 
 the colour we observe in snow or milk, heat the sen- 
 sation produced by approaching the fire, and so in in- 
 numerable other instances. But tiiese, and all others 
 
OF LOGIC. 35 
 
 of the like kind, are by no means definitions, exciting 
 new ideas in the understanding, but merely contri- 
 vances to remind us of known ideas, and teach their 
 connexion with the established names. It is, neverthe- 
 less, worth our notice, that what logicians call defi- 
 nitions of the name, extend properly no farther than 
 these explanations, serving to mark the connexion of 
 our ideas and words ; and are therefore justly account- 
 ed arbitrary, inasmuch as the connexions themselves 
 are altogether so. 
 
 Sec. XIX.... .Complex ideas alone capable of that kind 
 of description which goes by the name of a defnition* 
 
 But now in definitions properly so called, we first 
 consider the term we use, as the sign of some inward 
 conception, either annexed to it by custom, or our own 
 free choice ; and then the business of the definition is 
 to unfold and explicate that idea. As therefore the 
 whole art lies, in giving just and true copies of our 
 ideas ; a definition is then said to be perfect, when it 
 serves distinctly to excite the idea described in the 
 mind of another, even supposing him before wholly un* 
 acquainted with it. This point settled, let us next en- 
 quire into what those ideas are which are capable of 
 being thus unfolded. And in the first place, it is 
 evident, that all our simple ideas are necessarily ex- 
 cluded. We have seen already, that experience ahxne 
 is to be consulted here, insomuch, that if either the 
 objects, whence they are derived, come not in our way, 
 or the avenues appointed by nature for their reception 
 are wanting, no description is sufficient to convey them 
 into the mind. But where the understanding is alrea- 
 dy supplied with these original and primitive concep- 
 tions, as they maybe united together in an inficity of 
 different forms ; so may all their several combinations 
 be distinctly laid open by enumerating the simple ideas 
 concerned in the various collections, and tracing the 
 order and manner in which they are linked one to ano- 
 ther. Now these combinations of simple notices con- 
 stitute what we call our complex notions ; whence it is 
 evident that complex ideas, and those alone, admit of 
 
 H 
 
86 DUNCAN'S ELEMENTS 
 
 that kind of description, which goes by the name of a 
 definition. 
 
 Sec XX, When a complex idea may be said to be ful- 
 ly unfolded* 
 The business of definitions is now, I think, pretty- 
 plain. They are, as we have seen, pictures or repre- 
 sentations of our ideas ; and as these representations 
 are then only possible, when the ideas themselves are 
 complex ; it is obvious to remark, that definitions can- 
 not have place, but where we make use of terms, 
 standing for such complex ideas. But perhaps the rea- 
 der may still expect, that we should enter a little more 
 particularly into the nature of a definition, describe its 
 parts, and show by what rules it ought to proceed, in 
 order to the attainment of its proper end. To give, 
 therefore, what satisfaction we are able upon this point, 
 Yre must again call to mind, that the design of a defini- 
 tion is, se to unfold the idea answering to any term, as 
 that it may be clearly and distinctly transferred into 
 the mind of another. But now our complex ideas, 
 ■which alone arc capable of this kind of description, 
 being, as we have said, nothing more than diiferent 
 combinations of simple ideas ; we then know and com- 
 prehend them perfectly, when we know the several 
 simple ideas of which they consist, and can so put thern 
 together in our minds, as is necessary towards the 
 framing of that peculiar connexion, which gives every 
 idea its distinct and proper appearance. 
 
 Sec. XXI.... Two things required in a definition : tt 
 enumerate the ideas, and explain the manner of their 
 combination. 
 
 Two things are therefore required in every defini- 
 tion. First, that all the original ideas, out of which 
 the complex one is formed, be distinctly enumerated. 
 Secondly, that the order and manner of combining 
 them into one conception, be clearly explained. Where 
 a definition has these requisites, nothing is wanting to 
 its perfection ; because every one who reads it, and un- 
 derstands the terms, seeing at once what idea* he is 
 t» j6in together, and also in what manner, can at plea- 
 
OF LOGIC. , M 
 
 sure form in his own mind the complex conception 
 answering to the term defined. Let us, for instance, 
 suppose the word) square, to stand for that idea, by 
 which we represent to ourselves a figure, whose sides 
 subtend quadrants of a circumscribed circle; The parts 
 of this idea, are the sides bounding the figure. These 
 must be four in nftmber, and all equal among them- 
 selves, because they are each to subtend a fourth part 
 of the same circle. But besides these component 
 parts, we must also take notice of the manner of put- 
 ting them together, if we would exhibit the precis© 
 idea, for which the word square here stands. For four 
 equal right lines, any how joined, will not subtend 
 quadrants of a circumscribed circle. A figure with 
 this property, must have its sides standing also at 
 right angles. Taking in, therefore, this last conside- 
 ration, respecting the manner of combining the parts, 
 the idea is fully described, and the definition thereby 
 rendered complete* For a figure, bounded by four 
 equal sides, joined together at right angles, has the 
 property required ; and is, moreover, the only right* 
 lined figure to which that property belongs* 
 
 Sec. XXII.... How nve are to proceed, to arrive at just 
 and adequate definitions . 
 
 And now, I imagine, it will be obvious to every 
 one in what manner we ought to proceed, in order to 
 arrive at just and adequate definitions. First, we are 
 to take an exact view of the idea to be described, trace 
 it to its original principles, and mark the several sim- 
 ple preceptions that enter into the composition of it. 
 . Secondly, we are to consider the particular manner in 
 which these elementary ideas are combined, in order to 
 the forming of that precise conception, for which the 
 term we make use of stands. When this is done, and 
 the idea wholly unravelled, we have nothing more to 
 do, than fairly transcribe the appearance it makes to 
 our own minds. Such a description, by distinctly ex- 
 hibiting the order and number of our primitive con- 
 ceptions, cannot fail to excite, at the same time, in the 
 mind of every one that reads it, the complex idea r«- 
 
83 DUNCAN'S ELEMENTS 
 
 suiting from them ; and therefore attains the true and 
 proper end of a definition. 
 
 e&ap. vii. 
 
 OF THE COMPOSITION AND RESOLUTION 
 
 OF OUR IDEAS, AND THE RULES OF 
 
 DEFINITION THENCE ARISING. 
 
 Sec. L. ..In compounding our Ideas, we proceed by sue* 
 
 » cessive gradation. 
 
 THE rule, laid down in the foregoing chapter is, 
 general, extending to all possible cases ; and js, 
 indeed, that to which alone we can have recourse, 
 ■where any doubt or difficulty arises. It is not, how- 
 ever, necessary, that we should practise it in every par- 
 ticular instance. Many of our ideas are extremely 
 complicated ; insomuch that to enumerate all the sim- 
 ple preceptions out of which they are formed, would be 
 a very troublesome and tedious work. For this rea- 
 son, logicians have established certain compendious 
 rules of defining, of which it may not be amiss here to 
 give some account. But in order to the better under- 
 standing of what follows, it will be necessary to ob- 
 serve, that there is a certain gradation in the com- 
 position of our ideas. The mind of man is very li- 
 mited in its views, and cannot take in a great number 
 . of objects at once. We are, therefore, fain to proceed 
 by steps, and make our first advances subservient to 
 those which follow. Thus in forming our complex 
 notions, we begin at first with but a few simple ideas, • 
 such as we can manage with ease, and unite them to- 
 gether into one conception. When we are provided 
 •with a sufficient stock of these, and have, by habit 
 and use, rendered them familiar to our minds, they be- 
 come the component parts of other ideas, still more 
 complicated, and form what we may call a second or- 
 der of compound notions. This process, as is evident^ 
 may be continued to any degree ©f composition wt 
 
OF LOGIC. 89 
 
 please, mounting from one stage to another, and en- 
 larging the number of combinations. 
 Sec. 11... .Hence ideas of this class best comprehended) 
 
 when vje advance gradually through all the several 
 
 orders. 
 
 But now in a series of this kind, whoever would 
 acquaint himself perfectly with the last and hightst 
 order of ideas, finds it much the most expeditious me- 
 thod, to proceed gradually through all the intermedi- 
 ate steps. For was he to take a»y very compounded 
 idea to pieces, and without regard to t]*e several 
 classes of simple perceptions, that have already been 
 formed into distinct combinations, break in at once 
 into its original principles, the number would be so 
 great, as perfectly to confound the imagination, and 
 ^overcome the utmost reach and capacity of the mind. 
 When we see a prodigious multitude of men, jumbled 
 together in crowds, without order, or any regular po- 
 sition, we find it impossible to arrive at an exact know- 
 ledge of their number. But if they are formed into 
 separate battalions, and so stationed as to fall within 
 the leisurely survey of the eye ;by viewing them succes- 
 sively, and in order we come to an easy and certain de- 
 termination. It is the same in our complex ideas. 
 "When the original preemptions, out of which they are 
 framed, are very numerous, it is not enough that we 
 take a view of them in loose and scattered bodies. We 
 must form them into distinct classes, and unite these 
 classes in a just and orderly manner,' before we can ar- 
 rive at a true knowledge of the compound notices re- 
 sulting from them. 
 
 Sec. 111.,, .Our Definitions ought to keep pace with our 
 Ideas, atfd observe alike gradation. 
 
 This gradual progress of the mind to its compound 
 notions, through a variety of intermediate steps, plain- 
 ly points out the manner of conducting the definitions 
 by which these notions are conveyed into the minds of 
 others. For as the series begins with simple >and easjr 
 combinations, and advances through a succession of 
 different orders, rising one above another in the de- 
 gree of composition j it is evident, that in a train of de« 
 H 2 
 
$0 DUNCAN'S ELEMENTS 
 
 tnitiohs expressing these ideas, a like gradation is to 
 be observed. Thus the complex ideas of the lowest or- 
 der, can no otherwise be described, than by enumerat- 
 ing the simple ideas out of which they are made, and 
 explaining the manner of their union. But then in 
 the second, or any succeeding order, as they are form- 
 ed out* of those gradual combinations, that, constitute 
 the inferior classes, it is not necessary in describing 
 them, to mention one by one, all the simple ideas of 
 which they consist. They may be more distinctly and 
 briefly unfolded, by enumerating the compound ideas of 
 a lower order from whose union they result, and which 
 are all supposed to be already known, in consequence of 
 previous definitions. Here then it is, that the logical 
 method of defining takes place ; which that we may the 
 better understand, I shall explain somewhat more par- 
 ticularly, the several steps and gradations of the mind, 
 in compounding its ideas, and thence deduce that pecu- 
 liar form of a definition, which logicians have thought 
 jit to establish. 
 
 See. IV.... The steps by which the Mind proceeds from 
 Particular to General Ideas. 
 All the ideas we receive, from the several objects of 
 mature that surround us, represent distinct individuals. 
 These individuals, when compared together, are found 
 in certain particulars to resemble. Hence, by collect- 
 ing the resembling particulars into one conception, we 
 forra the notion of a species. And here let it be ob- 
 served, that this last idea is less complicated than that 
 ky which we represent any of the particular objects 
 contained under it. For the idea of the species ex- 
 cludes the peculiarities of the several individuals, and 
 retains only such properties as are common to them all. 
 Again, by comparing several species together, and ob- 
 serving their resemblance, we form the idea of the 
 genus ; where, in the same manner as before, the com- 
 position is lessened, because we leave out what is pecu- 
 liar to the several species compared, and retain only the 
 particulars wherein they agree. It is easy to conceive 
 the mind, proceeding thus from one step to another, 
 aud advancing through its several classes of general no- 
 
OF LOGIC. »1 
 
 S 
 
 tions, until at last it comes to the highest genus of 
 all, denoted by the word beings where the bare idea of 
 existence is only concerned. 
 
 Sec. V....T/j<? conduct of the Mind in compounding its 
 Ideas, as it advances through the different orders of 
 preception. 
 
 In this procedure, we see the mind unravelling a 
 complex idea, and tracing it in the ascending scale, from 
 greater to less degrees of composition, until it termi- 
 nates in one simple preception. If now we take the 
 series the contrary way, and beginning with the last 
 or highest genus, carry our view downwards, through 
 all the inferior genera and species, quite to the indivi- 
 duals ; we shall thereby arrive at a distinct apprehen- 
 sion of the conduct of the understanding in compound- 
 ing its ideas. For in the several classes of our pre- 
 ceptions,'the highest in the scale is, for the most part, 
 made up ©f but a few simple ideas, suck as the mind 
 can take in and survey with ease. This first general 
 notion, when branched out into the different subdivi- 
 sions contained under it, has in every one of them 
 something peculiar, by which they are distinguished 
 among themselves ; insomuch that in descending from 
 the genus to the species, we always superadd some 
 new idea, and thereby increase the degree of composi- 
 tion. Thus the idea denoted by the word figure, is 
 of a very general nature, and composed of but few sim- 
 ple preceptions, as implying no more than space every 
 where bounded. But if we descend farther, and con- 
 sider the boundaries of this space, as, that they may 
 be either lines or surfaces, we fall into the several spe« 
 cies of figure. For where the space is bounded by one 
 or more surfaces, we give it in the name of a solid fgure $ 
 but where the boundaries are lines, it is called a plain 
 figure. 
 
 Sec. VI... .The Idea of the Species formed by superadd 
 
 ding the specific Difference to the Genus* 
 
 In this view of things, it .is evident, that the spe* 
 
 cies formed by superadding a new idea to the genus* 
 
 Here, for instance, the genus is circumscribed space. 
 
92 DUNCAN'S ELEMENTS 
 
 If now to this we superadd the idea of a circumscrip- 
 tion by line, we frame the notion of that species of 
 figures which are called plain ; but if we conceive the 
 circumscription to be by surfaces, we have the spe- 
 cies of solid figures* This superadded idea is called 
 the specific difference, not only as it serves to divide 
 the species from the genus, but because, being differ- 
 ent in all the several subdivisions, we thereby also dis- 
 tinguish the species one from another. And as it is 
 likewise that conception, which*, by being joined to 
 the general idea, completes the notion of the species ; 
 hence it is plain, that the genus and specific difference 
 are to be considered as the proper and constituent parts 
 of the species* If we trace the progress of the mind 
 still farther, and observe it advancing through the in- 
 ferior species, we shall find its manner of proceeding 
 to be always the same. For every lower species is 
 formed by superadding some new idea to the species 
 next above it. ; insomuch, that in descending the scale 
 ©four preceptions,*.the understanding passes through 
 different orders of complex notions, which become more 
 and more complicated at every step it takes. Let us 
 resume here, for instance, the species of plain figures. 
 They imply no more than space bounded by lines. 
 But if we take in an additional consideration of the 
 nature of these lines, as, whether they are right or 
 curves, we fall into the subdivisions of plain figure, 
 distinguished by the ■names rectilinear, curvilinear and 
 mixtilinear* 
 
 Sec. VII,.,, And in all the inferior species by superad- 
 ding the specific to the nearest genus. 
 And here we arc to observe, that though plain 
 figures, when considered as one of those branches that 
 come under the notion of figure in general, take the 
 name of a species ; yet compareU with the classes of 
 curvilinear, rectilinear, aid mixtilinear, into which 
 they themselves may be divided, they really become a 
 genus, of which the before-n.entiqned subdivisions con- 
 stitute the several species. These species, in the same 
 manner as in the case of plain and solid figures, con- 
 sist of the genus and specific difference, as their con*. 
 
• 
 
 OF LOGIC. 9* 
 
 stituent parts. For in the curvilinear kind, the cur* 
 vity of the lines bounding the figure, makes what is 
 called the specific difference ; to which if we join the 
 genus, which here is plain figure; or space circumscrib- 
 ed by lines, we have all that is necessary towards com- 
 pleting the notion of the species. We are only to 
 take notice, that this last subdivision, having two ge- 
 nera above it, viz. plain figure, and figure in general; 
 the genus, joined with the specific difference, in order 
 to constitute the species of curvilinear, is that which 
 lies nearest to the said 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 descending 
 scale of our ideas — Figure in general, plain figures, 
 curve-lined figures — the two first are considered as ge- 
 nera in respect to the third ; and the second in order, 
 or that which stands next to the third, is called the 
 nearest genus. But now as it is this second idea, 
 which, joined with the notion of curvity, forms the spe- 
 cies of curve-lined figures ; it is plain, that the third or 
 last idea in the series, is made up of the nearest genus 
 and specific difference. This rule holds invariably, 
 however far the series is continued ; because in a train 
 of ideas thus succeeding one another, all that precede 
 the last are considered as so many genera, in respect of 
 that last; and the last itself is always formed, by su- 
 peradding the specific difference to the genus next it. 
 
 Sec. V III.... T/ie idea of an individual composed of tbt 
 lowest species and numeric difference. 
 
 Here then we have an universal description, applica- 
 ble to all our ideas, of whatever kind, from the high- 
 est genus, to the lowest species. For taking them in 
 order downwards from the said general idea, they eve- 
 ry where consist of the genus proxi mum, and differen- 
 tia specifica, as logicians love to express themselves. 
 But when we come to the lowest species of all, com- 
 prehending it only individuals, the superadded idea, 
 by which these individuals are distinguished one front 
 another, no longer takes the name of the specific differ* 
 
94 DUNCAN'S ELEMENTS 
 
 ence. For here it serves not to denote distinct spe- 
 cies, but merely a variety of individuals, each of which* 
 having a particular existence of its own, is therefore 
 numerically different from every other of the same 
 kind. And hence it is, that in this last case, logici- 
 ans choose to call the superadded idea by the name ©f 
 the numerical difference ; insomuch that as the idea of 
 a species, is made up of the nearest genus and specific 
 difference, so the idea of an individual consists of the 
 lowest species and numeric difference. Thus the circle 
 is a species of curve-lined figures, and what we call the 
 lowest species, as comprehending under it only indivi- 
 duals. Circles in particular are distinguished from one 
 another by the length and position of their diameters. 
 The length, therefore, and position of the diameter of 
 a circle, is what logicians call the numerical differ- 
 ence ; because these being given, the circle itself may 
 be described, and an individual thereby constituted. 
 
 Sec. IX..... Definitions to follow one another in train, 
 and pass through the same successive gradations as 
 cur compound ideas. 
 
 And thus we have endeavoured to trace, in theiest 
 manner we are able, the progress of the mind jn com* 
 . pounding its ideas. It begins, we see, with the most 
 general notions, which consisting of but a few simple 
 notices, are easily combined and brought together into 
 one conception. Thence it proceeds to the species com- 
 prehended under Hhis general idea, and these are form- 
 ed by joining together the genus and specific difference. 
 And as it often happens, that, these species may be still 
 further subdivided, and run on in along series of con- 
 tinued gradations, producing various orders of com- 
 pound perceptions ; so ail these several orders are regu- 
 larly and successively formed,by annexing in every step, 
 the specific difference to the nearest genus. When by this 
 method of procedure, we are come to the lowest order 
 of all ; by joining the species and numeric difference, we 
 frame the ideas of individuals. And here the series ne- 
 cessarily terminates, because it is impossible any farther 
 to bound or limit our conceptions. This view of tht 
 
OF LOGIC. 98 
 
 composition of our ideas, representing their constituent 
 parts in every step of the progression, naturally points 
 out the true and genuine form of a definition. For as 
 definitions are no more than descriptions of the ideas for 
 Which the terms defined stand; and as ideas are then 
 described, when we enumerate distinctly and in order, 
 the parts of which they consist ; it is plain, that by 
 making our definitions follow one another, according 
 to the natural train of our conceptions, they will be sub- 
 ject to the same rules, and keep pace with the ideas 
 they describe. 
 
 Scc« X.... The form of a Definition in all the various 
 orders of Conception. 
 As therefore the first order of our compound notions, 
 er the ideas that constitute the highest genera, in the 
 different scales of perception, are formed, by uniting 
 together a certain number of simple notices ; so the 
 terms expressing these genera, are defined by enumera- 
 ting the simple notices, so combined. And as the species 
 comprehended under any genus, or the complex ideas 
 e>f the second order, arise from superadding the specific 
 difference to the said general idea; so the definition of 
 the names of the species is absolved, in a detail of the 
 ideas of the specific difference, connected with the term of 
 the genus. For the genus having been before defined, the 
 term by which it is expressed stands for a known idea, 
 and may therefore be introduced into all subsequent de*. 
 finitions, in the same manner as the names of simple 
 perceptions. It will now, I think, be sufficiently obvious, 
 that the definitions of all the. succeeding orders of com- 
 pound notions, will every where consist oj the term of 
 the nearest genus joined with an enumeration of the ideas 
 that constitute the specific difference ; and that the defini- 
 tion of individuals unites tiu name of the lowest species) 
 with the terms by which we express the ideas of the nu- 
 meric difference. . 
 
 Sec. XL... The logical method of defining perfect in its 
 kind ; 
 IJere then we have the true and proper form of a 
 ie£uition # ia all tke various orders of ccmceptioa* 
 
36 DUNCAN'S ELEMENTS 
 
 This is that method of defining, which is commonly 
 called logical, and which, we see, is perfect in its kind, 
 inasmuch as it presents a full and adequate description 
 of the idea, for which the term defined stands. There 
 are still two things worthy of observation, before wc 
 take leave of this subject. First, that the very frame 
 and contexture of these definitions, points out the order 
 in which they ought to follow one another. For as 
 the name of the genus is admitted into a description, 
 only in consequence of its having been before defined ; 
 it is evident, that we must pass gradually through all 
 the different orders of conception. Accordingly, logi- 
 cians lay it down as a rule, that we are to begin always 
 with the highest genus, and carry on the series of de- 
 finitions regularly, through all the intermediate genera 
 and species, quite down to the individuals. By this 
 means our descriptions keep pace with our ideas, and 
 pass through the same successive gradations ; insomuch, 
 that the perusal of them must excite those ideas in the 
 understanding of another, in the very order and man- 
 ner in which they are put together by the mind in its 
 uniform advances from simple to the most complicated 
 notions. Now this is the true and proper end of de- 
 fining, and indeed the highest perfection of that art. 
 
 Sec. XII. And applicable to all words whatsoever ca- 
 pable of a definition* 
 
 There is yet another thing to be observed on this 
 head, namely, that the form here prescribed, is appli- 
 cable to all words whatsoever, capable of a defini- 
 tion. For as every term we use, must denote some idea, 
 either general or particular ; and as all our complex 
 notions relating to both these classes of perception from 
 the highest genus quite down to the individuals, come 
 within the rules of description here given ; it is evi- 
 dent, that this particular manner of unfolding an idea, 
 may be extended to all the possible complex concep- 
 tions we can connect with our words. By the rules 
 therefore of this method, definitions may be applied to 
 all terms standing for complex ideas ; and as these, by 
 what we have shown, at large in the two foregoing 
 
OF LOGIC. 9f 
 
 chapters, are the only definable articles of speech ; it 
 necessarily follows, that the directions here given arc 
 universal, extend to all particular instances, and arc 
 alike applicable in all languages. And thus at length) 
 we have not only deduced that peculiar form of a defi- 
 nition which obtains among logicians, but shown it 
 also to be perfect in its kind, and to take in the whole 
 compass of language. 
 
 BOOK. II. 
 
 OF JUDGMENT, OR INTUITION. 
 
 Cfmp* I. 
 
 OF THE GROUNDS OF HUMAN 
 JUDGMENT. 
 
 Sec. I..... Intuition respects the relations between out 
 Ideas when they are immediately perceivable, 
 
 WHEN the mind is furnished with ideas, its next 
 step in the way to knowledge is, the compa- 
 ring these ideas together, in order to judge of their 
 agreement or disagreement. In this joint view of our 
 idea;, if the relation is such, as to be immediately dis- 
 coverable by the bare inspection of the mind ; the judg- 
 ments thence obtained are called intuitive, from a word 
 that denotes to look at : for in this case, a mere atten- 
 tion to the ideas compared, suffices to let us see, how 
 far they are connected or disjoined. Thus, that the 
 whole is greater than any of its parts, is an intuitive 
 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 reason, why we call 
 I 
 
$8 DUNCAN'S ELEMENTS 
 
 the act of the mind forming these judgments intuition 3 
 as it is indeed no more than an immediate perception 
 of the agreement or disagreement of any two ideas. 
 
 Sec. II... .Experience and Testimony the Ground of 
 judging as to Facts* 
 But here it is to be observed, that our knowledge of 
 this kind, respects only our Ideas, and the relations 
 between them, and therefore can serve only as a foun- 
 dation to such reasonings, as are employed in investi- 
 gating these relations. Now it so happens, that many 
 of our judgments are conversant about facts, and the 
 real existence of things which cannot be traced by the 
 bare contemplation of'our ideas. It does not follow, 
 because I have the idea of a circle in my mind, that 
 therefore a figure answering to that idea, has a real , 
 existence in nature. I can form to myself the notion 
 of a centaur, or golden- mountain, but never imagine 
 on that account, that either of them exists. What 
 then are the grounds of our judgments, in relation to 
 facts ? I answer, these two : experience and testimony* 
 By experience we are informed of the existence of the 
 several objects which surround us, and operate upon 
 our senses. Testimony is of a wider extent, and reaches 
 not only to objects beyond the present sphere of our 
 .observation, but also to facts and transactions, which, 
 being now past, and having no longer any existence, 
 could not, without this conveyance, have fallen under 
 ourcognizance. 
 
 Sec. III.... Three Foundations of human Judgement* 
 viz. 1. Intuition* the Ground of scientifcal know- 
 ledge ; 
 
 Here then we have three foundations of human 
 judgment, from which the whole system of our know- 
 ledge may with ease and advantage be deduced. First, 
 intuition* which respects our ideas themselves, and 
 their relations, and is the foundation of that species of 
 reasoning, which we call demonstration* For whate- 
 ver is deduced from our intuitive perceptions, by a 
 clear and connected aeries of proofs, is said to be de- 
 monstrated, and produces absolute certainty in the 
 
OF LOGIC. 99 
 
 mind. Hence the knowledge obtained in this manner, 
 is what we properly term science ; because, in every 
 step of the procedure, it carries its own evidence along 
 with it, and leaves no room for doubt or hesitation* 
 And what is highly worthy of notice ; as the truths 
 of this class express the relations between our ideas, 
 and the same relations must ever and invariably sub- 
 sist between the same ideas, our deductions, in the way 
 of science, constitute what we call eternal, necessary, 
 and immutable truths. If it be true, that the whole 
 is equal to all its parts, it must be so unchangeably j 
 because the relations of equality being attached to the 
 ideas themselves, must ever intervene where the same 
 ideas are compared. Of this nature are all the truths 
 of natural religion, morality, and mathematics ; and in 
 general whatever may be gathered from the bare view 
 and consideration of our ideas. 
 
 Sec. IV.. ..2. Experience the Ground of our Knowledge 
 of the Powers and Qualities of Bodies. 
 
 The second ground of human judgment is experience ; 
 from which we infer the existence of those objects that 
 surround us, and fall under the immediate notice of our 
 senses. When we see the sun, or cast our eyes towards 
 a building, we not only have ideas of these objects 
 within ourselves, but ascribe to them a real existence 
 out of the mind. It is also by the information of the 
 senses, that we judge of the qualities of bodies ; as 
 when we say that snow is white, fire hot, or, steel 
 hard. For as* we are wholly unacquainted with the in- 
 ternal structure and constitution of the bodies that 
 produce these sensations in us, nay, and are unable to 
 trace any connexion between that structure and the 
 sensations themselves, it is evident that we build our 
 judgments altogether upon observation, ascribing to 
 bodies such qualities as are answerable to the percep- 
 tions they excite in us. But this is not the only ad- 
 vantage derived from experience, for to that, too, are 
 we indebted for all our knowledge regarding the co- 
 existence of sensible qualities in objects, and the ope- 
 rations of bodies one upon another. Ivory, for in- 
 
100 DUNCAN'S ELEMENTS 
 
 stance,. is hard and elastic ; this we know by experi- 
 ence, and indeed by that alone. For being altogether 
 strangers to the true nature both of elasticity and hard- 
 ness, we cannot, by the bare contemplation of our 
 ideas, determine how far the one necessarily implies 
 the other, or whether there may not be a repugnance 
 between them. But when we observe them to exist 
 botli^ in the same object, we are then assured from 
 experience that they are not incompatible ; and when 
 ■we also find, that a stone is hard and not elastic — and 
 that air, though elastic, is not hard — we also conclude, 
 upon the same foundation, that the ideas are not ne- 
 cessarily conjoined, but may exist separately in differ- 
 ent objects. In like manner, with regard to the opera- 
 tions of bodies, one upon another, it is evident, that 
 our knowledge this way is all derived from observa- 
 tion. Aqua regia dissolves gold, as has been found by 
 frequent trial ; nor is there any other way of arriving 
 at the discovery. Naturalists may tell us, if they please, 
 that the parts of aqua regia are of a texture apt to in- 
 sinuate between the corpuscles- of gold, and thereby 
 loosen and shake them asunder. If this is a true ac- 
 count of the matter, I believe it will, notwithstanding, 
 be allowed, that our conjecture, in regard to the con- 
 formation of these bodies, is deduced from the experi- 
 ment, and not the experiment from the conjecture. It 
 was not from any previous knowledge of the intimate 
 structure of aqua regia and gold) and the aptness of 
 their parts to act or be acted upon, that we came by 
 the conclusion above mentioned. The internal consti- 
 tution of bodies is in a manner wholly unknown to us: 
 and could we even surmount this difficulty, yet as the 
 separation of the parts of gold implies something like 
 an active force in the menstruum, and we are unable 
 to conceive how it comes to be possessed of this acti- 
 vity ; the effect must be owned to be altogether beyond 
 our comprehension. But when repeated trials had once 
 continued it, insomuch that it was admitted as an esta- 
 blished truth in natural knowledge, it was then easy 
 for men to spin out theories of their own invention, 
 and contrive such a structure of parts both for gold 
 
OR LOGIC. 101 
 
 *nd aqua regia, as would best seYve to 4 explain the 
 phenomenon, upon the principles of that- .system of 
 philosophy they had- adopted. ' .1 n^ighc easily' show, 
 from innumerable other instances, how much our 
 knowledge of the mutual action of bodies depends upon 
 observation- The bite of a viper will kill. Plants are 
 some salutary, others noxious. Fire dissolves one body, 
 and hardens another. These are truths generally 
 known ; nor is it less evident that we owe their disco- 
 very wholly to experience. 
 
 Sec. \ ....Why many yseful Inventions owe their Birth 
 to Chance. 
 And hence it is easy to account for what to some 
 writers has appeared a very great paradox ; that many 
 of the most important inventions in human life have 
 taken their rise from chance, and instead of coming* 
 out of the schools of philosophers, are for the most 
 part ascribed to men of no figure in the commonwealth 
 of learning. Sowing, planting, the use of compass, 
 and such like, are not deductions of human reason, 
 but discoveries which owe their birth to observation 
 and trial. No wonder, therefore, if these inventions 
 derived their beginning from such, as, being engaged 
 in the active and busy scenes of life, were" more in the 
 way of those experiments which lead to discoveries of 
 this nature. And here, as the particular callings and 
 professions of men, and oft-times chance, has a great 
 ascendant, it need not seem strange, if some of the 
 most useful arts in society appear to have had an ori- 
 ginal purely casual. 
 
 Sec. VI.. ..Natural Knowledge, from the Grounds on 
 which it rests, aptly termed experimental Philosophy. 
 From what has been said, it is evident, that as intu- 
 ition is the foundation of what we cull scientifical.} 
 knowledge, so is experience of natural. For this last 
 being wholly taken up with the objects of sense, or 
 those bodies that constitute the natural world — and 
 their properties, as far as w T e can discover them, being 
 to be traced only by a long and painful series of obser« 
 vations j it is apparentj that in order to improve this. 
 I 2 
 
102 DUNCAN'S ELEMENTS 
 
 branch of knowledge, fve 'must betake ourselves to the 
 Jiiet-iod $>£ ti : ial afnd /xperimtent. Accordingly, we find, 
 that v;!ike thi's was neglected,' ihtle advance was made 
 In the philosophy of nature ; whereas a contrary pro- 
 ceeding has enriched the present age with many valu- 
 able discoveries ; insomuch that natural knowledge, in 
 allusion to the foundation on which it stands, has been 
 very aptly called experimental philosophy. 
 
 Sec. VII. ...Though much of our Knowledge of Body 
 depends on Testimony, yet Experience is the ulti- 
 mate Foundation of it. 
 
 But though experience is what we may term the im- 
 Miediate foundation of natural knowledge, yet with re- 
 spect to particular persons, its influence is very nar- 
 row and confined. The bodies that surround us are 
 numerous ; many of them lie at a great distance ; and 
 some quite beyond our reach. Life too is short, and 
 so crowded with cares, that but little time is left for 
 any single man to employ himself in unfolding the 
 mysteries of nature. Hence it is necessary to admit 
 many things upon the testimony of others, which, by 
 this means, becomes the foundation of a great part of 
 cur knowledge of body. No man doubts of the power 
 of aqua regia to dissolve gold, though perhaps he ne- 
 ver himself made the experiment. In these, therefore, 
 and such like cases, we judge of the facts, and opera- 
 tions of nature, upon the mere ground of testimony. 
 However, as we can always have recourse to experi- 
 ence, where any doubt or scruple arises, this is justly 
 considered as the true foundation of natural philoso- 
 phy being indeed the ultimate support upon which our 
 assent rests, and whereto we appeal, when the highest 
 degree of evidence is required. 
 
 Sec. VIII. 3. Testimony the Ground of Historical 
 Knowledge. 
 But there are many facts that will not allow of an 
 appeal to the senses, and in this case testimony is the 
 true and only foundation of our judgments. All hu- 
 man actions, of whatever kind, when considered as 
 already past, are of the nature here described j because 
 
OF LOGIC. 105 
 
 having now no longer any existence, both the facts 
 themselves, and the circumstances attending them, 
 can be known only from the relations of such as had 
 sufficient opportunities of arriving at the truth. Testi- 
 mony, therefore, is justly accounted a third ground of 
 human judgment: and as from the other two we have 
 deduced scientijical and natural knowledge, so may we 
 from this derive historical ; by which I would be un- 
 derstood to mean, not merely a knowledge of the civil 
 transactions of states and kingdoms, but of all facts 
 whatsoever, where testimony is the^ultimate founda- 
 tion of our belief. 
 
 Sec. IX.... The second Operation of the Mind, common* 
 ly extended beyond Intuition* 
 Before I conclude this chapter, it will be necessary 
 to observe, that though the second operation of the 
 mind, properly speaking, extends not beyond intuitive 
 perceptions, yet logicians have not confined themselves 
 to so strict a view of it ; but calling ft by the name 
 judgment, thereby denote all acts of the mind, where 
 only two ideas are compared, without the immediate 
 interposition of a third. For when the mind joins or 
 separates two ideas, though perhaps this is done in 
 coBsequence of a train of previous reasoning, yet if the 
 understanding proceeds upofTestablished notions, with- 
 out attending to that train of reasoning, its determi- 
 nations are still considered as acts of judgment. Thus, 
 That God created the universe, that men are accounta- 
 ble/or their actions, are frequently mentioned by logici- 
 ans, as instances of the mind judging. And yet it is 
 apparent, that these judgments are by no means of the 
 kind we call intuitive ; nay, that it requires mucli ex- 
 ercise of the reasoning faculty, before a man can trace 
 their connexion with the perceptions of that name. I 
 could in the same manner easily show, that even our 
 judgments of experience and testimony, when pursued 
 to their source, derive all their power of persuasion, 
 from being linked with intuitive truths. But I shall 
 wave this enquiry for the present, as being of a nature 
 too subtile for a work of this kind. The remark itself, 
 however, was needful, as well to illustrate the proper 
 
104 DUNCAN'S ELEMENTS 
 
 distinction between the powers of the understanding* 
 as to explain the reason, why hi this part of logic, we 
 extend the second operation of the mind beyond those 
 limits, that in strictness of speech belong to it. Let us 
 now proceed to consider a little more particularly the 
 nature and variety of these our judgments. 
 
 Cfmp- ii. 
 
 OF AFFIRMATIVE AND NEGATIVE 
 PROPOSITIONS. 
 
 Sec. I.....77i£ subject and predicate vf a Proposition 
 explained. 
 
 WHILE the^comparing of our ideas is considered 
 merely as an act of the mind, assembling them 
 together, and joining or disjoining them according to 
 the result of its perceptions, we call it judgment ; but 
 when our judgments are put into words, they then bear 
 the name of propositions. A proposition, therefore, is a 
 sentence expressing some judgment of the mind, where- 
 by two or more ideas are affirmed to agree or disagree. 
 Now, as our judgments include at least two ideas, one 
 of which is affirmed or denied of the other, so must a 
 proposition have terms answering to these ideas. The 
 idea, of which we affirm or deny, and of course the 
 term expressing that idea, is called the subject of the 
 proposition. The idea affirmed or denied, as also the 
 term answering it, is called the predicate. Thus in the 
 proposition, God is omnipotent : G&d is the subject, it 
 being of him that we affirm omnipotence ;- and omni- 
 potence is the predicate, because we affirm the idea, ex- 
 pressed by that word to belong to God. 
 
 Sec. II The Copula, &c* 
 
 But as in propositions, ideas are either joined or 
 disjoined ; it is not enough to have terms expressing 
 those ideas, unless we have also some words to denote 
 
OF LOGIC. 105 
 
 their agreement or disagreement. That word in a propo- 
 sition, which connects two ideas together, is called the 
 copula; and if a negative particle be annexed, we 
 thereby understand, that the ideas are disjoined. The 
 substantive verb is commonly made use of for the co- 
 pula, as in the above-mentioned proposition, God is 
 omnipotent ; where it represents the copula, and signi- 
 fies the agreement of the ideas God and omnipotence* 
 But if we mean to separate two ideas, then, besides the 
 substantive verb, we must also use some particle of ne- 
 gation, to express this repugnance. The proposition, 
 man is not perfect, may serve as an example of this 
 kind, where the notion of perfection, being removed 
 from the idea of man, the negative particle, not, is in- 
 serted after the copula, to signify the disagreement be- 
 tween the subject and predicate. 
 
 Sec. III.. ..Propositions sometimes expressed by a single 
 word. 
 Every proposition necessarily consists of these three 
 parts; but then it is not alike needful, that they be all 
 severally expressed in words ; because the copula is of- 
 ten included in the term of the predicate ; as when we 
 say, he sits; which imports the same as he is sitting. 
 In the Latin language, a single word has often the force 
 of a whole sentence. Thus ambujat is the same, as Hie 
 est ambulans ; amo, as ego sum amans ; and so in innu- 
 merable other instances ; by which it appears, that we 
 are not so much to regard the number of words in a 
 sentence, as the ideas they represent, and the manner 
 in which they are put together. For whenever two 
 ideas are joined or Disjoined in an expression, though 
 of but a single word, it is evident, that we have a sub- 
 ject, predicate, and copula, and of consequence a com- 
 plete proposition. 
 
 Sec. IV.. ..Affirmative and Negative Propositions. 
 
 When the mind joins two ideas, we call it an affirma- 
 tive judgment ; when it separates them, a negative ; 
 and as any two ideas compared together, must necessa- 
 rily either agree or not agree, it is evident, that all our 
 judgments fell under these two divisions. Hence, 
 
t06 . DUNCAN'S ELEMENTS 
 
 likewise, the proposition expressing these judgments, 
 are all either affirmative or negative. An affirmative 
 proposition connects the predicate with the subject, as, 
 a stone is heavy : a negative proposition separates them, 
 as God is not the author of evlk Affirmation, there- 
 fore, is the same as joining two ideas together; and 
 this is done by means of the copula. Negation, on the 
 contrary, marks a repugnance between the ideas com- 
 pared ; in which case a negative particle must be called 
 in, to show that the connexion* included in the copula. 
 does not take place. 
 
 Sec. V ....When the negative particle serves to disjoin 
 ideas. 
 
 And hence we see the reason of the rule commonly 
 laid down by logicians, that in all negative proposi- 
 tions, the negation ought to affect the copula. For as 
 the copula, when placed by itself, between the subject 
 and the predicate, manifestly binds them together ; it 
 is evident, that in order to render a proposition nega- 
 tive, the particle of negation must enter it in such man- 
 ner, as to destroy this union. In a word, then only are 
 two ideas disjoined in a proposition, when the negative 
 particle may be so referrccLto the copula, as to break the 
 affirmation included in it, and undo that conpexion it 
 would otherwise establish. When we say, for instance, 
 no man is perfect ; take away the negation, and the co- 
 pula of itself plainly unites the ideas in the proposition. 
 But as this is the very reverse of what is intended, a 
 negative mark is added, to fchow that this union does 
 not here take place. The negation, therefore, by de- 
 stroying the effect of the copula, changes the very na- 
 ture of the proposition, insomuch that instead of bind- 
 ing two ideas together, it denotes their separation. On 
 the"contrary, in this sentence, the man who departs not 
 from an upright behavipur, is beloved of God ; the pre- 
 dicate, beloved of Gud> is evidently affirmed of the sub- 
 ject an upright man-; so that notwithstanding the nega- 
 tive particle, the proposition is still affirmative. The 
 reason is plain ; the nagation here affects not the copu- 
 la, but making properly, a part of the subject, serves, 
 
OF LOGIC. 107 
 
 with other terms in the sentence, to form one complex 
 idea, of which the predicate, beloved of God, is directly 
 affirmed. This, perhaps, to some may appear a mere 
 logical refinement, contrived to justify the scholastic 
 rule for distinguishing between affirmative and nega- 
 tive propositions. But if it be considered, that this dis- 
 tinction is of great importance in reasoning, and can- 
 not in many cases be made with certainty, but by means 
 of this criterion here given, the reader will see suffici- 
 ent reason for my taking so much pains to illustrate it. 
 
 Sec. VI.., .How a Copula comes to be a part of a ne- 
 gative proposition. 
 
 Perhaps it may still appear a mystery, how a copu- 
 la can be said to be a part of a negative proposition, 
 whose proper business it is to disjoin ideas. This dif- 
 ficulty, however, will vanish, if we call to mind, that 
 every judgment implies a direct affirmation, and that 
 this affirmation alone makes the true copula in a propo- 
 sition. But as our affirmations are of two kinds, viz. ei- 
 ther of agreement or of disagreement, between the ideas 
 compared; hence there is also a twofold expression of 
 our judgments. In the case of agreement, the copula 
 alone suffices; because it is the proper mark whereby 
 we denote an identity or conjunction of ideas. But 
 where perceptions disagree, there we must call in a ne- 
 gative particle : and this gives us to understand that 
 the affirmatipn implied in the copula, is not of any. con- 
 nexion between the subject and predicate, but of their 
 mutual opposition and repugnance. 
 
 Cfrap. in. 
 
 OF UNIVERSAL AND PARTICULAR 
 PROPOSITIONS. 
 
 Sec. I,.. .Division of Propositions, into Universal and Jt-. 
 
 Particular. 
 
 f T^HE next considerable division of propositions, is 
 
 A into universal and particular. Our ideas, accord- 
 
103 DUNCAN'S ELEMENTS 
 
 ing to what has been already observed in the first part," 
 are all singular, as they enter the mind, and repre- 
 sent individual objects. But as by abstraction we can 
 render them universal, so as to comprehend a whole 
 class of things, and sometimes several classes at once ; 
 hence the terms expressing these ideas must be in 
 like manner universal. If, therefore, we suppose any 
 general term to become the subject of a proposition* 
 it is evident, that whatever is affirmed of the abstract 
 idea belonging to that term may be affirmed of all 
 the individuals to which that idea extends. Thus when 
 we say, men jare mortal ; we consider mortality, not as 
 confined to one or any number of particular men, 
 but as what may be ♦affirmed without restriction of 
 the whole species. By this means, the proposition be* 
 comes as general as the idea which makes the subject 
 of it, and indeed derives its universality entirely from 
 that idea, being more or less so, according as this may 
 be extended to more or fewer individuals. But it is 
 further to be observed of these general terms, that they 
 sometimes enter a proposition in their full latitude, 
 as in the example given above ; and sometimes appear 
 with a mark of limitation. In this last case, we are 
 given to understand, that the predicate agrees not to 
 the whole universal idea, but only to a part of it ; 
 as in the proposition, some men are wise : for here 
 wisdom is not affirmed of every particular man, but 
 restrained to a few of the human species. 
 
 Sec t II„;Propositio?is universal where the subject is so } 
 without a mark of restriction* 
 
 Now from this different appearance of the general 
 idea, that constitutes the subject of any judgment, ari- 
 ses the division of propositions into universal and/;ar- 
 ticular. An universal proposition is that, wherein the 
 subject is some general term, taken in its full latitude, 
 insomuch that the predicate agrees to all the individuals 
 comprehended under it, if it denotes a proper species ; 
 and to all the several species and their individuals, if 
 it marks an idea of a higher order. The words, a//, 
 eve rj> } no } none 9 Ike. are the proper signs of this univer* 
 
OF LOGIC. 109 
 
 satity ; and as they seldom fail to accompany general 
 truths, so they are the most obvious criterion whereby 
 to distinguish them* All animals have a power of be* 
 ginning motion* This is an universal proposition ; as 
 we know from the word all, prefixed to the subject 
 animal, which denotes that it must be taken in its 
 full extent. Hence the power of beginning motion 
 may be affirmed of all the several species of aaimals ; 
 as of birds, quadrupeds, insects, fishes, Sec. and of all 
 the individuals of which these different classes consist, 
 as of this hawk, that horse, and so for others. 
 
 Sec. III,*:Propositions particular where seme utiiQer* 
 sal Subjects appear with a Mark of Limitation* 
 
 A particular proposition has in like manner some ge- 
 neral term for its subject, but with a mark of limita- 
 tion added, to denote, that the predicate agrees only to 
 some of the individuals comprehended under a species, 
 or to one or more of the species belonging to any ge- 
 nus, and not to the whole universal idea. Thus, some 
 stones are heavier than iron ; some men have an uncom- 
 mon share of prudence. In the last of these proposi- 
 tions, the subject, some men, implies only a certain 
 number of individuals, comprehended under a single 
 species. In the former, where the subject is a genus, 
 that extends to a great variety of distinct classes, 
 some stones may not only imply any number of particu- 
 lar stones, but also several whole species of stones ; 
 inasmuch as there may be not a tew, with the property- 
 there described. Hence we see, that a^proposition does 
 not cease to be particular, by the predicate's agreeing 
 to a whole species, unless that species, singly and dis- 
 tinctly considered, makes also the subject of which we 
 affirm or deny. For if it belongs to some genus, that 
 has other specie? 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, con* 
 stitutes the proposition particular. 
 K 
 
iio DUNCAN'S ELEMENTS 
 
 Sec. TV."..*. A sure and infallible Criterion, whereby t» 
 distinguish between universal and particular Proposi- 
 tions, 
 
 Here then, we have a sure and infallible mark, 
 ■whereby to distinguish between universal and particu- 
 lar propositions. Where the predicate agrees to all the 
 individuals comprehended under the notion of the sub- 
 ject, there the proposition is universal ; where it be- 
 longs only to some of them, or to some of the species 
 of the general idea, there the proposition is particular. 
 This criterion is of easy application, and much safer 
 than to iepend upon the common signs of all, every , 
 some, none, &c. because these being different in dif- 
 ferent languages, and often varying in their significa- 
 tion, are very apt in many cases to mislead the judg- 
 ment. Thus if we say, all the soldiers -when drawn 
 Tip, formed a square of a hundred men a side : it is evi- 
 dent that the predicate cannot be affirmed of the sever- 
 al individuals, but of the whole collective idea of the 
 subject ; whence, by the rule given above, the proposi- 
 tion is not "universal. It is true, logicians lay down 
 many observations, to enable us to distinguish 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 ap. 
 plied with ease; whereas the directions, which we meet 
 with in treatises of logic, being drawn for the most part, 
 from the analogy of language, and common forms of 
 speech, are not only burdensome to the memory, but of- 
 ten very doubtful and uncertainin their application. 
 
 Sec. V Singular Propositions contained under the 
 
 head of particulars. 
 
 There is still one species of propositions that remains 
 te be described ; and which the more deserves our no- 
 tice, as it is not yet agreed among logicians, to which 
 of the two classes mentioned above, they ought to be 
 referred. I mean singular propositions \ or those wiiere 
 the subject is an individual. Of this nature are the fol- 
 lowing : sir Isaac Newton was the inventor of fusions ; 
 this book contains mqny useful truths* What occasions 
 
OF LOGIC. Ill 
 
 some difficulty, as to the proper rank of these proposi- 
 tions, is, that the subject being taken according to the 
 whole of its extension, they sometimes have the same 
 effect in reasoning, as universals. But if it be con- 
 sidered, that they are, in truths the most limited kind 
 of particular propositions, and that no proposition can, 
 with any propriety, be called universal, but where the 
 subject is some universalidea ; we shall not be long in 
 determining to which class they ought to be referred. 
 When we say, some books contain useful truths, the 
 proposition is particular ; because the general term ap- 
 pears with a mark of restriction. If, therefore, w r e say, 
 this book contains useful truths ; it is evident, that the 
 proposition must be still more particular, as the limita- 
 tion, implied in the word, this, is of a more confined 
 nature, than in the former case, I know, there are in- 
 stances, where singular propositions have the same ef- 
 fect in reasoning, as universals ; yet is not this, by rea- 
 son of any proper universality, belonging to them ; but 
 because the conclusion, in such cases being always sin- 
 gular, maybe proved by a middle term which is also 
 singular ; as I could easily demonstrate,. were this a pro- 
 per place for entering into a discussion of that nature* 
 
 Sec. YL.. .The Fourfold Division of Propositions* 
 
 : We see, therefore, that all propositions are either 
 affirmative or negative ; nor is it less evident, that in 
 both cases, they be universal or particular. Hence 
 arises that celebrated fourfold division of them, into 
 universal affirmative, and universal negative ; parties 
 lar affirmative, and particular negative ; which com- 
 prehends, indeed all their varieties. The use of this 
 method of distinguishing them will appear more fully 
 afterwards, when we come to treat of reasoning and 
 syllogism. , 
 
112 DUNCAN'S ELEMENTS 
 
 e&ap. IV. 
 
 OF ABSOLUTE AND CONDITIONAL 
 PROPOSITIONS. 
 
 *ec. J.:*Bistinction of Qualities into Essential and 
 Accidental. 
 
 THE objects, about which we are chiefly convers- 
 ant in this 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 small part 
 cf our knowledge to distinguish rightly these varia- 
 tions, and trace the reasons upon which they depend. 
 Tor it is observable, that amidst all the vicissitudes of 
 nature, some things remain constant and invariable ; 
 nor are even the changes to which we see others liable, 
 effected, but in consequence of uniform and steady 
 laws, which, when known, are sufficient to direct us in 
 cur judgments about them. Hence philosophers, in 
 distinguishing the objects of our perception into vari- 
 ous classes, have been very careful to note, that some 
 properties belong essentially to the general idea, so ai 
 not to be separable from it but by destroying its very- 
 nature ; while others are only accidental, and may be 
 affirmed or denied of it, in different circumstances. 
 Thus, solidity, a yellow colour, and great weight, arc 
 considered as essential qualities of gold ; but whether 
 it shall exist as an uniform, conjoined mass, is not 
 alike necessary. We see that by a proper menstruum, 
 it may be reduced to a fine powder ; and that intense 
 heat will bring it into a state of fusion. 
 
 jSec. !!»*••* Hence a considerable Diversity in our Man- 
 ner of judging* 
 Now, from this diversity in the several qualities of 
 things, arises a considerable difference as to the man- 
 ner of our judging about them. For in this first place, 
 all such properties, as are inseparable from objects, 
 when considered as belonging to any genus or species, 
 are affirmed absolutely and without reserve, of that ge- 
 
OF LOGIC. 113 
 
 tieral idea. Thus we say ; gold is very weighty ; a 
 stone is hard ; animals have a power of self-motion. 
 But in the case of mutable or accidental qualities, as 
 they depend upon some other consideration, distinct 
 from -the generalidea ; that also must be taken into the 
 account, in order to form an accurate judgment. Should 
 we afRrm, for instance, of some stones, that they are 
 very susceptible of a rolling motion ; the proposition, 
 while it remains in this general form, cannot with any* 
 advantage be introduced into our reasonings. An apt- 
 ness to receive that mode of motion flows from the fi- 
 gure of the stone ; which, as it may vary infinitely, our 
 judgment then only becomes applicable aud determin- 
 ate, when the particular figure, of which volubility is a 
 consequence, is also taken into the account. Let us 
 then bring in this other consideration, and the proposi- 
 tion will run as follows : stones of a spherical form are 
 easily put into a rolling motion* Here we see the con- 
 dition upon which the predicate is affirmed, and there- 
 fore know in what particular cases the proposition may- 
 be applied. 
 
 Sec. III.. ..Which gives rise to the division of Proposi- 
 tions into Absolute and Conditional. 
 
 This consideration of propositions, respecting the 
 manner in which the predicate is affirmed of the subject, 
 gives rise to the division of them into absolutt and con- 
 dtTional. Absolute propositions are those, wherein we 
 affirm some property inseparable from the idea of the 
 subject, and which, therefore, belongs to it in all possi- 
 ble cases ; as, God is infinitely wise : virtue tends to the 
 ultimate happiness of man. But where the predicate is 
 not necessarily connected jadth the idea of the subject, 
 unless upon some consideration distinct from that idea, 
 there the proposition is called conditional. The reason 
 of the name is taken from the supposition annexed, 
 which is of the nature cf a condition, and may be ex* 
 pressed as such. Thus ; if a stone is exposed to the rays 
 of the s uny it will contract some degree of heat. If a 
 river runs in a very declining channel^ its rapidity wilt 
 €oustantly increase. 
 
 K 2 
 
114 DUNCAN'S ELEMENTS 
 
 Sec. TV*,,, The great importance of this division) as it 
 renders Propositions determinate ; 
 
 There is not any. thing of greater importance in phi- 
 losophy, than a due attention to this division of pro- 
 positions. If we are careful never to affirm things abso- 
 lutely, but where the ideas are inseparably conjoined ; 
 and if, in our other judgments, we distinctly mark the 
 conditions, which determine the predicate to belong to 
 the subject : we shall be the less liable to mistake, in 
 applying general truths to the particular concerns of 
 human life. It is owing to the exact observance of 
 this rule, that mathematicians have been so "happy in 
 their discoveries ; and that what they demonstrate of 
 magnitude in general, may be applied with ease in all 
 obvious occurrences. 
 
 Sec. \ T ,,„And reduces them from particulars to ge- 
 nerals. 
 
 The truth of it is, particular propositions are then 
 known to be true, when we can trace their connexion 
 •with universals : and it is, accordingly, the great busi- 
 ness of science, to find out general truths, that may be 
 applied with safety in all obvious instances. Now the 
 great advantage arising from determining with care 
 the conditions upon which one idea may be affirmed or 
 denied of another, is this ; that thereby particular pro- 
 positions really become universal, may be introduced 
 with certainty into our reasonings, and serve as stand- 
 ards to conduct and regulate our judgments. To illus- 
 trate this by a familiar instance : if we say, some wa- 
 ter acts very forcibly ; the proposition is particular : 
 and as the conditions, on which this forcible action 
 depends, arc not mentioned, it is as yet uncertain in 
 what cases it may be applied. Let us then supply these 
 conditions, and the proposition will run thus ; water 
 conveyed in sufficient quantity along a steep descent, 
 nets very forcibly. Here we have an universal judg- 
 ment, inasmuch as the predicate, forcible action, may 
 be ascribed to all water under the circumstances men- 
 tioned. Nor is it less evident, that the proposition in 
 this new form is of easy application ; and in fact we 
 
OP LOGIC. lis 
 
 find, that men do apply it in instances where the for- 
 cible action of water is required ; as in corn-mills, and 
 many other. works of art. Thus we see, in what man- 
 ner we are to proceed, in order to arrive at universal 
 truths, which is the great end and aim of science; 
 And indeed, would men take the same care, duly to 
 express the conditions on which they affirm and deny, 
 as mathematicians do, in those theorems which they 
 term hypothetical, I doubt not, but we might be able 
 to deduce many truths, in other parts of philosophy, 
 with no less clearness, force, and perspicuity, than has 
 hitherto been thought peculiar to the science of quantity. 
 
 OF SIMPLE AND COMPOUND 
 PROPOSITIONS. 
 
 Sec; I,. ..Division of Propositions into Simple and 
 Compound, 
 
 HITHERTO we have treated of propositions, 
 where only two ideas are compared together. 
 These are, in the general, called simple ; because, hav- 
 ing but one subject and one predicate, they are the ef- 
 fect of a simple judgment that admits of no subdivi- 
 sion. But if it so happens, that several ideas offer 
 themselves to our thoughts at once, whereby we are 
 led to affirm the same thing of different objects, or dif- 
 ferent things of the same object ; the propositions, ex- 
 pressing these judgments, are called compound: because 
 they may be resolved into as many others as there are 
 subjects or predicates in the whole complex determina- 
 tion of the mind. Thus, God is infinitely wise and in* 
 finitely powerful; here there are two predicates, in* 
 finite wisdom and infinite power, both affirmed of the 
 same subject ; and accordingly, the -proposition may 
 be resolved into two others, affirming these predicates 
 severally. In like manner, in the proposition, neither 
 kings nor people are exempt from death, the predicate 
 is denied of froth subjects, and may therefore be sepa* 
 
116 DUNCAN'S ELEMENTS 
 
 rated from them, in distinct propositions. Nor is it 
 less evident, that if a complex judgment consists of 
 several subjects and predicates, it may be resolved into 
 as many simple propositions as are the number of dif- 
 ferent ideas compared together* Riches and honours 
 are apt to elate the mind, and increase the number of 
 cur desires. In this judgment, there are two subjects 
 and twcvpredicates : and it is at the same time apparent, 
 that it may be resolved into four distinct propositions. 
 Riches are apt to elate the mind. Riches are apt to 
 increase the number of our desires. And so of honours. 
 Sec. II.. ..The proper Notion of a Compound Proposi* 
 tion ascertained. 
 Logicians have divided these compound propositions 
 into a great many different classes ; but in my opini- 
 on; not with aNdiie regard to their proper definition. 
 Thus conditionals, casuals, relatives, itfe. are mention- 
 ed as so many distinct species of this kind, though in 
 fact they are ila more than simple propositions. To 
 give an instance of a conditional : If a stone is expos- 
 ed to the rays of the sun, it will contract some degree of 
 heat. Here we have but one subject and one predi- 
 cate ; for the complex expression, A stone exposed to 
 the rays of the sun, constitutes the proper subject of 
 this proposition, and is no more than one determinate 
 idea. The same thing happens in casuals. Rehoboam 
 •was unhappy, because he followed evil counsel. P aeny 
 not, that there is here an appearance of two proposi- 
 tions arising from the complexity of the expression ; 
 but when we come to consider the matter more near- 
 ly, it is evident that we have but a single subject and 
 predicate.... The pursuit of evil counsel brought misery 
 upon Rehoboam. It is not enough, therefoie, to ren- 
 der a proposition compound, that the subject and pre- 
 dicate are complex notions, requiring sometimes a whole 
 sentence to express them ; for in this case, the com- 
 parison is still confined to two ideas, and constitutes 
 what we call a simple judgment. But where there are 
 several subjects or predicates, or both, as the affirma- 
 tion or negation may be alike extended to then) all, the 
 proposition, expressing such a judgment, is truly a coU 
 
OF logic. nr 
 
 lection of as many simple ones, as there are different 
 ideas compared. Confining onrselves, therefore, to 
 this more strict and just notion of compound proposi- 
 ons, they are all reducible to two kinds, viz. copula- 
 tives and disjunctives. 
 
 Sec. III... .Compound Propositions either Copulative. 
 
 A copulative proposition is, where the subjects and 
 predicates are so linked together, that they may be all 
 severally affirmed or den ied one of another. Of this na- 
 ture are the examples of compound propositions given 
 above. Riches and honours are apt to elate the mind, and 
 increase the number of our desires. Neither kings nor 
 people are exempt from death. In the first of these, 
 the two predicates may be" affirmed severally of each 
 subject, whence we have four distinct propositions. 
 The other furnishes an example of the negative kind, 
 where the- same predicate being disjoined from both 
 subjects, may be also denied of them in separate pro* 
 positions. 
 
 Sec. IV.... Or Disjunctive. 
 The other species of compound propositions are those 
 called disjunctives ; in which, comparing several pre- 
 dicates with the same subject, we affirm, that one of 
 them necessarily belongs to it, but leave the particular 
 predicate undetermined. If any one, for example, 
 says : This world either exists of itself or is the work 
 of some all-wise and powerful cause ; it is evident, that 
 one of the two predicates must belong to the world ; 
 but as the proposition 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 centre about which the earth revolves. 
 Friendship finds men equal, or makes them so. It is the 
 nature of all propositions of this class, supposing the r» 
 to be exact in point of form, that upon determining the 
 particular predicate, the rest are of course to be re- 
 moved ; or if all the predicates but one are removed ; 
 that one necessarily takes place. Thus, in the exam- 
 ple above, if we allow the world to be the work of some 
 wise and powerful cause, we of course deny it to be 
 
118 DUNCAN'S ELEMENTS 
 
 self-existent ; or if we deny it to be self-existent, we 
 must necessarily admit that it was produced by some wise 
 and powerful cause. Now this particular manner of 
 linking the predicates together, so that the establishing 
 one displaces all the rest. ...or the excluding all but one 
 necessarily establishes that one... .cannot otherwise be 
 effected than by means of disjunctive particles. And 
 hence it is", that propositions of this class take their 
 names from these particles, which make so necessary a 
 part of them, and indeed, constitute their very nature, 
 considered as a distinct species. But I shall reserve 
 what farther might be said on this head, till I come to 
 treat of reasoning, where the great use and importance 
 of disjunctive propositions will better appear. 
 
 Cfmp. vi. 
 
 OF THE DIVISION OF PROPOSITIONS INTO SELF- 
 EVIDENT AND DEMONSTRABLE. 
 
 Sec. I Design of this Chapter. 
 
 AS we are soon to enter upon the third part of lo- 
 gic, which treats of reasoning — and as the art of 
 reasoning lies in deducing propositions whose truth 
 does not immediately appear, from' others more known 
 -. — it will be proper, before we proceed any farther, to 
 examine a little the different degrees of evidence that 
 accompany our judgments ; that we may be the better 
 able to distinguish in what cases we ought to have re- 
 course to reasoning, and what those propositions are, 
 upon which, as a sure and unerring foundation, we may 
 venture to build' the truth of others. 
 
 Sec. II Propositions divided into Self-evident and 
 
 Demonstrable, 
 When any proposition is offered to the view of the 
 mind, if the terms, in which it is expressed, are under- 
 stood ; upon comparing the ideas together, the agree- 
 ment or disagreement asserted is either immediately per- 
 ceived, or found to lie beyond the present reach of the 
 understanding. In the first case, the proposition is said 
 
OF LOGIC. 119 
 
 to be self-evident^ and admits not of any proof ; because 
 a bare attention to the ideas themselves produces full 
 conviction and certainty ; nor is it possible to call in 
 any thing, more evident by way of confirmation. But 
 where the connexion or repugnance comes not so readi- 
 ly under the inspection of the mind, there we must have 
 recourse to reasoning ; a,nd if by a clear series of proofs 
 we can make out the truth proposed, insomuch that self- 
 evidence shall accompany every step of the procedure, 
 we are then able to demonstrate what we assert ; and 
 the proposition itself is said to be demonstrable. When 
 we affirm, for instance, that it is impossible for the same 
 thing to be v and not to be; whoever understands the 
 terms made use of, perceives at first glance the truth of 
 what is asserted ; nor can he, by any efforts, bring him- 
 self to believe the contrary. The proposition therefore 
 is self-evident, and such that it is impossible by reason- 
 ing to make it plainer ; because there is no truth more 
 obvious, or better known, from which, as a consequence 
 it may be deduced. But if we say, this world had a be- 
 ginning ; the assertion is indeed equally true, but shines 
 not forth with the same 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 consent, until by reasoning we arrive at a clear 
 view of the absurdity involved in the contrary supposi- 
 tion. Hence this, proposition is of the kind we call 
 demonstrable, inasmuch 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 
 follows as an unavoidable consequence. 
 
 Sec. IlL.vJFA? the second operation of the Mind is 
 . confined wholly to Intuition* 
 
 From what has been said, it appears that reasoning 
 is employed only about demonstrable' propositions, and 
 that our intuitive and self-evident perceptions are the 
 ultimate foundation on which it rests. And now we 
 see clearly the reason, why in the distinction of the 
 powers of the understanding, as explained in the in- 
 troduction to the treatise; the second operation of the; 
 
120 DUNCAN'S ELEMENTS 
 
 mind was confined wholly to intuitive acts. Our first 
 step, in the way to knowledge, is to furnish ourselves 
 with ideas. When these are obtained, we next set our- 
 selves to compare them together, in order to judge o£ 
 their agreement or disagreement. If the relations we 
 are in quest of, lie immediately open to the view of the 
 mind, the judgments expressing them are self evident ; 
 and the act of the mind, forming these 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 necessary to employ 
 search and examination, and call in the assistance of 
 self-evident truths, which is what we properly term 
 reasoning. Every judgment, therefore, that is not in- 
 tuitive, being gained by an exercise of the reasoning 
 faculty, necessarily belongs to the third operation of 
 the mind, and ought to be referred to it in a just divi- 
 sion of the powers of the understanding. And indeed, 
 it is with this view chiefly, that w T e have distinguished 
 propositions into self-evident and demonstrable. Un- 
 der the first head are comprehended all our intuitive 
 judgments, that is, all belonged to the second opera- 
 tion of the mind. Demonstrable propositions are the 
 proper province of the reasoning faculty, and consti- 
 tute by far the most considerable part of human know- 
 ledge. Indeed reason extends also to matters of expe- 
 rience and testimony^ where the proofs adduced are not 
 of the kind called demonstration. But I am here only 
 considering the powers of the mind as employed in tra- 
 cing the relations between its own ideas, in which 
 view of things, every true proposition is demonstrable ; 
 though very often we find ourselves incapable of disco- 
 vering and applying those intermediate ideas upon 
 which the demonstration depends. 
 
 Sec. IV '....Self-evident Truths the Jirst Principles of 
 Reasoning. 
 
 Demonstrable propositions, therefore-, belonging pro- 
 perly to the third operation of the mind, I shall, for 
 the present, dismiss them, and return to the consider^ 
 atioa of self-evident truths* These as I have already 
 
OF LOGIC. 121 
 
 observed, furnish the first principles of reasoning ; and 
 it is certain, that if in our researches, we employ only 
 such principles as have this character of self-evidence, 
 and apply them according to the rules to be after- 
 wards explained, we shall be in no danger of error, in 
 advancing from one discovery to another. For this I 
 may appeal to the writings of the mathematicians, 
 which, being conducted by the express model here 
 mentioned, are an incontestable proof of the firmness 
 and stability of human knowledge, when built upon so 
 sure a foundation. For not only have the propositions 
 of this science stood the test of ages, but are found 
 attended with such invincible evidence, as forces the 
 assent of all who duly consider the proofs upon which 
 they are established. Since then mathematicians are 
 universally allowed to have hit .upon the right method 
 of arriving at truths— -since they have been the hap- 
 piest in the choice, as well as application of their prin- 
 ciples — it may not be amiss .to explain here the divi- 
 sion they have given of self-evident propositions ; that, 
 by treading in their steps, we may learn something of 
 that justness and solidity of reasoning, for which they 
 are so deservedly esteemed. 
 
 Sec. V Definitions a great help to Clearess andEvi* 
 
 dence in Knowledge. 
 
 First, then it is to be observed, that they have been 
 very careful in ascertaining their ideas, and fixing the 
 significations of their terms. For vhis purpose they 
 begin with definitions, in which the meaning of their 
 words is so distinctly explained, that they cannot fail 
 to excite in the mind of an attentive reader the very 
 same ideas as are annexed to them by the writer. And 
 indeed I am apt to think, that the clearness and irre- 
 sistible evidence of mathematical knowledge, is owing 
 to nothing so much as this care in laying the founda- 
 tion. Where the relation between any two ideas is 
 accurately and justly traced, it will not be difficult for 
 another to comprehend that relation, if insetting him- 
 self to discover it, he brings the very same ideas into 
 •comparison. But if, on the contrary, he affixes to his 
 
122 DUNCAN'S ELEMENTS 
 
 ■words ideas different from those that were in the mind 
 of him who first advanced the demonstration ; it is 
 evident, that as the same ideas are not compared, the 
 same relation cannot subsist, insomuch that a proposi- 
 tion will be rejected as false,- which had the terms been 
 rightly understood, must have appeared unexception- 
 ably true, A square, v for instance, is a figure bounded 
 by four equal right lines, joined together at right an- 
 gles. Here the nature of the angles makes no less a 
 part of the idea, than the equality of the sides ; and 
 many properties, demonstrated of the square, flow from 
 its being a rectangular figure. If, therefore, we sup- 
 pose a man who has formed a partial notion of a square, 
 comprehending only the quality of its sides, without 
 regard to the angles, reading some, demonstration that 
 implies also this latter Consideration ; it is plain he 
 would reject it as not universally true, inasmuch as it 
 could not be applied where the sides were joined to- 
 gether at unequal angles. For this last figure, answer- 
 ing still to his idea of a square, would be yet found 
 without the property assigned to it in the proposition. 
 But if he comes afterwards to correct his notion, and 
 render his idea complete, he will then readily own the 
 truth and justness of the demonstration. 
 
 Sec. VI.... Mathematicians by beginning with them, pro* 
 cure a ready reception to the truths they advaTice* 
 
 We see, therefore, that nothing contributes so much 
 to the improvement and certainty of human know- 
 ledge, as the having determinate ideas, and keeping 
 them steady and invariable in all our discourses and 
 reasonings about them. And on this account it is, that 
 mathematicians, as was before observed, always begin 
 by defining their terms, and distinctly unfolding the 
 notions they are intended to express. Hence such as 
 apply themselves to these studies, - having exactly the 
 same views of things, and bringing always the very 
 same ideas into comparison, readily discern the rela- 
 tions between them, when clearly and distinctly repre- 
 sented. Nor is there any more natural and obvious 
 reason for the universal reception given to mathemati. 
 
OF LOGIC. 123 
 
 cal truths, and for that harmony and correspondence 
 of sentiments which makes the* distinguishing charac- 
 ter of the literati of this class. 
 
 bee. VII.... The establishing of Principles the Second 
 Step in Mat; hematic al Knowledge. 
 When the/ likve taken this first step, and made 
 * n the ideas, whose relations they intend to inves- 
 tigate, their next care is, to lay down some self-evi- 
 dent truths, which may serve as a foundation for 
 their future reasonings. And here; indeed, they pro- 
 ceed with remarkable circumspection, admitting no 
 principles" bui: what flow immediately from their defini- 
 tions, and necessarily force themselves upon a mind in 
 any degree attentive to its precoptioOK Thus a cir- 
 cle is a figure formed* by a right line, moving round 
 some fixed point in the same plane. The fixed point, 
 round which the line is supposed to move, and where 
 one of its extremities terminates, is called the centre 
 *f the circle. The other extremity, which is conceiv- 
 carried round, until it returns to the point 
 wlu out, describes a curve running into 
 
 itself, and termed the circumference. All right lines, 
 drawn from the centre to the circumference, are called 
 radii. From- these definitions compared, geometrici- 
 ans derive this self-evident truth, that the radii of the 
 same circle are all equal one to another. I call it self- 
 evident, because nothing more is required, to. lay it 
 open to the immediate preception of the mind, than an 
 attention. to the ideas. compared. For from the very 
 nature of a circle it is plain, that the circumference is 
 every where distant from the centre, by the' exact 
 length of the describing line ; and that the several ra- 
 dii are in truth nothing more, than one and the same 
 line variously posited within the figure. This short 
 . ription will, -I hope, serve to give some little in- 
 sight into fche manner of deducing mathematical prin- 
 ciples, as v. til as into the nature of that evidence 
 which accompanies them* 
 
 Sec. V ill. ...Propositions divided into Speculative and 
 Practical. 
 And now I proceed to observe, that in all proppsU 
 
124 DUNCAN'S ELEMENTS 
 
 tions we cither affirm or deny some property of the 
 idea that constitutes the subject of our judgment, of 
 v/c maintain that something may be done or effected. 
 The first sort is called speculative propositions, as in 
 the example mentioned above, the radii of the same 
 tircle ore all equal one to another. The others are cal- 
 led practical^ for a reason too obvious to be mention- 
 ed; thus, that a right line maybe drawn from one 
 point to another, is a practical proposition ; inasmuch 
 as it expresses that something may be done. 
 
 Sec. lX....i/iwe Mathematical Principles distinguish* 
 ed into Axioms find Postulates* 
 
 From this twofold consideration of propositions, ari- 
 ses the twofold division of mathematical principles, 
 into axioms and postulates. By an axiom they under- 
 stand any self-evident speculative truth : as, that the 
 whole is greater than its parts : that things equal to 
 tne and the same thing, are equal to one another. But 
 a self-evident practical proposition is what they call a 
 postulate. Such are these of Euclid ; that a finite right 
 line maybe continued directly forwards: that a circle may 
 be described about any centre with any distance. And 
 here we are to observe, that as in an axiom, the 
 agreemeet or disagreement between the subject and 
 predicate, must come under the immediate inspection 
 of the mind; so in a postulate, not only the possibility 
 of the thing asserted must be evident at first view, but 
 also the manner in which it may be effected. But 
 •where this manner is not of itself apparent, the propo- 
 sition comes under the notion of the demonstrable kind, 
 and is treated as such by the geometrical writers. 
 Thus, to draw a line from one point to another, is as- 
 sumed by Euclid as a postulate, because the manner of 
 doing it is so obvious, as to require no previous teach- 
 ing. But then it is not equally evident, how we art 
 to construct an equilateral triangle. For this reason he 
 advances it as a demonstrable proposition, lays down 
 rules for the exact performance, and at the same time 
 proves, that if these rules are followed, the figure will 
 be justly described. 
 
OF LOGIC. 125 
 
 Sec. X;..And demonstrable Propositions into Theo- 
 rems and Problems. 
 This naturally leads me to take notice, that as self- 
 evident truths are distinguished into different kinds, ac- 
 cording asthey are speculative or practical ; so is it al- 
 so with demonstrable propositions. A demonstrable spe- 
 culative proposition is by; mathematicians called a theo- 
 rem. Such is the famous 47th proposition of the first 
 book of the Elements, known by the name of the Pytha- 
 gor'ic theorem, from its supposed inventor, Pythagoras, 
 viz. That in every right-angled triangle, the square des- 
 cribed upon the side subtending the right angle, is equal 
 to both the squares described upon the sides containing 
 the right angle. On the other hand, a demonstrable prac- 
 tical proposition is called a problem ; as where Euclid 
 teaches us to describe a square, upon a given right line* 
 
 Sec. XI. ...Corollaries are obvious adductions from The- 
 orems or Problems. 
 Since I am upon this subject, it may not be amiss to 
 add, that besides the four kinds of propositions already 
 mentioned, mathematicians have also a fifth, known by 
 the name of corollaries. These are usually subjoined to 
 theorems ov problems, and differ f&om them only in this, 
 that they flow from what is there demonstrated, in so 
 obvious a maimer as to discover' tkeir dependence upon 
 the proposition whence they are deduced, almost as sopn 
 as proposed. Thus Euclid having demonstrated, that in 
 every right-lined triangle., all the three angles taken toge- 
 ther are equal to two rigli£ angles ; adds, by way of co- 
 rollary, that all the three angles of any one triangle take% 
 together, are equal to all the three angles of any other 
 triangle, taken together : which is evident at first sight; 
 because in all cases they are equal to two right ones, 
 and things equal to two and the same thing, are equal 
 to one another. 
 
 Sec. XII.,.. Scholia serves the purposes of Annotations 
 
 or a Comment. 
 
 The last thing I shall take notice of, in the practice 
 
 of the mathematicians, is what they call their scholia* 
 
 They are indifferently annexed to dsfmitionsj proposi- 
 
 L 2 
 
126 DUNCAN'S ELEMENTS 
 
 tions, or corollaries ; and answer the same purposes Is 
 annotations upon a classic author. For in them occasion 
 is taken, to explain whatever may appear intricate and 
 obscure in a train of reasoning ; to answer objections ; 
 to teach the application and uses of propositions ; to 
 lay open the original and history of the several disco- 
 veries made in the science ; and in a word, to acquaint 
 us with all such particulars as deserve to be known, 
 whether considered as points of curiosity or profit. 
 
 Sec. XIII This Method of the Mathematicians 
 
 universal^ and a sure guide to Certainty* 
 Thus we have taken a short view of the so much 
 celebrated method of the mathematicians ; which, to 
 any one who considers it with a proper attention, must 
 needs appear universal, and equally applicable in other 
 sciences. They begin with definitions. From, these 
 they deduce their axioms and postulates, which serve 
 as principles of reasoning ; aud having thus laid a firm 
 foundation, advance to theorems and problems, esta- 
 blishing all by the strictest rules of demonstration. The 
 corollaries flow naturally and of themselves. And if 
 any particulars are still wanting to illustrate a subject, 
 or complete the reader's information ; these, that the 
 series of reasoning may not be interrupted or broken, 
 are generally thrown into scholia. In a system of 
 knowledge so uniform and well connected, no wonder 
 if we meet with certainty ; and if those clouds and 
 darknesses, that deface other parts of human science, 
 and bring discredit even upon reason itself, are here 
 scattered and disappear. 
 
 Sec. XIV ....Self evident Truths known by the appa- 
 rent unavoidable Connection between the Subject and 
 Predicate. 
 
 But I shall for the present wave these reflexions, 
 •which every reader of understanding is able to make 
 of himself, and return to the consideration of self-evi- 
 dent propositions. It will, doubtless, be expected, af- 
 ter what has been here said of them, that I should 
 establish some criteria^ or marks, by which they may 
 fcc distinguished. But I frankly own my inability in 
 
OF LOGIC. 127 
 
 this respect, m not being able to conceive any thing in 
 them more obvious and striking, than that self-evidence 
 which constitutes their very nature. All I have there- 
 fore to observe on this head, is, that we ought to make 
 it our first care, to obtain clear and determinate ideas. 
 When afterwards we come to compare these together, 
 if we perceive between any of them a necessary and 
 unavoidable connection, insomuch that it is impossible 
 to conceive them existing asunder, without destroying 
 the very ideas compared ; we may then conclude, that 
 the proposition expressing this relation is a principle, 
 and of the kind we call self-evident. In the example 
 mentioned above, the radii of the same circle are all 
 equal between themselves, this intuitive evidence shines 
 forth in the clearest manner ; it Ugjng impossible for 
 any one, who attends his own ideas, nit to perceive the 
 equality here asserted. For as tlie circumference it 
 every where distant from the centre by the exact 
 length of th> describing line ; the radii drawn from 
 the centre of the circumference, being severally equal 
 to this one line, must needs also be equal among them- 
 selves. If we suppose the radii unequal, we at the same 
 time suppose the circumference more distant from the 
 centre in some places than in others ; from whichsup- 
 position, as it would exhibit a figure quite different 
 from a circle, we see there is no separating the predi- 
 cate from the subject in this proposition, without de- 
 stroying the idea in relation to which the comparison 
 was made. The same thing will be found to hold in 
 all our other intuitive perceptions, insomuch that we 
 may establish this as an universal criterion^ whereby 
 to judge of, and distinguish them. I would not, how- 
 ever, be understood to mean, as if this ready view of 
 the unavoidable connection between some ideas was 
 any thing really different from self-evidence. It is, 
 indeed, nothing more than the notion of self-evidence? 
 si little unfolded, and as it were laid open to the inspec- 
 tion of the mind. Intuitive judgments need no other 
 distinguishing marks, than that brightness which sur- 
 rounds them ; in like manner as light discovers itself 
 by its owe f resence ; and the splendor it universally 
 
128 DUNCAN'S ELEMENTS 
 
 ^s. But I have said enough of self-evident pro- 
 '' lis, and shall therefore now proceed to those of 
 
 diffuses. 
 
 'positions, and shall therefore now proceed to those of 
 the demonstrable kind; which, being gained in conse- 
 quence of reasoning, naturally leads us to the third 
 part of logic^wliere this operation of the understanding 
 is explained. 
 
 IJOOK III. 
 
 V -- Ttt 
 
 
 OF REASONING. 
 
 tRbap*' 1. 
 
 OF REASONING IN GENERAL, AND THE 
 PARTS OF WHICH IT CONSISTS. 
 
 Sec, \..,*Remote Relations discovered by means of in* 
 
 termediate Ideas. 
 
 Wl 
 E have seen how the mind proceeds in furnish- 
 ing itself with ideas, and framing intuitive 
 perceptions. Let us next enquire into the manner o£ 
 discovering those more remote relations, which, lying 
 at a distance from the understanding, are not to be 
 traced but by means of a higher exercise of its powers. 
 It often happens in comparing ideas together, that 
 their agreement f or. disagreement. cannot be discerned 
 at first view, especially if they are of such a nature, as 
 not to admit of an exact application one to another. 
 When, for instance, we compare two figures of a dif- 
 ferent make, in order to judge of their equality or in- 
 equality, it is plain, that by barely considering the £• 
 
OF LOGIC. 129 
 
 jure* themselves, we cannot arrive at an exact deter- 
 mination ; because, by reason of their disagreeing 
 forms, it is impossible so to put them together, as that 
 their several parts shall mutually coincide. Here the» 
 it becomes necessary to look out for some third idea f 
 i that will admit of such an application as the present 
 •ase requires ; wherein if we succeed, all difficulties 
 vanish, and the relation we are in quest of may be 
 traced with ease. Thus right-lined figures are all re- 
 ducible to squares, by means of which we can measure 
 their areas, and determine exactly their agreement or 
 disagreement in point of magnitude. 
 
 Sec. II.... jT^/j manner of arriving at Truth andterm* 
 ed Reasoning. 
 If now it be asked, how any third idea can serve t# 
 discover a relation between two others ; I answer f 
 by being compared severally with these others ; for 
 such a comparison enables us to see how far the ideas f 
 with which this third is compared, are connected or 
 disjoined between themselves. In the example men* 
 tioned above, of two right-lined figures, if we com- 
 pare each of them with some square whose area il 
 known, and find the one exactly equal to it, and the 
 other less by a square-inch greai-t than that of the se- 
 cond. This manner of determining the relation be- 
 tween any two ideas, by the invention of some third 
 with which they may be compared, is that which we 
 call reasoning, and indeed the chief instrument, by 
 which we push on our discoveries, and enlarge our 
 knowledge. The great art lies, in finding out such in- 
 termediate ideas, a3, when compared with the others 
 in the question, will furnish evident and known truths ; 
 because, as will afterwards appear, it is only by means 
 of them, that we arrive at the knowledge of what is 
 Jaidden and remote. 
 
 Sec. III. ... The parts that constitute an Act of Reason* 
 ing and a Syllogism, 
 From what has been said, it appears that every act 
 of reasoning necessarily includes three distinct judg- 
 ments j two, wherein tbe ideas, whose relatign trfc 
 
130 DUNCAN'S ELEMENTS 
 
 "want to discover, are severally compared with, the mid- 
 ^dieidea, and a third, wherein they are themselves con- 
 nected or disjoined according to the result of that com- 
 parison. Now as in the second part of logic, our 
 judgments when put into words, were called proposi- 
 tions... .so here, in the third part, the expressions, of our 
 t reasonings are termed syllogisms. And hence it fol- 
 lows, that as every act of reasoning implies three se- 
 veral judgments, so every syllogism must include three 
 distinct propositions. When a reasoning is thus pil-t 
 into words, and appears in form of a syllogism, the 
 intermediate idea t made use of to discover the agree- 
 ment or disagreement we search for, is called the mid- 
 dle term ; and the two ideas themselves, with which 
 this third is compared/ go by the name of the extremes. 
 
 Sec. IV, ...Instance, Man and Accountableness. 
 
 But as these things are best illustrated by examples ; 
 •let us, for instance, set ourselves to enquire, whether 
 men are accountable for their actions. As the relation 
 •between the ideas of man and account alien ess Route's 
 not within the immediate view of the mind, our fhst 
 care must be, to find out some third idea, that will ena- 
 ble us the more easily to discover and trace it. A very 
 small measure of rerlexionis sufficient to. infirm us, 
 that no creature can be accountable for his actions, un- 
 less we suppose him capable of distinguishing the' good 
 from the bad ; that is unless we suppose him -posst 
 of reason. Nor is this alone suiticient. For .what 
 "would it avail him, to know gobd \ actions, if he 
 
 -had no freedom of choice, nor could avoid the o.^e, and 
 pursue the other ? Hence it o'efcomes necessary to I 
 in both considerations in the presenVense. It is fit 
 same time equally apparent, that wherever there is 'this 
 ability of distinguishing good from bad action?. 
 suing the one and avoiding the other,' there "also a - 
 ture is accountable. We, have then got a xy. 
 "with which account a^icness is inseparably connected, viz. 
 reason and liberty ; which are here to-be considered as 
 making up. one complex conception. Let us now take 
 this middle idea, and compare it with tlw otkw fW i* 
 
OF LOGIC. 1st 
 
 the question, viz. man, and we all know by experience 
 that it may be affirmed of him. Having thus, by means 
 of the intermediate idea, formed two several judgments, 
 viz. that man is possessedof reason and liberty ; and that 
 reason and liberty imply accountableness ; a third obvious- 
 ly and necessarily follows, viz. that man is accountable 
 for his actions. Here then we have a complete act of rea- 
 soning, Id which, according to what has been already- 
 observed, there are three distinct judgments ; two that 
 may be stiled previous, inasmuch' as they lead to the 
 other, and arise from comparing the middle idea with 
 the two ideas in the question ; the third is a consequence 
 of these previous acts, and flows from combining the ex- 
 treme ideas between themselves. If i\ow we put this rea- 
 soning into words, it exhibits what logicians term a syl* 
 logism, and, when proposed in due form, runs thus : 
 
 Every creature possessed of reason and liberty is account** 
 •ble for his actions. 
 . Man is a creature possessed of reason and liberty. 
 
 Therefore man is accountable forh,is actions. 
 
 Sec, V.... Premises, conclusion, extremes, middle term* 
 In this syllogism we may observe, that there are three 
 several propositions, expressing the three judgments 
 implied in the act of reasoning, and so disposed as to 
 represent distinctly what passes within the mind, in 
 tracing the more distant relations of its ideas. The two 
 first propositions answer the two previous judgments in 
 reasoning, and are called the premises, because they 
 are placed before the other. The third is termed the 
 conclusion, as being gained in consequence of what was 
 asserted in the premises. We are also to remember, 
 that the terms expressing the two ideas whose relation 
 we enquire after, as here man and accountableness, are in 
 general, called the extremes; and that the intermediate 
 idea, by means of which, the relation is traced, viz. a crea~ 
 ture possessed of reason and liberty, takes the name 
 of the middle term* Hence it follows, that by Xhepre* 
 raises of a syllogism, we are always to understand the 
 two propositions,- where the middle term is severally* 
 compared with extremes ; for these constitute the pre- 
 vious judgments, whence the truth we are in quest of 
 
l$2 DUNCAN'S ELEMENTS 
 
 li by reasoning deduced. The conclusion is that ether 
 proposition, in which the extremes themselves are 
 joined or separated, agreeably to what appears upon the 
 above comparison. All this is evidently seen in the fore- 
 going syllogism, where the two first propositions, which 
 represent the premises, and the third, which makes the 
 conclusion, are exactly agreeable to the definitions here 
 given. 
 
 Sec VI.... Major and Minor Term y Major and Minor 
 Proposition* 
 
 Before we take leave of this article, it will be far- 
 ther necessary to observe, that as the conclusion is 
 made up of the extreme terms of the syllogism ; so 
 that extreme, which serves as the predicate of the con* 
 elusion, goes by the name of the major term : the 
 other extreme, which makes the subject in the same 
 proposition, is called the minor term. From this dis- 
 tinction of the extremes, arises also a distinction be- 
 tween the premises, where these extremes are several- 
 ly compared with the middle term. That proposition, 
 which compares the greater extreme, or the predicate 
 of the conclusion, with the middle term, is called the 
 major proposition : the other, wherein the same mid- 
 dle term is compared with the subject of the conclu- 
 sion, or lesser extreme, is called tne minor proposition. 
 All this is obvious from the syllogism already given, 
 where the conclusion is, man is accountable for his ac- 
 tions. For here the predicate, accountable for his 
 actions, bsing connected with the middle term in the 
 first of the two premises. Every creature possessed of 
 reason and liberty is accountable for his actions, gives 
 what we sail the major proposition. In the second of 
 the premises, man, is a creature possessed of reason and 
 liberty, we find the lesser extreme, or subject, of the 
 conclusion, viz. man, connected with the same middle 
 term, whence it is known to be the minor proposition* 
 I shall only add, that when a syllogism is proposed in 
 -due form, the major proposition is always placed first, 
 the minor next, and the conclusion last, according aa 
 wc have done in tkat offered abovc t 
 
OF LOGIC. 133 
 
 S^c. VII.., •Judgment and Proposition, Reasoning 
 and Syllogism distinguished. 
 Having thus cleared the way, by explaining. suck 
 terms, as we are likely to have occasion for in the pro- 
 gress of this treatise ; it may not be amiss to observe, . 
 that tho' we have carefully distinguished between the 
 act of reasoning, and a syllogisjn, which is no more 
 than the expression of it, yet common language is not 
 so critical on this head ; the term reasoning being 
 promiscuously used, to signify either the judgments 
 of the mind, as they follow one another in train, 
 or the propositions expressing these judgments. 
 Nor need we wonder that it is so, inasmuch as our • 
 ideas, and the terras appropriated to them, are so con- 
 nected by habit and use, that our thoughts fall as it 
 were spontaneously into language, as fast as they 
 arise in the mind ; so that even in our reasonings 
 within ourselves, ve are not able wholly to lay aside. - 
 words. But notwithstanding this strict connexion be- 
 tween mental and verbal reasoning, if I maybe allow- 
 ed that expression, I thought it needful here to dis- 
 tinguish them, in order to give a just idea of the man- 
 ner of deducing one truth from another. While the 
 mind keeps the ideas of things in view, and combines 
 its judgments according to the real evidence attending 
 them, there is no great danger of mistake in onr rea- 
 sonings ; because we carry our conclusions no farther 
 than the clearness of our perceptions warrants us. 
 But where we make use of words, the case is oftea 
 otherwise ;' nothing being more common,^ than to let 
 them pass without attending to the ideas they repre- 
 sent ; insomuch that we frequently combine expres- 
 sions, which upon examination appear to have no de? 
 terminate meaning. Hence it greatly imports us.t© 
 distinguish between reasoning and syllogism ; and to 
 take care, that the one be in all cases the true and just 
 representation of the other. However, as I am un- 
 willing to recede too far from the common forms of 
 speech, or to multiply distinctions without necessity, I 
 shall henceforward consider propositions as representing 
 the real judgments of the mind, and syllogisms as the 
 
 M 
 
134 DUNCAN'S -ELEMENTS 
 
 true copies of our reasonings ; which indeed they ought 
 always to be, and undoubtedly always will be',' to men 
 ■who think justly, and are desirous of arriving at truth. 
 Upon this supposition there will be no danger in using 
 the words judgment and proposition promiscuously ; or 
 in considering reasoning as either a combination of va- 
 rious judgments, or of the propositions expressing them ; 
 because, being the exact copies one of another, the re- 
 sult will be in all cases the same. Nor is it a small ad- 
 vantage, that we can thus conform to common speech, 
 without confounding our ideas, or running into ambi- 
 guity. By this means we bring ourselves upon a level 
 with other men, readily apprehend the meaning of their 
 expressions*, and can with ease convey our own notions 
 •and sentiments into their minds. 
 
 Sec. VIII... ./« a single Act of Reasonings the Premi- 
 ses must be intuitive Truths. 
 These things premised, we may in the general define 
 re*asoning to be an act or operation of t lie mind, dedu- 
 cing some unknown proposition, from other previous ones 
 that are evident and known. These previous proposi- 
 tions, in a simple act of reasoning, are only two in 
 number; and it is always required that they be of 
 themselves apparent to the understanding, insomuch 
 that we assent to and perceive the truth of them as 
 soon as proposed. In the syllogism given above, the 
 premises are supposed to be self-evident truths, other- 
 wise the conclusion could not be inferred by a single 
 act of reasoning. If, for instance, in the major, every 
 creature possessed of reason and liberty is accountable 
 for. his actions, the connexion between the subject and 
 predicate could not be perceived by a bare attention 
 to the ideas themselves ; it is evident, that this propo- 
 sition would no less require a proof, than the conclu- 
 sion deduced from it. In this case, a new middle term 
 must be sought for, to trace the connexion here sup- 
 posed ; and this of course furnishes another syllogism, 
 by which* having established the proposition in ques- 
 tion, we are then, and not before, at liberty to use it 
 in any succeeding train of reasoning. And should it 
 so happen, that in this second essay, there was still 
 
OF LOGIC. 135 
 
 some previous proposition whose truth did not appear 
 at first sight ; we must then have recourse to a third 
 syllogism, in order to lay open that truth to the mind ; 
 because so long* as the premises remain uncertain, the 
 conclusion built upon them must be so too. When 
 by conducting our thoughts in this manner, we at last 
 . arrive at some syllogism, where the previous proposi- 
 tions are intuitive truths ; the mind then rests in full 
 security, as perceiving that the several conclusions it 
 has passed through, stand upon the immovable found- 
 ation of self-evidence, and, when traced to their 
 source, terminate in it. 
 
 Sec. IX.. ..Reasoning, in the highest Exercise of ;V, 
 only a Concatenation of Syllogisms. 
 
 We see, therefore, that in order to infer a conclu- 
 sion by a single act of reasoning, the premise? must 
 be intuitive propositions. Where they are not, pre- 
 vious syllogisms are required,, in which case reasoning 
 becomes a complicated act, taking in a variety of suc- 
 cessive steps. This frequently happens in tracing* the 
 more remote relations of our ideas, where many mid- 
 dle terms being called in, the conclusion cannot be 
 made out, but in consequence-of a series of sy41ogi$m$ 
 following one another in train. But although in this 
 concatenation of propositions, those that form the pre- 
 -mises of the last syllogism, are often considerably re- 
 moved from self-evidence ; yet if we trace the reason- 
 ing backwards, we shall find them the conclusions of 
 / previous syllogisms, whose premises approach nearer 
 and nearer to intuition, in proportion "as 'we advance, 
 and are found at last to terminate in it. And if after 
 having thus unravelled a demonstration, we take it the 
 contrary way, and observe how the mind, setting out 
 with intuitive perceptions, couples them together to 
 form a conclusion — how, by introducing this conclu- 
 sion into another syllogism, it still advances one step 
 farther ;,and so proceeds, making every new discovery- 
 subservient to its future progress. — we shall then per- 
 ceive clearly., that reasoning, in the highest exercise 
 of that faculty, is no more than an orderly combina- 
 
136 DUNCAN'S ELEMENTS 
 
 tibn of those simple acts, which we have already so 
 fully explained. The great art lies, in so adjusting 
 ©ur syllogisms one to another, that the propositions 
 severally made use of, as premises, may be manifest 
 consequences of what goes before." For as by this 
 jaieaHS, every conclusion is deduced from known and 
 established truths, the very last in the series, how far 
 soever we carry it, will have no less certainty attend- 
 ing it, . than the original intuitive perceptions then*-- 
 selves, in which the whole chain of syllogisms takes its 
 rise. 
 
 Sec. X.... Requires intuitive Certainty in every Step of 
 the Progression. 
 Thus we -see, that reasoning, beginning with first 
 principles, rises gradually from one judgment to ano- 
 ther, and connects them in such manner, that every 
 stage of the progression brings intuitive certainty 
 along with it. And now at length we may clearly un- 
 derstand the definition given above, of this distinguish- 
 ing faculty of the human mind. Reason, we have said, 
 is the ability of deducing unknown truths, from prin- 
 ciples or propositions that are already known. This 
 evidently appears, by the foregoing account, where 
 ; we see, that no proposition is admitted into a syllo- 
 gism, to serve as one of the previous judgments on 
 which the conclusion rests, unless it is itself a known 
 and established truth, whose connexion with self-evi- 
 dent principles has been already traced. 
 
 Sec. .XI ... .Self-evident Truths, the ultimate Founda- 
 tion of all Science and Certainty. 
 There is yet another observation which naturally of- 
 fers itself, in consequence of the above detail ; viz. 
 that all the knowledge acquired by reasoning, how far 
 soever we carry our discoveries, is still built upon our 
 intuitive perceptions. Towards the end of the last 
 part, we .divided propositions into self-evident and de- 
 monstrable, and represented those of the self-evident 
 kind, as the foundation- on which the whole super- 
 structure of human science rested. _ Th'is doctrine is 
 now abundantly confirmed by what has been delivered 
 
OF LOGIC. 1ST 
 
 in the present chapter. We have found, that every 
 discovery of human reason, is the consequence of a 
 train of syllogisms, which, when traced to their source, 
 always terminate in self-evident perceptions. When 
 the mind arrives at these primitive truths, it pursues 
 not its enquiries farther, as well knowing, that no 
 evidence can exceed that which flows from an imme- 
 diate view of the agreement or disagreement between 
 its ideas. And hence it is, that in unravelling any part 
 of knowledge, in order to come at the foundation on 
 "which it stands ; intuitive truths are always the last 
 resort of the understanding, beyond which it aims not 
 to advance, but possesses its notions in perfect security, 
 as having now reached the very spring and fountain of 
 all science and certainty. 
 
 Cfjap. IL 
 
 OF THE SEVERAL KINDS OF REASONING, AND 
 FIRST OF THAT BY WHICH WE DETERMINE 
 THE GENERA AND SPECIES OF THINGS. 
 
 Sec. I.... Reasoning Twofold, 
 
 WE have endeavoured, in the foregoing chapter, 
 to give as distinct a notion as possible, of rea- 
 soning, and of the manner in which it is conducted. Let 
 us now enquire a little into the discoveries made by 
 this faculty, and what those ends are, which we have 
 principally in view in the exercise of it. All the aims 
 of human reason may^ in the general, be reduced* to 
 these two : 1. To rank things under those universal 
 ideas to which they truly belong ; and 2. To ascribe to 
 them their several attributes and properties, in conse- 
 quence of that distribution. 
 
 Sec. II.. ..The first kind regards the Genera and Spe- 
 cies of Things. 
 First, then I say, that one great aim of human rea- 
 son is, to determine the genera and species of things. 
 We have seen, in the^ first part of this treatise, how 
 .the mind proceeds in framing general ideas. We have 
 also seen, ia the second part, how, by means of these 
 M 2 
 
138 DUNCAN'S ELEMENTS 
 
 general ideas, we come by universal propositions. Now 
 as in these universal propositions, we affirm some pro- 
 perty of a genus or species, it is plain, that we cannot 
 apply this property to particular objects, till we have 
 first, determiued, whether they are comprehended un- 
 der that general idea, of which the property is affirm- 
 ed. Thus there are certain properties belonging to all 
 even numbers, w + hich nevertheless cannot be applied to 
 any particular nurxber. until we have first discovered 
 it to be of the species expressed by that general name. 
 Hence reasoning begins with referring things to their 
 several divisions and classes in the scale of our ideas ; 
 and as these divisions are all distinguished by pe- 
 culiar names, we hereby learn to apply the terms ex- 
 pressing general conceptions, to such particular 1 objects, 
 as come under our immediate observation. 
 
 Sec. IIIf.TJie Steps by which we arrive at Conclu* 
 sions of this sort. 
 
 Now in order to arrive at these conclusions, by which 
 ihe several objects of perceptions are brought under 
 general names, two things are manifestly necessary. 
 Fiist, that we take a view, of the idea itself denoted by 
 that general name, and carefully attend to the distin- 
 guishing marks which serve to characterize it. Se- 
 condly, that we compare this idea with the object un- 
 der consideration, observing diligently wherein they 
 agree or differ. If the idea is found to correspond 
 with the particular object, we then, without hesitation, 
 apply the general name ; but if no such correspondence 
 intervenes, the conclusion must necessarily take a con- 
 trary turn. Let us, for instance, take the number 
 eight, and consider by what steps we are led to pro- 
 nounce it an even number. First then we call to mind 
 •the idea signified by the expression, an even number^ 
 viz. that it is a number divisible into two equal parts* 
 We 'then compare this idea with the number eight, and 
 finding Jthem manifestly to agree, see at once the ne- 
 cessity of admitting the conclusion. These several 
 judgments therefore, transferred into language, and rt» 
 fUrctd to th« fcr» of a syilogUia; appear ikus i 
 
OF LOGIC. 130 
 
 Every number that may be divided into two equal parts* 
 is an even number 
 The number eight may be divided into two equal parts* 
 Therefore the number eight, is an even number. 
 
 Sex IV.... Those steps always followed, though in fa* 
 miliar cases we do not always attend to them. 
 
 ' I have made choice of this example, not so much for 
 the sake of the conclusion, which is obvious enough 
 and might have been obtained without all that parad© 
 of words ; but chiefly because it is of easy compre- 
 hension, and serves, at the same time distinctly to ex- 
 hibit the form of reasoning by which the understand- 
 ing' conducts itself in ,all instances of this kind. > And 
 here it may be observed, that where the general idea, to 
 which particular objects are referred, is very familiar 
 to the mind, and frequently" in view ; this reference, 
 and the application of the general name, seem to be 
 made without any apparatus of reasoning. When we 
 see a horse 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, suggest- 
 ing it instantaneously to the mind. We are not, 
 however, to imagine on this account, that the under- 
 standing departs from the usual rules of just thinking. 
 A frequent repetition of acts begets a habit ; and ha- 
 bits are attended with a certain promptness of execution, 
 that prevents our observing the several steps and gra- 
 dations, by which any course of action is accomplish- 
 ed. But in other instances, where we judge not by 
 precontracted habits, as when the general idea is very 
 complex, or less familiar to the mind ; we always pro- 
 'ceed according to the form of reasoning established 
 above. A goldsmith, for instance, who is in doubt as 
 to any piece of metal, whether it be of the species cal- 
 led gold, first examines its properties, and then com- 
 paring them with the general idea signified by that 
 name, if he find a perfect correspondence, no longer 
 hesitates under what class of metals to rank it. Now 
 what is this, but following step by step those rules ol 
 reasoning, which we have before laid doirn as the star>J : 
 
140 DUNCAN'S ELEMENTS 
 
 ards, by which to regulate our thoughts in all conclu- 
 sions of this kind ? 
 
 Sec. V.....27j<? Great Importance of this Branch of 
 Reasoning, 
 Nor let be imagined, that our researches here, be- 
 cause in appearance bounded to the imposing of gene- 
 ral names upon particular objects, are therefore trivi- 
 al and of little consequence. Some of the most consi- 
 derable debates among mankind, and such too, as 1 
 nearly regard their lives, interest, and happiness, turn 
 wholly upon this article. Is it not the chief employ- 
 ment of our several courts of judicature, to determine, 
 in particular instances, what is law, justice, and equi- 
 ty ? Of what importance is it, in many cases, to decide 
 aright, whether an action shall be termed murder or 
 •manslaughter ? We see, that no less than the lives and 
 fortunes of men depend often upon these decisions. 
 The reason is plain. Actions, when once referred to a 
 general idea, draw after them all that may be affirmed 
 of that idea ; insomuch that the determining the species 
 of actions, is all one with determining what proportion 
 of praise or dispraise, commendation or blame, &c. 
 ought to follow them. For as it is allowed that murder 
 deserves death, by bringing any particular action under 
 the head of murder, we of course decide the punishment 
 due to it. 
 
 Sec. VIm.i^ the exact observance of it practised by 
 Mathematicians. 
 * But the great importance of this branch of reason- 
 ing, and the necessity of care and circumspection, in 
 referring particular objects to general ideas, is still far- 
 ther evident from the practice of the mathematicians. 
 Every one who has read Euclid, knows, that he fre- 
 quently requires us to draw lines through certain points, 
 and according' to such and such directions. The fi- 
 gures thence resulting are often squares, parallelo- 
 grams, or rectangles. Yet Euclid never supposes this 
 from their bare appearance, but always demonstrates it 
 upon the strictest principles of geometry. Nor is the 
 inethod he takes, ia any thing diffeixttt.fro;ni that des* 
 
OF LOGIC. 141 ' 
 
 eribed above. Thus, for instance, having- defined a 
 square to be a figure bounded by four equal sides, join- 
 ed together at right angles ; when such a figure arises 
 in any construction previous to the demonstration of a 
 proposition, he yet never calls it by that name, until he 
 has shown that the sides are equal, and all its angles 
 right ones. Now this is apparently the same form of 
 reasoning 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 syllogism. I shall only add, 
 that when Euclid has thus determined the species of 
 any figure, he is then, and not before, at liberty to as- 
 cribe to it all the properties already demonstrated of 
 that figure, and thereby render it subservient to the 
 future course of his reasoning. 
 
 Sec. VII.,*.Fixed and invariable Ideas, with a steady 
 application of Names, renders this part of Know- 
 ledge both easy and certain. 
 
 Having thus sufficiently explained the rules by whick 
 we are to conduct ourselves, in ranking particular ob- 
 jects under general ideas, and show their conformity to 
 the practice and manner of the mathematicians ; it re- 
 mains only to observe, that the true way of rendering 
 this part of knowledge both easy and certain, is, by- 
 habituating ourselves to clear and determinate ideas, 
 and keeping them steadily annexed to their respective 
 names. For as all our aim is, to apply general words 
 aright, if these words stand for invariable ideas, that 
 are perfectly known to the mind, and can be readily 
 distinguished upon occasion, there will be little danger 
 of mistake or error in our reasonings. Let us suppose, 
 that by examining any object, and carrying our atten- 
 tion successively from one part to another, we have "ac- 
 quainted ourselves with the several particulars observa- . 
 ble in it. If among these we find such as constitute 
 some general idea, framed and settled beforehand by 
 the understanding and distinguished by a particular 
 name^; the resemblance, thus known and perceived, 
 necessarily determines the species of the object, and 
 thereby gives it a right to tie jaame by whick that spc« 
 
142 DUNCAN'S ELEMENTS 
 
 ties is called. Thus, four equal sides, joined together 
 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 par- 
 ticular figure a square^ until it appears to have these 
 several conditions ; and contrarily, wherever a figure 
 is found with these conditions, it necessarily takes the 
 name of a square* The same will be found to hold in 
 all our other reasonings of this kind; where nothing 
 can create any difficulty but the want of settled ideas. 
 If, for instance, we have not determined within our- 
 selves, the precise notion denoted by the word man- 
 slaughter* it will be impossible for us to decide, whe- 
 ther any particular action ought to bear that name : 
 because, however nicely we examine the action itself, 
 yet being strangers to the general idea with which it 
 is to be compared, we are utterly unable to judge of 
 their agreement or disagreement. But if we take care 
 to remove this' obstacle,. and distinctly trace the two 
 ideas under consideration, all difficulties vanish, and 
 the resolution becomes both easy and certain. 
 
 Sec. VIII By such a Conduct ; , Certainty and De- 
 
 moristration might be introduced into other Parts of 
 Knowledge as well as Mathematics* 
 
 Thus we see of what importance it is, towards the 
 improvement and certainty of human knowledge, that 
 we accustom ourselves to clear and determinate ideas, 
 and a steady application of words. Nor is this so easy a 
 task as some may, perhaps, be apt to imagine ; it re- 
 quiring both a comprehensive understanding, and great 
 command of attention, to settle the precise bounds of 
 our ideas, when they grow to be very complex, and 
 include a multitude of particulars. Nay, and after 
 these limits are duly fixed, there is a certain quickness 
 of thought and extent of mind required, towards keep- 
 ing the several parts in view, that in comparing our 
 ideas one with another, none of them may -be over- 
 looked. Yet ought not these difficulties to discourage 
 us ; though great, they arc not un surmountable, and 
 tiic advantages arising from success will amply recom- 
 
OF LOGIC. 143 
 
 pence our toil. The certainty and easy application of 
 mathematical knowledge is wholly owing to the exact 
 observance of this rule. And I am apt to imagine, 
 that if we were to employ the same care 4 about all our 
 other ideas, as mathematicians have done about those 
 of. number and magnitude, by forming them into ex- 
 act combinations, and distinguishing these combina- 
 tions by particular names, in order to keep them steady 
 and invariable ; we would soon have it in our power 
 to introduce certainty and demonstration into other 
 parts of human knowledge. 
 
 ctfmp, in. 
 
 OF REASONING AS IT REGARDS THE POWERS 
 AND PROPERTIES OF THINGS, AND THE RE- 
 LATIONS OF OUR GENERAL IDEAS. 
 
 Sec. I... .The Distinction of Reasonings as it regards 
 tlie Sciences, and as it concerns common Life. 
 
 WE come now to the second great end which men 
 have in view in their reasonings, namely, the 
 discovering and ascribing to things their, several attri- 
 butes and properties. And here it will be necessary to 
 distinguish between reasoning, as it regards the sci- 
 ences, and as it concerns common life. In the sciences, 
 our reason is employed chiefly about universal truths, 
 it being by them alone that the bounds of human 
 knowledge are enlarged. Hence the division of things 
 into various classes, called otherwise genera and spe- 
 cies. For these universal ideas, being set up as the re- 
 presentatives of many particular things, whatever is 
 affirmed of them, may also be affirmed of all the indi- 
 viduals to which they belong. Murder, for instance, is 
 a general idea, representing a certain species of human 
 actions. Reason tells us, that the punishment due to it 
 is death. Hence every particular action coming under 
 the notion of murder, has the punishment of death allot- 
 ted to it. Here then we apply the general truth to some 
 obvious instance, and this is what properly constitutes 
 •the reasoning- of common life. For men in their ojrdi? 
 
14-4 DUNCAN'S ELEMENTS 
 
 nary transactions and intercourse one with another, 
 have for the most part to do only with particular ob- 
 jects. Our friends and relations, their characters and 
 behaviours, the constitution of the several bodies that 
 surround us, and the uses to which they may be appli- 
 ed, are what chiefly engage our attention. In all these 
 we reason about particular things j and the whole re- 
 sult of our reasoning is, the applying the general truths 
 of the sciences to the ordinary transactions of human 
 life. When we see a viper, we avoid it. Wherever 
 we have occasion for the forcible action of water, to 
 move a body that makes considerable resistance, we 
 take cave to convey it in such a manner, that it shall 
 fall upon the object with impetuosity. Now all this 
 happens, in consequence of our familiar and ready ap- 
 plication of these two general truths : the bite of a vi- 
 per is mortal : water falling on a body with impetuosi- 
 ty , acts very forcibly towards setting it in motion. In 
 like manner, if we set ourselves to consider any parti- 
 cular character, in order to determine the share of 
 praise or dispraise that belongs to it, our great con- 
 cern is, to ascertain exactly the proportion of virtue 
 • and vice. The reason is obvious. A just determina- 
 tion, in all cases of this kind, depends entirely upon 
 • an application of these maxims of morality: virtuous 
 .actions deserve praise ; vicious actions deserve blame. 
 
 Sec. II.... The Steps by which we proceed in the Reason- 
 ing of common Life. 
 
 Hence it appears, that reasoning, as it regards com- 
 mon life, is no more than the ascribing the general pro- 
 perties of things to those several objects with which 
 we are immediately concerned, according as they are 
 found to be ot that particular division or class tor 
 which the properties belong. The steps, then, by which 
 we proceed, are manifestly these. First, we refer the 
 object under consideration to some general idea or 
 class of things. We then recollect the several attri- 
 butes of that general idea ; and, lastly, ascribe all 
 those attributes to the present object. Thus in consi- 
 dering the character of Sempronius } if we find it to be 
 
OF LOGIC. 145 
 
 of the kind called virtuous ; when we at the same time 
 reflect, that a virtuous character is deserving of esteem, 
 it naturally and obviously follows, that Sempronius is 
 so too. These thoughts put into a Syllogism^ in or- 
 der to exhibit the form of reasoning here required runs 
 thus : 
 
 Every virtuous man is worthy of esteem., 
 Sempronius is a virtuous man : 
 Therefore Sempronius is worthy of esteem. 
 
 Sec. III.... The Connexion and Dependence of the tivt- 
 grand Branches of Reasoning one upon another. 
 By this* syllogism it appears, that before we affirm 
 any thing of a particular object, that object must be 
 referred to some general idea. Sempronius is pronounced 
 worthy of esteem, only in consequence of his being a 
 virtuous man, or coming under that general notion. 
 Hence we see the necessary connexion of the various 
 parts of reasoning, and the dependence they have one . 
 upon another. The determining the genera and spe- 
 cies of things is, as we have said, one exercise of hu- 
 man reason ; and here we find that this exercise is the 
 first in order, and previous to the other, which con- 
 sists in ascribing to them their powers, properties, ancl 
 relations. But when we have taken this previous step,' 
 and brought particular objects under general names ; 
 as the properties we ascribe to them are no other than- 
 those of the general idea, it is -plain, that in order to a 
 successful progress in this part of knowledge, we must 
 thoroughly acquaint ourselves with the several rela- 
 tions and attributes of these our general ideas. When 
 this is done, the other part will be easy, and require 
 scarce any labour of thought, as being no more than 
 an application of the general form of reasoning repre- 
 sented in the foregoing syllogism. Now, as we have 
 already sufficiently shown, how we are to proceed in 
 determining the genera and species of things, which 
 as we have said, is the previous step to this second 
 branch of human knowledge ; all that is farther want- 
 ing to a due explanation of it is, to offer some consi- , 
 derations, as to the manner of investigating the ge- 
 neral relations of our ideas. This is the highest exer* 
 N 
 
146 DUNCAN'S ELEMENTS 
 
 cise of the powers of the understanding, and that by- 
 means whereof, we arrive at the discovery of univer- 
 sal truths ; insomuch that our deductions in this way, 
 constitute that particular species of reasoning, which, 
 we have before said, regards principally the sciences. 
 
 Sec. IV....TW0 things required to make a good Rea- 
 sorter. 
 But that we may conduct our thoughts with some 
 order and method, we shall begin with observing, that 
 the relations of our general ideas are of two kinds. 
 Either such as immediately discover themselves, upon 
 comparing the ideas one with another; or such, as be- 
 ing more remote and distant, require art and contriv- 
 ance to bring them into view. The relations of the 
 €rst kind, furnish us with intuitive and self-evident 
 truths : those of the second are traced by reasoning, 
 and a due application of intermediate ideas. It is of 
 this last kind that we are to speak here, having dis- 
 patched what was necessary with regard to the other 
 in the second part. As therefore in tracing the more 
 distant relations of things, we must always have re- 
 course to intervening ideas, and are more or less suc- 
 cessful in ourrescarches, according to our acquaintance 
 with these ideas, and ability of applying them ; it is 
 evident, that to make a good reasoner, two things are 
 principally required. First, an extensive knowledge 
 of those intermediate ideas by means of which things 
 may be compared one with another. Secondly, the skill 
 and talent of applying them happily, in all particular 
 instances that come under consideration. 
 
 Sec. V... .First, an extensive Knowledge of intermedi- 
 ate Ideas. 
 * Eirst, I say, that in order to our successful progress 
 in reasoning, we must have an extensive knowledge of 
 those intermediate ideas by means of which things may 
 be compared one with another. For as it is not every 
 idea that will answer the purpose of our enquiries, but 
 such only as are peculiarly related to the objects aboi.it 
 which we reason, so as by a comparison with them, to 
 fornish evident and known truths t nothing is mbit 
 
OF LOGIC. 24* 
 
 apparent, than that the greater variety of conception* 
 we can call into view, the more likely we are to find 
 some among them that will help us t6 the truths here 
 required. And indeed it is found to hold in experiene, 
 that in proportion as we enlarge our view of things, 
 and grow acquainted with a multitude of different ob» 
 jects, the reasoning quality gathers strength. For by 
 extending our sphere of knowledge, the mind acquires 
 a certain force and penetration, as being accustomed 
 to examine the several appearances of its ideas, and 
 observe what light they cast one upon another. 
 
 Sec. VI.... To excell in any one Branch of Learning, 
 we must in general be acquainted with the whole cir- 
 cle of Arts and Sciences. 
 
 And this I take to be the reason, that in order to 
 excel remarkably in any one branch of learning, it is 
 necessary to have at least a general acquaintance with 
 the whole circle of arts and sciences." The truth 
 of it is, all the various divisions of human knowledge 
 are very nearly related among themselves, and -innu- 
 merable instances serve to illustrate and set off each « 
 other. And although it is not to be denied, tha^: by 
 an obstinate application to one branch of study, a man 
 may make 'considerable progress, and acquire some de- 
 gree. ot: eminence in it ; yet his views will be always 
 narrow and contracted, and he will want that master- 
 ly discernment which not only enables us to pursue 
 our discoveries with ease, but also in laying them open 
 to others, to spread a certain brightness around them. 
 I would not, however, here be understood to mean, 
 that a general knowledge alone is sufficient for all the 
 purposes of reasoning. I only recommend it as .pro- 
 per to give the mind a certain sagacity and quickness, 
 and qualify it for judging aright in the ordinary oc-» - 
 currences of life. But when our reasoning regards a 
 particular science, it is farther necessary, that we more 
 nearly acquaint ourselves with whatever relates to that 
 science. A general knowledge is a good preparation, 
 and enables us to proceed with ease and expedition in 
 whatever branch of learning we apply to. But then 
 
US DUNCAN'S ELEMENTS 
 
 in the minute and intricate questions of any science* 
 -we are by no means qualified to reason with advantage, 
 until we have perfectly mastered the science to which 
 they belong ; it being hence chiefly that we are fur- 
 nished with those intermediate ideas, which lead to a 
 just and successful solution. „ 
 
 Sec. VII... .Why Mathematicians sometimes answer not 
 the expectation their great learning raises. 
 
 And here, as it comes so naturally in my way, I can* 
 not avoid taking notice of an observation that is fre- 
 quently to be met with, and seems to carry in it at 
 first sight something very strange and unaccountable. 
 It is, in short, this, that mathematicians, even such at* 
 are allowed to excel in their own profession, and to 
 have discovered themselves perfect masters in the art 
 of reasoning, have not yet been always happy in treat- 
 ing upon other subjects ; but rather fallen short, not 
 only what might naturally have been expected from 
 them, but of many writers much less exercised in the 
 rules of the argumentation. This will not appear so 
 very extraordinary, if we reflect on what has been 
 hinted' above. Mathematics is an engagittg study : and 
 inert who apply themselves that way, so wholly plunge 
 into it, that they are for the most part but little ac- 
 quainted with other branches of knowledge. When r 
 'therefore, they quit their favorite subject, and enter 
 .upon others, that are in a manner new and strange to 
 them, no wonder if they find their invention at a 
 stand. Because, however perfect they may be iruthe 
 art of reasoning, yet wanting here those intermediate 
 ideas whieh are necessary to furnish out a due train of 
 propositions, all their skill and ability fails them. For 
 a bare knowledge of the rules is not sufficient. • We 
 must farther have materials'whereunto to apply them. 
 And when these are once obtained, then it is that an able 
 reasoner discovers his superiority, by the just choice he 
 makes, and a certain masterly disposition, that-in eve- 
 ry step of the procedure carries evidence and convic- 
 tion along with it. Andhence it is, that such mathe- 
 maticians as have of late years applied themselves to 
 
OF LOGIC. U9 
 
 oilier sciences, 'and not contented with a superficial 
 knowledge, endeavoured to reach their inmost re- 
 cesses ; such mathematicians, I say, have by mere 
 strength of mind, and a happy application of geome- 
 trical reasoning, carried their discoveries far beyond 
 -what was heretofore judged the utmost limits of hu- 
 man knowledge. This is a truth abundantly known to 
 all who are acquainted with the late wonderful im- 
 provements in natural philosophy. 
 
 Sec. V III. ..Secondly , the Skill of applying Intermedi- 
 ate Ideas happily in particular instances, 
 
 I come now* to the second thing required, in order 
 to a successful progress in reasoning, namely ; the skill 
 and talent of applying intermediate ideas happily in 
 all particular instances that come under consideration. 
 And here I shall nottake up much time in laying down . 
 rules and precepts, because I am apt to think they 
 would do but little service. Use and exercise are th^ 
 best instructors in the present case : and whatever lo- 
 gicians may boast, of being able to form perfect rea- 
 soners 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 understanding. In 
 short, 'tis the habit alone of reasoning that makes a 
 reasoner. And therefore the true way to acquire this 
 talent, is, by being much conversant in those sciences 
 where the art of reasoning is allowed to reign in the 
 greatest perfection. Hence it was, that the ancients, 
 who so well understood the manner of forming the 
 mind, always began with mathematics as the founda- 
 tion of their philosophical studies. Here the under- 
 standing is by degrees habituated to truth, contracts, 
 insensibly a certain fosdness for it, and learns never 
 to yield its assent to any proposition, but where the. # 
 evidence is sufficient to produce full conviction. For 
 this reason Plato has called mathematical demonstra-' 
 tions the cathartics or purgatives of the soul, as be- 
 ing the proper means to cleanse it from error, and re- 
 store that natural exercise of its faculties in which 
 •just thinking consists. And indeed I beJieve it will 
 N 2 
 
150 DUNCAN'S ELEMENTS 
 
 be readily allowed, that no science furnishes so many 
 instances of a happy choice of intermediate ideas, and 
 a dexterous application of them, for the discovery of 
 truth and enlargement of knowledge. 
 
 .Sec. IX*"** The Study of Mathematical Demonstrations 
 . of great avail in this respect. 
 
 If, therefore, we would form our minds to a habit of 
 reasoning closely and in train, we cannot take any- 
 more certain method, than the exercising ourselves in 
 mathematical demonstrations, so as to contract a kind 
 of familiarity with them, " not that we look upon it 
 as necessary, (To use the words of the great Mr. 
 LockeJ that all men should be deep mathematicians, 
 but that, having got the way of reasoning which that 
 study necessarily brings the mind to, they may be 
 able to transfer it to other parts of knowledge, as they 
 shall have occasion. For in all sorts of reasoning every 
 single. argument should be managed as a mathematical 
 demonstration, the connexion and dependence of ideas 
 should be followed, till the mind is brought to - the 
 source on which it bottoms, and can trace the cohe- 
 rence through the whole train cf proofs. It is in the 
 general observable, that the faculties of our souls are 
 improved and m?.de useful to us just after the same 
 manner as our bodies are. Would yeu have a man 
 write or paint, dance or fence well, or perform any 
 other manual operation, dexterously and with ease ? 
 Let him have ever so much vigour and activity, sup- 
 pleness and address naturally, yet no body expects 
 this from him, unless he has been used to it, and has 
 employed time and pains in fashioning and forming 
 his hand, or outward parts to these motions. Just so 
 It is in the mind ; would you have a man reason well, 
 .you must use. him to it betimes, exercise his mind in 
 observing the connexion of ideas, and following them 
 in train. Nothing does this 'better than mathematics ; 
 which, therefore, I think should be taught all those 
 who have the time and opportunity, not so much to 
 make them mathematicians, as to make them reasona- 
 ble creatures 5 for though we all call ourselves so, be- 
 
OF LOGIC. 151 
 
 i 
 
 cause we are born to it, if we please ; yet we may 
 truly say, nature gives us but the seeds cf it. We are 
 born to be, if we please, rational creatures ; but 'tis 
 use and exercise only that makes us sb, and we are in- 
 deed so, no farther than industry and application has 
 carried us. " Conduct of the Understanding, 
 
 Sec. X As also of such Authors on other Subjects, a$ 
 
 are distinguished for Strength and Justness of Re a* 
 soning. 
 
 But although the study of mathematics be, of all 
 others, the most useful to form the mind and give it 
 an early relish of truth, yet ought not other parts of 
 philosophy to be neglected. For there also we meet 
 with many opportunities of exercising the powers of 
 the understanding ; and the variety of subjects natu- 
 rally lead us to observe all those different turns of 
 thinking that are peculiarly adapted to the several 
 ideas we examine, and the truths we search after.* 
 A mind thus trained, acquires a certain mastery over 
 its own thoughts, insomuch that it can range and mo- 
 del them at pleasure, and call such into view as best 
 suit its present designs. Now in this the whole art of 
 reasoning consists, from among a great variety of dif- 
 ferent ideas, to single out those that are most proper 
 for the business in hand, and to lay them together in * 
 such order, that from plaia and easy beginnings, by 
 gentle degrees, and a continual train of evident truths, 
 we may be insensibly led on to such discoveries, as at 
 our first setting out, appeared beyond the reach of the 
 human understanding. For this purpose, besides the 
 study of mathematics before recommended, we ought 
 to apply ourselves diligently to the reading of such 
 authors as have distinguished themselves for strength 
 of reasoning, and a just and accurate manner of think- 
 ing. For it is observable, that a mind exercised and' 
 seasoned to truth seldom rests satisfied in a bare eon- 
 templation of the arguments offered by others, . but 
 ^will be frequently essaying its own srength, and pur- 
 suingits discoveries upon the plan it is most accustom- 
 ed to. Thus wc insensibly contract a Jiabit of tracing 
 
152 DUNCAN'S ELEMENTS 
 
 truth from one stage to another, and of investigating 
 those general relations and properties which we af- 
 terwards ascribe to particular things, according as we 
 find them comprehended under the abstract ideas to 
 which the properties belong. And thus having parti- 
 cularly shown how we are to distribute the several ob- 
 jects of nature under general ideas, what properties 
 jwe are to ascribe to them in consequence of that distri- 
 bution*, and how to trace and investigate the properties 
 themselves ; I think I have sufficiently explained all 
 that is necessary towards a due conception of reason- 
 ing, and shall therefore here conclude this chapter. 
 
 OF THE FORMS OF SYLLOGISMS. 
 
 Sec, I....TAe Figures of Syllogisms* 
 
 HITHERTO we have contented ourselves with a 
 general notion of syllogisms, and of the parts of 
 which they consist. It is now time to enter a little 
 more particularly into the subject, to examine their 
 
 • various forms, and to lay open the rules of argumen- 
 ' tation proper to each. In the syllogisms mentioned in 
 
 the foregoing chapters, we may observe, that the middle 
 \erm is the subject of the major proposition, and the 
 ^predicate of the minor*. This disposition, though the 
 m6st natural and obvious, is not, however, necessary ; 
 it frequently happening, that the middle term is the 
 subject in both the premises, or the predicate in both ; 
 and sometimes, directly contrary to its disposition in 
 the foregoing chapters, the predicate in the major , and 
 the subject in the minoie* Hence the distinction of syl- 
 logisms into various "CTnds, called figures by logician's. 
 • Toy figure, according to their use of the word, is* no- 
 
 • thing else but the order and disposition of the middle 
 term In any syllogism. And as this disposition is," we 
 see. four-fold, so the figures of syllogisms thence aria- 
 
OF LOGIC. 1535 
 
 ing are four in number* When the middle term is the 
 subject of the major proposition, and the predicate of 
 the minor, we have what is called fhe Jirst figure. If 
 on the other hand, it is the predicate of both the pre- 
 mises, the syllogism is said to be in the second figure* 
 Again, in the third figure, the midddle term is the sub-. 
 ject of the two premises. And lastly, by-making it the 
 predicate of the major, and subject of the .minor, we 
 obtain syllogisms in the fourth figure. 
 
 Sec. II... .The Moods of Syllogisms. 
 But besides this fourfold distinction of syllogisms, 
 there is also a farther subdivision of > them in every fi- 
 gure, arising from the quantity and quqlity,zs they are 
 called, of the propositions* By quantity we mean the 
 consideration of propositions as universal or particular, 
 by quality as affirmative or negative. Now as in all the 
 scveraldispositionsof the middle term, the propositions, 
 of which a syllogiim consists, may be either universal 
 or particular, affirmative or negative ; the due determi- 
 nation of these, and so putting them together as the 
 laws of argumentation require, constitute what logici- 
 ans call the moods of syllogisms. Of these moods there 
 are a determinate number to every figure, "including 
 all the possible ways in which propositions differing in 
 quantity or quality can be combined, according to any 
 disposition of the middle term, in order to arrive at a 
 just conclusion. The shortness of the present work 
 will not allow of enteringjnto a more particular des- 
 cription of these several distinctions and divisions. I 
 shall therefore content myself with referring the rea- 
 der to the: Port Royal art of thinking, where he will 
 find the moods and figures of syllogisms distinctly ex- 
 plained, and the rules proper to each very neatly de- 
 monstrated. 
 
 Sec. III.... Foundation of the other 'Divisions of Syl- 
 logisms.. . '. 
 The division of syllogisms according to mocd and 
 figure, respects those especially, which are known by 
 the name of plain simple syllogisms ; that is, which are 
 bounded to three propositions, all simple, and where. 
 
154 DUNCAN'S ELEMENTS 
 
 the extremes and middle term are connected, accord- 
 ing to the rules laid down above. But as the mind is 
 not tied down to any one precise form of reasoning, 
 but sometimes makes use of more, sometimes of few- 
 er premises, and often takes in compound and conditi- 
 onal propositions, it may not be amiss to take notice 
 "cf the different forms derived from this source, and ex- 
 plain the rules by which the mind conducts itself in 
 the use of them. 
 
 Sec. IV.... Conditional syllogisms. 
 When in any syllogism, the major is a conditional 
 proposition, the syllogism itself is termed conditional 
 Thus : 
 If there is a God, he ought to be worshipped. 
 But there is a God: 
 
 Therefore he ought to be worshipped, 
 In this example, the major or first proposition, is we 
 see, conditional, and therefore the syllogism itself is 
 also of the kind called by that name. And here we 
 are to observe, that all conditional propositions are 
 made up of two distinct parts ; one expressing the 
 condition upon which the predicate agrees or disagrees 
 with trie subject, as in this now before us, if there is a 
 God; the other joining or disjoining the said predi- 
 cate aild subject, as here, he ought to be worshipped. The 
 first of these parts, or that which implies the condi- 
 tion, is called the antecedent ; the second, where we 
 join or disjoin the predicate and subject, has the name 
 of the consequent. 
 
 Sec. V.,»*Grou?id of Illation in conditional Syllogisms, 
 . These things explained, we are farther to observe, 
 that in all propositions of this kind, supposing thera 
 to be exact in point of form, the relation between the 
 antecedent and consequent, must ever he true and 
 real ; that is, the antecedent must always contain 
 some certain and genuine condition which necessa- 
 rily implies the .consequent; for otherwise, the pro- 
 position itself will be false, and therefore ought not 
 to be admitted into our reasoning?. Hence it follows, 
 that when any conditional proposition is assumed, if 
 we admit the antecedent of that proposition, we must, 
 
OF LOGIC. 15* 
 
 at the same time, necessarily admit the consequent : 
 but if we reject the consequent, we are, in like man« 
 ner, bound to reject also the antecedent. For as the 
 antecedent always expresses some condition which. ne- 
 cessarily implies the truth of the consequent; by ad- 
 mitting the antecedent, we allow of that condition, 
 and therefore ought also to admit the consequent. In 
 like manner, if it appears that the consequent ought 
 to be rejected, the antecedent evidently must be so 
 too ; because, as we just now demonstrated, the ad- 
 mitting of the antecedent would necessarily imply the 
 admission also of the consequent. 
 
 Sec. Vl.„,The two Moods of Conditional Syllogism. 
 
 From what has been said, it appears, that there are 
 two ways of arguing in hypothetical syllogism, which 
 lead to a certain and unavoidable conclusion. For as the 
 major is always a conditional proposition, consisting of 
 an antecedent and a consequent ; if the minor admits 
 the antecedent, it is plain, that the conclusion must ad- 
 mit the consequent. This is called arguing from the 
 admission ofthe antecedent to the admission of the con- 
 sequent, and constitutes that mood or species. of hypo* 
 tlietical syllogisms, which is distinguished in the schools 
 by the name of the modus ponens, inasmuch as by it the 
 whole conditional proposition, both antecedent and 
 consequent, is established. Thus, 
 
 If God is infinitely wise, and acts with perfect freedom^he 
 
 does nothing but what is best 
 But God is infinitely wise, and acts with perfect freedom, 
 Therefore he does nothing but what is best. 
 
 Here we see the antecedent or first part ofthe con- 
 ditional proposition is established in the minor, and the 
 consequent or second part in the conclusion ; whence 
 the syllogism itself is an example of the modus penens* 
 But if now we on the contrary suppose, that the minor 
 rejects the consequent, then it is apparent, that the 
 conclusion must also reject the. antecedent. In this case 
 we are said to argue from the removal ofthe consequent, 
 to the, removal of the antecedent ; and the particular 
 mood or species of syllogism thence arising is called bjr 
 
156 DUNCAN'S ELEMENTS 
 
 logiciansthe modus tollehs ; because in it, both antece- 
 dent and consequent are rejected or taken away, as ap- 
 pears by the following example : 
 
 If God were not a being of infinite goodness, neither would 
 he consult the happiness of his creatures. 
 But God does consult the happiness of his creatures : 
 Therefore He is a Being of Infinite Goodness. 
 
 Sec, VIL... T/zey include all the Legitimate Ways of 
 Arguing. 
 These two species take in the whole class of conditi- 
 onal syllogisms, and include all the possible ways of 
 arguing that lead to a legitimate conclusion ; because 
 we cannot here proceed by a contrary process of rea- 
 soning, that is, from the removal of the antecedent to 
 the removal of the consequent, or from the establish- 
 ing of the consequent to the establishing of the ante- 
 cedent. For although the antecedent always expresses 
 some real condition, which, once admitted, necessarily 
 implies the consequent, yet it does not follow, that 
 there is therefore no other condition ; and if so, then, 
 after remoring the antecedent, the consequent may 
 still hold, because of some other determination that in- 
 fers it." When we say: If a stone is exposed some 
 time to the rays of the sun, it will contract a certain 
 degree of heat ; the proposition is certainly true, and, 
 admitting the antecedent, we must also admit the con- 
 sequent. But as there are other ways by which a stone 
 may gather heat, it will not follow from the ceasing 
 of the before -mentioned condition, that therefore the 
 consequent cannot take place. In other words, we 
 cannot argue, but the stone has not been exposed to the 
 rqys of the suy, ; therefore neither has it any degree of 
 heat ; inasmuch 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 antece- 
 dent to the removal of the consequent, no more can we 
 from the admission of the consequent to the admis- 
 . sion of the antecedent. Because as the consequent 
 may flow from a great variety of different suppositi- 
 ons, the allowing of it does not determine the precise 
 ■aupposition, but only that some of them must take 
 
OF LOGIC. 15t 
 
 place. Thus in the foregoing reposition, if a stone 
 is exposed some time to the rays of the sun, it will con- 
 tract a certain degree of beat : admitting the conse- 
 quent, viz. that it has contracted a certain degree of 
 heat) we are not therefore bound to admit the ante- 
 cedent, that it has been some time exposed to the rays of 
 the sun ; because there are many other causes whence 
 that heat may have proceeded. These two ways of 
 arguing, therefore, hold not in conditional syllogisms. 
 Indeed, where the antecedent expresses the only condi- 
 tion on which the consequent takes place, there they " 
 maybe applied with safety ; because, wherever that con- 
 dition is not, we are sure that neither can the consequent 
 be, and so may argue from the removal of the one to * 
 the removal of the other ; as, on the contrary, where- 
 ver the consequent holds, it is certain that the condition 
 must also take place ; which shows, that by establish- 
 ing the consequent, we at the same time establish the 
 antecedent. But as it is a very particular case, and 
 that happens but seldom, it cannot be extended into a 
 general rule, and therefore affords not any steady and 
 universal ground of reasoning upon the two foregoing 
 suppositions. 
 
 Sec. Villi... The Manner of Arguing in Disjunctive 
 Syllogisms, 
 
 As from the majors being a conditional proposition, 
 we obtain the species of conditional syllogisms ; so 
 where it is a disjunctive proposition, the syllogism, to 
 which it belongs, is called disjunctive, as in the follow- 
 ing example : 
 
 The world is cither self-existent, or the work of some- fi-' 
 nite or of some infinite being. 
 
 But it is not self-existent, nor the work of a finite being : 
 
 Therefore it is the work of an infinite being. 
 
 Now a disjunctive proposition is thatwbere of seve* 
 ral predicates we afnrm one necessarily to belong to 
 the subject, to the exclusion of all the rest, but leave 
 that particular one undetermined. Hence it follows, 
 that as soon as we determine the particular predicate, 
 all the rest are of course to be rejected ; or if we re- 
 ject all the predicates but one, that one necessarily 
 O 
 
158 DUNCAN'S ELEMENTS 
 
 takes place. When, therefore, in a disjunctive syllo- 
 gism, the several predicates are enumerated in the #jcr- 
 jor....\f the minor establishes any one of these predi- 
 cates, the conclusion ought to remove all the rest ; or 
 if, in the minor, all the predicates but one are remov- 
 ed, the conclusion must necessarily establish that one* 
 Thus in the disjunctive syllogism given above, the ma- 
 jor affirms one of three predicates to belong to the 
 earth, viz. self -existence, or that it istlie work of a finite, 
 or that it is the work of an infinite being. Two of these 
 predicates are removed in the minor, viz. self-existence, 
 and the work of a finite being. Hence the conclusion 
 necessarily ascribes to it the third predicate, and af- 
 firms, that it is the work of an infinite being. If now 
 we give the syllogism another turn, insomuch that the 
 minor may establish one of the predicates, by affirming 
 the earth to be the production of an infinite being.... 
 then the conclusion must remove the other two, assert- 
 ing it to be neither self-existent, nor the work of a fi- 
 nite being. These are the forms of reasoning in this 
 •species of syllogisms, the justness of which appears at 
 first sight ; and that there can be no other, is evident 
 frpni the very nature of adisjunctive proposition. 
 
 Sec. ...IX. Imperfect or mutilated Syllogisms. 
 In the several kinds of syllogisms hitherto mention- 
 ed, we may observe, that the parts are complete ; that 
 is, the three propositions of which they consist are re- 
 presented in form. But it often happens, that some 
 one of the premises is not only an evident truth, but 
 also familiar and in the minds of all men ; in which 
 case it is usually omitted, whereby we have an imper- 
 fect syllogism, that seems to be made up of only two 
 proposition. Should we, for instance, argue in this 
 manner : 
 
 Every man is mortal ; 
 
 Therefore every king is mortal ; 
 the syllogism appears to be imperfect, as consisting byt 
 of two propositions. Yet it is really complete, only the 
 minor \every king is a man"] is omitted, and left to the 
 reader to supply, as being a proposition so familiar and 
 evident, that it cannot escape him. 
 
OF LOGIC. 159 
 
 - Sec. X. Enthymemes* 
 
 These seemingly imperfect syllogisms are called 
 EnthymemeS) and occur very frequently in reasoning, 
 especially where it makes a part of common conversa- 
 tion. Nay, there is a particular elegance in them, be- 
 cause not displaying the arguments in all its parts, 
 they leave somewhat to the exercise and invention of 
 the mind. By this means we are put upon exerting 
 ourselves, and seem to share in the discovery of what 
 is proposed to us. Now this is the great secret of fine 
 writing, so to frame and put together our thoughts, 
 as to give full play to the reader's imagination, and 
 draw him insensibly into our very views and course of 
 reasoning. This gives a pleasure not unlike to that 
 ■which the author himself feels in composing. It besides 
 shortens discourse, and adds a certain force and liveli- 
 ness to our arguments, when the words in which they 
 are conveyed, favour the natural quickness of the mind 
 in its operations, and a single expression is left to ex- 
 hibit a whole train of thoughts. 
 
 Sec. XI, t ;Gronnd of Reasoning in immediate Conse* 
 quences, . • 
 
 But there is another species of reasoning with two' 
 propositions, which seems to be complete in itself, and 
 where we admit the conclusion, without supposing any . 
 tacit or suppressed judgment in the mind, from which 
 it follows syllogisticaliy. This happens between pro- . 
 positions where the connexion is such, that the admis- 
 sion of the one, necessarily, and at the first sight, im- 
 plies the admission also of the other. ' For if it so falls 
 out, that the proposition, on which the other depends, is 
 self-evident, we content ourselves with barely affirm- 
 ing it, and infer that other by a direct conclusion. 
 Thus, by admitting an universal proposition, we are 
 forced also to admit of all the particular propositions 
 comprehended under it, this being the very condition 
 that constitutes a proposition universal. If then that 
 universal proposition chances to be self-evident, the 
 particular ones follow of course, without any farther 
 train of reasoning. Whoever allows, for instance, 
 
160 DUNCAN'S ELEMENTS 
 
 that things equal to one and the same thing are equal t& 
 one another, must at the same time allow, that two tfr/- 
 angles, each equal to a square, whost side is three 
 inches, are also equal between themselves. This argu- 
 ment therefore, 
 
 Things equal to one and the same thing, are equal to on* 
 another; 
 
 Therefore those two triangles, each equal to the square of 
 a line of\three inches, are equal between themselves ; 
 is complete in its kind, and contains all. that is neces- 
 sary towards a just and legitimate conclusion. For the 
 Jirst or universal proposition is self-evident, and there- 
 fore requires no farther proof. And as the truth of the 
 particular is inseparably connected with that of the 
 universal, it follows from it by an obvious and una- 
 voidable consequence. 
 
 Sec. XI J... .All reducible to Syllogisms of some one 
 form or other. 
 
 Now in all cases of this kind where propositions are 
 deduced one from another, on account of a known and 
 evident connexion, ye are said to reason by immediate 
 consequence. Such a coherence of propositions, mani- 
 fest at first sight, and forcing itself upon the mind, fre- 
 quently occurs in reasoning. Logicians have explain- 
 ed at sorse leangth, the several suppositions upon which 
 it takes place, and allow of all immediate consequences 
 that follow in conformity to them. It is, however, 
 •observable, that these arguments, though seemingly 
 Complete, because ' the conclusion follows necessarily 
 from the single proposition that goes before, may yet 
 be considered as real enlhjmemes, whose major, which 
 is a conditional proposition,^ wanting. The syllo- 
 gism but just mentioned, when represented according 
 to this view, will run as lollows : 
 
 If things equal to one and the same thing are equal to one 
 another; these two triangles, each equal to a square 
 whose side is three inches, are also equal between them- 
 selves. 
 But things equal to one and the same thing, arejequal to 
 
 one another; 
 Therefore also these triangles, &c. are espial between 
 themselves. 
 
OF LOGIC. 161 
 
 This observation will be found to hold in all immedi- 
 ate consequences whatsoever, insomuch that they are 
 in fact no more than enthymemes of hypothetical syl- 
 logisms. But then it is particular to them, that the 
 ground, on which the conclusion rests, namely, its co- 
 herence with the minor, is of itself apparent, and seen 
 immediately to flow from the rules and reasons of logic. 
 As it is, therefore, entirely unnecessary to express a 
 self-evident connexion, the major, whose office that is, 
 is constantly omitted ; nsy, and seems so very little 
 needful to enforce the conclusion, as to be accounted 
 commonly no part of the argument at all. It must 
 indeed be owned, that the foregoing immediate conse- 
 quence might have been reduced to a simple, as well 
 as an hypothetical syllogism. This will be evident to 
 any one who gives himself the trouble to make the ex- 
 periment. But it is not my design to enter farther in- 
 to these niceties, what has been said sufficing to show, 
 that all arguments consisting of but two propositions, 
 are real enthymemes, and reducible to complete syllo- 
 gisms of some one form, or other. As, therefore, the 
 ground on which the conclusion rests> must needs be 
 always the same with that of the syllogisms to which 
 they belong, we have . here an universal •criterion,' 
 whereby at all times to ascertain the justness-aad valid- 
 ity of our reasonings in this way. 
 
 Sec. XIII. ,;A Sorites of plain simple Syllogisms, 
 
 The next species of reasoning we shall take notice 
 of here, is what is commonly known by the .name of a 
 sorites. This is a way of arguing, in which a great 
 number of propositions are so linked together, that the 
 predicate of one becomes continually the subject of the 
 next following, until at last a conclusion is formed, by 
 bringing together the subject of the first proposition 
 and the predicate of the last. Of this kind is the fol- 
 lowing argument : 
 
 God is omnipotent, 
 
 An omnipotent being can do every thing possible, 
 
 He that can do every thing possible, can do whatever in- 
 volves not a contradiction.; 
 
 Therefore God can do whatever involves net a contradiction. 
 
 02 
 
162 DUNCAN'S ELEMENTS 
 
 This particular combination of propositions may be 
 continued to any length Ave please, without in the least 
 -weakening the ground upon which the conclusion rests. 
 The reason is, because the sorites itself may be resolv- 
 ed into as many simple syllogisms as there are middle 
 terms in it ; where this is found universally to hold, 
 that when such a resolution is made, and the syllogisms 
 are placed in train, the conclusion of the last in the 
 series is also the conclusion of the sorites. This kind 
 of argument, therefore, as it serves to unite several syl- 
 logisms into one, must stand upon the same foundation 
 with the syllogisms of which it consists ; and is, in- 
 deed, properly speaking, no other than a compendious 
 way of reasoning syllogistically. Any one maybe sa- 
 tisfied of this at pleasure,' if he but takes the trouble of 
 resolving the foregoing sorites into two distinct syllo- 
 gisms,. For he will there find, that he arrives at the 
 same conclusion, and that, too, by the very same train 
 ©f thinking, but with abundantly more words, and the 
 addition of two superfluous propositions. 
 
 Sec. XIV.... 6 Sorites of Hypothetical Syllogisms, 
 
 What is here said of plain simple propositions, may 
 be well applied to those that are conditional ; that is, 
 any number of them may be so joined together in a 
 series, that the consequent of one, shall become contin- 
 ually the antecedent of the next following ; in which 
 case, by establishing the antecedent of the first propo- 
 sition, we establish the consequent of the last, or by 
 removing the last consequent, remove also the first an- 
 tecedent. This way of reasoning is exemplified in the 
 following argument : 
 
 If we love any person, all emotions of hatred towards him 
 cease. 
 
 If all emotions of hatred towards a person cease, we cannot 
 rejoice in his misfortunes. 
 
 If we rejoice not in his misfortunes, we certainly wish 
 him no injury. 
 
 Therefore if we love a person, we wish him no injury. 
 It is evident that this sorites, as well as the last, may- 
 be resolved into a series of distinct syllogisms, with 
 this only difference, that here the sylk Tisms are all con- 
 
OF LOGIC. 163 
 
 ditional. But as the conclusion of the last syllogism in 
 the series is the same with the conclusion of the sorites, 
 it is plain, that this also is a. compendious way of rea- 
 soning, whose evidence arises from the evidence of the 
 several single syllogisms into which it may be resolved. 
 
 Sec. XV....77ie Ground of Reasoning by Induction. 
 I come now to that kind of argument, which logici- 
 ans call induction; in order to the right understanding 
 of which, it will be necessary to observe, that our ge- 
 neral ideas are for the most part capable of various sub- 
 divisions. Thus the idea of the Lowest species may be 
 subdivided into»its several individuals ; the idea of any 
 genus, into the different species it comprehends ; and 
 so of the rest. If then we-suppose this distribution to 
 be duly made, and so as to take in the whole extent of 
 the idea to which it belongs ; then it is plain, that all 
 the subdivisions or parts of any idea taken together con- 
 stitute tha* whole idea. Thus the several individuals 
 of any species taken together constitute the whole spe- 
 cies, and all the various species comprehended under 
 any genus, make up the whole genus. This being allow- 
 ed, it is apparent, that whatsoever may be affirmed of 
 all the several subdivisions and classes of any idea, 
 ought to be affirmed of the whole general idea to which 
 these subdivisions 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 the 
 species of any genus, may also be affirmed of the whole 
 genus ; because all the individuals, taken together, are 
 the same with the species, and all the species taken to- 
 gether, the same with the genus. 
 
 Sec. XVI The Form and Structure of an Argu« 
 
 ment by Induction. 
 This way of arguing, where we infer universalfy 
 concerning any idea, what we had before affirmed or 
 denied separately, of all its several subdivisions ancj. 
 parts, is called reasoning by induction. Thus if we sup- 
 pose the whole tribe of animals, subdivided into men, 
 beasts, birds, insects, and fishes, and then reason con- 
 cerning them after this manner : All men have a 
 
164 DUNCAN'S ELEMENTS 
 
 power of beginning motion ; all beasts, birds, and in* 
 sects, have a power of beginning motion ; all fishes 
 have a power of beginning motion ; therefort ail ani- 
 mals have a power of beginning, motion : The argu- 
 ment is an induction* When the subdivisions are just, 
 so as to take in the whole general idea, and the enu- 
 meration is perfect, that is, extends to all and every of 
 the inferior classes or parts ; there the induction is 
 complete, and the manner of reasoning^ by induction 
 is apparently conclusive,' 
 
 Sec, XVII.... The Ground of Argumentation in a Di- 
 lemma* 
 
 The last species of syllogisms I shall take notice of, 
 in this chapter, is that commonly distinguished by the 
 name of a dilemma, A dilemma is an argument by 
 which we endeavour to prove the absurdity or falsehood * 
 of some assertion. In order to this we assume a con- 
 ditional proposition ; the antecedent of which is the as- 
 sertion to be disproved and the consequent a disjunc- 
 tive proposition, enumerating all the possible suppo- 
 sitions upon which that assertion can take place. If 
 then it appears, that all these several suppositions 
 ought to be rejected, it is plain, that the antecedent, or 
 assertion, itself, must be so too. When, therefore, 
 such a proposition as that before-mentioned, is made 
 the major of any syllogism — if the minor rejects all 
 the -suppositions contained in the consequent, it fol- 
 lows necessarily, that the conclusion ought to reject 
 the antecedent, which, as we have said, is the very as- 
 sertion to be disproved. This particular way of ar- 
 guing, 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 syllogism, 
 where the consequent of the major is a disjunctive pro- 
 position, which is wholly taken away or removed in the 
 minor. Of this kind is the following : 
 
 If God did not create the world perfect in its kind, it 
 
 must 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. 
 
OF LOGIC. 16S 
 
 Therefore he created the world perfect in its kind. Or 
 nvbicb is the same thing : 'Tis absurd to say that he did not 
 create the world perfect in its kind. 
 
 Sec. XVIII... ,An universal Description of it. 
 
 The nature then of a dilemma is universally this* 
 The major is a conditional proposition, whose conse- 
 quent contains all the several suppositions upon which 
 the antecedent can take place. As, therefore, these 
 suppositions are wholly removed iathe minor ^ it is 
 evident, that the antecedent must be so too ; insomuch 
 that we here always argue from the removal of the 
 consequent to the removal ^f the antecedent. That 
 is, a dilemma is an argument, in the modus tollens of 
 hypothetical syllogisms, as logicians love to speak. 
 *Hence it is plain, that'if the antecedent of the major 
 is an affirmative proposition, the conclusion of the .di- 
 lemma will be negative ; but if it is a negative propo- 
 sition, the conclusion will be affirmative. I cannot 
 dismiss the subject without observing*, that as there, is 
 something very curious and entertaining in the struc- 
 ture of a d He mm a , so is it a manner or reasoning that 
 occurs frequently in mathematical demonstrations. 
 Nothing is more common with Euclid, when about to 
 show the equality of two given figures, or, which is the 
 same thing, to prove the absurdity of asserting them 
 unequal ; nothing, I say, is more cqmmon with him, 
 than to assume, that if the one is not equal to the other 9 
 it must be either greater or less : and having destroy- 
 ed both these suppositions, upon which alone .the asser- 
 tion can stand, he thence very naturally inters, that the 
 assertion itself is false. Now this is precisely the rea- 
 soning of a dilemma, and in~e very step' coincides with 
 the frame and composition of that argument, as w« 
 have described it above» 
 
DUNCAN'S ELEMENTS 
 
 — «w» •# © ■» tarn- 
 
 <5Pjbap, V. 
 
 OF DEMONSTRATION. 
 
 Sec. I....0/" Reason'mgby a Concatenation of Syllogisms* 
 
 HAVING dispatched what seemed necessary to be 
 said with regard to the forms of syllogisms, we 
 now proceed to supply their use and application in rea- 
 soning. We have seen, that in all the different ap- 
 pearances they put on, we still arrive at a just and le- 
 gitimate conclusion. Now it often happens, that the 
 conclusion of one syllogism becomes a previous pro- 
 position in another, by which means great numbers of 
 them are sometimes linked together in a series, and 
 truths are made to follow one another-in train. And 
 as in such a concatenation of syllogisms, all the van- 
 Cm s ways of reasoning that are truly conclusive, may be 
 ■with safety introduced ; hence it is plain, that in de- 
 ducing any truth from its first principles, especially 
 ■when it lies at a considerable distance from them, we 
 are at-libertyto combine all the several kinds of argu- 
 ments above explained, according as they are found best 
 to suit the end and purpose of our enquiries. When a 
 proposition is thus, by means of syllogisms, collected 
 from others more evident and known, it is said to be 
 proved ; so that we may in the general define the proof 
 of a proposition, to be a syllogism, or series of syllo- 
 gisms, collecting that proposition from known and evi- 
 dent truths. But more particularly, if the syllogisms, 
 of which the proof consists, admit of no premises but 
 definitions, self-evident truths, and propositions alrea- 
 dy established, then is the argument so constituted cal- 
 led a demonstration ; whereby it appears, that demon- 
 strations are ultimately founded on definitions and self- 
 evident propositions. 
 
 Sec. II.. ..All Syllogisms whatsoever Reducible to the 
 
 first Figure. 
 But as a demonstration oft-times consists of a long 
 
OF LOGIC. 167 
 
 chain of proofs, where all the various ways of arguing 
 have place, and where the ground of evidence must o£ 
 ceurse be diffenfnt in different parts, agreeably to the 
 form of the argument made use of; it may not per- 
 haps be unacceptable, if we here endeavour to reduce 
 the evidence of demonstration to one simple principle, 
 whence, as a sure and unalterable foundation, the cer- 
 tainty of it may in all cases be derived. In order to 
 this we must first observe, that all syllogisms whatso- 
 ever, whether compound, multiform, or defective, are 
 reducible to plain simple syllogisms in some one of the 
 four figures. But this is not all. Syllogisms of the 
 first figure in particular admit of all possible conclu- 
 sions : that is, any proposition whatsoever, whether an 
 universal affirmative, or universal negative, a particu- 
 lar affirmative or particular negative, (which fourfold 
 division, as we have already demonstrated in the second 
 part, embraces all their varieties) any one, I say, of 
 these may be inferred, by virtue of some syllogism in 
 the first figure. By this means it happens, that the syl- 
 logisms of all the other figures are reducible also to 
 syllogisms of the first figure, and may be considered as 
 standing on tht same foundation with them. We cannot 
 here demonstrate and explain the manner ©f this re- 
 duction, because it would too much swell the bulk of 
 this treatise. It is enough to take notice, that the 
 thing is universally known and allowed among logici- 
 ans, to- whose writings we refer such as desire farther 
 satisfaction in this matter. This then being laid down, 
 it is plain, that any demonstration whatsoever may be 
 considered~as composed of a series of syllogisms, all in 
 the first figure. For since all the syllogisms, that en- 
 ter the demonstration, are reduced to syllogisms of some 
 one of the four figures, and since the syllogisms of 
 ail the other figures are farther reducible to syllogisms 
 of the first figure, it is evident, that the whole demon- 
 stration-may be resolved into a series of these last syl- 
 logisms. Let us now, if possible, discover the ground 
 upon which the conclusion rests, in syllogisms of the 
 first figure ; because, by so doing, we shall come at an 
 universal principle of certainty, whence the evidence 
 
163 DUNCAN'S ELEMENTS 
 
 of all demonstrations, in all their parts, may be ulti- 
 mately derived. 
 
 Sec. HI*... The ground of Reasoning in the first Figure, 
 The rules then of the first figure are briefly these. 
 The middle term is the subject of the major proposi- 
 tion, and the predicate of the minor. The major is al-, 
 ways an universal proposition, and the minor always 
 affirmative. Let us now see what effect these rules 
 will have in reasoning". The major is an universal pro- 
 position, of which the middle term is the subject, and 
 the predicate of the conclusion the predicate. Hence 
 it appears, that in the major, the predicate of the con- 
 elusion is always affirmed or denied universally of the 
 middle term. Again, the minor is an affirmative pro- 
 position, whereof the subject of the conclusion is the sub- 
 ject, and the middle term the predicate. Here then 
 the middle term is affirmed of the subject of the con- 
 elusion :' that is, the subject of the conclusion is affirmed 
 to be comprehended under, or to make apart of the mid* 
 die term. Thus then we see what is done in thepremises 
 of a syllogism of the first figure. The predicate of the 
 conclusion is universally affirmed or denied of some idea. 
 The subject of the conclusion is affirmed to be, or to 
 make a partof that idea. Hence it naturally and una- 
 voidably follows, that the predicate of the conclusion 
 ought to be affirmed or denied of the subject. To 
 illustrate this by an example, we shall resume one of 
 the syllogisms of the first chapter : 
 
 Every creature, possessed of reason and liberty, is account- 
 able for his actions. 
 Man is a creature possessed of reason and liberty : 
 Therefore man is accountable for his actions. 
 Here, in the first proposition, the predicate of the 
 conclusion, aecountableness, is affirmed of all creatures 
 that have reason and liberty. Again, in the second 
 proposition, man, the subject of the conclusion, is af- 
 firmed to be, or to make a part of this class of creatures. 
 Hence the conclusion necessarily and unavoidably fol- 
 lows, viz. that man is accountable for his actions. I say 
 this follows necessarily and unavoidably. Because, if 
 reason and liberty be that which constitutes a creature 
 
OF LOGIC. 169 
 
 accountable, and man has reason and liberty, it is plain 
 - he has that which constitutes him accountable* In like 
 manner, -where, the major is a negative proposition, or 
 denies the predicate of the conclusion universally of the 
 middle term ; as the minor always asserts the subject 
 of the conclusion to be or make a part of that middle 
 term, it is no less evident, that the predicate of the 
 conclusion ought in this case to be denied of the sub- 
 ject. So that the ground of reasoning, in all syllo- 
 gisms of the first figure, is manifestly this : Whatever 
 may be affirmed universally of any idea, may be affirm- 
 ed of every or any number of particulars comprehended 
 wider that idea* And again : Whatever may be deni~ 
 ed universally of any idea, may be in like manner deni- 
 ed of every or any number of its individuals. These 
 two propositions are called by logicians the dictum de 
 omni, and dictum de nullo, and are indeed the great 
 principles of syllogistic reasoning ; inasmuch as all 
 conclusions whatsoever, either rest immediately upon 
 them, or upon propositions deduced from them. But 
 what adds greatly to their value is, that they are really 
 self-evident truths, and such as we cannot gainsay, 
 without running into an express contradiction. To 
 affirm, for instance, that no man is perfect, and yet ar- 
 gue that that some men are perfect ; or to say that all 
 men are mortal, and yet that some men are not mortal, is 
 to assert a thing to be and not to be at the same time. 
 
 Sec. IV ., ..Demonstration, an Infallible Guide to Truth 
 and Certainty. 
 
 And now I think we are sufficiently authorized to 
 affirm j that in all syllogisms of the first figure, if the 
 premises are true, the conclusion must needs be true. 
 If it be true that the predicate of the conclusion, whe- 
 ther affirmative or negative, agrees universally to some 
 idea.... and if it be also true, that the subject of the 
 conclusion is a part of or comprehended under that idea ; 
 then it necessarily follows,^ that the predicate of the 
 conclusion agrees also to the svdject. Fcr to assert the 
 contrary, would be to run counter to some one of the 
 two principles before established j that is 5 .it would be 
 P 
 
170 DUNCAN'S ELEMENTS 
 
 to maintain an evident contradiction. And thus we 
 are come at last to the point we have been all along en- 
 deavouring to establish ; namely, that every proposi- 
 tion, which can be demonstrated, is necessarily true. 
 For as every demonstration may be resolved into- a se- 
 ries of syllogisms, all in the first figure, and as in any 
 one of these syllogisms, if the premises are true, the 
 conclusion must needs be sp too : it evidently follows, 
 that if all the several premises are true, all the several 
 conclusions are so, and consequently the conclusion al- 
 so of the last syllogism, which is always the proposition 
 to be demonstrated. Now that all the premises of a 
 demonstration are true, will easily appear, from the ve- 
 ry nature and definition of that form of reasoning. A 
 demonstration, as we have said, is a series of syllogisms, 
 all whose premises are either definitions, self-evident 
 truths, or propositions already established. Definitions 
 are identical propositions, wherein we connect the des- 
 cription of an idea with the name by which we choose 
 to have that idea called ; and therefore as to their 
 truth there can be no^kjspute. Self-evident propositi- 
 ons appear true of themselves, and leave no doubt or 
 uncertainty in the mind. Propositions before esta- 
 blished, are no other than conclusions, gained by one 
 or more steps from definitions and self-evident princi- 
 ples ; that is, from true premises, and therefore must 
 Beeds be true. Wl;ence all the previous propositions 
 of a demonstration, being, we sec, manifestly true, the 
 last conclusion, or proposition to be demonstrated, mus t 
 be so too. So that demonstration not only leads to cer- 
 tain truth, but we have here a clear view of the ground 
 and foundation of that certainty. For as in demonstrat- 
 ing, we may be said to do nothing more than combine 
 a series of syllogisms together, all resting on the same 
 bottom; it is plain, that one uniform ground of cer- 
 tainty runs though the whole, and that the conclusions 
 are every where built upon some one of the two prin- 
 ciples before established, as the foundation of all our 
 reasoning. These two principles are easily reduced in- 
 to one, and may be expressed thus : Whatever predicate, 
 whether affirmative or negative, agrees universalij to 
 
OF LOGIC. in 
 
 cny idea^ the same must needs agree to every or any 
 number of individuals comprehended under that idea* 
 And thus at length we have, according to our first de- 
 sign, reduced the certainty of demonstration to one sim- 
 ple and universal principle which carries its own evidence 
 along with it and which is, indeed, the ultimate foun- 
 dation of all syllogistic reasoning. 
 
 Sec. V. The rules of Logic furnish a sufficient criterion 
 for the distinguishing between Truth and Falsehood. 
 
 Demonstration, therefore, serving as an infallible 
 guide to truth, and standing on so sure and unaltera- 
 ble a basis, we may now venture to assert, what I doubt 
 not will appear a paradox to many ; namely, that 
 the rules of logic furnish a sufficient criterion for the 
 distinguishing between truth and falsehood. For since 
 every proposition that can be demonstrated is necessa- 
 rily true, he is able to distinguish^ truth from false- 
 hood, who can with certainty judge when a proposition 
 is duly demonstrated. Now a demonstration is, as we 
 have said, nothing more than a concatenation of syl- 
 logisms, all whose premises are definitions, self-evi- 
 dent truths, or propositions previously established* 
 To jui^e, therefore, of the validity of a demonstration^ 
 we must be able to distinguish whether the definitions 
 that enter it are genuine, ana truly descriptive of the 
 ideas they are meant to exhibit ; whether the proposi- 
 tions assumed without proof as intuitive truths, have 
 really that self-evidence to which they lay claim ; 
 whether the syllogisms are drawn up in due. form, and 
 agreeable to the laws of argumentation ; in fine, whe- 
 ther they are combined together in a just and orderly 
 manner, so that no demonstrable propositions serve any 
 where as premises, unless they are conclusions of pre- 
 vious syllogisms. Now it is the business of logic, in 
 explaining the several operations of the mind, fully to 
 instruct us in all these points. It teaches the nature 
 and end of definitions, and lays down the rules by which 
 they ought to be framed. It unfolds the several spe- 
 cies of propositions, and distinguishes the self-evident 
 from the demonstrable. It delineates also the differ- 
 
172 DUNCAN'S ELEMENTS 
 
 cnt forms of syllogisms, and explains the laws of argn- 
 mentation proper to each. In fine, it describes the ' 
 manner ©f combining syllogisms, so as that they may 
 form a train of reasoning, and lead to the successive 
 discovery of truth. The precepts of logic, therefore, 
 as they enable us to judge with certainty, when a pro- 
 position is duly demonstrated, furnish a sure criterion 
 for distinguishing between truth and falsehood. 
 
 Sec, VI,,.. And extending to all Cases where a certain 
 Knowledge of Truth is attainable. 
 
 But perhaps it maybe objected, that demonstration 
 is a thing very rare and uncommon, as being the pre* 
 rogative of but a few sciences, and therefore the crite- 
 rion here given can be of no great use. I answer, that 
 -wherever by the bare contemplation of our ideas, truth 
 is discoverable, there also demonstration may be ob- 
 tained. Now that I think is an abundantly sufficient 
 criterion, which enables us to judge with certainty, 
 in all cases where the knowledge of truth comes with- 
 in our reach ; for with discoveries that lie beyond the 
 limits of the human mind, we have properly no business 
 nor concernment. *When a proposition is demonstra- 
 ted, we are certain f its truth. When, on the con- 
 trary, our ideas are such as have no. visible connexion 
 nor repugnance, and therefore .furnish not the proper 
 means of tracing their agreement or disagreement, 
 there we are sure that knowledge, scientifical know- 
 ledge 1 mean, is not attainable. But where there is 
 some foundation of reasoning, which yet amounts not 
 to the full evidence of demonstration, there the pre- 
 cepts of logic, by teaching us to determine aright of 
 the degree of proof, and of what is still wanting to 
 render it full and complete, enable us to make a due 
 ettimate of the measures of probability, and to propor- 
 tion our cssent to the grounds en which the proposi- 
 tion stands. And this is all we can possibly arrive at, 
 or even so much as hope for, in the exercise of facul- 
 ties so imperfect and limited as ours. For it were 
 the height of folly, to expect a criterion that should 
 enable us to distinguished truth from falsehood, ia 
 
OF LOGIC. 173 
 
 cases where a certain knowledge of truth is not at- 
 tainable. 
 
 Sec. Vll....The Distinction of Demonstration into di- 
 rect and indirect. 
 
 We have now done with what regards the ground 
 and evidence of demonstration ; but before we con- 
 clude this chapter,, it may net be improper to take no- 
 tice of the distinction of it into direct and indirect. 
 A direct demonstration is, when beginning with defi- 
 nitions, self-evident propositions, or known and allow- 
 ed truths, we form a train of syllogisms, and combine 
 them in an orderly manner, continuing the series 
 through a variety of successive steps, until at hist wq 
 arrive at a syllogism, whose conclusion is the proposi- 
 tion to be demonstrated. Proofs of this kind leave no 
 doubt or uncertainty behind them ; because all the se- 
 veral premises being true, the conclusions must be so 
 too, and of course the very las: conclusion, or proposi- 
 tion to be proved. I shall rot, therefore, any farther 
 enlarge upon this method of demonstrating ; having, I 
 hope, sufficiently explained it in the foregoing part of 
 this chapter, and shown wherein the force and validity 
 of it lies. The other species of demonstration is the 
 indirect^ or, as it is sometimes called, the apclogicaL 
 The manner of proceeding here is, by assuming a pro- 
 position which directly contradicts that we mean to 
 demonstrate, and thence by a continued train of rea- 
 soning, in the way of a direct demonstration, deducing 
 some absurdity or manifest untruth. For hereuj 
 we conclude that the proposition assumed was false, 
 and thence again, by an immediate consequence, that 
 the proposition to be demonstrated is true. 1 
 did, in his third book, being to demonstrate, that cir- 
 cles which touch one another inwardly h'avf not the 
 same centre ; assumes the direct contrary to .this, vis. 
 that they have the s,.me centre : and hence by an evi- 
 dent train of reasoning, proves, that a part is equal to 
 the whole. The supposition therefore leading to the 
 absurdity he concludes to be false, viz. that circles 
 Witching one another inwardly haze the same centre^ 
 P 2 
 
174 DUNCAN'S ELEMENTS 
 
 and thence again immediately infers, that they have 
 not the same centre. 
 
 Sec, VIII. ..Ground of Reasoning in indirect Demon- 
 strations. 
 Now because this manner of demonstration is ac- 
 counted by some not altogether so clear and satisfac- 
 tory nor to come up to that full degree of evidence, 
 ■which we meet with in the direct way of proof; I 
 shall, therefore, endeavour here to give a particular il- 
 lustration of it, and to show that it equally with the 
 other leads to truth and certainty. In order to this 
 "we must observe, that two propositions are said to be 
 contradictory one of another, when that which is as- 
 serted to be in .the one, is asserted not to be in the 
 other. Thus the propositions — circles that touch one 
 another inwardly have the same centre — and circles that 
 touch one another inwardly have not the same centre—^ 
 are contradictories ; because the second asserts the di- 
 rect contrary of what is asserted in the first. Now in 
 all contradictory propositions, this holds universally, 
 that one of them is necessarily true, and the other ne- 
 cessarily false. For if it be true, that circles, which 
 touch one another inwardly, have not the same centre, 
 it is unavoidably falst*, that they have the same centre. 
 On the other hand, if it be false that they have the 
 same centre, it is necessarily true, that they have not 
 the same centre. Since therefore, it is impossible for 
 them to be both true or both false at the same time, 
 it unavoidably follows, that one is necessarily true, and 
 the other necessarily false. This then being allowed, 
 which is indeed self-evident, if any two contradictory 
 propositions are assumed, and one of them can by a 
 clear train of reasoning be demonstrated to be false, 
 it necessarily follows that the other is true. For as 
 the one is necessarily true, and the other necessarily 
 false, when we come toMiscover which is the false pro- 
 position, we thereby also know the other to be true. 
 
 Sec. IX... .Indirect Demonstrations a sure Guide to 
 
 Certainty. 
 Now this is pre z\"c1y the manner of an indirect de- 
 
OF LOGIC- 173 
 
 monstratfon, as is evident from the account given of it 
 above. For there we assume a proposition, which di- 
 rectly contradicts that we mean to demonstrate, and 
 having, by a continued series of proofs, shown it to be 
 false, thence infer that its contradictory, or the propo- 
 sition to be demonstrated, is true. Asitherefore this 
 last conclusion is certain and unavoidable 1 , let us next 
 enquire, after what manner we come to be satisfied of 
 the falsehood of the assumed proposition, that so no 
 possible doubt may remain, as to the force and validity 
 of demonstrations of this kind. The manner, then, is 
 plainly this. Beginning with the assumed proposition, 
 we by the help of definitions, self-evident truths, or 
 propositions already established, continue a series of 
 reasoning, in the way of a direct demonstration, until 
 at length we arrive at some absurdity or known false- 
 hood. _ Thus Euclid, in the example before mentioned, 
 from tne supposition that circles touching one another 
 inwardly have the same centre, deduces, that a part is 
 equal- to the whole. Since, therefore, by a due and or- 
 derly process of reasoning, we come at last to a false con- 
 clusion, it is manifest, that all the premises cannot be 
 true. For were all the premises true, the last conclu- 
 sion must be so too, by what has been before demon- 
 strated. Now as to all the other premises made use of 
 in the course of reasoning, they are manifest and 
 known truths by supposition, as being either definitions, 
 self-evident propositions, or truths established. The 
 assumed proposition is that only as to which any doubt 
 or uncertainty remains. That alone, therefore, can 
 be false, and indeed, from what has been already shown, 
 must unavoidably be so. ,And thus we see, that in in- 
 direct demonstrations, two contradictory propositions 
 being laid down, one of which is demonstrated to be 
 false, the other, which is always the proposition to be 
 proved, must necessarily be true ; so that here, as well 
 as in the direct way of proof, we arrive at a clear and 
 satisfactory knowledge of truth. 
 
 Sec, X,.. .A particular Case of Indirect Demonstration* 
 
 This is universally the method of reasoning in all 
 
176 DUNCAN'S ELEMENTS 
 
 apological or indirect demonstrations ; but there is one 
 particular case, which has something so singular and 
 curious in it, that well deserves to be mentioned by it- 
 self; more especially, as the ground on which the con- 
 clusion rests will require some farther illustration. It 
 is, in short, this : that if any proposition is assumed, 
 from which in a direct train of reasoning we can deduce 
 its contradictory, the proposition so assumed is false, 
 and the contradictory one true. For if we suppose the 
 assumed proposition to be true, then, since all the^other 
 premises that enter the demonstration are also true, we 
 shall have a series of reasoning, consisting wholly of 
 true premises ; whence the last conclusion, or contra- 
 dictory of the assumed proposition, must be true like- 
 wise. So that by this means we should have two con- 
 tradictory propositions both true at the same time, 
 which is manifestly impossible. The assumed proposi- 
 tion, therefore, whence this absurdity flows, must ne- 
 cessarily be false, and consequently its contradictory, 
 which is here the proposition deduced from it must be 
 true. If then any proposition is proposed to be demon- 
 strated, and we assume the contradictory of that pro- 
 position, and thence directly infer the proposition to be 
 demonstrated, by this very means we know that the 
 proposition so inferred is true. For since from an as- 
 sumed proposition we have deduced its contradictory, 
 we are thereby certain that the assumed proposition is 
 false ; and if so, then its contradictory, or that deduc- 
 ed from it, which in this case is the same with the pro- 
 position to be demonstrated, mu3t be trim. 
 
 Sec. XI. ...A due Knowledge of the Principles of Logic 
 indispensably necessary to make us proper judges ef 
 Demonstration ; 
 
 That this is not a mere empty speculation, void of 
 all use and application in practice, is evident from the 
 conduct of the mathematicians, who have adopted this 
 manner of reasoning, and given it a place among their 
 demonstrations. We have a curious instance of it in 
 the twelfth proposition of the ninth book cf the ele- 
 ments, Euclid there proposes to demonstrate, that in 
 
OF LOGIC. 177 
 
 Oiiy series of numbers, rising fr ojn unity in geometrical 
 progression, all the prime numbers, that measure the last 
 term in the series, will also measure the next after unity. 
 In order to this he assumes the contradictory of the pro- 
 position to be demonstrated, namely ; that some prime 
 number measuring the last term in the series, dees not 
 measure the next, after unity, and thence by a continued 
 train of reasoning proves, that it actually does measure 
 it. Hereupon be concludes the assumed proposition to 
 be false, and that which is deduced from it, or its con- 
 tradictory, which is the very proposition he proposed 
 to demonstrate, to be true. Now that this is a just 
 and conclusive way of reasoning, is abundantly mani- 
 fest, from what we have so clearly established above. 
 I would only here observe, how necessary some know- 
 ledge of the rules of logic is, to enable us to judge of 
 the force, justness, and validity of demonstrations j 
 since siich may sometimes occur, where the truth of the 
 proposition demonstrated will neither be owned nor 
 perceived, unless we know before-hand, by means of 
 logic, that a conclusion so deducea, is necessarily true 
 and valid. For though it be readily allowed, that by 
 the mere strength of our natural faculti s &, v:c c-r, zt 
 once discern, that of two contradictory prepositions, 
 the one is necessarily true, and the other necessarily 
 false : yet when they are so linked together in a de- 
 monstration, as that the one serves as a previous propo- 
 sition, whence the other is deduced ; it does not so im- 
 mediately appear, without some knowledge of the prin- 
 ciples of logic, why that alone, which is collected by 
 reasoning, ought to be embraced as true,* and the other, 
 whence it is collected, to be rejected as false. 
 
 Sec. XII.... And of itself sufficient to guard us against 
 Error* and false Reasoning. 
 
 Having thus, I hope, sufficiently evinced the certain- 
 ty of demonstration in all in branches, and shown the 
 rules by which we ought to proceed, in order to arrive 
 at a just conclusion, according to the various ways of 
 arguing made use of; I hold it needless to enter upon 
 a particular consideration of those several species of 
 
m DUNCANS ELEMENTS 
 
 false reasoning which logicians distinguish by the 
 name of sophisms. He that thoroughly understa-nds 
 the form and structure of a good argument, will of 
 himself readily discern every deviation from it. And 
 although sophisms have been divided into many classes, 
 which are all cailed by sounding names, that therefore 
 carry in them much appearance of learning ; yet are 
 the errors themselves so very palpable and obvious, 
 that I should think it lost labour to write for a man 
 capable of being misled by them. Here, therefore, we 
 choose to conclude this third part of logic, and shall 
 in the next book give some account of method, which, 
 though inseparable from reasoning, is nevertheless 
 always considered by logicians us a distinct operation 
 of the mind; because its influence is not confined to 
 the mere exercise of the reasoning faculty, but extends 
 in some degree to all the transactions of the under- 
 standing. 
 
 BOOK IV. 
 
 OF METHOD. 
 
 OF METHOD IN GENERAL, AND THE DI- 
 VISION OF IT INTO ANALYTIC AND 
 SYNTHETIC. 
 
 Sec. I..*. The understanding sometimes employed input- 
 ting together known truths, 
 WE have now done with the three first operations 
 of the mind, whose office it is to search after 
 truth, and enlarge the bounds of human knowledge. 
 There is yet a fourth, which regards the disposal and ar- 
 rangement of our thoughts, when we endeavour so to 
 put them together, that their mutual connexion and 
 
OF LOGIC. 179 
 
 dependence may be clearly seen, This is what logicians 
 call method, and place always the last in order, in ex- 
 plaining the powers of the understanding ; because it 
 necessarily supposes a previous exercise of our other fa- 
 culties, and some progress made in knowledge, before 
 we can exert it in any extensive degree. It often hap- 
 pens, in the pursuit of truth, that unexpected discove- 
 ries present themselves to the mind, and those, too, re- 
 lating to subjects very remote from that about which 
 we are at present employed. Even the subjects them- 
 selves of our enquiry, are not always chosen with a 
 due regard to order, and their dependence one upon 
 another. Chance, our particular way of life, or some 
 present and pressing views, often prompt us to a varie- 
 ty of researches, that have but little connexion in the 
 nature of things. When, therefore, a man accustom- 
 ed to much thinking, comes, after any considerable in- 
 terval of time, to take a survey of his intellectual ac- 
 quisitions, he seldom finds reason to be statisfied with 
 that order and disposition, according to which they 
 made their entrance into his understanding. They are 
 there dispersed and scattered, without subordination, 
 or any just and regular coherence ; insomuch that the 
 subserviency of one truth to the discovery of another, 
 does not scl readily appear to^the mind. Hence he is 
 convinced of the necessity of distributing them into 
 various classes, and combining into an uniform sys- 
 tem whatever relates to one and the same subject. 
 Now this is the true and proper business of method ; 
 to ascertain the various divisions of human knowledge, 
 and so to adjust and connect the parts in every branch* 
 that they may seem to grow one out of another, and 
 form a regular body of science, rising from first prin- 
 ciples, and proceeding by an orderly concatenation *of 
 truths. 
 
 Sec. 11*. ..Sometimes in the Search and Discovery of 
 such' as are unknown. 
 
 In this view of things, it is plain, that we must be be- 
 forehand well acquainted with the truths we are to 
 combine together ; otherwise how ccuid we discern 
 
i 80 DUNCAN'S ELEMENTS 
 
 their several connexions and relations, or so dispose o£ 
 them as their mutual dependence may require ? But 
 now it often happens, the understanding is employed, 
 not in the arrangement and composition of known 
 truths, but in the search and discovery of such as are 
 unknown. And here the manner of proceeding is very 
 different, inasmuch as we assemble at once our whole 
 stock of knowledge relating to any subject, and, after 
 a general survey of things, begin with examining them 
 separately and by parts. Hence it comes to pass, that 
 whereas at our first setting out, we were acquainted 
 only with some of the grand strokes and outlines, if I 
 may so say, of truth, by thus, pursuing her through her 
 several windings and recesses^ we gradually discover 
 those more inward and finer touches, whence she de- 
 rives all her strength, symmetry and beauty. And 
 here it is, that when, by a narrow scrutiny into things, 
 we have unravelled any part of knowledge, and traced 
 it to its first and original principles, insomuch that the 
 whole frame and contexture of it lies open to the view 
 of the mind ; here, I say, it is, that, taking it the con- 
 trary way, and beginning with these principles, we 
 •can so adjust and put together the parts, as the order 
 and method of science requires. 
 
 Sec. III.... Illustrated by the Similitude of a Watch, 
 
 But as these things are best understood when illus- 
 trated by examples, especially if they are obvious, and 
 taken from common life ; let us suppose any machine, 
 for instance, a watch, presented to us, whose structure 
 and composition we areas yet unacquainted with, but 
 want, if possible, to discover. The manner of pro- 
 ceeding, in this case, is, by taking the whole to pieces, 
 and examining the parts separately one after another. 
 When by such a scrutiny we have thoroughly inform- 
 ed ourselves of the frame and contexture of each, we 
 then compare them together, in order to judge of their 
 mutual action and influence. By this means we gra- 
 dually trace out tiie inward make and composition of 
 the whote, and come at length to discern, how parts of 
 £uch a form, and so put together as we found, in unra- 
 
OF LOGIC. 1S1 
 
 veiling and taking them asunder, constitute that par- 
 ticular machine called a watch, and contribute to all 
 the several motions \and phenomena observable in it. 
 This discovery being made, we can take things the con- 
 trary way, and, beginning with the parts, so dispose 
 and connect them, as their several uses and structures 
 require, until at length we arrive at the whole itself, 
 from the unravelling of which these parts resulted. 
 
 Sec, 1ST ....Ground of the Analytic and Synthetic Me- 
 thods. 
 And as it is in tracing and examining the works of 
 art, so it is in a great measure in unfolding any part of 
 human knowledge. For the relations and mutual ha- 
 bitudes of things, do not always immediately appear, 
 upbn comparing them one with another. Hence we 
 have recourse to intermediate ideas, and, by means of 
 them, are furnished with those previous propositions 
 that lead to the conclusion we are in quest of. And if 
 it so happen, that the previous propositions themselves 
 are not sufficiently evident, we endeavour,' by new 
 middle terms, to ascertain their truth, still tracing 
 things backward in a continued series, until at length 
 we arrive at some syllogism, where the premises are 
 first snd self-evident principles. This done, we become 
 perfectly satisfied as to the truth of all the conclusions 
 we have passed through, inasmuch as they are now seen 
 to stand upon the firm and immovable foundation of 
 our intuitive perceptions. And as we arrived at this 
 certainty, by tracing things backward to the original 
 principles whence they flow, so may we at any time re- 
 new it by a direct contrary process, if, beginning with, 
 these principles, we carry the train of our thoughts 
 forward, until they lead us by a connected chain of 
 proofs, to the very last conclusion of the series. 
 
 Sec. V.. ..Division of Method into Analytic and Syn- 
 thetic. 4/ 
 Hence it appears, that in disposing and putting to- 
 gether our thoughts, either for our own use, that the 
 discoveries we have made may at all times lie open to 
 the review of the mind ; or, where we mean to com- 
 
 Q 
 
182 DUNCAN'S ELEMENTS 
 
 municate and unfold these discoveries to others, there 
 are two ways of proceeding, equally within our choice. 
 For we may so propose the truths relating to any part 
 of knowledge, as tliey presented themselves to the mind 
 in the manner of investigation, carrying on the series 
 of proofs in a reverse order, until they at last termi- 
 .nate in first principles : or, beginning with these prin- 
 ciples, we take the contrary way, and from them de- 
 duce, by a direct train of reasoning, all the several 
 propositions we want to establish. This diversity in 
 the manner of arranging our thoughts gives rise to the 
 twofold division of method established among logici- 
 ans. For method, according to their use of the word, 
 is nothing else but the order and disposition of cur 
 thoughts relating to any subject. When truths are so 
 proposed and put together, as they were or might have 
 been discovered, this is called the analytic method, or 
 the method of resolution ; inasmuch as it traces things 
 backward to their source, and resolves knowledge into 
 its first and original principle. When, on the other 
 hand, they are deduced from these principles, and con- 
 nected according to their mutual dependence, inso- 
 much that the truths first in order tend always to the 
 demonstration of those that follow, this constitutes 
 what we call the synthetic method, or method of compo- 
 sition. For here we proceed by gathering together 
 several scattered parts of knowledge, and combining 
 them into one whole, or system, in such manner, that 
 the understanding is enabled distinctly to follow truth 
 through all her different stages and gradations. 
 
 Sec. VI.... Called otherwise the Method of Invention 
 and the Method of Science, 
 
 There is farther, to be taken notice of, in relation 
 to these two species ©f method ; that the first has also 
 -obtained the name pf the method of invention, because 
 it observes the order in which our thoughts succeed one 
 another, in the invention or discovery of truth. The 
 other, again, is often denominated the method of doc-, 
 trine r ar instruction, inasmuch as in laying our thoughts 
 before others, we generally choose to proceed in the 
 
OF LOGIC. 18* 
 
 synthetic manner, deducing them from their first prin- 
 ciples. For we are to observe, that although there is 
 great pleasure in pursuing truth in the method of inves- 
 tigation, because it places us in the Condition of the 
 inventor, and shows the particular train and process of 
 thinking by which he arrived at his discoveries ; yet it 
 is ^not so well accommodated to the purposes of evi- 
 dence and conviction. For at our first setting out, we 
 are commonly unable to divine where the analysis will 
 lead us ; inasmuch that our researches are for some 
 time little better than a mere groping in the dark. 
 A nd even after light begins to break in upon us, we are 
 still obliged to many reviews, and a frequent compari- 
 son of the several steps of the investigation among 
 themselves. Nay, when we have unravelleHihe whole, 
 and reached the very foundation on which our discove- 
 ries stand, all our certainty, in regard to their truth* 
 will be found in a great measure to arise from that 
 connexion we are now able to discern between them 
 and first principles, taken in the order of composition* 
 But in the synthetic manner of disposing our thoughts, 
 the case 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 ; so that in our progress 
 from one part of knowledge to another, we have al- 
 ways a clear perception of the grounds on which our as- 
 sent rests. In communicating therefore, our discove- 
 ries to others, this method is apparently to be chosen, 
 as it wonderfully improves and enlightens the under- 
 standing, and leads to an immediate perception of truth. 
 And hence it is, that in the following pages, we choose 
 to distinguish it by the name of the method of science ; 
 not only as in the use of it we arrive at science and cer- 
 tainty, but because it is in fact the method, in which 
 all those parts of human knowledge, that properly bear 
 the name of sciences, are and ought to be delivered. 
 But we now proceed to explain these two kinds of me- 
 thod more particularly. 
 
184 DUNCAN'S ELEMENTS 
 
 OF THE METHOD OF INVENTION. 
 
 Sec, I. Origin of the several Arts and Inventions of 
 Human Life, 
 
 BY the method of invention we understand such a 
 disposition and arrangement of our thoughts, as 
 follows the natural procedure of the understanding, and 
 presents them in the order in which they succeed one 
 another, in the investigation and discovery of truth. 
 Now it is plain, that to handle a subject successfully 
 accordinggp> this method, we have no more to do than 
 observe the several 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, especially when 
 reduced to that which is in the schools termed an art ; 
 that the rules, by which we conduct ourselves, are no 
 other than a series of observations drawn from the at- 
 tention of the mind to what passes, while we exercise 
 our faculties in that particular way. For when we set 
 about any invention or discovery, we are always pushed 
 on by some inward principle, disposition, or aptitude 
 shall I call it, which we experience in ourselves, and 
 •which makes us believe, that the thing we are in quest 
 of, is not altogether beyond our reach. We therefore 
 begin with essaying our strength, and are sometimes 
 successful, though perhaps more frequently not. But 
 as the mind, when earnestly bent upon any pursuit, is 
 not easily discouraged by a few disappointments, we are 
 only set upon renewing our endeavours, and* by an ob- 
 stinate perseverance, and repeated trials, often arrive 
 at the discovery of what we have in view. Now it is 
 natural for a man of a curious and inquisitive turn, af- 
 ter having mastered any part of knowledge with great 
 labour and difficulty, to set himself to examine how he 
 happened to miscarry in his first attempts, and by what 
 particular method of procedure he at length came to be 
 
OF LOGIC. 185 
 
 successful. By this means we discover on the one 
 hand, those rocks and shelves which stand most in our 
 way, and are apt to disturb and check our progress ; and 
 on the ether, that more sure and certain course, which 
 if we continue in steadily, will bring us to the attain- 
 ment of what we are in pursuit of. Hence spring all 
 the arts and inventions of human life, which, as we 
 l^ave already said, are founded upon a series of rules and 
 observations, pointing out the true and genuine manner 
 of arriving at any attainment. When the mind res*s 
 satisfieddn a bare contemplation of the rules, and the 
 reasons on which they are founded, this kind of know- 
 ledgt is called speculative* But if we proceed farther, 
 and endeavour to apply these rules to practice, so as to 
 acquire a habit of exerting them on all proper occa- 
 sions, we are then said to be possessed of the a*t itself. 
 
 Sec. lf...JFhj; in treating of the Method of Invention^ 
 ive must give ^ome account of the Art itself 
 
 From what has been said, it appears, that, in order 
 distinctly to explain the method of invention, we must 
 take a view of the understanding, as employed in the 
 . search and investigation of truth. For by duly attend- 
 ing to its procedure and advances, we shall not only 
 discover the rules by which it conducts itself, but be 
 enabled also to trace out the several helps and contri- 
 vances it makes use of, for the more speedy and effec-' 
 tual attainment of its ends* And when these particulars 
 are once known, it will not be difficult for us, in laying 
 open our discoveries to others, to combine our thoughts 
 agreeably to the method here required. Because, hav- 
 ing fixed and ascertained the rules of it, and being per- 
 fectly acquainted with the conduct and manner of the 
 mind, we need only take a view of the several truths, 
 as they succeed one another in the series of investiga- 
 tion, set them in order before us, and fairly transcribe 
 the appearance they make to the understanding. Hence 
 it is, that logicians, in treating of the metnod of in- 
 vention, have not merely confined themselves to the 
 laying down of directions for the disposal and arrange- 
 ment of our thoughts j but have rather explained the 
 Q2 
 
186 DUNCAN'S ELEMENTS 
 
 art itself, and established those rules by which the mind 
 ought to proceed in the exercise of its inventive powers. 
 For they rightly judge, that if these were thoroughly 
 understood, the other could no longer remain unknown. 
 By this means it happens, that the method of invention 
 is become another expression for the art of invention, 
 and very often denotes the conduct and procedure of the 
 understanding in the search of truth. And as some 
 knowledge of the principles of the art, is in a manner 
 absolutely necessary towards a true conception of the 
 rules by which we ought to govern and dispose our 
 thoughts in treating subjects after this method ; we 
 shall, therefore, follow the example of other logicians, 
 and endeavour to give some short account of the busi- 
 ness of invention, and of those several helps and con- 
 trivances by which the mind is enabled to facilitate 
 and enlarge its discoveries. 
 
 Sec. III... .Attention and a Comprehensive understand- 
 ing the preparatory qualifications to Invention, 
 
 It has been already observed, that when the mind 
 employs itself in the search of unknown truths, it be- 
 gins with assembling at once its whole-stock of know- 
 ledge relating to the subject, and after a general sur- 
 vey of things, sets about examining them separately 
 and by parts. Now as in this separate examination, 
 the number of parts continually increase upon us — and 
 as it is farther necessary, that we survey them on all 
 sides, compare them one with another, and accurately 
 trace their mutual habitudes and respects — it is from 
 hence apparent, that in the exercise of invention, two 
 things are of principal consideration. First, an en- 
 larged and comprehensive understanding, able to take 
 in the great multitude of particulars, that frequently 
 come under our notice. Secondly, a strong habit of 
 attention, that lets nothing remarkable slip its view, 
 and distinguishes carefully all those circumstances 
 which tend to the illustrating and clearing the sub- 
 ject we are upon. These are the great and preparatory 
 qualifications, without which it were vain to hope, that 
 any considerable advance could be made in enlarging 
 
OF LOGIC. 187 
 
 the bounds of human knowledge. Nor ought we to 
 esteem it a small advantage, that they are in some mea- 
 sure in our own power, and may, by a proper cultiva- 
 tion, be improved aud strengthened to a degree almost 
 beyond belief. We find by experience, that the study 
 of: mathematics in particulars greatly serviceable to 
 this end. Habits, we all know, grow stronger by^ex- 
 ercise ; and as in this science there is a perpetual call 
 upon our attention, it by degrees becomes natural to 
 us, so as that we can preserve it steady and uniform, 
 through long and intricate calculations, and that 
 with little or no fatigue to the" understanding. But a 
 yet more wonderful advantage, arising from the cul- 
 ture of the mathematics, is this, that hereby we in 
 some measure extend the dimensions of the human 
 mind, enlarge its compass of perception, and accustom 
 it to wide and comprehensive views of things. For 
 whereas at our first setting out, we often find it ex- 
 tremely difficult to master a short and- easy demon- 
 stration and trace the connexion of its several parts : 
 yet as we advance in the science, the understanding is 
 seen gradually to dilate, and stretch itself to a greater 
 size ; insomuch that a long and intricate series of rea- 
 soning is often taken in with sca«:e any labour of 
 thought ; and not only so, but we can in some cases, 
 with a single glance of our minds, run through an en- 
 tire system of truths, and extend our view at once to 
 all the several links that unite and hold them together. 
 
 Sec. IV.... "Judicious choice of intermediate Ideas ano- 
 ther great requisite in this Art. 
 
 When we are furnished with these two preparatory 
 qualifications, the next requisite to the discovery of 
 truth is, a judicious choice of intermediate ideas. We 
 have seen, in the third part of this treatise, that many 
 of our ideas are of such a nature as not to discover 
 these several habitudes and relatioas by any immediate 
 comparison on? with another. In 'this case, we must 
 have recourse to intermediate ideas ; and the great art 
 lies in finding out such as have an obvious and perceiv- 
 able connexion with the ideas whose relations we en- 
 
188 DUNCAN'S ELEMENTS 
 
 quire after. For thus it is, that we are furnished with 
 known and evident truths, to se*ve as premises for the 
 discovery of such as are unknown. And indeed the 
 whole business of invention seems,, in a great measure, 
 to lie in the due assemblage and disposition of these 
 preliminary truths. For they not only lead us, step 
 by step, to the discovery we are in quest of, but are 
 so absolutely necessary in the, case, that without them 
 it were vain to attempt it ; nothing being more Cer- 
 tain, than that unknown propositions can no otherwise 
 be traced but by means of some connexion they have 
 with such as are known. Nay, reason itself, which is 
 indeed the art of knowledge, and the faculty by which 
 we push on our discoveries ; yet by the very definition 
 of it implies no more, than an ability $f deducing un- 
 known truths from principles or propositions that are 
 already known. Now, although this happy choice of 
 intermediate ideas, so as to iurnish a due train of pre- 
 vious propositions, that shall lead us successively from 
 one discovery to another, depends in some measure 
 upon a natural sagacity and quickness of mind ; it is 
 yet certain, frora experience, that even here much may 
 be effected by a stubborn application and industry. In 
 order to this, it is in the first place necessary, that we 
 have an extensive knowledge of things, and some ge- 
 neral acquaintance with the whole circle of arts and 
 sciences. Wide and extended views add great force 
 and penetration to the mind, and enlarge its capacity 
 of judging. And if to this we join in thesecond place, 
 a more particular and intimate study of whatever re- 
 lates to the subject about which our enquiries are em- 
 ployed, we seem to bid fair for success in our attempts. 
 For thus we are provided with an ample variety out of 
 which to choose our intermediate ideas, and are there- 
 fore more likely to discover some among them that will 
 furnish out the previous propositions necessary in any 
 train of reasoning.* 
 
 Sec. V.. ..Sagacity and a quickness of understanding 
 greatly promoted by the study cf Algebra* 
 
 It is not, indeed, to be denied, that when we have 
 
GF LOGIC. 189 
 
 even got all our materials about us, much still depends 
 upon a certain dexterity and address, in singling out 
 the most proper, and applying them skillfully for the 
 discovery of truth. This is that talent which is known 
 by the name of sagacity, and commonly supposed to 
 be altogether the gift of nature. But yet I think it is 
 beyond dispute, that practice, experience, and a watch- 
 ful attention to the procedure of our own minds, while 
 employed in the exercise of reasoning, are even here of 
 very great avail. It is a truth well known to those 
 who have made any considerable progress in the study 
 of algebra, that an address and skill in managing ^in- 
 tricate questions may be very often obtained, by a care- 
 ful imitation of the best models. For although when we 
 first set out about the solution of equations, we are puz- 
 zled at every step, and think we can never enough ad- 
 mire the sagacity of those who present us with elegant 
 models in that way ; yet by degrees we ourselves ar- 
 rive at a great mastery, not only in devising proper 
 equations, and coupling them artfully together, so as 
 from the more complicated to derive others that are 
 simple ; butaho in contriving useful substitutions, ta 
 free our calculations from fractions, and those intrica- 
 cies that arise from surds and irrational quantities; 
 Nor is it a small pleasure attending the prosecution of 
 this study, that we thus discern the growing strength 
 of our minds, and see, ourselves approaching nearer and 
 nearer to that sagacity and quickness of understand- 
 ing which we see so much admired in others, and were 
 at first apt to conclude altogether beyond our reach. 
 
 Sec. VI Where Art and Management are required 
 
 in the business of invention. 
 
 We have now considered those requisites to inven- 
 tion, that have their foundation in the natural talents 
 of the mind : and enlarged and comprehensive under- 
 standing, a strong habit of attention, a sagacity and 
 quickness in discerning and applying intermediate ideas* 
 Let us next take a view of such other helps, as more im- 
 mediately depend upon art and management, and show 
 the address of the mind, in contriving means to facili- 
 
190 DUNCAN'S ELEMENTS 
 
 tate its discoveries, and free it from allunnecessary fa- 
 tigue and labour. For we are to observe, that though 
 the capacity of the intellect may be greatly enlarged by 
 use and exercise, yet still our views are confined within 
 certain bounds, beyond which a finite understanding 
 cannot reach. And as it often happens, in the inves- 
 tigation of truth, especially where it lies at a consider- 
 able distance from first principles, that the number of 
 connexions and relations are so great, as not to be 
 taken in at once by the most improved understanding; 
 it is therefore one great branch of the art of invention, 
 to take account of these relations, as they come into 
 view, and dispose them in such manner, that they al- 
 ways lie open to the inspection of the mind, when dis- 
 posed to turn its attention that way. By this means, 
 -without perplexing ourselves with too many considera- 
 tions at once, we have yet these relations at command, 
 when necessary to be taken notice of in the prosecution 
 of our discoveries : and the understanding, thus free 
 and disengaged, can bend its powers more intensely to- 
 wards that particular part of the investigation it is at 
 present concerned with. Now in this, according to my 
 apprehension, lies the great art of human knowledge ; 
 to manage with skill the capacity of the intellect, and 
 contrive such helps: as may bring the most wide and -ex- 
 tended objects within the compass of its natural powers. 
 When, therefore, the multitude of relations increase 
 very fast upon us, and grow too unwieldy to be dealt 
 with in the lump, we must combine them in different 
 classes, and so dispose of the several parts, as that they 
 may at all times lie open to the leisurely survey of the 
 rnind. By this means we avoid perplexity and confu- 
 sion, and are enabled to conduct our researches, with- 
 out being puzzled with that infinite crowd of particu- 
 lars, that frequently fall under our notice in long and 
 difficult investigations. For by carrying our attention 
 successively from one part to another, we can, upon oc- 
 casion, take in the whole ; and knowing also the order 
 and disposition of the parts, may have recourse to any 
 of them at pleasure, when its aid becomes necessary in 
 the course of our enquiries* 
 
OF LOGIC. 191 
 
 Sec. VII. .;An orderly disposition of great use in 
 adapting objects to the capacity of the understanding ; 
 First then I say, that an orderly combination of things 
 and classing them together with art and address, brings 
 great and otherwise unmanageable objects, upon a level 
 with the powers of the mind.- We have seen, in the 
 first part of this treatise, how by taking numbers in a 
 progressive series, and according to an uniform faw of 
 composition, the most bulky and formidable collections 
 are comprehended with ease, and leave distinct impres- 
 sions in the understanding. For the several stages of 
 the progression serve as so many steps to the mind, by 
 which it ascends gradually to the highest combinations; 
 and as it can carry its views from one to another, with 
 great ease and expedition, it is thence enabled to run 
 over all the pnrts separately, and thereby rise to a just 
 conception of tfee whole. The same thing happens in 
 all our other complex notions, especially when they 
 grow very large and complicated ; for tfren it is that 
 we become sensible of the necessity of establishing a 
 certain order and gradation in the manner of combining 
 the parts. This has been already explained, at some 
 length, in the chapter of the composition and -resolu- 
 tion of our ideas; where we have traced the gradual 
 progress of the mind through all the different orders of 
 perception, and shown, that the most expeditious way 
 of arriving at a just knowledge of the more compound- 
 ed notices of the understanding, is by advancing regu- 
 larly through all.tjie intermediate steps. Hence it is 
 easy to perceive what advantages must arise from a like 
 conduct in regard to those several relations and connex- 
 ions, upon which the investigation 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 use of upon occasion, and furnish their 
 assistance towards the discovery of w T hat we are in quest 
 of. Now this is of principal consideration in the business 
 of invention, to have our thoughts so much under com- 
 mand, that, in comparing things together, in order to 
 discover the result of their mutual connexions and de- 
 pendence, all the several ligltfs that tend to the cleariwg 
 
192 DUNCAN'S ELEMENTS 
 
 the subject we are upon, may lie distinctly open to the 
 understanding, so as nothing material shall escape its 
 view : because an oversight of this kind, in summing 
 up the account, must not only greatly retard its ad- 
 vances, but in many cases check its progress altogether. 
 
 Sec. VIII.. ,,And enabling us to proceed gradually and 
 with ease in the investigation of Truth, 
 
 . But secondly, another advantage arising from this 
 orderly disposition, is, that hereby we free the mind 
 from all unnecessary fatigue, and leave it to fix its at- 
 tention upon any part separately, without perplexing it- 
 self with the consideration of the whole. Unknown 
 truths,' as we have already ©bserved, are only to be 
 traced by means of the relation between them and others 
 that are known. When, therefore, these relations be- 
 come very numerous, it must needs greatly distract the 
 mind, were itto have its attention continually upon the 
 stretch after such a multitude of particulars at once. 
 But now, by the method of classing and ordering our 
 perceptions above explained, this inconvenience is 
 wholly prevented. For a just distribution of things, as 
 it ascertains distinctly the place of each, enables us to 
 call any of them into view at pleasure, when the present 
 consideration of it becomes necessary. Hence the mind 
 proceeding gradually through the several relations of 
 its ideas, and marking the results of them at every step, 
 can always proportion its enquiries to its strength ; and 
 confining itself to such a number of objects as it can 
 take in and manage with ease, sees more distinctly all 
 the consequences that arise from comparing them one 
 with another. When, therefore, it comes afterwards 
 to take a review of these its several advances, asby this 
 means the amount of every step of the investigation is 
 fairly laid open to its inspection, by adjusting and put- 
 ting these together, in due order and method, it is en- 
 abled at last to discern the result of the whole. And 
 thus, as before in the composition of our ideas so like- 
 wise here in the search and discovery of truth, we are 
 fain to proceed gradually, and by a series of successive 
 
 stages. For these are so many resting places to the 
 
OF LOGIC, 193 
 
 mind, whence to look about it, survey the conclusions 
 it has already* gained, and see what helps they afford, 
 towards the obtaining of others which it must still pass 
 through, before it reaches the end of the investigation. 
 Hence it often happens, that very remote and distant 
 truths, which lie far beyond the reach of any single ef- 
 fort of the mind, are yet by, this progressive method, 
 successively brought to light, and that too with less fa- 
 tigue to the understanding than could at first have well 
 been imagined. For although the whole process, ta- 
 ken together, is frequently much too large to come 
 within the view of the mind at once ; and therefore, 
 considered in that light, may be said truly to exceed 
 its grasp; yet the several steps of the investigation 
 by themselves are often easy and managable enough, 
 so that by proceeding gradually from one to another, 
 and thoroughly mastering the parts as we advance, we 
 carry on our researches with wondrous dispatch, and 
 are at length conducted to that very truth, with a view 
 to the discovery of which the inquishion itself was set 
 on foot. 
 
 Sec. IX.... Algebra and Arithmetic, properly speaking, 
 both Arts of Invention, 
 But now perhaps it may not be improper, if we en- 
 deavour to illustrate these observations by an example, 
 and set ourselves to trace the conduct andmanner of 
 the mind, when employed in the exercise of invention. 
 There are two great branches of the mathematics pecu- 
 liarly fitted to furnish us with models in this way. 
 Arithmetic I mean, and Algebra. Algebra is univer- 
 sally known to be the very art and principle of inven- 
 tion ; and in arithmetic, too, we are frequently put 
 upon the finding out of unknown numbers, by means of 
 their relations and connexions with others that are 
 known : as where it is required to find a number equ^l 
 to this sum of two others, or the product of two others. 
 I choose to borrow my examples chiefly from this last 
 science, both because they will be more within the 
 reach of those for whom this treatise is principally de- 
 signed ; as likewise, because arithmetic furnishes the 
 best models of a happy sagacity and management, \\\ 
 
 R 
 
194 DUNCAN'S ELEMENTS 
 
 classing and regulating our perceptions. So that here , 
 more than in any other branch of human knowledge, 
 we shall have an opportunity of observing, how much, 
 an, orderly disposition of things tends to the ease and 
 success of our enquiries, by leaving us to canvass the 
 parts separately, and thereby rise to a gradual concep- 
 tion of the whole, without entangling ourselves with 
 too many considerations at once, in any single step cf 
 the investigation. For it will indeed be found, that a 
 dexterity and address, in the use of this last advantage, 
 serves to facilitate and promote our discoveries, almost 
 beyond imagination or belief. 
 
 Sec. X....77i^ method of classing our Perceptions in 
 . Arithmetic. 
 
 We have already explained the manner of reducing 
 numbers into classes and of distinguishing these clas- 
 ses by their several names. And now we are farther 
 to obs#ve, that the present method of notation is so 
 contrived, as exactly to fall in with this form of num- 
 .bering. For as in the names of numbers, we rise irom 
 units to tens, from tens to hundreds, from hundreds to 
 thousands, ZJfc. so likewise in their notation, the same 
 figures, in different places, signify 'these several combi- 
 nations. Thus 2 in the first place, on the right hand 
 denotes two units, in the second place, it expresses so 
 many tens, in the third hundreds, in the fourth thou- 
 sands. By this means k happens, that when a number 
 is written down in figures, as every figure in it expresses 
 some distinct combination, and all combinations toge- 
 ther make up the total sum ; so may the several figures 
 be considered as the constituent parts of the number. 
 Thus the number 2436, is evidently, by the very no- 
 tation, distinguished into four parts, marked by the 
 four figures that serve to express it. For the first de- 
 notes two thousand, the second, four hundred, the third 
 thirty or three tens, and the fourth six. These several 
 parts, though they, here appear in a conjoined form, may 
 yet be also expressed separately thus, 2000, 400, 30, 
 and 6, and the amount is exactly the same. 
 
OF LOGIC. 195 
 
 Sec. XL.*. The helps thence derived towards an easy 
 addition of numbers* 
 This then being the case, if it is required to find a 
 number equal to the sum of two others given ; our bu- 
 siness is, to examine separately these given numbers, 
 and if they appear too large and bulky to be dealt with 
 by a single elfort of thought, then, since the very nota- 
 tion, distinguishes them into different parts, we must 
 content ourselves with considering the parts asunder, 
 and finding their sums one after another. For since 
 the whole is equal to all its parts, if we find the sums 
 of the several parts of which any two numbers consist, 
 we certainly find the total sum of the two numbers. 
 And therefore, these different sums, united and put to- 
 gether, according to the established rules of notation 
 will be the very number we are in quest of. Let it be 
 proposed for instance, to find a number equal to the 
 sum of these two : 2436, and 4532. As the finding 
 of this by a single effort of thought would be too vio- 
 lent an exercise for the mind, 1 consider the figures, 
 representing these numbers, as the parts of which they 
 consist, and therefore set myself to discover their sums 
 one after another. Thus 2, the first figure on the 
 right hand of the one, added to 6, the first figure on 
 the right hand of the other, makes 8, which is therefore 
 the sum of these two parts. Again, the sum of 5 
 and 3, the two figures or parts in the second place, is 
 likewise 8. But now as figures in the second place, 
 denote not simple units, but tens ; hence it is plain, 
 that 5 and 3 here, signify five tens and three tens, or 
 50 and 30, whose sum therefore must be eight tens or 
 80. 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 stand 
 also in the second place, and so really express, as it 
 ought to do, eight tens, or 80. And thus it is hap- 
 pily contrived, that though in the addition of the tens, 
 I consider the figures composing them as denoting on- 
 ly simple units, which makes the operation easier and 
 less perplexed ; yet by the place their sum obtains in the 
 number found, it expresses the real amount of the parts 
 
196 DUNCAN'S ELEMENTS 
 
 added, taken in their full and complete values. The 
 same thing happens in summing the hundreds and thou- 
 sands ; that is, though the figures expressing these 
 combinations, are added together as simple units ; yet 
 their sums, standing in the third and fourth places of 
 the -number found, thereby really denote the hundreds 
 and thousands, and so represent the true value of the 
 parts added. 
 
 Sec. XII..*. Because in the several steps by which it is 
 carried on, the mind is put to liii-le or no fatigue. 
 
 Hence then we have a manifest proof of the great 
 advantages derived from an artful method of classing 
 our perceptions. For as the numbers themselves are by 
 .this means distinguished into different parts which 
 brings them more readily within the compass of the un- 
 derstanding ; so by taking these parts separately, the 
 operations about numbers are rendered very easy and 
 simple. And indeed it is particularly worthy cur no- 
 tice, and though in adding two very large numbers to- 
 gether, the whole process is of sufficient length ; yet 
 the several steps by which it is conducted, are managed 
 with incredible dispatch, and scarce any fatigue to the 
 jnind. This is apparent in the example given above, 
 where we see, 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 
 summed. But what is yet more wonderful, though in 
 the progress of a long operation, the figures rise in their 
 value as we advance, and grow to signify thousands, 
 millions, billions, 4?V. yet so happily are they contriv- 
 ed for expressing the different parts of numbers, 
 that in- every step of the procedure we consider them 
 as denoting only simple units, all other deficiencies be- 
 ing made up, by the places their sums obtain in the to- 
 tal amount. And thus it is so ordered in this admira- 
 ble form of notation, that however large the numbers 
 are that come under examination, they are neverthe- 
 less managed with the same ease as the most simple 
 and obvious collections ; because in the several ope- 
 rations about .them, the mind is neither tied down to 
 
OF LOGIC. 197 
 
 the view of too many parts at once, nor entangled with 
 any considerations regarding the bulk and composition 
 of those parts. 
 
 Sec. XIlI..:This farther Illustrated by an Example in 
 Multiplication. 
 
 And if these advantages are so very manifest in the 
 first and simplest rules of arithmetic, much more do they 
 discover themselves in those that are intricate and com- 
 plex. Let a man endeavour in his thoughts to find 
 the product of two numbers, each consisting of twen- 
 ty or thirty places, and that without considering the 
 part3 separately ; I believe he will soon be sensible, 
 that it is a discovery far beyond the limits of the hu- 
 man mind. But now in the progressive method above ex- 
 plained, nothing is more simple and easy. For if we take 
 the first figure on the right hand of the one number, 
 and by it multiply every figure of the other separately ; 
 these several products, connected according to the esta- 
 blished laws of notation, must truly represent the total 
 product of this other, by that part of the multiplying 
 number. Let us suppose, for instance, the figure in 
 the unit's place of the multiplier to be 2, and the three 
 last places of the multiplicand to be 4.32. Then, 2 
 multiplying 2 produces 4, which therefore is the first 
 part of the product. Again, 2 multiplying 3 pro- 
 duces 6. But now 3 standing in the second place of 
 the multiplicand, denotes its real value three tens, or 
 30, which therefore taken twice, amount to six tensor 
 60. And accordingly the figure 6, coming after 4 al- 
 ready found, is thereby thrown into the second place 
 of the product, and so truly expresses 60, its full and 
 adequate value. The same thing happens in multi- 
 plying 4, which standing 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 ip the total pro- 
 duct. Because coming after 64, the two parts alrea- 
 dy found, it is thereby determined to the third place, 
 where it of course expresses so many hundreds. This 
 process, as is evident, may be continued to any length 
 we please j and it is remarkable, that in like manner as 
 R 2 
 
198 DUNCAN'S ELEMENTS 
 
 in addition, though the value of the figures in the 'mul- 
 tiplicand continually rises upon us, yet we all along 
 proceed with them as simple units ; because the places 
 ©f the several products in the total amountj represent 
 the just result of multiplying the figures together, ac- 
 cording to their true and adequate value. 
 
 Sec. XIV....Cy the disposition of the several Products 
 in order to Addition, 
 
 Having thus obtained the product by the first figure 
 of the multiplier, we next take that in the second place, 
 and proceed with it in the same manner. This second 
 operation gives us the effect of that figure, consider- 
 ed as a simple digit. But as it stood in the second 
 place, and therefore really denoted so many tens, hence 
 it is plain, that the product now gained must be yet 
 multiplied by ten, in order to express the true product 
 sought. This is accordingly done in the operation, 
 by placing the first figure of this second product under 
 the second figure of the first product. For this, when 
 they come to be added together, has the same effect 
 as annexing a cypher, or multiplying by ten, as every 
 one knows who is in the least acquainted with the rules 
 of arithmetic. In like manner, when we multiply by 
 the figure in the third place, as this new product is 
 placed still one figure backwards, we do in effect an- 
 nex two cyphers to it, or multiply it by a hundred* 
 And this we ought certainly to do ; because having 
 considered the multiplying figure as denoting' only sim- 
 ple units, when it really expressed so many hundreds, 
 the first operation gives no more than the hundreth 
 part of the true product. The case is the same in 
 multiplying by the fourth or fifth figures, because, the 
 products still running backwards, we thereby in effect 
 annex as many cyphers to them as bring them up se- 
 verally to their respective adequate value. By this 
 means it happens, that though the figures of the mul- 
 tiplier in every advance, denote still higher and higher 
 combinations, yet we all along proceed with them as 
 simple digits ; the disposition of the several products 
 in order to addition making up for all the deficiencits 
 
OF LOGIC. 199 
 
 that arise from this way of considering them. When 
 in this method of procedure, we have obtained the pro- 
 duct of the multiplicand into all the different parts 
 of the multiplier, by adding these products together we 
 obtain also the total product of the two numbers. For 
 since the whole is equal to all its parts, nothing is 
 more evident, than that the product of any one num- 
 ber into another, must be -equal to its product into all 
 the parts of that other : and therefore the several par- 
 tial products united into one sum, cannot but truly 
 represent the real product sought. 
 
 Sec. XV. .. ^Arithmetical operations, by being carried on 
 in a Progressive method, rendered easy and intelligible. 
 
 Thus we see, that in questions of multiplication 
 though the whole process is sometimes sufficiently long 
 and tedious, yet the several steps by which it is carried 
 on are all very level to the powers of the understand- 
 ing. For from the account given above it appears, that 
 nothing more is required in any of them than barely to 
 multiply one digit by another. But now this easy rule 
 of operation is wholly derived from the before-menti- 
 oned address # in classing our perceptions. For to this it 
 is owing, that the numbers under consideration are dis- 
 tinguished into parts, and that the several parts are also 
 clearly represented to the mind in the very form of 
 notation. Now as these parts have an invariable re- 
 lation one to another, and advance in their value by 
 an uniform law of progression ; the understanding by 
 means of such a link can easily hold them together, 
 and carry its views from stage to stage without per- 
 plexity, or confusion. Hence it happens, that howe- 
 ver large and mighty the numbers are, so far as to ex- 
 ceed the immediate grasp of the mind ; yet by run- 
 ning gradually through the several combinations of 
 which they are made up, we at length comprehend 
 them in their full extent. And because it would be 
 impossible for the understanding to multiply very large 
 numbers one into another, by a simple effort of tho't ; 
 therefore here also it considers the parts separately, 
 and, taking them in an orderly scries, advances by a 
 
*200 DUNCAN'S ELEMENTS 
 
 variety of successive steps. It is true indeed, in the 
 progress of the operation, the several figures rise in their, 
 value : but this consideration enters not the work it- 
 self. For there, as we have already seen, though the 
 characteis are taken as denoting only simple units, yet 
 the order and disposition of the partial products, exhi- 
 bits 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 scarce any difficulty, the 
 whole process is carried on with wondrous dispatch. 
 And thus by a series of easy operations, we at length 
 rise to discoveries, which in any other method of pro- 
 cedure, would have been found altogether beyond the 
 reacn of the mind. 
 
 Sec. XVI.... The art of Classing our Perceptions the 
 great Mean and Instrument of Invention. 
 
 Since therefore by a due and orderly disposition of 
 our ideas, we can brmg the most wide and extended 
 objects upon a level with the powers of the understand- 
 ing: and since by this also we abridge the fatigue and 
 labour of the mind, and enable it to carry on its re- 
 searches in a progressive method, without which con- 
 trivance, almost all the more remote and distant truths 
 of the sciences must have lain for ever hid from our 
 knowledge ; 1 think we may venture to affirm, that the 
 art of regulating and classing our perceptions is the 
 great mean and instrument of invention-. It is for this 
 reason that I have endeavoured in so particular a man- 
 ner to illustrate it from examples in numbers ; because 
 we have here not only a perfect model of the art itself, 
 but see also in the clearest manner, what helps it fur- 
 nishesV towards a ready comprehension of objects, and a 
 masterly investigation of truth. Nor let any one find 
 fault, as if we had insisted 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 arithmetic ; yet it is not every one that 
 sets himself to consider the. address and sagacity that 
 Kiay be seen in the contrivance of them, or to unravel 
 
OF LOGIC. 201 
 
 those principles of investigation, which we have here 
 so clearly deduced from them. And this I take to be 
 the reason, that we sometimes meet with instances of 
 men, who though thoroughly versed in the art cf in- 
 vention ; with regard to some particular branches of 
 knowledge ; yet if taken out of their usual track, find 
 themselves immediately at a stand, as if wholly bereft 
 of genius and penetration. With such men invention 
 is a mere habit, carried on in a manner purely mecha- 
 nical, without any knowledge of the grounds and rea- 
 sons upon which the several rules of investigation art 
 founded. Hence they are unfurnished with those gene- 
 ral observations, which may be alike usefully applied 
 in all sciences, with only some little necessary varia- 
 tions, suited to the nature of the subject we ' are upon. 
 And indeed I know of no surer way to arrive at 
 a fruitful and ready invention, than by attending care- 
 fully to the procedure of our own minds, in the exer- 
 cise of this distinguished faculty ; bexause from the 
 particular rules relating to any one branch, we are 
 often enabled to derive such general remarks, as tend 
 to lay open the very foundation and principles of the 
 art itself. 
 
 Sec. XVII.... The manner of proceeding in the resolu- 
 tion of Algebraic questions. 
 
 If now we turn our thoughts from arithmetic to aU 
 gebra, here also we shall find, that the great invention 
 lies, in so regulating and disposing 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 several relations of things in a 
 kind of symbolical language, so to represent them to 
 the imagination, as that we may, carry our attention 
 from one to another, in any order we please. Hence, 
 however numerous those relations are, yet by taking 
 only such a number of them into consideration at once, 
 as is suited to the reach and capacity of the under- 
 standing, we avoid perplexity and confusion in our re- 
 searches, and never put our faculties too much upon 
 the stretch, so as to loose ourselves amidst the muUU 
 
202 DUNCAN'S ELEMENTS 
 
 plicity of onr own thoughts. As therefore in arithme- 
 tic, we rise to a just conception of the greatest num- 
 bers as considering them made up of various progres- 
 sive combinations ; so likewise in algebra, those mani- 
 fold relations that often intervene, between known 
 and unknown quantities, are clearly represented to the 
 mind, by throwing^hem into a series of distinct equa- 
 tions. And as the most difficult questions relating to 
 numbers are managed with ease ; because we can take 
 the parts air figures separately, and proceed with them 
 one after another ; so also the most intricate problems 
 of algebra are in like manner readily unfolded, by ex- 
 amining the several equations apart, and unravelling 
 them according to certain established rules of opera- 
 tion. And here it is well worth our notice, that in 
 very complicated problems, producing a great number 
 of different equations, it for the most part so happens, 
 that every one of them includes a variety of unknown 
 quantities. When therefore we come to solve them 
 separately, as it would too much distract and entangle 
 the mind, to engage in the pursuit of so many differ- 
 ent objects at once ; our first business is, by artfully 
 coupling the several equations together, or by the va- 
 rious ways of multiplication, subtraction, addition, and 
 substitution, to derive others from them more simple, 
 until at length by such a gradual process we arrive at 
 some new equation, with only one unknown quantity. 
 This done, we set ourselves to consider the equation 
 last found, and having now to do with an object suit- 
 ed to the strength and capacity of the mind, easily by 
 the established rules of the art, discover the quantity 
 sought. In this manner we proceed with all the se- 
 veral unknown quantities one after another, and having 
 by a series of distinct operations traced them separate- 
 ly, the question is thereby completely resolved. 
 
 Sec. XVIII....0/" those other Artifices which may be 
 considered as Subsidiary helps to Invention* 
 
 , Hence it appears, that the business of invention, as 
 practised in algebra, depends entirely upon the art of 
 abridging our thoughts, reducing the number of par- 
 
OF LOGIC 203 
 
 ticulars taken under consideration at once to the few» 
 est possible, and establishing that progressive method 
 of investigation, which we have already so fully ex- 
 plained from examples in arithmetic. I might easily 
 show that the same observation holds equally in other 
 sciences ; but having already exceeded the bounds I 
 at first prescribed to myself in this chapter, shall only 
 add, that besides the grand instruments of knowledge 
 already mentioned, there are innumerable other artifi- 
 ces, arising out of the particular nature of the subject 
 we are upon, and which may be considered as subsidi- 
 ary helps to invention. Thus in geometry, many de- 
 monstrations of problems and theorems are wholly de- 
 rived from the construction of the figure made use of, 
 and the drawing of lines from one point to another. 
 In like manner in algebra, the devising of proper equa- 
 tions from the conditions of the question proposed, and 
 contriving neat expressions for the unknown quanti- 
 ties, contribute not a little to t|ie easy solution of pro- 
 blems. And when we have even carried on the inves- 
 tigation to some single equation with only one unknown 
 quantity ; as that unknown quantity may be various- 
 ly perplexed and entangled with others-that are known, 
 so as to require a multiplicity of diiferent operations, 
 before it can be disengaged, which often involves us in 
 long and intricate calculations, and brings surds and 
 irrational quantities in our way ; algebraists, to pre- 
 vent in some measure these inconveniences, and short- 
 en as much as possible the process, have fallen upon 
 several methods of substitution, which are of great ser- 
 vice in very complicated questions. But these and such 
 like artifices of invention, cannot be explained at 
 length in this short essay. It is enough to have given 
 the reader a hint of them, and put him in the way of 
 unravelling them himself, when he comes to apply his 
 thoughts to those particular branches of knowledge 
 where they are severally made use of. 
 
 Sec. XIX. »*0f the great advantages arising from a 
 happy Notation or expression of our Thoughts, 
 
 There is one thing however, that in a particular 
 
204 DUNCAN'S ELEMENTS 
 
 manner deserves to be taken notice of, before we dismiss 
 this subject ; and that is the great advantages that 
 may redound to science, by a happy notation or 
 expression of our thoughts. It is owing entirely to 
 this, and the method of denoting the several combina- 
 tions of numbers by figures standing in different places, 
 that the most complicated operations in arithmetic are 
 managed with so much ease and dispatch. Nor is it lesj 
 apparent, that the discoveries made by algebra, are 
 wholly to be imputed to that symbolical language made 
 use of in it. For by this means we are enabled to repre- 
 sent the relations of things in the form of equations, 
 and by variously proceeding with these equations, to 
 trace out tsep by step the several particulars we are in 
 qmest of. Add to all this, that by such a notation, the 
 eyes and imagination are also made subservient to the 
 discovery^ of truth. For the thoughts of the mind rise 
 up, and disappear, according as we set ourselves to call 
 them into view ; and therefore, without any particular 
 method of fixing and ascertaining them as they occur, 
 the retrieving them again when out of sight, would of- 
 ten be no less painful than the very first* exeieise of de- 
 ducing them one from another. When therefore in 
 the pursuit of truth we carry our attention forward 
 from one part of the investigation to another, as ne- 
 vertheless we have frequent occasion to look back upon 
 the discoveries already passed through, could these be 
 no otherwise brought into view, than by the same 
 course of thinking in which they were first traced, so 
 many different attentions at once must needs greatly 
 distract the mind, and be attended with infinite trdu- 
 ble and fatigue. But now, the method of fixing and 
 ascertaining our thoughts by a happy and well-chosen 
 notation, entirely removes all these obstacles. For 
 thus, when we have occasion to run to any former dis- 
 coveries, as care is taken all along to delineate them 
 in proper characters, we need only cast our eye upon 
 that part of the process where they stand expressed, 
 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 progress, and 
 
OF LOGIC. 205 
 
 running over the several conclusions already gained, 
 aee more distinctly what helps they furnish towards the 
 obtaining of those others we are still in pursuit cf. 
 Nay further, as the amount of every step of the inves- 
 tigation lies fairly before us, by comparing them vari- 
 ously among themselves, and adjusting them one to 
 another, we come at length to discern the result of the 
 whole, and are enabled to form our several discoveries 
 into an uniform and well-connected system of truths, 
 which is the great end and aim of all our enquiries. 
 
 Sec. XX.... Recapitulation* 
 
 Upon the whole then it appears, that in order to 
 proceed succesfully in the exercise of invention, we 
 must endeavour as much as possible to enlarge the ca- 
 pacity of the mind, by accustoming it to wide and com- 
 prehensive views of things : that we mull habituate 
 ourselves to a strong and unshaken attention, which 
 carefully distinguishes all the circumstances that come 
 in our way, and lets nothing material slip its notice : 
 in fine, that we must furnish ourselves with an ample 
 variety of intermediate ideas, and be much in the exer- 
 cise of singling them out and applying them for the 
 discovery of truth. These preparatory qualifications 
 obtained, what depends upon art lies chiefly in the 
 manner of combining our perceptions, and classing 
 them together with address, so as to establish a pro- 
 gressive method of investigation. And here it is cf 
 great importance to contrive a proper notation or ex- 
 pression of our thoughts, such as may exhibit them ac- 
 cording to their real appearance in the mind, and dis- 
 tinctly represent their several divisions, classes, and 
 relations. This is clearly seen in the manner of com- 
 puting by figures in arithmetic, but more particularly 
 in that symbolical language, which hath been hitherto 
 so successively applied in unravelling of algebraical 
 problems. j^hus furnished, we may at any time set 
 about the investigation of truth ; and if we take care 
 to note down the several steps of the process, as the 
 mind advances from one discovery to another, such an 
 arrangement or disposition of our thoughts constitutes 
 S 
 
206 DUNCAN'S ELEMENTS 
 
 what is called the method of invention. For thus it is 
 plain that we follow the natural procedure of the under- 
 standing, and make the truths we have unravelled to 
 succeed one another, according to the order in which 
 they present themselves to the mind, while employed 
 in tracing and finding them out. And here again it well 
 deserves our notice, that as by this means the whole in- 
 vestigation lies distinctly before us ; so by comparing' 
 the several steps of it among themselves, and observing 
 the relation they bear one to another, we are enabled 
 to form our discoveries into a regular system of know- 
 ledge, where the truths advanced are duly linked toge- 
 ther, and deduced in an orderly series from first princi- 
 ples. This other manner of combining our thoughts, 
 is distinguished by the name of the method of science^ 
 which therefore now offers itself to be explained, and 
 is accordingly the subject of the ensuing chapter. 
 
 Cfcap. II. 
 
 OF THE METHOD OF SCIENCE. 
 
 Sec. I:. .Knowledge as derived from the contemplation 
 of our ideas j of a necessary and unchangeable nature ; 
 
 IN order to give the juster idea of the rules peculiar 
 to this species of method, and establish them upon 
 their proper foundation, it will be necessary to begin 
 with settling the meaning of the word science, and 
 showing to what parts of human knowledge that term 
 may be most fitly applied. We have already observed, 
 in the first chapter of the second book, that there are 
 three several ways of coming at the knowledge of 
 truih. First, by contemplating the ideas in our own 
 minds. Secondly, by the information of the senses. 
 Thirdly, by the testimony of others. When we set 
 ourselves to consider the ideas in our own minds, we 
 variously compare them together, in order to judge of 
 their agreement or disagreement. Now as all the truths 
 deduced in this way, flow from certain connexions and 
 relations, discerned between the ideas themselves ; and 
 
OF LOGIC. 207 
 
 a? when the same ideas are brought into comparison, 
 the same relations must tver and Unvanbly subsist 
 between them ; hence it is plain, that the knowledge 
 acquired by the contemplation of our ideas, is of a ne- 
 cessary and unchangeable nature. But farther, as 
 these relations between our ideas, are not only supposed 
 to be real in themselves, but also to be seen and dis- 
 cerned by the mind ; and as when we clearly perceive 
 a connexion or repugnance betweeen any two ideas, we 
 cannot avoid judging them to agree or disagree accord- 
 ingly ; it evidently follows, that our knowledge of this 
 kind is attended with absolute certainty and conviction, 
 insomuch, that it is impossible for us to withhold our 
 assent, or entertain any doubt as to the reality of truths 
 so offered to the understanding. . The relation of equa- 
 lity between the whole and all its parts, is apparent to 
 every one who has formed to himself a distinct notion 
 of what the words whole and part stand for. No man, 
 therefore, who has these two ideas in his mind, can 
 possibly doubt of the truth of this proposition, that the 
 ivholc is equal to all its parts. For this would be only 
 endeavouring to persuade himself, that that was not, 
 which he plainly and unavoidably perceives to be. So 
 that in all cases, where we discern a relation between 
 any of our ideas, whether immediately by comparing 
 the one with another, or by means of intermediate 
 ideas, that lay it open distinctly to the understanding ; 
 the knowledge thence arising is certain and infallible. 
 3 say infallible ; because we not only perceive and own 
 the truth of propositions so offered to the mind, but, 
 having at the same time a,clear view of the ground on 
 which our assent rests, are entirely satisfied within our- 
 selves, that we cannot possibly be deceived in this per- 
 ception. 
 
 Sec. J I.... As flowing from the information of the senses, 
 begets undoubted assurance, but excludes not all possi- 
 bility of being deceived ; 
 
 . This second way of coming at knowledge, is by the 
 means of the senses. From them we receive informati- 
 on of the existence of objects without us, of the unioia 
 
208 DUNCAN'S ELEMENTS 
 
 and conjunction of different qualities in the same sub- 
 ject, and of the operations of bodies one upon another. 
 Thus our eyes tell us, that there is in the universe such 
 a body as we call the sun, our sight and touch, that 
 light and heat, or at least the power of exciting those 
 perceptions in us, co-exist in that body ; and lastly, by 
 the same sight we also learn, that fire has the power 
 of dissolving metals, or of reducing wood to charcoal 
 and ashes. But now with regard to this kind of know- 
 ledge we are to observe, that though when the organs 
 of the body are rightly disposed and operate in a na- 
 tu^gl way, we never doubt the testimony of our senses, 
 but from most of the schemes of life upon their infor- 
 mation : yet are not the truths of this class attended 
 with that ahsolute and infallible assurance, which be- 
 longs to those derived from the contemplation of our 
 own ideas. We fiad that the senses frequently represent 
 objects as really existing, which yet have no being but 
 in our own imaginations ; as in dreams,, phrensies, 
 and the deliriums of a fever. A disorder too in the 
 organs, makes us often ascribe qualities to bodies, en- 
 tirely different from those they appear to possess at 
 other times. Thus a man in the jaundice shall fancy 
 every object presented to him yellow ; and in bodily- 
 distempers, where the taste is greatly vitiated, what 
 naturally produces the idea of sweetness, is sometimes 
 attended with a Gju> te contrary sensation. It is true, 
 these irregularities neither ought, our indeed do they, 
 with considerate men, in any ways tend, to discredit 
 the testimony of experience. Ke that, awake, in his 
 senses, and satisfied that hjs organs operated duly, 
 should take it into his head tcy doubt whether fire 
 would burn, or arsenic poison him, and therefore 
 rashly venture upon these objects, would soon be 
 convinced of his error, in a way not much to his liking*. 
 As nevertheless the senses do sometimes impose upon us 
 there is no absolute and infallible security that they 
 may not at others ; therefore the assurance they pro- 
 duce, though reasonable, satisfying, and sufficiently 
 well founded to determine us in the several actions 
 and occurences of life, is yet of such a nature, as not 
 
OF LOGIC. 209 
 
 necessarily to exclude all possibility of being deceived 
 Hence some men go so far as to maintain, that we ought 
 to distrust our senses altogether; nay, whole sects among 
 the ancients, because of this bare possibility, which really 
 extends no farther than to matters of experience and 
 testimony, yet established it as a principle, that we ought 
 to doubt of every thing. Nor are there wanting philo- 
 sophers among the moderns, who, upon the same 
 grounds, deny the existence of bodies, and ascribe the 
 perceptions excited in us, not to the action of external 
 matter, but to certain established laws In nature, which 
 operate upon us in such manner as toproduce all thqise 
 several effects that seem to How from the real^ presence 
 of objects variously effecting our perception. It is not 
 my design here to enter into a particular discussion of 
 these matters : all I aim at, is to show, that the testi- 
 mony of the senses, though sufficient to convince sober 
 and reasonable men, yet does not sb unavoidably ex'iort 
 our assent, as to leave no room for suspicion or dis- 
 trust. 
 
 Sec. Ill .... As founded upon testimony, is of a still ma 
 certain nature,' though in many cases embraced wit fl- 
 out wavering or disirust. 
 
 The third and last way of coming at truth is by the 
 report and testimony of others. This regards cmeriy 
 past facts and transactions, which, having no longer" 
 any existence, cannot be brought within the present 
 sphere of our observation. For as these could never 
 have fallen under our cognizance, but by the relations 
 of such as had sufficient opportunities ot being inform- 
 ed ; it is hence apparent, that all our knowledge of 
 this kind is wholly founded upon the conveyance of 
 testimony. But now, although this in many cases is a 
 sufficient ground of assent, so as to produce a ready be- 
 lief in the mind, yet is it liable to still greater objec- 
 tions than even the reports ui experience. Ouj sensesyj 
 it is true, on some occasions aecefye us. and therefore 
 they may possibly on others. But this bare possibility 
 creates little or no distrus.t^ because there are u: 
 rules of judging, when they operate according to na- 
 S 2 
 
2!0 DUNCAN'S ELEMENTS 
 
 » 
 
 ture, and when they are prevented or given up to ca- 
 price. It is otherwise in matters of mere human testi- 
 mony. For there, besides the supposition that the per- 
 sons themselves may have been deceived, there is a 
 farther possibility, that they may have conspired to 
 impose upon others by a false relation. This considera- 
 tion has the greater weight, as we frequently meet 
 with such instances of disingenuity among men, and 
 know it to be their interest in some particular cases, to 
 dissemble and misrepresent the truth. It would, never- 
 theless, be the height of folly, to reject all human tes-^ 
 timony without distinction because of this bare possi- 
 bility. Who can doubt whether there ever were in the 
 world such conquerors as Alexander and Julius Cesar ? 
 There is no absolute contradiction, indeed, in suppo- 
 sing, that historians may have conspired to deceive us. 
 But such an universal concurrence to a falsehood, with- 
 out one contradicting voice, is so extremely improba- 
 ble, and so very unlike what usually happens in the 
 world, that a wise man could as soon persuade himself 
 to believe the grossest absurdity, as to admit of a sup- 
 position so remote from every appearance of truth. 
 Kence the facts of history, When well attested, are 
 yeadily embraced by the mind ; and though the evidence 
 attending them be not such as produces a neeessary and 
 infallible assurance, it is yet abundantly sufficient to 
 justify our belief, and leave those without excuse, who 
 upon the bare ground of possibility, are for rejecting 
 entirely the conveyance of testimony. 
 
 Sec. IV ....Science belongs entirely to that branch of know- 
 ledge which is derived from the contemplation of our 
 Ideas. 
 
 Upon the whole, then, it appears, that absolute 
 certainty, such as is attended with unavoidable assent, 
 and excludes all possibility of being deceived, is to be 
 found only in the contemplation of our own ideas. In 
 matters of experience and testimony, men, we see, 
 may frame pretences for suspicion and distrust : but in 
 that part of knowledge which regards the relations of 
 tur icteas, none such can have place. Tor as all these 
 
OF LOGIC. 211 
 
 several relations are either immediately discerned by 
 the mind, or traced by means of immediate ideas, 
 where self-evidence is supposed to accompany every 
 step of the procedure, it is absolutely impossible for a 
 man to persuade himself that that is not, which he 
 plainly and necessarily perceives to be. Now it is to 
 knowledge, attended with this last kind of evidence 
 alone, that in strictness and propriety of speech we at- 
 tribute the name of science. For science implies per- 
 ception and discernment, what we ourselves see and 
 cannot avoid seeing ; and therefore has place only in 
 matters of absolute certainty, where the truths ad- 
 vanced are either intuitive propositions, or deduced 
 from them in a way of strict demonstration. And as 
 this kind of certainty is no where to be found, but in 
 investigating the relations of our ideas ; hence it is 
 plain, that science, properly speaking, regards wholly 
 the first branch of human knowledge ; that which we 
 have said is derived from a contemplation of the ideas 
 in our own minds. 
 
 Sec. V ... .Our Knowledge of the real Existence of Ob- 
 jects not Intuitive, 
 
 But here I expect it will be asked, if science and de- 
 monstration belong only to the consideration of our 
 own ideas, what kind of knowledge it is, that we have 
 relating to bodies, their powers, properties, and opera- 
 tions one upon another ? To this I answer, that we 
 have already distinguished it by the name of natural 
 or experimental. But that we may see more distinctly 
 wherein the difference between scientifical and natural 
 knowledge lies, it may not be improper to add the fol- 
 lowing observations. When we cast our eyes towards 
 the sun, we immediately conclude, that there exists an 
 object without us, corresponding to the idea in our 
 minds. We are, however, to take notice, that this con- 
 clusion does not arise from any necessary and unavoid- 
 able connexion discerned., between the appearance of 
 the idea in the mind, and the real existence of the ob- 
 ject without us. We all know by experience, that ideas 
 jn,ay be excited, and that too by a seeming operation 
 
212 DUNCAN'S ELEMENTS 
 
 of objects upon our senses, when there are in fact no 
 such objects existing ; as in dreams, and the deliriums 
 of a feser. Upon what then is the before-mentioned 
 conclusion properly grounded ? Why, evidently upon 
 this : that as we are satisfied our organs operate duly, 
 and know that every effect must have a cause, nothing 
 is more natural than to suppose, that where an idea is 
 excited in the mind, some object exists corresponding 
 to the idea, which is the cause of that appearance. But 
 as this conclusion, by what we have, seen, is not neces- 
 sary and unavoidable, hence there is no intuition in the 
 case, but merely a probable conjecture, or reasonable 
 presumption, grounded upon an intuitive truth. 
 
 Sec. "VI..,. Absolute Certainty in natural Knowledge 
 confined to %v hat falls under our immediate notice* 
 
 Again, when a piece of gold is dissolved in aqua re- 
 gia, we see indeed and own the effect produced, but can- 
 not be said, in strictness and propriety of speech, to 
 have any perception or discernment of it. The reason 
 is, because being unacquainted with the intimate : ia- 
 ture both of aqua 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 facts and opera- 
 tions of nature extends not with certainty beyond the 
 present instance, or what falls under our immediate 
 notice ; so that in all our researches relating to them, 
 we must proceed ijn the way of trial and experiment, 
 there being here no general or universal truths, v here- 
 on to found scientijical deductions. Because the solu- 
 tion of gold in aqua regia 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 these bodies, that the effect here mentioned depends 
 we have no absolute certainty in any new experiment 
 we propose to make, that the objects to be applied one 
 to another have that precise texture and constitution 
 from which this solution results. Che-mists know by 
 experience, that bodies which go by the same name, 
 and have the game outward appearance, are not always, 
 
OF LOGIC. 213 
 
 however, exactly alike in their powers and operations. 
 In rain do they often search for those properties in 
 one piece of antimony, which, on former occasions, - 
 they may have found in another ; and hy this means, 
 to their no small mortification, find themselves fre- 
 quently disappointed, in very costly and promising ex- 
 periments. Nor have we any express and positive as- 
 surance, that the very bodies with which we have for- 
 merly made experiments, continue so exactly the same, 
 as to afford the like appearances in any succeeding 
 trial. A thousand changes happen every moment in 
 the natural world, without our having the least know- 
 ledge or perception of them. An alteration in our at- 
 mosphere, the approach or recess of the sun, his decli- 
 nation towards the north or south, not only vary the 
 outward face of things, but occasion many changes in 
 the human constitution itself, which we yet perceive 
 not when they happen ; nor should ever be sensible of, 
 but by the effects and consequences resulting from 
 them. And whether alterations analogous to these 
 Jhay not sometimes be produced in the frame and tex- 
 ture of many bodies that surround us, is what we can- 
 not with certainty determine. Hence, from an expe- 
 riment's succeeding in one instance, Ave cannot infal- 
 libly argue, that it will succeed in another, even with 
 the same body. The thing may indeed be probable, 
 and that in the highest degree ; but as there is still a 
 possibility that some change may have happened to the 
 body, unknown to us ? there can be no absolute cer- 
 tainty in the case. 
 
 Sec. VII.... What kind of Knowledge of Body would 
 deserve the name cf Science, 
 
 Had we such an intimate acquaintance with the 
 structure both of aqua regie and gold, as to be able 
 thence to discern why the one so operates upon the 
 other as to occasion its dissolution ; insomuch that 
 from the ideas of them in our own minds, we could 
 clearly deduce, that bodies of such a make applied one 
 to another, must necessarily produce the effect here 
 mentioned j our knowledge would then be scientifcal. 
 
214 DUNCAN'S ELEMENTS 
 
 and stand upon the foundation cither of intuition or 
 demonstration^ according as the perception was imme- 
 diate, or attained by means of intervening ideas. In 
 this case, therefore, having two standard ideas in our 
 minds, whose relations we. perfectly well know; wher- 
 ever we found objects conformable to these ideas, we 
 could then pronounce with certainty, that the applica- 
 tion of them one to another would be attended with the 
 above effect : because, whatever is true in idea, is un- 
 avoidably so also in reality of things,, where things 
 exist answerable to these ideas. If it be true in idea, 
 that a parellelogram is the double of a triangle, stand- 
 ing upon the same base, and between the same parel- 
 lels ; the same will be true of every real triangle and 
 parellelogr/un, that exist with the conditions here men- 
 tioned. We are likewise to observe, that the changes 
 to which bodies are daily liable, could produce no con- 
 fusion or perplexity in natural knowledge, did it stand 
 upon the foundation here mentioned. For in such a 
 case, the.powers and properties of objects being dedu- 
 ced from the ideas of t\rmi in our own minds, would 
 no otherwise be applied to things really existing, than 
 as these things are found perfectly conformable to our 
 ideas. When, therefore, an alteration happened in 
 any body, as it would by this mean? differ from that 
 standard idea whence its former properties were seen 
 to flow, we must of course be sensible, that some suit- 
 able change would follow in the properties themselves, 
 and that its powers and operations, in regard of other 
 bodies, would not be in all repects the same. 
 
 Sec» VIII,... Experience the only foundation of Natu- 
 ral Knowledge. 
 
 But what is still more remarkable, we should, upon 
 this supposition, be able to determine the mutual ac- 
 tion and influence of bodies, without having recourse 
 to trial or experiment. Had we, for instance, a perfect 
 knowledge of the intimate nature and composition of 
 an animal body, and of that particular poison that is 
 infused into it by the bite ©f a viper, so as clearly and 
 olistictly to discern how they are adapted one to ano- 
 
OF LOGIC. 215 
 
 ther; we might thence scientifically deduce, without 
 the help of experiments, that the bite of a viper 
 would so unhinge the human fabric, and produce such 
 ferments and combustions in it, as must necessarily be 
 followed by a total extinction of all the vital functions, 
 and leave that admirable machine a mere lifeless lump. 
 But as such perfect and adequate ideas of objects, and 
 their mutual habitudes one to another, are plainly be- 
 yond the reach of our present faculties ; it were vain for 
 us to think of improving natural knowledge by abstract 
 reasoning or stientifical deductions. Experience is here 
 the true and proper foundation of our judgments, nor 
 can we by any other means arrive at a discovery of the 
 several powers and properties of bodies. How long 
 might a man contemplate the nature of hemlock, exa- 
 mine the structure of its parts in a microscope, and 
 torture and analyse it by all the processes of chemistry, 
 before he could pronounce with certainty the effect it 
 will have upon a human body? One single experiment 
 lays that open in an instant, which all the wit and in- 
 vention ot ixen would never of themselves have beer* 
 able to trace. The same holds in all the other parts of 
 natural philosophy. Our discoveries relating to. electri- 
 city, the powers and properties of the load-stone, the 
 force of gunpowder, &c. were not gained by reason- 
 ing, or the consideration of our abstract ideas, but by 
 means of experiments made with the bodies themselves. 
 Hence it happened, that while the philosophy of Aris- 
 totle prevailed in the schools, which dealt much in 
 metaphysical notions, occult qualities, sympathies, an- 
 tipathies, and such like words without meaning ; the 
 knowledge of nature was at a ?tand : because men pre- 
 tended to argue abstractedly about the things of which 
 they had no perfect and adequate ideas, whereon to 
 ground such a method of reasoning. But now in the 
 present age, that we have returned to the way of trial 
 and experiment, which is indeed the only true founda- 
 tion of natural philosophy; great advances have al- 
 ready been made, and the prospect of still greater lies 
 before us. 
 
216 DUNCAN'S ELEMENTS 
 
 Sec. IX.,.. Difference between Scientifical and Natural 
 Kn$w ledge* 
 
 And thus at length we may sufficiently understand 
 ■wherein the proper difference lies, between scientifiai 
 and natural knowledge. In matters of science we argue 
 from the ideas in our own minds, and the connexions 
 and relations they have one to another. And as when 
 these relations are set clearly and plainly before us, we 
 cannot avoid peceiving and owning them, hence all 
 the truths of this class produce absolute certainty in the 
 mind, and are attended with a necessary and unavoid- 
 able assent. It is otherwise in the case of natural know- 
 ledge. Intuition and inward perception have here no 
 place. We discern not the powers and properties of 
 those objects that surround us, by any view and com- 
 parison of the ideas of them one with another, but 
 merely by experience, and the impressions they make 
 on the senses. But now the reports of sense happening 
 in some instances to deceive us, we have no infallible 
 assurance that they may not in others; which weakens 
 not a little the evidence attending this kind of know- 
 ledge, and leaves room for suspicion and distrust. Nay, 
 what is yet more considerable, as we have no perfect 
 and adequate ideas of bodies, representing their inward 
 constitution, or laying open the foundation upon 
 which their qualities depend, we can form no universal 
 propositions about them, applicable with certainty in 
 all particular instances. Fire, we say, dissolves metals. 
 This, though expressed indefinitely, is, however, only 
 a particularly truth, nor can be extended with absolute 
 assurance, beyond the several trials made. The reason 
 is, that being ignorant of the inward frame and com- 
 position both of fire and metals ; when objects are offer- 
 ed to us under that name, we have therefore no posi- 
 tive certainty that they are of the very make and tex- 
 ture, requisite to the success of the experiment. The 
 thing may indeed be probable in the highest degree ; 
 but for want of standard and settled ideas, we can 
 never arrive at a clear and absolute perception in the 
 case. 
 
OF LOGIC. 217 
 
 »5ec. X....77j£ manner of Reasoning in Natural Know* 
 ledge* 
 As nevertheless, it is certain that many general con» 
 elusions in natural philosophy are embraced without 
 doubt or hesitation ; nay, that we form most of the 
 schemes and pursuits of life upon that foundation ; it 
 will naturally be asked here, how come we by this assu- 
 rance ? I answer, not scientifically, and in the way of 
 strict demonstration, but by analogy, and an induction 
 of experiments. We distinguish fire, for instance, by 
 such of its qualities as lie more immediately open to the 
 notice of the senses ; among which light and heat are 
 the most considerable. Examining still farther into its 
 nature, we find it likewise possessed of the power of dis- 
 solving metals. But this new property not having any 
 necessary connexion that we can trace, with those other 
 qualities by which fire is distinguished, we cannot there* 
 fore argue with certainty, that wherever light and heat, 
 &c. are, the power of dissolving metals co-exists 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 presume there may be really some 
 such connexion, tho* our views are too short and imper- 
 fect to discover it. Hence we are led to frame a general 
 conclusion, arguing from what has already happened, 
 to what will happen again in the like cases insomuch 
 that where we meet with all the other properties of fire 
 in any body, we have not the least doubt, but that upon 
 trial, the power above-mentioned will be found to be- 
 long to it also. This is called reasoning by analogy; 
 and it is, as we see, founded entirely upon induction, 
 and experiments made f with particular objec s ; the 
 more precise and accurate our ideas of these objects are, 
 and the greater the variety of experiments upon which 
 we build our reasoning, the more certain and undoubt- 
 ed will the conclusions be. 'Tis.in this manner we ar- 
 rive at all the general truths of natural knowledge : as 
 that the bixe of a certain animal is mortal ; that a needle 
 touched by a loadstone points to the north ; that gravi- 
 ty belongs universally to all bodies; and innumerable 
 others, which, though not capable of strict demonstra- 
 T 
 
218 DUNCAN'S ELEMENTS 
 
 tion, are nevertheless as readily embraced upon the 
 foundation of analogy, as the most obvious and intui- 
 tive judgments ; nay, and become fixed and steady prin- 
 ciples of action, in all the aims and pursuits of life. 
 
 Sec. XI....//0W even Scientijical Reasoning maybe in* 
 troduced into it* 
 
 And here again it is particularly remarkable, that 
 having ascertained the general properties of things by 
 analogy, if we proceed next to establish these as postu* 
 lata in philosophy, we can, upon this foundation, build 
 strict and mathematical demonstrations, and thereby 
 introduce scientijical reasoning into natural knowledge. 
 In this manner, six Isaac Newton having determined the 
 laws of gravity by a variety of experiments, and laying 
 it down as a principle, that it operates according to 
 those laws through the w 7 hole system of nature ; has 
 thence, in a way of strict demonstration, deduced the 
 whole theory of the heavenly motions. For granting 
 once this postulatum, that gravity belongs universally to 
 all bodies, and that it acts according to their solid con- 
 tent, decreasing with the distance in a given ratio ; 
 "what sir Isaac has determined in regard to the planetary 
 motions, follows from the bare consideration of our 
 own ideas ; that is, necessarily and scientifically. Thus 
 likewise 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 ; we can upon this foundation esta- 
 blish mathematically the theory of vision. The same 
 happens in mechanics,hjdrostatics 1 pneamatics< i hc.whcY& 
 from postulata ascertained by experience, the whole 
 theory relating to these branches of knowledge follow* 
 in a way of strict demonstration. And this 1 take to be 
 the reason why many parts of natural philosophy arc 
 konored with the name of sciences* Not that they are 
 ultimately founded upon intuition ; but that-the several 
 principles peculiar to them being assumed upon the 
 foundation of experience, the theory deduced from 
 these principles is established by scientijical reasoning'. 
 
OF LOGIC. 21% 
 
 Sec. XII. ...Yet still Experience is the ultimate Ground 
 of our Assent. 
 Could we indeed discern any necessary connexion be- 
 tween gravity and the known essential qualities of mat- 
 ter, insomuch that it was inseparable from the very idea 
 pf it ; the whole theory of the planetary motions would 
 then be strictly and properly scicntijiral^ For seeing, 
 from the notion of gravity, we can demonstratively de- 
 termine the laws that bodies will observe in their revo- 
 lutions, in any known circumstances ; if the circum- 
 stances relating to any system of bodies can be traced, 
 and gravity is supposedessential to them, we can then, 
 from the bare consideration of our own ideas, deduce 
 all their motions and phenomena. Now this is precise- 
 ly what sir Isaac has done in regard to our planetary 
 system. Hs has determined the circumstances of the 
 bodies that compose it, in respect of situation, distance, 
 magnitude, See. all which being supposed, if they are 
 essentially actuated by gravity, their several revolutions 
 and appearances must be equally essential. 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 there- 
 fore, tho' our reasoning in this pr.rt of philosophy be 
 truly scienti£cal, yet as the principle upon which that 
 reasoning is grounded, is derived from experience, the 
 theory itself must needs ultimately rest upon the same 
 foundation. And thus even the doctrine of the pla- 
 netary motions, though seemingly established by ma- 
 thematical reasoning, falls yet, in strictness and pro- 
 priety of speech, under the head of natural knowledge. 
 For in this precisely consists the difference between 
 science, and what we call the philosophy of nature ; that 
 the one is grounded ultimately on intuition, the other 
 on experience. As the observation here made holds alike 
 in all the other branches of natural philosophy, into 
 •which scientijical reasoning has been introduced; it is 
 hence apparent, that they are not sciences, in the strict 
 and proper sense of the word, but only by a certain 
 latitude of expression common enough in all languages. 
 What we have therefore said above, relating to theim- 
 
220 DUNCAN'S ELEMENTS 
 
 possibility of improving natural knowledge, by scienti- 
 fical deductions, is not contradicted by any thing ad- 
 vanced in this section. We there meant deductions 
 grounded ultimately on. intuition, and derived from a 
 consideration of the abstractideas of objects in our own 
 minds ; not such as flow from postulata, assumed upon 
 the foundation of experience. For these last, as we have 
 already observed, are not truly and properly scientifi- 
 cal, but have obtained that name merely on account of 
 the way of reasoning in which they are collected from 
 the said postulata. 
 
 Sec. XIII. ...77i£ manner of Reasoning in Historical 
 Knowledge, 
 
 If then absolute and infallible certainty is not to be 
 fcbtaiaed in natural knowledge, much less can, we ex- 
 pect it in historical. For here testimony is the only 
 ground of assent ; and therefore the possibility of our 
 being deceived, is still greater than in the case of ex- 
 perience. Not only he who reports the fact may himself 
 have formed a wrong judgment; but could we even 
 get over this scruple, there is still room to suspect, that 
 be may aim at imposing upon us by a false narration. 
 In this case, therefore, it is plain, there can be no in- 
 tuition or inward perception" of truth, no strict and ab- 
 solute demonstration, and consequently no science. 
 There is, however, a way of reasoning even here, that 
 begets anentire acquiescence, and leads us to embrace 
 without wavering, the facts and reports of history. If, 
 for instance, it appears, that the historian was a man 
 of veracity; if he was a competent judge of what he 
 relates ; if he had sufficient opportunities of being in- 
 formed; if the book that bears his name was really 
 written by him ; if it had been handed down to us 
 uncorrupted ; in fine, if what he relates is probable 
 in itself, falls in naturally with the other events of 
 that age, and is attested by contemporary writers: 
 by these and such like arguments, founded partly on 
 criticism, partly on probable conjecture, we judge of 
 past transactions ; and though they are not capable of 
 scientiJicai^rooL yet in many cases we arrive at an un- 
 
OF LOGIC. 221 
 
 doubted assurance of them. For as it is absurd to de- 
 mand mathematical demonstration in matters of fact, 
 because they admit not of that kind of evidence ; it is 
 no less so to doubt of their reality, when they are prov- 
 ed by the best arguments their nature and quality will 
 bear. 
 
 Sec. XIV. ...Scepticisms necessarily excluded from mat- 
 ters of Science ; 
 
 Ana" thus we see, in the several divisions of human 
 knowledge, both what i3 the ground of judging, and 
 the manner of reasoning, peculiar to each. In scientific 
 cal knowledge, which regards wholly the abstract ideas 
 of the mind, and those relations and connexions they 
 have one with another ; our judgments are grounded 
 on intuition, and the manner of reasoning is by demon- 
 stration. In natural knowledge, respecting objects that 
 exist without us, their powers, properties,, and mutual 
 operations ; we judge on the foundation of experience 
 and reason by induct ion and analogy. Lastly, in historical 
 xnowl edge, \sh\z\\ is chiefly conversant about past facts 
 and transactions, testimony is the ground of judgment, 
 and the way of reasoning is by criticism and probable 
 conjecture. And now I think we are able effectually to 
 overthrow that absurd kind of scepticism maintained by 
 some of the ancients which brings all propositions up- 
 on a level, and represents them as equally uncertain. 
 What gave the first rise to this doctrine was, caprice 
 of certain philosophers, whoobserving that the reports 
 ot sense and testimony were in some instances deceitful, 
 took thence occasion to suppose that they might be so 
 likewise in others, and thereupon established it as a 
 principle, that we ought to doubt of every thing. But 
 even with repecf to this doubting, we are to observe, 
 that it can in fact extend no farther, than to matters of 
 experience and testimony, being totally and necessarily- 
 excluded from scientifcal knowledge. When ideas make 
 their appearance in the understanding, it is impossible 
 for us to doubt of their being there. And when the 
 relations of any of our ideas are clearly and distinctly 
 discerned by the mind, either immediately, which is 
 T 2 
 
222 DUNCAN'S ELEMENTS 
 
 intuition, or by means of intervening ideas, which is 
 demonstration ; itwould be in vain for us to endeavour 
 to persuade ourselves that that is not, which we plain- 
 ly, and unavoidably perceive to be. In this case, there- 
 fore, we cannot withhold our assent ; truth forces its 
 way over all opposition, and breaks in with so much light 
 upon the mind, as to beget "absolute' and infallible cer- 
 tainty. 
 
 Sec. JLY„„Andto be admitted with caution in matters 
 of experience and testimony. 
 
 Indeed in natural and historical knowledge scepticism 
 may have place ; because, as we have said, there is a possi- 
 bility of our being deceived. But then it is to be observed, 
 that a bare possibility is a very weak ground whereon 
 to bottom any philosophical tenet. It is possible, that 
 Great Britain may be swallowed up by the sea before 
 to-morrow; but 1 believe no man is on this account in- 
 clined to think that it will be so. It is possible, the 
 whole human race may be extinguished the next in- 
 stant ; yet this possibility creates no apprehension that 
 the thing itself will really happen. In a word, we ought to 
 judge of things by the proofs brought to support them, 
 .not by bare abstrast possibilities ; and when we have 
 all the evidence, they are capable of, that alone is suf- 
 ficient to convince, though perhaps the contrary cannot 
 be shown to imply a'contradiction. Will any wise and 
 considerate man doubt whether there be such a place 
 as Africa^ because we cannot prove, by any necessary 
 argument, that it is absolutely impossible all the relati- 
 ons concerning it should be false? Strict and rigorous 
 demonstrations belong not to history, or the philoso- 
 phy of Nature. The way of reasoning, in these bran- 
 ches of knowledge, is by arguments drawn from expe- 
 rience and testimony. And when the truth of any pro- 
 - position is in this manner sufficiently ascertained, inso- 
 much that it appears with all the evidence it is capable 
 ©f, and we kave as great reason to believe that it is, as 
 we could possibly have, supposing it were, is not this 
 upon the matter as satisfactory as a demonstration? It 
 must be owned, indeed, there is no inward perception 
 1 
 
OF LOGIC. 223 
 
 in the case ; and therefore our assent cannot be said 
 to be necessary and unavoidable. Men may in these 
 matters be sceptics^ if they please ; and if they are re- 
 solved upon it, it is. in vain to contend with obstinacy 
 and pervcrseness. I cannot, however, but observe, that 
 if they will really act up to their own principles, and 
 treat all things in good earnest as uncertain, that ad- 
 mit not of strict scientifical proof, their conduct must 
 be the very madness of folly. No man can demonstrate 
 mathematically, that poison has not been conveyed 
 into his meat or drink. And if he will be so very cau- 
 tious as not to taste of either, till he has reached this 
 degree of certainty, I know no other remedy for him, 
 but that in great gravity and wisdom he must die for 
 fear of death. The truth of it is, the most zealous 
 patrons ot scepticism^ after all their pretended doubts 
 and scruples find it yet convenient to behave, in the se- 
 veral occurrences of life, as if they gave entire credit to 
 the reports of sense and testimony. They will no more 
 venture upon a dose of arsenic, or rush into the midst of 
 a glowing furnace, than if they verily believed death 
 would be the consequence. And though in this it must 
 be owned they act discreetly, *yet have we hence at the 
 sarse time a very convincing argument of the absurdity 
 of those notions they affect to entertain. In reality, 
 can any thing be more ridiculous, than to give into a 
 scheme of thinking, which we find ourselves necessitat- 
 ed to contradict in almost every occurrence of life ? 
 Opinions are not to be taken up out of caprice and fancy, 
 but to serve as principles of action, and standing rules 
 of behaviour. When they answer not this main pur- 
 pose, they are unavailing and fruitless, and an obsti- 
 nate adherence to them, in spite of the repeated admo- 
 nitions of experience, justly deserves to be branded 
 for folly. We shall not, therefore, attempt to multiply 
 arguments in a matter so obvious, it sufficiently answer- 
 ing our present punpose to have shown, that doubting 
 and uncertainty have no place in scientifical know- 
 ledge r and that even in matters of history, and the 
 facts of nature, and undistinguishing scepticism would 
 be in the highest degree absurd. 
 
224 DUNCAN'S ELEMENTS 
 
 Sec. XVI.... Science applicable to theVencerns of Hu- 
 man Life* 
 But here, perhaps, it will be asked, Why all this 
 mighty noise about science, when, even according to 
 the present account, it seems to be so very capricious 
 and arbitrary a thing ?. For seeing it is wholly confined 
 to the consideration of our ideas, and we are at liberty 
 to frame and combine those ideas at pleasure, this in- 
 deed opens a way to castles in the air, of our own 
 building, to many chimerical and fanciful systems, 
 which men of warm ^nd lively imaginations love to 
 entertain themselves with, but promises little of that 
 knowledge which is worth a wise man's regard, and 
 respects the great ends and purposes of life. Where is 
 the advantage of barely contemplating our ideas, and 
 tracing their several habitudes and relations, when it 
 is in truth the reality of things that we are chiefly con- 
 cerned to know, and those respects they bear to us and 
 one another ? To this I answer : that if indeed our 
 ideas no way regarded things themselves, the know- 
 ledge acquired by their means would be of very little 
 consequence" to human life. But since as we have al- 
 ready observed, whatever is true in idea, is unavoidably 
 so also in the reality of things, where things exist an- 
 swerable to these ideas ; it is apparent, that by copy- 
 ing our ideas with care from the real objects of nature, 
 and framing them in a conforaiity to those conjunctures 
 and circumstances in which we are most likely to be 
 concerned, a way is laid open to discoveries of the 
 greatest importance to mankind. For in this case, our 
 several reasonings and conclusions, holding no less of 
 the objects themselves, than of the ideas by which 
 they are represented, may be therefore applied with 
 certainty to these objects, as often as they fail under 
 our notice. Thus mathematicians, having formed to 
 themselves ideas of cones, cylinders, spheres, prisms, 
 &c. variously compare them together, examine their 
 several properties, and lay down rules by which to 
 calculate their relative bulk and dimensions. But now 
 as bodies answering in figure to these ideas come fre- 
 quently under our observation, we have by this means 
 
OF LOGIC. 225 
 
 an opportunity of applying mathematical knowledge to 
 the common concerns of life ; and by determining 
 precisely the quantity of extension in each body, can 
 the better judge how far they will answer the purposes 
 we have in view. The same thing happens in politics 
 and morality. If we form to ourselves ideas of such 
 communities, connexions, actions and conjuctures,as do 
 or may subsist among mankind ; all our reasonings and 
 conclusions will then respect real life, and serve as 
 steadymaxims of behaviour in the several circumstances 
 to which it is liable. It is not, therefore, enough that 
 we set about the consideration of any ideas at random ; 
 we must further take care that those ideas truly regard 
 things themselves ; for although knowledge is always 
 certain, when derived from the contemplation of our 
 own ideas, yet is it then only useful and worthy our re- 
 gard, when it respects ideas taken from the real objects 
 of nature, and strictly related to the concerns of hu- 
 man life. 
 
 , Sec. XVII.... The method of science begins with ascer- 
 taining our Ideas; 
 
 Having thus shown that there is such a thing as 
 science, fixed and ascertained the bounds of it, and 
 explained its great use and importance in the affairs 
 of mankind ; it now remains that we lay down the 
 rules of method peculiar to this branch of know- 
 ledge, and give some account of the manner in which 
 that certainty and conviction which are inseparable 
 from it, may be most naturally and effectually pro- 
 duced. Science, as we have said, regards wholly the 
 abstract ideas of the mind, and the relations they have 
 one to another. The great secret, therefore, of at- 
 taining it lies in so managing and conducting our 
 thoughts, as that these several relations may be laid 
 open to the view of the understanding, and become 
 the necessary and unavoidable objects of our percep- 
 tion. In order to this we must make it our first care, 
 distinctly to frame and settle the ideas about which 
 our enquires are to be employed. For as the relations 
 subsisting between them can no otherwise be discernedj 
 
226 DUNCAN'S ELEMENTS 
 
 than by comparing them one with another — and as 
 this comparison necessarily supposes that the idea, 
 themselves are actually in the mind, and at that very 
 time under our immediate inspection — it plainly fol- 
 lows, that all science must begin with fixing and ascer- 
 taining those ideas. Now our ideas, as has been al- 
 ready observed in the first book, come all very natu- 
 rally within the diyision of simple and complex. ~ Sim- 
 ple ideas are excited by actual impressions made upon 
 the understanding ; and as they exist under one uni- 
 form appearance, without variety or composition, arc 
 in no danger of being mistaken, or confounded one 
 with another. It is otherwise in our complex concep- 
 tions. For these consisting of many simple ideas 
 joined together, great care must be taken, that we ac- 
 quaint ourselves with the true number combined, and 
 the order and manner of their connexion. By this 
 means alone are these our most intricate notices, kept 
 distinct and invariable, insomuch that in all our several 
 views of them, they ever have the same appearance, 
 and exhibit the same habitudes and respects. Here, 
 therefore, properly speaking, the art of knowledge 
 begins. For although we find it easy enough tobo'und 
 and settle our ideas, where they consist of but few 
 simple perceptions ; yet when they grow to be very 
 complicated, it often requires great address and ma- 
 nagement to throw them into such .views as may pre- 
 vent that confusion which is apt to arise from tlie joint 
 consideration of a multiplicity of different objects. 
 Hence that gradation in the composition of our ideas 
 which we have explained at large in the last chapter 
 of the first boek. For as they are by this means form- 
 ed into different orders, and these orders arise continu- 
 ally one out of another ; the understanding, by taking 
 them in a just succession, gradually mounts to the 
 highest conceptions, and can, at any time, with incre- 
 dible ease and expedition, bring all their parts disinct- 
 ly into view. To know, therefore, the full value of this 
 contrivance, we must attentively consider the strict 
 connexion that obtains between the several classes of 
 ©ur perceptions when disposed in such a series. Eve- 
 
OF LOGIC. »r 
 
 ry succeeding order is formed out of those combina- 
 nations that constitute the rank next below it. And 
 as in advancing from one degree to another, we are 
 always to proportion the number of notices united, to 
 the strength and capacity ©f the mind ; it is apparent, 
 that by such a procedure, the ideas will be thoroughly 
 ascertained in every step, and, however large and 
 bulky, lie yet fairly .within our g-asp. This obvious- 
 ly accounts for!' that wonderful clearness of apprehen- 
 sion, which we often experience within ourselves, even 
 in regard to the most complicated conceptions. For 
 though the multitude of parts in many cases be great, 
 I may say beyond belief, yet as they have been all 
 previously formed into separate classes, and the clas- 
 ses themselves distinctly settled in the understanding ; 
 we fii'd it easy, by such a series of steps, to rise to any 
 idea, how complex soever, and, with a single glance 
 of thought, to embrace it in its full extent. 
 
 Sec. XVIII.. ..And Communicating them hy means of 
 Definitions* 
 
 But it is not enough that we barely form ideas in 
 our own minds: we must also contrive a way to ren- 
 der them stable and permanent that, when they disap- 
 pear upon calling off our attention, we may know how 
 to retrieve them .again with certainty. This is best 
 done by words and descriptions, which serve not only 
 to subject them to their own review,but also 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 easy and advantageous com- 
 munication of truth ; it ought always to be our first 
 care, when we set about unfolding our discoveries, to 
 exhibit the several conceptions to which they relate, 
 in a just and accurate series of definitions. For till we 
 have distinctly transferred our ideas into the under- 
 standings of those to whom we address ourselves, 
 and taught their connexion with the appropriated 
 iounds, all our reasonings will evidently be without 
 effect. If men comprehend not the true import of our 
 words, and arc therefcre led by them to bring wrong 
 
228 DUNCAN'S ELEMENTS 
 
 ideas into comparison, they can never sure see connex- 
 ions and habitudes that really subsit not. But if, on 
 the contrary, the terms we use, excite those very per- 
 ceptions in others, which they denote in our own 
 minds; then, as the several relations pointed out will 
 lie fairly open to view, they must needs be discerned 
 with great readiness and ease, and stamp the character 
 of certainty upon all our deductions. 
 
 Sec. XIX.... The names of simple Ideas constitute the 
 original and elementary terms of Language. 
 
 Thus we see, that the method of science begins with 
 unfolding our ideas, and communicating them by 
 means of definitions. And here it is of great impor- 
 tance to observe, that there must be in all languages, 
 certain original and elementary names, whence our 
 descriptions take their first rise, and beyond which wc 
 cannot trace the meaning and signification of sounds* 
 For since our very definitions are made up of words, 
 if we suppose not such primitive and fundamental 
 terms, into which they all resolve themselves, and 
 where they at last necessarily terminate, it is evi- 
 dent there would be no end of explaining. Now it is 
 peculiar tro our simple ideas, that they cannot be origi- 
 nally excited by words, but must always make their 
 first entrance into the understanding by the actual 
 operation of objects upon it. When, therefore, in a 
 series of definitions, we arrive at the names of these 
 ideas, 'tis plain we can pusli our descriptions no far- 
 ther, but are necessitated to suppose, that the percep- 
 tions themselves have already found admission into the 
 mind. If they have not, definitions avail nothing ; nor 
 can they any other way be impressed upon us, than 
 by betaking ourselves to the several objects in which 
 the power of producing them resides. Hence it ap- 
 pears, that the primary articles of speech, into which 
 the whole of language may be ultimately resolved^ 
 are no other than the names of simple ideas. These, 
 we see, admit not definitions. It is by experience and 
 observation, that we grow acquainted with their mean- 
 ing, and furnish ourselves with the perceptions thejr 
 
OF LOGIC. 229 
 
 jerve to denote. For finding that those in whose soci- 
 ety we live, make use of certain articulate sounds, to 
 mark the various impressions of objects, we too an- 
 nex these sounds to the same impressions, and thus 
 Come to understand the import of their words. This 
 way of knowledge takes place, in regard to all our 
 simple ideas ; but in many of those that are complex, as 
 they are the mere creatures of the understanding, and 
 exist no where out of the mind, there are, of course, 
 no real objects without Us, whence they may be origi- 
 nally obtained. If, therefore, they could not be com- 
 municated by descriptions, we should be left wholly 
 without the means of transferring them into the minds 
 of others. But happily it so falls out, that all cor» 
 "plex conceptions whatsoever may be distinctly exhibit- 
 ed in definitions. For as they are no more than differ- 
 ent combinations of simple ideas, if these simple ideas 
 have already got admission into the understanding, 
 and the names serving to express them are known ; it 
 will be easy, by describing the order, number, and pe- 
 culiar connexion of the notices combined, to raise in 
 the mind of another the complex notion resulting from 
 them. 
 
 Sec. XX.. ..A Knowledge of these previously supposed 
 in handling any Subject scientifically* 
 
 Since then it is by simple ideas and their names, 
 that we unfold all the other conceptions of the mind ; 
 it manifestly follows, that in handling any subject, 
 scientifically, we must always suppose those to whom 
 we address ourselves, previously furnished by experi- 
 ence with these first principles and elements of know- 
 ledge. Nor is this by any means an unreasonable pos* 
 tulatum : because the simple ideas that relate to the 
 sciences, being few in number, and coming very often 
 in our way, it is hardly possible we should be unac- 
 quainted with them, or not have frequently heaid their 
 names in converse with others. What principally de- 
 mands our care is, to apply those names aright and ac- 
 cording to the strict use and propriety of the language 
 in which wc write. 'Tis seldom allowable to change 
 
 u 
 
230 DUNCAN'S ELEMENTS 
 
 the signification of words, especially those by which 
 we denote simple ideas. If, however, such a liberty 
 should at any time be found necessary, We may still 
 make ourselves understood, by mentioning the idea un- 
 der its common name, and signifying its connexion 
 with the newly appropriated sound. Indeed it some- 
 times happens, that new and unusual ideas of this kind 
 are to be taken under consideration, which we must 
 therefore express by terms of our own invention. In 
 this case, as the ideas themselves cannot be laid open 
 by definitions, we refer to the several objects whence 
 they may be obtained ; which though it excites not 
 the perceptions immediately, yet sufficiently answer* 
 our purpose, by putting men in a way of being furnish- 
 ed with them at pleasure. 
 
 Sec. XXL... The order and connexion of our Definitions* 
 
 This foundation being laid, the communication of 
 our complex conceptions by definitions becomes both 
 easy and certain. For since the ideas themselves are 
 formed into different orders, and these orders arise con- 
 tinually one out of another ; nothing more is required 
 on our part, than to observe a like method and grada- 
 tion in our descriptions. As, therefore, the first order 
 of our compound notions is formed immediately from 
 simple ideas ; so the terms appropriated to this order 
 must be defined by the names of these ideas. And as 
 the second and all the .succeeding orders arise continu- 
 ally out of those combinations that constitute the clas- 
 ses next below them, so the definitions corresponding 
 to these different orders gradually take in the terms by 
 which the several inferior divisions are regularly and 
 successively expressed. In such a series of descriptions, 
 it is evident, at first sight, that nothing can be ob- 
 scure and unintelligible. For as it begins with the 
 names of simple ideas, whose meaning is supposed to 
 be known — and as in every order of definitions, such 
 terms only occur, as have been previously explained in 
 the preceeding distributions-— by advancing regularly 
 from one to another, we gradually furnish ourselves 
 with whatever is necessary towards a distinct concep- 
 
OF LOGIC 231 
 
 tion of all that is laid before us. Nor is it a small 
 advantage attending this disposition, that the several 
 ideas described are hereby excited in the understand- 
 ing, in the very order and manner in which they are 
 framed by a mind advancing uniformly from simple to 
 the most complicated notions. Hence we see distinct- 
 ly the various dependence of things, and being put in* 
 to that very train of thinking which leads directly to 
 science and certainty, are drawn insensibly to interest 
 ourselves in the pursuit ; insomuch, that while in fact 
 we do no more than follow a guide and conductor, we 
 fan yet hardly forbear fancying ourselves engaged in 
 the actual exercise of deducing one part of knowledge 
 from another. 
 
 Sec. XXII.. ..0/ the immediate and intuitive Relations 
 
 betioeen our Ideas. 
 
 When we have thus fixed and ascertained our ideas, 
 and distinctly exhibited them in definitions, we then 
 enter upon the important task of tracing their several 
 habitudes and relations. In order to this, we set about 
 comparing them among themselves, and viewing them 
 in all the variety of lights, by which we can hope to 
 arrive at a discovery of their mutual agreement or 
 disagreement. And here it happens, that some rela- 
 tions forwardly oiler themselves to the notice of the 
 understanding, and become the necessary objects of 
 perception, upon the very first" application of our ideas 
 one to another. Those are, therefore, immediately- 
 owned, and constitute our primary and intuitive judg- 
 ments, being attended with the highest degree of evi- 
 dence, and producing absolute certainty in the mind. 
 B iu ill many cases, the connexion or repugnance be- 
 tween our ideas, even when true and real, comes not 
 yet within our immediate view, but requires search 
 and examination to discover it. On this occasion,^we 
 have recourse to intermediate notices, and if by means 
 of them we can muster up a train of evident and known 
 truths, which, disposed in a regular series of argumen- 
 tation, lead at last to a conclusion expressing the rela- 
 tions we are in cuest of, the proof theiice arising is 
 
232 DUNCAN'S ELE MENTS 
 
 called demonstration. Now as the conviction attending 
 demonstration, is no less necessary and unavoidable than 
 that which proceeds from intuition; it evidently fol- 
 lows, that whether the delations between our ideas 
 are immediately discerned by the mind, or whether 
 they are traced by means of intervening perceptions, in 
 either case we arrive at science and certainty. This, 
 however, is particularly to be observed, that the more 
 remote and distant respects, being deduced from such 
 as are obvious and self-evident, the propositions expres- 
 sing these last demand our first notice, and ought to be 
 previously established, before we enter upon higher in- 
 vestigations. When, therefore, in the method of 
 science, we have finished the business ot definitions ; 
 it must be our next care, distinctly to unfold in propo- 
 sitions, those immediate and intuitive relations, which 
 are necessarily seen and owned by the mind, upon the 
 very first comparing of our ideas one with another. These 
 propositions have obtained the name of Jirst principles, 
 because, occurring first in the order of knowledge, 
 and being manifest of themselves, they suppose not 
 any prior truths in the mind, whence they may be evi- 
 denced and explained. % It is not needful to enlarge 
 here upon the necessity of circumspection and care, in 
 setrling these primitive and fundamental perceptions. 
 For since the whole superstructure of our knowledge 
 rests ultimately upon them, it is evident at first sight, 
 that a mistake in this-case must at once overturn and 
 annihilate^ all- our future reasonings. But having al- 
 ready explained the nature of these propositions in th« 
 second book, unfolded the notion of self-evidence, and 
 taught the manner of distinguishing between the truths 
 of this class, and" those that are demonstrable; we 
 fell all, for the present, wave any farther consideration 
 of this subject, referring the reader to what is there 
 advanced, if he desires fuller information. 
 
 Sec. XXIU....Of the application of Self evident truths 
 in demonstrating such as are remote and distant. . 
 
 The first and more immediate relations of our ideas 
 being thus pointed out, 'our next business is, to investi- 
 
OF LOGIC. 233 
 
 gate such as are remote and distant. And here it is 
 that we have occasion for intermediate notices, and a 
 skilful application of intuitive truths. But though 
 self-evident propositions he the ultimate foundation of 
 our reasoning, we are not, on that account, to imagine, 
 that the art of improving knowledge lies in assembling, 
 at random-, a large and comprehensive stock of these. 
 Even general principles, considered by themselves, avail 
 but little towards the investigation of truth. They are, 
 indeed, useful as media of certainty, by preserving the 
 evidence of our reasonings distinct, which never fail to 
 convince, if, being pursued to their source, they are 
 found to resolve themselves into, and ultimately termi- 
 nate in these principles. But when we set about the 
 increase and enlargement of science, far other helps 
 are required. For here the whole secret consists, in 
 devising and singling out such intermediate ideas, as, 
 being compared with those others whose relations we 
 enquire after, may furnish out a train of obvious and 
 known truths, serving distinctly to investigate the said 
 relations. Euclid, In the first book of the elements, 
 hasHlemonstrated, that the three inward angles of a 
 triangle taken together, are equal to two right angles. 
 The reasoning, by which he establishes that proposition, 
 resolves itself into this general principle : things equal 
 to one and the same thing, are equal to one another. 
 Will any one, however, pretend to say, that a bate 
 consideration of the principle itself led him t© that dis- 
 covery . ? the merest novice in mathematics would, up- 
 on this supposition, be equally qualified for the business 
 of invention, with one that had made the greatest pro- 
 gress ; inasmuch as these 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 compared, were found severally equal ; 
 thereby ascertained the proposition in question, by- 
 showing it to terminate in the above axiom, though 
 perhaps the axiom itself was never once thought of, 
 during the whole course of the investigation. 
 
 U 2 
 
234 DUNCAN'S ELEMENTS 
 
 Sec. XXIV.... Reasoning, though resolvable into gene- 
 ral truths, rests immediately upon particular self- 
 evident propositions. 
 
 And here it may not be improper to observe, that 
 though it be usual in reasoning, when we arrive at any 
 particular self-evident proposition, to refer to the ger- 
 neral axiom under which it is comprehended : yet is 
 not this done out of absolute necessity, 01 ft r the sake 
 of any additional confirmation. All intuitive truths, 
 whether general or particular, standing upon the same 
 foundation of immediate perception, are necessarily 
 embraced for their own sake, and require no mutual 
 illustration one from another. When, therefore, ve 
 have found, that the three angles of a triangle, and 
 two right angles, are severally equal to the angles form- 
 ed by one right line standing upon another, we thence 
 immediately discern their equality between themselves, 
 independent of the general axiom into which this 
 truth may be resolved. Nor do we in reality refer to 
 that axiom, by way of evidence and proof; but merely 
 to show the coincidence of the example under notice, 
 with a previously-established general principle. The 
 same thing happens in all other demonstrations whatso- 
 ever, which, terminating thus in particular self-evi- 
 dent truths, are therefore of themselves sufficient to 
 .certainty, and acquire not any new force by being ul- 
 timately referred to general maxims. This I mention 
 here, to obviate a common prejudice, whence many are 
 led to imagine, that particular intuitive propositions 
 derive their evidence from those that are general, as 
 being necessarily included in them. But since they 
 both stand upon the same foundation of certainty, 
 and are admitted in consequence of immediate percep- 
 tion, they have therefore an equal claim to self-evi- 
 dence, and cannot be made plainer by any mutual ap- 
 peal. 
 
 Sec. XXV.... Particular Self-evident propositions so 
 called here y in opposition to general principles. 
 
 As, however, it is usual in the method of science to 
 
OF LOGIC. 23* 
 
 lay down certain general principles by way of founda- 
 tion for our future reasonings; some will perhaps, ab- 
 ject, that this seems to be a needless precaution, since 
 d -monstrations may subsist without them, and commonly 
 terminate in particular self-evident truths, peculiarly 
 connected with the subject under consideration. In 
 oider, therefore, to give a distinct idea, of the true de- 
 : of this previous step, we shall begin with observ- 
 ing, that by the particular propositions in which de- 
 monstrations terminate, must not be understood such as 
 are so, according to the strict definition of the word, 
 or in opposition to universal ; but only confined and 
 limited truths, when compared with others that are 
 more general. Thus the proposition, circles^ equal to 
 one and the same circle, are equal between themselves, 
 is, in strictness and propriety of speech, universal, be- 
 cause the subject is taken in its full extent, and the 
 pred, i es to all the individuals comprehended un- 
 
 der it. We here, notwithstanding, consider it as on- 
 ly a particular truth; because it is of a very limited 
 nature, when compared with the general axiom men- 
 tioned above ; things equal to one and the same things 
 are equal to one another. For this not only extends to 
 all the various species of figures, but takes in every ob- 
 ject without exception, that comes under the denomi- 
 nation of quantity. 
 
 Sec. XXV 'I..,. General Principles serve, first, to Con- 
 tract the bottom of our Reasoning. 
 
 This point settled, it will easily appear, that the me- 
 thod of premising general principles in the sciences 
 answers these two great and valuable purposes. First, 
 to cbntract the bottom of our reasoning, and bring it 
 within such bounds as are sufficiently accommodated 
 to the capacity of the mind. For demonstrations be- 
 ing carried on by means of intermediate ideas, which 
 must always have some peculiar connexion with the 
 matter in hand, the particular self-evident propositions 
 in which they terminate, are almost as various as the 
 subjects to which they relate. Thus in investigating 
 the equality of different objects, whether angles, trian- 
 
236 DUNCAN'S ELEMENTS 
 
 gles, circles, squares, Sec. the intuitive truths, oa 
 which the proofs rest, always regard the particular spe- 
 cies, and may be therefore multiplied, in ihjinitum, as 
 "well as the species themselves. But now it is remark- 
 - able, that all these several truths, numerous as they 
 may appear, are yet reducible to this one general prin- 
 ciple already mentioned ; things equal to one and the 
 same thing are equal to one another. The same obser- 
 vation will be found to hold in other parts of human 
 knowledge ; insomuch that though the particular 
 truths, on which we bottom our reasonings, are really 
 innumerable ; yet may they be all, without exception, 
 resolved into a very few general maxims, and thereby 
 brought readily within the compass of the understand* 
 ing. When, therefore, we begin with premising these 
 general truths, and as we advance in science, take care 
 universally to resolve our demonstrations into them ; 
 this must needs add a wonderful clearness and perspi- 
 cuity to our reasonings, and by establishing them upon a 
 foundation previously admitted, and of whose strength 
 and firmness we are abundantly satisfied, give them that 
 irresistable force and influence, which serves to produce 
 absolute certainty. Nor can we possibly imagine any 
 thing more elegant and beautiful, than thus to behold 
 knowledge rising from a firm and fathomable root, 
 bearing its head aloft, and spreading forth into innu- 
 merable branches of science ; which, though various- 
 ly implicated and entangled, and stretching to a vast 
 extent, yet by their union in one common stock, derive 
 thence so sure and stable a support, that all the as- 
 saults of cavil and scepticism are not able to destroy 
 or loosen their connexion. 
 
 Sec. XXV 'II... .Secondly, to ascertain the Justness of 
 it with more Ease, and less Hazard of Miscarriage. 
 
 But, secondly, another purpose served by general 
 principles is, that they enable us with less fatigue and 
 labour and less hazard of miscarriage, to satisfy our- 
 selves as to the justness of those reasonings by which, 
 science is established. For since demonstrations, when 
 pursued to their source, terminate always in particular 
 
OF LOGIC. 23? 
 
 intuitive truths, -which are therefore the ultimate foun- 
 dation of certainty ; it greatly improves u?, to beware, 
 that we receive not any propositions under this name, 
 until we have distinctly settled them in our own minds, 
 and attained a full and clear perception of that self-evi- 
 dence, on account of which they are admitted without 
 proof. But now these propositions being many in num- 
 ber, and differing according to the nature of the subject 
 about which our researches are employed ; it mustgreat- 
 'ly perplex and retard our reasonings, were we to check 
 ourselves every time they occur, in order to examine 
 them by the rules of first principles. Nor is it a matter 
 of slight consideration, that in the heat and hurry of 
 demonstrating, while the mind is advancing eagerly 
 from one discovery to another, we should be often 
 tempted«to pass them over hastily, and without that 
 attention their importance requires ; which must ex- 
 pose us to many errors and mistakes. These inconve- 
 niences are effectually prevented by the method of pre- 
 mising general truths : because upon referring particu- 
 lar propositions to them, as the connexion is obvious at 
 first sight, and cannot possibly escape our notice, the 
 evidence is discerned to be the very same with that of 
 the principles to which they belong. And thus by a 
 bare reference, without the trouble of particular ex- 
 aminations, the grounds of reasoning are ascertained, 
 and our demonstrations found ultimately to rest on 
 maxims previously established. 
 
 Sec* XXVI II.. ..Of the manner of linking propositions 
 togtthtr, in order to the for miyig of legitimate demon- 
 strations.. 
 
 Having explained the use of general principles, 
 shown them to be the great media of certainty, and 
 found, that in order to enlarge the bounds of science, 
 we must have recourse to intermediate ideas, as by 
 means of them we are furnished with the several pre- 
 vious truths, of which reasoning consists ; it now re- 
 mains, that we enquire in what manner these truth* 
 are to be disposed and linked together, towards the 
 forming of just and legitimate demonstrations. We have 
 
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