^^^^'
JO .^.iJto.
THE,
ELEMENTS
o
OF
G
I C.
iJQUR BOOKS.
BOQK I.
Ci" the original of our ideas, rheir various divisions, and the manner in which ihey contribute to the increase of knov.ledofe ; with a philo- so
progress, man language. BOOK II.
Of the grounds of human judg- ment, the doctrine cf pro- positions, their use in reason- ing, and division into self- evident and demonstrable.
phical account c£ the rise, and nature of hu-
BOOK III.
Of reasoning and demonstra- tion, with their application to the investigation of knowl- edge, and the conamon af- fairs of life.
BOOK IV.
Of the methods of invention, and science, where the sev- eral degrees cf evidence are examined, the notion of cer- tainty is fixed and stated, and the parts cf knowrledge in vrhich it may be attained.
DESIGNED PARTICULARLY FOR
T'oimg Gentlemen at* the Un'roersity ; ^
AND TO PREPARE THE V/AY TO THE STUDY OF PHILOSOPHY AXD THE MATHEMATICS.
5y WILLIA?^I DUXXAN,
Professor of Philcsophy in MarishaL College, Aberdeen.
Dcctrina sed vim promovet insitam ; Rectiqiie cultus pectora roborant Hop...
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I
TO THE
RIGHT HONORABLE
STEPHEN POYNTZ, Esc^,
SIR,
If I take this opportunity of publishin^^ to the world the esteem I have for a character to wiiich learning is so greatly indebted, I hope you will not think your- self injured by such a declaralion from a man that honors you, and who looks upon the liberty of put- ting- the foIIoYsing; work under your patronage, as one of the happy incidents of his life.
From the first moment I form.ed the design of it, I had it in my tlioughts to address it to you ; and indeed what couid be more natural, than that I should be ambitious of inscribing a treatise upon the ele- ments of philosophy, to one, who has so eminently distinguished himself by his extensive knowledge in that, as well as all the other branches of human learning ?
Your great abilities in every kind, have deservedly recommended you to the notice of your king and country, and occasioned your being courted and im- portuned to accept those high offices of state, which others pursue with so much eagerness, and find it often diScult to obtain, by all the arts and endeavors of ambition. Nor have your talents been con^.ned to the view of your country alone. Foreign nations have seen and admired you, and still speak with the greatest applauses of your wise and able conduct, wnen it was your province to act as a British minister abroad.
4
DEDICATION.
%^ the qualities of a great statesman are not those aione by which you have rendered yourself ilkistri- ous. The virtues of private life no less actuate and adorn your whole behavior, and add a new dignity to the high station to which your merit has raised you. Affability, complacency of manners, and, above ail, an extensive humanity and benevolence, which takes pleasure in doing good, are distinguishing parts of your character, and have contributed no less than your other extraordinary endowments, to that uni- versal acknov/ledgement v/hich is paid you by your count ly.
Tliat you may long live to be an ornament and blessing to the nation, and to enjoy the pleasure which arises from a consciousness of the esteem and approbation of all good men, is the sincere and hearty prayer of,
Sir,
Your most obliged^ aiid 7nost obedient
Humble Sci'vant,
V/. DUNCAN,
■ [ 5 ]
INTHODUCTION.
Sec. I. — Importance of the Knonvledge of Ourselves,
O.
F all the human sciences, that concerning man is cer- tainly 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 are happy or miserable in proportion, as we know how to frame a right judgment of things, and shape our actions agreeably to the circmnstances in which we -are placed. No study, therefore, is more important than that which in'rroduces us to the knowledge of ourselves. ■ Hereby we become acquainted with the ex;ent 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, Ave arrive by degrees, at that just- ness and truth of understanding, wliich is the great perfecdon of a rational being.
Sec. IL — Di^erjent gradatijns of Perfecticni hi Things.
If we look attentively into things, and survey thein in thei** full extent, Vv'-e see them rising one above another in variou^ - degrees cf eminence. Among the inanimate parts of matter* some exhibit nothing vv-orthy our attention : their parts seem as ic were jumbled together by mere chance, nor can we dis- cover any beauty, order, or regularity in their composition. In others, we discern the finest arrungement, and a certain elegance of contexture,^that makes us ainx to them a notion cf vrofth and excellence. Thus metals, and precious stones, are conceived as far surpassing those unformed m.assescf earth, that lie eveiy where exposed to viev/.. If we trace na- ture 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 m-echanism to percep- tion, and from perception, in ail its various degrees, to reason and understanding.
Sec. III. — Usefulness of Culture^ and particularly cf the Study of Logic.
But though reason be the boundary by which man is distin- ^ guished from the other creatures that surround him, yet we arj '
V i
vi INTRODUCTION.
far from finding it the same in all. Nor is this inequality to 1)6 wholly ascribed to the original make of men's minds, or the diiference of their natural endowments. For if we look abroad into the several nations of the world, some are over-ruu w*ith ignorance and barbarity ; others ficurish in learning and the sciences : and wliat is yet more renaarkable, the sam^a people have in different ages, been distinguished by these very opposite characcers. It is therefore by culture, and a due ap- plication to the poY.-ers of our minds, that we increase their capacity, and carry human reason to perfection. Where this method is followed, knowledge and strength of understand^ ing never faU. to ensue ; v.^here it is neglected, we remain ig- norant of our own w'orth ; and those latent qualities of the soul, by which she is fitted to survey this vast fabric of the world, to scan the heavens, and search into the causes of things, lie buried in darkness and obscurity. No part of knowledge, therefore, yields a fairer prospect of improveinent, than that which takes account of the understanding, examines its powers and faculties, and shews the ways by vvhich it comes to attain its various notions of things. This is proper- ly the design of Logic, which may be jusdy styled the history vi the human mind, inasmuch as it traces the progress of our knov.dedge, from eur first and simple perceptions, through aU their diSerent combinations, and all those num.erous deduc- tions that result from variously comparing them one with an- other. It is thus that we are let into the natural frame and contexture of cur ov.ni m.inds, and learn in what manner ws. ought to conduct our thoughts, in order to arrive at truth, and avoid error. We see how to build one discovery upon anoth- er, and, by preserving the chain of reasonings uniform and un- broken, to pursue the relations of things through all their la- byrinths aiid windings, and at length exhibit them to the view of the soul, with all the advantages of light and conviction.
Sec. IV. — Operation.^ of the Mind. But as the understanding, in advancing from one part of knovvdedge to another, proceeds by a just gradation, and ex- erts various acts, according to the diJerent progress it has made, logicians haive been careful to note these several sreps, and have distinguished them in their writings by the name of the operations of the mind. These they nsake foiu- in num- ber, and agreeably to that have divided the v.hole system of logic into four parts, in vrhich these acts are severally explain- ed; and the conduct and procedure of the mind, in its differ-
INTRODUCTION. y'n
ciit stages of improvement, regulated by proper rules and ob- servations. Now-, in order to judge how far logicians have f-Uo^ved nature, in this distinction of the powers of the un, derstanding, let us take a shore view of the mind, and the iTianner of its progress, according to the experience we have of it in ourselves, and see whither the chain of our own thoughts v/ill without constraint lead us.
Sec. V. — Perception^
First, then, we find ourselves surrounded with a variety of ©bjects, which, acting diiferently 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 of the operations of om* own minds, and attend to them as a new set of impressions. But in all tliis there is only bare consciousness. The mind, vx^thout proceeding any further, takes notice of tiie impres- sions that are made upon it, and views tilings in order as they present themselves one after anotlier. This attention of the utiderstanuing co the objects acting upon it, whereby it be- comes sensible ot the impressions they make, is called, by lo- gicians, perception ; and the notices themselves, as they ex- i.st in the mind, and are there treasured up to be the materi- als cf thinking and knowledge, are distinguished by the name ti' ideas.
Sec. VI. — Judgment,
But the mind does not always rest satisfied in theb are 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. In this complicated view of things, it readily discerns, that soine agree and others dis- agree, and joins or separates them, according to this percep- tion. Thus, upon comparing the idea of two added to tv,-o> , with the idea of four, we, at first glance, perceive their agree- Kient, and thereupon pronounce that t'.vo and two are equal to four. Again, that white is not black, that five is less than .seven, are truths to vrhich we immediately assent, as soon as V. e compare those ideas together. This is the first and sixit- p-est act of the mind, in determining the relation of things, vvhen, by a bare attention to its own ideas, coniparing any two of them together, it can at once see liov,- far they are con- nected or disjoined. The knowledge thence derived is called I'ltuiii-je^ as requiring no pains or examination ; and the act
viii INTRODUCTIOM.
of the mind assembling its ideas together, and joining or dis- joining them, according to the result of its perceptions, is vrhat logicians term jndgjmr.t.
Sec. VII. — Reasoning.
Intuition affords the highest degree of certaint}' ; it breaks in witii an irresistable light upon tne understanding, and leaves no room for doubt or hesitation. Could we in all cases, by thus putting two ideas together, discern imniediatel}"- their agreement or disagreement, we should be exempt fpom error, and ail its fatal consequences. But it so ho-ppens, that many of ovu- ideas are of such a nature, that they cannot be thus ex- amined in concert, or by any immediate application one to another ; and then it becomics necessary to rind out scm.e oth- er ideas that will admdt of this application, that by means of them we may discover the agreeiVient we search for. Thus the mind wanting to know the agreement or disagi-eement in extent between tvv^o enclosed fields, w-hich it cannot so put to- gether as to discover their equality or inequality by any im- mediate comparison, casts about for some intenr^ediate idea,- which, by being applied iirst to the on8,"'^nd then to the oth- er, will discover the relation it is in quest of. Accordingly it assum.es some stated length, as a yard, 2«c": and measuring the fields one after the other, comes by tXat me?.ns to the knowl- edge of the agreement or disagreemicnt in question. The in- tervening ideas made use of on these occasions, are called proofs ; and the exercise of the mind in finding them out, and applying them for the discover}'' of the truths it is in search cf, is what we term reasonhi^-. And here lee it be observed, that the knowledge gained by reasoning is a deduction from oiu- intuitive perceptions, and ultimately founded on them. Thus in the case before mentioned, having found by measur- ing, that one of the fields m^akes three-score square yards, an^l the other only fifty-five, v/e thence, conclude, that the first field is larger than the second. Here the two first perceptions are plainly intuitive, and gained by an immediate application of the naeasure 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, but is a deduction from the two preceding judg- ments, in v.-hich the ideas arc severally com^pared v/ith a third, and their relation thereby discovered. Yv'e sec, therefore, that reasoning is a much mors ccmplicated act of the mind-
INTRODUCTION. ix
than simple judgment, and necessarily presupposes It, as be- ing ultimately founded on the perceptions thence gained, and implying the various comparisons of them, one with another. This is the great exercise of the human faculties, and the chief instrument by Avhich we push on cur discoveries, and enlarge our knowledge. A quickness of mind to find out in- termediate ideas, and apply them skilfully in detemiining the relations of things, is one of the principal distinctions among men, and that which give some so remarkable a superiority- over others, that we are apt to look upon them as creatures cf another species.
Sec. yni.^Ma/iod.
Thus far we have tr?.ced the progress of the m.ind in think- ing, and seen it rising by natural and easy steps from its first and simple perceptions, to the exercise of its highest and most distinguishing faculty. Let us now view it in another light, as enriched with knowledge, and stored with a variety of dis- coveries,^ acquired by a due application of" its natural powers. It is obvious to consider it in these circumstances, as raking a general survey of its whole stock of intellectual acquisitions, disposing them under certain heads and classes, and tying theni together, according to those connexions and dependen- cies it discerns between them. It often happens, in carrying on our enqmries from subject to subject, that we stumble upoii •unexpected truths, and are encountered by discoveries which our present train of thinking gave no prospect cf bringing in our way. A man of clear apprehension, and distinct reason, who, after due search and examination, has mastered any part of knowledge, and even made important discoveries in it, be- yond 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 regular system, where their mutual dependence may be easily traced, and the parts seem to grov/ one out of another. This .is that operation of the mind, known by the nam.e of disposition or method, and com.es in the last in order, according to the di- vision of the logicians, as presupposing some tolerable mtea- sure of knowledge, before it can have an opportunity of e.\- erting- itself in any extensive degree.
B
X INTRODUCTION.
Sec. IX. — 'Perception and Judgment terms of a very extendve signification.
We see, then, that this fourfold distinction of the powers of the mind, in.perception, judgment, reasoning, and disposition, as well as the order in which they are placed, have a real foun- d?,tion in nature, and arise from the method and procedure of our own thoughts. It is true, there are many other actions and iTiodjiica^ions of the understanding, besides those above mentioned, as believing, doubting, assenting, &c. but these are all implied in the act of reasoning, in the like manner, as com.- prehending, abstracting, remembering, iTiay be referred to the lirst op'ra,tion of the mind, or percepvion. This vs-ill appear more fully in the sequel, when we conie to handle the several parts of logic separately : at present we shall content ourselves with this general account of things ; only it seems necessarv to observe, that ptrception and judgment, in the propriety of the English tongue, have a inuch more extensive signification than logiciai%s commonly allow them. We not only perceive the ideas in bur own minds, but we are said also to perceive their agreem.ent or disagreement ; and hence arise the com- mon phrases of intuitive perceptions, perceptions of trudi, and of the justness of arguments of proofs ; where it is mani- fest, that the word is a^:)piied not only to our judgments, but also to our reasonings. In a word, v,-h?.tever comes under the vie\v of the mind, so as to be distinctly represented and taken notice of, whethei anidea, proposition, chain of reason- ing, or the order and connexion of things, is thereby rendered an ol:iject of percep don, and gives employment to this frst and rnost simple of our faculties. In like manner, the viordjudg- onent, is seldom, in common discourse, confined to obvious and self-evident truths. It rather signiiies those conjeciures and guesses that we form, in cases which admit not of un- doubted certainty, and wheje we are left to determine by coiii- paring the various probabilities of things. Thus a man of sagacity and penetration, who • sees far into the humours and passions of mankind, and seldom mistalces in the opinions he frames of characters and actions, is said to judge well, or think judiciously. -For these reasons, it might not be im- prvOj;)er'to change the common names of the two first opera- tions of the mind, calling the one simple apprehension, and the other i'ltuition ; which two words seem belter to express their nature, and the manner in wh.ich they are conversant about their several objects. This accurc-icy of distingtiishing, where
IXTRCDUCTION. xi
there is any the least dinerence, is in a peculiar manner neces- sary 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 thing?, and thereby avoid being misled by their similitude or resemblance.
Sec. X. — Logic divided into Four Parts. .Its Use/id- 71 ess and Excelienci'.
Having thus given a general idea of the four operations of the mind, and traced their connexion and dependence upon one another, I would next observe, that in consequence of this division of the powers of the understanding, Icgic is also divid- ed into four parts, which treat severally of tht^se acts, and give rules and directions for their due conduct and regulation. The operations themselves we have from nature ; but hov/ to exert them justly, and employ them with advantage in the search of truLU,*is a knowledge that m.ay be acquired by study and observation. It is certain, that we nieet with false rea- sonings as well as just. Some men are distinguished by an accuracy of thinking, and a happy talent of unravelling aini throwing light upon the most obscure and intricate subjec'-s. Others confound the easiest speculations ; their understand- ings seem to be formed awry, and they are incapable of either conceiving clearly themselves, or making their thoughts in- telligible to orhers. If then we set ourselves carefully to ob- serve what it is that makes the one succeed so %>, ell, and hovr- the others come to miscarry, these reniarks v/iil furnish us with an art of the highest use and excellency in the conduct cf life. Now this is the precise business of lojic-^to explain the-. jTature of the human mind, and the proper manner of conduct- ing its several powers, in order to the attainment of truth and knowledge. Ic lays open those errors and mistakes we ar^ apt, through inattention, to run into, and teaches us how to distinguish between truth, and what carries only the appear- ance of it. By this means, we grow acquainted widi the na- ture and force of the understanding, see what things lie within its reach, where we may attain certainty and demonstration, and when we must be contented with bare probability. These 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 knowledge, if we really wish to succeed in our enquiries. But we shall now proceed to treat of i'S parts separately, according to the division given of theiij above.
ELEMENTS of LOGIC
BOOK I.
OF SIMPLE APPREHENSION, OR PERCEPTION.
CHAP. I,
OF THE ORIGINAL OF OUR IDEAS.
Sec. I. — Shnple jifi/irehension and Ideas.
X HE first thing we observe, when we take a view of what passes within us, is, that we are capable of re- ceiving 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 cbjects act- ing upon it, is what we call simple apjirehtunon^ and is, in fact, the mind itself taking a view of things, as represented to it by its ov/n consciousness. It is by this means that tve come to be furnished with all those ideas about which our thoughts are employed. For being sensible of the impressions made upon us, and attending to the perceptions they bring, we can renew them again upon occasion, even when the objects that first produced them are removed. No^y, our ideas a.re nothing else but these renev>-ed representations of what v:t have at any time perceived and felt, by means of v/jiic'-' :mng,s are agjan brought under the vieAV of the mind, and seem to have a kind of existence in it.
14 DUNCAN'S ELEMENTS
It is true, we can upon many occasions combine our ideas variously together, and thereby foiTn to our- selves representations of things that never had an ex- istence in nature, as when we fancy a centaur, or a golden mountain ; but it is still certain, that the origi- nal ideas, out of vvdiich these are made, are such as has been conveyed into the mind by some former im- pressions. It remains therefore to enquire how we come by our first notions and perceptions of things. Whence does the understanding derive these original impressions and characters, which it can combine in so many different ways, and represents to itself, un- der such infinite varieties ? To this I answer, that if w^e attend carefully to what passes in our minds, we shall observe two inlets of knovv ledge, from whence, as from two fountains, the understanding is supplied with all the materials of thinking.
Sec. II. ''111 our original Ideas derived either from
Sensation^ First, out^vard objects, acting upon our senses, rouse in us aA*ariety of perceptions, according to the din'erent manner in which they afilect us. It is thus that we acquire ideas of liglit and darkness, heat and cold, sweet ^lud bitter, and all those other impressions which we term sensible qualities. This great source and inlet of knowledge is com-monly distinguished by the name of sensation, as comprehending all the no- tices conveyed into the mind, by impulse made upon the organs of sense.
Sec. III.— Or Rejiection,
But these ideas, numerous as they are, are wholly derived to us from without : there is therefore yet an- other source cf impressions, arising from the mind's attention to its own acts, when, turning inwards upon itself, it takes a view of the perceptions that are lodg-
OF LOGIC. 15
ed there, and the various Vv-ays in which it employs it- self about them. For the ideas furnished by the senses, give the mind an opporlimity of exerting its several powers ; and as all our thoughts, under whatever form they appear, are attended witli consciousness, hence the impressions they leave, v/hen we com.e to •turn the eye of tlie soul upon them, enrich the under- standing v.'ith a new set of perceptions, no less distinct than those conveyed in by the senses. Thus it is that we gej: ideas of thinking, doubting, believing, willing, &c. vrhicix are the difierent acts and workings of our minds, represented to us by our own consciousness. This second source of ideas is called refiection^ and evidently presupposes sensation ; as the impressions it furnishes are only of the various powers of the un- derstanding, employed about perceptions already in the mind.
Sec. IV. — 'Risp and Progress of Human Knowledge. These considerations, if we duly attend to them, will give us a clear and distinct view of the naturrwl procedure of the human intellect, in its advances to knowledge. We can have no perception of the oper- ations of our ovrn minds, until they are exerted ; nor can they be exerted before the understanding is fur- nished with ideas about which to employ them ; and as these ideas, that give the first employment to our .faculties, are evidently the perceptions of sense, it is plain, that all our knowledge must begin here. This, then, is the first capacity of the iiuman mind, that it is fitted to receive the impressions m.ade upon it by out- ward objects afiecting 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, remembering, considering, &c. all which are attended with an internal feeling and conscious- ness. And thii leads us to the second step the mind
16 DUNCAK's ELEMENTS
takes in its progress towards knowledge, viz. that it can, by its own consciousness, represent to itself these its several workings and operations, and thereby furn- ish the understanding with a new stock of ideas. From these simple beginnings, 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 examining them in an infinite variety of lights, by which means it is enabled to enlarge the objects of its perception, and finds itself possessed of an inexhaustible stock of materials. 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 itself in the arts of judging and reasoning, by which the capacious mind of man pushes on its views of things, adds dis- covery 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 progress of the soul, from the very first dawnings of perception, till it reaches the perfection of human knowledge ; nor shall we, among all its vast stock of discoveries, or that infinite variety of conceptions whereof they con- sist, be able to find one original idea which is not de- rived from sensation or reflection, or one complex idea which is not made up of those original ones.
Sec. Y ."Division of our Ideas into Slm^ile and Complex.
Having thus shown how the mind comes to be first furnished with ideas, we shall next proceed to the con- sideration 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
or LOGIC. 17
•conveyed into the mind by sensation and reilection, and which exist there, simple, unifDrm, and v/ithout any shadow of variety. Secondly, those more com- plex notions of things, that result from the various combinations of our simple ideas, v.iietlier they are conceived to exist of themselves, in any particular subject, or are united and joined together bv the mind enlarging its conceptions of things, and pursuing the ends and purposes of knov/ledge. These two classes comprehend our whole stock of ideas ; and, wlien considered separately, in that order wherein they most naturally seem to offer themselves to cur :thcughts, will, X hope, give such a view of the conduct and m?ji- ner of the mind, as may contribute not a little to in- troduce us to an acquaintance with ourselves, and make us sensible of tlie capacity and extent of the hurnan intellect. Vv'e proceed, 'therefore, to a more partlculai' account of this division cf cur ideas.
CHAP. II.
OF SI.MPLE IDEAS.
'. I- — ^-Ini'iic Ideas zi
^""^ class of our ideas are those which I {ii<:.
tmguish by the name of simple perception; becallse I they exist m the mind under one unifbrm appearance ^ Witnout variety or composition. For thciieh ex^^r- , iiai objects convey at once into the under::tandine ! many diherent. ideas, all united together, and mak^
mg as It Were one whole : yet the impressions them- I selves -are evidently distinct, and.are conceived bv the I 3imd, each under a form peculiar to itseli^ Thus ' tne ideas of colour, extension, and motion, may be
iS DUNCAN'S ELE1?.TENTS
tc.ksn 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 difierent objects, or v/ere exhibited to our notice at difierent times. \^^e are therefore carefully to distinguish be- tween our simple and primitive conceptions, and those different com-binations of them, which are of- ten suggested to the mind by single objects acting upon it. The iirst constitute our original notices of things, and are not distinguishable into different ideas, , but enter by the senses simple and unmixed. They ' are also the materials, out of which all the others, how complex and complicated soever, are formed ; and therefore ought deservedly to be looked on as the foundation and ground-work of our knowledge.
Sec. 11.— 'Simple Ideas of Sensation.
' Now if v/e take a survey cf these ideas, and their several divisions and classes, we shall find them all suggested to us, either by our senses, or the atten- tion of the mind to what passes v. ithin itself. Thus our notices of the difierent qualides of bodies, are all 'of the kind we call simple ideas, and may be reduced to five general heads, accordirig to the several organs whicli are affected by them. Colours, Sec. and sounds are conveyed in by the eyes and ears ; tastes and smells by the nose and palate ; and heat, cold, solidi- ty, ^Q. by the touch. Besides these, there are oth- ers which niake impressions on several of our sens- es, as extension, figure, rest, and m.otion, Sec. the ideas of wliich wc receive into our minds both by seeing and feeling.
Sec. III.— o:;;-:J£- Ideas of Reflection, ^c. If v.'C next turn our ". icvr upon vrhat passes within ourselves, we sh.all find another set cf simple ideas
OF LOGIC. 19
ations of our own minds. Perception or thinking-, and volition or AviHing, are what every man experi- ences in himself, and cannot avoid being sensible of. I shail only observe further, that besides all the above* mentioned perceptions, there are others that come into our minds by all the ways of sensation and re- flection ; such are tlie ideas of pleasure and pain, power, existence, unity, succession, &c. v/hich ar«j derived into our understandings both by the action of objects without us, and the consciousness of vrhat v.e feel within. It is trac some of these ideas, as cF extension and duration, cannot be conceived altogeth- er without parts, neve'rti"!eiess, they are justly ranked among our simple ideas ; because tlieir parts being all of the same kind, and without the m-ixture of any other idea, neither of tliem can be resolved into tv.o distinct and separate conceptions. Thus they still ^answer the definition given above, of being one uni- form appearance in the mind, with variety or plural- ity. But to prevent confounding our simple ideas cf space and duration, v/itli these complex modes cf them marked out by the several measures com.m.on- ly in use, as yards, miles, days, years, ixc. it may perhaps be most proper to consider the least portions of either whereof we can form a clear and distinct perception, as the siniple ideas of that kind out of which all their other modes and com.binations are formed. Such an instant, or point, may be con- ceived to be the same in respect of duration or space, as unity is in re_spect of numbers ; and will serve best to show, how by a continued addition or repetition, our m.ore enlarged and complex ideas are made up.
20 DUNCAN'S ELE^.IENTS
Sec. IV.— .SV:72,^'/.i- Ideafi have no AdmissiGn But by (ha: iiTop.er Inlets cf Mature. Kavlng thus given a n^eneral view of our simple idsas, I have still two coservations to make ccncern- ing them. The first is, thtl they are such as can only be conveyed into the mind by the proper chan^ r.el3 and avenues provided by nature ; insomuch that \i we are destitute m any of those inlets, by which the impressions that produce them are want to be iidniitted. all the ideas thence arising: are absolutely lost to us ; nor can we, by any quickness of under- standiujj, find a remedy for this want. A man born blind is incaj>able of the ideas of light and colours ; m like manner as one who is deaf can form no no- tion or conception of sounds. Hence it appears, that these our simple ideas are just such as nature has^ iumic-hed them, and have no dependence en our will ; we can neither destroy them when in the un- derstandln/j, nor i^shion or invtrnt any new one, not taken in by the crdiiiary means of perception. So that we here see the utmost bounds of human knovvl- Cuge, v/hic!], however miguLy and enlarged, cannot exceed the limits of those cur simple original ideas, and their various combinations. Sec. V. — They furnish ampde Materials of Kno^vljdg^.
And this lead 3 me to the second observation I proposed to make, which is, that though the m.ind cannot, in multiply :::g its coiiceplions of things, ad- vance one step beyond the materials furnished it by £ense and consciousness ; jxt as it has a pcAver ut com!>ining, mcdifyiT:^?;, a;nd eniargingthera, in all the chiierent ways' in which they can be put together, it therefore finds itseif in possession of an inexhaustible treasure of ideas, suaicient to employ it to the full extent of ail its povvcrs, and furnish matter for ail
OF LOGIC. 2i
those yarious opinioDs, fancies, and views of thing-s, that make up the subject of its thoughts and con- templations. Let us but reflect upon the single idea of unity or one, and observe v.iiat a variety of combi- nations are formed, by continually adding it to itself ; insomuch that the understanding finds no stop or boundary, in its progress from number to number.' in vrhat an infinity of different lights may extension alone be considered I what lim.its can be set to that endkss diversity of figures, which it is in the powxr of the imagination to fashion and represent to itself ? If to these we add those numberless other cornbina- tions 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 eiiercise cf the human faculties is connned within narrow bounds. But bavin? traced the proe:ress of the mind throuirh its original and simple ideas- until it begins to enlarge its conceptions by uniting and tying them together ; it is nov/ lime tc take a suney of it as thus employed in multiplying its views, that we may see by what ssleps it advances from one degree of improvement to another, and how it contrives to manage that infinit<e stock of materials it finds itself possessed of.
Sec. YI.— T/ie Bivi.non rf comjiiex Ideas into those 'jJ real ILxisiaice^ and those framed by the Aiind.
Whoever attentively considers his own thoughts, and takes a view of the several complicated ideas that from tiiTie to time citer themselves to his understand- ing ; will readily observe, that m.any of them are such as have been derived from without, and suggest- ed by different objects affecting his perception ; oth- ers, again, are fornied by the mind itself variously coiTibining its simple ideas, as seems best to answer
22 DUNCAN'S ELEMENTS
those ends and purposes it has for the present in vie^.y. Of the first kind are all our ideas of substances, as of a man, a horse, a stone, gold. Oi the second are those arbitrary collections of things, which we on many occasions put together, either for their useful- ness in the commerce of liTe, or to further the pursuit of knowledge : such are our ideas of stated lengths, whether of duration or space ; c.r. hours, months, miles, leagues, 8cc. which divisions are apparently the crea- tures of the mind, inasmuch as we often hnd 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, man- slaughter, &c. which complex notions v/e do not al- ways derive from an actual viev/ of v/hat these Vv^ords describe, but often from combining 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. T'hcse two classes com- prehend all our complex conceptions, it being impos- sible to conceive any that are not either suggested to the understanding by some real existences, or formed by the mind itself arbitrarily uniting and compound- ing its ideas. Vv'e shall trep.t of each in order.
CHAP. III.
07 ova IDEAS OF SUBSTANCES.
Sec. I. — Ideas of Substances^ Collections of Siiyiple Iclcasi, held together by some unknovon support.
T
HE first head of complex ideas mentioned in the foregoing chripter, is that of substances, which I choose to handle before the other j becauscj as vrill
OF LOGIC. 23
aftcnvards appear, the notices derived from this source very much help us in forming; those arbitrary collec- tions, vrhich make up the second division. For in many cf them we take cur hints from the reality of things, and combine ideas that actULilIy exist togeth- er, though often with an exclusion of others, as will be explained wdien v/e come to treat of abstract and uni- versal notions. It has been already observed, that the impressions ccnveyes:! into the understanding from external objects, consist for the most part of many different ideas joined together, ^vhich all unite to makeup one v>hole. These collecclolis of various ideas, thus co-existing in the same common subject, o.nd held together by some unknown bond of union, have been distinguished by the name of substances, a word v\-hich implies tlieir subsisting of themselves, without dependenc^e (at least as far as our laiowkdge reaches) on any other created beings. Such are the ideas Vv e have of gold, iron, v/ater, a man, &c. For if we fix upon any one of these, for instance, gold, the notion under vrliich vre represent it to ourselves is that of a body yellovr, very weighty, hard, fusible, m.aileable, Sr.c. where we may observe, that the sev- eral properties 'that go to the com.position of gokh are represented to us by clear and evident perceptions ; the union too of these properties, and their thereby constituting a distinct species of body, is clearly ap- prehended by the mind : but vv^hen we would push cur enquiries farther, and know wherein this union consists, what holds the properties together, and gives them their self-subsistance, here v,'e f.iid ourselves at a loss. Ilovv^ever, as we cannot conceive qualities. Without at the sraiie time supposing some subject in which they adhere, hence we are naturally led to tbrm the notion cf a support, which, serving as a founda- tion for the co-existence and union of the dif^rent
1>4 DUNC/vN's ELIL^MEXTS
properties of things, gives them that separate ami independent existence under Avhlch they are present- ed 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 vrhere by themselves, they are accordhigiy all called substances. Thus a house, a bovvJ, a stone, &c. having each their distinguishing properties, and being conceived to exist independent one of another, the idea of substance belongs alike to them all.
Sec. II. — The Division of Modes into Essential and Accidental.
In substances, therefore, there are two things to be •considered : first, the general notion of self-subsist- ence, which, as I have said, belongs equally to them all ; and then the several qualities, or properties, by v.hich the different kinds and individuals are distin- guished one from another. These qualities are oth- erwise called modes, and have been distinguished in- to essential and accidental, according as they are per- ceived to be separable or inseparable from the subject to which they belong. Extension and solidity are es- sential modes of a stone ; because it cannot be con- ceived without them ; but roundness is only an ac- ■cidental mode ; as a stone may exist under any shape or figure, and yet still retain its nature and other properties.
'Sec. III. — The Kc'ion of Self-Siib&ictcnce inseparable from subsistence,
I might run fartlier into these divisions and sub- division's, in which logicians have been very fertile ; but as they tend little to the advancement of real knowledge, and serve rather to lili the memory vvfith^ T^'ords and their s:G:niiic?itions, tlian furnish, clear and
OF LOGIC. 2S
distinct apprehensions of things, I shall not trouble the reader with them. It is more material to observe, that the change of properties in any substance, tho' it oft-times changes the nature of that substance, that is, its species or kind ; yet it never destroys the gen- eral notion of self-existence, but leaves that equally clear and applicable, as before any such alteration happened. Wood, by the application of fire, is turn- ed into charcoal ; but charcoal, however different from vrood, is still a substance. In like manner, wax may be converted into flame and smoke ; a human body will moulder into dust : yet these alterations destroy not their being or existence : tliey are still substances as before, though under a different form and appearance. In the several experiments made by chemists, bodies undergo many changes, and put on successively a great variety of different shapes, and yet, by the skill and address of the operator, they are often brought back to their first and pi-imitive form. Vv'hat alteration can we suppose the nre, or the application of any- other body, to make, miless on the configuration, tey.ture, or cohesion of the minute parts ? When these are changed, the body is propor- tionably changed ; ^.vhen they return to their original state, the body lil;.e>vise puts on its first and natural appearance.
Sec. IV. — Foimd ation of the different Species of Cor- poreal Substances.
All that is ef sential to matter, therefore, is the co- hesion of solid extended parts : but as these parts are capable of in/ lumerable configurations — as their tex- ture may be t ery various, and the internal constitution thence arising be of consequence extremely difterent in different bodies— we may from these considerations- conceive yjretty clearly the source and foundation of D
26 DUNCAN'S ELEMENTS
all the different species of corporeal substances. Nor is this a notion taken up at random, or one of those chimerical fancies in philosophy, derived rather from a warmth and liveliness of imagination, than observa- tions drawn from things themselves. Do we not dai- ly see our food, by the changes it undergoes in the different avenues of the body, converted first into blood, and thence employed in nourishing, building up, and enlarging, the several parts of that wonderful fabric ? Rain, descending from the clouds, and mix- ing v.'ith the mould or earth of a garden, becomes ali- ment for trees of various kinds, puts on a diversity of forms, according to the different channels and con- veyances through which it passes ; and at last, after innumerable changes and tnuismutEdions, sprouts forth in leaves, opens in buds, or is converted into the sub- stance of the tree itself. Can Vv'e conceive any greater difference between the component parts of gold, and those of stone, than betv»-een the moistened particles of garden mould, and those ne v forms and Rgures un- der Avhich they appear, after they have been thus fashioned by nature for the pu/poses of growth and nourishment ?
Sec. V. — Essence of Substances nrjthing but the inter- nal structure and constitution ;
If this be duly attended to, it will not appear won- derful to assert, that the variety'of material substanc- es arises wholly from the different coniiguration, size, texture, and motion of the minute parts. As these happen to be variously combined, and knit tc- f^ether, under different forms, bodies put on a diversi- ty of appearances, and convey into the mind by the senses all those several impressions, by which they are distinguished one from another. This internal constitution or structure of parts from which the sev-
OF LOGIC. sr
cral properties that distinguish any substance flow, is called the essence of that substance, and is, in fact, unknown to us, any farther, than by the perceivable impressions it makes upon the org-ans of sense. — •Gold, as has been said, is a body yellow, very weigh- ty, hard, fusible, malleable, S^c. Tliat inward struc- tiure, and conformation of its mJnute particles, by which they are so closely linked together, and from which the properties above irierxtioned are conceived to flow, is called its essence ; and the properties themselves are the perceivable marks thai make.it kno'vvn to us, and distmguish it from all other sub- stances ; for our senses are not acute enough to reach its inward texture and constitution. The parts them- selves, as well as their arrangem^ent, lis far beyond the utmost penetration of human sight, even when as- sisted by microscopes, and all the other contrivances of art.
Sec. VI. — Is \vholly unknoivn to us and serves to dis- tinguish the Species ;
Thus, as to the essence or internal constitution of gold, vre are wholly in the dark ; but many of the prop- erties derived from this essence, make obvious and distinct* impressions, as the weight, hardness, and yel- lovr colour. Sec. These properties combined together, and conceived as co-existing in the same common subject, m.ake up our complex idea of gold. The same may be said of all the other species of corporeal substances, as lead, glass, water, &c. cur ideas of them being nothing else but a collection of the ordi- nary qualities observed in them.
Sec. VII. — Yet zV is nghtly presumed to be distinct in all the several kinds.
This, hoVi^ever, ought to be observed, that though the essence or iny, ard si;i"^^c:v.ve c: bodies is tUtcgeth-
28 DUNCAN'S ELEMENTS
er unknown to us, yet we rightly judge, that in all the several species, the essences are distinct. For each species being a collection of properties, which, taken together, are different from those of every other spe- .cies, the conformation of parts, on which these prop- erties 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 ; ar.d therefore the inward structure or constitution from v/hich these qualities flow, cannot be the same in both. But after all, this is the only thing we can with certainty affirm concerning tliese essences, which ly- ing so wholly in the dark, we shall do well to lay them aside in our reasonings about things, and adhere to those more intelligible and settled ideas acquired by joining together tlieir various properties and powers. For thus only is true knovrledge promoted, when we argue from kno^"\ai qualities, and not from a supposed internal constitution, v/hich, hoAvever real in itself, yet comes not within the reach of our faculties^ and therefore can never be a ground to us for any discov- eries or improvements.
Sec. VIII. — By ivhat steps nve arrive at the JSi'otions of Immaterial K^ubstances ;
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 tliese sensible ideas received from without, v/e also experi- ence in ourselves thinking and volition. These ac- tions have no connexion 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 tliinking, and
OF LOGIC. i9
the motion or arrangement of parts ; but it also per- ceives, that consciousness, a simple individual act, can never proceed from a compounded substance, capa- ble of being divided into many. Let us suppose, for instance, a system of matter endowed with thought ; then either all the parts, of which this system is com- posed, must think, which would make it not one, but a multitude of distinct conscious beings ; or its power of thinking must arise from the connexion of the parts one with another, their motion and disposition, &c. which, all taken together, contribute to the produc- tion of tlicught. But it is evident, that the motion of parts, and manner of combinmg them, can produce notliing but an artful structure, and various modes of motion. All machines of human composition, as watches, clocks, S:c. however artfudy their pans are set together, however complicated their structure- though vre conceive innumerable diiTercnt motions,, variously conjoined, and naming one into another vv^ith an endless diversity, yet never produce any thing but figure and motion. If a clock tells the hour a^d minute of th^ day, it is only by the motion of the dif- ferent hands;pointing successively at the figures mark- ed on the hour-plate for that purpose. We never imagine this to be the effect of thought or intelli- gence ; nor conceive it possible, by any refinement of structure, so to improve the comjDosition, as that, it shall become capable of knowledge and consciousness. The reason is plain ; thought is something altogeth- er different from motion and figure ; there is not the least connexion betvveen them ; and therefore it can never be supposed to result from them.
Sec. IX. — Which Kve otherwise call S/iirits.
This then being evident, that intelligence cannot arise from an union or combination of unintelligibla
^n DUNCAN'S ELEMENTS j
parts ; if we suppose it to belong to any system of! matter, 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 p. multitude of distinct conscious beings. And be- cause matter, how far soever we pursue the minute- ness of its parts, is still capable of repeated divisions, ;, even to infinity ; it is plain, that this absurdity will ^ follow us, through all the suppositions that make thought inherent in a materia.1 substance. Finding, therefore, consciousness incompatible with the cohe- sion of solid seperable parts, vre are necessarily led to ; place it in some other substance^ of a distinct nature ' xind properties, which v/e call spirit.
Sec. X. — Body and Sfihit distinct Substances.
And here it is carefully to be observed, that the several species of corporeal substances, though distin- . guished one fi'om another, and ranked under different names ; yet, agreeing in some com.mon properties, -which, taken together, make up the notion of body, | are thence all conceived to partdke of? this general nature, and to differ only as different modifications of the same substance. Whatever consists of solid ex- tended ppirts, is called matter ; and as ail the various species of body, however distinguished from one an- other by their several properties, have yet this in common, that they are made up of such solid seper- abie parts, hence they fall naturally under the gener- al denomination of material beings, and are not con- ceived to differ, but in their form. Thus gold, anti- mony, wood, Sec. alike partake of the notion of body ; they are ail equally material substances, and have no other difference, but what arises from the different structure and conformation, 8cc. of parts, as we have shewn above. But sfiirit is something altogether
OF LOGIC. 31
distinct from body, nay, and commonly placed in op- position to it ; for which reason, the beings of this class are called immaterial ; a word that implies not any thing of their nature, but merely denotes its con- trariety to that of matter.
Sec. XI. — There may be many varicus Species of Sub- stances^ besides those that come iviihin the reach of our Faculties.
Body and spirit, therefore, differ not as species of the same substance, but are really distinct kinds of substances, and serve as general heads under which to rank all the particular beings that fall within the compass of our kno^vledge. For we having no ways of perception but sense and consciousness, can have no notices of things, but as derived from these two inlets. By our senses we are informed of the exist- ence of solid extended substances ; and reiiectioii tells us, that there are thinking conscious ones. Be- yond these our conceptions reach not ; and therefore, though there m.ay be many other kinds, as diiferent from them as they are from one another, yet having no faculties suited' to them, they are as remote from our knowledge, as light and colours from the appre- hension of a man born blind. I believe it will hard- ly be doubted but the substance of the Creator differs more from that of his creatures, than any two created substances can from one anotlier ; and therefore when we call God a spirit, M'e 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 imagine, because this namie is applied as vrell to the mind of man as the Creator, that therefore they partake of one commoa
52 DUNCAN'S ELEMENTS
nature, and differ only as different modifications of the same substance. This I mention here, to check the presumption of the human mind, always forward to conclude, that every thing comes v/ithin its reach, and to deny existence to whatever exceeds the conpre- hension of its scanty and limited powers. Beings of a superior class may enjoy many ways of perfection unknown to us, from which they receive notices as different from those in our minds, as the ideas we apply to spirit are from the ideas v,'e 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 v/ant of the ideas of light and colours in a blind man v/ould be a good argument a- gainst the reality or possibility of such perceptions^
Sec. XII. — Difference in the manner of conceiving Corporeal and Sjiiritual Substances.
Before I dismiss this subject, it may not be im- proper to take notice of a remarkable difference as to the manner of our conceiving corporeal and spirit- ual substances. Those of the first kind convey them- selves into the mind by impressions made upon the organs of sense ; and as these impressions are difler- ent in different bocfies, the ideas they produce must of course vary in proportion. Thus we get precep- tions of distinct powers and properties, and range bo- dies into classes, according as we find them to agree or disagree in their observable qualities. But it is not so in our notion of spirits ; for having no con- ception of their powers and operations but by what we feel and experience within ourselves, we cannot ascribe to them properties or ways of knowledge, distinct from those suggested to us by our o^vn con- sciousness. And hence it is, that though we readily
OF LOGIC. "SS
oivn there may be various r?Jiks cf spiritual beings, •yet we are uot to imagine theiA divided from one cj\- -otiier by any diversity of powers and operations, but merely by possessing the same powers, Sec. in a higher or' lower degree. It is not, however, repug- nant to reason, that they should be distinguished by their several properties in like m.anner as sensible •thin<-'-s are by tiie d-fferent q<ialities obcervable in •them ; but properties of intellectual natures, distinct from those of our 0-^-1 minds, being altogether re- mote from our conception, cannot serve as a means tvhereby to distinguish their different orders. We are therefore necessitated to conceive of them in a manner suited to our way of knowledge ; and ^vhen vre would rank them into species, according to the degrees of superiority theyare imagined to possess hi the scale of being, we ascribe to them v/hat we find most excellent in ourselves, as knov/ledge, thinking, foresight, Sec. and those in different measures pro- portioned to the station peculiar toeacti rank or spe- cies. But that this is a very imperfect way of dis- tingtiishing the various orders cf intellectued beings, will not, I think, need many words to make it ap- pear ; especially if we consider, that the manner of comm.unicating their thoughts, without the interven- tion cf bodily organs, is a thing to us altogether in- comprehensible) and necessarily leads us to suppose, that they have ways of perception and knov/jcdge' vvhich our faculdcrs cannot give us any notice o£
Sec. XIII. — The donnas of Knorjlcdge in our /ircsaU state very ?zarroiu.
But I shall not pursue these reflections farther ;
wdiat has been said sufncingto give us some Uttle in-
«jip:ht into the extent and capacity of our ov/n minds ;
to convhice us that our present state will not admit of
E
,34 DUNCAN'S ELEMENTS
a perfect and adequate comprehension of things ; an^ to let us see, that there may be other v/ays of knowl« edge, beyond the reach of the faculties we now enjoy ; which yet, in succeeding 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 perpet- ual series of approaches towards him, who. is the standard of perfection and happiness.
CHAP. IV.
OF .IDEAS FRAiVrEX) BY THE MIND.
Sec. I.- — In framing many comfilex Ideas^ the Mind is wholly active^ andfiroceeds by a voluntary choice.
irliTHERTO we have considered only such combi- nations of cur simple ideas as have a real union in na- ture, and are suggested to the mind, by things them- selves variously aiiecting our perception : it is now time to take a view of the other class of our complex notions ; I mean those arbitrary collections of differ- ent ideas, v,iiich v/e on many occasions bring together ' by that power vrhich v/e hnd in ourselves, of uniting, comparing, and diversifying our notices of things. In the reception of simple ideas, and even in those of substances, the understanding is wholly passive, and the perceptions produced correspond to the impressions made upon it. When we see a house, or a tree, they necessarily appear each under its proper form; nor is it in our power to receive from these objects other ideas than what they are fit- ted to produce. But in this second class of complex conceptions, the mind acts voluntarily and of choice ; it conibines only such ideas us are supposed best to
OF LOGIC. 35
suit its present purpose ; and alters or changes these combinations, by inserting some, and throwing out others, according as the circumstances of things re- quire their being viewed in different lights. Now as this is by far the most comprehensive branch of our ideas, and inckides those that most frequently occur in the search and pursuit of knowledge, I shall en- deavour to treat them in the exactest order and meth- od ; and for tliat purpose range theill under several heads, according to the different acts of the mind ex- erted in framing and putting them together.
Sec. II. — Three several Acts exerted by the Mind i:i framing its arbitrary IcUas, viz. Composition ;
These acts may in the general all be reduced to three. 1. Ccmposition, when we join many sim.ple ideas together, and consider them, as one picture or representation. Such are our ideas ct beauty, grati- tude, a furlong, 8cc. And here let it be observed, that the mind sometimes confines itself to the various con- skieration 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, vre come by the several combinations of numbers, as a dozen, a score, a million. At other times we unite perceptions of different kinds ; in which case the composition is more manifest, and the idea itself becomes of course mgre complicated. Harmony, for instance, is a compound idea, made up of many" different sounds united ; all which the mu- sician must have, and put together in his mind, be- fore the ear can be entertained with the actual per- formance. Now although the act of the mind is in some measure exerted in the framing of all our com- plex notions, yet as many of them mclude certain limited and panieular considerations; arising from
ether optraticr.s cf the mind employed about thcmj it is necessary to take .account of these acts also, if we would conceive clearly tiie manner in wxiich the several Lpecies of o^r compound ideas are fonxied.
Sec. III. — Abstraction ;
2. The next operation therefore of the mind, about its ideas, is 2bi,tracticv^ whcPi we separate from aijy of our coDceptiates ail those circumstances that reri- der it pailicniar, or the representative cf a single de- terminate object ; by which means. Uistead qi stand- ing for an individual, it is made to denote a whole rank cr class of things. Thus upon setir.g, for in- stance, a square or circle, we leave out the consider- ation of their bulk, and every thing else peculiar to them., as they imm.ediately aiTectour sight, retaining only the notion of their fjgvire and shape. - In this manner we get our general ideas ; for such naked ap- pearances, separated from the circumstances of time, place, tic. serve the mind as standards by which to rank and denominate particular objects. When there- fore vve m^eet with a figure answering to that shape and form we ha.d hSxl up in our understandings, it is imm.ediately referred by the mind to this pattern, and called by its name, which by this means becom.es proper to the v/hcle species. Thus a square, or cir- cle, are urdv-rsal terms, common to all figures 'of that particular shape, and alike applicable to them wherever they'^xist : in like manner as the ideas themselves, are general^ and representatives of aii the kind.
g^n_ lY , 4nd Co7nparison.
3. Tiie third and last act of the mind about its ideas, is the conijiurhig them one with a.nctl!cr> v. hen we carry our consideration of things beyond tiie ob-
OF LOGIC. 37
jtcts themselves, and examine their respects and cor- respondences in reference to other things which the mind brings into view at the same time. It is thus we sret ail our ideas of rclatio?::, as of greater, less, older, youn2:er, father, son, and innumerable others- This threefold vie^v of cur ideas, as either com.pound- ed 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 LU opncrtunitv of observing whatever is most curious and useful in this fondaniental branch of knoAviedge, ti'd of explaining the ma.nner and procedure of the understanding in enlarging its vie tv 3, and multiply- ins- the objects of perception. That we may there- fore conceive of this matter with the greater order and clearness, we jihall make each of these several itdeas the subject of a distinct article.
ART. I.
OF CGI'IPOUXD IDEAS.
See. l.—Comf.cund Ideas considered here mcrehj as
Combinations of the Understandi7:g. T T 7
VV E be;2;in therefore with those ideas wliich may be properly termed compound., as being derived from that power tlie mind has of uniting many conceptions iiito one. Though this class comprehends^^in some sort, all our complex notions, yet they are at present considered merely as tliey arc combinatioiis of the understanding, and with a wiew to those particular ideas out of which they are framed. Here, as was already observed, the mind scmecimxes proceeds hj enUrging and diversifyhi^ the same idea ; at other times it brings together ideas of diaerent kinds ; and
53 DUNCAN'S ELExMENTS
m both ways finds infinite scope and variety. But that we may follow the natural procedure of the in- tellect, and trace it in its advances from simple to inore complicated acts, we shall first take a view of It as employed about one and the same idea, where • perhaps we may meet with such instances of address, inanag-ement and contrivance, as will appear perfectly r.stonishing to one who has never set himself seri- ously to consider the manner and conduct of his own mind.
Sec. II. — U?2Uy the Original and Foundation of all our Ideas of jYumbcr. The m.ost 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 num- bers, in which we readily perceive an endless diver- sity. All these ideas are nevertheless evidently dis- tinct among themselves, the addition of a single unit constituting a number as clearly diSerent from that immediately before it, as any two the most remote Ideas are from one another.. But that the understand- ing may not lose itself in the consideration of those infinite combinations of which unity is capable, it pro- ceeds by regular steps ; and beginning with the orig- inal idea itself, pm'sues it through all its varieties, as they are formed by the repeated continual addition of unit after unit.. Thus numbers are made to follow one another in an orderly progression, and the sev- eral successive collections aj;e distinguished by par- ticular names.
Sec. III. — The artfid comfiosiiion of the names of JK'um- bers a great helji to our conceptions ;
And here v,e may take notice of a wonderful arti- &ce made use of by the niind, to facilitate and help it
OF LOGIC. ^9
forward in its conceptions. For as the advance from number to number is endless, were they all to be xiistinguished by different denominations that had no connexion or dependence one upon another, the mul- titude of them must soon overcharge the memory, and render it impossible for us to go any p-reat way in the progress of num.bering. For this reason it is -so contnved, that the change of names is restrained to a few of the first combinations, all the rest that follow being marked by a repetition of the sam.e terms, variously compounded and linked together. Thus thirteen is ten and three, fourieen,.ten and four, and so on to twenty, or two tens, when wq begin again with one, tvro. Sec. until we advance to thirty, or three tens. In this manner the progression contin- ues ; and when we arrive at ten tens, to prevent con- fusion 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 th{|isand, at vrhich pe- riod the computation begins anew, running through ail the former combinations, as ten thousand, a hun- dred thousand, ten hundred thousand ; v^^hich last collection, for the reasons mentioned above, has the name of a million appropriated to it. With this mill- ion, we can begin as before, until it is repeated a mill- ion of times ; when, if we change the denomination to billions, and advance m the same manner throuo-h trillions, quartillians, the series may be carried on vdthout confusion, to any length we please.
Sec. IV. — Jnd cf. the firindfial Reasons that our Ideas of ^, umbers are so remarkably distinct.
This artful combination of names to mark the grad- ual increase of numbers, is perhaps one cf the great- est refinements of the human understanding, and particularly deserves our admiration ior the mamier
•40 IDUNCAN's ELEMENTS
of the composition ; the several denominations bein?^ so contrived as to distingTiish exactly the sca^jes of the progression, and point out the distance from the beginning of the series. By this means it happens, that our ideas of numbers are of all others the m.ost accurate and distinct ; nor does the multitude of units assembled together, in the least puzzle or confound the understanding. It is indeed amazing, that the mind of man, so limited and narrov^ in its views, should vet here seem to shake off its natural vveak- ness, and discover a capacity for managing with ease the most bulky and formidable collections. If we enquire particularly into the reason of this, we shall find it wholly owing to the address of the mind in thus distinguishing numbers by different names, accord- ing to the natural order of progression. For as those names are made to grov/ one oiit of another, they may be aptly compared 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,'' however great and seemingly un- managable ; yet, if it is once determined to a particu- lar name, %ve iind 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 nurr.ber under consideration, but also the several intermcdicite parts, as they are united to make up the whole.
ggc. V. ^-s they help us to a clear Ptrctpnon of the
interjactnt Paris.
Nov/ it is to this clear and accurate view of the in- terjacent ideas, that we ov/e our so distinct percep- tion of the various combinations of numbers. And indeed v/e may observe, in tlie general, that all our ideas of quantity, especially when thej grow to be very
OF LOGIC. 4i
large, are no otherwise ascertained than by that per- ception v,"e have of the intervening parts, 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 and houses, we are able to determine pretty nearly of its remoteness ; but if, without such a kncvrledge of the intervening spaces, we should pretend to judge of the distance of objects, as V, hen we see the spire of a steeple behind a wall, or beyond a mountain, every one's experience is a proof hovv^ 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 p^.ct period of cur lives, without consideration of the number of years or months, v/e fxud that our idea of the time elapsed grov/s more dis- tinct, in proportion as we become sensible of the in- termxcdiate parts of our existence. At first we are apt to judge the distance extremely short ; but when we set ourselves 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 ^nd brings new periods of life into view.
Sec. VI. — J'llihout narnes^ we cannot make any jiro^ gress in Numbering.
Hence it will be easy to conceive how much the mind is helped forward in its perception of number, by that ready comprfchension of all the several stages in a progression, which peculiarly belongs to ideas of this class. But this, as I nave before intimated, we derive from the orderly series and connexion of nam^es, insomuch that where they cease, the computation of num/Oers also ceases with them. We can have no idea of any sum, without a knoT>1edge of all the terms- that go before, according to the natura][^rdcr in which they ioilovr one another ; so that he who cannot, in » F
42 DUNCAN'S ELEMENTS
regular way, count to ninety-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 unserviceable, nor can he represent to his mind the several interjacent com- binations, v/ithout which it is impossible 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 on- ly because it is by number that we measure ail other things, as duration, extension, motion, &c. but also because it lets us into the most natural view of the conduct and procedure of the understanding, and Biakes us sensible of the great art and address that is necessary in the classing our very com.plex concep- tions. Ke that can so put together the component parts of an idea, as that they shall lie obvious to the notice of the mind, and present themselves, when oc- casion requires, in a just and orderly connexion, Aviil not find ii very difficult to obtain clear and accurate perceptions, in most of those subjects about A^.ich our thoughts are conversant. For the great art of knowledge lies in managing with skill the capacity <if the intellect, and contriving such helps as, if they strengthen not its natural powers, may yet expose them to no unnecessary fatigue, by entangling and perplexing them vrith considerations remote from the business in hand. When ideas become very complex, and by the multiplicity of their parts grow too un- vdeldly 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 ena- bled to. take in the whole ; und if we can draw it into
OF LOGIC. 45
swell an orderly combination, as will naturally lead the attention, step by step, in any succeeding consid- eration of the same idea, we shall ever have it at com- mand, and with a single glance of thought be able to run over all its parts. I have therefore explained here, at some length, the conduct of the mmd m numbering ; it seeming to me the best model m this kind,whether we consider the many advantages de- rived from such an orderlv disposition of our ideas, or the great art and skill displayed in binding thes6 idea$ together. This also is farther remarkable, m the consideration of number, that from it chiefiy 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, rem>aining as obvious to the un- derstanding, alter a great and continued run of pro- gressions, as when ii ilrst began the computation.
Sec. VIII. The Consideration of Jvumber^ of great
Use in ascertaining our Ideas of Space and Duration, If we nov/ turn our thoughts towards space and duration, here too we shall find that we very seldom arrive at clear and distinct ideas of either, but when we introduce the consideration of num.ber. The m^ore obvious 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 put us upon the contrivance of certain stated meas- ures by which precisely to determine the quantity in each. Thus, inches, feet, yards, miles, Sec. ascertain our ideas of extension ; as minutes, hours, days, years. Sec. measure the progress of duration. The iesser parts, as Iving most open to the notice of the understanding, and being more on a level with its powers, are retained with tolerable exactness ; and
U DUNCAN'S ELEMENTS
the larger portions, when the number of repetitions of which they are made up is kno\Mi, are thereby al- so reduced into clear and determinate conceptions. A foot, and yard, are measures easily comprehended by the mind ; nor do v/e find any difficulty in con- ceiving a mile, when we consider it as equal to a certain number of yards. If we are stii] for increas- ing the standard, w-e may take the semi-diameter of the earth, and supposing it equal to 8000 miles, make use of it as a measure by which to ascertain the dis- tance of the sun or fixed stars. Just so it is in dura- tion ; from hours we rise to days, months, and years ; 4)y these, repeated, and added together, we measure .time past, or can run forward at pleasure into futuri- ty, and that without any confusion or perplexity.
Sec. IX. — Without they are apt to degenerate into a cov fused and irregtdar Heap.
It is however to number alone that we owe this distinctness of perception, inasmuch as space and tim.e, considered apart from the regular and orderly repetition of miles or }^ears, leave no determinate im- py^^ssions in the mind, by which to knov/ and distin- guish their several portions. Ideas of either, thus taken in at a venture, are a confused and irregular heap, especially w'here we endeavour to enlarge and Tna;3nify our views, and give full play to the powers cf our intellect. Something indeed the mdnd con- ceives, vast and mighty, but nothing that is precise, accurate and just. But v,hen it begins to consider tliese ideas as made up of parts, and fixing upon such as are proportioned to its reach, sets itself to examine Iiov/ often they are repeated to make up the v/hole, the perceptions of the understanding put on a nev/ fcnn, a.nd discover their exact bounds and limits.
OF LOGIC. 45
Sec. 'yi.^Inf.nity an Object too mighty for the Sui-vey of the Human Mind. And thus, as before in number, so here in exten- sion and duration, the mind begins \vith simple and obvious notices, advancing by degrees to more en- larged and intricate conceptions. A day, or a fur- long, are of easy apprehension to the understanding, and by their subdivisions into still lesser spaces, ex- hibit themselves distinctly in all their parts. Vv^ith these variously repeated, we travel through space and time ; so that being able to reduce all our ideas of this class, however mighty and enlarged, to the clear and determinate perceptions of number, we can con* duct our thoughts vrithout perplexity, and never fmd ourselves puzzled, but vrhen, presuming too much on our own strength, we launch into speculations, that stretch beyond the powers cf the human, intellect. — Number may be compared to a line, that, setting. out from unity, runs on in a continued increase of length, wit'iout 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 accu- • rale and just. But when we let loose our under- standings, alter a boundless remainder, and Vv'ould fathom the depth of infinity, w^e find ourselves lost amidst the greatness of ouro^^Ti conceptions. Some notions, it is true, v/e have, but such as, exceeding the dim.ensicns cf the mind, lie involved in darkness and obscurity ; and being destitute of order, method, and connexion, afford no foundation \\ hereon to build ai?7 just and accurate conclusion.
Sec. XI. — Js^ever represented in it fi full Dimensions., but by an endless and ever grooving Idea. And this perhaps may be trie reason Avhy many modern philosophers, m tiieir discourses concerning
/.
46- DUNCAN'S ELEMENTS -
infinity, have run into apparent contradictions ; be- cause, encountering an object too large for the sur- vey of the understanding, they found themselves sur- rounded with inextricable difficulties, which their scanty and defective ideas vrere 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 are not wholly without a notion of the infinity of number, yet it is not such a one as com- - prehends 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 take in the whole prospect ; and indeed it is properly that part of it which lies be-- yond the reach of our perception, and still remains. to be taken into the account, to vrhich we give the name..,, of infinity.
Sec. XII. — Duration^ "d'heth^T comidered as fiast or to come. Boundless^ nvhence our Idea of lit emit y.
This idea of the infinity of number, imperfect as^ it may seem, is nevertheless that by which the mind ascends to the conception of eterrdty and immensity. For when we consider duration, either as past or to com.e, 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 efibrts, v/e must ovrn 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 it- self may decay ; and those bright luminaries that adorn the firmament of heaven, be eytinguished. But the course of time will not be thereby disturbed ; that fiows uniform and invariable, nor is bounded by
OF LOGIC. ^r
the period of their existence. This double view of duration, as having ah^eady revolved through num- berless ages, and yet still advancing into futurity in an endless progression, properly constitutes our ideas ' of eternity. We speak indeed of an eternity past, an ! eternity to come, but both these are bounded at one - extreme : the former terminates in the present mo- Bient, 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 infi- nitely extended, aiid which represents eternity in its ! full dimensions.
\ Sec. XIII. The Idea of Immeiidty derived from the
Condderation ofS/mce ex^er growing on all sides of us. \ As, in the consideration of time, we fix upon the I .present moment, regarding it as the middle point which divides the Vvhoie line of duration into tvvo equal \ parts ; so, in the consideration of space, that particu- i lar place in which we exist is looked upon as a kind ' of centre to 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 I of miles, and millions of miles, without ever arriving I at the end of the progression. It is not difficult, in- deed, 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 I sees immieasurabie spaces beyond, capable of receiv- I ing nevvT worlds, which it can pursue,^as rising one ! above another in endless succession. This consider- ation of space ever growing on all sides of us, and yet never to be exhausted, is that which gives us the idea i of iminensity : which is in fact nothing else but the infinity of number, applied to certain portions of ex- tension, as miles, or leagues, Sec. and these conceived
48 [DUNCAN'S ELEMENTS
as extended every way around us, in infinite and in- numerable right lines.
Sec. XIV. — Compound Ideas resulting from the Union of Perceptions of different Kinds.
Hitherto we have considered the mind as employ- ed about one and the same idea, enlarging and diver- sifying it in various forms. We have seen it rising from the most simple and obvious notices to the con- ception of infinity itself; ana taken a view of it in all the different stages of its improvement. Let .us now proceed to the more complicated act of composition, when the mind brings several ideas of diiferent kinds together, and voluntarily combines them into one complex conception. Such for instance, is our idea of a tune., as com.prehending a variety of notes, with m.any different modulations of sound. And here it is to be observed, that though the complex idea may be excited in us, by hearing the air itself struck off upon a proper instrument ; yet, considered originally, it still belongs to this class of perceptions, which are distinguished as the arbitrary collections of the mind.^ It vras the musician, or composer, that combined the several notes, and determined the order in which they were to follov*" one another ; nor had t'nat peculiar composition of sounds any real union in nature, be- fore tiiey were tlius brought together in his mind. Of the same nature are most of our ideas of .human actions ; for though many of thcmx come to our no- tice by seeing the actions themselves, or hearing them described by others, as distilling^ cawitig^ treason.) &c. yet it is plain that they must have been projected and contrived in the m.ind of man before tiiey had a real existence.
OF LOGIC. 4§
Sec. XV. — How the mind is determined in making these Combinations.
It is here that the understanding has the greatest scope, and finds most employment for its active pow- ers : nor indeed is it possible to set any bounds to the ideas of this class ; the combinations already made being almost innumerable, and those yet in the pow- er of the mind affording an endless diversity. It may not, howevei> be amiss to consider how we conduct ourselves amidst so great a variety, and by v/hat rules we proceed in making those combinations to which we have affixed particular nam.es, while others, per- haps, no less obvious, are neglected. The idea of killing, for instance, joined to that of a father, makes a distinct species of action, kno%\^i by the name of fiarricide. It was doubtless as obvious to. distinguish between the killing of an old man and a child, vrhich yet we find is not done ; both these actions being com- prehended under the general name of murder. By what views therefore does the mind regulate its com- binations ? Why is it determined to one collection of ideas rather than another ? This cannot be ■ well un- derstood, without observing, that it is the end cf lan- guage to comm.unicate our thoughts one to another. V/ords are the siirns 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 com- merce of life, would be first distinguished by particu- lar nam^es ; the frequent occasion men have of men- tioning these among themselves, rendering this abso- lutely necessary. But as many of these conceptions are collections of different simple ideas, hence we are insensibly led to such peculiar combinations, as arc most serviceable to purposes of mutual intercourse iuid communicatiou,
G
5© DUNCAN^s ELEMENTS
^ec. X^T[. — Ideas of Human Jctions often formed^ be^ 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 fore- sight, they will naturally observe many new occurren- ces, likely to arise from this coalition of mankind, and their living together in crov/ds. Perhaps the age in which they live, has not produced an instance of one man's killing another ; yet from the knowledge of their ot\ti frame, and their power of doing hurt, they conceive this as a possible case, and are willing 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 re- ally 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 considerthe relation in which the person killed may stand to the murderer, here there appears a manifest difference ; ^s it adds to the crime, when committed upon a beiy^factor, and ren- ders it particularjy heinous in the case of a father. — Tljs last, therefore, is made to constitute a distinct species of iictiou, and has a peculiiir punishment allot- ted to it. Thus we see how men, according to their diiierent manner of life, and the relations they stand in to one anr>ther, are naturally led to form sevei-al collections of simple ideas, preferably to others, as foreseeing they may have frequent occasion to take notice of such precise combinations. And because it would be tedious in conversation, every time the^e
OF LOGIC 51
complex notions occur, to enumerate all the ideas of which they consist ; therefore, for the sake of ease and dispatch, tliey give them particular names, and there- by render the compositions- fixed and permanent.
Sec. XVII. — The necessity of Mutual Intercourse avd MeJi's particular Aims in Life^agreat Source cfCom' plex 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, o/ our pursuits, method of fife, and different aims, throw occasions in our way, of combining such and such perceptions together, might be easily made to appear, by a short view of the com- binations themselves. Human actions, as oecurring- most frequently, and affording large matter of con- versation, debate, and inquiry among men, have been Tery nicely modified, and distinguished into classes, according to the several circumstances most likely to attend them. In like manner, the arts and sciences, in propoilion as they are eultivaeed, leading us into many compound views of things, which otherv/ise- would never offer themselves to the consideration of the mind ; the complex ideas of this sort, with the names by which they are expressed, are, we find, the work of such paa-ticular nations, where these arts and sciences have chieuy flourished. The Greeks, for instance, excelled in learning and polite knowledge ; hence many of the terms belonging to rhetoric, poe- try, philosophy, physic, Sec. come originally from their language. Modern fortification has received its greatest improvements among the French; and accordingly the ideas and terms of the art are mostly- derived from writers of that nation. In Italy, archi- tecture, music, and painting, have been the great ex- ercise of the men of genius ; it is tlierefore amon^
52 DUNCAN'S ELEMENTS
them that we iind the several complex notions belong- ing to these parts of study, as well as the names by which they are expressed ; nor can w^e discourse ac- curately and minutely of the above mentioned arts, without having recourse to the language of that cli- mate. And if we descend into the particular callings and professions of men, they have all their peculiar coilections of ideas, distinguished by their several riames, and hardly known but to such as are conver- ssant in that manner of life. Thus calcination, coho- bation, filtration, Sec. are 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 combinations, seldom occur in common life, the generality of mankind, we see, are in a great measure unacquainted wiih them.
JSec. XVIII. — >Hence different Sets of them prevail in different Countries : and Words in one JLanmuige have none to answer them in another.
I might pursue these speculations farther, and*shovv hov/ the several fashions, customs, and manners of one nation, leading th'cm 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 w^ordsthat ansv/er.in another. The procedure and forms of our courts of justice have introduced many terms into the English law, which stand for collections of ideas framed among no other people. Nor w^ould it be possible to render these terms by ruiy single w^ords of another language ; because, where ideas themselves prevail not, there are 'no names provided to express them. In this case, therefore, it becomes necessary to use circumlocu- tions, and enumerate the several ideas comprehended
OF LOGIC. 5e
ip the collection, if we would so express ourselves, as to be understood in the language of other nations. — Nay, even among tlie 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 different from what they had before.
Sec. XIX. — This, too, the cause that Languages arc in a perfietual fiux .
Thus languages are in a perpetual fliix, and by de- grees vary so much from their original frame, as to become unintelligible even to the descendants of those v/ho speak them. If we run back into the ages of chivalry in England, when tiles and tournaments were in fashion, how- m.any complex ideas, peculiar to that mode of life, shall we find familiar among the men of those times, v/hich are no'.v little known or attended tor On the contrary, the improvements in arts and sciences that have since taken place, have led us into innum.erable ^ievrs of things, to which our fore-fath- ers Vv' ere perfect strangers. Eut I shall not push these refiections any farther, believing that what has been said will be sufficient to show the origin and progress cf cur compound ideas, and how the mind is directed in the choice of the combinations it makes. Wc therefore proceed to the consideration of abstract ideas^ which make the subject of the following article.
54 DUNCAN'S ELEMENTS
ART. II.
OF ABSTRACT OR UNIVERSAL IDEAS.
Sec. I. — General Ideas formed by the Abstraction of the Mi7id.
H
AviNG dispatched what was necessary to be said- concerning our compoundjdeas, considered merely as they are combinations of the understanding, it is no^r time to explain how we come by our general notions which serve to represent to us a multitude of individ- uals, and are the standards by v/hich we rank things into sorts. And this, as we have before intimated, is done by the abstraction of the raind ; which act may be extended to all our ideas, whether simple, com- pound, or of substances. If, for instance, we fix our attention on any particular colour, a& scarlet, v/e can leave out the consideration of all present circumstanc- es, as the subject in which it inheres, the time and place of seeing it, &c. and retaii:iing only the impres- sion itself, make it a representative of that quality or appearance, wherever we chance ta meet with it. It is thus that abstract and universal ideas are framed ; for the mind regarding only the scarlet colour, which one day it observes perhaps in a piece of cloth, anoth- er in a picture, and a third in the rainbow ; the ap- pearance is conceived to be the same in all these ob- jects, and therefore is called by the same name. Sec. II, — AU 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 tilings.
OF LOGIC. 55
whether ^ve derive them from sensation or reflection,
are of their own nature particular, and represent to us
S single, determinate objects. ^Vhen we see a horse,
I for instance, in the fields, our idea is that of an indi-
j vidual. If we hear a sound, it is something particu-
i lar, and different from what vre hear at any other
i time. Every perception of the m^ind is distinct from
) every other perception ; nay, and every idea brought
into view by the imagination, as when we frame the
image of a lion standing before us, is still singular,
.and represents a single object.
Sec. III. — The Idea of the S/iccies rfpresents ivhat is ccmimon to different Individuals .
But when we come to take a view of these several
"Daniculars, 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,
w^e 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 re-
. sem.blance, excluding what is peculiar to each single
' animal, 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 ar.imal in which that
shape, veice, and structure is found ; for the word
; horse, implying only these particulars, must belong
, to all ci^atures wherein they exist. This is the first
step or gradation in the forming of abstract notions,
when the mind confines itself to the consideration of
individuals, and fi'ames an idea that comprehends
such only under it. The rank or class of things an-
ivrering to this idea, is called species in the language
-of the schools. So a horse is a certain species of an-
S6 DUNCAN'S ELEMENTS
imals, an oak is a species of trees, and a square is a species of four-sided figures.
Sec. IV .—The Idea of the GeJius represents vjhat ia common to several Species.
When we have thus learned to rank individuals into sorts and classes, according to the resemblance found among them, the mind proceeds next to con- sider the species themselves, and often in these too observes a certain likeness. Whereupon, throv/ing cut all those particulars v/herein the several species are found to disagree, and retaining oniy such as are common to them eJl, we thereby frame a stiJl more general idea, comprehending under it a variety of different species. Thus a sparrow, a hawk, and ea- gle, Sec. are distinct species of birds, which have each their peculiar shape and make. They nevertheless resemble one another, in being covered with feath- er.s, and provided with wings that bear them through the air. Out of these particulars we form a new idea, including all the common properties of the feath- ered kind ; and appropriating to it the name of birdy mark by that word another class of things, of a high- er order than any of the former. This superior -di- vision, 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- tionsy in rising from Particulars to Generals.
And thus have I given a short, but I hope intelli- gible account, of the business of genera and species^ about which so much has been said in the writings of lop;ician5. Species, in strictness and propriety of speech, is such a rank or class of things, as compre- hends under it only individuals : genm advances stilt
OF LOGIC. 57
higher, and takes in a variety of distinct species. It is, however, to be observed, that the mind in rising from particulars to generals, does not confine itself to one or two gradations, but may carry its views through the whole extent of things, until at length it arrive at an idea embracing the universal compass of nature. For when vre have ranked tilings ;nto scriis, and reduced these again to tiie higher order or jy-.-jz-*, these ^fwera are still found to resemble one anotiier in some particulars, Avhich being collected into one '.dca, form a neAv and more comprehensive division of thinpjs. Thus bird is a genun^ embracing all the varieties of the feathered kind. Fish implies the several species of living creatures v/hich inhabit the waters. Quad- jufied and insect are also universal ideas, that take in many inferior distributions and classes. Yet all these different orders of being, have this in common, that they are provided v.ith organical bodies, fitted for the purposes of life and spontaneous motion. An idea, tlierefore, comprehending only these last particulars, will equally belong to all the divisions before enumer- ated ; and the v, ord cmimal, by which it is expressed, becomes a general name for the several creatures en- dued with life, sense, and spontaneous motion. If we are for carrying our views still farther, and framing a yet more universal notion, Vv-e can cast cur eyes upon both the animate and inanimate parts of nature ; where- in we fmd this mutual correspondence, that they ex- ist, and continue in being. This last idea, therefore, of being in geneml, comprehends under it all the vari- eties of things, and may be universally applied to whatever has life or existence ; so that in respect of the present frame of nature, it is the highest and most universal idea vre have.
H
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VI. — Whence many intermediate Steps beiweeii the highest Genus and lowest S/idcies.
In this series of notions, rising one above another, in the degree of universality ; that division, vvhich comprehends under its several genera, is called in the schools the higher genus ; which denomination con- tinues, until we arrive at the last advance of the un- derstanding, when, being come to the most general of all ideas, that admits not of a superior, it is distin- guished by the name of genus generalissimmn. In like manner the several genera^ comprehended under a higher ge-nus^ are, in respect of it, considered as spc- dss ; and as these two last have species under them, the inferior divisions are, for distinction's sake, term- ed lower species. Thus the prcgrcssion continues, and when v/e come to the iov/est subdivision of all, com- prehending only individuals, which, as I have before iiitimated, constitutes the proper species, this the schools denominate the species spe&ialissijna. All that lie betYv'een it and the highest distribution of things, are the intermediate genera and species, which are termed, each in their turn, genus generaiius, or species ipecialior, according as we consider them in the as- cending or descending scale of our ideas ; or, to speak in the language of logicians, according to their ascent or descent, in linea praclicajnentali. I should not Iiave entered so far into these verbal disquisitions, had not the terms here explained, been such as frequently oc- cur in the vvriti'ngs of philosophers ; insomuch, that v/ithout some knowledge of them, we must often be at a loss, in the pi'osecution of these studies. Besides, it is both curious and uselul, to see the gradual pro- gress of the mind, in its advances from paiticular to general conceptions — to observe it ranging its ideas into classes, and establishing a just and regular sub-
OF LOGIC. 59
ordination in its views and notices of things. This is the shortest way to knowledge, and aubrds the best lueans of preserving the order and due connexion of cur thoughts, so as to make them subservient to the increase of science. For when we see how things comprehend, or are comprehended in, one another, we are able to discover the mutual dependence of all the several branches of knowledge Avhich leads us into the true and natural method of conducting our under- standings in tlie search of truth.
Sec. VII. — General Ideas the Creatures of tht Under'- standing. From what has been said, it is evident, that general ideas are the creatures and inventions of the under- standing. Nature, it is true, in the production of things, makes many of them alike : but it is the mind alone, that collects the particulars in which they agree, into one idea, and sets it up as a representative of ma- ny individuals. And nov/ I think. we may venture upon that much-agitated question, where do the gen- era and species of things exist ? To which I answer, in the mind. Universality belongs not to things them.- selves, it being apparent, that they are all particular m tlieir existence. Ilcv/ever, as they often have ma- ny properties in common, the understanding, by unit- ing these into one conception, obtains a general idea, under which it ranks all the several objects v/herein these properties are found. So far indeed we must allow, th.at the particular 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 distinguished from one an^ other. Thus the collection of simple ideas, signified by the word bird^ is to be found, for instance, in a
CO DUNCAN'S ELEMEInTS
/larj/:, cr any other single animal, to ^vhich we applji' that general name : but the notion itself, abstracted from all the particulars to v»'hich it belongs, has evi- clenily no existence out of the understanding. There is not a being in nature that can be called a bi7^d in general, or that does not necessarily imply, in the very conception of it, several simple ideas, besides those marked by tliat vv^ord. For the name, in this case, signities no more than an anirnal covered with feath- ers, and provided v/ith wings, without regard either to shape, bulk, or the particular time and place of its er.istence. These last considerations, hov/ever, are inseparable from the reality of things, and therefore must be added to the general idea, before we can con- ceive any thing conformable to it actually brought into being.
Sec. VIII. — Co7ir.idered ajiart^ they exist only in the Mind^ but in co'rijunction ivith other Ideas in the in- divldiials cornnttiiended under theryj.
Hence we see at once, vviiat sort of an existence gen- eral natures have. Considered apart, and by them- fselves, they are v»'hoIIy the workmanship of the un- derstanding, and derive their being and reality from it ; but viewed in conjunction with other ideas that co-exist v.dth them in the several objects of nature, they are to be found in the individuals to which they refer ; and therefore, according to tliis way of concep- tion, may be saitl to have an existence in them. Thus, so long as t]ie ideas ansv/ering to the words irecin or tree^ coutinue general and undetermined, they have no real objects answering them in nature ; nor can tlie collections of simple ideas, marked by these names, while ail others are supposed excluded, exist any •vhere out of the understanding. Nevertheless, as ali 4he simple ideas, included in the general notion of
OF LOGIC. 6b
man^ are to be found in every particular man — and all those implied in tne notion of a tree^ in eveiy particu- lar tree — iience the general nature of ma7i^ exists in every individual rnan^ as does the general nature of a t)'€s^ in every individual tree^
Sec. IX. — Differe~iice cf 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 them- are evidently combinaiionB of different simple ideas, and according to Ihat way of considering tliem., are , included in the first division of our complex concep- tions, those, namely, framed by the composition of the mind ; .yet Vr^e 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 combined 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 m.otion, a covering of feathers, wings, kc. none of which can be left out v, ithout destroying the very nature of the idea, and niaking it something- quite diiFerent from what it v/as before. This way" of considering things according to the nun^ber of their parts and propertiec, is called by logicians the com-' Jirehension of an idea. But the uni-versality of our notions imiplies quite another turn of thinking, in as much as it fixes the regard of the m^ind, upon the- subject to v/hich our ideas extend, or the mdividuals and species, comprehended under them. In this sense, the idea ansv\^ering to the word bird^ takes in the sev- eral species of the feathered creation, the ha^iuk^ the eagle ^ sharroiv^ lark^ and. innumerable others, to all which it may, with equal propriety, be applied. And here it is remarkable, that the idea loses nothing Oi
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its force or comprekendon^ by being restricted to a par- ticular kind, When I say the bird of Jove^ thoiigh 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 ex- tended to ail the different tribes of feathered animals. Sec. X. — The coinprehcndon a?icl extension of our Ideas.
We see, therefore, that our com.pound ideas may continue the same in respect of their attributes, or the number of parts, and yet vary considerably in the de- gree of universality. The general ideaof ?/?fm 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 knov/ledge falls short of perfection, and afterv/ards make the like observation of the men of the present age ; in both cases, the word man stands for one and the same col- lection of simple ideas ; but in respect of the individu* als to which it is applied, there is a great and manifest difference. That is, the tel'm inan^ denotes one in- variable com.pound idea ; v/hich, notv/ithstanding, considered as a general notion, may be contracted or enlarged at pleasure. And as in the former case, the several parts of the compound idea are called its com- prehendon ; so in the latter, the individuals, to which the universal idea is applied, are called its extension, I might add miany more observations on this subject, but choose rather to stop here, having said enough to explain. the difference between compound and abstract ideas, and show the reason of my ranging thern un- der distinct heads.
OF LOGIC. €3
ART. III.
CF OUR IDEAS OF RELATIONS.
Sec. I. — 'Ideas of Relations exceeding numerous.
1 coM^ nov7 to the third and last division of those ideas, which I consider as the creatures and work- 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 re- gard to others, brought under consideration at the same time. And when it does so, and thence derives new notices of things, tlie ideas thus got are called rela- tions, and make, I am apt to think, the largest class of all our perceptions. For every single object Vv-iil admit of almost innumerable comparisons with oth- ers, and in this sense may become a very plentiful source of ideas to the understanding. Thus, if we compare one thing vdth another, in respect of bulk^ we get the ideas oi greater^ less, or equality ; if in re- spect of time, of older and younger ; and so for ether relations,- which we can pursue at pleasure, almost v.'ithout end ; whence it is easy to conceive, how very extensive this tribe of our perceptions must be.
Sec. II. — Men. chiefly determined to particular CoTiipar- ir,ons by the Wants and Exigences of Life,
I shall not pretend to trace out these ideas particu- larly, nor indeed so much as to enumerate their sev- eral divisions ; it being enough to observe, that here, as well as in the other kinds of our -complex ideas, Ave bound ourselves, for the most part, to such com- parisons, as tlie exigences of society, the v/ants of life,* and the different professions of men, render neces- sary ; and are more or less accurc^te in tracing out
64 DUNCAN'S ELEMENTS
the relations of things, according to the degree cf im- portance they appear to have in these respects. The relations of men one to another, arising either from the ties of biood, their several ranks and places in the communitv, or a mutual intercourse of good cfiices, being of great A\'sight and concern in the commerce of life, have in a particular manner engaged our at- tention, and are therefore very minutely described. — For the sam^e reason, men have found it necessary, to determine, as exactly as possible, the various depend- ence of things, as their happiness is nearly connected v.ith this knowledge. When vre consider objects raerely in respect of existence, as either giving or re- ceiving it, we come by the ideas of cause and effect : nor need I mention how much the welfare of man- kind 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 con- ducted upon a previous supposition, that certain knov.n causes wUl have their usual regular effects, and such and such actions be attended v\'ith such and such con- sequences.
Sec. III. — -Relaticns cf Creator cyid Creaturey'Cfc.
But there are other relations of this kind, besides those that regard mjerely existence ; as when we also take into the account the additional gifts of a capacity for happiness, and the mea.Ds of attaining it ; which constitutes the relation oi Creator and creature^ m the more solemn accepteition of these v/ords. Again, when v/e consider the great Author of our being, not only as the Creator of -the universe, but also as preserving r.nd holding it together, and presidintj over the present name of things with uncontrouled dominion ; he then appears under the notion of a vioral Governor^ to whom -ive arc accountable fcr cui' act:cn3, and the use we
OF LOGIC. 65
make of those powers and faculties we derive from ]>im. Now as it is of the highest consequence for men, not to be unacquainted with these, and such like relations ; hence we find, tliat the wisest nations, and such as best understood the true application of tlie powers of the mind, have always made it their chief ♦otudy to regulate and ascerLain these ideas, and trace them in all their consequences. And thus we may, in some measure, perceive how the mind proceeds in comoarihg 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 habitndes of things, I shall only add upon this subject, these two observations.
Sec. I v. — Our Ideas of relations very dear and distinct. First, that our ideas of relations, are for the most part very clear and distinct. For the compelling of tilings together, being a voluntary act of the mind, Vv-e cannot but suppose that it must be acquainted wiih its o^^^l \-iews in the comparison ; and of course have a clear conception of the foundation of that relation, it sets itself to enquire into. Thus the relation of cause and effect, implying only that one thing produc- es, or is produced by another, which notions are al- ways distinctly settled in the understanding before it goes about to m.ake the comparison ; it is evident, that the idea representing this mutual respect of objects, will be no less clear, than are the notions themselves 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 knovrn. For I can well enough conceive, that one thing has produced anoth- er, and that therefore they stand related as cause and effect, though my ideas of the things themselves may I
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perhaps be very obscure, and come far short of repre- senting their real nature and properties. I doubt not but it will be readily owned, that our idea of the uni- verse, 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 v/ell understand what is meant by calling God the Author of the Avorld ; and though we comprehend not the manner of his produc- ing it, find no difficulty in framing the ideas, the rela- tive words Creator and creature stand for
Sec. V. — Ideas of Relatians among the most imfiortant 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 under- standing, and afford the largest field for the exercise and improvement of human knowledge. Most of our enquiries 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 mag- nitudes of diiterent figures a.nd dimensions, in order to judge with certainty of their relative properties. The philosopher attaches himself to the chain of caus- es and effects, and endeavours to trace out the various dependence of things considered in this light. In fine, whither do all our researches tend, but by means of certain known properties and relations, to find out others that stand some hovv" connected vv^ith them ? As for the importance of these conceptions, no one can call that in qu'^stion, who reflects ; that from our relations to our Creator and one another, arise all the duties of mcrulity and religion, and that the correspondence of
OF LOGIC. 67
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 ^^dll procure us happiness or mis- ery. Whence it is evident, that without an exact knowledge of these relations, M^e must wander on in life with great uncertainty, and may often plunge into calamities and misfortunes, by those very pursuits from which we expected nothing butjoy and pleasure.
Sec. VI. — Recapitulation.
Thus have I gone through the several divisions of our ideas, which I have endeavoured to represent in such a manner as their vast extent may most easily appear, and the conduct of the mind in framing them be distinctly apprehended. I might easily run into other distinctions, by considering thein 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 sufficient to convey a notion 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 knowledge, 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 percep- tions at once, which are nevertheless readily- distin- guished by the mind, and appear each under a form peculiar to itself. These constitute our primary and original notices, and are easily kno^vn from all others, in as much as they are entirely void of plurality, and
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cannot be dhided into two or more different ideas. They are also the materials out of which the others are formed, and are therefore, by way of distiction, 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 inhnite number of Avays ; and from their various combinations result ail our com- plex ideas, which are of two principal kinds. First, such as are derived from without, ajid represent these combniations of simple ideas, that have a real exis- tence in nature. Of this sort are ail our ideas of sub- stances. 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 comprehends all those ideas v/hich may be properly termed our o^vn, as being the real workmanship of the understanding ; so they fall very naturally under three distinct heads. For either the mind combines sever- al simple ideas together, in order to form them into one conception, in which the number and quality of the ideas united, are principally considered ; and thus it is we come by all our compound notions : cr it fixes upon any of its ideas, whether simple, com- pound, or of substances ; and, leaving out the circum- stances of time, place, real existence, 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^ exam- ines their mutual connexions, and thereby furnishes itself with a new set of notions, knov/n by the name of relations, which, as has been already remarked, .make by no means the least important class of our perceptions. This division of our ideas, as it seems lobe the most natural, and truly to represent the man- ner m v/hich thev are introduced into the mind, so I
OF LOGIC. 63
believe it will be found to comprelvc:^d them in c!i their varieties. I shaii therefore now proceed to offer some observations upon language, c.s being the grtut instioinient, by which we are ei liable d to iiiuke our ideas and perceptions knowTi to oihers.
CHAP. V.
OF WORDS, CONSIDERED AS THE SIGN OF OUR IDEAS.
Sec. I. — IFords furnish the I^teans cf recording our oim Thoughts.
W E have seen hew the ir^ind comes to be first fur- niched with ideas, and by what metriods it contrives to diversify and enlarge its stock : let us now consider the means of maldng kno-(,vn cur thoughts to ethers, that we may not only understand how knowledge is acquired, but also in what manner it may ])e commu- nicated with the greatest certainty and advantage. For our ideas, thcugn manifDld and various, are nev- ertheless, all within cur own breasts, invissible to oth- ers, nor can of themselves be mude to appear. But God designing us for society, and to have a fellowship wuth those of our kind, has provided us with organs fitted to frame crrticulate sounds, and given us also a capacity of using those sounds as signs of internal conceptions. Hence spring words and languages ; for ha^'ing once pitched upon any sound, to stand as the mark of an idea in the mind, custom, by degrees, establishes such a connexion between them, that the appearance of the idea in the understanding always brings to our remembrance the sound oi* name by which it is expressed ; as, in like manner, the hear- ing of tiiC sound never iails to excite the idea for
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which it is made to stand. And thus it is easy to con- ceive, 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 : if he can but contrive to register his words, in the order and disposition in which the present train of his thoughts presents 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. Accordingly we find, that the inven- tions of writing and painting, by enabling us to fix and perpetuate such perishable things as sounds, have also furnished us with the means of giving a kind of permanency to the transactions of the mind, insomuch that they may be in the same manner sub- jected to our review, as any the other abiding objects of nature.
Sec. II. — And of the mutual Communication of Knowl- edge from one Man to another.
But besides the ability of recording our ovni thoughts there is this farther advantage in the use of external signs, that they enable us to communicate our senti- ments to otiiers, and also receive information of what passes in their breasts. For any number of men, having agreed to establish the same sounds as signs of the same ideas, it is apparent, that the repetition of these sovmds 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 converse, to the very same set of ideas, nothing is more evident, than that by repeating those names, according to the tenor of my present concep-
OF LOGIC. n
lions, I shall raise in their minds the same course of thought as has taken possession ofmyo-v^m. Hence, by barely attending to what passes within themselves, they will 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 per- ceive, how a man may communicate his sentiments, knowledge, and discoveries toothers, if the language in which he converses, be extensive enough to mark all the ideas and transactions of his n-iind. But as this is not always the case, and men are often obliged to invent terms of their own, to express new views and conceptions of things ; it may be asked, how, in these circumstances, we can become acquainted with the thoughts of another, when he makes use of vrords to which we have never aimexed 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 improve- ment of language, the foUovving observations will, I am apt to think, be found of considerable moment.
Sec. III. — Simple Ideas cannot be conveyed into the Mind^ by Words, or a Description ;
First, that no Vv^ord can be to any man the sign of an idea, till that idea combes to have a real existence in his mind. For names being only so far intelligi- ble, as they denote knovai 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 un- derstanding, than, finding it easy to connect them with the established names, we can join in any agree- ment of ihis kind made by others, and thereby enjoy the benefit made by their discoveries. The first thing,
/
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therefore, to be considered, is, how these ideas may- be conveyed into the mind ; that, being there, we may learn to connect them with their appropriated sounds, ar.d 30 becorae capable of understanding others, v.'hen liicy Hiake use of these sounds in laying open and CGinriunicating their thoughts. Now to comprehend t'-ls distinctly, it will be necessary to call to niind, the before mentioned division of our ideas into simple ajid complex. And first, as for our sim^ple ideas, it ]iis been already observed, that they can find no sd- it.il -sion into the mind, but by two original fount? ins of lu'iow ledge, sensation and reflexion. If therefore any of these have as yet no being in the understand- ing, it is impossible by words, or a description, to ex- cite thcni there. A m.an, who had never felt the im- pression of heat, could not be brought to comxprehend tiiat sensation, by any thing we might say to e^rplain it. If we would really produce the idea in him, it must be by applying the proper object to his senses, andbringhig him within the influence of a hot body. AVhen tiiis is done, and experience has taught him the perception to which men have annexed the name, hi'at^ it then becomes to him the sign of that idea ; and he tiiencefoith understands the meaning of a term, which, before, all the words in the world would not liave 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 con- veyance for the ideas of tiiis class, can neverbe brought to understand the names by which they are expressed. The reason is plain ; they stand for ideas that have no existence in his mind ; and as the organ appropri- £.ted to their reception is v/anting, all other contri- yances are \ain,i;or can they, by any force of descrip- tion, be itiised in his imagination. But it is quite otiicrwise in our complex notion. For these being
OF LOGIC. 72
no more than certain combinations of simple ideas put together in various 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 emmierating the several ideas concerned in the composition, and marking the order and manner in which they are united, to raise any complex concep- tion in the mind. Thus the idea answering to the word rahidow, may be readily excited iu the imagina- tion of another, who has never seen the appearance itself, by barely describing, the figure, largeness, po- sition, and order of colours ; if we suppose these sev- eral simple ideas, with their names, suiiaciently known to him.
Sec. IV. — T/ie Aaiure of Complex Ideas Drfjiablc, those of Simple Ideas not. And this naturally leads me to a second observa- tion upon this subject, namely : that words standing for complex ideas are all definable; but those, by v.diich ve denote simple ideas, are not. For the per- ceptions of this latter class, having no other entrance into the mind, than by sensation or reflection ; can only be acquired by experience from, the several ob- jects of nature, proper to produce those perceptions in us. Words, indeed, may very well serve to remind us of them, if they have already found admission in- to the understanding, and their connexion with the es- tablished names is knovvm ; but they can never give them their original being and existence there. And hence it is, that when any one asks the meaning of a word denoting a simple idea, we pretend not to ex- plain it to him by a definition, wtW knowing that to be impossible ; but supposing him already acquainted with the idea, and only ignorant of the name by which K
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it is called, we either mention it to him by some oth- er name, with which we presume he knows its con- nexion, or appeal to the object 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 tho't him a stranger to these languages, might appeal to an object producing the idea, by saying, it denoted the colour we observe in snonv or milk. But this is by no mea-ns a definition of the word, exciting a new idea in his understanding ; but merely a contrivance to remind him of a known idea, and teach him its connexion v/ith the established name. For if the idea after which he inquires, has never yet been rais- ed in his mind — as suppose one, who had seen no other colours than black and ivhite, should ask the meaning of the word scarlet — it is easy to perceive, that it would be no more possible to make him com- prehend it by woitIs, or a definition, than to inculcate the same perception into the imagination of a man bor» blind. The only method in this case, is, to pre- sent some object, 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 an Agreement in the JVames of Simple Ideas.
Should any one's curiosity now prompt him to en- quire, how it comes to pass, that men agree in their names of the simple ideas, seeing they cannot view the perceptions in one another's minds, nor make known these perceptions by words to others ; I an- swer, that the effect here mentioned is produced by experience and observation. Thus, finding, for in- stanae, that the name, heat, is annexed to that impres- sion which men feel when they approach the fire, I
OF LOGIC. rs
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 imagine, that the same objects operate alike upon the organs of the human body, and produce an uniformity of sensations. No man fancies, that the idea raised in him by the taste of sug-ar, and which he calls sweetness, differs from that excited in another by the like means ; or that ivormivaod, to v/hose relish he has given the epithet bitter, produces in oth- ers the sensation which he denotes by the word snveet. Presuming, therefore, upon the conformity of percep- tions, when they arise from the same objects, we easi- ly agree as to the names of our simple ideas ; and if at any tim^, by a more narrow scrutiny into things, new ideas of this class come in our wa.y, which we choose to express by terms of our own irrv^ention ; these names are explained not by a ueFinition, but by referring to the objects, whence the ideas themselves may be obtained.
Sec. VL — The Co-nveyance of Complex Ideas by Deji- nitions, a wise Contrivance in JSTature ;
Being in this manner furnished with simple ideas, and the names by which they are expressed, the mean- ing of terms that stand for complex ideas is easily at- tained ; because the ideas themselves answering to these terms, may be conveyed into the mind by defi- nitions. For our complex notions, as v/as already ob- served, are only certain combinations of simple ideas. When, therefore, these are enumerated, and the man- ner in which they are united into one conception ex- plained, nothing more is wanting to raise that concep- tion 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
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of nature, in thus furnishmg us with the very aptest Tiieans of communicating our thoughts. I or were it not so ordered, that we could thus convey our com- ■ple:: ideas from one to another by definitions, it v/ould 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 tlie understanding, and have no real objects in nature, in conformity to which they are framed — rif we couid not make them knov/n by a description, they must lie forever hidden within our ov/n breasts, and be con- fined to the narrow acquaintance of a single mind. .\11 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 oth- ers by words and descriptions — could not extend their iniiuence beyond his own imagination, or give joy to • any but the original inventor.
*^tc.\Yl.—r And of great avail towards the Imjirove- ment aj Knowledge. There is this farther a-dvantage in the ability we enjoy, of communicating our complex notions by de- finitions ; that as these make by far the largest class of our ideas, and most frequently occur in the pro- ^;ress and improvement of knowledge ; so they are by this m.eans imparted with the greatest readiness, than which nothing could tend more to the increase and spreading of science. For a dehnity is soon pe- rused, and if the terms of it are v/ell understood, the idea its:;lf finds a^n easy a-dmission into the mind. Whereas in sim.ple perceptions, where v/e are refer- red to the objects producing them, if these cannot be come at, as is sometimes the case, the names, by which they are expressed must remain empty sounds.
OF LOGIC. 77
But new ideas of this class occurring very rarely in the sciences, they seldom create any great obstruc- tion. It is otherwise v/ith our complex notions ; for every step we take, leading us into new combinations and views of things, it becomes hecessary to explain these to others, before they can be made acquainted with our discoveries^ And as the manner of defini- tions is easy, requiring no apparatus but that of words, which are always ready, and at hand ; hence v.e can, with the less diincuity, rem.ove such obsta- cles, as might arise from terms of our own invention, v.^hen they are made to stand for nev/ complex ideas, suggested to the mind by some present train of thhik- ing. And thus at last we are let into the mystery hinted at in the beginning of this chapter, -viz. how we may beccine acquainted with the tlioughts of an- other, when he. makes use of words to which we have as yet joined no ideas. The answer is obvious, from Vvhat has been already said. If the terms denote simple perceptions, he must refer us to those objects of nature, whence the perceptions them.selves are to b^ obtained ; but 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 sumcient to take notice, that our knov/ledge this way can be extended -^only by experi- ence and observation. But the theory of definitions making a material pai^ of logic, and being indeed of great importance tovrards the improvement of human knovv'ledge, it wiii be necessary to lay it a little more t>pen to the view of the reader.
Sec. VIII. — TAe Compositioii and Resclution of our Com f ilex Ideas.
Complex ideas are, as has been already said, no other tlian simple ideas put together in various forms.
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But then it is to be observed, that in making these collections, the mind is not always tied down to the immediate view of tne simple perceptions out of which they are framed. For if we suppose the un-^ derstanding already furnished with a considerable stock of compound notions, these again may be made the constituent parts of others still more compound- ed, insomuch that the new idea thence arising may be termed a combination of complex conceptions. Thus the idea annexed to the word animal, includes many perceptions under it, as life, sense, spontaneous motion, Sec. In the like manner by the terai ration- al, we denote a variety of simple ideas. If now com- bining these two conceptions together, we form the still more complex notion of a rational animal ; the idea thus got is truly a collection of compound no- tices. 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 com- posed of other lesser numbers, which, all put togeth- er, 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, untii-we arrive ^ the units cut of which they are composed; we thereby totally unravel the collection, and being able to push our researches no farther, rest satisfied in the view thus offered to the understanding. Just so it is in the examinslion of our complex ideas. For ■when any very compounded notion comes under the inspection of the mind, in omer to be traced to its first principles — we begin with resolving it into oth- er ideas less complicated ; and taking these again to pieces, one by one, still go on v/ith the search, until
OF LOGIC. rg
we have broken the v/hole into our first and simple perceptions, beyond which the pursuit cannot possi- bly be carried. And this is the reason why I have all along called our simple ideas the foundation and ground- work of human knowledge ; because, in un- ravelling the conceptions of the mind, we find our- selves at length bounded by these ideas, which are indeed the last resort of the understanding.
Sec. IX. — The Karnes of Simfde Ideas may be consid' ered as the Elementary Parts of Language.
From what has been said, it will be easy to con- ceive 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 are also unknown, their terms, too, ought to be still farther defined. In this manner may a series of definitions be carried on, un- til we arrive at the names of simple ideas, which not being defixuable, the analysis must necessarily 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 elementary pails 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 kno^vn ; or, if they are not, experience alone must be consulted, and not definitions or explications. And here it is v/ell v/orth our notice, that a« the names of these our original conceptions, constitute the primi- tive and fundamental articles of speech, upon which the whole superstructure of human language is built,
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so they are, of all others, the least doubtful and un- certain in their si gnili cation. Because, standing each for one simple perception, not precariously excited in the mind, but the effecL of certain posv'ers in things, fitted to produce that sensation in us ; there is no danger of error or mistake. He that once knows siveetness to be the name of the taste received from sup"ar, whiteness of the colour in snow or tniik, and heat of the sensation produced by approaching the fire, will not be apt to misapply those words, or -^n- nex them to perceptions of a different kind. And as the names of complex ideas may all be resolved into these primitive terms, it is apparent, tl.at we are suf- ficiently provided with the means of communicating -our thoughts one to another ; and that the mistakes so frequently complained of en this head, are wholly owing to ourselves, is not sufficiently defining th.e terms we use, or perhaps not connecting them with clear and determinate ideas.
CHAP. VI.
OF DEFINITIOX, AND ITS SEVERAL KINDS.
Sec. l.—'TIie variety of Dejinitions firoceeds from the -various Ajijilication of Words.
H
AviNG laid these foundations, shovm v.hat words are, and what are not definable, and taught the man- ner of resolving our notions, as v/eli as language it- self, into its first and original principles ; v.^e now pro- ceed to explain a little more particularly the nature of a definition, and the several kinds made use of, ac- cording to the different viev/s m.en have in communi- cating their thoughts one to another. Definitions are inteiided to make known the meaning of words stand-
OF LOGIC. 81
ing; for complex ideas ; aiid were we always careful to form those ideas exactly in our minds, and copy our definitions from that appearance, much of the confusion and obscurity coniplaiued of in languages might be prevented. But, unhappily for us, we are by no means steady in the application of names, re- ferring them sometimes to one thing, sometimes to another ; which often creates great uncertainty in their signification, and obliges us to give a different turn to our definitions, according to the different re- ference of the terms defined. In order, therefore, to render this -whole matter as clear and obvious as pos- sible, 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, endea- vour to account for the several methods of denning, mentioned in the writings of logicians.
Sec. II.— JVords harve a threefold Reference ; to our Oxm Ideas^ those rf others^ and the real being of tilings.
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 trae and proper signification. When a man speaks, it is that he may be understood ; and the words he employs to convey his thoughts, are such as by use he has learned to connect with the ideas then present to his mind. But because those with whom we converse, are 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 minds ; and this is the foundation of what is called propriety in lan- guage, when men take care to affix such notions to their words, as are commonly applied to them by those of most understanding in the country where they live. The third and last reference of words is to things
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themselves. For many of our ideas are taken from the several objects of nature, where v/ith we are sur- rounded ; and being considered as copies of things really existing, the words, by which they are express- ed, are often transferred from the ideas themselves, to signify those objects which they are supposed to represent. Thus the word, sun, not only denotes the idea excited in the mind by that sound, but is also fre- quently made to stand for the luminous body itself, which inhabits the centre of this our planetary system. Now, according to 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 supposed to make their appearance in the minds of others ; and lastly, it is something still dif- ferent, to draw images or pictures, that shall carry in them a confonTiity 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 ar- bitrary.
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 mean- ing of any term, as that the complex idea annexed to it by the speaker, may be excited in the understand- ing of him with whom he converses. And this is plainly no more than teaching the connexion of our words and ideas,. that others may understand the sense of our expressions, and know distinctly what notions we affix to the terms we use. When we say, for in- stance, that by the word square we mean a figure bounded by four equal sides, joined together at right angles j what is this but a declaration, that the idea
OF LOGia 83^
of a quadrilateral, equilateral, rectangular figure, is that which in discourse or writing we connect with the term square ? This is that kind of definition, which logicians call the dejinitlon of the name ; because it dis- covers 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 sig- nify any ideas, hence it is plain, that the definitions of names are arbitrary, every man having a liberty to affix what notions he pleases to his words. But the convenience of communication making it necessary for men speaking the same language to agree as near- ly as possible in the signification of sounds, a con- formity has accordingly been studied. Nevertheless, we find that differences will, from time to time, creep in, which must create great confusion in men's dis- courses and reasonings, if they are not careful to de- fine their terms, that their signification 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 advancem.ent of human knowledge depends upon a right use of definitions,. For as by means of them they every where preserve the same detennined significations to their words, hence there is little dispute as to the meaning of their expressions, almost all men understanding them in the same sense- And thus it happens, that such as apply their thoughts this way, having perfectly the same views of things, readily comprehend the discoveries already made, and are thereby enabled with joint la- bour, and an exact conforijpity of notions, to carry on the improvement of this branch of knowledge. And if men in other parts of learning, were alike careful to fix the meaning of their terms, the progress of science must be greatly furthered, and all those ver- bal disputes, that now so much interrupt the course ©f our improvements, might be prevented.
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Sec. IV. — Dejirdtions of the JSfamenot always true and real Definitions ;
This then ought to be our first care, when we en- ter 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 defini- tions 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 prop- er to conform, as near as possible, to common accep- tation, that thereby our thoughts may find a more ea- sy and ready entrance into the minds of others. If it should now be asked, Avhat are the rules of a good tlefiniticn ; I answer, that as in definitions of the name, we aim at no more than teaching the connexion of vv ords and ideas ; every contrivance, by which we are enabled to excite the idea annexed to any Avord in the mind of another, will serve the purpose of a defini- tion. Now the ideas v/e join with our words are of ^wo kinds : either such as we have reason to believe ure already in the minds of others, though perhaps they knov/ not the names by whicii they are called ; or such as, being new and of our own formation, can be no otherwise made knoAvn than by a description. In the first case, there is no necessity for laying open the idea itself, because being already known, any con- trivance to remind us of it is sufllcient. When we say, for instance, that a clock is an instrument^ by ivhich we measure the hours of the day ; it is plain, that the idea answering to the word clocks is not here unfold- ed ; but we being before nand 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 denned. For, by saying that •ivhite is the colour we observe in snow or milk, heat the sensation produced by approaching the fire, v/e
OF LOGIC. 85
srufficientiy make known what ideas Vv'e connect with the terms, ivhite and heat^ which is the true purpose of a definition of the name. Hence it appears, that many of those explanations of words, which logicians call definitions 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 unac- quainted with them, but merely contrivances to re- mind us of known ideas, and teach us the names by which they are called.
Sec. V. — But only ivhen thexj Coincide with the Defini' tion of the Thin^.
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, bef:)re they can learn to connect them with any particular names. And here it is, that the defi- nition of the name coincides with what logicians call the definition of the thing, as in either case we pro- ceed by unfolding the idea itself for which the term denned stai"ids. And indeed this alone is what con- stitutes a definition, in the true and proper sense of the word, as will appear more fully afterwards, when v/e come to consider the terms v/e use, as referred to the real objects of nature. We'sh'all therefore post- pone this consideration of the definition of the name, till we come to treat of the definition of the thing, w^hen it will m^ore naturally fall in our way. It may not, however, be amiss to observe, that when we say the definitions of the name are arbitrary, 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
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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 ay which it is expressed, being, as we have said, wholly arbitrary, the considering the description of that idea as the definition of that particular nam.e must be so too. Sa that although definitions, considered as descriptions of our ideas, are steady and invariable, yet the appli- cation of them to particular sounds, (which is all that we understand by the definition of the name) is whol- ly a work of our own free choice. Sec. VI. — Definition of Words according to the com- mon use of Language not Arbitrary.
But secondly, besides considering words as the signs of our own ideas, we are also very apt, on many Gccasi-ons, to refer them to the ideas in the minds of other men. Now, to define a term, in this view, is to investigate its meaning or acceptation, according to the common use of speech. Here then it is plain, that definitions are not arbitrary. For although in- regarding words as the marks of our own ideas, we may give them what meaning we please ; yet when we consider them in reference to the thoughts of others, they have a fixed and steady signification; namely, that which custom and the propriety of Ian- guage has assigned them. The words, ability and genius^ nnay, 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 liberty to use them promiscuously. But if the common course of lan- guage hath confined the word genius to express the natural strength and talents of the mind, and the word ability to denote those which are acquired, v/ho- ever pretends to explain the proper acceptation of tiiese terms, is bound to take notice of tiiis difference.
OP LOGIC. 57
As propriety of speech makes our language intelligi- ble, and gives our thoughts a ready entrance into the minds of others, it well deserves our application and care. The best vray to acquire it is from the writings and discourses of those who seem to ha'\ e had the clearest notions, and to have applied their terms with the exactest choice and fitness.
Sec. VII. — D'ifimtio7is of the Thing refer to the real Objects of Xattire.
We come now to the third and last species of defi- nition, that namely, which considers words as refei'- red 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 heat and light to the planets around him ; it is not enough that we give an account of the idea, answering to that word in our minds. We must ftirther take care, that the idea itself carries in it a real conformity to the object it is supposed to repre- sent. And hence it is, that all definitions of this kind, when justly made, are in reality pictures or repre- sentations, taken from the being and existence of things. For they are intended to express their na- ture and properties so as to distinguish them from all others, and exhibit them clearly to the vievv 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.
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Sec. VIII.— Grow wc? of the distinction between the aV- fcnition of the Name and of the Thing. And this also lets us into the ground of that dis- linctlon so universally received betv/een definitions of the name and of the thing. The first are arhitra- rv, and not liable to debate or contradiction. The second are propositions, capable of proof and illus- tration, and which may therefore be contested. The reason is obvious. Definitions of the name serve on- ly to mark what ideas we connect with our words. — And as sounds are of themselves indifferent to signify any ideas, vre are entirely 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 jjleasure, but of such only as carry in them a conformity to the several objects to which the vrords refer. A man may use the term,^ square^ to express that idea, which others denote by the v/ord, 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. He tells us that by a square he means a three-sided figure ; and wJio 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 meaning 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 dependence upon the fancy and caprice of men. It is true,- the properties of the tnangle may, after this definition, be affirmed oi th^ square ; but as in either case, the idea to v/hich these properties be- long, is the same, the propositions only expressing our judgments, and not our judgments themselves, suffer a seeming variation.
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Sec. IX. — A fireviou-s connexion betiueen A^ames and Things^ cuts off all Arbitrary Explications.
But where words are made to denote particular ob- jects, previous to any definitions given, there arbitra- ry explications cannot have place. For in this case, we are not put upon explaining what ideas we con- nect v/ith our Avords, biit a connexion being already supposed between the name and the thing signified, our business is to unfold that idea by which the ob- ject 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 connexion being once set- tled, we are no longer left to arbitary definitions, but must describe it by such properties as are really to be found in it, and vriil best serve to distinguish it when it comes in our way ; as by saying it is a substance yellow, very hea\y, malleable, fusible, 8cc. Sec. X. — Whij Mathematical Definitions have been ac- counted mere Definitions of the JVaine ;
From what has been said, it appears, that in the language of logicians, definitions of the thing respect only substances and beings that have a real existence in nature, serving to describe them by their proper- ties and attributes. And this, I doubt not, is the rea- son, that the definitions of the mathematicians are not considered as definitions of the thing, but of the name ; because the ideas therein described, are the mere creatures of the understariding, and not suppos- ed to be copied from patterns existing w-ithout us. A circle, a triangle, a square, &cc. such as mathema- ticians conceive them, are no where to be found in na- ture, that we know of. Hence it might justly be ac- counted absurd, to call our definitions of these, defini- tions of the things when thev serve not to describe anv M
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real objects of nature, but merely to unfold the con- ceptioris of the mind. And yet if we look into tiie iTiritter narroAvly, we shall find, that the rules follow- ed in these deRnlticns 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 prcpertics, some of which are com- mon to different ranks, others peculiar to the tribe defined. The common properties constitute what iog-icians call the genus, and those tliat are peculiar, the difcraice Now the genus and dijference make lip the logical dciinition of the thing, as will be more clearly understood from what follows.
Sec. XI. — When yet they coincide rjith the logical dcf- ration of the things and therefore 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 defi- nitions of the name, in which we are left wholly to arliitrary explications. For however wx may change the name of one figure for another in discourse or writing, using the term square to denote a triangle^ or tlie word triangle to express a square, it is certain the ideas themselves are invariable, and no less capa- ble of being distinguished by their properties, than the several species of substances. Thus if we suppo3e the v/ord square to denote that species of fig- ures, Avhose sides severally subtend quadrants of a circumscribed circle, we shall find oui'selves equally siiut out from arl'jitrary explications, as in the defini- tion of the names of substances. For as this happens in no figures but those which are bounded by four equal sides joined together at right angles ; itfollov/s
OF logic: 91
evidently, that the true and proper deiinitlon 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 division of definitions, into those of the name and thing, is not sufficiently calcu- lated to give us right apprehension.s, as to v.hat is and what is not arbitrary in the explication of ^vords. It may not, therefore, be improper, if we here endeavor to clear up this matter a little, and free it from those obscurities in wiiich it has hitherto been involved. To this end we shall premise the follov.'ing observa- tions.
Sec. XII. — Drjirdiions^ properly speakings never re- gard Things.^ but merely our Qi:;n 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, re- gard immediately things themselves, but merely the ideas in our ovrn mJnds. This, I doubt not, will ap- pear a paradox to many, wlio will be apt to enquire, v/hether the definition oi gold, be not taken from that, metal, independent of the various conceptions of men about it. To this I answer, that indeed in framing cur idea of g-cld, v/e regard chieHy the thing itseli, uniting in our conception sucli properties as are most conspicuous, and csrve 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. Nov/ this can no otherv/ise be done, but by enumerating the several properties of which our own complex notion is formed. And indeed it were in the highest degree' absurd to imagine, that men in, explaining things: to others, should make use of any
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marks or characters, but those by which they are known to themselves. Hence it comes to pass, that ail our defmitions are in fact nothing else but trans- cripts of the ideas in our minds. Where these are imperfect, 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 tlie object described. And this v/ill very well serve to account for that great diversity of definitions we often m^eet with, even of one and the same object. Because men, in consequence of their- difFerent pursuits and applications, falling often into- difierent views of things, must needs vary no less in their definitions, than in the ideas themselves from Avhich these definitions are copied. He, whose ob- servation goes no farther than the more obvious quali- ties of gold, will content himself with describing it b)~ its colour, weight, and perhaps malleability and fusi- bility. On the other hand, a goldsmith, having en- quired farther into the nature of that metal, and find- ing several other properties that equally belong 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 former, fixedness, and solubility in egua regia^ Sec. And so in proportion as men's various pursuits lead them into a more accurate examination of things, their explications will take a diiTerent tura, suitable to the ideas they have fi^amed rrithin themselves. , . ■
Sec. yA\\.—-Ijhtivrticn betnveen the Dcfir.ition cf 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 distinction cf them into these of the name and thing,.
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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 de- finitions are expressive of the real essence of things,, whereas they are in ti'uth 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 : be- cause their essences being immutable and always the same, the definition would in this case serve to cor- rect the idea, and might be considered as a standard, by which to judge whetiier tlie idea Avas rightly fram- ed. I deny not, that vvords are often transferred from our ideas to signify the objects which these ideas, represent ; as when we talk 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 oth-- crs, all we aim at is, distinctly to lay open our concep- tions about them. Hence it appears, that what lo- gicians call a definition of the thing, is in truth no more than an unfolding of the idea, by "\vhich that thing is represented to the understanding. But now in math- ematicq.1 definitions, and indeed all others whatsoever, this also is our whole aim and intent, to exhibit and lay open thos.§ ideas,, of which tlie words we use are the signs^ And thus it happens, that in innumerable, instances, v/hat logicians call the defnitio?t of the namey. is yet found to coincide witii and proceed by the very same rules, d^^Xh^ defnition of the thing ; which clear- ly demonstrates the necessity of banisliing this frivo- lous distinction, and establishing some precise and determinate notion, expressive of tlie ti'ue nature of a definition, and comprehending it in its full extent.
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Sec. XIV. — Drfmitions in all cases descrijuions of cur Ideas.
Nor will this appear so diujcult a task, if we call to Tnind, that v/ords are in all cases the signs of" our ideas, and no otherwise signify things, than as they stand for those ideas by v/hich things are represented to the understanding. By defining our words, there- fore, vv'e can mean no more, than the laying open to the view of otliers, the ideas of v\'hich these v/orcls are the signs. For thus it is, that the meaning of our expressions comes to be known, and that we find our- fcclves capable of transferring our thoughts and con- eeptions into the minds of those with whom we con- verse. Where wcrds are referred to things them- selves, there we explain tlje ideas by vrhich thess things are represented ; v.iiere they denote concep- tions framed by the mind, tliere Ave la.y open these conceptions, and endeavour to exhibit them accord- ing to their real appearance Avithin our own breasts. But in both cases, it is our ovrn ideas, it is the per- cepiions of our ov.n minds, either as taken frcm things without, or framed by the understanding itself, that we explicate and unfold.
Sec. XV. — J\''ot ari-lirary^ a-i being confined to the Kc- jiresentalion of certain cleterrniiiate J\^otiohs.
And thus Ave have at leneth settled the true and genuine notion of a definition, comprehending all its varieties, from AAiiateA'cr science taken^- or to Avhatev- er object extended. For from Avhat aa'c have said, it evidently follows, that a definition is the unfolding of some conception of the mind, answering to the wx>rd or term made use of as the sign of it. Now, as in exhibiting any idea to another, it is necessary that the description be such as may excite that precise idea in his mind :. hence it is nlain, that deflmticns>
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properly speaking, are not arbitrary, but confined to the representing- of certain determinate settled no- tions, such, naniely, as are annexed by the speaker or \^-riter to the words he uses. As, nevertheless, it is universally allowed that the signilication of words is perfectly voluntary, and not the effect of any natur- al and necessary connexion befween them and the ideas for vfhicli they stand, some mav perhaDs won- der why definitions are not so tC'f>. In order, there- fore, to unravel this difficulty, and show distinctly Avhat is, and what is not arbitrary in speech, we must carefully distinguish between the connexion of our words and ideas, and the unfolding of the ideas them* selves.
Sec. XVI. — T/ie Ccrmexion bet^.veen Words avd Ideas, a Jic-fcciiy voluntary Establhlnnenl.
First, as to the connexion of our words and ideas, this, it is plain, is a purely arbitrary institution. When, for instance, vre have in our minds, the idea of any particular species of metals, the calling it by tlie nam^e gokU is an effect of the voluntary choice of men speak- ing the same language, and not of any peculiar apt- ness in that sound to express that idea. Other na- tions, we find make use of diiTerent 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 metal vvhich we call silver^ had custom in the beginning so established it.
bee. XVII, — The JDescri/iizona of Ideas not so, but bouudsd to the Refivesentaiion of that precise A}.- pearcnce by nvhick they arc dhtinguished among themselves.
But although we are thus entirely at liberty, iu connecting any idea with any souna, yet it is quite
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otherwise in unfolding the ideas themselves. For every idea, having a precise appearance of lis ov/n, 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 pecu- liar appearance. When we have formed to our- selves the idea of a figure bounded by four equal sides, joined together at right angles, we are at lib- erty to express that idea by any sound, and may call it either a square or a triavgle. But whichever of these names we use, so long as the idea is the same, the description, by which we would signify it to an- other, must be so too. Let it be called square or tri- angle^ it is still a figure having four equal sides, and all its angles right ones. Hence we clearly see, what 13, and what is not arbitrary in the use of words. The establishing any sound, as the mark of some deter- minate idea in the mind, is the effect of free choice^ and a voluntary combination among men. And as diflcrent nations make use of different sounds, to de- note the same ideas, hence proceeds 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 constitutes a definition, is by no means an arbitrary thing. For here, as I have already observed, we are bound to exhibit that pre- cise conception, which either the use of language or our own particular choice, hath annexed to the term we use.
Sec. XVIII. — Causes of the Obscuriiy that has hither- to fierfilexed the Theory 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 c: these
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precise ideas. But then in the application of defini- tions to particular names, Vv e are altogether left to our own free choice. Because as the ({onnectinp- of any idea with any sound, is a perfectly arbitrary insti- tution ; the applying the description of that idea, to that sound, must be so t<5o. When, therefore, IcP-i- cians tell us, that the definition of the name is aibi- trary, they mean no more than this ; that as dinerei>^ ideas may be connected with any term, accord;np--to ti:e good pleasure of him that uses it, in like manner may different descriptions be applied to that term., suitable to the ideas so connected. But this connex- ion being settled, and the term considered asthes'^n oi some fixed idea in the understandings, we are So longer left to arbitrary explications, butm.ust study- such a description as corresponds with that prec'iVe idea. Now this alone, according to what has b^-a before laid do^vn, ought to be accounted a definition V.'iiat, I am apt to think, has occasioned no small confusion m this matter is, that many explanations 01 words, wiiere no idea is unfolded, but merely the connexion between sopie word and ide^ asse-ted have yet been dignified with the name of definitions' 1 bus, m the instance before given, when we say that a cock IS an instrument by wiiich Vv-e measure ^ime • tiiis is by some called a definition. And yet' it is plain, that we are beforehand supposed to have an idea of this instrument, and only taught that the wo-d dock, serves in common language to denote that idea Ly tms rule all explications of words in our d-ctiora- ries will be definitions ; nay, as was already observ- ed, the names of even simple ideas may be thus de- hned. li/me, we may say is the colour we observe m snow or milk, heai the sensation produced by an- proachmg the fire, and so in innumerable other in- stances. But these, and all others of the like kind,
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are by no means definitions, exciting new ideas in tiie understanding, but merely contrivances to remind us of known ideas, and teach their connexion witli the established names. It is, nevertheless, worth our notice, that what logicians call definitions of the name, extend properly no farther than these explan- ations, serving to mark the comiexion of our ideas and words ; and are therefore justly accounted arbitrary, inasmuch as the connexions themselves are altogeth- er so.
Sec, XIX. — Comfilex ideas alone capable of that kind of description ivhich goes by the name of a definition.
But now in. definitions properly so called, we first consider the term we use, as the sign of some inward conception, either amiexed 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 wliole ai:t 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 unacquainted with it. This point settled, let us next enquire into v/hat those ideas are which are capable of being thus unfolded. And in the first place, it is evi- dent, that all our simple ideas are necessarily exclud- ed. Vv'e have seen already, that experience alone is to be consulted here, insomuch, that if either the ob- jects, 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 rnind. But where the understanding is al- ready supplied with these original and primitive con- ceDtions,*a3 they may be united together in an infinity .of different forms ; so may all their several combina- tions be diiitinctly laid open by enumerating the sim-
OF LOGIC. 99
pie ideas concerned in the various collections, and tracing the order and manner in which they are linked one to another. Now these combinations of simple notices constitute what we call our complex notions ; whence it is evident that complex ideas, and those a- lone, admit of that kind of description, which goes by the name of a definition.
Sec. XX.-^rF/ze7z a comfilex idea ?nay be said to be fully v.nfolded.
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 Avhere we make use of terms, standing for such complex ideas. But perhaps the reader may still expect, that we should enter a little more particularly into the nature of a definition, de- scribe 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, wx must again call to mind, that the design of a definition is, so to unfold the idea answering to any term, as that it may be clearly and distinctly transferred into the mind of another. Eut now our complex ideas, which alone are capable of this kind of description, being, as we have said, nothing more than different combinations of simple ideas ; we then know and comprehend them perfectly, when we knov/ the several simple ideas of which they consist, and can so put them together in our minds, as is necessa- ry towards the framing of that peculiar connexion, which gives every idea its distinct and proper appear- ance.
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Sec. XXL— Z'wo things required in a definition: to en- umerate the ideas^ and explain the manner of their
CGTdbination.
Trro things are therefore required in every defini- tion. First, that all the original ideas, out of v/hich the complex one is formed, be distinctly enumerated. Secondly, that the order and mannei; of combining them into one conception, 'be clearly explained. — ^'V'.here a de/inition has these requisites, nothing is •wanting to its perfection ; because every one wiio reads it, and understands the terms, seeing at once v/hat ideas he is to join together, aid 'also in what manner, can at pleasure form in his own mind the conplex conception answering to the term denned. Let us, for instance, suppose the word, .s5-^;are, to stand for that idea, by which Ave represent to ourselves a figure, whose sides subtend quadrants of a circum- sci-ibed circle. The parts of this idea, ?.re the sides ]:)oundh;g the figure. These must be four in num- ber, and all equal among themselves, because they ere each to subtend a fourth part of the same circle. But besides these component parts, we must also take : notice of the manner of putting them together, if v/e should exhibit the precise idea, for which the v/ord square here stands. For four equal nght lines, any ■ how joined, will not subtend quadrants of a circum- scribed circle. A figure with this property, must have its sides sta.nding also at right angles. Taking in, therefore, this last consideration, respecting the -manner of combining the parts, the idea is fully de- scribed, and the definition thereby rendered complete. P'or a figure, i)ounded by four equ?J sides, joined to- gether at right angles, has the property required*; aiid is, moreover, the only riglit-liaed figure to which that property belongs.
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Sec. XXII. — Hovj -ve are to proceed^ to arrrve at just and adequate definitions.
And nuw, I imagine, it will be obvious to every one in v/h"at manner vre ought to proceed, in order to ar- rive at just and adequate definitions. First, we are to take an exact \'iew of the idea to be described, trace it to its original principles, and mark the several sim- ple perceptions that enter into the composition of it. Secondly, we are to consider the particular manner in which these elementary ideas are combined, in or- der to the forming of tliat precise conception, for which the term Ave make use of stands. When tiiis is done, and the idea v\-]iolIy unravelled, we ha^-e noth- ing more to do, than fairly transcribe the appearance it makes to oirr ovm minds. Such a description, by distinctly exhibiting the order and number of our primitive conceptions, cannot fail to excite, at the same time, in the mind of every one that reads it, the complex idea resulting from them ; and therefore at- tains the true i:AiCi proper end of a definition.
OF THE CO'TPOSITIOX AXD RESOLUTION OF OUR
IDEAS, AND THE RULES OF DEFINITION
THENCE ARISING.
Sec. I In cov7Jiou7uli"g cur Idras^ tve proceed by suC'
cessive gradatioji.
JL HE rule laid down in the foregoing chapter is gen- eral, extending to all possible cases ; and is, indeed, that to which alone vve can have recourse, where any doubt or diaiculty arises- It is not, however, neces- sary, that we should practice it in every particular instance. Ivlany of our ides.s are extremely ccmpli-
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cated ; insomuch that to enumerate all the simpM perceptions out of which they are formed, would be a very troublesome and tedious work. For this reas- on, logicians have established certain compendious rules of denning, of which it may not be amiss here to give some account. But in order to the bet- ter understanding of what follows, it will be necessa- ry to observe, that there is a certain gradation in the composition of our ideas. The mind of man is very limited in its views, and cannot take in a great num- ber of objects at once. We are, therefore, fain to proceed by steps, and make our first advances sub- servient to those which follow. Thus in forming our complex notions, we begin at first with but a few sim- ple ideas, such as we can manage with ease, and unite them together into one conception. When we are provided witli a sufiicient stock of these, and have, by habit and use, rendered them familiar to our minds, they become the component parts of other ideas, still more complicated, and form what v/e may call a sec- ond order of compound notions. This process, as is evident, may be continued to any degree of composi- tion we please, mounting from one stage to another, and enlarging the number of combinations.
Sec. II, — Hence ideas of this class best comprehencledy when ive advance gradually through all the several orders.
But now in a series of this kind, whoever would acquaint himself perfectly with the last and highest order of ideas, finds it much the most expeditious method, to proceed gradually through all the inter- mediate steps. For was he to take any very com- pounded idea to pieces, and without regard to the several classes of simple perceptions, that have al- ready been formed into distinct combinations, break
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ill at once into its original principles, the number would be so great, as perfectly to confound the imag- ination, 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 position, we find it impossible to ar- rive at an exact knowledge of their number. But if they are formed into separate battalions, and so sta- tioned as to. fall within the leisurely survey of the eye ; by viewing them successively, and in order, we come to an easy and certain determination. It is the same in our complex ideas. When the original per- ceptions, out of which they are framed, are very nu- merous, it is not enough that vv"e take a view of them in loose and scattered bodies. ^Ve must form them into distinct classes, and unite these classes in a just and orderly manner, before we can arrive at a true knowledge of the compound notices resulting from them..
Sec. III. — Our Definitions ought to keep, pace with our Ideas^ and observe a like 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 easy combinations, and advances through a succes- sion of different orders, rising one above another in the degree of composition ; it is evident, that in a train of definitions expressing these ideas, a like gra- dation is to be observed. Thus the complex ideas of the lov/est order, can no otherwise be described, than by enumerating the simple ideas out of which they are made, and explaining the manner of their union. But then in the second, cr any succeeding order, as
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they are formed out of those gradual combinations^ that constitute the inferior classes, it is not necessa- ry 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 a'lrep.dy knovrn, in consequence of previous definitions. Here then it is, that the logical method of defining- takes place ; which, that we may the better under- stand, I shall explain somewhat more paitxularlv, the several steps and gradations of the mind, in com- pounding its ideas, and thence deduce that peculiar ibrm of a deiinition, which logicians have thought nt to establish.
Sec. IV. — The stcfis by ivhich the Miizd proceeds from Particular to General Ideas.
All the ideas we receive, from the several objects of nature that surround us, represent distinct individ- uals. These individuals, wdien compared together, are found in certain particulars to resemble. Hence, by collecting the resembling particulars into one con- ception, we form the notion of a s/iecics. And here let it be observed, that this last idea is less compli- cated than that by wdiich we represerit any of the particular objects contained under it. For the idea of the species excludes the peculiarities of the sever* ai individuals, and retains only such properties as are common to them all. Again, by comparing several species together, and observing their resemblance, we form the idea of thd gcm:s ; where, in the same manner as before, the composition is lessened, because vv^e leave out v/hat is peculiar to the several species compared, and retain only the particulars wherein they agree. It is easy to conceive the mind, proceed-
OF LOGIC. los-
ing thus from one step to another, and advancing through its several classes of general notions, 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. — The conduct of the Mind in comjiounding its Ideas, as it advances through the different orders of perception.
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 terminates in one simple perception. If now we take the series the contrary way, and beginning v>-ith the last or highest genus, carry our vievv' downwards, through all the infe^or genera and species, quite to the individurls ; we shall thereby arrive at a distinct apprehension of the conduct of the understanding in compounding its ideas. For in the several classes of our perceptions, the highest in the scale is, for the most part, m.ade up of but a few sim.ple ideas, such as the mind can take in and survey with ease. This first general notion, when branched out into the dif- ferent subdivisions contained under it, has in every one of them something peculiar, by which they are dis- tinguished among themselves ; insomuch that in de- scending from the genus to the species, we alwavs superadd som.e new idea, and thereby increase the degree of composition. Thus the idea denoted by the word/^wre, is of a very general nature, and coni- posed of but few simple perceptions, as implying no more than space every where bounded. But if v/e descend farther, and consider the boundaries of this space, as, that they m.ay be either lines or surfaces, we fall into the several species of figure. For where tiie space is bounded by one or more surfaces, we O
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fj,ive it the Dame of a srAid figure ; but where the boundaries arc lines, it is called zl jilain figure .
Sec. VI. — 'The Idea of the S/iecies formed by sujieradd- ing the sjiecific Difference to the Genus.
In this view of things, it is evident, that the species are formed by superadding a new idea to the genus ^ Here, for instance, the genus is circumscribed space. 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 v.e conceive the circumscription to be by surfaces, we have the species of solid figures. This superadded idea is call- ed the specific diiferc7ice^ not only as it sei-ves to di- vide the sptciss from the gcnufi, but because, being different in ai-1 the several subdivisions, v/e thereby also distinguish the species one from anciher. And as it is likewise that conception, Avhich, by being join- ed to the general idea, completes the notion of the c/ieciec ; hence it is plain, that the genus and specific difference are to be considered as the proper and ccn- biituent parts cf the species. If we trace the progress of the mind still farther, and observe it advancing through the inferior 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 m descending the scale of our perceptions, the under- standing passes through different orders of complex notions, wliich become more and more complicated lit every step it takes. Let us resume here, for in- stance, the species of plain figures. They imply no more than space bounded by lines. But if we take in an additional consideration of the natm'e 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.
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Sec. Vn.— v-^^rf 271 all the inferior species by szcfieradd^ ing the specijic to the nearest gemis.
And here we are to observe, that though plain fig- ures, when considered as one of those branches thai ccme under the notion of figure in general, take the name of a species ; yet compared with the classes of curvilinear, rectilinear, and mixtilinear, into whicU they themselves may be divided, they really become a genus, of which the before mentioned subdivisions constitute the several species. These species, in the same manner as in the case of plain and solid figures, consist of the genus and specific difference, as their constituent parts. For in the curvilirisar kind, the curvity of tiie lines bounding the figure, makes what is called the s/iecijic difference ; to which if we join the genus, which here is plain figure, or space cir- cumscribed by lines, we have ail that is necessary towai'ds completing the notion of the species. Vv e are only to take notice, that this last subdivision, hav- ing two genera above it, viz. plain Jlgure, arid ^figure in general i the genus, joined with the specihc ditfer- ence, in order to constitute the species 61 curvilinear^ is that which lies nearest to the said species. It is the notion oi plain figure^ and not oi'Jigztre in general, that, joined with the idea of ciii-vity^ makes up the complex conception of curved-lined figures. For in this descending sc-ale of our ideas — Fig^ire in general, idain figures^ curve-lined figures — the two first are considered as genera in respect to the third ; and the second in order, or tliat vvhich stands next to the- third, is called the nearest gciius. But now as it is this second idea, v/hicli, joined with the notion of curvity, forms the species of curve-lined figures ; it is plain, that the third or last idea in the series, is made up of the nearest gams and. specific diff'ercnce. This rule
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holds invariably, however far the series is continued'; because in a train of ideas thus succeeding one anoth- er, all that precede the last are considered as so ma- ny genera, m respect of that last ; and the last itself is always formed, by superadding the specific differ- ence to the genus next it.
Sec. VIII. — The idea of o^n individual cmiiiosed of the (oweat species and rMmeric difference..
Here then we have an universal description, appli- cable 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 every where consist of 'i\\Q^ genus proxhnum^ and dif ftrentia sjiecifica^ as logicians love to express them- selves. But when we come to the lowest species of all, comprehending in it only individuals, the superadd- ed idea, by which these individuals are distinguished one from another, no longer takes the name of the fH^ecific difference. For here it serves not to denote distinct species, but merely a variety of individuals, each of v/hich, having a particular existence of its own, is tiierefore nnmericailij different from"every oth- er of the same kin<l. And hence it is, that in this last case, logicians choose to call the superadded idea by the name of the numerical (/?^f-re?!C(? ; insomuch thict as the idea of a species, is made up of the near- tst genus and specific diffire?ice^{s6 the idea of an in- dividual consists of the lowest hpecibs oxiCt niuneric dif- ference. Tkus the circle is a species of curve-iined figures, and what we call the lowest species^ as com- prehending under it only individuals. Circles in par- ticular are dlstuiguished from one another by the length and position of their diameters. The length, tlierefore, and position of the diameter of a circle, is uhat logicians cull tiie niunerical difference ; becau3<^
OF LOGIC. 109
these being given, the circle itself may be described, and an individual thereby constituted.
Sec. IX. — Dejinitions to follow one another in train^ and pass through the same successive gradations as our cornfiouyid ideas.
And thus we have endeavored to ti^ace, in the best manner we are able, the progress of the mind in compounding its ideas. It begins, Ave see, with the most general notions, which, consisting of but a few . simple notices, are easily combined and brought to- gether into one conception. Thence it proceeds to the species comprehended under this general idea, and these are formed by joining together the genus and sfiecijic difference. And as it often happens, that these species may be still further subdivided, and run on in a long series of continued gradations, producing various orders of compound perceptions ; so all these several orders are regularly and successively formed, by annexing in ei'ery step, the sfiecific difference to the nearest genus. When by this method of proce-- dure, 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 neces- sarily terminates, because it is impossible any farther to bound or limit our conceptions. This view of the com.positicn of cur ideas, representing their ccnstitu- ent parts in every^ep of the progression, naturally points out the true and. genuine form of a definition.. For as deSnitions are no more tlian the. descriptions of the ideas for which tlie terms denned stand ; and as ideas are then described, when we enum.erate dis- tinctly and in order, the parts of which they consist ; it is plain, that by making our definitions foIlov\^ one anotlier, according to tlie natural train of our concep- tions, they will be su1:>ject to the same rules, and keep pace '.yith the idea^' they describe,.
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Sec. X. — The form of a Definition in all the various' orders of Cor.ccption.
As therefore the first order of our Gompoimd no- tions, or 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 enumerating the simple 7ictices so combined. And as the species comprehended under any genus, or tjie complex ideas of the second order, arise from super- adding the specific difference to the said general idea ; so the definition of the names of the species is absolv- ed, in a detail of the ideas of the sjiecifc difference^ con- nected ivith the term of the g£nus. For the genus hav- ing been before defineil, the term by which it is ex- pressed stands for a known idea, and may therefore be introduced into all subsequent definitions, in the same manner as the names of simple perceptions. It will nov/, I think, be sufficiently obvious, that the de- finitions of all the succeeding orders of compound no- tions, will every wliere consist of the term of the nearest genus joined with an e^iumeration of the ideas that con- ctitute the specif c difference ; and that the definition of individuals unites the name of the lowest species, with the terms by which we express the ideas of the numeric difference.
Sec. XL — The logical method of definmg perfect in its kind ;
Here then v/e have the ti-ue and proper fomi of a definition, in all the various orders of conception. This is that method of defining, w hich is commonly called logical, and which, we see, is perfect in its kind, inasmuch as it presents a full and adequate descrip- tion of the idea, for which the term defined stands. There are still two things worthy of observation, be-
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fore we take leave of this subject. First, that the very frame and contexture of these definitions, points out the oiKler in which they ought to follow one another. For as the name of the genus is admitted into a de- scription, only in consequence of its having been be- fore defined ; it is evident, that we must pass gradu- ally through all the diiTerent orders of conception. Accordingly, logicians lay itdo-vvn as a rule, that we are to begin always with the highest genus, and car- ry on the series of definitions 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 suc- cessive gradations ; insomuch, that the perusal of them must excite those ideas in the understanding of another, in the very order and manner in which they are put together by the mind in its uniform advances from simple to the most complicated notions. Now this is the ti-ue and proper end of defining, and in- deed the higiiest perfect!on of that art.
Sec. XII.— 'y^;i<i apjilicable to all words whatsoever ca^ fiabic of a dejlrdtion.
There is yet another thing to be observed on this head, namely, that the form here prescribed, is appli- cable to all vvords v/hatsoever, capable of a definition; For as every term v/e use, must denote some idea, either general or particular ; and as all our com.plex notions relating to both these classes of perception from the highest genus quite down to the individuals, come v/ithin the rules of description here given ; it is evident, that this paiticular manner of unfolding an idea, may be extended to all the possible ccmplex conceptions v/e can connect with ourv/ords. By the rules therefore of this method, definitions may be ap- plied to all terms standing for complex ideas ; aiad
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as these, by what Ave have shown at large in the two foregomg chapters, are the only definable articles of speech ; it necessarily follows, that the directions here given are universal, extend to ail particular in- stances, and are alike applicable in ail languages. — And thus at length, we have not only deduced that peculiar form of a dennition which obtains among lo- gicians, 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. CHAP. L
OF THE GHOUNDS OF HU3IAN JUDGMENT.
Sec. T. Intuition 7'esfiecta the relation between our I-
deas when they are immediately perceivable.
When the mind is furnished with ideas, its next step in the way to knowledge is, the comparing these ideas together, in order to judge of their -agreement or disagreement. In this joint view of our ideas, if the relation is such, as to be immediately discovera- ble by the bare inspection of the mind ; the judg- .jnents thence obtained are called ifituitive^ from a word that denotes to look at: for in this case, a mere attention 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 intui- tive judgment, nothing more being required, to con-
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vince ii5 of its truth, than an attention to the ideas oiivhals ziidpart. And this, too, is tiie reason, why v/e call the act of the mind forming these judgments intuithn ; as it is indeed no more than an immediate perception of the agreement or disagreement of any tvvo ideas.
Sec. II. — Exfierience and Testimony the Ground of judging as to Tacts. But here it is to be observed, that cur knowledge cf this kind, respects only our ideas, and the rela- tions between them, and therefore can serve only as a foundation to such reasonings, as are employed ia investigating these relations. Nov/ it so happens, that many of our judgments are conversant about facts, and the real existence of tilings 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 iliDl 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 th.at account, that either of them exists. Vv hat then are the grounds of our judgments, in relation to facts ? I answer, these two : exjiericnce and testimonij. By ejcperience we are iniorm-ed of the existence of the several objects whicli surround us, and opei^te upon cur senses. Testlincny is of a wider extent, and reaches not only to objects beyond the present sphere of our observation, but also to facts and transactions, vrhich, being now past, and having no longer any existence, could not, without tnis conveyance, have fallen under our cognizance. Sec. III. — Three Fc:mdatio'ns of human Judgment^ viz. 1. Lituition^ the Ground of scientifcal knowledge ;
Here then we have three foundations of human judgment, from which the v^diole svsteni of our laaowl- P
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edge may with ease and advantage be deduced. First, inndtion, wiiich respects our ideas themselves, and their relations, and is the foundation of that species of reasoning v/hich we call demonstration. For what- ever is deduced from our intutive perceptions, by a clear and connected series of proofs, is said to be de- monstrated, and produces absolute certainty in the mind. Kence the knowledge obtained in this man- ner, is what wc properly term science ; because, in every step of the procedure, it carries its own evi- dence along with irt, and leaves no room for doubt or hesitation. And what is highly wortliy of notice ; as the truths of this class expressthe relations between our ideas, and the sam.e relations must ever and inva- riably subsist betv/een the same ideas, our deduc- tions, 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 ; because the relations of equal- ity being attached to the ideas themselves, must ever intervene where the same ideas are compared. Of this nature are ail the truths of natural religion, morality, and mathematics ; and in general whatever may be gathered from the bare view and considera- tion of our ideas.
Sec. IV.--2. ErheriencetheGrortndof our Knowledge of the Povjers and Qualities of Bodies.
The second ground of human judgment is experi- ence ; from Avhich we infer the existence of those objects that surround us, and fall under the immedi- ate notice of our senses. When we see the sun, or cast our eyes towards a building, v/e not only have ideas of these objects within ourselves, but ascribe to them a real existence out of the m^ind. It is also by the information of the senses, that we judge of.
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the qualities of bodies ; as wherx ^ve say thrtt snow is white, fire hot, or, steel hard. For as we are vrhol- ly unacquainted with the internal structure and con- stitution of the bodies that produce these sensations in us, nay, and are unable to trace any connexion be- tween that structure and the sensations themselves, it is evident that we build our judgments altogether upon observation, ascribing to bodies such qualities as are ansv\'erab]e to the perceptions they excite in us. But this is not the only advantage derived from experience, for to that, too, are v.-e indebted for all our knowledge regarding the co-existence of sensible qualities in objects, and the operations of bodies one upon another. Ivory, for instance, is hard and elast- ic ; this we know by experience, and indeed by that alone. P'or being altogether strangers to the true nature both of elasticity and hardness, we cannot, by the bare contemplation of our ideas, determine hew far the one necessarily implies the other, lor whether there may not be a repugnance between them. But when we observe them to exist both in the same ob- ject, 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 necessarily conjoin- ed, but may exist separately in diiTerent objects. In like manner, with regard to the operations of bodies, one upon another, it is evideTit, that our knowledge this way is all derived from obser-y-ation. .dqua regia dissolves gold, as has been found by frequent trial ; nor is there a.ny other vv'ay of arriving at the discove- ry. Naturalists may tell us, if they please, that the parts of aqua regia are of a texture apt to insinuate between the corpuscles of gold, and thereby loosen and shake them asunder. If this is a true account of
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the matter, I believe it will, notv/ithstanding, be al- lowed, that our conjecture, in regard to the conforma- tion of these bodies, is deduced from the experiment, and not the experiment from the conjecture. It was i>ot from, any previous knowledge of the intimate structure of ag-ua rsgia and gold, and the aptness of tlicir parts to act or be acted upon, that we came by the conchision above-mentioned. The internal con- btilULion of bodies is in a manner wholly unknov\m to us : and could v/e even surmount this diiiiculty, yet as the separation of the parts of gold imxplies some- thiii^ like an active force in the menstruum, and Ave c.re unable to conceive how it comes to be possessed of this activity ; the effect must be owned to be alto- gether beyond our comprehension. But when, re- peated trials had once coniirm.ed it, insomuch that it was admitted as an established truth in natural kno'^vl- edge, it was then easy for men to spin out theories of their own invention, and contrive such a structure of par;;s both [ovgold and agua regia, as would best serve to explain the phenomenon, upon the principles of tnat system of philosophy they had adopted. I mxight easily shovv^ from kinumeraole other instances, hov/ much our knowledge of the mutual action of bodies depends upon observation. The bite of a viper will hill. Plants are some sahitary, others noxious. Fire dissolves one body, and hardens another. These are truths generally knov/n ; nor is it less evident tliat v/e owe their discovery wholly to experience.
Sec. v.- — IVhy mamj use/id Lroentions o'-ive their Birth to Chance.
And hence it is easy to account for what to some wri»:ers lias appeared a very great paradox ; that ma- ny of the mobt important inventions in human life
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have taken their rise from chance, and instead of coming out of the schools of philosophers are for the most ascribed to men of no figure in the common- wealth of learning. Sowing, planting, the use of compass, and such like, are not deductions of human reason, but discoveries which ovve their birth to ob- servation and trial. No wonder, therefore, if these inventions derived their beginning from such, as, be- ing 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 original purely casual.
Sec. Yl.-^A'atura! Ktio^vledge^ from the Grounds on =<.^'iiich it rebts^ aptly termed expenmental Philosophy .
From Vv'hat lias been said, it is evident, that as in- tuition is the foundation cf what we call scientiftcal ■ knovvledge, so is experience of natural. For this last being wholly taken up with the objects of sense, or those bodies that constitute the natural Vv^orld — and their properties, as far as we can discover them, be- ing to "be traced only by a long and painful series cf observations ; it is apparent, that in order to im.prove tliis branch of knowledge, we must betake ourselves to the method cf trial and experiment. According- ly, v.'e find, that while this was neglected, little ad- vance was m.adein the philosophy of nature ; where- as a contrary proceeding has enriched the present age with many valuable discoveries ; insomuch that natural knovdedge, in allusion to the foundation on "which it stands, has been very aptly called expert- mental philosophy.
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Sec. VIL — Though much of our Knowledge of Body depends on Testimony^ yet Extierience is the ultimate Foundation of it.
But though experience is vvhat we may term the immediate foundation of natural knowledge, yet with respect to particular persons, its influence is very narrow and^ confined. The bodies that surround us are numerous ; many of them lie at a great distance ; and some quite beyond our reaci-u Life too is short, and so crowded with cares, that but little time is left for any single man to employ himself in