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THE
ELEMENTS OF LOGIC.
IN FOUR BOOKS.
THE
ELEMENTS OF LOGIC.
IN FOUR BOOKS.
BOOK I.
Of the Original of our Weas, their various Divisions, and the Manner in which they contribute to the Increase of Knowledge ; with a Philoso- phical Account of the Rise, Progress, and Nature of Hu- man Language.
BOOK 11. Of the grounds of Human Judg- ment, the Doctrine cf Propo- sitions, their Use in Reasoning, and division into Self-evident and Demonstrable.
BOOK III. Of Reasoning and Demonstra- tion, with their Apphcation to the Investigation of Know- ledge, and the common Af- fairs of Life.
BOOK IV.
Of the Methods of Invention and Science, where the seve- ral Degrees of Evidence are examined, the notion of Cer- tainty is fixed and stated, and the Parts of Knowledge in \vhich it may be attained de* monstrated at large.
DESIGNED PARTICULARLY FOR YOUNG GENTLEMEN AT
THE UNIVERSITY,
AND TO PREPARE THE Wa. TO THE STUDV OF PHlLOSOrHT
AND THE MATHEMATICS^
BY WILLIAM DUNCAN,
rROFESSOR OE rHI.OSOPHV IN THE MAKZSCHAL COLLEGE OP- ABERDEEN.
Doctrina sed Vim promovet insitam : Kectique cultus Pectora roborant. hor. "
A NEW EDITION.
EDINBURGH l
PRINTED FOR W. & J. DEAS,
BV ABERNETHY AND WALKER.
1807.
O^^R^^
U ''^i^ 13 1968
OF
BC
lOI
D7 I 207
TO
I
THE RIGHT HONOURABLE
STEPHEN POYNTZ, Esq.
I
I
SIR,
If I take this opportunity of publishing to the world the esteem I have for a cha- racter to which learning is so greatly in- debted, I hope you will not think yourself injured by such a declaration from a man that honours you, and who looks upon the liberty of putting the following work un- der your patronage, as one of the happy in- cidents of his life. •?
Yl DEmCATION.
From the first moment I formed the design of it, I had it in my thoughts to address it to you ; and indeed what could be more natural, than that I should be am- bitious of inscribing a treatise upon the elements 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 nn every kind, have deservedly recommended you to the_ no- tice of your king and country, and occa- sioned your being courted and importuned to accept of those high offices of state which others pursue with so much eager- ness, and find it often difficult to obtain, by all the arts and endeavours of ambi- tion. Nor have your talents been con- fined to the view of your own country- alone : — foreign nations have seen and •admired you, and still speak with the
DEDICATION, Vll
greatest applauses of your wise and able conduct, when it was your province to act as a British minister abroad.
But the qualities of a ^reat statesman are not those alone by which you have rendered yourself illustrious. The vir- tues of private life no less actuate and adorn your whole behaviour, and add a new dignity to the high station to which your merit has raised you. Affability, complacency of manners, and, above all, an extensive humanity and benevolence, Avhich takes pleasure in doing good, are distinguishing parts of your character, and have contributed no less than your other extraordinary endowments, to that universal acknowledgment which is paid you by your country.
That you may long live to be an x)rnament and blessing to the nation, and
!■
viii PEDICATION,
to enjoy the pleasure which arises from a consciousness of the esteem and approba- tion of all good men, is the sincere and hearty prayer of.
Sir,
Youf much obliged
and most obedient
humble Servant,
W. DUNCAN.
TiTE
ELEMENTS OF LOGia
INTRODUCTION.
I. Of all the human sciences, that con- n^poftance-of cerning man is certainly the most worthy the knowledge tA man, and' the most necessary part of ^^ o"^selves. knowledge. We find ourselves in this world surround- tjd 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 % right judgment of things> and shape our actions agree- ably to the circumstances in which we are placed. No study therefore is more important than that: whicli introduces us to the knowledge of ourselves. Hereby we become acquainted with the extent and capacity of the human mind j and learning to distinguish what ob- jects it is suited to, and in what manner it must pro- ceed, in order to compass its ends, we arrive by degrees at that justness and truth of understanding, v/hich i« the ^reat perfection of a rational being.
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Different o-rada- ^^' ^^ we look attentively Into tilings, tions of perfec- and survey them in their full extent, we ticn m things, ggg them rising one above another, in va- rious degrees of eminence. Among the inanimate parts of matter, some exhibit nothing worthy our at- tention ', their parts seem, as it were, jumbled together by mere chance ; nor can -M^e discover any beauty, order, or regularity in their composition. In others we discern the finest arrangement, and a certain ele- gance of contexture, that makes us affix to them a no- tion of worth and excellence. Thus, metals and pre- cious stones are conceived as far surpassing those un- formed masses of earth that lie every where exposed to view. If we trace Nature onward, and pursue her through the vegetable and anim^al kingdoms, we find her still multiplying her perfections, and rising, by a just gradation, from mere mechanism to perception, and from perception, in all its various degrees, to reason and understand Im?-.
Tr r 1 f ill But though reason be the boundary
culture, and by Vv^hich man IS distmguished from the piirticularly of other creatures that surround him, yet we rue study of ,^^.g £^^ from finding it the same in all. Nor is this inequality to be wholly ascribed to the original make of men's minds, or the difference of their natural endowments. For if we look abroad into the several nations of the world, some are over- run with ignorance and barbarity, others flourish in learning and the sciences ; and, what is yet more re- nrarkabie, the same people have, in different ages, been distinguished by these very opposite characters. It is therefore by culture, and a due application of the pov/eps of our minds, that we increase their capacity, and carry human reason to perfection. Wherever this method is followed, knowledge and strength of understanding never fail to ensue : where it is neglect- ed, we remain ignorant of our own worth ; and those latent qualities of. the soul, by which she is fitted to si.rvey this vast fabric o"^ the world, to scan the Hea^ V ns, and search into the causes of things, lie buried in
darkness and obscurity. No part of knowledge, there- fore, yields a fairer prospect of improvement th;m that which takes account of the understanding, examines ti'3 powers and faculties, and shews the ways by which it comes to attain its various notions of things. This is properly the des:ign of Logicy which may be justly styled the History of the Human Mind, inasmuch as it traces the progress of our knowledge, from cur first and simple perceptions, through all their diiTerent com- binations, and all those numerous deductions that re- suit from variously comparing them one with another. It is thus that we are let into the natural frame and contexture of our own minds, and learn in what man- ner we ought to conduct our tsioui^ihts, in order to ar- rive at truth and avoid error. We see how to build one discovery upon another, and by preserving the chain of reasoning uniform and unbroken, to pursue the relations of things through all their labyrinths and windings, and at length exhibit them to the view of the soul, with all the advantages pf light and convic- tion.
IV But as the understanding, in ad- Operations of vancing from one part of knowledge to the mind. one another, proceeds by a just gradation, and exerts various acts, according to the different progress it has made. Logicians have been careful to note these several steps, and have distinguished them in their writings by the name of the Operations of the Mind. These they make four in number, and, agreeably to that, have di- vided the whole system of Logic into four parts, in which these acts are severally explained, and the con- duct and procedure of the mind, in its different stages of improvement, regulated by proper rules and obser- vations. Now, in order to judge how far Logicians have followed nature in this distinction of the powers of the understanding, let us take a short view of the mind, and the manner of its progress, according to the experience we have of it in ourselves, and see whither the chain of our own thoughts will without constraint lead us.
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^eicepdcn. ^' First, then, we find ourselves sur-
rounded with a variety of objects, which, acting diiFerently on our senses, convey distinct im- pi'essions into the mind, and thereby rouse the atten- tion and notice of the understanding. By reflecting too on what passes within us, we become sensible of the operations of our own minds, and attend to them as a new set of impressions. But in all this there is only bare consciousness. The mind, without proceeding any farther, takes notice of the impressions that are made upon it, and views things in order, as they pre- sent themselves one after another. This attention of the understanding to the objects acting upon it, where- by it becomes sensible of the impressions they make, is called by Logicians Perception; and the notices them- selves, as they exist in the mind, and are there treasu- red up to be the materials of thinking and knowledge, are distinguished by the name of Ideas. - , VI. But the miind does not always rest
Judgment. • r ^ - ^ ^ • 1 ^ t
satisned m the bare view and contempla- tion of its ideas. It is of a more active and busy na- ture, and likes to be assembling them together, and comparing them one with another. In this complica- ted view of things, it readily discerns that some agree, and others disagree, and joins or separates them ac- cording to this perception. Thus, upon comparing the idea of two added to two, with the idea of four, we at first glance perceive their agreement, and there- upon pronounce that two and two are equal to four. Again, that white is not black, that five is less than seven, are truths to which we immediately assent, as soon as we compare those ideas together. This is the first and simplest act of the mind in determining the relations of things, when, by a bare attention to its own ideas, comparing any two of them together, 'it can at once see how far they are connected or disjoined. The knowledge thence derived, is called Intuitive^ as requiring no pains or examination ; and the act of the mind assembling its idea^ together, and joining or dis- joining them according to the result of its perceptions^ is what Logicians term Judgments
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VII. Intuition afFords the highest den;ree „ f. . . , , . . , *^ . ••It Reasoiiinc:.
or certainty j it breaks in with an irresistible *
light upon the understanding, and leaves no room for doubt or hesitation. Could we in all cases, by thus putting two ideas together, discern immediately their agreement or disagreement, we should be exempt from error, and all its fatal consequences. But it so happens, that many of our ideas are of such a nature, that they cannot be thus examined in concert, or by any imme- diate application one to another \ and then it becomes necessary to find out some other ideas that will admit of this application, that by means of them we may discover the agreement or disagreemient we search for. Thus, the mind wanting to know the agreement or disagreement in extent between two inclosed fields, which it cannot so put together as to discover their , equality or inequality by an immediate comparison, casts about for some intermediate idea, which, by br- ing applied first to the one, and then to the other, will discover the relation it is in quest of. Accordingly, it assumes some stated length, as a yard, &c. and mea- suring the fields, one after the other, comes by that means to the knowledge of the agreement or disagjree- ment in question. The intervening 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 discovery of rhe truths it is in search of, is what we term Reasoning. And here let it be observed, that the knowledge gained by reasoning, is a deduction from our intuitive perceptions, and uitim.itely founded on them. Thus, in the case before mentioned, having found by measuring, that one of the fields makes three- score square yardjj, and the other only fifty-five, we thence conclude that the first field is larger than the second. Here the two first perceptions are plainly intuitive, and gained by an imm.ediate application of , the measure of a yard to the two fields, one after another. The conclusion,, though it produces no less certain knowledge, yet difi^ers from the others in this, that it. IS not obtained by an immediate comparison of <-hc
J3a
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ideas contained in it one with another, but is a deduc- tion from the two preceding judgments, in which the ideas are severally compared with a third, and their relation thereby discovered. We see, therefore, that reasoning is a much more complicated act of the mind than simple judgment, and necessarily presupposes it, as being ultimately founded on the perceptions thence <;ained, and implying the various comparisons of them one with another. This is the great exercise of the Iiuman faculties, and the chief instrument by which M'e push on our discoveries, and enlarge our know- ledge. A quickness of mind to find out intermediate ideas, and apply them skilfully in determining the rela- tions of things, is one of the principal distinctions a- mong men, and that which gives some so remarkable a superiority over others, that we are apt to look upon them as creatures of another species. ., , , VIII. Thus far we have traced the progress
01 the mmd m thnikmg, and seen it rismg by natural and easy steps from its first and simple per- ceptions, to the exercise of its highest and most distin- guished faculty. Let U3 now view it in another light, as enriched with knowledge, and stored with a variety of discoveries, acquired by a due application of its na- * lural powers, it is obvious to consider it in these circumstances,, as taking a general survey of its whole stock of inteliectuai acquisitions, disposing them under certain heads and classes, and tying them togetlicr, according, to those connections and dependencies it. discerns between them. It often happens, in carrying oni our inrfuiries from subject to subject, that we stumble upon unexpected truths, and are encountered by discoveries, which our present train of thinking gave rio prospect of bringing in cur way, A man of. clear apprehension and distinct reason, who, after due- search and examination, has nrastered any part of know- ledge, aiid even made important discoveries in it, be-- yond what he at first expected, will not sulTer his- thoughts to lie jumbled toget^er in the same confused/ manner as chance offered them, he will be for com-!---
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binlng them into a regular system, where their mutual dependence may be easily traced, and the parts seem to grow one out of another. This is that operation of the mind, known by the name of Disposition or Method^ and comes in the last in order, according to the division of the Logicians, as presupposing some tolerable mea- sure of knowledge, before it can have an opportunity of exerting itself in any extensive degree.
IX. We see then that this fourfold dis- perception and tinction of the powers of the mind in per- judgment, ception, judgment, reasoning, and disposi- terms of a very
tion, as well as the order in which they are ^^^ensive sig-
, , , , ^ ... ^ nification.
placed, have a real foundation m nature,
and arise from the method and procedure of our own thoughts. It is true, there are many other actions and modifications of the understanding, besides those above mentioned, as believing, doubting, assenting, &c. but these are all implied iri the act of reasoning, in the like manner as comprehending, abstracting, remembering,, may be referred to the first operation of the mind, or perception. This will appear more fully in the sequel, when we come to handle the several parts of Logic se- parately : at present we shall content ourselves with this general account of things j only it seems necessary to observe, th:{t perception ^^nd Judgment y in the proprie- ty of the English tongue, have a much more extensive signification than Logicians commonly allow them. We not only perceive the ideas in our own minds, but we are said also to- perceive fheir agreement or disa- greement ; and hence arise the common phrases of intuitive perceptions, perceptions of truth, and of the justness of arguments or proofs ; w^here it is manifest that the word is applied not only to our judgments, but also to our reasonings. In a word, whatever comes under the view of the mind, so as to be distinctly re- presented and taken notice of, whether an idea, propo- sition, chain of reasoning, or the order and coiniection of things, is thereby rendered an object of perception, and gives employment to this first and most simple of our faculticGr la like manner, the word Judgment h
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seldom in common discourse confined to obvious and self-evident truths : It rather signifies those conjectures and guesses that we form, in cases which admit not of undoubted certainty, and where we are left to de- termine, by comparing the various probabilities of things^ Thus, a man of sagacity and penetration, who sees far Into the humours and passions of mankind, and seldom mistakes in the opinions he frames of characters and actions, is said to judge well, or think judiciously. For these reasons, it might not be improper to change the common names of the two first operations of the mind, calling the one Simple Apprehension^ and the other Intuition ; which two words seem better to ex- press their nature, and the manner in which they are conversant about their several objects. This accuracy ^of distinguishing, where there is any the least differ- ence, is in a peculiar m.anner necessary in a treatise of Logic, as it is the professed design of that science to teach us how to form clear and distinct notions of things, and thereby avoid being misled by their simili- tude or resemblance.
T . .• • 1 t X. Havlnfj thus given a general idea of Logic divided , ^ ^ . ^ . ^ . ,
into four parts, the four operations of tne mmd, and Its usefulness traced their connection and dependence and excellency, ^j-^^ upon another, I would next observe, that in consequence of this division of the powers of |:he understandiuij, Logic is also divided into four parts, which treat severally of these acts, and give rules and directio'.is for their' due conduct and regulation. The operations themselves we have from nature ; but how to exert tliem justly, and employ them with ad- vantage in the search of truth, is a knowledge that may be acquired by study and observation. It is certain that we meet with false reasonings as well as just. Some men are distinguished by an accuracy of think- ing, and a happy talent of unravelling and throwing light upon m.ost obscure and intricate subjects. Others confound the easiest speculations; their understand- ,ings seem to be formed awry, and they are incapable qI either conceiving clearly themselves^ or making, their
thoughts nitelHgible to others. If then we set our- seh'es carefully to observe what it is that makes the one succeed so well, and how the others come to mis- carry, these remarks will furnish us with an art of the highest use and excellency in the conduct of life. Now this is the precise business of Logic — to explain tlie nature of the human mind, and the proper manner of conducting its several powers, in order to the at- tainment of truth and know^ledge. It lays open those errors and mistakes we are apt, through inattention, to run into, and teaches us how to distinguish between truth, and what carries only the appearance of it. By this means we grow acquainted with the nature and force of the understanding, see what things lie within its reach, where we may attain certainty and demon- stration, and when we must be contented with bare probability. These considerations sufficiently evince the usefulness and benefit of the science, which ought to be established as the foundation and groundwork of all our other knowledge, if we really wish to succeed in our inquiries. But we sh'all now proceed to treat of its parts separately, according to the division given of them above*
THE
ELEMENTS OF LOGIC.
BOOK I.
OF SIMPLE APPREHENSION, OR PERCEPTION.
CHAP. I.
. OF THE ORIGINAL OF OUR IDEAS.
Simple appre- I, 1 HE first thing we observe, when we
idTaT" ^^^ ^^^^ ^ ^'^^' ^^ ^'^^^^ passes within us, is, that we are capable of receiving impres- sions from a variety of objects, that distinct notices are thereby conveyed into the understanding, and that we are conscious of their being there. This attention of the mind to the objects acting upon it, is what we call Simple Appi-eheiisioriy and is in fact the mind itself taking a view of things, as represented to it by its own consciousness. It is by this means that we come to be furnished with all those zV/^j" about which our thoughts are employed ; for, bein^g^ sensible of the impressions made upon us, and attending to the perceptions they bring, we can renew them again upon occasion,' even
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when the objects that first produced them are removed. Now our ideas are nothing else but these renewed representations of what we have at any time perceived and felt, by means of which things are again brought under the view of the mind, and seem to have a kind' of existence in it. It is true, we can upon many occa- tions combine our ideas variously together, and there- by form to ourselves representations of things that ne- ver had an existence in nature, as when we fancy a centaur or a golden mountain j but it is still certain, that the original ideas, out of which these are made, are such as have been conveyed into the mind by some former impressions. It lemiains therefore to inquire how we come by our first notions and perceptions of things. Whence does the understanding derive those original impressions and characters, which it can com- bine in so many different ways, and represent to itself under such infinite varieties? To this I answer, that if we attend carefully to what passes in our minds, we shall observe two inlets of knowledge ; from whence, as from two fountains, the understanding is supplied with all the materials of thinking.
II. First, outward oJDiects, acting upon ,,, „^ ...
' . *^j /* n r All our original
our senses, rouse m us a variety of percep- ideas derived ei- tions, according to the different manner in ther from sensa- whiich they affect us. It is thus that we ^^""' come by the ideas of light and darkness, heat and cold sv/eet and bitter, and all those other impressions which we term sensible qualities. This great source and in- let of knowledge is commonly distinguished by the name of Sensation, as comprehending all the notices conveyed into the mind, by impulses made upon the organs of sense.
III. But these ideas, numerous as they ^ „ .
,,,,., - . .^ Or reflection.
are, are wholly derived to us from v/ith-
out ; there is therefore yet another source of impres- sions, arising from the mind's attention to its own acts, when, turning inwards upon"^ itself, it takes a view of the perceptions that are lodged there, and the various ways in which it employs itself about them -, for the
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ideas furnished by the senses give the mind an oppor- tunity of exerting its Several povrers ; and as all our thoughts, under whatever form they appear, are attended with consciousness, hence, the impressions they leave, when v;'e come to turn the eye of the soul upon them, enrich the understanding with a new set of perceptions, no less distinct than those conveyed in by the senses. Thus it is that we get ideas of thinking, doubting, be- lieving, willing, &c. which are the different acts and workings of our minds, represented to us by our own consciousness. This second source of ideas is called Refection^ and evidently presupposes sensation, as the impressions it furnishes are only of the various powers of the understanding, employed about perceptions al- ready in the mind.
Rise and pro- ^ ' These considerations, if we duly gress of human attend to them, will give us a clear and knowledge. distinct view of the natural procedure of the human intellect, in its advances to knowledge. We can have no perception of the operations of our own minds, until they are exerted; nor can they be exerted before the understanding is furnished 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 human mind, that it is fitted to receive the impres- sions made upon it by outward objects affecting the senses \ which impressions thus derived into the under- standing, and there lodged for the view of the soul, em- ploy it in vartous acts of perceiving, remembering, con- sidering, &c. all which are attended with an inter*- nal feeling and consciousness. And this leads us to the second step the mind takes in its progress towards knowledge, viz. that it can by its own consciousness represent to itself these its several workings and ope- rations, and thereby furnish 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
IS
things, has a power of combining, modifying, and ex- amining them in :in infinite variety of lights, by which means it is enabled to enlarge the objects of its percep- tion, 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 aB 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 discovery to discovery, and often ex- tends 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 dawn- ings of perception, till it reaches the perfection of hu- man knowlrdge *, nor shall we, among all its vast stock of discoveries, or that infinite variety of conceptions whereof they consist, be able to find one original idea which is not derived from sensation or reflection, or one complex idea which is not made up of those ori- ginal ones.
V. Having thus shewn how the mind t^- • • r
, ^r r . , , • 1 • 1 Division of our
comes to be nrst lurnished with ideas, we ideas into sim-
shall next proceed to the consideration of pleandcom- the ideas themselves, and endeavour to give ^^^^' i^uch 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 con- veyed int6 the mind by sensation and reflection, and which exist there simple, uniform, and without any shadow of variety. \SecondIy, those more complex no- tions of things that result from the various combina- tions of our simple ideas, whether they are conceived to exist of themselves in any particular subject, or are •united and joined together by the mind enlarging its conceptions of things, and pursuing the ends and pur- poses of knowledge. These two classes comprehend our whole stock of ideas ; and, when considered se- parately in that order wherein they most naturallv 3«»ent
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t:^ offer themselves to our thoughts, will, I hope, fylVe such a view of the conduct and manner of the mind, as may contribute not a little to introduce us to an ac- t^uaintance with ourselves, and make us sensible of the capacity and extent of the human intellect. We pro- ceed therefore to a more particular account of this di- vision of our ideas.'
CHAP. II.
OF SIMPLE IDEAS.
Simple ideas, I. The first class of our ideas are those >^Ji^ which I distinguish by the name of Simple
I'erception •, because they exist in the mind under one uniform appearance, without variety or composition. For though external objects convey at once into the imderstanding many different ideas ..11 united together, and making, as it were, one whole, yet the impressions themselves are evidently distinct, and are conceived by the mind, each under a form peculiar to itself. Thus the ideas of colour, extension, and motion, may be taken in at one and the ^ame time from the same body ; yet these three perceptions are as distinct in themselves as if they all proceeded from different ob- jects, or were exhibited to our notice at different times. We are therefore carefuUy to distinguish between our simple and primitive conceptions, and those different combinations of them which are oftea suggested to the mind by single objects .tcting upon it. The first con- stitute our original notices of things, and are not dis- tinguishable into different ideas, b,ut 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 groundwork of our knowledge.
ri* Now it we take a survey of these simple ;de.;.5 cf ideas, and their several divisions and clas- sensation. ses, we shall find thexn all suggested to us either by our senses, or the attention of the mind to what passes within itself. Thus our notices of the different quu'l> tics of bodies, are all of the kind we call Simple Ideas, and may be reduced to five general heads, according to the several organs which- are affected by them. Co- lours, &c. and sounds, are conveyed in by the eyes and ears •, tastes and smells, by the nose and palate ; and heat, "cold, and solidity, ^c. by the touch. Besides these, there are others which make impressions on several of our senses j as extension, figure, rest, and motion-, &c. the ideas of wliich we recei\^e into ouc minds both by seeing and feeling.
Hi. If we next turn our view, upon simple Idea^ of what passes within ourselves, we shall find reflection, &:. another set of simple ideas arising from our conscious- ness of the acts' and operations of our own minds. Perception or thinking, and volition or - willing, are what every man experiences in himself, and cannot a-void being sensible of. I shail only observe ftinher^ that, besides all the above-mentioned perceptions, there are others that come into our minds-by all the ways of sensation and reflection : such are the ideas of pleasured and pain, power, existence, unity, succession, &c. which are derived into our understandings both by the action of objects without us, and the consciousness of what we feel within.: It is true, some of these ideas, as of extension and durtttion, cannot be conceived altogether without parts, nevertheless they are justly ranked a- mong our simple ideas j because their parts being all of the same kind, and without the mixture of any other idea, neither of them can be resolved into two distinct and separate conceptions. Thus the y still answer the definition given above, of being one uniform appear- ance in the mind, without variety or plurality. But to prevent confounding our simple ideas of space and duration with those complex modes of them marked out by the several measures commonly in use, as vardr,
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jniles, days, years, Sec. it maVj, perhaps, be most pro- per to consider the least portions of either whereof we can form a clear and distinct perception, as the simple ideas of that kind out of which all their other modes and combinations are formed. Such an instant, or point, may be conceived to be the same in respect of duration, or space, as unity is in respect of number ; and will serve best to shew how, by a continued addi- tion or repetition, our more enlarged and complex ideas are made up. c- 1 . J IV. Havinsr thus given a general view
Simple ideas . © *^t i n i
havenoadmis- Oi our sunple ideas, 1 have still two ob-
«toix,but by the servations to make concerning them. The proper inkts ot fj^g^ jg ^J^^^ ^.J^^y ^^q g^jj>}^ ^^ ^.^^i only be
convey e-d mto the mind by the proper channels and avenues provided by nature ; insomuch, that if we are destitute of any of those inlets, by which the impressions that produce them are wont to be ad- mitted, all the ideas thence arising are absolutely lost to us 5 nor can we, by any quickness of understanding, find a remedy for this want. A man born blisd is in- capable of the ideas of light and colours v in like mari- ner as one who is deaf can form no notion or concep- tion of sounds. Hence it appears, that these our sim- ple ideas are just such as nature has furnished them, and have no dependence on our will : we can neither destroy them nor invent any new one, not taken in by the ordinary means of perception. So that we here see the utmost bounds of human knowledge -, which, however mighty and enlarged, cannot exceed the limits of those our simple original ideas, and their various, combinations.
They furnish V. And this leads me to the second ob- ample materials servation I proposed to make, which is, of knowledge, ^j-^^^ though the mind cannot in multiply- ing its conception of things, advajice one step beyond the materials furnished it by sense and consciousness j yet as it has a power of combining, modifying, and enlarging them, in all the different ways in which they ^n be put together^ it therefore finds itself in posses-
\
sion of an inexliaustible treasure of Ideas, suflicient to employ It to the full extent of ail its powers, and fur- nish matter for all those various opinions, fancies, and views of things, that make up the subject of its thoughts and contemphtions. Let us but reflect upon the single idea of unity, or one, and observe what a variety of combinations are formed, by continually add- ing it to itself; insomuch, that the understanding finds no stop or boundary in its progress from number to number. In what aa infinity of. different lights may extension alone be considered 1 What limits can be set to that endless diversity of figures, -which it is in the power of the imagination to fashion and represent to itself! If. to these we add those numberless ether combinations that result from variously compounding and comparing the rest of our simple ideas, we shall have little reason to complain of being limited to a scanty measure of knowledge, or that the exercise of the human faculties is confined within, narrow bound>. But having traced the progress of the mind through its original and simple ideas until it begins to enlarge its conceptions by uniting and tying them together, it is now time to take a survey of it as thus employed in multiplying its views, that we may see by what steps it advances from one :degree of improvement to ano- ther, and how it contrives to manage that infinite stock of materials it finds itself possessqd of.
VI. Whoever attentively considers his The division of own thoughts, and takes a view of the se- complex ideas veral complicated ideas that from time to ^^to those of •
rr 1 1 1 • 1 1 real existences,
time otter themseLves to his understand- and those fram- ing, will readily observe that many of them ed by the mind. are such as have been derived from without, and su^^- gested by different objects affecting his perception ; others again are formed by the mind itself, variously combining its simple ideas, as seems best to answer those ends and purposes it has for the present in view. Of the first kind are all our ideas of substance *, as of a man, a horse, a stone, gold. Of the second ar^: those arbitrary collections of things which we on many
IB
occrvSions put together, either for their iisefuhicss in the commerce of life, or to further the pursuit of knowledge : such are our ideas of stated lengths, whe- ther of duration or space •, as hours, months, miles, h'agues, Sec. which divisions are apparently the crea- tures of the mind, inasmuch as we often find them different in diiFerent 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 nlso referred to this head •, as treason, incest, man- vlauglitcr, $cc.; which com^plex notions we do not al- ways derive from an actual view of what these words describe, but often from combining the circumstances of them in our minds, or, which is the most usual way, by hearing tlieir names explained, and the ideas they stand for enumerated. These two classes com- prelicnd 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 compounding its ideas. "We shall treat of each in order.
CHAP. III.
OF OUR IDEAS OF SUBSTANCES.
ideas of sub- I. The first head of complex idea^,
stances, coUec- mentioned in the foregoing chapter, is that M^^^/h^ld"^^^ of substances, which I choose to handle ietherbysome before the Other, because, as will after- unknown sup- wards appear, the notices derived from port. xhiQ source very much help us in forming
those arbitrary collections which make up the second division. For in many of them we take our hints from the reality of things, and combine ideas that actually exist together, though often with an exclusion of others, as will be explained when we come to treat ©f abstract and universal notions. It has been already
A
19
observed, that tlie impressions conveyed Into the under- standing from external objects, consist for the most part of many different ideas joined together, which all unite to make up one whole. These collections of various ideas, thus co-existing in the same cornmon , subject, and held together by some unknown bond of union, Iiavebeen distinguished by the nzmQoisubstaJices ; a word which implies their subsisting of themselves, without dependence (at least as far as our knowledge reaches) on any other created beings. Such are the ideas we have of gold, iron, water, a man, &c. For if we fix upon any one of these, for instance gold, the notion under which we represent it to ourselves is that of a body yellow, very weighty* hard, fusible, mallea- ble, &c. ; where we may observe, that the several pro- perties that go to the composition of gold, are repre- sented to us by clear and evident perceptions j the union too of these properties, and their thereby con- stituting a distinct species of body, is clearly appre- hended by the mind : but when we would push our inquiries farther, and know wherein this union consists, what holds the properties together, and gives tl"kem their self-subsistence, here w^e find ourselves at a loss. However, as we cannot conceive qualities, without at the same time supposing some object in which they adhere, hence we are naturally led to form the notion of a support, which serving as a foundation for the co- existence and union of the different properties of things, gives them that separate and independent existence under which they are represented to our conception. This support we denote by the name substance ; and as it is an idea applicable to all the different combina- tions of qualities that exist anywhere by themselves, they are accordingly all called substances. Thus a house, a bowl, a stone, &c. having each their distin- guishing properties, and being conceived to exist inde- pendent one of another, the idea of substance belongs alike to them all.
120
The division of ^^' ^" substances therefore there are two modes into things to be Considered : First, the gene- essential and ral notion of self-subsistence, which, as I accidental. have said, belongs equally to them all ; and then the several qualities, or properties, ,by which the different kinds and individuals are distinguished one from another. These qualities are otherwise call- ed modes, and have been distinguished into essential and accidental, according as they are perceived to be separable or inseparable from the subject to which they belong. Extension and solidity are essential modes of a stone, because it cannot be conceived without them ; but roundness is only an accidental mode, as a stone may exist under any shape or figure, and yet still retain its nature and other properties.
^,, . c III. I might run farther into these divi- 1 he notion of . ,>=?,... . ,.,,..
self-subsistence sions ana sub-diVisions, m which logicians
inseparable have been very fertile ; but as tlicy tend from substan- i^fj-|^ ^q ♦■he advancement of real know- ledge, and serve rather to fill the memory with words and their significations than furnish clear and distinct apprehensions of things, I shall not trou- ble the reader with them. It is more material to ob- serve, that the change of properties, in any substance, though it oftentimes changes the nature of that sub- stance, that is, its species or kind ; yet it never de- stroys the general notion of self-subsistence, but leaves that equally clear and applicable as before any such alteration happened. Wood by the application of fire is turned into charcoal ; but charcoal, however differ- ent from wood, is still a substance. In like manner, wax may be converted into iiame and smoke,, a human body will moulder into dust, yet these alterations de- stroy not their being or existence j they are still sub- stances as before, though under a different form and appearance. In the several experiments made by che- mists, bodies undergo many changes, and put on suc- cessively 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 primitive form. What
21
alteration can we suppose the fire, or the applicatiofi of any other body, to make, unless on the configura- tion, texture, or cohesion of the minute parts ? When these are changed, the body is proportionably changed j when they return to their original state, the body like- wise puts on its first and natural appearance.
IV. All that is essential to matter there- foundation of fore, is the cohesion of solid extended the different parts ; but as these parts are capable of species of cor- innumerable confisjurations ; as their tex- P^^^^^ ^^°' ture may be very various, the internal constitution thence arising be of consequence extreme- ly different in different bodies, we may from these con- siderations conceive pretty clearly the source and foun- dation of all the different species of corporeal substan- ces. Nor is this a notion taken up at random, or one of those chimerical fancies in philosophy, derived ra- ther from a warmth and liveliness of imagination, than observations drawn from things themselves. Do we not daily see our food, by the changes it undergoes in the different avenues of the body, converted first into blood, and thence employed in nourisliing, building up, and enlargirig the several parts of that wonderful fa- bric ? Rain descending from the clouds, and mixing with the mould or earth of a garden, becomes aliment for trees of various kinds, puts on a diversity of forms, according to the different channels and conveyances through which it passes ; and at last, after innumera- ble clianges and transmutations, sprouts forth in leaves, opens in buds, or is converted into the substance of the tree Itself, Can we conceive any greater differ- ence between the component parts of gold and those of stone, than between the moistened particles of gar-e den-mould and those new forms and figures under which they appear, after they have been thus fashion- ed by nature, for the purposes of growth and nourish-* ment ?
22
1-s.cncootsub. V- ^^ ^^^'^ b- ^"^y attended to, it wilf stances nothing not appear wonderful to assert, that the but the internal variety of material substances arises wholly structure and f^Q^^ ^^g different configurations, size, constitution. , . r i •
texture, and motion or the mmute parts.
As these happen to be variously combined, and knit together 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 consti- tution or structure of parts, from which the several properties that distinguish any substance flow, is call- ed the essence of that substance, and is in fact un- known to us, any farther than by the perceivable im- pressions it makes upon the organs of sense* Gold, as has been said, is a body yeilow, very weighty, hard, fusible, malleable, Sec. Tiiat inward structure and con- formation of it-^ minute particles, bywhich they are sa closely linked together, and from which the properties above mentioned are conceived to flow, is called iti essence •, and the properties themselves are the percei- vable marks that make it known to us, and distinguish it from all other substances ; for our senses are not acute enough to reach its inward texture and constitu- tion. The parts themselves, as well as their arrange- ment, lie far beyond the utmost penetration of human sight, even when assisted by microscopes, and all tha other contrivances of art.
T^ , ,, VI. Thus, as to the essence or internal
Is wholls' un- • • r 1 1 1 »i • 1
known to us, Constitution of gold, we are wholly in the
nor serves to dark ; but many of the properties derived distinguish the f^Qj^ ^Yi[^ essence, make obvious and dis- species. . , . . -Ill
tinct impressions, as the weight, hardness,.
and yellow colour, &c. These properties combined to- gether, and conceived as co-existing in the same com- mon subject, make up our complex idea of gold. The same may be said of all the other species of corporeal substances; as lead, glass, water, &c. our ideas of them being nothing else but a collection of the ordi- nary qualities observed in them.
23
VII. This however ought to be obscr- y^^ j^ rio-KtIy ved, that though the essence or in ward struc- presumed to be ture of bodies is altogether unknown to us, distinct in all yet we rightly judge, that, in Till the several ^^^j^^^^^*^ species, the essences are distinct. For each species being a collection of properties, which^ taken together, are different from those of every other species, the conformation of parts, on which these pro- perties depend, must in like manner be different y and this, as we have said, constitutes the essence. Iron and glass are evidently distinct kinds of body ; tlieir perceivable qualities have little or nothing common ; and therefore the Inward structure or constitution from which these qualities flow, cannot be the same in both. But after all, this is the only thing we can with cer- tainty affirm concerning these essences, which lying so wholly in the dark, we shall do well to lay them aside in our reasonings about things, and stick to those more intelligible and settled ideas got by joining together their various properties and powers. For thus onlv is true knowledge promoted, when we argue from known qualities, and not from a supposed internal constitu- tion,'which, however real in itself, yet comes not with- in the reach of our faculties, and therefore can never be a ground to us for any discoveries or improvements.
VIII. Material substance, as I have said, - , , , J 1-1 r Til- ^y ^v"^t steps
mciuaes the idea or solid, cohering, ex- we arrive at
tended parts, and is divided into different the notions of
classes, according to the different impres- "^|"^''^teriul
I ■ ^1 r substances;
sions made upon the organs of sense. But, besides these sensible ideas received from with- out, we also experience in ourselves thinking and volition. These actions have no connection with the known properties of body ; nay, they seem plainly in- consistent with some of its most essential qualities. For the mind not only discovers no relation between thinking and the motion or arrangement of parts but it also perceives that consciousness, a simple Indi- vidual act, can never proceed from a compounded substance, capable of being divided into manv. I,ot
24
us suppose, for instance, a system of matter endowed with thought *, then cither all the parts of which this system is composed must think, which would make it not one but a multitude of distinct conscious beings ; or its power of thinking must arise from tlie connec- tion of the parts one with another, their motion and disposition, &c. which, all taken together, contribute to the production of thought. But it is evident that the motion of parts, and manner of combining them, can produce nothing but an artful structure, and vari- ous modes of motion. All machines of human com- position, as watches, clocks, &c. however artfully their parts are set together, however complicated their structure ; though we conceive innumerable different motions, variously conjoined, and running one into another with an endless diversity, yet never produce ;».ny thing but figure and motion. If a clock tells the hour and minute of the day, it is only by the motion of the different hands, pointing successively at the fi- gures marked on the hour-plate for that purpose. We never imagine this to be the effect of thought or in- telligence •, nor conceive it possible, by any refinement of structure, so to improve the composition, as that it shall become capable of knowledge and consciousness. The reason is plain : thought is something altogether different from motion and figure *, thore is not the least connection between them ; and therefore it can never be supposed to result from them, which we o- ^^' This then being evident, that intel-
thervvise call ligence cannot arise from an union or spirits. combination of unintelligible 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 a multitude of distinct conscious beings. And because matter, how far soever we pursue the minuteness of its parts, is still capable of repeated divisions, even to infinity, it is plain that this absurdity will follow us through all tbe suppositions that make thought inherent in a ma-
25
t-erial substance. Finding, therefore, conscidusness in- compatible with tlie cohesion of soUd separable parts, we are necessarily led to place it in some other sub- stance of a distinct nature and properties, which we call J pi r it.
X. And here It is carefully to be ob- cody and spi- ser\*ed, that the several species oi corporeal rit distinct sub- substance;, though distinguished one from stances, another, and ranked under different names, yet, agree- ing in some common properties, which, taken together., make up the notion of body, are thence ail conceived to partake of this general nature, and to differ only as different modifications of the same substance. What- ever consists of solid extended parts, is called Mat- ter.; and as all the various species of body, however distinguished from one another by their several pro- perties, have yet this in common, that they are made up of such solid separable parts *, hence they fall na- turally under the general denomination of material beings, and are not Conceived to differ but in their form. Thus gold, antimony, wood, .&c. alike partake of the notion of body : they are all equally material substances, and have no other difference but what arises from the different strictudre and cqnformation, &c. of parts, as v/e have shewn above. But spirit is •something altogether distinct from body ; na,y, and commonly placed in opposition to it ; for which rea- son, the beings of this class are called immaterial : a •word that implies not any thing of their nature, but merely denotes its contrariety to that of m:.tter,
XI. Body and spirit, therefore, differ ^-^^^ , not as species of the same substance, but many various are really distinct kinds of substances, and species of sub- serve as general heads, under which to ^^^"5, beiides Tank all the particular beings that fall come within within the compass of our knowledge, the reach of For we, having no ways of perception but °^^ faculties, -sense and consciousness, can have no notices of things
but as derived from these two inlets. By our senses we are informed of the existence of solid e\t^>nded
D
26
substances ; and reflection tells us that there are think- ing con-^cious ones. Beyond these, our conceptions reach not j and therefore, though there may be many other kinds as diiTerent from them as they are from om another, yet having no faculties suited to them, they are as remote from our knowledge as light and colours from tiie apprehension of a man born blind.. I believe it will hardly be doubted but the substance of the Creator differs more from that of his creatures than any two created substances can from one ano- ther ; and therefore, when we call God a spirit, we ought not rashly to presume that he is so in the same fense in which the human soul is a spirit. The word is indeed used by us, to denote in general all thinking intelligent substances ; in which sense God is very fitly called a spirit. But it were the height of folly to ima- gine, because this name is applied as well to the mind of rtian as the Creator, that therefore they partake of one common nature, and differ only as different mo- difications of the same substance. This I mention here, to check the presumption of the human mind, al- ways forward to conclude that every thing comes with- in its reach, and to deny existence to whatever exceeds the comprehension of its scanty and limited powers. Beings of a superior class, may enjoy many ways of percepvion 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 we apply to body. Solid and thinking beings are, it is true, the on- ly ideas of substance that we are able to frame; but this is no more an argument against the existence of other kinds, than the want of the ideas of light and colours in a blind man would be a good argument against the reality or possibility of such perceptions.
XII. Before I dismiss this subject, it Difference in |^ improper to take notice of a
the manner of ^ , ,, ,.rr i r
conceiving cor- Temarkable ditterence as to the manner ot poreal and spi- eur coucciving corporeal and spiritual sub- ritual substan. g^^j-j^es. Those cf the first kind convey "^* themselves into the mind, by impressions
made upon the organs of sense; and as these impressions
27 are different in different bodies, the ideas they produce Riust of course vary ni proportion. Thus we get percep- tions of distinct powers and properties, und ran^i^e todies into classes according as we find them to ;igree or disagree in these 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 camiot ascribe to them properties, or ways of knowledge, distinct from those suggested to us by our own consciousness. And hence it is, that though we readily own there may be various ranks of spiritual beings, yet we are not to imagine them divided from one another by any diver- sity of powers and operations, but merely by possess- ing the same powers, &c. in a higher or lower degree. It is not, however, repugnant to reason that they should be distinguished by their several properties, in like manner as sensible things are by the different qualities observable in them ; but properties of intellectual na- tures, distinct from those of our own minds, being al- together remote from our conception, cannot serve us as a means whereby to distinguish their diff*eren^ orders. We are therefore necessitated to conceive of them in a manner suited to our way of knowledge ; and when we would rank them into species, according to the de- grees of superiority they are imagined to possess in the scale of being, we ascribe to them what we find most excellent in ourse-ves, as knowledge, thinking, fore- siglu, Sec. ; and those in different measures proportion- ed to the station peculiar to each rank or species. But that this is a very imperfect way of distinguishing the ViH'ious orders of intellectual beings, will not, I think, need many words to make appear ; especially, if we consider that the manner of communicating our thoughts without the intervention of bodily organs, is a thing to us altogether incomprehensible, and neces- sarily leads us to suppose, that they have ways of per- ception and knowledge which our faculties cannot give us any notice of.
D2
'28 ^. , , , XIII. But I shall not pursue these re-
xtit bounds of . ,• i i_ i r • , r
knowledge in nectioiis larther ; what has been said suf-
our present ficjng to give US some Httle insight into state very nar- ^j^g extent and capacity of our own minds ; to convince us that our present state will not admit of a perfect and adequate comprehension of things 5 and to let us see that there may be other ways of knowledge, beyond the reach of the faculties, we now enjoy j which yet, in succeeding stages of our existence, we may arrive at, when being freed from the present cumbersome Joad of the body, we shall mount up to stations of greater eminence, and advance by a perpetual series of approaches towards him who is the standard of perfection and happiness.
CHAP. IV.
OF IDExIS FRAMED BY THE MIND.
in framing !• HiTHERTo we have considered only many complex such combinations of our simple ideas as ideas, the mmd j^^ye a real union in nature, and are sug- tive and pro- g^sted to the mind by things themselves ceedsbyavo- variously affecting our perception *, it is luntary choice, now time to take a view of the other class of our complex notions *, I mean those arbitrary col- lections of different ideas which we on many occasions bring together, by that power which we find in our- selves, 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 corre- spond to the impressions made upon it. When v/e see a house or a tree, they necessarily appear each un- der its proper form y nor is it in our power to receive from these objects other ideas than what they are fit-
2^
ted to produce. But in this second class of complex conceptions, the mind acts voluntarily and of choice j it combines only such ideas as are supposed best to suit its present purpose ; and alters or changes these combinations, by inserting some and throwing out o- thers, according as the circumstances of things require their being viewed in different lights. New, as this is by far the most comprehensive branch of our ideas, and includes those that most frequently occur in the search and pursuit of knowledge, I shall endeavour to treat of them in the exactest order and method ; and for that purpose range them under several heads, ac- cording: to the different acts of the mind> exerted in framing and putting them together.
ir. These acts may in tlie general be Three several all reduced to three. 1. Composition ^ when acts exerted by we join many sim.ple ideas together, and ^^^ ^^^"^^i jn
■?, , '. ^ . £3' rraniiDff its ar-
consider them as one picture or represen- bitrarv idea? tation. Such are.our ideas of beauty, gra- viz. composi- - titude^ a furlong, &c. Ami here let it be ^'^"> obser\'ed, that the mind sometimes confines itself to the various, considerations of the same idea, and,, by enlarging it in different degrees, exhibits.it under a diversity of forms. Thus, by adding units together, in distinct separate collections, we come by all the se- veral 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 rhe idea itself becomes of course more complicnted. Harmony, for instance, is a compound idea, made up of many different Sounds united ; all which the musician must have, and put together in his mind, before the ear can be entertained with the actual performance. Now, although the act of the mind is in some measure exerted in the framing of all our com- plex notions, yet as m.any of them include certain limit- ed and particular considerations, arising from other operations of the mind employed about them, it is ne* c^ssary to take account of these acts also, if we would
D3
30
conceive clearly the manner in which the several spe» cies of cur compound ideas are formed.
abstraction ^^^' ^' "^^^ ^^^^ operation therefore of
the mind, about its ideas, is ahstraciiofi, when WQ separate from any of our conceptions all those circumstances that render it particular, or the represen- tative of a single determinate object *, by whicii means, jjj instead of standing for an individual, it is made to de- " note a whole rank or class of things. Thus upon see- ing, for instance, a square, or circle, we leave out the consideration of their bulk, and every thing else pecu- liar to them, as they immediately affect our sight, re- taining only the notion of their figure and shape. In this manner we get our gefieral ideas •, for such naked appearances, separated from the circumstances of time, place, &:c. serve the mind as standards by which to rank and denominate particular objects. When, there- fore, Vv'e meet with a figure answering to that shape and form we had laid up in our understandings, it is immediately referred by the mind to this pattern, and called t>y its name j which, by this means, becomes proper to the whole species. Thus, a squar'e or circle are universal terms, common to all figures of that par- ticular shape, and alike applicable to them wherever they exist ; in like manner, as the ideas themselves are general, and representatives of all of the kind.
IV. 3. The third and last act of the son ^' ^^"^ about its ideas, is the cojnparing them
one with another, when we carry our con- sideration of things beyond the objects themselves, and examine their respects and correspondences in refer- ence to other things, which the mind brings into view at the same time. It is thus we get all our ideas of \ relations, as of greater, less, older, younger, father, son, I and innumerable others. This threefold view of our ideas, as either compounded of many others put to- gether, or made universal by the abstraction of the mind, or as representing the various relations and ha- bitudes of things, will give us an opportunity of ob* •serving whatever ip most curious and useful in this
31
fundamental branch of knowledge, and of explaining the manner and procedure of the understanding in en- larging its views, and multiplying the objects of per- ception. That .we may therefore conceive of this mat- ter with the greater order and clearness, we shall make each of these several ideas the subject of a dis- tinct section.
Sect. I. — of compound ideas.
I. We begin therefore with those ideas,
which may be properly termed compound, ^l^r^^^x6.tv^ as being derived from that power the mind ed, here mere- has of unitmg many conceptions into one. iy ^^ combina-
ThouLrh this class comprehends, in some ^Jons of the un-
c' i .. ' derstandmg.
sort, all our complex notions, yet they are
at present considered merely as they are combinations of the understanding, and with a view to those parti- cular ideas out of which they are framed. Here, as was already observed, the mind sometimes proceeds by enlarging and diversifying the same idea ; at other times it brings together ideas of djfFerent kinds j and in both ways finds infinite scope and variety. But that we may follow the natural procedure of the intel- lect, and trace it in its advances from simple to more 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^ manage- ment, and contrivance, as will appear perfectly aston- ishing to one who has never set himself seriously to consider the manner and conduct of his own mind.
II. The most obvious and simple idea .t • ,
, . 1 r • In 1 1 Unity the on-
wenave, is that oi tiniiijy or otie, J3y.add- ginai founda-
ing it to itself contniually, and retaining tion of all our the several collections in our minds, we "ieasofnum- come by all the different combinations of numbers^ in which we xeadily perceive an endless di- versity. All these, ideas; arjp: nevertheless evidently. dis-
32
tinct among themselves, the addition of a single unit constituting a number as clearly different 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 beginnmg with the origi- nal idea itself, pursues 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 seve- ral successive collections are distinguished by particular names.
The artful H^- And here we may take notice of a
composition of wonderful artifice, made use of by the the nnmes of ^nij-jd ^q facilitate and help it forward in it^
numbers, a . t-' i i r
great help to Conceptions. . ror as the advance irom our concep- number to number is endless,^ were they ^»<?"si all to be distinguished by different deno-
minations that had no connection or dependence one upon another, the multitude of them must soon over- charge the memory, and render it impossible for us to go any great way in the progress of numbering. For : this reason it is so contrived, 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 same terms, variously compounded and linked together. Thus thirteen is ten and three, fourteen ten and four, and so on to tiueiityy or two tens, when we begin again with one, two, &c. until we advance to thirty^ or three tens. In this manner the progression continues ; and when we arrive at ten tens, to prevent confusion by a too frequent repetition of the same word, that sum is distinguished by the name of an Hmtdred, Again, ten hundred is called a Thousand, at which pe- riod the computation begins anew, running through all the former combinations, as ten thousand, an hun- dred thousand, ten hundred thousand j which last col- lection, for the reasons mentioned above, has the name of a Million appropriated to it. With this million v/e
can begin as before, until it is repeated a million of times ; when, if we change the denomination to Bil- lionsy and advancs in the same manner through 7V/7-> lionsy QiiartiUionsy the series may be carried on, with- out confusion, to any length we please.
IV. This artful combination of names, and one of the to mark the eradual increase of numbers, principal is perhaps one of the greatest refinements ^^^sons that
r -i y 1 t 1 • our ideas ot
or the human understandmg, and particu- numbers are larly deserves our admiration for the man- so remarkably ner of the composition •, the se^^eral deno- distinct, minations being so contrived, as to distinguish exactly the stages of the progression, and point out their dis- tance from the beginning of the series. By this means it happens that our ideas of numbers are, of all others, the most accurate and distinct; nor does the multitude of units assembled together, in the least puzzle or confound the understanding. It is indeed amazing, that the mind of man, so limited and narrow in its views, should yet here seem to shake ofF its natural, weakness, and discover a capacity of managing with ease the most bulky and formidable collections. If we inquire particularly Into the reason of t'lis, we shall find it wholly owing to the address of tha mind, in thus distinguishing numbers by different names, ac- cording to the natural order or progression ; for as those names are made to grow one out of another, they may be aptly compared to a chain, all of whose parts are linked together by an obvious and visi- ble connection. Hence it comes to pass, that when, we fix our thoughts upon any number, however great and seemingly unmanageable •,. yet, if it is once deter- mined to a particular name, we find it easy to run back through all the stages of the progression, even till we arrive at unity itself. By this means we see, with a single glance of our minds, not only the two extremes of the number under consideration, but also the several intermediate parts, as they are united to make up the whole.
34
As they help us . ^' ^^^ '^ ^^ ^^ this dear and accurate to a clear per- view of the interjacent ideas, that we owe -ception of the our SO distinct perception of the various fnterjiccnt combinations of numbers. And indeed we may observe in the general, that all our ideas of quantity, especially when they grow to be very large, are no otherwise ascertained than by that perception we have of the intervening parts, lying, if I may so saV) between the extremes. When we look at an object considerably dist mt 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 knowledge of the intervening spaces, we should pretend to judge of the distance of objects, as when we see the spire of a steeple behind a wall, or beyond a mountain, every one*s experience is a proof how liable we are, in these cases, to be deceived. Just so it is in judging of duration. When we carry back our thoughts to any past period of our lives, without consideration of the number of years or months, we find that our idea of the time elapsed, grows more dis- tinct in proportion as we become sensible of the inter- mediate 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 mind brings new periods of life into view.
Without ^^' ^^^^" ^^ ^^^^^ ^^ ^^^y ^^ conceive
names, we can- how much the mind is helped forward in not make any its perception of number, by the ready progress in comprehension of all the several stages in ^* a progression, which peculiarly belongs to ideas of this class. But this, as I have before intima- ted, we derive from the orderly series and connection of names •, insomuch, that where they cease, the com- putation of numbers also ceases with them. We can have no idea of any sum, without a knowledge of all the terms that go before, according to the natural order in which they follow one another •, so that he |
who cannot, in a regular way, count to nineiy-nlne, will never, while that incapacity continues, be able to form the idea of an hundred, because the chain that holds the parts together, is to him wholly unservice- able, nor can he represent to his mind the several in- terjacent combinations, without which it is impossible in this case to arrive at a distinct perception,
VII. I have insisted the more largely upon this, not only because it is by num- vamag^s^lf ad- ber that we measure all other things, as dress in class- duration, extension, motion, &c. but also »ng our com- because it lets us into the most natural [|Jj*j^g^*^"^*^^" view of the conduct and procedure of the understanding, and makes us sensible of the great art and address that is necessary in the classing our very complex conceptions. He that can so put together the component parts of an idea, as that they shall lie ob- vious to the notice of the mind, and present them- selves, when occasion requires, in a just and orderly connection, will not find it very difficult to obtain clear and accurate perceptions in most of those subjects a- bout which our thoughts are conversant ; for the great ^rt of knowledge lies in managing with skill the capa- city of 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 per- plexing them with considerations remote from the business in hand. When. ideas become very complex, and by the multiplicity of their parts grow too unwieldy to be dealt with in the lump, we must Ciise the view of the mind, by taking them to pieces, and setting be- fore it the several portions separately, one after ano- ther. By this leisurely survey we are enabled to take in the whole j and if we can draw it into such an orderly combination as will naturally lead the attention, step by step, in any succeeding consideration of the same idea, we shall ever have it at command, and with a single glance of thought be able to run over ail its parts. I have therefore explained here, at some length, the conduct of the mind in numbering j it seeming t»
36
vf\e the best model In this kind, whetlier we consider the many advantages derived from such an orderly dis- position of our ideas, or the great art and skill display- ed in binding these ideas together. This also is far- ther remirkable in the consideration of number, that from it chiefly we derive the notion we have of infi?iity ; it being apparent that in adding number to number there is no end •, the possibility of doubling, or in- creasing our stock in any degree, remaining as obvious to the understanding, after a great and contiimed run of progressions, as when it first began the computa- tion.
The consider- VIIT. If we now tum our thoughts to- ation of num- wards space and duration^ here tc»o we shali ber, of great ^^^ ^j^^j. ^g y^j. seldom arrive at clear taining our ^"^ distinct ideas of either, but when we ideas of space introduce the consideration of number, and duration, npj^g more 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 cer- tain stated measures, by which precisely to determine the quantity in each. Thus inches, feet, yards, miles, &c. ascertain our ideas of extension ; as minutes, hours, days, years, &c. measure the progress of dura- tion. The lesser parts, as lying most open to the notice of the understanding, and being more on a level with its powers, are retained with tolerable exactness ; ahd the larger portions, when the number of repetitions of which they are made up is known, are thereby also reduced into clear and determinate conceptions. A •foot and yard are measures easily comprehended by ■the mind *, nor do we find any difficulty in conceiving a mile, when we consider it as equal to a certain num- ber of yards. If we are stilj for increasing the stand- ard, we may take the semidiameter of the earth, and supposing it equal to 8000 miles, make use of it as a measure by which to ascertain the distance of the sun or fixed stars. Just so it is in duration ; fyom. hours -M^e rise to days, months, and years *, by these repeated^
37
^nd added together, we measure time past, or can run forward at pleasure into futurity, and that without any confusion or perplexity.
IX. It is however to number alone that
, • J . • ^ r ^- • ^v ithout it,
we owe this distnictness ot perception, m- ^,^^^. ^^^ ' ^^ asmuch as space and time, considered degenerate in-, apart from the regular and orderly repeti- f^ a confused tion of miles or years, leave to determinate ^" ' ^^^^S^^^^ impressions in the mind, by which to know and distinguish their several portions. Ideas of either, thus taken in at a venture, are a confused and irregular heap, especially where we endeavour to en- large and magnify our views, and give full play to the powers of the intellect. Something indeed the mind conceives vast and mighty, but nothing that is precise, accurate, and just. But when it begins to consider these ideas as made up of parts, and fixing upon such ' as are proportioned to Its reach, sets itself to examine how often they are repeated to make up the whole, the perceptions of the understanding put on a new form, and discover their exact bounds and limits.
X. And thus, as before in number, so , r •
- . . , , . 1-1 Infamty aa
tiere m extension and duration, the mind object 'too
begins with simple and obvious notices, mighty for the
advancinp[ by degrees to more enlarged f^^^^Y of the i ■ ^ ,. ^ ° ,• A 1 human mind.
andx intricate conceptions. A day, or a
furlong, are of easy apprehension to the understand- ing -, and by their subdivisions Into still lesser spaces, exhibit themselves distinctly in all their parts. With these variously repeated, we ^travel tlirough space and time ; so that being able to reduce all our ideas of this class, however mighty and enlarged, to the cl^ar and determinate perceptions of number, we can conduct our thoughts without perplexity, and never find our- selves puzzled but when, presuming too much on our own strength, we launch into speculations that stretch beyond the powers of the human intellect. Number may be compared to a line, that, setting out from uni- ty, runs on in a continued increase of length, without a possibility of ever arriving at its ultimate period..
E
bo far as \re pursue it in our thoughts, and trn-ce its regular advances, so fir our ideas are accurate and just. But when we let loose our understandiniis after a boundless remainder, and would fathom the depth of infinity, we find ourselves lost amidst the greatness of our own conceptions. Some notions, it is true, we have, but such as, exceeding the dimensions of the mind, lie involved in darkness and obscurity j and being destitute of order, method, and connexion, afford no foundation whereon to buiM any just, and accurate conclusion.
Never repre- ^I* And this perhaps may be the reason sented in Its why many modem philosophers, in their full dimen- discourses concernino- infinity, have run
P'.ons, but by . ,9 . i
an endless -dtid ^^^'^^ apparent Contradictions j because, en- fver-growing countering with an object too large for i^*^^- the survey of the understanding, they
found themselves surrounded ^'ith inextricable difficul- ties, which their scan'y and defective ideas were by no jheans able to dissipate or remove. The truth of it is, finite ideas alone are proportioneil to a finite under- standing ; and although we are not wholly without a notion of th6 infinity of number, yet it is not such a oi*e as comprehends and exhausts its objects, or exhi- bits 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 efrbrt of thought take in the whole prospect ; and indeed it is properly that part of it which lies beyond the reach of our perception, and still remains to be taken into the account, to which w^e give the name of infinity.
^ . XII. This idea of the infinity of num-
whether con- ber, uiiperfect as It may seem, is ncver- sidered as past thclcss that by which the mind ascends to or to come, ^|^g conception of ctevfiittj and imwcnsitii,
boundless; ., , * . . , *^ , . • i
whence our l'^^" when we consider duration, either as idea of eter- past or to come, we find nothing to stop 5ii^y- the progress of our thoughts in the repe-
tition of years, or millions of years : the farther we proceed, the more the idea grows upon us ; and when
we have weaned ourselves with vain efTort^, we ma.st own at last that we can no inore'sLrrive at the. end Gl duration than at the end of number. It Is true, the several generations of men rise and disappear hi -■^v^/ quick successions *, earth itself may decay , and thosu- briszht hmiinaries that adorn tlie firinament of heaven be extinguished ; but the course of time will not Do thereby disturbed j that flows uniform and invariable, nor is bounded by the period of their existence. Thii double view of duration, as having already revolved through numberless ages, and yet still advancing into futurity in an endless progression, properly constitutes our. idea of etertuij. We speak indeed of an eternity past, and an eternity to come •, but both these are bounded at one extreme : the former terminates in thci present moment, and therefore has an end •, the latter sets out from the same period, and therefore has a be- ginning ; but, taken together, they form a line both ways infinitely extended, and which represents eternity in its full dimensions.
XIII. As, in the consideration of time, x^e idea of we fix upon the present moment, regard- immensity de-
inc^ it as the middle point which divides rived from the ^11,,. - , -^ . . ^ , consideration
.t4ie whole line oi duration into two equal ^^ ,g ^^.^^
parts ; so, in tlie consideration of space, growing on all that particular place in which we exist is sides ol us. looked upon as a kind of centre to the whole expan- sion. From thence we let Ipose^our thoughts on e\ery side, above, below, around, and find we can travel on, in the repetition of miles and millions of miles, with- out ever arriving at the end of the progression. It is not difficult indeed to carry our conceptions to tlie ut- most bounds of the universe ; at least so far as it falls within our notice. But- then the imagination rests not here i it sees immeasurable spaces beyond, capable of receiving new worlds, which it can pursue, as rising one above another in an endless succession. This consideration of space ever growing on all sides of us, and yet never to be exhausted, is that which rives us the idea of innrwr.sifn ; which is in fact nothing ehe
E2
■ 4-0
bui the innnity of number, lipplied to certain portions of extension, as mile'^, or leagues, &c. and these con- ceived as extent'**:! every way around us, in infinite an^ innu:r*^^rable right lines.
XIV. Hitherto we have considered the
Compound • , i i i i i
ideas resukiiTT Jfnuid as employed about one and the same Crom the '^ idea, enlarging and diversifying it in vari- iMiionofper- ous forms. We havG Seen it rising from ceptions o ^j,^ most Simple and obvious notices to
diUerent kinds. . .■^^.-...^ ,,
tiie conception oi mnnity itselr j and taken a view of it ill all the different stages of its improve- ment. Let us now proceed to the more complicated act of composition, v/hen the mind brings several ideas of dilFerent khids together, and voluntarily combines them into one complex conception. Such, for in- stance, is our idea of a tune^ as comprehending a varie- ty of notes, with many different modulations of sound. And here it is to be observed, that though the com.plex 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 was the musician, or composer, that combined the several notes, and determined the order in which they v/ere to follow one another ; nor had the peculiar composition of sounds any real union in nature before they v/ere thus brought together in his mind. Of the same nature are most of our ideas of human actions ; for though many of tliem come to our notice by seeing the actions themvSelves, or hearing tliem described by others, as (Ustilling^ carvingy treascfiy &c. yet it is plain that tliey must have been projected and contrived in the mind of man before they had a real existence.
XV. It is here that the understanding
How the - , r 1 ^
mind is deter- ■"^s the greatest scope, an 1 nnd.s most mined in male- employment for its active powers •, nor ing these com- jndeed is it possible to set any bou'ids to tiiiatioas. ^1^^ .^^^g ^£ j.j^-g cXtl?,^^ the comblnaricns '
already madq being almost innumerable, and tlics^e
41
yet in the power of the mind afforcrmg an endless di- versity. It may not however be amiss to consider how we conduct ourselves amidst so great a variety, and by what rules we proceed in making those com- binations to which we have afhxed particular names* while others, perhaps, no less obvious, arc neglected.. The idea of killing, for instance, joined to that of a father, makes a distinct species of action, known by the name of parricide. It was doubtless as obvious to distinguish between the killing of an old man and a child, wliich yet we find is not done ; both these ac- tions being comprehended under the general name of uiurcler. By what views therefore docs the m.ind regulate these its combinations ? Why is it determined to one collection of ideas rather than another ? This cannot be well understood, without, observing, that it is the ciid of language to communicate our thoughts one to another. - Words are the signs of our ideas, and serve to express tlv? conceptions of the mind. Now it is apparent that such conceptions as are most: apt to occur in the commerce of life, would be fir^t distinguished by particular names *, the frequent occa- sion men have of mentioning these among themselves, je.ndering this absolutely necessary. But as many of these conceptions are collections of different simple ideas, hence we are insensibly led to such peculiar combinations as are most serviceable to purposes of mutual intercourse and communication.
XnTI. Let us suppose, in the first begin- nings of society, a company of legislators Lan'acti^"s • met together, in order to consult of pro- often formed^ per regulations for the rnvernment of i.he before the ac- community. If they are men of pru- ^'^"^ them-
1 n '^tivcs exist
dence and foresight, they u^iil naturally observe many nev/ occurrences likely to arise from thi^j coalition of mankind, and their living together in crowds. Perhaps the age in which they- live has not produced an instance of one man's killing another , yet from the knowledge of their own frame, and their power of doing hurf^ they conceive this as a possibLt^
i: 3
42
cise, and are willing to provide against it. Thus all the ideas that enter into the complex one of murder, are brought together and united into one conception, before the action itself really exists. It is not how- ever 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 e- qually affects both cases. But when they come to consider the relation in which the person killed may stand to the m.urderer, here there appears a manifest difference j as it adds to the crime when ct«imitted upon a benefactor, and renders it particularly heinous in the case of a father. This last, therefore, is made to constitute a distinct species of action, and has a pe- culiar punishment allotted to it. Thus we see how- men, according to their different nianner of life, and the relations they stand in to one another, are natural- ly led to form several collec*,ions of simple ideas, pre- ferably to others, as foreseeing they may have fre- quent occasion to take notice of such precise combina- tions. And because it would be tedious in conversa- tion, every time these complex notions occur, to enu- merate all the ideas of which they consist, therefore, for the sake of ease and dispatch, they give them par- ticular names, and thereby render the compositions £xed and permanent.
,^., . XVII. That it is in this manner we
? he necessity , i • , t • i , •
of mutual in- come by our complex ideas, which multi- tercourse, and ply upon US according as the exigencies men s particu- q£ society require, or our pursuits, method
Jar aims in r ^•r » i • n- • i^
l-'fe a great ^^ ^^^^> ^^^^ dittei'ent aims throw occasions
source of com- in our way of combining such and such
plex ideas. perceptions together, might be easily made
appear by a short view of the combinations themselves.
Human actions, as occurring most frequently, and
affording large matter of conversation, debate, and
inquiry among men, have been very nicely modified,
and distinguished into classes, according to the several
circumstances most likely to attend thenv. In like
43
Banner the arts and sciences, in proportion as they ire cultivated, leading us into many coinpound views )f tilings, which otherwise would never oflbr them- lelves to the consideration of the mind ; the complex deas of this sort, with the names by which they are expressed, are, we find, the work of such particular lations where these arts and sciences have chiefly flourished. The Greehy for instance, excelled in [earning and polite knowledge ; hence many of the terms belonging to Rhetoric, Poetry, Philosophy, Phy- tic, &c. .come originally from their language. Mo- dern fortification has received its greatest ir/jpiovements among the French ; and accordingly the ideas and terms of the art are mostly derived from writers of thai nation. In Itali/^ architecture, music, and paint- ing, have been the great exercise of the men of ge- nius •, it is therefore among them that we find the se- veral complex notions belonging to these parts of study, as well as the names by which they are expressed ; nor can we discourse accurately and minutely of the above-mentioned arts, without having recourse to the language. of that climate. And if we descend into the particular callings and professions of m.en, they have all iheir peculiar collections of ideas, distinguished by their several names, and hardly known but to such as are conversant in that manner of life. Thus calclna' tiofty cohcbatioJiy filtration^ &c. are words standing for complex ideas frequently framed in the minds of che- mists, and therefore familiar to men of that employ- ment. Yet as these, and such like combinations, sel- dom occur in common life, the generality of mankind, we see, are in a great measure unacquainted with them.
XVII. I might pursue these specula- Hence differ- tions farther, and shew how the several ent sets of fashions, customs, and manners of onf na- ^^^"^ prevail tion, leading them to form many complex countrTesJ'Ind notions which come not so naturally in words in'one the way of another ; different sets of ideas Unguage have prevail in different countries, and of course "^^'^^ *° ^'*"
44
swer them in have nnmcs appropriated to them in one anot-ier. language, to which there are no words
that answer in un;.;taer. The procedure and forms of our courts of justice have introduced many terms into the EnglisJi law, which stand for collections of ideas framed among no other people. Nor would it be possible to reTider these terms by any single words of another language ; because where the ideas themselves prevail not, there are no names provided to express them. In this case, therefore, -it becomes necessary to use circumlocutions, and enumerate .the several ideas comprehended in the collection, if we would so express ourr,eN.es as to be understood in the language ot other nations. Nay, even among the same people, -the change of customs and opinions frequently brings new sets of ideas, which of course must be distinguish- ed by particular names ; while, at the same time, the notions of former ages grow into disuse, and tlie words answering them are wholly laid aside, or employed in a signification different from what they had before. This too the ^^^- ^^^s languages are in,a perpe
cause thut Ian- tu d flux, and by degrees vary so much guagesareina from their original frame as to become perpetuiil flux, unintelligible even to the descendants of those who speak them. If we rim back into the ages of chivalry in Englandy when tilts and tournaments were in fashion, how many complex ideas, peculiar to that mode of life, shall we find familiar among the men oi" thosf- t ines, which are now little known or attended to J On the contrary, the improvements iYj arts and sciences that have since taken place, have led us inco innumerable views of things to which our fore; fathers were perfect strangers. But I shall not pusK these reflections any farther, believing that what hai been said will be sufficient to shew the origin and pro- gress of our compound ideas, and how the mind is directed in the choice of the combinations it makes We therefore proceed to the consideration of abstract ideas, which make the subject cf the following sec- tion.
45
Sect. II — '^Of Ahs tract or Utilversal Ideas,
I. Having dispatched what was neces- qq^(.^.^\ j^e^s sary to be said concerning our compound formed by th> ideas, considered merely as they are com- abstraction of binations of the understanding, it is now ^^'^ "^^^ time to explain how we come by our general notions, which serve to represent to us a multitude of indivi- duals, and are the standards by which we rank things into sorts. And this, as we have before intimated, is done by the abstraction of the mind ; which act may be extended to all our ideas, whether simple, compound, or of substances. If, for instance, we fix our atten- tion on any particular colour, as scarlet, we can leave out the consideration of all present circumstances, as the subject in 'which it inheres, the time and place of seeing it, &c. and retaining only the impression itself, make it a representative of that quality or appearance, wherever we chance to meet with ir. It is thus that abstract and universal ideas are framed , for the mind regarding only the scarlet colour, which one day it ob- serves perhaps in a piece of cloth, another in a picture, and a third in the rainbow, the appearance is conceived to be the same in all these objects, and tlierefore is called by the same name.
II. But to enter a little more, closely ^jj ^^^ ^.^ into this matter, and shew that these our ceptior.s of the general conceptions arc the mere creatures un-'erstanding of the understanding, it may not be amiss p-"icular.
to take notice, that all our perceptions of things, whe- ther we derive them from sensation or reflection) are of their own nature particular, and represent to us sin- gle determinate objects. Wiien we see a horse, for instance, in the fields, our idea is ihat of an individual/ IF we hear a sound, it is somethii^.g panicularj aiui
46
diffei^ent from what v/e hear at any other thnc. Evei y perception of the mind is distinct from every other peiccption ; nay, and every idea brought into view by the imagination, as vi'hen v/e frame the image of a lion standing before us, is still singular, and represents a single object.
III. But v/hen we come to take a view the spedes le- ^^ these several particulars, we readily ob- prcsents v>rhat Serve among some of them- a resemblance j is common to and framing to ourselves an idea of those
different indl- ^^- -^^ ^,j,-^j^ ^^,^ ^£ ^^^^ ^^.^ f^^^^^ ^^
viauuls, o / ^
agree, we thereby get a general notion, applicable to many individuals. Thus horses are found to resemble one another in shape, voice, and structure of parts. The idea which takes in only the particulars of this resemblance, excludine what is trecuiiar to each" smgle animal, becomes of course common to all crea-. tures of that, kind, and is therefore the representative of a whole class of beings. Accordingly the name of that general idea is given to every animal in which that shape, voice, and structure is found •, for the v/ord horse, implying only these particulars, must belong to all creatures wherein they exist. This is the first step or gradation in the forming of- abstract notions, when the mind conHnes itself to the consideration of indivi- duals, a!]d frames an idea that comprehends such only under it. The rank or class of things answering to tliisidea, is called species, in the language of the schools : so a horse is a certain svecics of anmials, an o:Mi is a socch's of trees, and a square is a species of four- sided iigures. ^,„ . , ^ ■ IV. When we have^thus learnt to rank
1 he trie;: of .,..,, . , , ,
t>i, -r...,. s r*. nunviduals mto sorts and classes, accord-
Lii'i ^ciius re- . '
pies-'ats what ing to the resemblance found among them, sti co.Timon to the mind proceeds next to consider the stycru spe- species themselves, and often in these toOi observes a certain likeness. Whereupon,, throwing out all those particulars wherein the several species are found to disagree, and retaining only such as are common to them all, v/e'thereb>^ fraine a still
4T
iTiore general Idea, comprehending under it a variety c/ different species. Thus a sparrow, a hawk, an eagle, Sec, arc distinct species of birds, which have each their peculiar shape and make. They nevertheless resemble one another, in being covere<l with feathers, and pro- vided with wings that bear them through the air. Out of these particulars we form a new idea, including all the common properties of the feathered kind j and appropriating to it the name blrdy mark by that word another class of thijigs, of a higher order than any of the former. This superior division, which extends to several species at once, is called in the schools the genusy and is the second step the mind takes in advan- cing to universal notions.
V. And thus have I given a short, but T^g n^jn^ ^^^ I hope intelligible, account of the business advwiceby oi Q-cr.era and species^ about which so much "^^-^'-ftist gra- has been saici ni the wr.tmgs of the logj- rJsingfrom par. cians. S.pecieSy in strictness and propriety ticular to ge- of speech, is such a rank or class of things nerals. as comprehends under it only individuals ; genus ad- vances still higher, and takes in a variety of distinct species. It is however to be observed, th-^t the mind. In rising from particulars to generals, is not confined itself to one or two gradations, but may carry its views through the whole extent of things until at length It arrives at an idea embracing the universal compass of nature. For when we have ranked things into sorts, and reduced these again to tlie higher order or genus, these genera are still found to resemble one another in some particulars ; which being collected In- to one idea, form a new and more comprehensive di- vision of things. Thus bird is a genusy embracing all the varieties of the feathered kind. Fish implies the several species of living creatures which inhabits the waters. Qjiadrwped and insect are also universal ideas, that take in many inferior diotributions and cla5:,t>es. Yet all these different orders of being have this In common, that they are provided witli organical bodies, fitted for die purposes of life and spontaneous motion*
48
An idea therefore comprehending only these last parti- culars, will .ec^uaUy belong to all the divisions before enumerated ; and the word animal^ by which it is e:(- pressed, becomes a general name for the several crea- tures endued with liie, sense, and spontaneous motion. If we are for carrying our views still farther, and framing a yet more universal notion, w^e can cast our eyes upon both the animate and inanimate parts of na- ture: wherein we find this mutual correspondence, that they exist, and continue in being. This last idea therefore of being in general, comprehends under it all the varieties of things, and may be universally applied to whatever has either life or existence ; so that in re- spect of the present frame of nature, it is the highest and most universal idea we have,
VI. In this series of notions, rising one Whence many ^^^^ another in the degree of universali- sups between ty, that division which comprehends un- the highcbt der it several genera, is called in the
genus and schools the hiphcr ■ g-eiius ; which denomi- lowest species. . . ° ° ., . ,
^ nation continues until we arrive at the
last advance of the understanding, when being come to the most general of all ideas, that admits not of a superior, it is distinguished by the name of the genus generalissimunj. In like manner, the several genera com-, prehended under a higher genus ^ are in jrespect of it considered as species ; and as these two last have spe- cies under them, the inferior divisions are for distinc- tion's sake termed loiuer species. Thus the progression continues, and when we come to the lowest sub-divi- sion of all, comp/ehending only individuals, which, as I have before intimated, constitutes the proper species, this the schools denominate the species special issinia. All that lie between it and the highest distribution of things, are the intermediate genera and species, which are termed, each in their turn, genus genera/ius, or spe- cies specialior^ 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 linca pradicattie?itali, I should not have
49
enterci^ so far into these verbal dlsqulsltioiis, had ilOJ: the terms here explained been such as frequently oC~ cur in the writings of philosophers ; insomuch that without some knowledge of them, wc must often be at a loss, in the prosecution of these studies. Besides, it is both curious and useful, to see the gradual pro- gress of the mind, in its advances from particular to general conceptions *, to observe it ranging its ideasr into classes, and establishing a just and regular subor- dination in its views and notices of things. This is the shortest way to knowledge, and affords the best means of preserving the order and due connection of our 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 knov/Iedge, which leads us into the true and natural method of conducting our understand- ings in the search of truth.
' VII. From what has been said, it is evi- ^g^^^ j • i dent that general ideas are the creatures the creatures and inventions of the understanding. Na- of the under- ture, it is true, in the production of ^'^^'^'^^"g:- things, makes many of them alike f but it is the mind alone that collects the particulars in wl-l-ch they agree into one idea, and sets it lip as a representath'e of ma- ny individuals. And now I think we mav venture upon that much agitated question, Where do the ge- nera and species ^of things exist ? To which I answer, In the mind. Ujiiversalitif belongs not to things them- selves, it being aj^parent that they are al! particular in their existence. Hoxvever, as they often have many properties in common, the understanding, by uniting these into one conception, obtains a general idea, un- der which it ranks all the several objects wherein these properties are found.* So far indeed w£ must allow, that the particular combination of properties which constitutes the genus or species, exists in all the indi- duals referred to that genus or snecies ; but tb.?n it in
F
so ■
\i\ conjunction with other properties, by which these individuals are distinguished from one another. Thus the collection of simple ideas, e^ignified by the word ^irdf is to be found for instance in a Jmwky or any o- tlier single animal to which we apply that general name ; but the notion itself, abstracted from all the particulars to which it belongs, has evidently n© ex- istence out of the understanding.. There is not a being in nature that can be called a '^/W in general, or that does not necessarily imply, in the very conception of it, several simple ideas, besides those marked by that word. For the name in this case signiiies no more than an animal covered w^Ith feathers, and provided with wings, without regard either to shape, bulk, or the particukir time and place of its existence. These last considerations however are inseparable from the reali- ty of 'things, and therefore must be added to the ge- neral i<lea, before we can conceive any thing confor- mable to it actually brought into being. Considered a- VIII. Hence we see at once what sort pxrt, they exist ^^ ^^ existence general natures have. Con-
onlv in tiic
mind byt in sidered apart, and by themselves, they are
conjunction wholly the workmanship of the under-
with other standing, and derive their being and reali-
ideas in the ^ r -^ u..* j- •
individuals ^7 ^^^^^"^ ^^ ? but Viewed m conjunction comprehended w'lth Other ideas that co-exist with them tmder them, in the several objects jbf nature, they are to be found in the individuals to wdiich they refer ; and therefore, according to this way of conception, may be said to have an existence in them. . Ihus so long as the ideas answering to the words man or tree, continue general and undetermined, they have no real objects answering them' in natuve ; nor can the collection of simple ideas, marked by these names, while all others are supposed excluded, exist any where out of the un- derstanding. Nevertheless, as aiil the simple ideas in- cluded in the general notion of 7nan, are to be foundr in every particular ?}ian ; and all those implied in. the notion oi -^ t(ee^ in every particular irce^ hence the.ge-
nct.il nature' of man exists in overy individuil ifia/iy vs ^o'csthe general nature of -^ ^'"^- in every individual /m,
IX. One thln^r still remains to be obser- j)j-^,^^,^ ^r vcd, witli regard to these our general i- ideas ccns;- deas, that though many of them are evi- «^e^ed as com- dently combinations of different simple i- ^j;^^''^!^;^^*^ ^' deas, and, according to that way of consi- dering them, are included in the first division of our complex conceptions, those namely framed by the. composition of the mind ; yet we are carefully to dis- tinguish between an idea -as it is compound, and as it is universal. In the first case, the mind chiefly consi- ders the several ideas that are com.bined together -, or, in other words, all the attributes, qualities, or parts that are contained in any idea. Thus, the idea of a bird includes life, sense, spontaneous motion, a cover- ing of feathers, wings, &c. none of which can be left out without destroying the very nature of the idea, and making It something quite different from what it waa.- before. This way of considering things according to the number of their parts and properties, is called by Logicians the cofnpreJiensiofi of an idea. But the univer- sality of our notions implies quite another turn of- thiiiking, in as much as it fixes the regard of the mind upon the subjects to which our ideas extend, or the in- dividuals and species comprehended under them. In this sense, the ideas answering to the word birdy take in the several species of the feathered creation, the hatvk^ the eagle, sparroiu, lark, and innumerable others, to all which it may with equal propriety be applied. And here it is remarkable, that the idea loses nothing of its force oi' comprehension, by being restricted to a particular kind. When I say the bird of Jove, thoiio^h it* 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 extend- ed to all the different tribes of feathered animals.
X. We see therefore that our compound ideas may continue the same in respect of their attributes, or th.>
F2
32
Yh^ compre- "'-^^^^^^ ^^ parts, and yet vary consider.i- Jiehsion and bly ill the degree of universality. The extension of general idea of inan Is trie same, whether ftur laeas. applied to tlie whole human race, ov those
of any particui.ir nation. "^Vhen I aiBrm, for instance, of mankind in general, that their knowledge falls short of perfection, and afterv»ards make the like observa- tion of the men of the present age, in both cases, the word fnan stands for one and the same collection of •simple ideas \ but in respect of the individuals to which it is applied, there is a great and manifest dlf- f^irence. That is, the term tnan, denotes one invaria- ble compound idea ; which, notwithstanding, consi- dered as a general notion, may be contracted or enlar- ged at pleasure. And as in the former case the se- veral parts of compound idea is called its comprehension ^ so in the latter, the individuals to which the universal idea is applied, is called its extension, I might add many more observations on tliis subject ; but choose r^\ther to stop here, having said enough to explain the difference between compound and abstract ideas, and shew the reason of iny ranging them under distinct heads.
' Sect. III. — Of our Ideas cf Relations.
Ideas of tela- ^* I COME now to the third and last dlvi-
tions exceed- sion of those ideas which I consider as the ing numerous, creatures and workmanship of the under- standing ; such namely as arise from the comparing of things one \yith another; for the mind in its views '^i not tied to single objects, but can examine their refer- ences and respects, in regard to others, brought under consideration at the same time : and when it does so, and hence derives new notices of things, the ideas thus got are called relations, and make, I am apt to
53
think, the largest class of all our perceptions. For e- very single object will admit of almost innumerable comparisons with others, and in this sense may be- come a very plentiful source of ideas to the under- standing. Thus, if we compare one thing with ano- ther in respect of bulk, we get the ideas oi greater, lessy or equality ; if, in respect of time, of elder and yoimger ; and so for other relations, which we can pursue at pleasure almost without end \ whence it is easy to con- ceive how very extensive this tribe of our perceptions must be.
11. I shall not pretend to trace out these ^^
• 1 .• 1 1 • J 3 ' I Men chleflv
ideas particularly, nor mdeed so much as determined to to enumerate their several divisions ; it particular com- belng enough to observe, that here, as well P'^nson by the as in the other kinds of our complex ideas, "^^'""^^ ^'^'J,^,^^"
, , 1 r 1 r g^-^Cies of life.
we bound ourselves tor the most part oi such comparisons as the exigencies of society, the wants of life, and.the different possessions of men, render ne- cessary > and are mere or less accurate in tracing out the relations of things, according to the degree of im- portance they appear to have in these respects. The relations of men one to another, arising either from the ties of blood, their several ranks and places in the community, or a mutual intercourse of good oiKces^ being of great weight and concern in the commerce of life, have in a particular manner engaged our atten- tion, and are therefore very minutely described. For the same reason, men have found it necessary to deter- mine, as exactly as possible, the various dependence of things, as their happiness is nearly connected with this knowledge. When we consider the objects merely in respect of existence, as either giving or receiving it, we come by the ideas of caiue and effect : nor need 1 mention how much the v/elfare of mankind depends upon an extensive view of things as they stand connect- ed in this relation ; it being evident that the several schemes and purposes of life are all conducted upon a previous supposition, that certain known ciiuses will
F3
54 ,
have their usual regular effects, and such and such actions be attended with such and such consequences. Relations of HI* ^ut there are other relations of
Creator and this kind, besides those that regard mere- crcature, ^c. Jy existence ; as when we also take into the account the additional gifts of a capacity for happi- ness, and tPie means of attaining it •, which constitutes the relation of Creator and creature^ in the more solemn -icceplation of these words. Again, when we consider the ^reat Author of our being, not only as the Creator of the universe, but also as preserving and holding it together, and presiding over the present frame of things with uncontrolled dominion, lie then appears under tae notion of a moral Gover?wr^ to whom we are ac- countable for our actions, and the use we make of those powers and faculties we derive from him. Now, iS it is of the highest consequence for men not to be unacquainted with these and such like relations, hence we find, that of the wisest nations, and such as best understood the true application of the powers of the • mmd, have always made it their chief study to regulate vuui ascertain these ideas, and trace them in all their consequences. And thus we may in some measure perceive how the mind proceeds in comparing its ideas together, and by what views it is chiefly governed, in framing the complex notions of this class, by which it represents the various habitudes of things, I shall only add upon this subject these two observations : — » ^ , . , c IV. I^'irst, that our ideas of relations
Our ideas of '
relations very are for the most part very clear and dis- flear and dis- tinct J for the Comparing of things to- ^^"^* gether being a voluntary act of the mind,
we cannot but suppose that it must be acquainted with its own views in the comparison, and of course have a clear conception of the foundation of that relation it sets itself to inquire into. Thus the relation of cause and effect, implying only that one thing produces, or 15 produced by another, which notions are always dis- , tinctly settled in the understanding before it goes a^-
65
bout to make the comparison, it is evident that the idea representing this mutual respect of objects, will be BO 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 cense not to be distinct, even where the subjects compared are but very imperfectly known. For I can well enough con- ceive that ojie thing has produced another, and that therefore they stand related as cause and effect, though my ideas of the things themselves may perhaps be very obscure, and come far short of representing their real nature and properties. I doubt not but it will be readily owned, that our idea of the tiniverse, consider- ed as comprehending the whole frame of created things, is very inadequate ; and I think it is still more appa- rent, that our notion of the Supreme Being comes not up to the excellence and perfection of his nature. Yet we very well understand what is meant by calling God the Author of the world, and, though we compre- hend not the manner of his producing it, find no diffi- culty in framing the ideas, the relative words Creator and creature stand for.
V. I have yet another observation to
make upon this subject-, and it is, that ^^'^^^^ ^^ "^^la. . . ^ - . J ' , ' tions among
our ideas of relations are among the most the most im-
important conceptions of the understand- portant con- ing, and afford the largest field for the ex- options of .
°- 1 • • '\ r 1 ^ "^e mind,
ercise and improvement of human know- ledge. Most of our inquiries regard relative ideas, and are set on foot with a view to investigate the mu- tual habitudes of things. The mathematician has ta- k^n quantity for his province, and teaches us how to compare magnitudes of different figures and dimensions, in order to judge with certainty of their relative pro- perties. The philosopher attaches himself to the chain of causes 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
56
find out others that stand somehow connected with them ? As for the importance of these conceptions, no one can call that in question who reflects, that from our relations to our Creator and one another, arise all the duties of morality and religion ; and that the cor- respondence of the several objects of nature to the or- gans of the body and faculties of the mind, is that by- which alone we can judge of what will procure u* happiness or misery. Whence it is evident, that with- out an exact knowledge of these relations, we must wander on in life with great uncertainty, and may of- ten plunge into calamities and misfortunes, by those very pursuits, from which we expected nothing but joy and pleasure.
VI. Thus havel ffone through the se-. Recapitulation. ir-- r -j -l-uti
^ veral divisions oi our ideas, which 1 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 apprehend- ed. I might easily run into other distinctions, by considering them as clear or okscurey adequate or maih- quate^ 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 ex- plained above seems to be of great importance towards settling in the understanding a just view of the pro- gress of human knov/ledge, and the steps by which it advances from one degree of improvement to another, I shall here run over it again in as few words as possible, that the Vv'hole process may be seen at once. Our ideas are all derived into the understanding, either by sensation or reflection. This however is observable, that one and the same object often excites a variety of perceptions at once, which are nevertheless readily distinguished by the mind, and appear each under a form peculiar to itself. These constitute our primary and original notices^ and are e?»sily known from all
'57
others, in as much as they are entirely void of plural!-* ty, and cannot be divided into two or more different ideas. They are also the materials out of whicli the others are formed, and are therefore, by way of distinc- tion, called Simple Ideas. But the mind, though it has no power over these, either to fashion or destroy them, can yet combine them in an infinite number of ways ; and from their various combinations result all our com- plex ideas, which are of two principal kinds. First, Such as arc derived from withoXit, and represent those combinations of simple ideas that have a real existence in nature. Of this sort are all our ideas of substances. Secondly, The conception 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 which may be properly termed our own, as being the real workmanship of the understanding, •so they fall very naturally under three distinct heads *, for either the mind combines several simple ideas to- gether, 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 conqyound notions) ; or it fixes upon any of its ideas, whether simple, compound, or of substances, and leaving cut the circumstances of time, place, real existence, and whatever renders it particular, considers the appearance alone, and makes that a representative of ail of the kind ; whence our ahstract 2iX\^ universal ixieas are derived ; or, lastly, It compares things one with another, examines their mutual connections, and thereby furnishes itself with a new set of notions, known by the name of r^/^/iowj ;• which, as has been already remarked,, make by no means the least im- portant class of our perceptions. This division of our ideas, as it seems to be the most natural, and truly to represent the manner in wdiich they are introduced in- to the mind, so I believe it will be found to compre- hend them in all their varieties. I shall therefore now proceed to offer some observations upon language^ as
58
bfeiug the great Instrument by v/hichwe are enabled to- make our ideas and perceptiona-'known to others.
CHAP. V.
OF WORD^S, CCNSIDEE.RD AS THE SIGNS OF OUR IDEAS.
Words furnish ^' '^^'^^ ^^^'ve seen how the mind comes the means of to be first furnished with ideas, and by- recording our what method It contrives to diversify and- own thoughts, ej-ji^j-ge j^s stock •, let us now consider thg means of making kno\vn our thoughts to others, that we may not only understand how knowledge is ac- quired, but also in what manner it may be communi- cated with the greatest certainty and advantage ; for our ideas, though manrfold and various, are neverthe- less all within our own breasts, invisible to others, nor can of themselves be made appear. But God design- ing us for society, and to have a fellowship with those of our kind, has provided us with organs fitted to frame articulate sounds, and given us also a capacity of using these sounds as signs of internal conceptions. Hence- spring words and languages ; for having once pitched upon any sound to stand as the mark of an idea in the mind, custom by degrees esrablishes such a con- nection between them, th-it the appearance of the idea in the understanding always brings to our remembrance the sound or name by which it is expressed -, as in like manner the hearing of the sound never fails to excite the idea for which it Is- made to stand. And thus it is easy to conceive how a man may record his own thoughts, and bring them again into view, in any suN- ceeding period of life : for this connection being once settled, as the same sounds will always serve to exclte- the same ideas, if he can but contrive tcr register his.
59
words in the order and disposition m which the pre- sent train of his thoi:ghts presents them to his imagina- tion, it is evident he will be able to recall these thoughts at pleasure, and that too in the veryj manner of their first appearance. Accordingly, we find tliat the in- ventions of writing and painting, by enabhng 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 subjected to our review as any the other abiding objects of nature.
II. But besides'the ability of recording ^^ , „f .i,w«, our own thoughts, there is this larther ad- tuai communi- vantage in the use of external signs, that cation of know-
they enable us to communicate our senti- ^^^g^ i^o"! oiie ' , , , . . ^ mantoanother.
ments to others, and also receive miorma-
tion 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 repeti- tion of these sounds must excite the like perceptions in each, and create a perfect correspondence of thoughts. When, for instance, any train of ideas succeed one another in any 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, no- thing is more evident than that by repeating those names according to the tenor of my present concep- tions, I shall raise in their minds the same course of thought as has taken possession of my own. Hfence, by barely attending to what passes within themselves, they will also become acquainted with the ideas in my understanding, and have them in a manner laid before their view. So that we here clearly perceive haw a man may communicate his sentiments, knowledge, and discoveries to others, if the language in which he con- verses be extensive enough to mark all the ideas and transactions of his mind. 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,
60
it mAv be asked, How in these circumstances we can become acquainted with the thoughts of anodier, when he makes use of words to which we have never annexed any ideas^ and that of course can raise no per- ceptions in our minds ? Now, in order to unveil this mystery, and give some little insight into the founda- tion, growth, and improvement of language, the fol- lowing observations will, I am apt to think, be found of considerable. moment.
III. First, That no word can be to any
camfot beacon- °^^" ^^^^ ^'^S^^ ^^ ^^ ^^^^^ ^^^^ ^^^^^ ^^^^
veyed into the comes to have a real existence in his mind, mind by For names being only so far intelligible as
words, or a ^-j^ denote known internal conceptions, descnption. 111 ^
where they have none such to answer
them, then they are plainly sounds without significa- tion, and of course convey no instruction or know- ledge i but no sooner are the ideas to which they be- long raised in the understanding, than finding it easy to connect them with the established names, we can join in any agreement of this kind made by others, and th(M*eby enjoy the benefit of their discoveries. The first thing tlierefore to be considered is, how these ideas may be conveyed into the mind ; that being there, we may learn to connect them with tlieir appropriated sounds, and so become capable of understanding o- thers, when they make use of these sounds in laying open and communicating their thoughts. Now to com- prehend this distinctly, it will be necessary to call to mind the before-mentioned division of our ideas into simple and. complex. And first, as for our simple ideas, it lias been already observed, that they can find no . admission into the mind, but by the two original fountains of knowledge,--N.sensation and reflection. If therefore any of these have as yet no being in the un- derstanding, it is impossible by words or a description to excite them there. A man who had never felt the impression of heaty could not be brought to compre- iiend thut sensation by any thing we might say to ex-
61
plahi it. If we woiilcl really produce the idea in liini) it must be by ''ipp'yii''[r the proper object to his senses) and bringing h'mi within the inllucnce of a hot body. When this is done, and experience has taught hinn the perception to which men have annexed the name heaty it then becomes to him the sign of that idea, and he thenceforth understands the meaning of a term, which before all the words in the world would not have been sufficient to convey into his mind. The case is the same in respect of light and colours. A man born blind, and thereby deprived of the only conveyance for the ideas of this class, can never be brought to under- stand the names by which they are expressed. The reason is plain : they stand for ideas that have no ex- istence in his mind ; and as the organ appropriated to their reception is wanting, all other contrivances are vain, nor can they by any force of description be raised in his imagination. But it is quite otherwise in our complex notions. For these being no more than cer- tain combinations of simple ideas put together in vari- ous forms, if the original ideas, out of which these collections are mafve, have already got admission into the understanding, and the names serving to express them are known, it v/ill be easy, by enumerating the several ideas concerned in the composition, and mark- ing the order and manner in which, they are united, to raise aivy complex conception in the m.ind. Thus the idea answering to the word rai?ibc%iJy may be readily excited in the imagination of another, who has never seen the appearance itself, by bnrely describing th<sr figure, largeness, position, and ordei of colours, if we suppose those several simple ideas, with their names, sufficiently known to him.
IV. And this naturally leads me to a ^, second observation uponthissubjcct, name- compIeTrde'l ly, that v/orris standing for complex ideas definable, are all definable, but those by which we f^^^^ ^^ simple denote simple ideas are not ; for the per- "^^""^ "°^* ceptions of this latter class having no other entrance
62
into the mind than by sensation or reflection, can only be got by experience from the several objects of na- ture, proper to produce these perceptions in us. Words indeed may very well serve to remind us of them, if they have already found admission into the understanding, and their connection v^'Ith tlie establish- ed names is known ; 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 explain it to him by a defmition, well knowing that to be impos- sible *, but supposing him already acquainted with the idea, and only ignorant of the name by which it is called, we either mention it to him by some other name, with which we presume he knows its connection, or appeal to the object where the idea itself is found. Thus, was any one to ask the meaning of the word ivhitey we should tell him it stood for the same idea ^s albus in Lathiy or blcinc in French ,- or if we thought him a stranger to these languages, might appeal to an object producing the idea, by saying it denoted the colour we observe in snciv -or milk. But this is by no means 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 connection with the established name. For if the idea after which he inquires, has never yet been raised in his mind j as suppose one who had seen no other colours than blacJz and white^ should ask the meaning of the word scarlety it is easy to perceive that it would be no more possible to make him comprehend it by words or a definition, than to discourse the same perception into the imaf^ination of a man born blind. The only method in this case is, to present some object, by looking at which the perception itself may be excited, and thus he will learn both the name and the idea together.
6
V. SliouUl rny one's curiosity now „ . ,
. •' . , . ^ i:<xpenence an«i
• prompt him to mquire, new it ccmes to ^^v,.
SeiVa".')!!
pass that men agree in their names of the bring men to simple ideas, seeincj they cannot vlevv^ the ^'"^ agreement
^ . . i-\ ^ • \ i.'i the names
perceptions in one another's mmcls, nor ^f gii^pie ide.s. make known these perceptions by words to others ? I answer, That tl.e effect here mentioned is produced by experience and obseivation. Thus finding, for instance, that the name heat is annexed to that im- pression which men feel when they approach the fire, I make it also tlie 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 theirs. 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 sugar, and which he calls sweetness^^ differs from that excited in another by the like means ; or th:it wormwood j to whose relish he has given the epithet bittery produces in others the sensation which he denotes by the word sweet. Pre- suming therefore upon this conformity of perceptions, when they arise from the same objects, we easily a- gree as to the names of our simple ideas *, and if at any time, by a more naiTow scrutiny into things, new ideas of thi;j class come in our way, which we choose to express by terms of our own invention, these-namcs are explained not by a definition, but by referring to the objects whence the ideas themselves may be ob- tained.
VL Being in this manner furnished with xhe convev- simplejdeas,andthenamesby whichtheyare ance of com-
expressed, the meaning; of terms that stand P^'^i' ^^'^''^^ ^^ c 1 • I • '^ M T 1 definitions, a
tor complex i.leas is easily got, because the ^^,jgg contri-
idcas themselves answering to these terms, vance in na- may be conveyed into the mind by defini- ture, tions. . For our complex notions, as was already ob- served, are only certain combinations of sim.ple ideas. When therefore these are enumerated, and the manner
G2
in which they are united into one conception explain- ed, nothing more is wanting to raise that conception in the understanding ; and thus the term denoting it comes of course to be understood. And here it is worth v/hile to reflect a little upon the wise contri- vance of nature, in tlius furnishing us with the very aptest means of communicating our thoughts \ for, were it not so ordered, that we could tluis convey our complex idqas from one to another by definitions, it would in many ci)ses be impossible to make them known at all. This is apparent in those ideas which are tlie proper work of the mind •, for, as they exist only in the understanding, and have no real objects in nature, in conformity to which they are framed, if we could not make them known by a description, they must lie for ever hid within our own breasts, and be confined to the narrow acquaintance of a single mind. All the fine scenes that rise from time to timie in the poet's fancy, and, by his lively painting, give such en- tertainment to his readers, were he destitute of this faculty, of laying them open to the view of others by words and descriptions, could not extend their influ- ence beyond his own imagination, or give joy to any but the original inventor.
J r VII. There is this farther advantage ni
and of great , , ... . ^ . . °
&vail towards the aoslity we enjoy ot communicatmg our j
the improve- complex notions by definitions j that as i inent oi know- ^ijgg^ make by far the largest class of our ^^^^* ideas, and most frequently occur in the
progress and improvem^ent of knowledge, so they are by this means imparted with the greatest readiness, tliiin which nothing could tend more to the increase and spreading of science \ for a definition is soon per- used, and if tlie terms of it are well urderstood, the idea itself finds an easy admission into the mind : whereas, in simple perceptions, where w; are. referred to the objects producing them, if these cannot be come at, as is somietimes the case, the m^mes by which they are expressed must remain empty sounds. Diit new
63
icie:is of this class occurring very rarely in the sciences, they seldom create any great obstruction : it is other- wise with our complex notions, for every step we take, leading us into new combinations and views of things, it becomes necessary to explain these to others before they can be made acquainted with our discove- ries : and as the manner of defmitions is easy, acquiring no apparatus but that of words, which are always ready and at hand, hence we can with the less difficulty temove such obstacles as might arise from terms of our own invention, when they are made to stand for hew complex ideas, sug^^ested to the mind by some pre- sent train of thinking : and thus at last we are let into the mystery hinted at in the beginning of this chapter, viz. how we may become acquainted with the thouj^hts of anotlier, when he makes use of words ro which we have as yet joined no ideas. The an- swer is obvious, from what has been already said. If the terms denote simple perceptions, he must refer us to those objects of nature whence the perceptions themselves are to be obtained j but if they stand for complex ideas, their meaning may be explained by a definition. As for the names of simple ideas, I shall here dismiss them, it being sufTicien. to take ce
that our knowledge this way can be extended only by experience and observation. But the theory of defini- tions making a material part of Logic, and being indeed of great importance towards the improvement of hu- man knowledge, it will be necessary to lay it a little more open to the view of the reader.
VIII. Complex ideas are, as has been ^-t ^ ^ _
A ' . i ne compo5i-
already said, no other than simple ideas tion and reso- put together in various forms. But then lution of om- it is to be observed, that in making these ^°"'I'^*^^- -'i^'^^- collections, the mind is not always tied down to the imm.ediate view of the simple perceptions out of which they are framed. For if we suppose the understanding already furnished with a considerable stock of com- pound notions, these again may be made the constiti>
G3
6G
cnt parts of others still more compounded, insomuch tluit the new idea thence arising may be termed a combination of complex conceptions. Thus the idea annexed to the woid aiihruily includes many perceptions under it, as life, sense, spontaneous motion, Sec. In like manner, by the term ratiotuil^ we denote a varie- ty of simple ideas. If now combining these two con- ceptions together, we form the still more complex no- tion of a rational animal, the idea thus got is truly a collection of compound notices. In a word, the same tiling Iiappens here as in numbers, which we may con- sider r.ot only as various collections of units, these being indeed their original and constituent parts, but also as sometimes composed of other lesser numbers ; which all put together, make up the respective- sums. Now in tracing any very large number, when for the case of the mind we consider it at first as composed of various others still leaser, if we next take these lesser parts to pieces, and pursue them.continually until we arrive at the units out of which they are composed, we thereby totally unravel the collection \ and being able to push our researches no farther, rest satisfied in the view thus offered to the understanding. Just so it is in the examination of our complex ideas. For when any very compounded notion comes under the inspec- tion of the mind in order to be traced to its first princi- ples, we begin with resolving it into other ideas less complicated •, and taking these again to pieces one by one, still go on with the search, until we have broken the whole into our first and simple perceptions, beyond which the pursuit cannot possibly be carried. And this is the reason why I have all along called our sim- ple ideas the foundation and groundwork of human knowledge \ because in unravelling the conceptions of the mind,, we find ourselves at length bounded by these ideas, which are indeed the last resort of the understanding.
67
IX. From what has been said, it will be ^he names of easy to conceive how, in defining a term simple ideas Standing for any very complex idea, other may be consi- terms may be introduced that also denote element'ary compound ideas, though of an inferior parts of Ian- class : for the first idea being resolvable g^^ge. into others less com.plicated, the definition which enu- merates these component ideas must consist of the names by which they are expressed : and if \t so hap- pen, that the ideas of this second class are also un- known, their terms too ought to be still farther defined. In this manner may a series of definitions be carried on until we arrive. at the names of simple ideas, which not being definable, the analysis must necessarily cease : and thus we see that as the simple ideas are the mate- rials and foundation of knowledge, so the names of simple ideas may be considered as the elementary parts of language, beyond which we cannot trace th^ meaning and signification of words. When we come to them, we suppose the ideas they stand for already known •, or if they are not, experience alone must be consulted, and not definitions or explications. And here it is well worth our notice, that as the names of these our original conceptions, constitute the primary and fundamental articles of speech, upon which the whole superstructure of human language is built, so they are of all others tlie least doubtful and uncertain in their signification ; because, standing each for one simple perception, not precariously excited into the mind, but the effect of certain powers in things fitted to produce that sensation in us, there is no danger of error or mistake. He that once knows sweetness to be the namie of the taste received from sugar, ivhitefiess of the colour in snow or m.ilk, and heat of the sensation produced by approaching the fire, will not be apt to misapply those words, or annex them to perceptions of a different kind. And as the names of complex ideas may all be resolved into these primitive terms, it is apparent that we are sufficiently provided with the
68
means of communicating our thoughts one to another ; and that the mistakes so frequently complained of on this head, are wholly owing to ourselves, in not suffi- ciently defining the terms we use, or perhaps not con* necting them with clear and determinate ider.s.
CHA^. VI.
OF DEFINITION, AND ITS SEVERAL KINDS.
I. Having laid these foundations>. definiIioTffro° ^hewn what words are, and what are not ceeds from the definable, and taught the manner of re- various appli- solving our notions, as well" as language , cation of itself, into its first and original principles,
we now proceed to explain a little more particularly the nature of a definition, and the several kinds made use of according to the different views men have in communicating their thoughts one to another. Definitions are intended to make known the meaning of words standing for complex ideas *, and were we al- ways careful to form those ideas exactly in our minds, and copy our definitions from that appearance, much of the confusion and obscurity complained of in lan- guages 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 reference of the terms defined. In order therefore to render this whole matter as clear and obvious as possible, we shall first consider to what it is that names, in the use of language, are most commonly applied ; and then, from the variety of this application, endeavour to ac- count for the several methods of defining, menuone-d in the writings of logicians,
60
II. Words then have manifestly a three- -^roi-ds kave a
fold reference : First, and more imme- threefold re-
diately, they denote the ideas in the rnind ference ; to
of him who uses them : and this is th^>r °"^' "^7 't'^'^ . . ,, . --_< those oi others,
true and proper signincation. vVnen a and the real
man speaks, it is that he may be under- being of stood j and the words he employs to con- "^^"-gs- vey his thoughts, are such as by use he has learnt to connect with the ideas then present to his mmd. But because those -with vv'hom we converse arc also suppo- sed to know the meaning of the terms we use, hence, Secondly, We consider our words as signs likev/ise of the ideas in their minds : and this is the foundation of what is called propriety in language, when m.en take care to afRx such notions to their words as are com- monly applied to them by those of most understanding in the country where they live. The third and last re- fert^nce of words is to things themselves : for many of our ideas are taken from the several objects of nature wherewith we are surrounded ; and being considered as copies of things really e^iisting, the* v/ords by which they are expressed, are often transferred from the ideas themselves, to signify those objects which they are supposed to represent. Thus the word j-w;/, not only denotes the idea excited in the mind by that sound, but is also frequently made to stand for the luminous body itself which inhabits the centre of this our plane- tary system. Now, according to this threefold appli- cation of names, their definitions and the manner of explaining them must be various ; for it is on.e thing to unfold the ideas in a man's own mind ; another to describe them as they are supposed to make their ap- pearance in the minds of others \ and lasrlv, it is some- thing stiil diiFerent to draw images or pictures that shall carry in them a conformity to the being and reality of things. But we sliail treat of each in order.
'.icailng our thoughts one to another;
■ '. ^> so frequently complained of on
y owing to ourselves, in not suffi-
ig the terms we use, or perhaps not con-
with clear and determinate ide?.s.
, s?ei"i '
CHA^. VI.
!
\ :l
INITIOS, AND ITS SEVERAL KINDS.
I. H-.viNG laid these foundations,
'^ <^.-x-n vhat words are, and what are not
..', and taught the manner of re-
•ig our notions, as well as language
:', Into its first and original principles,
^ row proceed to explain a little more
t the nature of a defmition, and the several
<; use of according to the different views men
■--■-- their thoughts one to another.
: to moke known the meaning^
. -'^r':^;;^^ for complex ideas ; and were>| "
u •s careful to form those ideas exap— ^"^^
our definitions from tl
_jsion and obscurity
ht be prerented.
., no means steady *—"
fcrtig them sometii which of*^ r., an<
ferenceofwoir oor ideas ate u'. wkewithwe:.:. as copies of tfii;.: ik|MeeM^
2T
rnii
bt
^
^MW-:
6'9
II. "Words then hi
)tlv a threc-
manij
' , \\ ('13 nuvi; <i
told relerence : rirst, and more imme- threcld re-
diately, they denote the ideas in the rnind ^^reie ; to
of him who uses them : itnd this is tb^ ""'' '^^ ''t""^^* . . .^ . . . thosot others^
true ana proper signincation. When a and le real
man speaks, it is that he may be under- Ixlnof stood j and the words be employs to con- '''''"-'• vey his thoughts, are such as by use he hasprnt to connect Vv'ith tlie ideas then present to his mii. But because those with Vv^hom we converse arc al^ suppo- sed to know the meaning of the terms we us^ hence, Secondly, We consider our words as signs l-lhr/ise of the ideas in their minds : and this is the foui»tion of what is called propriety in language, when xsn take care to affix such notions to their words as ie com- monly applied to them by those of m.ost undemanding in the country where they live. The third amlast re- ference of words is to things themselves : foi|aany of our ideas are taken from the several object^ c nature wherev/ith we are surrounded ; and being casidered as copies of things really ejiisting, the* v/ords \ \v they are expressed, are often transferred froi themselves, to signify tliose objects whit supposed to represent. Thus the Vv'ord denotes the idea excited in the mini but is also frequently made to sta body itself which inhabi tary system. N( cation of namej explaining to unfold the, dcscr
70
T*„c„;,. „, ^r in. First, then, Wheii we consider
jDennitions or • r \ • ^ • i
the name teach words as Signs of the ideas in the mind of
only the con- him who uses' them, a definition is no-
nectionofour ^i^^^^pr else but such an exphcation of the words and • c it i
ideas and are iTjeamng oi any term as that the complex
therefore arbi- idea annexed to it by the speaker may be- '^^^y- excired in the understanding of him with
whom he converses ; and this is plainly no more than reaching the connection of our words and ideas, that others m;!y understand the sense of our expressions, and know distinctly what notions we affix to the terms we use. When we say, for instance, that by the word- square we mean a figure bounded by four equal sides„, joined together at right angles, what is this but a de- claration that tlie idea' x>i 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 \\\q dejifiition of the tianie^ because it discovers the meaning of the words or names^ we make use of, by shewing the ideas for which they stand. Now as sounds are of themselves indifferent to- signifv any ideas, hence it is plain that the definitions- of nanies ar^ arbitrary, every man having a liberty to- affix what notions he pleases to his words ; bur the con- venience of communication making it necessary for men speaking the same language to agree as nearly as possible in the signification of sounds, a conformity has- accordiiisjlv been studied. Nevertheless, we find that differences w.li from time to time creep in, which must create great confusion in men's discourses and reason- ings, if they are not careful to define 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 advancement of human knowledge depends upon a right U5*e of definitions \ for as by mean§ of t)iem tliey every where preserve the same determined signification to their words, hence there is little di.'^pute as to the meaning of their expressions, almost all men undcr^
71
standing them in the same sense. And thus it hap- pens, 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 labour and an exact conformity of notions to carry on the improvement of thisbrancli of knowledge. And if men, in other parts of learning, were alike care- ful to fix the meaning of their terms, the progress of science must be greatly furthered, and all those verbal disput€S, that now so much interrupt the course of our improvement, might be prevented.
IV. This then ought to be our first care, j^,^^-,-,^^^ ^f , when we enter upon a design of illustra- the name not ting any particular branch of study> — to always true ascertain our ideas, and mark the names ^p^ real defim- by which they are expressed : and al- though definitions of words are indeed arbitrary, (for a man may affix what ideas he pleases to his terms, nor can any one contest this liberty with him,) yet it will be proper to conform as near as possible to common ac- ceptation, that thereby our thoughts may find a more jeasy and ready entrance into the minds of others. If it should now be asked. What are the rules of a good definition ? I answer, That as in definitions of the name, we aim at no more than teaching the connection of words and ideas, — every contrivance., by which we are enabled to excite the idea annexed to any word in the mind of another, will serve the purpose of a defi- nition. Now the ideas we join with our words are of two kinds : either such as we have reason to believe are already in the minds of others, though perhaps they know not the names by which they are called, or such as, being new and of our own formation, can be no otherwise made known than by a description. In the first case, there is no necessity for laying open the idea itself, because, being already known, any contrivance to remind us of it is sufficient. When we say, for in- stance, that a clock is an instrunie?U hy which we measure tlie- hours of the daijy it is plain that the idea answering
72
to the word cloch, is not here unfolded j but we being beforehand 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 de- fined ; for by saying that luhite is the colour we ob- serve in snow or milk, heat the sensation produced by approaching the fire, we sufficiently make known what ideas we connect with the terms ivh'ite and heaty which is the true purpose of a definition of the name. Hence it appears, that many of those explanations of v/ords, 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 unacquainted with them, but merely contrivances to remind us of known ideas, and teach us the names by which they are called.
but only when ^' ^^^ ^^^^^^ ^^^ ^^^^^ ^^ j^^" ^ith they coincide our words are new and of our own for- vvith the clefi- mation, then they are to be laid open by nition of the ^ description, because, being supposed unknown to others, we must first raise them in their minds before they can learn to connect them with any particular names : and here it is that the definitiofi 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 v/hich the term defined stands. And indeed this alone is what con- stitutes a definition in the true and proper sense of the word, as will appear more fully afterv/ards, when we come' to consider the terms we use as referred to the real objects of nature. We shall therefore .postpone this consideration of the definition of the name, till we come to treat of the definition of the thing •, when it will more naturally fall in our way. It may not however be amiss to observe, that when we say the definitions of the name are arbitrary, we mean not that the descriptions of ideas are so too ; for every idea having a peculiar appearance of its own, by which
73
it is distinguished from all others, nothing is more evi- dent than that the description must be such as to ex- hibit tiiat precise conception. But then the connection of any idea with the name by which it is expressed, being, as we have said, wholly arbitrary, the consider- ing the description of that idea as the definition of that particular name, must be so too ; so that, although de- finitions considered as descriptions of our ideas arc steady and invariable, yet the application of them to particular sounds (which is all that we understand by the definition of the name) is wholly a work of our own free choice.
YI. But, secondly, besides considering
}■■!•£ • J Dennition of
words as the signs of our own ideas, we ^^.^^.^^^ accord- are also very apt on many occasions to re- ing- to the conw fer them to the ideas in the minds of o- n-'on use of ther men. Now, to define a term in this ^^"?:uage, not
arbitrdry.
View, IS to mvcstigate its meaning or ac- ceptation, accoi'ding 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 tlie propriety of lan- guage has assigned them. The words abUitv and genius may by any man be made to stand for one aiid tlie same idea in his own mind ; and if he takes care to advertise us of this, he is at liberty to use them promiscuouslv : but if the common course of language hath confined the word genius to express the natural strength, and talents of the mind, — and the word abilit?/ to denote thpse which are acquired, whoever pretends to explain the proper acceptation of these terms, is bound to" take notice of this difference. As propriety of speech makes our language intelligible, and gives our thoughts a ready entrance into the minds of others, it well de- serves our application and care. The best way to ac- quire it is from the writings and discourses of thosr
H
74 ■
wlio seem to have Lad the clearest notions, and to have applied their terms with the exactest choice and fit- ness.
Definition of ^^^^' ^^'^ ^^^^ now to the third and the thing re- hist species of definition, that namely fers to the real which considers words as referred to things objects of na- them<?elves. . And here it is plain we are
not at liberty to feign and fashion our ex- plications 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 disuses heat and light to the planets nround him, it is not enough that we give an account of the idea answering to that word in our minds ; we must further take care that the idea itself carries in it a real conformity to the object it is supposed to re- present ; and hence it is, that all definitions of this kind, when justly made, are in reality pictures or re- presentations, taken from the being and existence of things ; for they are intended to express their nature vmd properties, so as to distinguish them from all o- thers, and exhibit them clearly to the view of the mind. It is for this reason that logicians call them definitions of thifigs, because they are supposed to refer not so much to the ideas in the understanding, as to the things themselves represented by those ideas.
VIII. And this also lets lis into the distinction he- g^o""^ ^f that distinction so universally tween the defi- received, between definitions of the name nition of the and the thing. The first are arbitrary, name^and of ^^^ ^^^ liable to debate or contradiction. the thine. ^n, , . . i i r
Ine second are propositions capable oi
proof and illustration, and which may therefore be contested. The reason is obvious. Definitions of the name serve only to mark what ideas we connect with our words : and as sounds are of themselves indifferent to signify any ideas, we are entirely at liberty to affix tQi them what notions we please. But it is otherwise \
1
?hc definition of the thing-, for here our worJs ser- ving to denote particular beings in nature, cannot be the signs of any Ideas at pleasure> but of such only as carry in them a conformity to the several objects to which the words refer. A man may use the term sqiiarc^ to express that idea w^aich others denote by the word triangle, and define it accordingly. In this case indeed he recedes from the common forms of speech \ but his definition cannot be charged with falsehood. Ho tells us that by a square he means a three-sided figure : and who can dispute the truth of this, if he really all along uses the v/ord 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 triangle may after this definition be affirmed of the square ; but, as in either c?rse, the idea to v/hich these properties belong is; the same, the propositions only expressing our judgments, and not our judgments themselves, suffer a seeming v-ariation. -
IX. But where words are made to de* ^ previous note particular objects, previous to any connection be- definitions given, their arbitrary explica- tween names tions cannot have place; for in this case cuts off aU we are not put upon explaining what ideas arbitrary ex- we connect with our words, but a connec- plications, tion being already supposed between the name and the thing signified, our business is to unfold that idea by which the object itself is most clearly and distinctly represented. Thus the word gold denotes that metal which is of highest value among men, and goes far- thest in the way of commerce. This connection be- ing once settled, we are no longer left to arbitrary de- finitions, but must describe it by such properties as are really to be found in it, and will best serve to distin- guish it when it comes in our way •, as by saying it is a substance^ yclloWy very heavy, 7nalleahleifusibley Sec.
76
X. From what has been salt], it appears. Why mathe- ^r ^ • % , r ^ • • ^ ^ ^ •
maticddefini- ™^ '" ^^^ language of logicians, defini- tions have been tions of the thing respect only substances accountedmere and beings that have a real existence in defimtjons ol ^y^^^^-Q . servlno; to describe them by their the name, . ,o ., . , S • t
properties and attributes. And this I
doubt not is the reason that the definitions of the ma- thematicians are not considered as definitions cf the thing but of the name, because the ideas therein de- scribed are the mere creatures of the understanding, and not supposed to be copied from patterns existing without us. A circle, a triangle, a square, Sec. such as mathematicians conceive them, are nowhere to be found in nature that we know of. Hence it might justly be accounted absurd, to call our definitions of these dijinitions of the things when they serve not to describe any real objects of nature, but merely to un- fold the conceptions of the mind : and yet if we look into the matter narrowly, we shall find that the rules followed in these definitions are precisely the same with those which logicians have laid down for the definition of the thing. All the several species of figures are described by their properties, some of which are common to different ranks, others peculiar to the tribe defined. The common properties constitute- ■what logicians call the getius, and those that are pecu- liar the difference. Now the genus and diference make up the logical definition of the thing, as will be more ciearlyunderstood from what follows. . , , XI. I am therefore apt to think, that
when yet they ■ ^ a r • • i r
coincide with mathematical detinitions, as they are or the k)gical de- the s.mie general form v^-lth the definitions hnitionofthe ^^ substances, and subject to the same thin":, and , , , . -^ , • i j ^
therefore rules, have been improperly considered as
ousrhtnotto mere definitions of the name, in which be accounted ^re are left wholly to arbitrary explications; uDitraiy. £^^^ however we may change the name
of one figure for another in discourse or writings using the term square to denote a triangles or the word
77
niang/c to express a square^ it is certain the ideas them- selves are invariable, and no less capable of being dis- tinguished by their properties than the several species of substances. Thus, if we suppose the word square to denote that species of figures whose sides severally subtend quadrants of a circumscribed circle, we shall find ourselves equally shut out from arbitrary explica- tions, as in the definition 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, it follows evidently, that the true and proper definition of a square, is that which exhibits the pre- cise idea here mentioned, and no other, to the mind. And thus it appears that the common division of defi- nitions, into those of the name and thing, is not suffi- ciently calculated to give us right apprehensions as to what is and what is not arbitrary,. In the explication of words. It mav not therefore be improper, if we here endeavour to clear up this m.atter a little, and free it from those obscurities in which it has hitherto been involved. To this end we shall premise the following observations.
XII. 1. First, That whatever logicians Definitions, may pretend about the definition of the properly thinij, it is vet certain that none of our speakmg, ne-
j P *-■. . ■" , , 1 . ver reeard
dehnitions, when pursued to their source,- thino-s but regard immediately things themselves, but merely our merely the ideas in our own minds. This °^^" ^'^*=^*- I doubt not will appear a paradox to many, who will be apt to inquire, Whether the definition of gold be not taken from that metal, independent of the various conceptions of men about it ? To this I answer, That indeed in framing our idea of gold, we regard chiefly the thing itself, uniting in our conception such pro- perties as are most conspicuous, and serve best to dis- tinguish 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 concep-
H3
78
tion into their minds. Now this can no otherwise be done but by cnumeratmg the several properties out of which our own complex notion is formed. And in- deed it were in the liighest degree absurd to imagine, that m(2n in explaining things to others, should make use ot' any marks or characters but those by which they arc known to themselves. Hence it comes to pass, tliat all our definitions are in fact nothing else t)ut transcripts of the ideas in our minds. Where these are imperfect, the defmitions must be so too j where they are just and adequate, the copies taken from them, if drawn out with accuracy, and care, can- not Jail to eT'Jiibit the object described. And this will very well serye to account for that great diversity of lieiinitions we often meet with, even of one and the same object ; because men, in consequence of their different pursuits and' applications, falling often into different viev/s of things, must needs vary no less in tlieir defmitions than in the ideas themselves from which these definitions arc copied. He whose obser- vation goes no farther than the more obvious qualities of gold, Vvill content himself with describing it by its colour, weight, and perhaps malleability and fusibility. On the other hand, a goldsmith having inquired far- ther into the nature of that metal, and finding several other properties that equally belong to it, will be apt to take these also into his complex idea, and according- ly introduce them in a delinition. Hence his descrip- tion will add to the former, fixedness and solubility in nqua regla^ &c. and so in proportion as men's various pursuits lead them into a more accurate examination of things, their explications will take a different turn, suitable to the ideas they have framed within them- selves.
Distinction be- XIII. 2. This then being evident, that tweenthede- our definitions respect not things them- finitlon of the selves, but the ideas in our own minds, I name an would in the next place observe, that the
thm<i; useless, ,. . . r , ^ t f ,
and to be re- distmction 01 them mto those ot the name
jected. and thing, is altogether useless, and tends
79
rnther to mislead us than give right apprehensions of the subject In hand ; for thus, men are apt to fancy that many of their definitions are expressive of the real essence of things, whereas they are in truth no more than transcripts of their own ideas : and as it sometimes falls out that these ideas are not collected with sufficient care from the objects they represent, we find by experience that a mistaken idea never fails to occasion a mistake also in the definition. But this could not happen were our definitions copied from things themselves, because their essences being immu- table and always the same, the definition would in this case serve to correct the idea, and might be con- sidered as a stamlard by which to judge whether the idea was rightly framed. I deny not that words are often transferred from our ideas to signify the objects which these ideas represent ; as when vre 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 cur minds, so in describing them to others, all we aim at is, distinctly to lay open our conceptions, about them. Hence it appears, that what logicians call a defiyiltion of the tJihigs, is in truth no more than an unfolding of the idea by which that thing is represented to the understanding. But now, in mathematical definitions, and indeed all others what- soever, this also is our whole aim and intent, to exhi- bit and lay open those ideas of which the words we use are the signs. And thus it happens, that in innumer- able instances, what logicians call the definition of the namey is yet found to coincide with and proceed by the very same rules as the definition ofi the thing ; which fclearly demonstrates the necessity of banishing this frivolous distinction, and establishing some precise and determinate notion, expressive of t^ne true nature of a definition, and comprehending it in its full extent. XIV. Nor will this appear so difficult t> £ • •
^ IT 11 ^ • J 1 1 Definition in
a task, II we call to mmd that words are all cases de- in all cases the signs of our ideas, and no scriptionsof otherwise signify things than as they stand ^"^ ^^^^^'
80
for those Ideas by which things are represented to tlie understanding. By defining our words therefore, we can mean no more than the laying open to the view of others the ideas of which these words are the signs ; for thus it is that the meaning of our expressions come to be known, and that we find ourselves capable of transferring our thoughts and conceptions into the minds of those withAvhom we converse. Where words are referred to things themselves, there we explain the ideas by which these things are represented ; where they denote conceptions framed by the mind, there we lay open these conceptions, and endeavour to exhibit them according to their real appearance within our own breasts. But in both cases it is our own ideas v it is the perceptions of our own minds, either as taken from things without, or framed by the understanding itself, that we explicate and unfold. Not arbitrary, XV. And tlius v/e have at length set- as being con- tied the true and genuine notion of a defi- fined to the nition, comprehendinG: all its varieties,
represi^ntation [■ , '^ . ° , ,
of certain de- ii'Oi^'i whatever science taken, or to what- terniinate no- ever object extended •, for from what we tions. have said it evidently follows, that a defi-
nition is the unfolding of some conception of the mitidy an^ sivering to the laord or term made use of as the sign of it* Now, as in exhibiting any idea to another, it is neces- sary that the description he such as may excite that precise idea in his mind, hence it i^ plain that defini- tions, properly speaking, are not arbitrary, but confined to the representing of certain determinate settled no- tions, such namely as are annexed by the speaker or writer to the words he uses. As nevertheless it is universally allowed that the signification of words is perfectly voluntary, and not the effect of any natural and necessary connection between them and the ideas for which they stand, some may perhaps wonder why definitions are not so too.. In order therefore to un- ravel this difficulty, and shew distinctly what is and what is not arbitrary in speech, we must carefully dis-
81
tingulbh between the connection of our words and ideas, and the unfoldnig of the ideas themselves.
XVI. First, As to the connection of i^he connec- our words and ideas, this it is plain is a tion between purelv arbitrary institution. When, for ^'^^ ^'"'^
r ' 1 ■' . • 1 1 • 1 r ideas, a per-
mstancc, we have in our minds the idea ot ^^^^.j^ ^^.j^n. dny particular species of metals, the call- tary establish- ing it by the name goldj is an effect of the nient. voluntary choice of men speaking the same language, and not of any peculiar aptness in that sound to express the idea. Other nations we find make use of different sounds, and with the same effect. Thus Aurum de- notes that idea in Lathiy and Or in French. And even the word gold itself, would have as well served to ex- press the idea of that metal which we call silvery had custom in the beginning so established it.
XVII. But although we are thus en- The descrip-
tirely at liberty, in connecting any idea t^^"^ ^^ ^^^'-^^
with any sound, yet it is quite otherwise ^^Inaedtothe
in unfolding the ideas themselves ; for representation
every idea, having a precise appearance of of that precise
its own, by which it is distinguished from appearance
',■'., . . .9 , , by which they
every other idea, it is manliest, that,, in ^^^ eimw-
laying it open to others, we must study guished among such a description as shall exhibit that themselves. peculiar appv?arince. Vv^lien we have formed to our- selves the idea of a figure bouad^^d by four ^^qua] sides, joined togpther at right a'lgles, we a^'e at liberty to ex- press that idea by any soond, anf". may caU it either a square or a triafigle, Biit ^vhichever of these names wf: use, so long as the idea ia tlie sanie^ the description by which wc would sir>;nify- it to another, must be so too. Let it be called square or triangUy it is still a fi- gure having fo'jr equal sides, and all its angles right ones. Hence we clearly see what is and what is not arb'trary in the use of words. The establishing any sound as the mark of some determinate idea in the mind, is the effect of free choice, and a voluntary com- bination among men \ and as different nations make
82
use of different sounds to denote the same ideas, hence proceeds all that variety of languages which we meet with in the world. But when a connection between our ideas and words is once settled, the unfolding of the idea answering to any w-ord which properly con- stitutes a definition, is by no means an arbitrary thing ; for here, as I have ah'eady observed, we are bound to exhibit that precise conception which either the use of ]angu:ige or our own particular choice hath annexed to the term we use.
^ „, XVIII. And thus it appears that defini-
obscurity that ^^^^^^ considered as descriptions of ideas in has hitherto the mind, are steady and invariable, being- perplexed the bounded to the representation of those nit^oifs^ precise ideas. But then in the application
of definitions to particular names, we are altogether left to our own free choice •, because, as the connecting of any idea with any sound is a perfectly- arbitrary institution, the applying the description of that idea to that sound must be so too. When there- fore logicians tell us that the definition of the name is arbitrary, they mean no more than this : That as dif- ferent ideas may be connected with any term, accord- ing to the 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 connection being settled, and the term considered as the sign of some fixed. idea in the understanding, we are no longer left to- arbitrary explications, but must study such a description as corresponds with that pre- cise idea. Now this alone, according to what has been before laid down, ought to be accounted a definition. What I am apt to think has occasioned no smalj confu- sion in this matter, is that many explanations of words, where no idea is unfolded, but merely the connection between some word and idea asserted, have yet been dig- nified with the name of definitions. Thus in the in- stance before given, when we say that a deck is an /;;-> strument by ivhich we measure time^ this is by some called
83
a definition ; and yet it is plain that v/e Tvrc beforehand -supposed to have an idea of this instrument, and only taught that the word clock serves in common language to denote that idea. By this rule all explications of w^ords in our dictionaries will be definitions ; nay, as was already observed, the names of even simple ideas may be thus defined. White we may say is the colour we observe in snow or milk, heat the sensation pro- duced by approaching the fire, and so in innumerable other instances. But these, and all others of the like kind, arc by no means definitions exciting new ideas in the understanding, but merely contrivances to remind us of known ideas, and teach their connection with the established names. It is nevertheless worth our no- tice, that what logicians call definitions of the name, -extend properly no farther than these explanations, serving to mark the connection of our ideas and words ; and are therefore justly accounted arbitrary, inasmuch -as the connections themselves are altogether so.
XIX. But now in definitions properly complex idea? so called, we first consider the term we alone capable use as the sign of some inward conception, ^[ ^\^^^ \^^'^
. , 1-1 ox description
either annexed to it by custom, or our ^Yhich goes by
own free choice; and then the business the name of a of the definition is to unfold and explicate definition. that idea. As therefore the whole art lies in giving Just and true copies of our ideas, a definition is then said to be perfect when it serves distinctly to excite -the idea described in the mind of another, evens up- posing him before wholly unacquainted with it. This point settled, let us next inquire into what those ideas are which are capable of being thus unfolded. And in the first place, it is evident, that all our simple ideas are necessarily excluded. We have seen already, that experience alone is to be consulted here, insomuch that if either the objects whence they are derived come not in our way, or the avenues appointed by nature for their reception are wanting, no description is suf- ficient to convey them into the mind. But where the
84
utulerstaiullng is already supplied with these original and primitive conceptions, as they may be united to- gether in an infinity of different forms, so may all their several combinations be distinctly laid open by enumerating the simple ideas concerned in the various collections, and tracing the order and manner in which they are linked one to another. Now these combina- tions of simple notices constitute what we call our complex notions ; whence it is evident that complex ideas, and those alone, admit of that kind of descrip- tion which goes by the name of a Definition.
\\-\ „ -, o^«, XX. The business of definitions is now
\V hen a com- ^ i • i i • mi
plex idea may I thuik pretty plam . They are, as we
be said to be have Seen, pictures or representations of fully unfolded. Q^Y Ideas 5 and as the'se representations are then only possible when the ideas themselves are complex, it is obvious to remark, that definitions can- not have place but where we make use of terms stand- ing 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, describe its parts, and shew 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, we must again call to mind, that the design of a defi- nition is, so to unfold the idea answering to any term, as that it may be clearly and distinctly transferred into the mind of another. But now our complex ideas, v/hich 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 com- prehend them perfectly when we know the several simple id«as of which they consist, and can so put them together in our minds as is necessary towards the framing of that peculiar connection which gives every idea its distinct and proper appearance. Two things XXI. Two things are therefore required
required in a in every definition. First, That all the definition : original ideas, out of which the complex
■ 85
one is formed, be distinctly enumerated.
(^ II m\ f J J i.* t.0 enumerate
Secondly, That the order and manner ot ^j^^ .^^,^^^^ ^^^^
combining them into one conception be explain the clearly explained. Where a definition has manner of these requisites, nothing is wanting to its ^ ^^!^ combi- perfection; because everyone who reads it, and understands the terms, seeing at once what ideas he is to join together, and also in what manner, can at pleasure form in his own mi'nd the complex concep- tion answering to the term defined. Let us, for in- stance, suppose the word square to stand for that idea, by which we represent to ourselves a figure whos& sides subtend quadrants of a circumscribed circle. The parts of this idea, are the sides bbunding the figure. These must be four in number, and all equal among themselves, because they are each to subtend a fourth part of the same circle. But besides these component parts, we must also take notice of the manner of putting them together, if we would exhibit the precise idea for which the word square here stands ; for four equal right lines, any how joined, will not subtend quadrants of a circumscribed circle. A figure with tliis property, must have its sides standing also at right angles. Taking in therefore this last considera- tion respecting the manner of combining the parts, the idea is fully described, and the definition thereby ren- dered complete ; for a figure bounded by four equal sides, joined together at right angles, has the property required, and is moreover the only right-lined figure to which that property belongs.
XXII. And "now I imagine it will be „ , . . o How we are
obvious to every one m what manner we to proceed t*
ought to proceed, in order to arrive at arrive at just
just and adequate definitions. First, We ^"J adequate
,.1 ^. r^i'j ^ definitions.
are to take an exact view or tne idea to
be described, trace it to its original principles, and
mark the several simple perceptions that enter into
the composition of it. Secondly, We are to consider
the particular manner in which these elementarj' vdow^
I ■
8r> o
are combined, in order to the forming of that precise conception for which the term we make use of stands. When this is done, and the idea wholly unravelled, we have nothing more to do than fairly transcribe the appearance it makes to our own minds. Such a de- scription, 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 attains the true and proper end of a definition.
CHAP. VII.
OF THE COMPOSITION AND RESOLUTION OF OUR IDEAS, AND THE RULES OF DEFINITION THENCE ARISING.
^ , I. The rule laid down in the foreeoinff
In compound- , ^ fe>
inff our ideas chapter IS general, extending to all possi- we proceed by ble cases J and is indeed that to which a- a successive jgj^g ^q ^^^ have recourse where any gra a ion. doubt or difficulty arises. It is not how- ever necessary that we should practise it in every par- ticular instance. Many of our ideas are extremely complicated, insomuch, that to enumerate all the sim- ple perceptions out of which they are formed, would be a very troublesome and tedious work. For this reason,^ logicians have established certain compendious rules of defining, of which it may not be amiss here to give some account. But, in order to the better under- standing of what follows, it will be necessary to ob- serve, that there is a certain gradation in the composi- tion of our ideas. The mind of man is very limited iH its views, and cannot take in a great number of ob- jects at once. "We are therefore fain to proceed by steps, and make ovir first advances subservient to those which follow* Thus, in forming our complex notions,
p
87
we begin at first with but a few simple ideas, such as we can manage with ease, and unite them together into one conception. When we are provided with a sufficient stock of these, and have by habit and use rendered them famiHar to our minds, they become the component parts of other ideas. still more complicated, and form what we may call a second order of com- pound notions. This process, as is evident, maybe continued to any degree of composition we please, mounting from one stage to another, and enlarging the number of combinations.
II. But now in a series of this kind, Hence ideas of whoever would acquaint himself perfectly this class best with the last and highest order of ideas, comprehended. finds it much the most expeditious method ^^^j!^*^^, gradu- to proceed gradually through all the inter- ally through mediate steps; for was he to take any ail the several very compounded idea to pieces, and with- ^^'^^^■^> out regard to the several classes of simple perceptions, that have already been formed into distinct combina- tions, break in at once into i;s original principles, th? number would be so great as perfectly to confound the imagination, and overcome the utm.ost reach and ca- pacity of the mind. "When we see a prodigious mul- titude of men jumbled together in crowds, without order, or any regular position, we find it. impossible to arrive at an exact knowledge of their number. I^ut if they are formed into separate battalions, and so station- ed 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 perceptions, out of which they are framed, are very numerous, it is not enough that we take a viev/ of them in loose and scattered bodies j we 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 tJie compound notices resulting from them.
12
88
, ^ . , III. This g;radual progress of the mind
».i'.ir definitions ^ • a ^- i i
ought to keep ^^ ^^^ compound notions, througn a varie-
p:vce with our ty of intermediate steps, plainly points out ideas, and oh- the manner of conducting the definitions >tfrve a hke ^ which these notions are conveyed into gradation. / • i r • i r i • i
the nnnds or others ; tor as the series be- gins with simple and easy combinations, and advances through a succession of different orders, rising one a- bove another in the degree of composition, it is evident tliat in a train of definitions expressing these ideas, a like gradiition is to be observed. Thus tlie complex ideas of the lowest order, can no otherwise be descri- bed than by enumerating the simple ideas out of which they are made, and explaining the manner of their union. But then in the second, or any succeeding order, as they are formed out of those gradual com- binations that constitute the inferior classes, it is not necelsary in describing them to mention one by one all the simple ideas of which they consist. They may be more distinctly and briefly unfolded by enumerating the compound ideas of a lower order, from whose union they result, and which are all supposed to be already known, in consequence of previous definitions. Here then it is that the logical method of defining takes glace ; which, that we may the better understand, I shall explain somewhat more particularly the several steps and gradations of the mind in compounding its ideas, and thence deduce that peculiar form of a de- finition which lopjicians have thought fit to establish. IV. All the ideas we receive from the le steps y g^ygj.^} Q^jects of nature that surround us, -which the J . • ,. ., , rr.,
mind proceeds represent distmct mdividuals. Inesc in-
from particular dividuals, when compared together, are to general found in certain particulars to resemble. Hence by collecting the resembling par- ticulars into one conception, we form the notion of a species. And liere let it be observed, that this last idea is less complicated than that by which we represent any of the particular objects contained under it ; ior
89
the idea of the species excludes the peculiarities of the several individuals, and retains only such pro- perties as are common to them all. Again, by com- paring several species together, and observing their re- semblance, we form the idea of the genus ; where, in the same manner as before, the composition is lessen- ed, because we leave out what is peculiar to the several species compared, and retain only the particulars wherein they agree. It is easy to conceive the mind proceeding thus from one step to another, and advan- cing through its several classes of general notions, until at last it comes to the highest genus of all, denoted by the word bei/igy where the bare idea of existence is only concerned.
V. In this procedure we see the mind The conduct unravelling a complex idea, and tracing it of the mind in in the ascending scale, from greater to less <-ompounding
1 r ^ • ' -x-^^'- its ideas, as it
degrees or composition, until it tcrmmatcs advances thro' in our simple perception. If now we take the different the series the contrary way, and beginning orders ci-per- witli the last or highest genus, carry our ^^P'-^^"* view downwards, through all the inferior genera and species, quite to the individuals, we shall thereby ar- rive at a distinct apprehension of the conduct of the understanding in compounding its ideas *, for in the se- veral classes of our perceptions, the highest in the scale is for the most part made up of but a few simple ideas, such as the mind can take in and survey with ease. This first general notion, when branched out into the. different subdivisions contained under it, has in every one of them something peculiar, by which they are distinguished among themselves ; insomuch, that in descending from the genus to the species, we always superadd some new idea, and thereby increase the degree of composition. Thus the idea denoted by the wordjigure, is of a very general nature, ^nd composed of but lew simple perceptions, as implying no more than, opace every where bounded. But if we descend far- ther, and consider the boundaries of this space as that
13
90
they may be either lines or surfaces, we fall into the several species of figure -, for where the space is bound- ed by one or more surfaces, we give it the name of a solid Jigiire ; but where the boundaries are lines, it is c al led a pla'm figure .
Th "[ ■ i h ^^' "^^ ^'^ view of things, it is evident species formed ^^'^^ ^^^"^ species is formed. by superadding by superadding a ncw idea to tlie genus. Here, for in- the specific stance, the genus is circumscribed space.
l^iJ^^^!"^*^ ^^ If 110W to this we superadd the idea of a ihc genus; . • .• u r r
cnxumscnption by Ime, we Irame tne no- tion of that species of figures which are called plaiji ; but if we conceive the circumscription to be by sur- ■ faces, we have the species of solid figures* Tliis super- added idea is called the specific difierence, not only as it serves to divide the species from the genusy but because, being different in all the several subdivisions, we there- by also distinguish the species one from another. And ss it is likewise that conception which, by being joined to the general idea, completes the notion of the species^ hence it is plain that the genus and specific difference are to be considered as the proper and constituent parts of the species. If we trace the progress of the mind still farther, and observe it advancing through the inferior species, we shall find its manner of proceeding to be always the same ; for every lower species is formed by superadding som!i new idea to the species next above it ; insomuch that in this descending scale of our per- ceptions, the understanding passes through different orders of complex notions, which become more and m<5re complicated at every ste^^ it takes. Let us re* sume here, for instance, the species of plain figures : they imply no more than space bounded by lines. But if we take in an additional consideration of the nature of these lines, as whether they are right or curves^ we fall into the subdivisions of plain figure, distinguished by the names Rectilinear^ Curvilinear and Alixtilinear.
91
VII. And here we are to observe, that
though plain figures, when considered as |'nferL\pecL
one of those branches that come under the by superadding
notion of figure in general, take the name the specific dif.
of a species, yet compared with the classes ^^^^"'^^ ^^ ^^^ - ^ ... ' ■' ...^ , . ... nearest genus,
of curvilinear, rectilinear, and mixtilinear,
into which they themselves may be divided, they really become a genus, of which the before-mentioned sub- divisions 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 j for in the curvilinear kind, the curvity of the lines bounding the figure makes what is called the specific differetice ; to which if we join the genus, which here is plain figure or space circumscribed by lines, we have all that is necessary towards completing the notion of the species. We are only to take notice, that this last subdivision having two genera above it, viz. plain figure and figure in general, the genus joined with the specific difference, in order to constitute the species of cuivilinears, is that which lies nearest to the said species. It is the notion of plain figure, and not of figure in general, that, join- ed with the idea of curvity, make up the complex conceptions of curve-lined figures ; for in this descend- ing scale of our ideas, figure in general, plain figures, curve-lined figures^ the two first are considered as genera in respect of the third \ and the second in order, or that which stands next to the third, is called the mar est genus. But now, as it is this second idea which, joined with the notion of curvity, forms the species of curvc'lined JigurcSf it is plain that the third or last idea in the series, is made up of the nearest genus and sjpe^ c'lfic difference. This rule holds invariably, however far the series is continued •, because in a train of ideas thus succeeding one another, all that precede the last are considered as so many genera in respect of that last, and the last itself is always formed by superadding the specific difference to the genus next it.
92
The idea of an VIII. Here then we have an universal individual description, applicable to all our ideas of composed of whatever kind, from the highest fjenus to
the lowest spe- ^11 ^t. ^ • r ^ 1 • 1
cies and nu- ^^^^ lowest speciCs ; for, taking them lu meric dif- Order downvvards from the said general ference. idea, they every where consist of the ^t"-
niis proxhmuni and dijferentia specijicay as logicians love to express themselves. But when we come to the lowest species of all, comprehending under it only in- dividuals, the superadded idea, by which these indi- viduals are distinguished one from another, no longer takes the name of the specific difference *, for here it serves not to denote distinct species, but merely a va- riety of individuals, each of which having a particular existence of its own, is therefore numerically different from every other of the same kind. And hence it is, that in this last case, logicians choose to c?dl the super- added idea by the name of the numerical difference ; in-» somuch that as the idea of a species is made up cf the nearest genus and specific differertce^ so the~ idea of an in- dividual consists of the Icivest species and 'numeric dif- ference. Thus the circle is a species of curve-lined fi- gures, and what we call the lowest species^ as compre- hending under it only individuals. Circles in particu- lar are distinguished from one another by the length and position of their diameters. The length therefore and position of the diameter of a circle, is what logi- cians call the numerical difference ; because these being given, the circle itself may be described, and an indi- vidual thereby constituted.
- . . IX. And thus we have endeavoured to
Deunitions to • 1 1 i i .i.
follow one ano- trace, m the best manner we are able, the
ther in train, progress of the mind in compounding its and pass ideas. It begins we see with the most
l!S.Tstct'sive general notions, which, consisting of but gradations as few simple notices, are easily combined our compound and brought together into one conception. ideas. Thence it proceeds to the species compre-
hended under this general idea \ and these are forni.cd
93
by joining together the genus and svecifcc aifference : and as it often happens that these species may be still fur- ther subdivided, and run on in a long series of conti- nued gradations, producing various orders of compound perceptions, so all these several orders are regularly and successively formed, by annexing in every step the specific difference to the nearest genus. When by this method of procedure, we are come to the lowest order of all, by joining the species and numeric aifference^ we frame the ideas of individuals : and here the series necessarily terminates, because it is impossible any farther to bound or limit our conceptions. This view of the composition of our ideas, representing their constituent parts in every step of the progression, na- turally points out the true and genuine form of a defi- nition ; for as definitions are no more than descrip- tions of the ideas for which the terms defined stand ; and as ideas are then described when we enumerate distinctly and in order the parts of which they consist, it is plain that, by making our definitions follow one another, according to the natural train of our concep- tions, they will be subject to the same rules, and keep pace with the ideas they describe.
X. As therefore the first order of our »rt, r .^ r compound notions, or the ideas that con- definition in all stitute the highest genera in the different the various or- scales of perception, are formed by uniting '^.^^^ o£concep- together a certain number of simple no- tices, so the terms expressing these genera, are defined hi) enumernting the simple ?iotices so combined. And as the species comprehended under any genus, or the complex ideas of the second order, arise from super- adding the specific difference to the said general idea, so tlie definition of the names of the species is absol- ved in a detail of tlie ideas of the specific difference connect" ed ivith the term of tlie genus. For the genus having been before defined, the term by which it is expressed stands for a known idea, and may therefore be intro- duced into all subsef^ucnt definitions, in the same
94
manner ns the names of simple perceptions. Ir will now I think be sufficiently obvious, that the definitions of all the succeeding orders of compound notions will every where consist of the term of the nearest genus joined ivlth avi enumeration of the ideas that constitute the specif c difference ; and that the definition of individuals utiites the name of the ^irf j/ species ivith the terms bij ivhich ive express the ideas of the numeric difference.
The loo-lcd ^^* K^'^^ ^^^"^ we have the true and
method of de- proper form of a definition, in all the va- fiiiing, perfect rious Orders of conception. This is that in Its kind, method of defining vwhich is commonly called hgical^ and which we see is perfect in its kind, inasmuch as it presents a full and adequate description of the idea for which the term defined stands. There are still two things worthy of observation, before we take leave of this subject. First, That the very frame and contexture of these definitions points out the or- der in which they ought to follow one another \ for as the name of the genus is admitted into a description, only in consequence of its having been before defined, it is evident that we must pass gradually through zA\ the difi^erent orders of conception. Accordingly, logi- cians lay it down as a rule, that we are to begin always with the highest genus, and carry on the series of de- finitions regularly tlirough all the intermediate genera and species, quite down to the individuals. By this means our descriptions keep puce with our ideas, and pass through the same successive gradations •, inso- much, 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 com- plicated notions. Now this is the true and proper end of defining, and indeed the highest perfection of that art. , ,■ , , XII. There is vet another thinsf to be
and apphcabie , , i • S i i i '
to all words obscrved on this head, namely, tnut tne whatsoever, form here prescribed, is applic;ible to all
capable of a words whatsoever, capable of a definition ;
denniticn. r ' ^ i .
for as every term we use must denote
9
i>
some idea, either" general or particular ; and as all our complex notions relating to both these classes of per- ception, from the highest genus quite down to the indi- viduals, come within the rules of description here given, it is evident, that this particular manner of unfolding an idea may be extended to all the possible complex conceptions we can connect with our words. By the rules therefore of this method, definitions may be ap- plied to aid terms standing for complex ideas ; and as these, by what we have shewn at large in the two foregoing chapters, are the only definable articles of speech, it necessarily follows, that the directions here given are universal, extend to all particular instances, and are alike applicable in all languages. And thus, at length, we have not only deduced that peculiar form of a definition which obtains among logicians, but shewn it also to he perfect in its kind, and to take m the whole compass of language.
THE
ELEMENTS OF LOGIC
BOOK II.
OF JUDGMENT OR INTUITION.
CHAP. I.
OF OUR GROUNDS OF HUMAN JUDGMENT.
Intuition re- I. * * HEN the mind Is furnished with
spects the re- ideas, its next step in the way to know- twe'enour' ledge is, the comparing these ideas to- ideas when gcther, in Order to judge of their agree- they are im- mentor disagreement. In this joint view mediately q£ ^^^ ideas, if the relation is such as to ^ * be immediately discoverable by the bare
inspection of the mind, the judgments thence obtained are called intuitive^ from a word that denotes to look at : for in this case, a mere attention to the ideas compa- tcd, suffices to let us see how far they are connected or disjoined. Thus, that the whole is greater than any of its part Si is an intuitive judgment, nothing more being re- quired to convince us of its truth than an attention to
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the Ideas of ':uhole and part. And this too Is the reason why we call the act of the mind forming these judg- ments, intuition / as it is indeed no more than an im- mediate perception of the agreement or disagreement of any two idea§.
II. But here it is to be observed, that gj^-pej-ience our knowledge of this kind, respects only and testimony our ideas, and the relations between them, the ground of and therefore can serve only as a founda- J^*^8"^S ^^ to
, . ' 1 I • tacts.
tion to sucii reasonmgs as are employed in investigating these relations. Now it so happens, that many of our judgments are conversant about facts and tlie real existence of things, which cannot be traced by' the bare contemplation of our ideas. It does not fol- low, because I have the idea of a circle in my niin(i^ that therefore a figure answering to that idea Jias a real existence in nature. I can form to myself th^ notion of a centaur, or golden m.ountaln, but never imagine on that account that either of them exist. What then are the grounds of our judgment in rela^- tion to facts i* I answer, These two, experience and tes- _ iimoiiy. By experience we are informed of the existence of the several objects which surround us and operate on our senses. Tesfunony is of a wider extent, and readies not only to objects beyond the present sphere of our observation, but also to facts and transactions, which being now past, and fiaving no longer any ex- istence, could not witliout this conveyance have fallen under our cognizance.
III. Here then we have three founda- Three founda- tions of human judgment, from which the tions of humaa whole system of our knowledge mav with ju^lgnient, viz. case and advantage be deduced. Ist, In- Jhe"^"ound of tuition^ which respects our ideas themselves scientifical and their relations, and is the foundation kiiowledge. of that species of reasoning which we call demonstration : for whatever is deduced from our intuitive perceptions by a clear and connected series of proofs, is said to be <lcmonstrated, and producea absolute certainty m the
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Riiiid. Hence the knowledge obtained in this manner, , is what we properly term science; because in every step of the procedure it carries its ovrn evidence along- with it, and leaves no voom for doubt or hesitation ; nnd what is highly worthy of notice, as the truths of this class express the relations between our ideas, and the same relations must ever and invariably subsist be- tween the snme ideas, our deductions in the way of science constitute what we call eternal, necessary, and ' immutable truths. If it be true that the whole is equal to all its parts, it must be so unchangeably, because the relations -of equality being attached to the ideas themselves, must ever intervene where the same ideas are compared. Of this nature are all the truths of na- tural religion, morality, and mathematics ; and in ge- neral whatever may be gathered from the bare view and consideration of our ideas.
IV. The second ground of human jude-
C. F-xpenence ^ • . ^^ i • i • r
the PTovnd of '"^"'^^-^ ^^ experience ; trom winch we niter
uur knowledge the existence of those objects that sur- of the powers roiuid US, and fall under the immediate j.nd equalities of ^^^.-^^ ^£ ^^^ senses. When we see the podies^ 1 -1 1-
sun, or cast our eyes towards a buiidmg,
we not only have ideas of these objects within our- selves, but ascribe to them a real existence out of the mind. It is also by the information of the senses that we judge of the qualities of bodies ; as when we say that §now is white, fire hot, or steel hard ; for as we are wholly unacquainted with the internal structure and constitution of the bodies that produce these sen- ^ sations in us, nay, and are unable to trace any connec- tion between that structure and the sensations them- selves, it is evident that we build our judgments alto- gether upon -observation, ascribing to bodies such qua- lities as are answerable to the perceptions they excite in us. But this is not the only advantage derived from experience, for to that tod) are we indebted for all our knowledge regarding the co-existence of sensible qua- lities in objects, and the operattow* of bodi<iSi Que upon
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another. Ivory, for instance, is hard and elastic : thi."?, we know by experience, and indeed by that alone , for being altogether strangers to the true nature both oi elasticity and hardness, we cannot by the bare con- templation of our ideas determine how far the one necessarily implies the other, or wheiher there may not be a repugnance between them. But when we observe them to exist both in the same object, we are then assured from experience, .that they are not in- compatible ; and when we also find that a stone is hard atid not elastic, and that air though elastic is not hard, we also conclude upon the same foundation, that the ideas are not necessarily coiijomed, but may exist separately in dilFerent objects. In like manner with regard to the operations of bodies one upon another, it is evident that cur knowledge this way is all derived from observation o y^qua regla disscives gold, as lias been found by frequent trial, nor is there any other way of arriving at the discovery. Naturalists may tell us, if they please, that the parts of aqua regia are of a texture apt to insinuate between the corpuscles of gold, and thereby loosen and shake them asunder. If this is a true account of the matter, I believe it will notwith- standing be allowed, that our conjecture in regard to the conformation of these bodies is deduced from the experiment, and not the experiment from the conjec- ture. It was not from any previous knowledge of the intimate structure of aqua rcgia and gold, and the apt- ness of their parts to act or be acted upon, that w& came by the conclusion above mentioned. ' The inter- nal constitution of bodies is in a manner Vv'holly un- known to us ; and could we even surmount this diffi- culty, yet as the separation of the parts of gold implies something like an active force in the menstruum^ and we are unable to conceive how it comes to be possess- ed of this activity, the effect must be owned to be al- together beyond our comprehension. But when repeat- ed trials had once confirmed it, insomuch that it was admitted as an established truth in natural knowledge^,
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it was then easy for men to spin out theories of their own invention, and contrive such a structure of parts both for gold and aqua regia, as would best serve to ex- plain the phenomenon upon the principles of that system of philosophy they had adopted. I might easi- ly shew, from innumerable other instances, how much our knowledge of the mutual action of bodies depends upon observation. The bite of a viper mhII kill ; plants are some salutary, others noxious ; fire dissolves one body, and hardens another. These are truths gene- rally known j nor ia it less evident that we owe their discovery wholly to experience.
-,,, _ V. And hence it is easy to account for
whv many • * i
useful inven- v/hat to some writers has ap|)eared a very
tionsowe their great paradox j that most of the important birth to inventions in human life have taken their
rise from chance, and instead of coming out of the schools of philosophers, are for the most part a- scribed to men of no figure in the commonwealth of learning. Sowing, planting, the use of the Compass, ~^}ul such like, are not deductions ofhuman reason, but discoveries which owe their birth to observaticffi and trial. No wonder, therefore, if these inventions de- rived their beginning from such as being engaged in the active and busy scenes of life, were more in the way of those experiments which lead to discoveries of this nature^ Artd here, as the parj:icular callings and professions of men, and oftentimes chance, has a great ♦Hscendant, it need not seem strange if some of the most useful arts in society appear to have had an ori- ginal purely casual.
Nr.tural know- ^^' F'^^OJT^ what has been said, it is evi- iedge from die dent, that, as intuition is the foundation of grounds on what we Call scientifii:al knowledge, so is
which it rests, • r , j r ^-l- ^ „^ \
aptly termed experience of natural; — for this last be- cxperimental ing whoUy taken up with the objects of philosophy. sense, or those bodies that constitute the natural world ; and their properties, as far as we can diicover them, being to be traced only by a long and
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painful series of observations, it Is apparent, tliat, in order to improve this branch of knowledge, we must betake ourselves to the method of trial and experi- ment. Accordingly, we find, that while this was neglected, little advance was made in the philosophy of nature ; whereas a contrary proceeding has enr'-ched the present age with many valuable discoveries ; inso- much that natural knowledge, in allusion to the founda- tion on which it stands, has been very aptly called experimental pJuIosophij.
VII. But though experience is what Though much we .may term the immediate foundation ofour'kncw- of natural knowledge, yet v/ith respect to i<^dge of body particular persons, its influence is very f*^P^"^"^°" •
I r 1 r-ni 1 1- 1 testimony, yet
narrow and connned. ine bodies that ex'serience is surround us are numerous, many of them the ultimate lie at a great distance, and some quite f'^^^^'-lation of beyond dur reach. Life too is short, and so crowded with cares, that but little time is left for -any single man to employ himself in unfolding the mysteries of nature. Hence it is necessary to admit many things upon the testimony of others, which bv this means becomes the foundation of a great part of our knowledge of body. No man doubts of the power qf aqua regia to dissolve gold, though perhaps he never himself made the experiment. In these, there- fore, and such like cases, we judge of the facts and operations of nature upon the mere ground of testi- mony. However, as v/e can always have recourse to experience where any doubt or scruple arises, this is justly considered as the true foundation of natural philosophy *, being indeed the, ultirhate support upon which our assent rests, and whereto we appeal, whea the highest degree, of evidence is required.
VIII. But there are many facts that ^ . will not allow of an appeal to the senses *, ihe ground of and in this case testimony is the true and historical only foundation of our judgments. AH, ^"°^^^^''^fc^* human actions, of whaterer kind^when considered as
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already past, are of the nature here described •, because having now no longer any existence, both the facts themselves and the circumstances attending them, can be known only from the relations of such as had suPii- cient opportunities of arriving at the truth. TesUmonif therefore is justly accounted a third ground of human judgment \ and as from the other two we have dedu- ced scientifical and natural knowledge, so may we from this derive historical ; by which I would be understood to mean, not merely a knowledge of the civil transac- tions of states and kingdoms, but of all facts whatso- ever, where testimony is the ultima.te foundation of our belief.
IX. Before I conclude this chapter, it operaticm of "^'^^ ^^ necessary to observe, that though the mind com- the sccond Operation of the mind, proper- monly extend- ly speaking, extends not beyond intuitive f beyond perceptions, yet logicians have not confi- ned themselves to so strict a viev? of it; but calling it by the mmejudg7?2e?2t, thereby denote all acts of the mind, where only two ideas are compared with- out the immediate interposition of the third ; for when the mind joins or separates two ideas, though perhaps this i^ done in consequence of a train of pre- vious reasoning, yet if the understanding proceeds upon establislied notions, without attending to that train of reasoning, its determinations are still consider- ed as acts of judgment. Thus, t/iat God created the HTiivfrse, that men are accountable for their actions^ are frequently mentioned by logicians as instances of the mind judging ; and yet it is apparent that these judg- ments are by no means ^f the kind we call intuitive ; pay, that it requires much exercise of the reasoning faculty before a man can trace their connection with the perceptions of that name. I could in the same manner easily shew, that even our judgments of expe- rience and testimony^ when pursued to their source, derive all their power of persuasion from being linked with intuitive truths. But I ehall wave this inquiry
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for the present, as being of a nature too subtle for & work of this kind. The remark itself, however, was needful, as well to illustrate the proper distinctioa be- tween the powers of the understanding, as to explain the reason, why in this part of logic, we extend the second operation of the mind beyond those limits that, in strictness of speech, belong to it. Let us now pro- ceed to consider a little more particularly the nature and variety of these our judgments.
CHAP. II.
or AFFIRMATIVE AND NEGATIVE PROPOSITIONS.
I. Where the comnarincf of our ideas r^, , .
. , , , * ^ c 1 ' ^ ^"^ subject
IS considered merely as an actor the mnid and predicate assembling them together, and joining or of a proposition disjoining them according to the result of ^^pl^i"^^- its perceptions, we call it judgfr.ent ; but when, out judgments are put iii+o words, they then bear the name oi propositions, A proposition tlierefore is a sen- tence expressing some judgment of the mind, whereby two or more ideas are affirmed to agree or disagree. Now as our judgments include at least two ideas, one of w^hich is affirmed or denied of the other, so must a proposition have terms answering to these ideas. The idea of which we affirm or deny, and of course the term expressing that idea, is called th6 subject of the proposition. The idea affirmed or denied, as also the term answering it, is called the predicate. Thus in the proposition, God is omnipotent : God is the subject, it being of him that we affirm omnipotence ; and onmipo^ tent is the predicate, because we affirm the idea, ex- pressed by that word, to belong to God.
II. But as in propositions ideas are ei- The copula, ther joined or disjoined, it is not enough &c.
to have terms expressing those ideas, unless we have
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^so some words to denote their agreement or disagree- ment. That word in a proposition which connects two ideas together, is called the copila ; and if a nega- tive particle be annexed, we thereby understand that the ideas are disjoined. The substantive verb is com- monly made use of for the copula, as in the above- mentioned proposition God is ommpote?it ; when it repre- sents the copula, and signifies the agreement of the i- deas of Gcd and omnipotence. But if we mean to sepa- rate two ideas \ then, besides the substantive verb, we must also use some partiple of negation to express this repugnance. The proposition, man is not perfect <^ may serve as an example of this kind, v/here the notion of perfection being removed from the idea of man^ the negative particle not is inserted after the copula, to signify the disagreement between the subject and pre- dicate.
Propositions ^^^' ^^^^7 P^OpOSition necessarily con-
sometimes ex- sists of these three parts, but then it is a- pressedby a like needful that they be all severally ex- single word, pressed in words ; because the copula is often, included in the term of the predicate, as when we say he sits ; which import^ the same as he is sitting. In the Latin language, a single word has often the force of a whole sentence. Thus amhulat is the same as ille est amhulans ; amo^ as ego sum amans ; and so in innumerable other instances ; by which it appears, that we are not so much to regard the number of words in a sentence as the ideas they represent, and the manner in which they are put together ; for whenever two i- deas are joined or disjoined in an expression, though of but a single word, it is evident that we have a sub- ject, predicate, and copula, and of consequence a com- plete proposition.
Affirmative ^' When the mind joins two ideas,
and negative we Call it an <7^rw^//-i'^ judgment ; when propositions, jj- separates them, a negative ,- and as any two ideas compared together, must necessarily either agree or not agree, it is evidewt that all our judgments
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fall under these two divisions. Hence, IHiewise, the propositions expressing these judgments, are all either affirmative or negative. An affirmative proposition connects the predicate with the subject, as a stone is heavy : a negative proposition separates them, as God is net the author of evil. Afflrmatiojt therefore is the same as joining two ideas together ; and this is done by means of the copula. N^gatiofj, on the contrary, marks a repugnance betw^een the ideas compared j in which, case a negative particle m.ust be called in, to shew that the connection included in the copula does not take place.
V. And hence we see the reason of the when tlie ne^ rule commonly laid down by logicians *, gative particle that in all negative propositions, the ne- serves to dis- gation ought to affect the copula ; for as ^°'" ^ the copula, when placed by itself between the subject and the predicate, manifestly binds them together, it Is evident, that, in order to render a proposition negative^ the particle of negation must enter it in such manner as to destroy this union. In a word, then, only two ideas are disjoined in a proposition, when the negative particle may be so referred to the copula as to break the affirmation included in it, and undo that connection it would otherwise establish. When we say, for in- stance, no man is perfect ; take away the negation, and the copula of itself plainly unites the ideas in the pro- position. But as this Is the very reverse of what is intended, a negative mark is added, to shew that this uuion does not here take place. The negation, there- fore, by destroying the effect of the copula, changes the very nature of the proposition, insomuch that in- stead of binding two ideas together, it denotes their separation. On the contrary, in this sentence •, The man ivho departs not from a?i upright behaviottr^ is beloved cf God : the predicate, beloved of God, is evidently af- firmed of the subject, an upright man ; so that not- withstanding the negative particle, the proposition is still affirmative. The reason is plain j the negation
here affects not the copula, but making properly a part of the subject, serves with other terms m the sentence to form one complex idea, of which the predicate, be- loved of Gody is directly affirmed. This perhaps to some may appear a mere logical refinem.ent, contrived to justify the scholastic rule for distinguishing between affirmative and negative propositions. But if it be considered that this distinction is of great importance in reasoning, and cannot in many cases be made witli certainty but by means of this criterion here given, the reader will see sufficient reason for my taking so much pai^.s to illustrate it.
How a copula ^^' Perhaps it may still appear a mys-^ conies to be tery, how a copula can be said to be a part of a n?ga- part of a negative proposition, whose pro- tive proposi- busir.css it is to disjoin ideas. Thi*
tiOH . ...
difficulty however will vanish, if we call to mind that every judgment implies a direct affirma- tion, and that this 'affirmation alone makes the true copula in a proposition. But as our affirmations are of two kinds, viz. either of agreement or of disagreement, between the ideas compared, hence there is also a two- fold expression of our judgments. In the case of a- greement, the copula alone suffices, because it is the proper mark whereby we denote an identity or con- junction of ideas ; but where perceptions disagree, there we must call in a negative particle ; and this gives us to understand that the affirmation implied in the copula is not of any connection between the sub- ject and predicate, but of their mutual opposition and reoiignance.
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CHAP. IIL
<5T UNIVERSAL AND PARTICULAR PROPOSITIOKS,
I. The next considerable division of Division of propositions, is into universal and pavt'icu^ Jjroposicions lar. Our ideas, according to what has ^^o universal been already observed in the first part, are ' p i i^u a . ail singular as they enter the mind, and represent intli- vidual objects. But as by abstraction we can render them universal, so as to comprehend a whole class of things, and sometimes several classes at once, hence the terms expressing these ideas must be in like man- ner universal. If therefore \t^e suppose any general term to become the subject of a proposition, it is evi- dent that whatever is affirmed of the abstract idea be- longing to that term, may be affirmed of all the indi- viduals to which the idea extends. Thus, when we say men are mortal^ we consider mortality;, not as con- fined to one or any number of particular men, but as what may be affirmed without restriction of the whole species. . By this means the proposition becomes as general as the idea which makes the subject of it, and indeed derives its universality entirely from that idea, being more or less so according as this may be extend- ed to more or fewer individuals. But it is further to be observed of these general terms, that they sometimes enter a proposition in their full latitude, as in the ex- ample given above ; 'and sometimes appear with a mark of limitation. In this last case we are given to understand, .that the predicate agrees not to the whole universal' idea, tut only to a part of it ; as in the pro- position, ^ome men arc uj'ise ; for here wisdom is not affirmed of every particular man, but restrained to a Xew of the human species. %
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.. 11. Now from this different appearance
ut^v^e^Jar"^ of the general idea, that constitutes the
where the sub- subject of any judgment, arises the divi-
jectisso,with- sion of propositions into universal and
out a mark o particular. An wnversal proposition is
restriction. ■', i • » i . . * ^ ,
that whcrem the subject is some general
term, taken in its full latitude, insomuch that the pre- dicate agrees to all the individuals comprehended under it, if it denotes a projper species ; and to all the several species and their individuals, if it marks an idea of a higher order. The words all^ every^ no^ noney &c. are the prop-er signs of this universality ; and as they sel- dom Tail to accompany general truths, so they are the most obvious criterion whereby to distinguish them. All animals have a poiver of beginning motion. This is an universal proposition, as we know from the word all prefixed to the subject anmuil^ which denotes that it must be taken in its full extent. Hence the power of beginning motion may be afBrmed of all the several frpecies of animals •, as of birds, quadrupeds, insects, fishes, &c. and of all the individuals of which these different classes consist, as of this hawk, that horse, and so for others.
Propositions ^^' ^ particular proposition has in
particular like manner some general term for its sub-
where some ject, but with a mark of limitation added, universa su - ^^ denote that the predicate agrees only ject appears .- i • j- -j i ^ i j 'i
with a mark to some oi the mdividuals comprehended of limitation, under a species, or to one or more of the species belonging to any genus, and not to the whole universal idea. Thus, some stones are heavier than iron ; some men have an uncommon share of 'prudence. In the last of these propositions, the subject some men im- plies only a certain number of individuals, comprehend* ed under a single species. In the former, where tfie gubject is a genus, that extends to a great variety of distinct classes ; some stories may not only imply any number of particular stones, but also several whole species of stones *, inasmuch as there may be not a few
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•with the property there described . Hence we sce>- that a proposition does not cease to be particular hy the predicate's agreeing to a vvhole species, unless that species, singly and distinctly considered, makes also the subject of which we alBrm or deny ; for if it be- longs to some genus that has other species under it, to which the predicate does not agree, it is plain that where this genus is that of which we affirm or deny, the predicate agreeing only to a part of it, and not to the whole general idea, constitutes the proj>osition particular.
IV. Here then we have a sure and in- a sure and ni- fallible mark whereby to distinguish be- fallible crite-
tween universal and particular proposi- non whereby -r-rri ^t ]• -^ ^ , , to clistineuish
tioDG. Where the predicate agrees to all tetweea-nni- the individuals comprehended under the versal and par- notion of the subject, there the proposition ticularproposi:- is universal ; where it belongs only to ^^^'''^' some of them, or to some of the species of the general idea, there the proposition is particular. This criterion is of easy application, and much safer than to depend upon the common signs of ^//, every ^ somc^ none^ &c, because th.ese being different in different languages^ and often varying in their signification, are very apt m many cases to mislead the judgment. Thus, if we say, all the soldiers ivhen dra-wfi up^ formed a square cf a?:. hundred men a side, it is evident that the predicate can- no-t be affirmed of the several individuals, but of the " whole collective idea of the subject ; whence by tlio rule given above, the proposition is not universal. It is true, logicians lay down many observations, to en~ tible us to distinguish aright on this head ; but if the -criterion here given be duly attended to, it will be of •more real service than an hundred rules *, for it is in- fallible, and n^ny be applied with ease ; whereas- the tiirections which we meet with in treatises of logic*, i)eing drawn for the most part from the* analogy of l^nguai^e and common forms of speech, are not onlv
L
no
burdensome to the memory, but often very doubtful rdid uncertain in their application.
Singular pro- . 7' ^^}^^'^ '^ ^^'^^ «"^ SP-'-^^^'^ O^' P^^PO- posttions con- S'.tions that remains to be described ; and
tained under which the more deserves our notice, as it the head of jg j^^j. y^^ agreed among logicians, to which ^ ' ot the two classes mentioned above they
ought to be referred. I mean singular propositions, or those where the subject is an individual. Of this na- ture are the following : Sir Isaac Nenvtoti ivas the ijiven- ier of Jlux'i07is : this book contains many useful truths, — What occasions some difficulty, as to the proper rank of these propositions, is, that the subject being taken according to the whole of its extension, they sometimes have the same effect in reasoning as universals : but if it be considered, that they are in truth the most limit- ed kind of particular propositions, and that no propo- sition can with any propriety be called universal but where the subject is some universal idea, we shall not be long in determining to which class they ought to be referred. When we say same books co7itain useful trufliSy the proposition is particular, because the general term appears with a mark of restriction. If therefore v/e say this hook contains useful truths y it is evident that the proposition must be still more particular, as the limita- tion implied in the word ////j, is of a more confined nature than in the former case. I know there are in- stances, where singular propositions have the same ef- fect in reasoning as universals ; yet this is not by rea- son of any proper universality belonging to them, but because the conclusion in such cases being always sin- oular, may be proved by a middle term which is also singular; as I could easily demonstrate, were this a proper place for entering into a discussion of that na- ture.
The fourfold VI. Wc See therefore, that all proposi- aivisionofpro- tions arc either affirmative or negative; positions. iiqj. jg jj Jogs evident that in both cases
thev may be uuiversalor particular. Hence arises that
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celebrated fourfold division of them Into universal affirmative and universal negative, particular affirmative and particular negative -, which comprehends indeed all their varieties. The use of this method of distin- guishing them will appear more fully afterwards, when we come to treat of reasoning and syllogism.
CHAP. IV.
OF ABSOLUTE AND CONDITIONAL PROPOSITIONS.
I, The o\"!Jects aoout which we are Distinction ci' chiefly conversant in this world, arc all of qualities Inio a nature liable to change. What mav be essential snd affirmed of them at one time, cannot often " at another ; and it makes no small part of our know- ledge to distinguish rightly these variations, and trace the msons upon which they depend. For it Is ob- servable, tliat amidst all the vicissitudes cf nature, some things remain constant and invariable ; nor are even the changes to which we see others liable, effect- ed but in consequence of uniform and steady laws, which, when known, are sufficient to direct us In our judgments about them. Hence philosophers, in dis- tinguishing the objects of our perception into various classes, have been very careful to note, that some pro- perties belong essentially to the general idea, so as not to be separable from It but by destroying its very na- ture ; while others are only accidental, and may be affirmed or denied of it, in different circumstances. Thus, solidity, a yellow colour, and great weight, are considered as essential qualities of gold ; but wliether it shall exist as an uniform conjoined mass, is not alike necessary. We see that by a proper me:istruum, it may be reduced to a fine powder ; and that intense heat will bring it into a state of fusion.
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Il-nceaconsi- ^^' "^^^^ '^^^ ^^^'"^ diversity in the se-^ (lerable diver- vcral qualities of things, arises a consider- sityinour able difference as to the manner of our manner of judgini{ about them J for, in the first place, All such properties as are insepara- f>le from objects, when considered as belonging to any genus or species, are affirmed absolutely and without reserve of that general idea. Thus, we s:iy gold is very •-iveigJiiij^ a sicne is hard, a?ni}i{>Is have a power of self- 7710- i'lon. But in the case of mutable or accidental qualities, ;is they depend upon some other consideration, distinct from tlie general idea, that also must be taken into the account, in order to form an accurate judgment. Should we aftirni, for instance, of some stones, that they are very susceptible of a rolling motion, the pro- position, while it remains in this general form, cannot with any advantage be introduced into our reasonings. An aptness to receive that mode of motion flows from The figure of the stone ; v/liich, as it may vary infinite- ly, our judgment then only becomes applicable and determined, v»-hen the particular figure, of which volu- bility is a consequence, is also taken into the account. liCt us then brijig in this other consideration, and the proposition will run as follows : stofies of a spherical form are easily put into a rolling motion. Here we see the condition upon which tlie predicate is aHirm.ed, and rhereforo know in what particular cases the proposition may be ijpplied.
' III. This consideration of propositions,
WtiIcIi gives ^* ^1 • i • t ^1 _
■ , ,? .• respectmp' the manner m Vv'nich the pre- nse to the ai- r b . . . ^ .
vision of pro- dicate IS amrmed of tne subject, gives rise positions into to the division of them into absolute and absolute aud coKditioual. Absolute propositions are those^
ccncii'tioxiui* «
wherein v/e affirm some property insepa- rable from the idea of the subject, and which therefore belongs to it in all possible cases *, as, God is irfiniiehf nvise : virtue tends to the ultimate happijiess of man. But where- the predicate is not necessarily connected with the idea of the subject, unless upon some consideration
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distinct from that idea, there the propcs'.tion is called conditional. The reason of the name is t.ikeii from the supposition annexed, which is of the nature of a con- dition, and may be expressed as su-:h : thus, JJ a stone is exposed to the rays of the sun^ it ivill mitract some de- gree of heat. If a river rims in a very declining channel y its rapidity ivifl constantly increase,
IV. There is not any thinnr of greater
1 o o The oreat ini-
importance in philosophy than a due at- portanceof tenlion to this division of propositions, ihis division. If we arc careful never to alHrm things as it renders absomtely, but where the ideas are ms^- Jj^.^^j-^^ii^.^.. parably conjoined ; and if iji our otlier ju^igments we distinctly mark the conditions which de- termine the predicate to belong to the subject, we shall be the less liable to mistake in applying general truths to the particular concerns of human life. It is owing to the exact observance of tliis rule that mathe- maticians have been so happy in their discoveries ; antl that what they demonstrate of magnitude in general,. may be applied with ease in all obvious occurrences.
V. The truth of it is, particular pro- ^^^ ^^^^^^^ positions are then known to be true when them from we can trace their connection with uni- particulars to v.ersals ;. and it is accordingly tlie great S^-'^^''-^^- business of science to find out general truths, that mny be applied with safety in ?\\ obvious instances. Now the great advantage arising from determining with care the conditions upon which one id/ja m.ay be afHrmed or denied of another, is this, that thereby particular pro- positions really become universal, may be introduced with certainty into our reasonings, and serve as stan- dards tp conduct and regulate our judgments. To illustrate this by a familiar instance: if we say, some luater acts very forcibly ^ the proposition is particular j and as the conditions on^whlch this forcible action de- pends are not m.entioned, it is as yet uncertain in what cases it may be applied. Let us then supply these conditions, and the proposition will run thus j u\itir-
L3
114
conveyed in sujpcient qiiani'itij along a steep descent y acts very forcibly. Here we have an universal judgment, inasmucli as the j3redicateyimZ'/i? action, rnuy be ascri- bed to all water ur^der the circumstances mentioned. Nor is it less evident that the proposition in this new form is of easy application ; and in fact we find, that men do apply it in instances where the forcible action of water is required j as in corn-mills, and many other works of art. Thus we see in what manner we are to proceed, in order to arrive at universal truths, which IS the great end and aim of science. And indeed, would men take the same care duly to express the conditions on which they afhrm and deny, as mathe- maticians d<i, in those theorems which they term hy- pothetical, I doubt not but we might be able to deduce many truths in other parts of philosophy with no less clearness, force, and perspicuity, than has hitherto been thought peculiar to the science of quantity.
CHAP. V.
CF SIMPLE AND COMPOUND PROPOSITIONS.
... c I. Hitherto we have treated of pro-
Division 01 . . , 1 ^ • J
-propositions positions where only two ideas are eom-
nito simple pared together. These are in the general and compound, called simple: because having but one subject and one predicate, they are the effect of a sim- ple judgment that admits of no subdivision. But if it so happens that several ide^s offer themselves to our thou'-'hts at once, wkereby we are led to aiHrm the same^ thing of different objects, or different things of the same object, the propositions expressing these *udc^ments are called compound: because thpy may be resolved into as many others as there are subjects or predicates 'in the whole complex determination of tlie
115
inind. Thus, God is i?ijifiitely luisey and infinitehj poiver-^ .Jul. Here there are two predicates, injimte luisdom and infinite poiver^ both afnrmed of the same subject •, and accordingly the proposition may be resolved into two others, afnrniing these predicates severally. In like nianner in. the proposition, neither Vings nor people are exempt from deaths the predicate is denied of both sub- jects, and may therefore be separated from them in distinct propositions. Nor is it less evident that if a complex judgment consists of several subjects and predicate-s, it may be resolved into as many simple propositions as are the number of ditierent ideas com- pared together. Riches and honotirs are apt to elate ths mindy and increase the fiumber of cur desires^ In this judgment there are two subjects and two predicates, and it is at the same time apparent that it may be re- solved into four di-stinct propositions. Riches are opt to elate the mind. Riches are apt to increase the number of our desires. And so of honours.
II. Logicians have divided these com- rp,
o , , , The proper
pound propositions into a great many notion of a different classes ; but, in my opinion, not compound pro- with a due regard to their proper defini- P^.^^^^o" ascer:- tion. Thus conditiofiais^ causals, rclaiivesy &c. arementioned as so many distinct species of this kind, though in fact they are no more than simple propositions. To give an instance of a conditional :.if a stone is exposed to the rays of the smiy it will contract some degree of heat. Here we have but one subject and one predicate •, for the complex expression, a stone ex- posed to the rays of the su7iy constitutes the proper sub- ject of this proposition, and is no more than one deter- nainate idea. The same thing happens in causals. Rehoboam was unhappy, because he followed £vj I counsel. I deny not that there is here an appearance of two pro- positions arising from the complexity of the expres- sion y but when we come to consider the matter more nearly, it is evident that we have but a single subjecr and predicate. The pursuit of evil counsel Irmght misery
116
h'pon' Rehohoam. It is not enough therefore to render a proposition compound, that the subject and predicate are complex notions, requiring sometimes a whole sentence to express them ; for in this case the compa- rison is still conhned to two ideas, and constitutes what we call a simple judt::;ment. But where there are several subjects or predicates, or both, as the affir- mation or negation hiay be alike extended to them all, the proposition expressing such a judgment is truly a collection of as many simple ones as there are different ideas compared. Confining ourselves therefore to this more strict and just notion of compound propositions, they are all reducible to two kinds, viz. copulatives and disjimctives,
^ , III. A copulative proposition is, where
Compound r i . i t , i
propositions the subjects and predicates are so Imked
either copu- together, that they may be all severally latives, affirmed or denied one of another. Of
this nature are the examples of compound propositions given above. Riches and honours are apt to elate the mimly and increase the number of our desires. Neither kings nor people are exempt from death. In the first of these, the two predicates may be affirmed severally of each subject, whence we have four distinct proposi- tions. The other furnishes an example of the negative kind, where the same predicate being disjoined from both subjects, may be also denied of them in separate propositions.
IV. The other species of compound or disjunctive, p^-gpogi^ions are those called disjunctives ; in which, comparing several predicates with the same subject, we affirm that one of them necessarily belongs to it, but leave the particular predicate undetermined. If any one, for example, says this vjorld either exists of itself or is the ivork of some all-wise a7jd powerful cause, it is evident that one of the two predicates must be- long to the world ♦, but as the proposition determines not'which, it is therefore of the kind we call disjunctive. Such too are the following : The sun. either moves round
nature of all propoBW
to be exact in -^'''"^ the particuijr; removeii ; or :; ved, iliat ("1^ '-■ eiamp.'f ff^ -^ ■ tie M'orii of ii' course deny it to oe ten l)eself-exi:t''.-*iweina< proke(ibv;o^■•;^^lv• pirticul'iiT mar,: so that the csiu. nckhpilk: . . ■ cmctotkn:::\'::~. k particles, n'.c' ■. tliis class talie dii'ir ; • iMbsonci • -■' fiicirverj !.:.;.:„ 1 shall reserve w: liilcometotiKtoiK Jndimpomncecli appear.
OFTHEDlYli; iViDL.N
ih
part 01; __
wd as the jf
f^'f'^^ns whose i;
ItWsranrM.
t p
■^(:retore:](iera
M«t3n(i predicate
• ' ^'•■"■^ 1 wkk
■ '''^tiCQa'p^
. constiiiites
i^ut where there
■ *tli» 25 tlie affir-
■"' ''-'tlieRull,
. - : !i truly a
■B a rfiere arc different
;<wbRiheieforetotliis
dCOT"""''"— • '■' ■,^,
..•.:-;;> ioiaeil - . .. -., jcierally . :i aacthei. Ot ::: .::.; rroposkions
.. Xuir ,. bie&Tstof
■ ; i:':;.';i s;\'en!l| ,:,:/:::itprop08i'
:.:•:•> negative - ' ' ,,'jd from
.v:-:^cf
.iiict.ves;
:-uv belongs ,vtrniineil.
ffc/il-*'
117
Ml? eartJii or is tli€ centre about ivhlch the earth resolves. Friendship finds men equals or makes them so. It is tlie nature of all propositions of this class, supposing them to be exact in point of form, that upon determining the particular predicate, the rest are of course to be removed ; or if all the predicates but one are remo- ved, that one necessarily takes place. Thus, in the example given above, if we allow the world to be the work of some wise and powerful cause, we of course deny it to be self-existent •, or if we deny it to be self-existent, we must necessarily admit that it was produced by some wise and powerful cause. Now this particular manner of linking the predicates together, so that the establishing one displaces all the rest, or the excluding all but one, necessarily establishes that one, cannot otherwise be effected than by means of disjunc- tive particles. And hence it is that propositions of this class take their names from those particles which make so necessary a part of them, and indeed constitute . their very nature, considered as a distinct species. But I shall reserve what farther might be said on this head till I come to treat of reasoning, where the great use and importance of disjunctive propositions will better appear.
CHAP. VI.
OF THE DIVISION OF PROPOSITIONS INTO SELF- EVIDENT AND DEMONSTRABLE.
I. As we are soon to enter upon the Design of this third part of logic, which treats of reason- chapter, ing, and as the art of reasoning lies in deducing pro- positions whose truth does not immediately appear from others more known, it will be proper before we
I ^
116
h'pon Rchohoam. It Is not enough therefore to render a proposition compound, that the subject and predicate are complex notions, requiring sometimes a whole sentence to express them ; for m this case the compa- rison is still conlined to two ideas, and constitutes what we call a simple judgment. But where there are several subjects or predicates, or both, as the afFir- mation or negation ftiay be alike extended to them all, the proposition expressing such a judgment is truly a collection of as many simple ones as there are different ideas compared. Confining ourselves therefore to this more strict and just notion of compound "propositions, they are all reducible to two kinds, viz. copulatives and disjunctives, ^ J III. A copulative proposition is, where
Compound i • ^ i j- r i i
propositions the subjects and predicates are so linked either copu- together, that they may be all severally latives, affirmed or denied one of another. Of
this nature are the examples of compound propositions given above. Riches and honours are apt to elate the mindy and increase the numler of our desires. Neither kings nor people are exempt from death. In the first of these, the two predicates may be affirmed severally of each subject, whence we have four distinct proposi- tions. The other furnishes an example of the negative kind, where the same predicate being disjoined from both subjects, may be also denied of them in separate propositions.
IV. The other species of compound or disjunctiYe. p^-gpositions are those called disjunctives ; in which, comparing several predicates with the same subject, we affirm that one of them necessarily belongs to it, but leave the particular predicate undetermined. If any one, for example, says this luorld either exists of itself, or is the luork of some a 11- wise and powerful cause, it is evidenr- that one of the two predicates must be- long to the world -, but as the proposition determines not which, it is therefore of the kind we call disjunctive. Such too are the following : The sun. either moves round.
117
the earthy or is tli€ cefitrc about luhwh the earth resolves, i^riendship finds men equals or makes them so. It is tlie nature of all propositions of this class, supposing them to be exact in point of form, that upon determining the particular predicate, the rest are of course to be removed ; or if all the predicates but one are remo- ^'ed, that one necessarily takes place. Thus, in the example given above, if we allow the world to be the work of some wise and powerful cause, we of course deny it to be self-existent *, or if we deny it to be self-existent, we must necessarily admit that it was produced by some wise and powerful caruse. Now this particular manner of linking the predicates together, so that the establishing one displaces all the rest, or the excluding all but one, necessarily establishes that one, cannot otherwise be effected than by means of disjiine- tive particles. And hence it is that propositions of this class take their names from those particles which make so necessary a part of them, and indeed constitute their very nature, considered as a distinct species. But I shall reserve what farther might be said on this head till I come to treat of reasoning, where the great use and importance of disjunctive propositions wdil better appear.
CHAP. VI.
OF THE DIVISION OF PROPOSITIONS INTO SELF- - EVIDENT AND DEMONSTRABLE.
I. As we are soon to enter upon the Design of this third part of logic, which treats of reason- chapter, ing, and as the art of reasoning lies in deducing pro- positions whose truth does not immediately appear from others more known, it will be proper before we
118
proceed any farther, to examine a little tlie different -degrees of evidence that accompany our judgments ; that we may be the better able to distinguish in what cases we ought to have recourse to reasoning, and what those propositlonaare, upon which, as a sure and uner'-ing foundation, we may venl^ure to build the truth of otiiers. T> V II- When any proposition is offered to
Propositions . J i i .
divided into the View Of the mmd, st the terms m which self-evident it is expressed are understood, upon com- and^uemon- paring the ideas together, the agreement or disagreement asserted is either imme- diately perceived, or found to lie beyond the present reach of tlw understanding. In the first case the pro- position is sai'l to be self-evide?tty and admits not of any proof, because a bare attention to the ideas themselves produces full conviction and certainty ; nor is it possi- ble to call in any thing more evident, by way of con- firmation. But where the connection or repugnance comes not so readily under the inspection of the mind, there wq must have recourse to reasoning *, and if by a clear series of proofs we can make out the truth pro- posed, insomuch that self-evidence shall accompany every step of the procedure, we are then able to de- monstrate what we assert, and the proposition itself is said to be ckrnofUtrahle. When we affirm, for instance, that it is impossible for the sa7ne thing to be and not to he ; whoever ujulerstands the terms made use of, perceives at first glance the truth of what is asserted •, nor can he by any efforts bring himself to believe the contrary. The proposition therefore is self-evident^ and such, that it is impossible by reasoning to make it plainer; be- cause there is no truth more obvious, or better known, from which as a consequence it may be deduced. But, if we say this I'jorld had a beginnings the assertion is in- deed equally true, but shines not forth with the same degree of evidence. We find great difficulty in con- ceiving how the world could be made out of nothing ; and arc not brought to a free and full consent, until by
119
reasoning we arrive at a clear view of the absurdity in- volved in the contrary supposition. Hence this pro- position is of the kind we call demon strable^ inasmuch as its truth is not. immediately perceived by the mind, but yet may be made appear by means of others more known and obvious, whence it follov/s as an unavoid- able consequence.
III. From what has been said, it appears that reasoning is employed only about de- second opera- monstrable propositions, and that our in- tion of the tuitive and s^lf-evident perceptions are "^i"^ is confi-
the ultimate foundation on which it rests. "^^ wholly to
intuition. And now we see clearly the reason why,
In the distinction of die powers of the understanding, as explained in the introduction to this treatise, the second operation of the mind was confined wholly to intu'it'ive acts. Our first step in the way to knovv'ledge, is to furnish ourselves with ideas. When these are obtained, we next set ourselves to compare them to- gether, in order to judge of their agreement or disa- greement. If the relations we are in quest of lie im- mediately open to the view of the mind, the judgments expressing them are self-evident j and the act of the mind forming these judgments is what we call iiititiUon. But if, upon comparing our ideas together, we cannot readily and at once trace their relation, it then becomes necessary to employ search and examination, and call in the assistance of self-evident truths, which is what we properly term reasoning. Every judgment there- fore that is not intuitive, being gained by an exercise of the reasoning faculty, necessarily belongs to the third operation of the mind, and ought to be referred to it in a just division of the powers of the understanding ; and indeed it is with this view chiefly that we have dis- tinguished propositions into self-evident and demonstra- ble. Under the first head are comprehended all our intuitive judgments ; that is, all belonging to the second operation of the mind. Demonstrable propositions are the proper province of the ve^soning faculty, and con-
120
stitute by far the most considerable part of biiman knowledge. Indeed, reason extends also to matters of experience and testimony, where the proofs adduced are not of the kind called Demonstration. But I am here only considering the powers of the mind, as em- ployed in tracing the relations between its own ideas, in which view of things every ti*ue proposition is de- monstrable J though very often we find ourselves in- capable of discovering and applying those intermediate ideas upon which the demonstration depends, e. ,r -1 .,. IV. Demonstrable propositions, therc-
S^lf-evxdeiit . i ^ i i • i
truths the first lore, belongmg properly to the third ope- principles of ration of the mind, I shall for the present reasoning. dismiss them, and voturn to the considera- tion of self-evident truths. These, as I have already observed, furnish the first principles of reasoning ; and it is certain, tliat if, in our researcl"kes, we employ only such principles as have this chari!cter of self-evi- dence, and apply them according to the rules to be afterv/ards explained, we shall be in no danger of error, in advancing from one discovery to another. For this , I may appeal to the writings of the mathematicians, which being conducted by the express model here mentioned, are an incontestable proof of the firmness and stability of human knowledge, when buiit upon so sure a foundation *, for not only have the propositions of this science stood the test of ages, but are found attended with that invincible evidence, as forces the assent of all who duly consider the proofs upon, which they are established. Since then mathematicians are universally allowed to have hit upon the right method of arriving at truths ; since they have been the hap- piest in the choice, as well as application of their principles, it may not be amiss to explain here the division they had given of self-evident propositions ; that by treading in their steps, we may learn some- thin<^ of that justness and solidity of reasoning for which they are so deservedly esteem*ed.
121
V. First then, It is to be obser/ed, tllat j^e^,,;,:^,^,, they have been very careful in ascertaining great help to their uleas, and fixing the signification of clearness and their terms. For this purpose they begin ^J^J^'^JJ!^ "^ with definitions] in v^rhich the meaning of ' their words is so distinctly explained, that they cannot tail to excite in the mind of an attentive reader the very same ideas as are annexed to them by the Vvrlter, And indeed I am apt to think that the clearness and irresistible evidence df mathematical knowledge, is owing to nothing, so much as this care in laying the foundation. Where the relation between any two ideas is accurately and justly traced, it will not be dif- ficult for another to comprehend that relation,- if in setting himself to discover it, he brings the very same ideas into comparison. But if, on the contrary, he affixes to his words ideas different from those that were in the mind of him Vvho first advanced tlie demonstra- tion, it is evident that, as the same ideas are not com- pared, the same relation cannot subsist ; insomuch that a proposition will be rejected as false, which, had the terms been rightly understood, must have appear- ed unexceptionably true. A square, for instance, is a figure bounded by four equal right lines, joined to- gether at right angles. Here the nature of the angles^ makes no less a part of the idea than the equality of the sides ; and many properties demonstrated of the square, flow from its being a rectangular figure. If therefore we suppose a man who has formed a partial notion of a square, comprehending only the equality ot its sides, without regard to the angles, reading some demonstration that implies also this latter considera- tion, it is plain he would reject it as not universallv true, Inasmuch as it could not be applied where the sides were joined together at unequal angles. Yoi' this last figure answering still to tliis idea oF a square, would be yet iound v/Ithout the property assigned to it in the proposition. But if he comes after v/ards to correct his notion, and render his id a complete, he ' M
122
will then readily own the truth and justness of the de* n^.onstratlon.
Mathematl- "^^ ^'^ ^^^ tlierefore, that nothing
Clans, by be- contributes SO much to the improvement ginning with and Certainty of human knowledge, as the them, procure ]^.^vii^nr determinate ideas, and keepine ception to the them Steady and invariable in all our dis- truths they ad- courses and reasonings about them. And vauce. Qi-j this account' it is that mathematicians,
as was before observed, always begin by defining their terms, and distinctly unfolding the notions they are intended to express. Hence such as apply them- selves to these studies, having exactly the same views of things, and bringing always the very same ideas into comparison, readily discern the relations between them, when clci.-Iy and distinctly represented. Nor is there any more natural and obvious reason for the universal reception given to mathematical truths, and for that harmony and correspondence of sentiments which makes the distinguishing character of the literati of this class.
VII. "When they have taken this first ine^of pri'nd-" ^^^P> ^^"^^ made known the. ideas whose pies the second relations they intend to investigate, their 'step in mathe- next care is to lav down some self-evident maticai know- ^j-^j^-j^s which may serve, as a foundation kd<];e. - , . ^ ^ . All
tor their tuture reasonings. And here
indeed they proceed with remarkable circumspection, admitting no principles but what flow immediately from their definitions, and necessarily force themselves upon a mind in any degree attentive to its perceptions. Thus a drck is a figure formed by a right line, moving round some fixed point in the same plane. Tlie fixed point round which the line is supposed to move, and where one of its extremities terminates, is called the rerJre of the circle. The other extremity, which is conceived to be carried round, until it returns to the point whence it first set out, describes a curve running into itself, and termed the circt/nifarrice. All right.
I
lines drawn from the centre to the circumference arc- called radii. From these definitions compared, geo- metricians derive this self-evident truth, that the radii of the same circle are all equal one to another. I call ic self-evident, because nothing more is required to lay it open to the immediate perception of the mind, than an attention to tlie ideas compared ; for from tho very genesis of a circle, it is plain that the circumfe- rence is eveVy wliere distant from the centre, by the €xact length of the describing line \ and that the seve- ral radii are in truth nothing more than one and the same line variously posited within the figure. Ihis short description will, I hope, serve to give some little insight into the manner of deducuig mathematical principles, as well as into the nature of that evidence which accompanies them.
VIII. And now I proceed to observe, „
. . i -r Propositions
that m all propositions we either affirm divided into or deny some property of the idea that speculative constitutes the subject of our judgment, ^"^ practical. or we maintain that something maybe done or effect- ed. The first sort are called speculative propositions, as in the example mentioned above, the radii of the same circle are all equal one to another. The others are called' practical, for a reason too obvious to be mentioned : thus, that a right line may be draiun from one point to another, is a practical proposition, inasmuch as it ex- presses that something may be done.
IX. From this twofold consideration ^
of propositions arises the twofold division ^"^" ""^^^ e- oi mathematical principles into axioms and ciples distiji- postulates. By an axiom they understand guished into any self-evident speculative truth : as, that ^^^^^''^^ ^"'^ the whole is greater than its parts : that ' ' '
things equal to one and the same thing, are equal to one another. But a self-evident practical proposition is what they call 7i postulate. Such are those oi Euclid ; that a finite right line may he continued directly for ivards ; that a circle may be described about a?iv centre iviiJt amj
M 'Z
msiance. And here vre are to observe, that as in an axiom, the agreement or disagreement between the subject and predicate must come under the immediate inspection of the mind : so in tx postulate^ not only the possibihty of the thing asserted must be evident at iirst view, but also the manner in wliich it may be (•(Fected. But where this manner is not of itself appa- rent, the proposition comes under the notion of the demonstrable kind, and is treated as such by the geo- metrical writers. Thus, to draiv a right line f rem one -point to another, is assumed by Eticiul as a jmiulate, be- cause the manner of doing it is so obvioits as to require no previous teaching. But then it is not equally evi- dent hoiu lue are to construct an equilateral triangle. For this reason he advances it as a demonstrable propo- sition, lays down rules for the exact performance, and i-ft the same time proves tliat if these rules are follow- ed, the figure will be justly described.
1 , , X. This naturally leads me to take no-
ble propcsi- tice, that as selj-evident truths are distm- tions into theo- guished into difFercnt kinds,' according as u-ms and pro- |.]jgy ^^^ speculative or practical, so it is also with demonstrable propositions. A demonstrable speculative proposition, is by mathemati- cians called 'A. theorem. Such is the famous 47th pro- ijositlon of the first Book of the Elements^ known by rhe name of the Pythagoric Theorem, from its supposed inventor Piithagoras^ viz. That in even/ right-angled triangle the square described upon the side subtending the right angle, is equal to both the squares described upon the sides containing the right angle. On the other hand, a demonstrable practical proposition is called -a pirohlen: ; as where Euclid teaches us to describe a square upon a given right line.
\ „ . XI. Since I am upon this subject, it
Corollaries are , . i i i i • i i
obvious de- r^'s^Y "ot be amiss to add, that besides the
ductions from four kinds of propositions already men- theorems or tioned, mathematicians have also a fifth, problems. Y^^^vn by the name of Corollaries. These
are usually subjoined to theorems or problems ^ and diiler
125
from them only in this, that they flow from what i& there demonstrated, in so obvious a manner as to dis- cover their dependence upon the proposition whence they are deduced, almost as soon as proposed. Thus Euclid, having demonstrated iliat in every right-litied triangle fJl the three angles taken together are equal to two right angles y adds by way of corollary, that all the three ^n'^les of any o?ie. triangle taken together ^ are equal to all the three aiigles of any other triangle taken together ; which is evident at first sight •, because in all cases they are equal to two right ones, and things equal, to one and the same thing, are equal to one another.
XII. The last tiling I shall take notice s^j-^oii^ 'serve of in the practice of the mathematicians, the purposes is what they c.di their scholia. They are of annotations inditferently annexed to definitions, propo- ^^ ^ comment. sitions, or corollaries \ and answer the same purposes as annotations upon a classical author. For in them occasion is taken to explain whatever may appear intri- •cate and obscure in a train of reasonin;: ; to answer .objections *, to teach the application and u^es of propo- sitions ; to lay open the original and history of the several discoveries made in the science ; and, in a ^'ord, to acquaint us with all such particulars as deserve to be known, whether considered as points of curiosity or profit.
XIII. Thus we have taken a short vi«w
of the so much celebrated method of the ™^"^^^'^;?^ mathematicians ; which to any one who maticlans uni- considers it with a proper attention, m.ust versal, anda needs appear universal and equally appli-- ^^''^^ S"/^*^ ^^ cable in other sciences. They begin v/ 1th *" ^^ '^* definitions. From these they deduce then- axioms and postulates, which serve as principles of reasoning ; and having thus laid a firm foundation, advance to theorems and problems, establishing all by the strictest rules of demonstration. The corollaries flow naturally and of themselves : and if any particulars are still wanting to illustrate a subject, or complete the r<2ader's iiiformii-
M3
126
tion, these, that the series of leasoning may not he in- terrupted or broken, are generally thrown into schoHa. In a system of knowledge so uniform and well con- nected, no wonder if we meet with certainty ; and if those clouds and darknesses that deface other parts of human science, and bring discredit even upon reason itself, are liere scattered and disappear. Self-evident XIV. But I shall for the present wave
truths known these reflections, which every reader of by the appa- understanding is able to make of himself, rent unavoid- ^^^^ return to the consideration of self-evi- able connec- , . . t -n i i i i
tlon between ^-^^^ propositions. It Will doubtless be
The subject expected, after what has been said of and predicate, them, that I should establish some criteria^. or marks, by which they may be distinguished. But I frankly own my inability in this respect, as not being able to conceive any thing in them more obvious and striking than that self-evidence which constitutes their very nature. All I have therefore to observe on this head is, that we ought to make it our first care to ob- tain clear and determinate ideas. When afterwards we come to compare these together, if we perceive be- tween any of them a necessary and unavoidable con- nection, insomuch that it is impossible to conceive them existing asunder, without destroying the very ideas compared, we may then conclude, that the pro- position expressing this relation is a principal, and of the kind we call Self-evident. In the example men- tioned above, the 'radii of the same circle are all equal he- tiveen themsehes, this intuitive evidence shines forth in the clearest manner ; it being impossible for any one who attends to his own ideas, not to perceive the equality here asserted. For as the circumference is every where distant from the centre by the exact length of the describing line, the radii drawn from the centre to the circumference, being severally equal to this one line, must needs also be equal among them- selves. If we suppose the radii unequal, we at the same time suppose the circumference more distant
127
from the centre In some places than In others ; from which supposition, as it would exhibit a figure quite different from a circle, we see there is no separating the predicate from the subject in this proposition, without destroying the idea in relation to which the comparison was made. The same thing will be found to hold in all our other intuitive perceptions, insomuch that we may establish this as an universal criterion whereby to judge of and distinguish them. I would not, however, be understood to mean, as if this ready view gf the unavoidable connection between some ideas was any thing really different from self-evidence. It is, Indeed, nothing more than the notion of self-evi- dence a little unfolded, and as it were laid open to the inspection of the mind. Intuitive judgments need no other distinguishing marks, than that brightness which surrounds them ; in like manner as light discovers it- self by its own presence, and the splendour it univer- sally diffuses. But I have said enough of self-evident propositions, and shall therefore now proceed to those of the demonstrable kind •, which being gained in con- sequence of reasoning, naturally leads us to the third part of logic, where this operation of the understand- ing is explained*
THE
ELEMENTS OF LOGIC
BOOK III.
OF REASONING.
CHAP. I.
r)7 REASONING IN GENERAL, AND THE FARTS OF WHICH IT CONSISTS.
^ I. VV E have seen how the mind pro-
emo.eie.a- ^^^jg -j-^ furnishinej itself with ideas, and tions discover- _ . . , . o ^ »
e'd by means of framing intuitive perceptions. Let us next intennediate inquire into the manner of discovering those *^^^'' more remote rehuions, which, lying at a
distance from the understanding, are not to be traced but by means of a higher exercise of its powers. It often happens in comparing ideas together, that their agreement or disagreement cannot be discerned at first ■view, especially if they are of such a nature as not to admit of aa exact application one to another. When, for instanc>^, we compare two figures of a different
129
nvakc, in order to judge of their equality or inequality, it is plain that by barely considering the figures them- selves, we cannot arrive at an exact detei hiination j because by reason of their disagreeing forms, it is im- possible so to put them together, as that their several parts shall m.utunlly coincide. Here then it becomes necessary to look out for some .third idea that will ad- mit of such an application as the present case requires, wherein, if we succeed, all difficulties vanish, and the relation we are in quest of may be traced with ease. U'hus, right-lined figures are all reducible to squares, by means of which we can measure their areas, and determine exactly their agreement or disagreement in point of magnitude.
II. If now it be asked, how any third ^^.^^ manner idea can serve to discover a relation between of arriving at two others .'' I answer. By being compared truth termed severally with these others; for such a reasoning, comparison enables us to see how far the ideas with which this third is compared, are connected or disjoin- ed between themselves. In the example mentioned above of two right-lined figures, if we compare each of them with some square whose area is known, and find the one exactly equal to it and the other less by a square inch, we imm.ediately conclude that the area ■ of the first figure is a square inch greater than that of the second. This manner of determining the relation between any two ideas, by the invention of some third with which they may be compared, is that which we call reasoning ,♦ and indeed the chief instrument by which we push on our discoveries and enlarge our knowledge. The great art lies in finding out such in- termediate ideas as when compared with the others in the question, will furnish evident and knov/n truths ; because, as will afterwards appear, it is only by means ' of them that we arrive at the knowledge of what is hidden and remote.
III. From what has been raid, it ?p- The parts that pears tliat every act of reasoning necessa- constitute an
130
act of reason- rily includes three distinct judgments j
mg anu a syl- j.,^^^ wherein the ideas whose reLition we log ism. ,.
want to discover, are severally compared
with the middle idea ; and a third, wherein they are themselves connected or disjoined according to the re- sult ot that comparison. Now, as in the Second Part of Logic, our judgments when put into words, were called propositions, so here, in the Third Part, the ex- pressions oF our reasonings are termed s^I'o^isnis. And hence it follows, .that as every act of reasoning implies three several judgments, so every syllogism must in- clude three distinct propositions. When a reasoning is thus put into words, and appears in form of a syllo- gism, the intermediate idea made use of to discover the agreement or disagreement we search for, is called the middle term ,- and the two ideas themselves with which this third Is compared, go by the name of the extremes.
Instance, man, ^^^ ' ^"^ ^^ ^^^^e things are best illus- snd account- trated by examples, let us, for instance, abkness. set ourselv^s to inquire ivhether me?i are
accountable for their actions? As the relation between the ideas ot man and accotcntablc'ness comes not within the immediate view of the mind, our first care must be to fmd out some third idea that v/ill enable us the more easily to discover and trace it. A very small measure of reflection is sufricient to inform us that no creature can be accountable for his actions, unless we suppose him capable of distinguishing the good from the bad ; that is, unless wc suppose him possessed of reason". Nor is this alone sufficient. For what would it avail iiim to know good from bad actions, if he had no freedom of choice, nor could avoid the one and pursue the other } Hence it becomes necessary to take in both considerations in tlie pcesent case. It is at the same time equally apparent, that wherever there is this ability of distinguishing good from bad actions, and pursuing the one «nd avoiding the other, there also "ii creature is accountable. We have then got a third
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i<!ea,%vith which arcoufitab/enfss is inseparably connected, Wz. riaso;i and liberty ; which are here to be considered as making up one complex conception. Let us now take this middle idea, and compare it with the other term in question, 1)17.. inntiy and we all know by expe- rience that it may be aflirmcd of him. Having thus, by means of the intermediate idea, formed two several judgments, vi-z. that man is possessed of reason and liber- ty ; and that reason and liberty iinply accountableness ; a third obvio'jsiy and necessarily follows, Wz. that man is accountable for his -actions. Here then we have a com- plete act of reasoning, in which, according to wliat has been already observed, there are three distinct judg- ments ; two that may be styled previous, inasmuch as they lead to the other, and arise from comparing the niiddle idea with t1:e two ideas in the question ; the third is a consequence of these previous acts, and flows from combining the extreme ideas between themselves. If now we put this reasoning into words, it exhibits what logicians term a' syllogism, and when proposed in due form, runs thus :
Rvery creature possessed of reason and liberty is account- able for his actions,
Mafi is a creature j)ossessed of reason and liberty ; there- fore man is accountable for his actions.
V. In this syllogism we may observe, t>^ . . , t , ' . . Premises, con-
that there are three several propositions, elusion, ex.
expressing the three judgments implied in tremes, middle the act of reasoning, and so disposed as to ^'^^^^^ represent distinctly what passes within the mind In tracing the more distant relations of its ideas. The two first propositions answer the two previous judg- ments in reasoning, and are called the premises ^ be- cause they are placed before the other. The third is termed the conclusion^ as being gained in consequence of what was asserted in the premises. Vv^e are also to remeniber that the terms expressing the two ideas whose relation we inquire after, as here w^,';,and ac- countableness y are in general called the estr ernes ; and
1S2
that the intermediate idea, by means of which the rela- tion is traced, Wz. a creature possessed of reason and ii- hertijy takes the name of the middle term^ Hence it follows, that by the premises of a syllogism we are al- ways to understand the two propositions where the middle term is severally compared with extremes ; for these constitute the previous judgments whence the truth we are in quest of is by reasoning deduced. The coficliision is that other proposition in which the extremes themselves are joined or separated, agreeably to what appears upon the above comparison. All this is evidently seen in the foregoing syllogism, where the two first propositions which represent the premi- ses, and the third that makes the conclusion, are ex- actly agreeable to the definitions here given. y,j . „ , VI. Before we take leave of this article.
Major and . '
minor term, it Will be larther necessary to observe,
major and mi- that as the conclusion is made up of the nor proposi- extreme terms of the syllogisms, so that extreme which serves as the predicate of the conclusion, goes by the nam.e of the major term ; the other extreme which makes the subject in the same proposition, is called the minar term. From this distinction of the extremes, arises also a distinction between the premises where these extremes are se- verally compared with tlie middle term. That pro- position which compares the greater extreme, or the predicate of the conclusion with the middle term, is called the major proposition *, the other, wherein the same middle term is compared with the subject of the conclusion or lesser extreme, is calletl the minor prpo-^ sition. All this is obvious from the syllogism already given, where the conclusion is, man is accountable for his actions; for here the predicate, accountable for his ac- tions^ being connected with the middle term in the first of the two premises, every creature possessed of rea^ son and liberty is accountable for his actions, gives what we call the major proposition. In the second of the premises, man is a creature possessed of reason and liberty y
133 .'
we find the lesser extreme or subject of the concia- sion, viz. man connected with the same middle term, whence it is ktiown to be the minor proposition. I ;,hall only add, that when a syllogism is proposed in due form, the major proposition is always placed first, the minor next,, and the conclusion last, according as we have done in that offered above.
VII. Having thus cleared the way by j^^g^^^^ ^^^^ explaining such terms as wc are likely to proposition, have occasion for in the progress of this reasoning; and Treatise, it may not be amiss to observe, syllogism, ais- that though we have careiully distmguish- ed between the act of reasoning Tind a syllogism^ which is no more than the expression of it, yet common lan- guage is not so critical on this head; the term reasoning being promiscuously used to signify either the judg- ments of the mind as they follow one another in train, or the propositions expressing these judgments. Nor need we wonder that it is so, inasmuch as our ideas and the terms appropriated to them, are so connected by ha- bit and use, that our thoughts fall, as it were, sponta- neously into language as fsst as they arise in the mind j so that even in our reasonings within ourselves, we aie not able wholly to lay aside words. But notwithstanding this strict connection bitween mental and ivr/W reason- ing, if I may be allowed that expression,- I ihought it needful here to distinguish them, in order to give \i just idea of the manner of deducing f.ne truth from another. While the mind keeps the idea of tiiin^rs in view, and combines its judgments according to the real evidence attending them, there is no great <langer oi mistake in our reasonings, because we carry our con- clusions no farther than the clearness of our percep- tions warrants us. But where we make use of v/ords, the case is often otherwise ; nothing being more com- mon than to let them pass without attending to the ideas they represent •, insomuch that we frequent- ly combine expressions which upon examination ai>- pear to have no determinate meaning:. Hence it <;t^ •^-
134
iy imports us to distinguish between reasoning .and syllogism, and to take care that the one be in aH cases the true and just representation of the other. How- ever, as I am unwilhng to recede too far from the com- mon forms of speech, or to multiply distinctions with- out necessity, I shall henceforward consider propositions as representing the real judgments of the mind, ami syllogisms as the true copies of our reasonings ; which indeed they ought always to be, and undoubtedly al- ways will be, to men who think justly, and are desi- rous of arriving at truth. Upon this supposition there will be no danger in using the words Judgment and Proposition promiscuously ; or, in considering reason- ing as either a combination of various judgments, or of the propositions expressing them ; because, being the exa<:t copies one of another, the result will be in all cases the same. Nor is it a small advantage that we can tlius conform to common speech without con- founding our ideas, or running into ambiguity. By this means w^e bring ourselves upon a level with other men, readily apprehend the meaning of their expres- sions, and can' v/ith ease convey our own notions and sentiments into their minds.
. , VIII. These things premised, we may
In a Single act . , i j r ■ ^ :
of re-dsoniro- ii"» the general dcnne reasonmg to be an
the premises act or operation of the mind^ deducing some must be intui- unknown proposition from other previous ones tive trutis. ^^^^^,, ^^^ evident and knoiun. These previ- ous propositions, in a simple act of reasoning, are only- two in number; and it is always required that they be of themselves apparent to the. understanding, inso- much that we assent to and perceive the truth of them as soon as proposed. In the syllogism given above, the premises are supposed to be self-evident truths, otherwise .the conclusion could not be inferred by a single act of reasoning. If, for instance, in the major, everif creature possessed of rrason and liberty is accountable for his actions, the connection between the subject and 'predicate could not be perceived by a bare attention to
135
the ideas themselves, it is evident that this proposition would no less require a proof than the conclusion de- duced from it. In this case a new middle term mast be sought for, to trace the connection here supposed •, and this of course furnishes another syllogism, by which, having established the proposition in question, we are then, and not before, at liberty to use it in any succeeding train of reasoning. And should it so hap- pen that in this s^^cond essay there was still some pre- vious proposition whose turn did not appear at first sight, we must then have recourse to a third syllogism, ' in order to lay open that truth to the mind ; because, so long as the premises remain uncertain, the conclu- sion built upon them must be so too. Wiien by con- ducting our thoughts in this manner, wc at last arrive at some syllogism, where the previous propositions are intuitive truths, the miud then rests in full security, as perceiving that the several conclusions it has passed through, stand upon the immoveable foundation of , self-evidence, and when traced to their source termi- nate in it.
IX. We see therefore, that in order to inter a conclusion by a single act or reason- ^.j^^ hlo-hest ing, the premises must be intuitive proposi- exercise of it, tions. Where they are not, previous syllo- o'^^^y a conca-
gisms are required, in which case reason- *^"'*^^^" °^ ? 1 ^ ,. ... syllogisms.
ing becomes a complicated act, taking m
a variety of successive steps. This frequently happens in tracing the more remote relations of our ideas, where many middle terms being called in, the conclu- sion cannot be made out, but in consequence of a Se- ries of syllogisms following one another in train. But although in this concatenation of propositions, those, that form the premises of the last syllogism are often considerably removed from self-evidence, yet, if we trace the reasoning backwards, we shall find them the conclusions of previous -syllogisms, whose premises approach nearer and nearer to intuition, in proportion as Y«^e advance, and are found at last to terminate in it.
N 2
156
And if after having thus unravelled a vlernonstration, we take it the contrary vi^ay, and observe how tlie niind, Setting out with intuitive perceptions, couples them together to form a conclusioi] ; how, by intro- tiucing this conclusion into another syllogism, it still advances one step farther, and so proceeds making every new discovery subservient to its future progress, v/e shall then perceive clearly, that reasoning, in the highest exercise of that faculty, is no more than an orderly combination of those simple acts which we have already so fully explained. The great art lies in so adjusting our syllogisms one to another, that the propositions severally made use of as premises, maybe manifest consequences of what goes before ♦, for, as by this means every conclusion is deduced from known and established truths, the very last in the series, how iar soever we carry it, will have no less certainty at- tending it than the original intuitive perceptions them- selves, in which the whole chain of syllogisms takes its rise.
Requires in- . ^- T^"^ "^^ ^^^ ^^''^ reasoning begin-
tuitive certain- ning with first principles, rises gradually
ty in every from one judgment to another, and conr
itep ot the nects them in sucli manner, that every
progression. ^ , . . / . , , '
Stage or the progression brmgs mtuitive
certainty along with it. And now at length we may clearly understand the definition given above of this distinguishing faculty of the human mind. Reason, we have said, is the ability of deducing unknown truihs fvoin principles or propositions that are already known. This evidently appears by the foregoing ac- count, where we see that no proposition is admitted into a syllogism, to serve as one of the previous judg- ments on which the conclusion rests, unless it is itself a known and established truth, whose connection with self-evident principles has been already traced, e ,r .J , XT. There is vet another observation
Self-evident ,, ^ rr • ^r ■
tiuths, the ul- which naturally oliers itselr, m conse- tinaate founda- queiice of the aboYC detail, viz. that all
137
the knowledge acquired by reasoning, how tjo^ ^f ^H sd- far soever we carry our discoveries, is encc iindcer- still built upon our intuitive perceptions, ^^^'^^^^y- Towards the end of the last part we divided proposi- tions into self-evident and demonstrable, and represent- ed those of the self-evident kind as the foundation on which the whole superstructure of human science rested. This doctriilw is now abundantly confirmed by v/hat has been delivered in the present chapter. We have found that every discovery of human reason is the consequence of a train of syllogisms, which, when traced to their source, always terminates in self-evident perceptions. When tlie mind arrives at these primi- tive truths, it pursues not its inquiries farther, as well knowing that no evidence can exceed that which flows from an infrnediate view- of the agreement or disagreement between its ideas. And hence it is, that, in unravelling any part of knowledge in order to come at the foundation on which it stands, intuitive truths are always the last resort of the understanding, be- yond which it aims not to advance, but possesses its no- < tions in perfect security, as having now reached the very spring and fountain- of all science and certainty.
CHAP. II.
c.F THE SEVERAL KINDS OF REASONING, AND FIRST OF THAT BY WHICH WE DETERMINE THE GENERA AND SPECIES OF THINGS^
I. We have endeavoured • in the fore- Reasoning going chapter to give as distinct a notion twofold, as possible of reasoning, arul of the manner in which it is conducted. Let us now inquire a little into the <liscoveries made by this facultv, and what those end^^
138
are wlilcli we have principally in view in the exercife of iu All the ^lims of human reason may in the general be reduced to these two: 1. To rank things under these universal ideas to which they truly belong ; and, 2. To ascribe to them their several attributes and pro- perties in consequence of that distribution. The first kind ^^' ^^^^t, then, I Say, that one great aim regards the of human reason is, to determine the genera and genera and species of things. "We liave
thlnl^s^ ^^ ^^^" ^" ^^'^ ^*^^^ P^^^ ^^ this Treatise, how * ' the mind proceeds in framing general
ideas. We have also seen in the second part, how, by means of these general ideas, we come by universal propositions. Now, as in these universal propositions, we affirm some property of a genus or species, it is plain that we cannot apply this property to particular objects till we have hrst determined whether they are comprehended under that general idea of which the property is affirmed. Thus there are certain proper- ties belonging to all even numbers, which, nevertheless, cannot be applied to any particular number until we have first discovered it to be of the species expressed by that general name. Hence reasoning begins with referring things to their several divisions and classes in the scale of our ideas ; and as these divisions are all distinguished by peculiar names, we hereby learn to apply the terms expressing general conceptions to such particular objects as come under our immediate obser- vation.
. , III. Now, in order to arrive at. these
which we ar- Conclusions, by which the several objects rive at con- of perception are brought under general elusions of this j^aiy-^es, two things are manifestly nece?-
°^^* sary. First, That we take a view of the
idea itself denoted by that general name, and carefully attend to the distinguishing marks which serve to characterize it. Secondly, That we compare this idea with the object under consideration, observing dili- gently wherein they agree or differ. If the idea is
139
found to correspond with the "particular object, we then withaut hesitation apply the general name ; but if no such correspondence intervenes, the conclusion must necessarily take a contrary turn. Let us, for in- stance, take the number eighty arnd consider by what steps we are led to pronounce it afi eveti number. -First then, we call to mind the idea signified by the expression an even tuimbtr^ viz. that it is a number di^ visible into two equal parts. We then compare this idea with the number eighty and finding them manifestly to agree, see at once the necessity of admitting the con- clusion. These several judgments, therefore, trans- ferred into language, and reduced to the form of a syllogism, appear thus :
Every number that ^m ay be divided into tivo equal parts y is an EVEN number. ■
The number EIGHT may be divided into two equal j^arts ;
T/iereJore the number eight is an EVEN number.
IV. I have made choice of this exam- Those steps al- pie, not so much for the sake of the con- ways followed, elusion, which is obvious enough, and though in mieht have been obtained without all that /TV^'^ '^f ^'^f
° . r 11 1 • /I 1 , . we do not al-
parade or words, but cnieiiy because it is ways attend to of easy comprehension, and serves at the them. same time distinctly to exhibit the form of reasoning by which the understanding conducts itself in all in-- stances of this kmf\. And here it may be observed, that where the general ideas to which particular objects are referred, is very familiar to the mind, and frequent- ly in view, this reference, and the application of the general name, seem to be made without any apparatus of reasoning. When we see a horse in the fields or a dog in the street, we readily apply the name of the species •, habit, and a familiar acquaintance with the general idea, suggesting it instantaneously to the mind. We are not however to imagine on this account, that the understanding departs from the usual rules of just thinking. A frequent repetition of acts begets a habit;
140
and habits are attended with a certain promptness of execution, that prevents our -observing the several steps and gradations by which any course of action is accom- plished. But in other instances, where we judge not by precontracted habits, as when the general idea is very complex, or less familiar to the mind, we always proceed according to the form of reasoning established above- A goldsmith, for instance, who is* in doubt as to any piece of metal, wliether it be of the species called goidy first examines its properties, and then comparing them with the general idea signified by that name, if he finds a perfect correspondence, no longer hesitates under what class of metals to rank it. Nov/ what is this but following step by step those rules of reasoning which we have before laid down as the standard by which to regulate our thoughts in all conclusions of this kind ?
The great im- ^' ■^°^" ^^^ ^^ ^^ imagined that our re- portanceofthis Searches here, because in appearance branch of rea- bounded to the imposing of general names soning, upon particular objects, are therefore
trivial and of little consequence. Some of the most considerable debates among mankind, and such too as nearly regard their lives, interest, and happiness, turn wholly upon this article. Is it not the chief employ- ment of our several courts of judicature, to determine in particular instances, what is law, justice, and equity? Of what importance is it in many cases, to decide aright, whether an action shall be termed murder or manslaughter ? We see that no less than the lives and fortunes of men depend often upon these decisions. The reason is plain. Actions when once* referred to a general idea, draw after them all that may be affirmed of that idea; insomuch that the determining the species of actions, is all one with determining what proportion of praise or dispraise, commendation or blame, &c. ought to follow them ; for as it is allowed that murder deserves death, by bringing any particular action under the head of murder, we of course decide the punishment due to it.
141
VI. But the great importance of this ^^^^ ,j^^ ^^^^^ branch of reasoning, and the necessity of observance of care and circumspection, in referring par- it practised by ticular objects to general ideas, is still "V'^theman-
r 1 • 1 r 1 • r 1 Cians. »
larther evident irom the practice ot the mathematicians. Every one who has read Enchd^ knows that he frequently requires us to draw lines tlirough certain points, and according to such and such directions. The iigure-s thence resulting are often squares, parallelograms, or rectangles. Yet £'w^//W ne- ver supposes this from their bare appearance, but al- ways demonstrates it upon the strictest principles of geometry. Nor is the method he takes in any thing different from that described above. Thus, for in- stance, having defined a square to be a figure bounded by four equal sides, joined together at right angles ; when such a figure arises in any construction previous to the demonstration of a proposition, he yet never calls it by that name until he has shewn that the sides are equal, and all its angles right ones. Now this is apparently the same form of reasoning we have before exhibited, in proving eight to be an even number ; as will, be evident to a.ny one who reduces it into a regu- lar syllogism. I shall only add, that when Euclid has thus determined the •species "of any figure, he is then, and not before, at liberty to ascribe to it ail the proper- ties already demonstrated of that figure, and thereby render it subservient to the future course of his reason- ing-
VII. Having thus sufficiently explained pj^^^ ^^^ j^'_
the rules by which we are to conduct variable ideas,
ourselves, in ranking particular objects with a steady
ufider eeneral ideas, and shewn their con- ^PP^'^^'^^o" f r ' '- 1 . r ^ names, renders
lortnity to the practice and manner or tne this nart of
mathematicians, it remains only to observe, knowledge
that the true way of renderinor this part of both eaiiy and
ki 1 1 .1 1 • • I certain.
nowledge both easy and certain, is, by
habituating ourselves to clear and determinate ideas,
and keeping them steadily amiexcd to their respective
^K<1
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<le ideas, that
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-^ n6 suppose
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mnif
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wards keeping the Jftml paring our iie« we ri ovetbki. Xet oii^i com^e uv, iW :^ *""■
amply recompense our applbfion of matlifff owing to (lie eiac ( ol»n apt to imagine, tiai ii ' care about ail our cthff i (Ione3l)outtlio5eofniffl log them into eiiccoc these combiwitions \i\ ■ bp tWn\ tod] ind c it in our power ' tion into other '
fROfERTltS 0? TH' OiJUENERiLlMi
^' ^^^E come not i ^"'•^'i^cbenbrffl
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" llodisi...
143
Nor is this so easy a isk as some may traduced into. perhaps be apt to im^^ie ; it requiring tuowfedgef* both a comprehensive uderstanding, and weUasmathe- great com-mand of'atterion, to settle the matics. percise bounds of our icas when they grow to be very complex, and include a lultitude of particulars. Nay, and after these limits ai duly fixed, there is a certain quickness of thought ad extent of mind required to- wards keeping the sevral parts in view, that in com- paring our ideas one 'ith. another, none of them be overlooked. Yet ouL't not these difficulties to dis- courage us J though p:it, they are not insurmount- able, and the advant?es arising from success will amply recompense ourtoil. The certainty and easy application of matheiatical knowledge is w-holly owing to the exact ob'vance of this rule. And I am apt to imagine, that ve were to employ the same care about all our othc ideas, as mathematicians have done about those of nmber and magnitude, by form- ing them into exact cmbinations, and distinguishing these combinations byparticular names, in order to keep them steady and ivariable, we should soon have it in our power to intjduce certainty and demonstra- tion into other parts o human knowledge.
CIAP. III.
OF REASONING, AS V REGARDS THE POWERS AND
PROPERTIES OF Tc OUR GENERAL IDtJ
:GS, and THE RELATIONS OF
I. We come now -> the second great yj^g distlnc- end which men have i view in their rea- tion of reason Soninj.{S, namely, Th«{iscovering and as- ^"S ^^ it re- cribin[T to thiniTS the* several attributes ^^^^^ ^^^ s"-
J ° ■ A 1 • •,, 1 ences, andasi
and properties. An< here it will be ne- concerns com- cessary to distinguish ,'etween reasoning, "ion life.
142
names. For as all our aim Is to apply general words aright, if these words stand for invariable ideds, that are perfectly known to the mind, and can be readily distinguished upon occasion, tliere will be little danger of mistake or error in our reasonings. Let us suppose that by examining -any object, and carrying our atten- tion successively from one part to another, we have acquainted ourselves with the several particulars i3bser- vabl« in it. If amo:ig these we find such as constitute some general idea, framed and settled beforehand by the unflerstanding, and distinguished by a particular name, the resemblance thus kndwn and perceived necessarily determines the species of the object, and thereby gives it a right to the name by which that species is called. Thus four equal sides, joined toge- ther at right angles, make up the notion of a square. As this is a, fixed and invariable idea, without which the general name cannot be applied, we never call any particular figure a square, until it appears to have these several conditions ; and, cj^ntrarily, wherever a figure it found with these conditions, it necessarily takes the name of square. The same will be found to hold in all our other reasonings of this kind, where nothing can create any 'difficulty but the want of settled ideas. If, for instance, we have not determined within our- selves, the precise notion denoted by the word man^ slaug/der, it will be impossible for us to decide whether any particular action ought to bear that nam.e ; be- cause, however nicely we examine the action itself, yet being strangers to the general idea with which it is to be comxpared, we are utterly unable to judge of their agreement or disagreement. But if we take care to remove this obstacle, and distinctly trace the two ideas under consideration, all difficulties vanish, and the resolution becomes both easy and certain. By such a VIII. Thus we See of what importance
conduct, cer- it Is, towards the improvement and cer- tainty and de- tainty of human knowledge, that we ac- monstration custom ourselves to clear and determinate ideas_5 and a steady application or words.
143
Nor is tills so easy a task as some may troduced into.
1 1 ^ ^ • • ',.. ^^^i,;,-;*^,,. other parts of
perhaps be apt to imagine -, it requirmg ^^^.^f^dg^ ^^
both a comprehensive understanding, and weUasmathe- great com-mand of' attention, to settle the matics. percise bounds of our ideas when they grow to be very- complex, and include a multitude of particulars. Nay, and after these limits are duly fixed, there is a certain quickness of thought and extent of mind required to- wards keeping the several parts in view, that in com- paring our ideas one with another, none of them be overlooked. Yet ought not these difficulties to dis- courage us ; though great, they are not insurmount- able, and the advantages arising from success will amply recompense our toil. The certainty and easy application of mathematical knowledge is wholly owing to the exact observance af this rule. And I am apt to imagine, that if we were to employ the same care about ail our other ideas, as mathematicians have done about those of number and magnitude, by form- ing them into exact combinations, and distinguishing these combinations by particular names, in order to keep them steady and invariable, we should soon have it in our power to introduce certainty and demonstra- tion into other parts of human knowledge.
CHAP. III.
OF REASONING, AS IT REGARDS THE POWERS AND PROPERTIES OF THINGS, AND THE RELATIONS OF OUR GENERAL IDEAS.
I. We come now to the second great The diotinc- end which men have in view in their rea- tion of reason- sonings, namely, The discovering and as- ^"S ^^ ^* ^^-^ crihincT to thiuirs their several attributes ^ the sci-
1 -All • -It 1 ences, and as It
and properties. And here it Will be ne- concerns com-
cessary to distinguish between reasoning, Q^on life.
144
as it regards the sciences, and as it concerns com- mon life. In the sciences, our reason is employed chiefly about universal truths, it being by them alone that the bounds of human knowledge are enlarged. Hence the division of things into various classes, call- ed othervi'ise genera and species. For these universal ideas, being set up as the representatives of many par- ticular things, whatever is affirmed of them, may also be affirmed of all the individuals to which they be- long. Murdery for instance, is a general idea, repre- senting a certain species of human actions. Reason tells us, that the punishment due to it is death. Hence every particular action coming under the notion of murdery has the punishment of death allotted to it. Here then we apply the general truth to some ob- vious instance •> and this is what properly constitutes the reasoning of common life ; for men, in their or- dinary transactions and intercourse' one with another, have for the most part to do only with particular objects. Our friends and relations, their characters and behaviours, the constitution of the several bodies that surround us, and the uses to which they may be applied, are what chiefly engage our at^rention. In all these we reason about particular things ; and the whole result of our reasoning is, the applying the ge- neral truths of the sciences to the ordinary transactions of human life. When we see a viper, we avoid it. Wherever we have occasion for the forcible action of water to move a body that makes considerable resis- tance, we take care to convey it in such a manner that it shall fall upon the object with impetuosity. Now all this happens in consequence o£ our familiar and ready application of these two general truths : The bite of a viper is mortal ; ivater falling upon a body *w:th impetuosity y acts very forcibly towards setting it i?i motion. In like manner, if we set ourselves to con- sider any particular character, in order to determine the share of praise or dispraise that belongs to it, our great concern is, to ascertain exactly the proportion
145
of virtue and vice. The reason is obvious. A ju^t determination in all cases of this kind depends en- tirely u|3on an application of these general maxims of morality : Virtuous actions deserve praise. Vicious acticns deserve ilame.
II. Hence it appears, that reasoning, as xhestepsbr
it regards common life, is no more than which we p'ro^
the ascribing the general properties of ceed in the
things to those several objects with which reasoning of o . 1. 1 1 1' common ate.
we are nnmediately concerned, according
as they are found to be of that particular division c^ class to which the properties belong. The steps then by which we proceed are manifestly these : First, we refer the object under consideration to some general idea or class of things : we then recollect the several attributes of that general idea : and lastly, ascribe all those attributes to the present object. Thus, in con- sidering the character of Seinproniusy if we find it to be of the kind called virtuous ; when we at the same time .reflect that a inrtuous ch-^x^ciex is deserving of esteem, it naturally and obviously follows, that Seinj^rojiius is so too. These thoughts put into a syllogisniy in order to exhibit the form of reasoning here required, run thus :
livery virtuous tnmi is %uortJiy cf esteem.
Scmproniiis is a virtuous man ;
Therefore Sempronius is ivorthy of es tee in.
III. By this syllogism f it appears, that, xhe connec-
.. before we affirm any thing of a particular tion and tit- -
^object, that object must be referred to pendence oi- " , 1 • 1 o - • the two erand
some general uien. oemprGuius is pro- -^^.^ ,, c
nounced worthy of esteem, only in conse- :reasoniug on^
xjuence of his being a virtuous man, or 'Jpon ano-
coming under that general notion. Hence ^^"^^'
:^e see the necessary connection of the various parts of
reasoning, and the dependence they have one upon an-
otljcr. The determining the genera and species of
things is, as we have said, one exercise of human rca-
,^Son ; aiul here we .find that this exercise is the first
in order, and previous to the other, which consists is
O
14(3
'Scribing to them their powers, properties, and rela^ ions. But when we have taken this previous step, .md brought particular objects under general names j ns the properties we ascribe to them are no other than those of the general idea, it is plain, that, in order to a successful progress in this part of knowledge, we must thoroughly acquaint ourselves with the several rela- tions and attributes of these our general ideas. When this is done, the other part will be easy, and require scarce any labour of thought, as being no more than ^n application of the general form of reasoning repre- sented in the foregoing syllogism. Now as we have al- ready sufficiently shewn how we are to proceed in de- termining the genera and species of things, which, as we have said, is the previous step to this second branch of human knowledge, all that is farther wanting to a due explanation of it, is to offer some considerations, as to the manner of investigating the general relations of our ideas. This io the highest exercise of thfe powers of the understanding, and that by means where- of we arrive at the discovery of universal truths ; in- somuch that our deductions in this way constitute that particular species of reasoning which we have before said regards principally the sciences.
^ ,. IV. But that v/e may conduct our
Two things 1 -^ 1 11
required to thou;,^hts With some order and method, we
make a grood shall begin with observing, that the rela-^
reasoner. tions of our general ideas are of two kinds ;
either such as immediately discover themselves, upon
comparing the ideas one with another ; or such, as be-
inp- more remote and distant, require art and contrivitice
to brintr them into view. The relations of the first
land furnish us with intuitive and self-evident truths j
those of the second are traced by reasonirig, and a due
application of intermediate ideas. It is of this last kind
that v/e are to speak here, having dispatched what was'
necessary with regard to the other in the second part.,
As therefore in tracing the more dist.uit relations of
thiniis, we must always have recourse to intervening
147
ideas, and are more or less succQS&ful' in oqr researches according to our acquaintance with these ideas pnd ability of applying them, it is evident, that, to make a good reasoner, two things are principally required : firsts An extensive knowledge of those- intermediate ideas by means of which things may be compared one with another; secondlij^ The skill and talent qf 'applying them happily, m all particular instai>ce^, that come uur cjer considerat'on.
V. First, I say, that, in order to our p-„,^ ^„ ^^t,^. successful progress in reasoning, we rnust siyel;no-,^']edge have an extensive knowledge of thos^ 9fin.(:e^B^Q<iiat<? intermediate ideas, by mieans of which '^^?*- things may be compared one with another ; for as it is not every idea that will answer the p^-pose of our in- quiries, bu^ such only as are peculiarly related to the objects about which we reason, so as, by a cornparison ii'Ltr. tuculj lO lui'jiisji ev:u:;Tji ana Known irutnyj ixG- thing 'is more apparent than that the greater variety of conceptions we can call into view* the more likely we are to find some among them that will help us to the trutlis here required. And indeed it is found to hold in experience, that in proportion as we enlarge our view of things, and grow acquainted with a multitude of ditfcjrent objects, the reasoning faculty gathers strength •, for by extending our sphere of knowledge, the miind acquires a certain force and penetration, as being accustomed to examine the several appear- ances of its ideas, and observe what light they cast one upon another.
VI. And this I take to be the reason, that, ^ , .
, 1 V , 1 . ' ' To excel in
m order to excel remarkably m any one any one
branch of learning, it is necessary to have branch of
at least a general acquaintance with the l^^rnmg, we
1 1 • 1 r ^ 1 • rr>i niust be m gc-
wnole circle or arts and sciences. ihe neral ac-
truth of it is, all the various divisions of -^uainted with
human knowledge are very nearly related the whole
.amon? themselves, and in innumerable in- '^^^\^^ " ^^'^
o / r»' t ^^-^ sciences,
Stances serve to illustrate and set orr ^ach
0 2
148
Gther. And ailhoiigh it is not to be denied, that, by an obstinate application to one branch of study> a iVian may make considerable progress, and acquire some de- gree of eminence in it, yet his views will be always nar- row and contracted, and he will want that masterly discernment, which not only enables us to pursue our discoveries v*'ith ease, but also in laying them open to others, to spread a certain brightness around them. I would not however here be understood to mean, that a general knowIedgi»'-«iIone is sufficient for all the pur- poses of reasoning •, I only recommend it as proper to give the mind a certain sagacity and quickness, and qualify it for judging aright in the ordinary occurren- ces of life. But when cur reasoning regards a parti- cular science, ; it is farther necessary that we more nearly acquaint ourselves with whatever relates to that science. A general knowledge is a good preparation, rind onamcs us to proceed witli (^as^ and expedition} in ■whatever branch of learning we apply to *, but then in the minute and intricate questions of any science, we are by no means qualified to reason with advantage, until we have perfectly mastered the science to v/hich they belong ; it being hence chiefly that we are fur- nished wich those intermediate ideas which lead to a just and iuccessful solution.
,,rv ■ ,1 VII. And liere, as it comes so naturally
why mathe- . ' ... . ^
maticiaivs in my way, I cannot avoid taking notice
..sometimes an- of an observation that is frequently to be
£wei- not tue ^^^ with, and seems to carry in it at first
expectation . , , . •' ,
their ereat Sight something very strange and unac-
iearnin^ countable. It is in short this, that maiJi:-
raises. mat'icinns^ even such -as are allowed to ex-
cel in their own profession, and to have discovered therriselves perfect masters in the art of reasoning, have not yet been always happy in treating upon other sub- jects •, but rather fallen short, not only of what might naturally have been expected from them, but of many writers much less exercised in the rules of argumenta- tion. This will not appear so very extraordinary, if
149
we reflect on what has been hinted above. Mathema- tics is an engaging study ; and jnen who apply them- selves that way, so wholly plunge into it, that they are for the most part but little acquainted with other branches of knowledge. When therefore they quit their favourite subject, and enter upon others that are in a manner Tiz^^ and strange to them, no wonder if they find their invention at a stand. Because however perfect they may be in the art of reasoning, yet:want- ine here those intermediate ideas which are necessarv to furnish out a due train of propositions, ail tneir skiU and ability fails them ; for a barC: knowledge of the rules is not sufficient : we must farther have materials whereunto to apply them- : Atid ^hen these are once obtained, then it is that an able reasoner disco- vers his superiority, by the just choice he makes, and a certain masterly dispcskion, that in every step of the procedure carries evidence and conviction along with it. And hence it is that snzh. mathematicians as have of late years applied themselves to other sciences, and not contented with a superficial knowledge, endeavour- ed to reacli their inmost recesses; such mathemati- cians, I say, have by mere strength of mind, and a happy application o{ geometrical .x^^'A^onrng, carried their discoveries far beyond what was heretofore judged the utmost limits of human knowledge* This is a truth abundantly known to all who are acqua'tnted with the late wonderful improvements in natural philoso- phy.
VIII. I come now to the -second thing required, in order to a successful progress skjji^of ^' i ^ in reasoning ; namely, the skill and talent ing intermedi- of applying intermediate ideas happily in ate ideas hap- all particular instances that come under {"^^.^^'P^"^'^"" consideration. And here I shall not take up much time in laying down rules and precepts, be- cause I am apt to think they would do but Futle ser- vice. Use and exercise are the best instructors in ti>^ present c^ge : and v/hatever logigiiins may boasts of
0 3
150
being able to form perfect reasoners by book and rule, yet we find by experience that the study of their pre- cepts does not always add any great degree of strength to the understanding. In short, it is the habit alone of reasoning that makes a reasoner ; and therefore the true way to acquire this talent is, by being much con- versant in those sciences where the art of reasoning is allowed to reign in the greatest perfection. Hence it was that the ancients, who so well understood the manner of forming the mind, always began with matJiemAtics as the foundation of their philosophical studies. Here the understanding is by degrees ha- bituated to truth, contracts insensibly a certain fond- nessfof it, ^nd learns never to yield its assent to any proposition but where the evidence is sufficient to pro- duce full conviction. For this reason Plato has called mathematical demonstrations the cathartics or purga- tives of the soul, as being the proper means to cleanse it from error, and restore that natural exercise of its faculties in which just thinking consists. And indeed I believe it will be readily allowed, that no science furnishes so many instances of a happy choice of in- termediate ideas, and a dexterous application of them, for the discovery of truth and enlargement of know- ledge.
o
The stud of" ^^' ^^ therefore we would form our mathematical minds to a habit of reasoning closely and demonstrations in train, we Cannot take any more cert5!n of great avail j^gfj^^od than the exercising ourselves in
m this respect ; , • i i •
mathematical demonstrations, so as to con- tract a kind of familiarity v/lth them. " Not that we ** look upon it as necessary [to use the words of the great Mr Loch) ^* that all men should be deep mathema- " ticians, but that, having got the way of reasoning " which .that study necessarily brings the mind to>^ -«« they may be able to transfer it to other parts of ** knov/ledge, as they shall have occasion ; for in all "sorts of reasoning, every single argument should be <* managed as a mathematical demonstration, the con^
151
" nection and dependence of ideas shauM be followed
*< till the mind is brought to the source on which it
' •<* bottoms, and can trace the coherence through the
<* whole train of proofs. It is in the general obser-
** vable, that the facukies of our souls are improved
*« and made usefnil to us just after the same manner as
«' our bodies ar€. Would you have a man write or
" paint, dance or fence well, or perform any other
*' manual operation dexterously and with ease ? Let
«' him have ever so much vigour and activity, supple-
** ness and address naturally, yet nobody expects this
^< from him unless he has been used to it, and has
" employed time and pains in fashioning and forming
<* his hand, or outward parts, to these motions. Just
«< so it is in the mind ; would you have a man rea*
«< son well, you muist use him to it betimes, exercise
« his mind in observing the connection of ideas, and
« following them in train. Nothing does this better
" than mathematics •, which therefore I think should
<' be taught all those who have the time and opportu-
*^ nity, not so much to make them mathematicians, as
« to make them reasonable creatures ; for though we
<« all call ourselves so, because we are born to it if we
•' please, yet we may truly say, nature gives us but
" the seeds of it. We are born to be, if we please,
" rational creatures j but it is use and exercise only
<* that makes us so ; and we are indeed so, no farther
<' than industry and application has carri:ed us." Cofi-
duct of the UtiderstandiHg.
X. But although the study of mathe- , r , • 1 r 11 1- 1 ^ r 1 ^^ ^^^° of such
matics be ot all others the most userul to authors on o-
form the mind and give it an early relish ther subjects,
of truth, yet ought not other parts of ^^ ^V^^'J^f ^""
•philosophy to be neglected j for there al- strenot^ and
so we meet with many opportunities of justness of re li-
exercising the powers of the understand- somng.
ing ; and the variety of subjects naturally leads us to
observe all those different turns of thinking that are
peculiarly adapted to the several ideas we examine.
152
and the truths we search after. A mind thus trained, acquires a certain mastery over its own thoughts, in- somuch that it can range and model them at pleasure, and call such into view as best suits its present de- •slgns. Now in this the. whole art of reasoning con- sists, from among a great variety of different ideas to single out those that are most proper for the business in hand, and to lay them together in such order, that from plain and easy beginnings, by gentle degrees, and a continual train or evident truths, we may be insen- sibly led on to such discoveries as at our first setting out appeared beyond the reach of the human under- standing. For this purpose, besides the study of ma- thematics before recommended, we ought to apply ourselves diligently to the reading of such authors as have distinguished themselves for strength of reasoning and a just and accurate manner of thinking. For it is observable, that a mind exercised and seasoned to truth, seldom rests satisfied in a bare contemplation of the arguments offered by others, but will be frequently - assaying its own strength, and pursuing its discoveries upon the plan it is most accustomed to. Thus we insensibly contract a habit of tracing truth from one stage to another, and of investigating those general relations and properties which we afterwards ascribe to particular things, according as we find them com- prehended under the abstract ideas to which the pro- perties belong. And thus having particularly shewn how we are to distribute the several objects of nature under -general ideas, what properties we are to ascribe .to them in consequence of that distribution, and how to trace and investigate the properties themselves, I: think I have sufficiently explained all that is necessary- towards a due conception of reasoning, and shall there-r -■ fore here conclude this chapter^..
153
CHAP. IV.
OF THE FORMS OF SYLLOGISMS.
I. Hitherto we have contented our- The ngnres of selves vi'ith a r^eneral notion of byllogisms, syllogisms. and of the parts of which they consist : it is now time to enter a little more particularly into the suhject, to examine their various forms, and to lay open tne rules of argumentation proper to each. In the syllogisms mentioned in the foregoing chapters, v/e may observe that the middle term is the subject of the major proposi- tion, and the predicate of the minor. This disposition, though the most natural an^ obvious, is not however necessary; it frequently happening that the middle term is the subject in both the premises, or the predicate in both ; and sometimes, directly contrary to its disposi- tion in the foregoing chapters, the predicate in the major y and the subject in the miner. Hence the dis- tinction of syllogisms into various kinds, called j^f/r^j* by logicians ; iox jigure^ according to their use of the word, is nothing else but the order and disposition of the middle term in any syllogism : and as this disposi- tion is we see fourfold, so the figures of syllogisms thence arising are four in number. "When the middle term is the subject of the major proposition, and the predicate of the minor ^ we have what is Ciilled thej^rj-^
figure. If, on the other hand, it is the predicate of both the premises, the syllogism is said to be in the second jigure. Again, in the third Jigure^ the middle term is tlie subject of the two premises. And lastly, by Making it the predicate of the major and subject of the minora we obtain syllogisms in the fourth figure.
II. But besides this i'ourfokl distinction The moods of of syllogisms, there is also a farther subdi- syllogisms. vision of them in every figure, arising from the quantity
154
and quality^ as they are called, of the propositions. By qiiantitij^ we mean the consideration of propositions as iniiversal or particular ; by quality^ as affirmative or negative. Now, as in all the several dispositions of the middle term, the propositions of which a syllogism consists may either be universal or particular, affirma- tive or negative \ the due determination of these, and so putting them together as the laws of argumentation require, constitute what logicians call the moods of syllo- gisms. Of these moods there are a deterrninate number to every figure, including all the possible ways in which propositions differing in quavUty or quality can be com- bined, according to any disposition of the middle term^ in order to arrive at ^ just conclusion. The shortness of the present work will not allow of entering into a more particular description of these several distinctions and divisions. I shall therefore content myself with Ttrfernng the reader to t)ia F zvt-F^y^zl Art >?/ Thinhingy where he will find the moods and figures of syllogisms distinctly explained, and the rules proper to each very; neatly demonstrated.
Foundation of . ^^^' ^h^ division of syllogisms accord. t}ie other di- ing to mood and figure, respects those, visions of syllo- especially which are known by the names gisras. q£ plain simple syllogisms ; that is, which
are bounded to three propositions, all simple, and where the extremes and middle term is connected, according to the rules laid down above. But as the mind is not tied down to any one precise form of rea- soning, but sometimes makes use of more, sometimes of feVv^er premises, and often takes in compound and conditional propositions, it may not be amiss to take notice of the different forms derived from this source, and explain the rules by which the mind conducts itself in the use of them. Conditional ' IV. When in any syllogism the major syllogisms.. js a conditional proposition, the syllogism itself is termed conditiofial. Thus :
15B
Ifttiere is a God, lie ought to he worshipped.
Bid there is a Gcd ;
Therefore he ought to be loor shipped. In this example, the major or first proposition Is, we see, conditional, and therefore the syllogism itself is also of the kind cviUed by that name. And here we are to observe, that all conditional propositions are made up of two distinct parts \ one expressing the condition upon which the predicate agrees or disagrees with the subject, as in this now before us, if there is a God ; the other joining or disjoining the said predicate and subject, as here, he ought to be ivorshipped. The first of these parts, or that which implies the condition, is called the antecedent ; the second, where we join or disjoin the predicate and subject, has the name of the consequent.
V. These things explained, we are far- ^ , r-n
- , 1 . ' II • • c Ground of iila-
ther to observe, that ni all propositions oi tion in condi-
this kind, supposing them to be exact in tional syiio- point of form, the relation between the g^^ms. antecedent and consequent must ever be true and real ; that is, the antecedent must always contain some cer- tain and genuine condition, which necessarily implies the consequent ; for otherwise, the proposition itself will be false, and therefore ought not to be admitted into our reasonings. Hence it follows, that when any conditional proposition is assumed, if v/e admit the antecedent of that proposition, we must at the same time necessarily admit the consequent ; but if we reject the consequent, we are in like manner bound to reject also the antecedent ; for as the antecedent always expresses some condition v/hich necessarily implies the truth of the consequent, by admitting the antecedent we allow of that condition, and therefore ought also to 3<lmit the consequent. In like manner, if it appears that the consequent ought to be rejected, the antece- dent evidently must be so too ; because, as we just now demonstrated, the admitting of the antecedent would necessarily imply the admission also of the con- sequent.
156
The two modes VI. From what has been said, it ap- of conditional pears, that there are two ways of arcruinc syllogisms. ^^ hypothetical syllogisms, which lead to a certain and unavoidable conclusion ; for as the vwior is always a conditional proposition, consisting of an antecedent and a consequent ; if the minor admits the antecedent, it is plain that the conclusion must admit the consequent. This is called arguing from the ad- mission of the antecedent to the admission of the consequent, and constitutes that mood or species of hjjiothetical syllogisms, which is distinguished in the schools by the name of the modus ponensy inasmuch as by It the whole conditional proposition, both antece- dent and consequent, is established. Thus :
If God is injimtelij ivise^ and acts ivith perfect, free^
dom^ he does nothing but ivJiat is best. But God is injinitelij luise, and acts nvith perfect free"
dom ; Therefore he does nothing but luhat is best. Here we see the antecedent or first part of the con- ditional proposition is established in the miiior^ and the consequent or second part in the conclusion •, whence the syllogism itself is an example of the modus pcnens. But if now we, on the contrary, suppose that the minor rejects the consequent, then it is apparent that tlie conclusion must also reject tlie antecedent. In this case we are said to argue from the removal or the consequent to the removal of the antecedent, and the particular mood or species of syllogisms thence arising is called by logicians the modus tolle^is ; because in it both antecedent and consequent are rejected or taken away, as appears by the following example :
If God ivcre not a Being of ij finite goodness^ neither
luould he consult the happiness of his creatures. But God does consult the happiness of his creatures ; Therefore he is a Being of uifnite goodness. \
_, . , J VII. Thei;^- two species take in the \
They include , , , r r^- i ^\ ■ i
5ill the lepiti- whole class ot conditional syllogisms, and i
fliate ways of luclude all the possible ways of arguing
arguing. that lead to a legitimate conclusion, be- I
157
:aus3 we cannot here proceed by a contrary process of reasoning ; that is, from the removal of the antece^ dent to the removal of the consequent, or from the establishing of the consequent to the establishing of the antecedent ; for although the antecedent always expresses some real condition, which once admitted necessarily implies the consequent, yet it does not follow that there is therefore no other condition ; and if so, then after removing the antecedent, the conse- quent may still hold, because of some other determi- nation that infers it. When we say. If a stone is.ex'- posed 70fne time to the rays of tJie suriy it ivill cctitract a certain degree of heat ; the proposition is certainly true, and admitting the antecedent, we must also admit the consequent. But as there are other ways by which a stone may gather heat, it will not follow, from the ceasing of the before-mentioned condition, that there- fore the consequent connot take place. In other words, we cannot argue, But the stone has not been ex-' 2)osed to the rays of the sun ; therefore neither has it any de^ gree of heat ; inasmuch as there are a great many other ways by which heat might have been communicated to it. And if we cannot argue from the removal of the an- tecedent to the removal of the consequent, no more can we from the admission of the consequent to the admission of the antecedent ; because as the conse- quent may flow from a great variety of different sup- , positions, the allowing of it does not determine the I precise supposition, but only that some one of them must take place. Thus, in the foregoing proposition, If a stone is exposed so}ne time to the rays f the su7i^ it will contract a certain degree of heat. Admitting the con- sequent, viz. that it has contracted a certain degree of heat ^ we are not therefore bound to admit the antecedent, that it has been some time exposed to the rays of the sun ; because there are many other causes whence that heat JTiay have proceeded. These two ways of arguing therefore hold not in conditional syllogisms. Indeed, where the antecedent expresses the only condition op
P
158
which the consequent takes place, there they may be i^pplied with safety ; because wherever that condition is not, we are sure that neither can the consequent be, and so may argu<5 fro-m the removal of the one to the removal of the other •, as, on the contrary, wherever the consequent holds, it is certain that the condition must also take place ; M^hich shews that, by establish- ing the consequent, we at the same time establish the •antecedent. But as it is a very particular case, and that happens but seldom, it cannot be extended into a general rule, and therefore affords not any steady and universal ground of reasoning upon the two foregoing suppositions. rj., VIII. As from the major'' s belnc a con-
1 he manner . .. i«i
of arguing in ditional proposition, we obtain the species tlisjunctive of conditional syllogisms, so where it is a syllogisms. disjunctive proposition, the syllogism to which it belongs is called disjutictive, as in the follow- ing example :
The luorld is either self-existent , or the luork of some finite y or of some infnite being.
But it is not self-existent y ?wr the work of a finite being ;
Therefore it is the luorh of an infnite being.
Now a disjunctive proposition is that where of se- veral predicates we affirm one necessarily to belong to the subject, to the exclusion of all the rest, but leave that particular one undetermined. Hence it follow^, that as soon as vie determine the particular predicate, all the rest are of course to be rejected ; or if we re- ]ect all the predicates but one, that one necessarily takes place. When therefore in a disjunctive syllogism, the several predicates are enumerated in the majors — if the minor establishes any one of these pradicates, the conclusion ought to remove all the rest ; or if in the minor all the predicates but one are removed, the con- clusion must necessarily establish that one. Thus, in the disjunctive syllogism given above, the major afHrms one of tliree predicates to belong to the earth, viz.
159
ielf-existetue, or that it is the work of ajlmte^ or that it is the ivork of an wfnite bewg. Two oi these predi- cates are removed in the ininor, viz. self-existence, aiul the ivork of a finite being. Hence the conclusion ne- cessarily ascribes to it the third predicate, and affirms that i-t is tJie work of an infinite being. If now we give the syllogism another turn, insomuch that the minor may establish one of the predicaies, by affirming the earth to be the productioti of .an it finite heir>g^ tlien the -conclusion must remove the other two, asserting it to be neither self-existent nor the ivork of a finite being* These are the forms of reasoning in this species of syllogisms, the justness of which appears at first sight ; and that there can be no other, is evident from j.he very nature of a disjunctive proposition.
IX. In the several kinds of syllogisms imperfect or hitherto mentioned, we may observe that miitilated the parts are complete ; that is, the three syllogisms. propositions of which they consist are represented In form. But it often happens that some one of the pre- mises is not only an evident truth, but also familiar, and in the minds of all men ; in which case it is usually omitted, whereby we have an imperfect syl- logism, that seems to be made up of only two propo- sitions. Sho'xld we, for instance, argue in this man- ner :
Every man is mortal ;
Therefore every king is mortal ; the syllogism appears to be imperfect, as consisting but of two propositions. Yet it is really complete, only the minor f every king is a tnanj is omitted, and left to the reader to supply, as being a proposition so familiar and evident, that it cannot escape him.
X. These seemingly imperfect syllo- gisms are called Enthymemesy and occur ^"'^^y"'^"^^- very frequently in reasoning, especially where it makes a part of common conversation. Nay, there is a par- ticular elegance in them, because not displaying the •argument in all its parts, they leave somewhat to tlie
160
exercise and invention of the mind. By this means Xve are put upon exerting ourselves, and seem to share in the discovery of w^hat is proposed to us. Now this is the great secret of fine writing, so to frame and put to- gether our thoughts, as to give full play to the reader's imagination, and draw him inserjsibly into our very views and course of reasoning. This gives a pleasure not uiilike to that which the author feels himself in composing. It besides shortens discourse, and adds a certain force and liveliness to our arguments, when the words in which they are conveyed favowr the natural quickness of the mind in its operations, and a single expression is left to exhibit a whole train of thoughts. Ground cf rea- •^^« ^^^^ there is another species of rea- soning in im- soning with two propositions, which seems mediatecor.se- f^ |j« complete in itself, and where we q' nces. admit the conclusion without supposing
any tacit or suppressed judgment in the mind, from which it foilow^s syllogisticaily. This happens between propositions where the connection is such,\that the admission of the one, necessarily, and at the first sight, implies the admission also of the other. For if it so falls cut that tlie proposition on which the other de- pends is self-evident, we content ourselves with barely affirming it, and infer that other by a direct conclusion. Thus by admitting an universal proposition, we are forced also to admit of all the particular propositions comprehended under it, this being the very condition tliat constitutes a proposition universal. If then that universal proposition chances to be self-evident, the particular ones follow of course, without any farther train of reasoning. V/lioever allows, for instance, ifh'it things equal to one and the same thing are equal to one .another i must at the same time allow that tivo triangles^ each eaual to a square ivhose side is three inches y are also c- ^^ual betu.ueen themselves. This argument therefore.
Things equal to one and the same thing., are equal to
one another ; Therefore those tivo triangles y each equal to the square of a line oj three inches y are equal between themselves.
161
h complete in its kind, and contains all that is neces- sary towards a just and legitimate conclusion •, for the first or universal proposition is self-evident, and there-' fore requires no farther proof.: and as the truth of the particular is inseparably connected with Jthat of the universal, it follows from it by an obvious and unavoida- ble consequence.
XII. Now in all cases of this kind where ^11 reducible propositions are deduced one from ano- to syllogisms
ther, on account of a known and evident ^^ ^*^"^^ °"^
. . , , . lorfti or other,
connection, we are said to reason by tmmc-
diate consequence. Such a coherence of propositions, manifest at first sight, and forcing itself upon the mind, frequently occurs in reasoning. Logicians have ex- plained at some length the several suppositions upon which it takes place, and allow of all immediate conse- quences that follow in conformity to them. It is how- ever observable, that these arguments, though seeming- ly complete, because the conclusion follows necessarily from the single proposition tha.t goes before, may yet i>e considered as real entJujmemcSi whose major ^ which is a conditional proposition, is wanting. The syllogism but just mentioned, when represented according to •this view, will run as follov/s .•
If things equal to one and the same thing are equal .to
one another ; these tiuo triangles^ each equal to a
square whose side is three inches y are also equal he-
tiveen themselves.
But things equal to one and the same things are equal
t to one another .,•
Tlurefore also these triangles, &c. are equal betiveen themselves. This observation will be found to hold in all imme^ diate consequences whatsoever, inscm.uch that they are in fact no more than enthymemes of hypothetical syllo- gisms. But then it is particular to them, that the ground on which the conclusion rests, namely, its co- herence with the mijior, is of itself apparent, and seen immediately to flow from the rules and reasons of loo-ic.
P3 ""
162
As it is therefore entirely unnecessary to express a self-evident connection, the jnajor, whose office that is, is constantly omitted -, nay, and seems so very little needful to enforce the conclusion, as to be accounted commonly no pa;rt of the argument at all. It must in- deed be owned, that the foregoing immediate consequence might have been reduced to a simple as well as an hy- jpothetical syllogism. This will be evident to any one who gives himself the trouble to make the experiment. But it is not my design to enter farther into these niceties, what h^ been said sufficing to shew, that all arguments consisting of but two propositions are real enthymemesy and reducible to complete syllogisms of some one form or other. As therefore the ground on which the conclusion rests, must needs be always the same with that of the syllogisms to which they belong, we have here an universal criterion whereby at all times to ascertain the justness and validity of our reasonings in this way.
A sorites of XIII. The next species of reasoning we
plain simple shall take notice of here, is what is com- syllogisms. monly known by the name of a sorites. This is a way of arguing, in which a great number of propositions are so linked together, that the predicate of one becomes continually the subject of the next fol- lowing, until at last a conclusion is formed, by bring- ing together the subject of the first proposition and the predicate of the last. Of this kind is the following argument :
God is cmnipotent.
An omnipotent being £an do every thing possible.
He that can do every thing possible^ can do whatever involves not a contradiction.
Therefore God can do whatever involves not a con--
tradiction.
This particular combination of propositions may be
continued to any length we please, without in the least
weakening the [ground upon which the conclusion rests.
The reason is, because the sorites itself may be resolved
163
into as many simple syllogisms as there are middle terms in it *, where this is found universally to hold, that when such a resolution is made, and the syllogisms are placed in train j the conclusion of the last in the series is also the conclusion of the sorites. This kind of argument therefore, as it serves to unite several syllo- gisms into one, must stand upon the same foundation with the syllogisms of which it consists, and is indeed, properly speaking, no other than a compendious way of reasoning syllogistically. Any one may be satisfied of this at. pleasure, if he but takes the trouble of resolving the foregoing sorites into two distinct syllo- gisms ; for he will there find, that he arrives at the same conclusion, and that too by the very same train of thinking, but with abundantly more words, and the addition of two superfluous propositions.
XIV. What is here said of plain simple a sorites of propositions, may be well applied to those hypothetical that are conditional ; that is, any number syltogisms, of them may be so joined together in a series, that the consequent of one shall become continually the antece- -dent of the next following •, in which case, by establish- ^ing the antecedent of the first proposition, we establish the consequent of the last, or by removing the last consequent, remove also the first antecedent. This way of reasoning is exemplified in the following argu- ment :
If we love any person, all emotions of hatred towards him tease.
If all emotion of hatred toivards a person cease, loe cannot rejoice in his misfortunes.
If we rejoice not in his misfortunes, we certainlu wish him no injury.
Therefore if we love a person, we wish him no in- jury. It is evident that these sorites^ as well as the last, may be resolved into a series of distinct syllogisms, with this only difference, that here the syllogisms are all conditional. But as the conclusion of tti« last syllo-
164
gism m the series Is the same with the conclusion of the soritesy it is plain, that this also is a compendious way, of reasoning, whose evidence arises from the evi- dence of the several single syllogisms into which it may be, resolved.
The ground of XV. I come now to that kind of argu- seasoning by ment which logicians call induction ; m nduction. order to the right understanding of which, it will be necessary to observe, that our general ideas are for the most part capable of various subdivisions. Thus the idea of the lowest species may be subdivided into its several individuals ; the idea of any genus in- to the different species it comprehends ; and so of the rest. If then we suppose this distribution to be duly made, and so as to take in the whole extent of the idea to which it belongs, then it is plain that all the subdivisions or parts of any idea taken together con- stitute that whole idea. Thus the several individuals of any sprecies taken together constitute the whole spe- cies, and all the various species comprehended under any genus, make up the w^hole genus. This being allowed, it is apparent, that whatsoever may be af- firmed of all the several subdivisions and classes of any idea, ought to be affirmed of the whole gene- ral idea to which these subdivisions belong. What may be atErmed of all the individuals of any species, may be affirmed of the whole species *, and what may be affirmed of all the species of any genus, may also be affirmed of the whole genus ; because all the indlvi- 4uals taken together, are the same with the species v and all the species taken together, the same with the genus.
The form and . ^^^' 'J^^'^ w^ay of arguing, where we structure of Infer universally concerning any idea, an argument what we had before affirmed or denied by induction, separately of all its several subdivisions and parts, is called reasoning by induction. Thus, if we suppose the whole tribe of animals subdivided into men, beasts, birds, insects, and fishes, and then vqsl-
J 63
son concerning thorn after this manner : A// men have a ponvcr of beginning motion ; all beastSy births and insects have a poiuer of beginning motion ; all jishes have a poiuer of beginning mction ; therefore all animals have a poiver of beginning motion. The argument is an induction. When tlie subdivisions are just, so as to take in the whole general idea, and x\\q enumeration is perfect, that is, extends to all and every of the inferior classes or parts, there the induction is complete, and the manner of rea- soning by induction is apparently conclusive.
XVII. The last species of syllogisms I xhe ground of shall take notice of in this chapter, is that argumentation commonly distinguished by the name of a "^ ^ dilemma. dilemma. A dilemma is an argument by which we endeavour to prove the absurdity or falsehood of some assertion. In order to this we assume a conditional proposition, the antecedent of which is the assertion to be disproved, and tlve consequent a disjunctive propo- sition, enumerating all the possible suppositions upon which that assertion can take place. Jf th^n it ap- pears that air these several suppositions ought to bc re- jected, it is plain that the antecedent or assertion it- self must be so too. When therefore such a propo- sition as that before mentioned is made the major of any syllogism, if the minor rejects all the suppositions contained in the consequent, it follows necessarily that the conclusion ought tO reject the antecedent, which, as we have said, is the very assertion to be disproved. This particular way of arguing, is that which logicians call a dilemma ; and from the account here given of it, it appears that we may in general define it to be an hypothetical syllogism nuhere the consequent of the major is a disjunctive proposition^ ivhich is iL-holly taken aivay or removed in the minor. Of this kind is the following : If God did net create the ivorld perfect in its kind, it must either proceed front nvant of ificlinatian^ or from nvant of pou.uer : But it could not proceed either frora ivant of inclina'" tion or from nvant of poiver ;
166
Therefore he created the ivorld perfect in its kind. Or, which Is the same thing, it is absurd to say that he did not create the ivorld perfect in its' kind. An universal XVIII. The nature then of a dilemma .
description is universally this. The mttjor is a con- J ®^^^- ditional proposition, whose consequent
contains all the several suppositions upon which the antecedent can take place. As therefore these suppo- sitions are wholly removed into the minor^ It is evident that the antecedent must be so too •, insomuch that we here always argue from the removal of the consequent to the removal of the antecedent. That is, a dilemma is an argument in the modus tollens of hypothetical syllo- gisms, as logicians love to speak'. Hence it is plain, that if the antecedent of the major is an affirmative proposition, the conclusion of the dilemma will be ne- gative : but if it is a negative proposition, the con- clusion will be affirmative. I cannot dismiss this sub- ^ ject without observing, that as there is something very curious and entertaining in the structure of a dilemma^ so Is it a manner of reasoning that occurs frequently in imathematical demonstrations. Nothing is more com- mon with Euclid, when about to shew the equality of two given figures, or, which is the same thing, to prove the absurdity of asserting them unequal *, nothing, I say, is more common with him than to assume, that if the one is not equal to the other , it must be either greater or less: and having destroyed both these suppositions, upon which alone the assertion can stand, he thence very naturally infers, that the assertion itself is false. Now this is precisely the reasoning of a dilemma y and in every step coincides with the frame and composition gi that argument^ as we have described it above.
IG'
reasomnff
CHAP. V.
OF DEMONSTRATION.
I. Having dispatched what seemed ne- q£ cessary to be said with regard to the by a concate- forms of syllogisms, we now proceed to nation of sylio- supply their use and application in reason- &^^^^- ing. We have seen that in all the different appear- ances they put on, we still arrive at a just and legiti- mate conclusion. Now, it often happens that the conclusion of one syllogism becomes a previous propo- sition in another, by which means great numbers of them are sometimes linked together in a series, and truths are made to follow one another in train. And as in such a concatenation of syllogisms, all the vari- ous ways of reasoning that are truly conclusive may be with safety introduced, hence it is plain, that, in de- ducing any truth from its first principles, especially when it lies at a considerable distance from them, we are at liberty to combine all the several kinds of argu- ment above explained, according as they are found best to suit the end and purpose of our inquiries. When a proposition is thus by means of syllogisms collected from others more evident and known, it is said to be proved ; so that we may in the general de- fine the proof of a jwopontion to be a syllogism, or series of syllogisms, collecting that proposition from known and evident truths. But more particularly, if the syl- logisms of which the proof consists admit of no pre- mises but definitions, self-evident truths, and propo- sitions already established, then is the argument so constituted called a demcnstratioti ', whereby it appears that demonstrations are ultimately founded on defini- tions and self-evident propositions.
168
All syllogisms ^^- ^^^ ^^ ^ demonstration often consists whatsoever of a long chain of proofs, where all the reducible to various ways of arguing have place, and the first figure. ^^^^^ ^^^ ground of evidence must of course be different in different parts agreeably to the J form of the argument made use of. It may not perhaps ' be unacceptable, if we here endeavour to reduce the evidence of demonstration to one simple principle, whence, as a sure and unalterable foundation, the certainty of it may in all cases be derived. In order to this we must observe, that all syllogisms whatsoever, whether compound, multiform, or defective, are redu- cible to plain simple syllogisms in some one of the four figures. But this is not all. Syllogisms of the first figure in particular, admit of all possible conclusions ; that is, any proposition whatsoever, whether an univer- sal affirmative or universal negative, a particular affir- mative or particular negative, which fourfold division, as we have already demonstrated in the Second Part, embraces all their varieties ; any one, I say, of these may be inferred by virtue of some syllogism in the first figure. By this means it happens, that the syllogisms of all the other figures are reducible also to syllogisms of the first figure, and may be considered as standing on th? same foundation with them. We cannot here demonstrate and explain the manner of this reduction, because it would too much swell the bulk of this Trea- tise. It is enough to take notice, that the thing is universally known and allowed among logicians j to whose writings we refer such as desire farther satisfac- tion in this matter. This then being laid down, it is plain, that any demonstration whatsoever may be con- sidered as composed of a series of syllogisms, all in the first figure ; for since all the syllogisms that enter the demonstration, are reduced to syllogisms of some one of the four figures ; and since the syllogisms of all the other figures are farther reducible to syllogisms of the first figure, it is evident that the whole demonstration may be resolved into a series of these last syllogisms.
169
Let us naw, if possible, discover the ground upon which the conclusion rests in syllogisms of the first fi- gure -, because by so doing, we shall come at an universal principle of certainty, wheiice the evidence of all demonstrations in all their parts may be ultimately derived.
III. The rules then of the first figure The around of are briefly these. The middle term is the reasoning in the subject of the major proposition, and the ^*^*^ %"^^ predicate of the minor. The major is always an univer- sal proposition, and the minor always affirmative. Let us now see what effect these rules will have in reason- ing. The major is an universal proposition, of which the middle term is the subject, and the jiredicate of the conclusion the predicate. Hence it appears, that in the major the predicate of the conclusion is always affirmed or denied universally of the middle term. Again, The minor is an affirmative proposition, whereof the subject of the conclusion is the subject, and the middle term the predicate. Here then the middle term is affirmed of the subject of the conclusion ; that is, the subject of the conclu- sion is affirmed to be Comprehended under, or to make a part of the middle term. Thus then we see what lis done in the premises of a syllogism of the first figure. The predicate of the conclusion is universally affirmed or denied of some idea. The subject of the conclusion is affirmed to be, or to make a part of that idea. Hence it naturally and unavoidably follows, thzt the j^redicate of the conclusion ought to be affirmed or denied of the subject. To illustrate this by an example, we shall resume one of the syllogisms of the first chapter::
Every creature possessed of reason and liberty y is accmnt- able for his actions :■
Man is a creature possessed of reasofi and liberty ;
Therefore man is accountable for his actions.
Here, in the first proposition, the predicate of the conclusion accoimtableness^ is affirmed of all creatures that have reason and liberty. Again, in the second pro- nosition, ma7i^ The subject of the conclusion is affirmed
170
{to be, or to make a part of this class of creatures. -Hence the conclusion necessarily and unavoidably fol- lows, viz-, that man is accountable for his actiofis, I say this follows necessarily and unavoidably j because if reason and liberty be that which constitutes a creature accountable^ and man has reason and liberty, it is plain he has that which constitutes him accou7itahle. In like manner, where the 7najor is a negative proposition, or denies the pr£clicnte of the conclusicPn universally of the ■middle term, as the minor always asserts the subject of the conclusion to be or make a part of that middle term, it is no less evident that t\\&, predicate of the conclusio?i ought in this case to be denied of the subject. So that the pround of reasoning in all syllogisms of the first figure, is manifestly this : Whatever may be ofjirmed universally of any idea, maybe affirm id of every or any 7iumber of par- ticulars comprehended under that idea. And again, What- ever may be denied miiversally of any idea, may be in lihe mhnner denied of every or any number of its individuals. These two propositions are called by logicians the dictum de omni, and dictum de nidlo, and are indeed the great principles of syllogistic reasoning \ inasmuch as all conclusions whatsoever, either rest immediately upon them, or upon propositions de<Juced from them. But what adds greatly to their value is, that they are really self-evident truths, and sach as we cannot gain- say, without running into an express contradiction. To affirm, for instance, that no man is perfect, and yet argue that some men -are perfect ; or to say that all men ar^e mortal, and yet that some men are not mortal, is to assert a thing to be and not to be at the same time. Demonstration ^^ ' ^^'^^ '^ow I think we are sufficient- an infullible ly authorised to affirm, that in all syllc- guide.to truth gisms of the first figure, if the premises «nt ccr amty. ^^^ true, the conclusion must needs be true. If it be true that the predicate of the conclusion, whether affirmative or negative, agrees universally to some idea ; and if it be also true that the subject of the conclu- jian is a part of or comprehended under that idea, then
I !
171
it necessarily follows, that the predicate of the conclusion agrees also to the subject ; for to assert the contrary, would be to run counter ta some one of the two princi- ples before established ; that is, it would be to maintaia an evident contradiction. And thus we are come at last to the point we have been all along endeavouring to establish, namely, that every proposition which can be demonstrated is necessarily true. For as every demon- stration may be resolved into a series of syllogisms all in the first figure, and as in anyone of these syllogisms, if the premises are true, the conclusion rnu>t needs be so too, it evidently follows, that if all the several pre- mises are true, all the several conclusions are so, and consequently the conclusion also of the last syllogism, which is always the proposition to be <;iemonstratcdi Now that all the premises of a demonstration are true, will easily appear, from the very nature nnd defihitio« of that form of reasoning. A demonstration, as we have said, is a series of syllogisms, all whose premises are either definitions, self-evident truths, or proposi- tions'"already established. Definitions are identical propositions, wherein we connect the description of an idea with the name by which we choose to have that idea called ; and therefore, as to their tr^ith there can be no dispute. Self-evident propositions appear true of themselves, and leave no doubt or uncertainty in the mind. Propositions before established, are no other than conclusions, gained by one or more steps from definitions ar.d self-evident principles •, that is, from true premises, and therefore must needs be true. Whence all the previous propositions of a demonstra- tion, being we see manifestly true, the last conclusion, or proposition to be demonstrated, must be so too. So that demonstration not only leads to certain truth, but we have here a clear view of the ground and founda- tion of that certainty ; for as in demonstrating we may be said to do nothing more than combine a scries of syllogisms together, all resting on the same bottom, it is plain that one uniform ground of certainty runs
02
172
tlirough the whole, and that the conclusions are every- where built upon some one of the two principles be- fore established as the foundation of all our reasoning. These two principles are easily reduced into one, and may be expressed thus : Whenever predicate^ ivheiher q^irmative or negative y agrees utjiv^ersaHi/ to any idea^ the same must needs agree to every or any number of individuals i-omprehended under that idea. And thus at length we have, according to our first design, reduced the certain- ty of demonstration to one simple and universal princi- ple, which carries its own evidence along with it, and which is indeed the ultimate foundation of all syllogis- tic reasoning.
The rules of ^* Demonstration, therefore, serving
logk furnish as an infallible guide to truth, and stand- .i sufficient en- \^^ q^ gQ gyj.^ and Unalterable a basis, we tenou ioT the. "^ *,^ ^.u^tju^
rfimhgukiihff ^"'^y ^^^"^ venture to assert, what 1 doubt
b6tAv€;en truth not will appear a paradox to many 5 ^Bd:falsehocwl,. namely, that the rules of logic furnish a sufficient criterion for the distinguishing between truth s.nd falsehood. For since every proposition that can be demonstrated, is necessarily true, he is able to dis- tinguish trauli from falsehood who can with certainty judige when a prop.osition is duly demonstrated* Now .a.dfimoiwtratiQn i&, asi we have said, nothing more than uconcaten^.tion' of syllogisms., all whose premises are defmitior-s, s^'lF-evident truths, or propositions previ- ously established-. To- judge therefore of the validity ©{ a. demonstration, we must be able lo distinguish whether the definitions that enter it are genuine, and truly descriptive of the ideas they are meant t) exhi- bit:. whietber the propositions assumed without proof -ar intuitive truths, have really tiiat self-evidence to which: they lay claim : whether the syllogisms are ^rawn up in due form, and agreeable to the laws of argunsrentation : in fine, whether they are combined to- gether in a'jnst and orderly manner, so that no de- monstrable propositions serve any where as premises, unless they are conclusions of previous syllogisms.
17S
K^ow it is the business of logic, in explaining' the several operations of the mind, fully to instruct «s in all these points. It teaches the nature -and end of definitions, and lays down the rules ' by which^ they ought to be frarne^l. It unfolds th« several s.pe- cies of proposition, and distinguishes the '^elf-evddent from the demonstrable. It delineates also the different forms of syllogisms, and explains the laws of argumen- iation proper to each. In fine, it describes the jnan- ner of combining syllogism's, so as that they may form- .a train of reasoning, and lead to the successive .dis- covery of trutlu The precepts of logic therefore, as they enable us to judge with certainty when a propo-; sition is duly demonstrated, furnish a sure criterion for the distinguishing between truth and falsehood.
VI. But perhaps it may be objected, .1^1 • ' ^/. "^ and extendin":
that demonstration is a thing very Tare ^^ ^u ^^^^^ *="
and uncommon, as being the prerogative r^here a cer-
of but a few sciences ; and therefore the tain kuow-
criterion here given can be of no great use. .^ ^^ ? u,° y , o , 1 1 r *^ attainable.
1 answer, that wherever, by the bare con- eft '-
templation of our ideas, truth is discoverable, tHei^e also demonstration may be obtained. Now that I think is an abundantly sufficient cnter.iony which en- ables us to judge with certainty in all cases where the. knowledge of truth comes within our reach ; for with- discoveries that Jie beyond the Jimitsof. the. buman mind, we have properly no business nor ci&ncernniient. . When a proposition is demonstrated, we are certain of its truth. When, on the contrary, our ideas are such as have no. visible connection ror repugnance, and therefore furnish not the proper means of tractng'their agreement or disagreement, there we are sure that knowledge, scientifical knowledge I mean, is not attain- able. But where there is some foundation of reason- - ing, which yet amounts not to the full evidence of de- monstration, there- the precepts of logic, by teaching us to determine aright of the degree of proof, and of what is still wanting to render it full and complete, ,
0 3
act of reason-
150
in^^ar:;: fy -f^^- d^ee distinct jud^
loglsm. ^wo Wxherein the idea
, . o ems;
^ whose relation we
a red
wi
themselves con-iprto^ ^. ,..".*"""' ^^^iciem me v are
s"Jt of that comp'Lon T'"' '•'=""'''^' '" '^'^ ^^■ ofWi.. „,'.?"!!?":. ^r^' ^' >n the Second Part
c
p.-.oxv.'x,, ui our reasonings
elude threlV.. ^ '' '^ -'^'^y ^^''^^'^ '^^^^ in- Tthu. n r ^'^^"^'" P^^P^'^^t:ons. When a reasoning i. thus put into words, and appears in form of a svllo!
the ;J? ^"'^^"^^^^^ ^^'' "^^de use of to discover Ue agreement or disagreement we search for, is called tne midaie term ; and the two ideas themselves with wnicn tins third is compared, go bv the name of the extremes.
Listance, man, ^^ ' ^^^ "^^ f-^^se things are best ilius- and account- trated by examples, let us, for instance, abJeness. set ourselves to Inquire -ivhther men are
accountahh for their acikm ? As the rel.tion between the ideas ot mm and accountah'.eness Qom^% not within the immediate view of the mind, our first care must be to find out seme third idea that v/ill enable us the more easily to discover and trace it. A very small measure^ of reflection is sufficient to inform us that no crenturj can be accountable for his actions, unless we suppose him capable of distinguishing the good from the bid ; that is, unless we suppose him possessed of rensor.. Nor is this alone sufficient. For what would it avail him to know good from bad actions, if he had no freedom o<^ choice, nor could avoid the one an ' the other.'' Hence it becomes necessary to both considerations in the piesent case. It is at the same, time equallv apparent, that wherever there : this ability of distinguishing good from bad ncti*^ , and pursuing the one and avoiding the other, there "ii creature is accountable. We have then got a v .
,\\ih which jTiV: '.asG.'i and lil^enif : king up one com this middle idea, in question, viz.
tliat it mav be : ?ans of the intern, lents, viz. that man nd that reason at: obvioiisiy and ne^. table for his -actio::}
. Tab I y c o nn ?ct ed ,
.c ;o be considered
. prion. Let us now
re it with the other
. e all know by expe-
I iiim. Having thus,
ea, formed two several
d of reason anj libera
'tf acccuntabUness ; a
., --1.0W5, VIZ. thut man .v rife then we have a com- act of reasoning, in whit, according to wliat has already observ'ed. '^ * re three distinct judg- 5 ; two that may .; previous, inasmuch as
cad to the other, ai e from comparing the
e idea with Ae two idf s in the question *, the
•sr^revious acts, and flows i« as between themselves. ti into words, it exhibits ^i 1, and when proposed
■t r '0
n and liheriij is accoittit"
IS a consequence combining the ex w we put this r logicians term a 2 form, runs thus ; :rij creature pos"^- ir /;// actions,
171 is a creature jKssessed Reason and liberty ; tlure- uin is acccuntah' a ons.
In this syliof^io ay observe, „
, 1 , ^ . . Premise?, con-
Iiere are three several J opositions, elusion, ex-
ssing the three judu'meJj implied in tremes, mulJJc
:t of reasoning, ?.i J ->osed as to ^^^^'
lent distinctly w: „. . ies within the mind In
g the more distant relions of Its ideas. The
irst propositions an?wel he two previous judg-
1 in reasoning, a I ailed the premises y be-
tliey are placed L .. . •
d the conclusion J as bci
at was asserted In the wmises
tiber tliat the terms Iressin
J relation we inquire Mr, as here
b/enessy are in geiv?r,il|lk-d the extremes
lence
^■^^^^
I
h\
H
m
174j
enable us to make a due estimate of the measures of ptobiibiiity> and to proportion our assent to the grourrd^. on; which the proposition stands. And this is all we- cafi possibly arrive at, or even so much as hope for^ ju the exercise of faculties so imperfect and limited as ours ; for it were the height of folly to ex- pect a criterion that should enable us to distinguish truth from falsehood, in cases wliere a certain know- ledge of truth is not attainable.
The distinc- ^^^* ^^^ h2iye now done with what re^
tion of de- gards the ground and evidence of demon- nionstration stration ; but before we conclude this in^re"^^^^ '^"^ chapter, it may not be improper to take notice of the distinction of it into direct and indirect. A /lirect demonstration is, when begin- ning with definitions, self-evident propositions, or known and allowed truths, we form a train of syllo- gisms, and combine them in an orderly manner, con- tirming the series through a variety of successive steps, until at last we arrive at a syllogism, whose conclu- sion is the proposition to be demonstrated. Proofs of this kind leave no doubt or uncertainty behind them, because all the .several premises being true, the can- elusions must be so too, and of course the very last conclusion or proposition to be proved. I shall not therefore any farther enlarge upon this method of de- monstrating, having 1 hope sufficiently explained it in the foregoing part of this chapter, and shewn wherein the force and validity of it lies. The other species of demonstration is the indirect^ or, as it is sometimes called, the apologicaL The manner of proceeding here is by assuming a proposition which directly contradicts ^hat we m-ean to demonstrate, and thence by a con- tinued train of reasoning, in the way of a direct de- monstration, deducing some absurdity or manifest un-^ truth ; for hereupon we conclude that the proposition assumed was false, and thence again by an immediate consequence, that the proposition to be demonstrated is true. Thus Endid^ in his third book, being to <lf*
175
monstrate that circles 'which touch Qne another intvardly
have not the same centre, assumes the direct contrary to
this, viz. that they have the jume centre 4 and hence by
an evident train of reasoning proves, that a part U
equal to the ivhole. The supposition therefore leading
to the absurdity, he concludes to be false, viz. that
circles touching one another in<wardly have the sam£ centre 7
and thence again immediately infers, that they have not
the same centre.
VIII. Now, because this manner of de- ^ , ^
. ' Ground of rea-
monstration is accounted by some not al- soning in indi- 'together so clear and satisfactory, nor to rect demon- eome up to that full degree of evidence '^^^^lons. ■which we meet with in the direct way of proof, I shall therefore endeavour here to give a particular il- lustration of it, and to shew that it equally with the other leads to truth and certainty. In order to this we must observe, that two propositions are said to be contradictory one of another, when that which is assert- ed to be in the one, is asserted not to be in the other. Thus the propositions : circles that touch one another in^ ivardly have the same centre : and circles tJicit touch one another ininxardly have not .the same centre, are contradicto- riesy because the second asserts the direct contrary of what is assertec- in the first. Now, in all contradict tory propositions this holds universally, that one of them is necessarily true, and the other necessarily false. For if it be true that circles which touch one another inwardly have not the same centre, it is unavoidably false that they have the same centre. On the other hand, if it be false that they have the same centre, it is necessarily true that they have not the same centre* Since therefore it is impossible for them to be both true or both false at the same time, it unavoidably fol- lows, that one is necessarily true, and the other ne- cessarily false. This then being allowed, which is in- deed self-evident, if any two contradictory propositions are assumed, and one of them can by a clear train of reasoning be deuionstrated to be false, it necessarily
176
folloWs that the other is true •, for as the one Is neces- sarily true, and the other necessarily false, when we come to discover which is the false proposition, we thereby also know the other to be true.
Indirect de- ^^' ^^^""^^ this is precisely the manner
monstrations of an mdirect demonstrationj as is evi- a sure guide dent from the account given of it above ; 10 certainty. £^j. tliere we assume a proposition which directly contradicts that we mean to demonstrate ; and having by a continued series of proofs shewn it to be false, tlience infer that its contradictory, or the proposition to be demonstrated, is true. As therefore this last conclusion is certain and unavoidable, let us next inquire, after what manner we come to be satis- fied of the falsehood of the assumed propositions, so that no possible doubt may remain as to the force and validity of demonstrations of this kind. The manner then is plainly tliis : Beginning with the assumed pro- position, we, by the help of definitions, self-evident truths, or propositions already established, continue a series of reasoning in the way of a direct demonstra- tion, until at length we arrive at some "absurdity or known falsehood. Thus Euclid, in the example be- fore mentioned, from the supposition that circles touchiTig one another inwardly have tl*e same centre, deduces l/iat a part is equal to the ivhole. Since there- fore, by a due and orderly process of reasoning, we come at last to a false conclusion, it is manifest that all the premises cannot be true. For were all the premises true, the last conclusion must be so too, by what has been before demonstrated. Now, as to all the other premises made use of in the coutse of reasoning, they are manifest and known truths by supposition, as being eitlier definitions, self-evident propositions, or truths established. The assumed pro- position is that only as to which any doubt or un- certainty remains : that alone therefore can' be false ; and indeed from what has been already shewn, must jinavoidably be so. And thus we see^ that iu indi«
177
rect demonstrations, two contradictory propositions being laid down, one of which is demonstrated to be false, the other, which is always the proposition to be proved, must necessarily be true ; so that here, as well as in the direct way of proof, we arrive at a clear and satisfactory knowledge of truth. . . , X. This is universally the method of rea-
A particular , . , . / • i- j
tase of indi- sonuig m all apological or mdirect demon- rect demon- stratlons j but there is one particular case, stratioii. which has something so singular and cu-
rious in it, that well deserves to be mentioned by it- self ; more especially, as the ground on which the conclusion rests will require some farther illustration. It is in short this : that if any proposition Is assumed, from which in a direct train of reasoning we can de- duce its contradictory, the proposition so assumed is false, and the contradictory one true. For, if we suppose the assumed proposition to be true, then, since all the other premises that enter the demonstra- tion are also true, we shall have a series of reasoning, consisting wholly of true premises ; whence the last conclusiba^ or contradictory of the assumed proposition, must be true likewise ; so that by this means we should have two contradictory propositions both true at the same time ; which is manifestly impossible. The assumed proposition therefore whence this absur- dity flows, must necessarily be false, and consequently its contradictory, which is here the proposition de- duced from it, must be true. If then any proposition is proposed to be demonstrated, and -ve assume the con^ tradictory of that proposition, and thence directly infer the proposition to be demonstrated, by this very means we know that the proposition so inferred Is true. For «ince from an assumed proposition v/e have deduced its contradictory, we are thereby certain that the as- sumed proposition is false ; and if so, then its contra-^- dictory, or that deduced from it, which in this case is the same with the proposition to be denriDnstrated, must be true.
- 1 7S
A due know- ^^' That tKis is not a mere empty spe- ledgeofthe culatioii, void of all use and application in principles of practice, IS evident from the conduct of «abr necSar " ^^^^ mathematicians, who have adopted to make us this manner of reasoning, and given it a proper judges place among their demonstrations. We of aemonstra- j^^^^ ^ curlo'us instance of it in the twelfth proposition of the ninth book of the Ele- ments. Euclid there proposes to demonstrate, that in any series of numhers^ rising from unity in geometrical pro- gression^ all the prime numbers that measure the last term in the series ^ luill also measure the next after unity. In or- der to this he assumes the contradictory of the propo- sition to be demonstrated* namely, that some prime num- ber measuring the last term in the series, does not measure the next after umty^ and thence by a continued train of reasoning proves, that it actually does measure it. Hereupon he concludes the assumed proposition to be false, and that which is deduced from it, or its contra- dictory, which is the very proposition he proposed to demonstrate, to be true. Now, that this is a just and conclusive way of reasoning, is abundantly manifest, from whit we tiave so clearly established above. I would only here observe, how necessary some know- ledge of the rules of logic is, to enable us to judge of the force, justness, and validity of demonstrations ; since such may sometimes occur, where the truth of the proposition demonstrated will neither be owned Hor perceived, unless we know beforehand, by means of logic, that a c )nclusioa so deduced is necessarily true and valid ; for though it .be readily allowed, that by the mere strength of our natural faculties, we can at once discern that of two contradictory propositions, the one is necessarily true, and the other necessarily false ; yet when they are so linked together in a demon- stration, as that the one serves as a previous proposi- tion, whence the other is deduced, it does not so im- mediately appear, without some knowledge of the prin- ciples of logic, why that alone which is collected by •
179
reasoning, ought to be embraced ais true, and the other, whence it is collected, to be rejected as false.
XII. Having thus I hope sulBclently e- .^d of itself suf- vinced the certainty of demonstration m fident to all its branches, and shewn the rules by guard against
which we ought to proceed, in order to ^''*°^ ^"'^ ^^^^^
° , *. ,. . reasoning,
arrive ar a just conclusion, according to the
various ways of arguing made use of, I hold it need- less to enter upon a particular consideration of those several species of false reasoning which logic^nis dis- tinguish by the name of sophisms. He that thoroughly understands the form and structure of a good argu- ment, will of himself readily discern every deviation from it. And although sophisms have been divided in- to many classes, which are all called by sounding names, that therefore carry in them much appearance of learning, yet are the errors themselves so very pal- pable and obvious, that I should think it lost labour to write for a man capable of being misled by them. Here therefore we choose to conclude this third part of logic, and shall in the next book give some account of methody which, though inseparable from reasoning, is nevertheless always considered by logicians as a dis- tinct operation of the mind ; because its influence is not confined to the mere exercise of the reasoning fa- culty, but extends in some degree to all the transac- tions of the understanding.
THE
ELEMENTS OF LOGIC.
BOOK IV.
OF METHOD.
CHAP. I.
^OF METHOD IN GENERAL, AND THE DIVISION OF IT IN- TO ANALYTIC AND SYNTHETIC.
The under- j^ yy ^ j^^^^ ^^^ ^^^^ ^j^^ ^j^^ ^j^^.^^
standino; some- ^ . r i • i i m
times employ- ^^^^ Operations or the mmd, whose office ed in putting it is to search after truth, and enlarge the together bounds of human knowledge. There is
wnown ru s. ^^^ ^ fourth whlch regards the disposal and arrangement of our thoughts, when we endeavour SO to put them together, that their mutual connection and dependence may be clearly seen. This is what logicians call method y and place always the last in order in explaining the powers of the understanding, because 'it necessarily supposes a previous exercise of our other . faculties, and some progress made in knowledge, be- fore we can exert it in any extensive degree. It often
181
happens in the pursuit of truth, that unexpected dis- coveries present themselves to the mind, and those too relating to subjects very remote from that about which we are at present employed. Even the subjects them- selves of our inquiry are not always chosen with a due regard to order and their dependence one upon another. Chance, our particular vt^ay of life, or some present and pressing views, often prompt us to a variety of re- searches thvit have but little connection in the nature of things. When therefore a man accustomed to much, thinking comes, after any considerable interval of time, to take a survey of his intellectual acquisitions, he sel- dom finds reason to be satisfied with that order and disposition according to which they made their entrance into his understanding. They are there dispersed and scattered, without subordination, or any just and regu- lar coherence : insomuch that the subserviency of o!ie truth to the discovery of another does not so readily ap- pear to the mind. Hence he is convinced of the ne- cessity of distributing them into various classes, aiid combining into an uniform system whatever relates to one and the same subject. Now this is the true and proper business of method ; to ascertain the various di- visions of human knowledge, and so to adjust and con- nect the parts in every branch, that they may seem to grow one out of another, and form a regular body of science, rising from first principles, and proceeding by an orderly con.catenation of truths.
II. In this view of thinus, it is plain ^ that we must be beiorehand well ac- tjie search ani quainted with the truths we are to com- discovery of bine together, otherwise how could we ^"'-'^ ^^ ^^'^ discern their several connections and r.Ia- "" -*^o^'»*- tlons, or so dispose of them as their mutual depen- dence may require ? But now it often happens the un- derstanding is employed, not in the arrangement and composition of known truths, but ifi the search and discovery of such as are unknown. And liere the m;uincr of proceeding i^ very different, inasmuch as
R
18^
we assemble at once our whole stock of kno'.trlectge relating to any subject, and after a general survey of things, begin with examining thenri separately and by parts. Hence it comes to pass, that whereas at our first setting out we were acquainted only with some of the grand strokes and outlines, if I may so .say of Truth, by thus pursuing her through her several wind- ings and recesses, gradually discover those more in- ward and finer touches, whence she derives all her {Strength, symmetry, and beauty. And here it is, that, when by a narrow scrutiny into things, we have un- ravelled any part of knowledge, and traced it to its first and original principles, insomuch that the wliole frame and contexture of it lies open to the view of the mind ; here I say it is, that taking it the contrary way, and beginning with these principles, we can so adjust and put tofrether the parts as the order and method of science requires r
Illustrated by ^^^- ^^^^ ^s these things are best under- the similitude stocd when illustrated by examples, espe- of a watch. cially if they are obvious and taken from common life, let us suppose any machine (for instance a watch) presented to us, whose structure and compo- sition we are as yet unacquainted with, but want if possible to discover. The manner of proceeding in this case is by taking the whole to pieces, and exami- ning the parts separately one after another. Wlien by such a scrutiny we have thoroughly informed ourselves of the frame and contexture of each, we then compare them together, in order to judge of their mutual ac- tion and influence. By this means we gradually trace out the inward make and composition of the whole, and come at length to discern how parts of such a form, and so put together as we found, in^unravelhng . nnd taking them asunder, constitute that particular . machine called a watch, and contribute to all the seve- ral motions and phenomena observable in it. This discovery being made, we can ti.k-^' tilings the contrary- way, and beginning with the parts, so dispose ancl
183
connect them as their several uses and structures re- quire, until at length we arrive at the whole itself, from the unravelling of which these parts resulted.
IV. And as it is in tracing and es- ^ ^ i r.L
. . , 1 /• ^> . . Ground of the
amining the works of art, so it is m a analytic and
great measure in unfolding any part of synthetic human knowledge j for the relations and ^-^^^^ods. mutual habitudes of things do not always imniediatelv appear upon comparing them one with another. Hence we have recourse to intermediate ideas, and by means of them are furnished with those previous pro- positions ti^at lead to the conclusion we are in quest of. And if it so happen that the previous propositions themselves are noc sufficiently evident, we endeavour by new middle terms to ascertain their truth, still tracing things backward in a continued series, until at length we arrive at some syllogism wher'^ the premises are first and 9elf-evide)it principles. This done, we become perfectly satisiled as to the truth of all the conclusions we have passed through, inasmuch as they are now seen to stand upon the firm and immoveable foundation of our intuitive perceptions. And as we arrive at this certainty by tracing things backward to the original principles whence they flow, so may we tit any time renew it by a direct contrary process, if beginning with these principles we carry the train of our thoughts forward, until they lead us by a con- nected chain of proofs to the very last conclusion of the series.
V. Hence it appears, that in disposing t>- • • r- , . \^ ' , 1-1 Division of
and putting together our thoughts, either method into
for our own use, that the discoveries we analytic and have made may at all times lie open to synthetic. the review of the mind *, or where we mean to com- municate and unfold these discoveries to others, theie are two ways of proceeding equally within our choice. For we -may so propose the truths relating to any part of knowledge as they presented themselves to the Kiind in the manner of investigation, carrying on the
R 2
184
series of proofs in a reverse order, until tlicy at last terminate in first principles j or. beginning with these principles, we may take the contrary, way, and from them deduce, by a direct train of reasoninjr, all the se- veral propositions we want to establish. This diversi- ty in the manner of arranging our thoughts, gives rise to the twofold division of method established among logicians ; for method, a«:cording to their use of the word, is nothing else but the order and disposition of our thoughts relating to any subject. When truths are so proposed and put together as they were or might have been discovered, this is called the analijtic methody or the method of resolution ; inasmuch as it traces things backward to their source, and resolves know- ledge into its first and original principle. When, on the other hand, they are deduced from these principles, and connected according to their mutual dependence, insomuch that the truths first in order tend always to the demonstration of tiiose that follow, this constitutes what we call the synthetic method y ox metftcd of coniposi^ tiofi. For here we proceed by gathering together the several scattered parts of knovi'^iedge, and combining them into one whole or system, in such manner that the understanding is enabled distinctly to follow truth through all her different stages and gradations.
VI. There is this farther to be talcen
Called other- • r • \ ^' ^ ^\.
-.^r.-co ^v^ ,, ^ notice or m relation to these two species
thod of inven- of method, that the fir?t has also obtained
lion and the the name of the method of inventicn^ be-
niethodof cause it observes the order in which our science. . , , i • i ■
thoughts succeed one another m the n/v-
vention or discovery of truth. The other again is often denominated the metliod of doctrine or instruction, iiias- much as in laying our thoughts before others, we gene- rally choose to proceed in the si/?ithetic manner, dedu- cing them from their first principles. For we are to observe, that although there is great pleasure in pursu- ing truth in the method of investigation, because it places us in the condition of the inventor, and shew»
185
■the particular train and process of thinking hy which he arrived at his discoveries, yet it is not so well accommodated to the purposes of evidence a^id convic- tion -, for at our first setting out we are commonly un- able to divine where the analysis will lead us, insomuch that our researches are for some time little better than a mere groping in the dark-: and even after light begins to bre«]ik in upon us, we are still obliged to many re- views, and a frequent comparison of the several steps of the investigation among themselves. Nay, when we have unravelled the whole, and reached the very foundation on. which our discoveries stand, all our certainty in regard to their truth will be found in a great measure to arise from that connection we are now able to discern between them and first principles, taken in the order of composition. But in the synthetic manner of disposing our thoughts, the case is quite different ; for as we here begin with intuitive truths, and advance by regular deductions from them, every step of the procedure brings evidence and conviction along with it ; so that in our progress from one part of knowledge to another, we have always a clear percep- tion of the ground on which our assent rests. In communicating therefore our discoveries to others, this method is apparently to be chosen, as it wonderfully improves and enlightens the understanding, and leads •to an immediate perception of truth. And hence it is, that, in the following pages, we choose to distinguish it by the name of the method of science ; not only as in -the use of it we arrive at sciettce and certainty, but be- cause it is in fact the method in which all those parts of human knowledge that properly bear the name of sciences i are and ought to be delivered. But we nov/ proceed to explain these two kinds of method nu>r£ .particularly.
K 3
186
CHAP. II.
OF THE METHOD OF INVENTION.
r.^- -^ ( ,u I- By the f?iethod of invention we uncler-
ijngin 01 the ./
several arts Stand such a disposition and arrangement and inventions of our thoughts as follows the natural of human life, procedure of the understanding, and pre- sents them in tlie order in wliich they succeed one another in the investigation and discovery of truth. Now it is plain, that to handle a subject successfully according to this method, we have no more to do than observe the several steps and advances of our minds, and fairly copy them out to the view of others. And indeed it will be found to hold in general, with regard to all the active parts of human life, especially when reduced to that which is in the schools termed an art, that the rules by which we conduct ourselves are no other than a series of observations drawn from the attention of the mind to what passes, while we exercise our faculties in that particular way ; for when we set about any invention or discovery, we are always push- ed on by some inward principle, disposition, or aptitude (shall I call it ?) which we experience in ourselves, and which makes us believe that the thing we are in quest of is not altogether beyond our reach. We therefore begin with essaying our strength, and are. sometimes successful, though perhaps more frequently not. But as the mind, when earnestly bent upon any pursuit, is not easily discouraged by a few disappointments, we are only set upon renev/ing our- endeavours, and by an obstinate perseverance and repeated trials, often arrive at the discovery of what we have in view. Now it is natural for a man of a curious and inquisitive turn, after .having mastered any part of knowledge with
187
great labour and difficulty, to set himself to examine how he happened to miscarry in his first attempts, and by what particular method of procedure he at length came to be successful. By this means we discover, on the one hand, those rocks and shelves which stand most in our way, and are apt to dis-turb and check our progress j and, on the other, that more sure and cer- tain course, which if we continue in steadily, will bring us to the attainment of what we are in pursuit of. Hence spring all the arts and inventions of human life, which, as wq have already said, are founded upon a series of rules and observations, pointing out the true and genuine manner of arriving at any attainment. When the mind rests satisfied in a bare contemplation of the rules, and the reasons on which they are found- ed, this kind of knowledge is called Speculative. But if we proceed farther, and endeavour to apply these rules to practice, so as to acquire a habit of exerting them on all proper occasions, we. are then said to be possessed of the art itself.
II. From what has been said, It appears, -vvhy in treat- that, in order distinctly to explain the me- ing of the me- thod of invention, we must take a view of ^^^^ ^^ inven- the understandinfT as employed in the \*^"' ^^^ °^"^^
r . -^ •^ - - , give some ac-
search and nivestigation of truth j for by count of the duly attending to its procedure and advan- an itself. ces, we shall not only discover the rules by which It conducts itself, but be enabled also to trace out the se- veral helps and contrivances it makes use of for the more speedy and effectual attainment of its ends : and when these particulars are once known, it will not be difficult for us, in laying open our discoveries to others, to combine our thoughts agreeably to the method here required ; because, having fixed and ascertained the rules of it, and being perfectly acquainted with the conduct and manner of the mind, we need only take a reviev^ of the several truths as they succeed one another in the series of investigation, set them in order before us, and fairly transcribe the appearance they make to
188
t?Ke understanding. Hence it Is that logicians, in treat- ing of the method of invention, have not merely con- fined themselves to the laying down of directions for the disposal and arrangement of ourthoughts, but have rather explained the a-rt itself^ and established those rules by which the mind ought to proceed in the exer- cise of its inventive powers; for they rightly judged, that if these were once thoroughly undersrood, the o- ther could no longer remain unknown. By this means it happens t\Y<\t\\\Q method of inve?iUon is become another expression for the art cf inveniiouy and very often de- notes the conduct and procedure of the understanding in the search of truth : and as some knowledge of the principles of the art is in a manner absolutely necessary towards a tra& conception of the rules by which we ought to govern and dispose our thoughts in treating subjects after this method, we shall therefore follow the example of other logicians, and endeavour to give some short account of the business of invention, and of those several helps and contrivances by which the mind is enabled to facilitate and enlarge its discoveries. Attention and ^^^' ^^ ^^^ been already observed, that a comprehen. vrhen the mind employs itself in the search €ive under- of lUnknown truths, it begins with assem- standmg the |^|- ^^ ^^^^ j^^ whole stock of knowledge
preparatory & i i • i r
qualifications relatmg to the subject •, and alter a gene-
to invention, ral survcy of things, sets about examining them separately and by parts. Now, as in this separate examination, the number of parts continually increase upon us \ and as it is farther necessary that we survey them on all sides, compare them one with another, and accurately trace their mutual habitudes and respects, it is from hence apparent, that, in the exercise of inven- tion, two things are of principal consideration. First, An enlarged and comprehensive understanding, able to take in the great multitude of particulars that frequent- ly come under our notice. Secondly, A strong habit of attention, that lets nothing remarkable slip its view^ and distinguishes carefully all those circumstances
189
which tend to the illustrathig and clearing the subject we are upon. These are the great and preparatory quahhcations, without which it were in vain to hope that any considerable advance could be made in en- larging the bounds of human knowledge : nor ought we to esteem it a small advantage that they are in some measure in our own power, and may, by a proper cultivation, be improved and strengthened to a degree almost beyond belief. We find by experience, that the study of mathematics in particular is greatly serviceable to this end. Habits we all know grow stronger by exercise, and as in this science there is a perpetual call upon our attention, It by degrees becomes natural to us, so as that we can preserve it steady and uniform through long and intricate calculations, and that with little or no fatigue to the understanding. But a yet more wonderful advantage arising from the culture of the mathematics is this, that hereby we in sqme measure extend the dimensions of the human mind, enlarge its compass of perception, and accustom it to wide and comprehensive views of things. For whereas at our first setting out, we often find it extremely difficult to master a short and easy dem.onstration, and trace the connection of its several parts, yet as we advance in the science, the understanding is seen gradually to dilate, ?Au\ stretch itself to a greater size ; insomuch that a long and intricate series of reasoning is often taken in witli scarce any labour of thought •, and not only so, but we can in some cases, with a single glance of our minds, run through an entire system of truths, and extend our view at once to all the several links that u» nite and hold them together.
IV. When we are furnislied with these . ,. .
,. r • i ^ A ludicious
two preparatory qualifications, the next choice of inter- requisite to the discovery of truth is, a mediate Idea? judicious choice of intermediate ideas, mother great We have seen in the third part of this '^r''''^ '"
1 r • 1 r this art.
treatise, that many oi our ideas are or
Mich a nature as not to discover their several habitudes ,
190
and reiatians by any immediate comparison one with another. In this case we must have recourse to inter- mediate ideas *, and the great art lies in finding out such as have an obvious and perceivable connection with the ideas whose relations we inquire after ', for thus it is that we are furnished with known and evi- tient truths, to serve as premises for the discovery of such as are unknown : and indeed the whole business of invention seems in a great measure to he in the due assemblage and disposition of these preliminary truths ; for they not only lead us step by step to the discovery we are in quest of, but are so absolutely necessary in the case, that without them it were in vain to attempt it ; nothing being more certain than that unknovvn propositions can no otherwise be traced but by means of some connection they have with such as are known. Nay, reason itself, which is indeed the art of know- ledge, and the faculty by which we push on our dis- coveries, yet by the very definition of it, implies no more than an ability of deducing unknown truths from principles or propositions that are already known. Nov/ although tliis happy choice of intermediate ideas, so as to furnish a due tr-ain cf previous propositions, that shall lead as successively from one discovery to another, depends in some measure upon a natural sagacity tha quickness of mind, it is yet certain from experience, that even here much may be effected by a stubborn application and industry. In order to this, it is in the first place necessary that we have an exten- sive knowledge of things, and some general acquaint- ance with the whole circle of arts and sciences. "Wide and extended views add great force and penetration to the mind, and enlarge its capacity of judging. And if to this we join, in the second place, a more particular and intimate study of whatevt'Y relates to the subject about which our inquiries are employed, we seem to bid fair for success in our attempts ; for thus we are provided with an ample variety out of which to choose jeur intermediate ideas^ and are therefore more likely
I
191
to (discover some among them that will furnish out the previous propositions necessary in any train of reason-
V. It is not Indeed to be denied, that sagadty an4 a when we have even got all our materials quickness of about us, much still depends upon a cer- understanding
t • 1 1 1 • • T greatly pro-
tam dexterity and address, m smgJmg out ^o^ed by the
the most, and applying them skilfully for study of the discovery of truth. This is that talent algebra, which is known by the nam.e of Sagacity, and com.- monly supposed to be altogether the gift of nature. But yet I think it is beyond dispute, that practice, ex- perience, and a watchful attention to the procedure of our own minds while employed in the exercise of rea- soning, are even here of very great avail. It is a truth well known to those who have made any considerable progress in the study of algebra, that an address and skill in managing intricate questions may be very often obtained, by a careful imitation of the best models. For although when we first set out about the solution of equations, we are puzzled at every step, and think we can never enough admire the sagacity of those who present us with elegant models in that way-, yet by de- grees we ourselves arrive at a great mastery, not only in devising proper equations, and coupling them art- fully together, so as from the more complicated to de- rive others that are simple, but also in contriving use- ful substitutions, to free our calculations from frac- tions, and those intricacies that arise from surds and irrational quantities. Nor is it a small pleasure at- tending the prosecution of this study, that we thus discern the growing strength of our own minds, and see ourselves nearer and nearer to that sagacity and quickness of understanding which we see so much ad- mired in others, and were at first apt to conclude alto- gethei' beyond our reach.
VI. We have now considered those re- where art and quisites to invention that have their found- management ation in the natural talents of the mind ; ^^^ required ia
192
the business of an enlarged and compreliensive und^r- iiwention. Standing, a strong habit of attention, a
sagacity and quickness in discerning and applying in- termediate ideas : let us next take a view of such other helps as more immediately depends upon art and management, and shew the address of the mind, in contriving means to faciliate its discoveries, and free it from all unnecessary fatigue and labour. For we are to observe, that though the capacity of the intellect may be greatly enlarged by use and exercise, yet still our views are confined within certain bounds, beyond which a finite understanding cannot reach : and as it often happens in tlie investigation of truth, especially where it lies at a considerable distance from the first principles, that the number of connections and rela- tions are so great, as not to be taken in at once by the most improved understanding, it is therefore one great branch of the art of invention, to take account of these relations as they come into view, and dispose of them in such manner, that they always lie open to the in- spection of the mind, when disposed to turn its atten- tion that way. By this means, without perplexing ourselves with too many considerations at once, we have yet these relations at command, when necessary to be taken notice of in the prosecution of our disco- veries •, and the understanding thus free and disenga- ged, can bend its powers more intensely towards that particular part of the investigation it is at present con- cerned with. Now in this, according to my appre- hension, lies the great art of human knowledge ; to manage with skill the capacity of the intellect, and contrive such helps as may bring the most wide and ex- tended objects within the compass of its natural powers. When therefore the multitude of relations increase very fast upon us, and grew too unwieldly to be dealt with in the lump, we must combine them in different classes, and so dispose of the several parts, as that they may at all times lie open to the leisurely survey of the mind. I3y this means we avoid perplexity and con-
195
fusion, and are enabled to conduct our researclics without being puzzled with that infinite crowd of par- ticulars that frequently fall under our notice in long and diflicult investigations ; for by carrying our atten- tion successively from one part to another, we can up- on occasion take in the whole *, and knowing also the order and" disposition of the parts, may have recourse to any of them at pleasure, when its aid becomes ne- cessary in the course of our inquiries.
VII. First then I say, that an orderly j^^ orderly combination of things, and classing them disposition of together with art and address, brings great g^^e^t use in and otherwise unmanageable objects upon Lasto^he" a level with the powers of the mind. We capr.city of the have seen in the First Part of this Trea- understanding. tise, how by taking numbers in a progressive series, and^according to an uniform law of composition, the most bulky and formidable collections are comprehend- ed with ease, and leave distinct impressions in the understanding ; for the several stages of the progression serve as so many steps to the mind, by which it ascends gradually to the highest combinations ; and as it can carry its views from one to another with great ease and expedition, it is thence Pi:abled to run over all the parts separately, and thereby rise to a just conception of the whole. The same thing happens in all our other com- plex notions, especially when they grow very large and complicated : for then it is that we become sensible of the necessity of establishing a certain order and grada- tion in the manner of combining the parts. This has been already explained at some length in the chapter of the Composition and Resolution of our ideas, where we have traced the gradual progress of the mind through all the different orders of perception, and shewn that the most expeditious way of arriving at a just know- ledge of the more compounded notices of the under- standing, is by advancing regularly through all the intermediate steps. Hence it is easy to perceive what advantages must arise from a like conduct in regard to
194
those several relations and connections upon which the investigation of truth depends ; for as by this means we are enabled to bring them ail within the reach of the mind, they can each in their turns be made use of upon occasion, and furnish their assistance towards the <iis- covery of what ,we are in quest of. Now this is of principal consideration in the business of invention, to have our thoughts so much under command, that in comparing things together, in order to discover the re- sult of their mutual connections and dependence, all the several lights that tend to the clearing the subject we are upon, may lie distinctly open to the understanding, so as nothing iraterial shail escape its view : because sn oversight of this kiixl in sumining up the account, must not only greatly retard its advances, but in many cabes check its progress aitogetlier.
VIII. But secondly, Another advantage and in enabllnn; • r „ ^u- j • j*
^ . ^A ansmg trom this ordeny disposition is,
us to proceed , i i r i • i r
gradually, and that hereoy we free tiie mind from all with eaee, in unnecessary fitigue, and leave it to fix its the nivestiga- attention upoii any part separately without
tion of truth. , . \ ir -i i -i • r
perplexing itseir with the consideration oi the whole. Unknown truths, as we have already obser- A^ed, are only to be traced by means of the relation between them and otiiers tliat are known. When therefore these relations become very numerous, it must needs greatly distract the mind, wQxe it to have its attention continually upon the stretch after such a multitude of particulars at once. But new, by tlie method of classing and ordering our perceptions above explained, this inconvenience is wholly prevented ; for a just distribution of things, as it ascertains distinctly the place of each, enables us to call any of them into view at pleasure when the present consideration of it becomes necessary. Hence the mind, proceeding gra- dually through the several relations of its ideas, and marking the results of them at every step, can always proportion its inquiries to its strength *, and confming itself to sucli a number of objects as it can take in and
195
manage .with ease, sees more distinctly all the cofise- quences that arise from comparing them one with ano- ther. When therefore it comes afterwards to take a review of these its several advances, as by this means the amount of every step of the investigation is fairly laid open to its inspection, by adjusting and putting these together in due order and method, it is enabled at last to discern the result of the whole -, ^nd thus, as before in the composition of our ideas, so likewise here in the search and discovery of truth, we are fain to proceed gradually, and by a series of successive stages ', for these are so many resting places to the minc^, whence to look about it, survey the conclusions it has already gained, and see what helps they afford towards the obtaining of others, which it must still pass through before it reaches the end of the investigation. Hence it often happens, that very remote and distant truths> which lie far beyond the reach of any single effort of the mind, are yet by this progressive method success- fully brought to light, and that too with less fatigue to the understanding than could at first have well been imagined ', for although the whole process, taken to- gether, is frequently much too large to come within the view of the mind at once, and therefore considered in that light may be said truly to exceed- its grasp, yet the several steps of the investigation by themselves are often easy and manageable enough ; so that by proceeding gradually from one to another, and thoroughly master- ing the parts-as we advance, we carry on our researches with wondrous dispatch, a^nd are at length conducted to that very truth, with a view to the discovery of which the inquisition itself was set on foot.
IX. But now perhai^s it may not be ., , j
^ f / Algebra and
improper, it we endeavour to illustrate arithmetic pro- these observations, by an example^ and set perly speaking,
ourselves to trace the conduct and manner ^^^^^ ^^}^ "^- ^C ,v . J , , 1-1 invention.
01 the mmd, when employed in the exer- cise ot invention. There are two great branches of the mathematics peculiarly fitted to furnish us with models
S2
196
ill this way : jinthnetic I mean, and algebra. Algebni is universally knov/n to be the very art and principle of invention ; and in arithmetic too, we are frequently pat upon the finding cut of unknown numbers, by means of their relations and connections with others that are known ; as where it is required to find a num- ber equal to this sum of two others, or the product of two others. I choose to borrow my examples chiefly from this last science, both because they vrill be more within the reach of those for whom this Treatise is principally designed *, as likewise, because arithmetic furnishes the best models of a happy sagacity and managcinent in classing and regulating our perceptions. 80 that here, more than in any other branch of human knowledge, we shall have an opportunity of observing how much an orderly disposition of things tends to the ease- and success of our inquiries, by leaving us ta can- vass the parts separately, and thereby rise to a gradual conception of the whole without entangling ourselves with too many considerations at once in any single step of the investigation. For it will indeed be found, that a dexterity and address in the use of this last advantage, serves-to facilitate and promote our discoveries, almost beyond imagination or belief.
The method of ^' ^^ ^^^'^ ^^^^^^^ explained the classing our manner of reducing numbers into classes, perceptions in and of distinguishing these classes by their arithmetic. several names. And now we are farther to observe, that the present method of notation is so contrived, as exactly to fall in with this form of num- bering ; for as in the names of numbers wt? rise from 7/;;r7x to tensy from tens to hundreds, from hundreds tQ tliGiisands, he. so likewi"se in their notation, the same figures, in different places, signify these several com- binations. Thus, 2 in the first place on the r^ght hand, denotes two units ; in the second place, it ex- presses so many tens ; in tlie third, hundreds ; in the fourth, thousands. By this means it happens^ that when a number is written down in figures, as every
197
figure In it expresses some distinct combination, and <iii these combinations together make up tlie total sum, so may the several figures be considered as the con- stituent parts of the number. Thus the number 21-36, is evidently by the very notation distinguished into four parts, marked by the four ^figures that serve to express it ; for the first denotes troo thousandy the second /i^^/r hundrecU the third th'irty or three tensy and the fourth six. These several parts, though they here appear in a conjoined form, may yet be il.o expressed separately thus: 2000,400, SO, and 6-, and the a- mount is exactly the same.
XI. This then being the case, if it is ^.j^.^ j^^j , required to find a number equal to tlie thence derived- sum of two others s^jiven, our business is to towi\rds an
examine senaratcly these given numbers, ^^^^ aacntum
,.;.,' ^ . ^ 1111 of numbers.
and II they appear too large and buiky to.
be dealt with by a single Q^voxt of thought, then, since tlie very notation disti?)guishes them into different parts, vve mu.^t content ourselves with considering the parts asunder, and finding their sums one after ano- ther ; for since the whole is equal to ail its parts, if we find the sums of the several parts of wiiich any two numbers consist, we certainly find the total sum of the two numbers* And therefore these different sums, united and put together according to the established rules of notation, will be the very number we are in quest of. Let it be proposed, for instance, to find a number equal to the sum of these two, 2436 and 4352. As -the finding of this by a single effort of thought would be too violent an exercise for the mind, I consider the figures representing these numbers as the parts of which they consist, and therefore set my- self to discover their sums one after another. Thus 2, the first figure on the right hand of the one, added to 6, the first figure on the right hand of the other, make 8 •, which is therefore the sum of these two parts. Again, the sum of 5 and 3, the two figures or p^rta in the second place, is likewise 8, But now as
S3
i'gures in the second place denote not simple t/niis but tenSf hence it is plain that 5 and 3 here signify live ie^is and three tefis, or 50 and 30, whose sum therefore must be eight tens^ or 80. And here again I call to mind, that having already obtained one figure of the sum, if I place that now found immediately after it, it will thereby stand also in the second place, and so really express, as it ought to do, eight tefiSy or 80. And thus it is happily contrived, that though in the addition of the tefiSy I consider the figures com.posing ' them as denoting only simple umis, which makes the operation easier and less perplexed, yet, by the place their sum obtair5S in the number found,* it expresses the real amount of the parts added, taken in their full and complete values-. The sam.e thing happens in summing the hundreds and thousands ; that is, though the figures expressing these combinations are added to- ^^ether as simple. units, yet their sums, standing in the third and fourth phecs of the number found, thereby really denote the hundreds and thousaods, and so re- present the true value of the parts added. Because in the -^^I' Here then we have a manifest severaUteps by proof of the great advantages derived which It IS car- fVom an artful method of classing our per- niindTs' put to ceptions ; foi* as the numbers themselves little or no are by this means distinguished into dif- fatigtie. fcrent parts, which brings them more
readily within the compass of the understanding, so by taking these parts .separately, the operations about numbers are rendered very easy and simple. And in- deed it is p^irticularly worthy our notice, and though in adding two very large numbers together, the whole process is of sufHcient length, yet the several steps by which it is conducted, are managed with incredible dispatch, and scarce any fatigue to the mind. This is apparent in the example given above, where we see, that in every advance from one part to another, nothing more is required than to add together the two figures^ in the like places of the numbers to be summed. But
199
what is yet more wonderful, though in the progress of a long operation the figures rise in their value as we advance, and grow to signify t/iousands, miHiotis^ hilUon^i &c. yet so happily are tliey contrived for expressing the diifercnt parts of numbers, that in every step of the procedure we consider them as denoting only simple ~ units, all other deficiencies being made up by the places their sums obtain in the total amount. And thus it is so ordered in this admirable form of notation, that however large the numbers are that come under examination, they are nevertheless managed with the same ease as the. most simple and obvious collections ; because in the several operations about them, the mind is neither tied down to the view of too many --"parts at once, nor entangled with any considerations regarding the bulk and composition of those parts.
XIIl. And if these advantages are so xh^s farther very manifest in the first anA simplest illustrated by- rules of arithmetic, much more do they an example'
discover themselves in those that are in- ^" multiplica-
1 1 *T I tion,
tricate and com.plex. JLet a man endea- vour in his thoughts to find the product of two num- bers, each consisting of twenty or thirty places, and that without considering the parts separately, I be- lieve he will soon be sensible that it is a discovery far beyond the limits of the human mind. But now in the progressive method above explained, nothing is more simple and easy. For if we take the first figure on the right hand of the one number, and by it multi- ply every figure of the other separately, these several products, connected according to the established laws of notation, must truly represent the total product of this other, by that part of the multiplying number. Let us suppose, for instance, the figure in the unit's place of the multiplier to be 2, and the three last places of the multipicnnd to be 432 : then, 2 multiply- ing 2 produces 4, which therefore is the first part of the product. Again, 2 multiplying 3 produces 6. Cut now 3 standing in the second place of the multi*
m
1^
i
r : •'" ^- :^ in :is real rju q^ \
V : taken I'arice, am. jci J,
And acccrdir.glv the £gure 6, coming after 4 aln If
' ^ -ice of le
F-- — :, c. ..v.; vv. . ; ,j^j ^
qu::te vitue. The 5^Lnw . , ^ : uitipl .g
4, which standing :a the pj^ce o» hasJfrds, it$ proi ct bT ^ is SOO. But t! nrt rhe B^re 8, 3-
duced nvm :? and 4, ._ - c :- rV . ,..,i
diicc i because, cotiiir.g i: .
lour.d, it i$ thereby derermiiaed to the third pi c, ^ 'Jj\ ' is
t • .my le: h
wc please ; and it is iv . , > nianii- is
la ► . . :..^ \^.ue en the r>:ures in ic
ot the several products ia the tend .
the just v^f mul:
cording iv .-_.. true -
Of tho d:>-t<^5i- XIV. i. .\ltheproiit
tJocc4:hesc- br tiie dr>t 0j:uie ca the muUiplier, ,l
Teni pn.xh:as jK»Xt : J place, ui w otvkr to ii- rk-^>.N , .,.
secoiK. ^ : It
figure, ct>nsidered a> a sim;>ie <itc^:> But as it s od
ir ' ~ ■ ■■ ■ -f -0
ed must be yet iv . . . order to ex; ss
the true product sc . accordiwgly doi in
the operatic' Ms se nd
protiuct un*.-.. - - ^_ iprodtj
tor this, when they cv^:r»e to be added together, hn he $aine ed<ct as aiuiexing a cypher, or multiplyin by ttm^ :- - v oxrs who'is in ^^ * -:qua eil
with Aiithnieiic* I: er, ^ en
we multiply by the ngur« ia the thind place, a^ lis new prvxiuct is (>laced $tiU csie ligure backward. *'o do in cdFcct aiuKx tw« cyphers to it, or multiply t»y
• ealia i,
. the pi >
:. rep re \i
together, c-
f
,1 jtiri*"' ^ •^
im
^01
'^, L.
tX^TV
201
^ 1 mdred. And this we ought certainly to do ; bc- juif, having considered the muhiplying tigure as de-
1 ti;^ only simple units, when it really expressed so li.ir hundreds, the first operation gives no more than (iiO undredth part of the true product. The case is the ime in multiplying by the fourth or filth figures, becase the products still running backwards, we there- Liy i effect annex as many cyphers to them as brmgs
.1 up severally to their respective adequate value. i>y lis means it happens, that though the figures of ■ ;" multiplier in every advance denote still higher lyid il: combinations, yet we ail along proceed with j.wA as simple digits ; the disposition of the several p; occts in order to addition making up for all the de- .iciecies that arise from this way of considering them. Whi in tiiis method of procedure we have obtained the roduct of the multiplicand into all the diiferent part of the multiplier, by adding these products to- gs rPr, we obtain also the total product of the two nun ers ; for since the whole is equal to all its parts, notlig is more evident than that the product of any one amber into another, must be equal to its product into 11 the parts of that other : and therefore the se- vere partial products united into one sum, cannot but trul represent the real product sought.
yj. Thus we see, that in questions of . . , . , , ,. . , , - r* , Arithmetical
mul plication, though the whole process operations, by
is scietimes sufficiently long and tedious, being carried yet '6 several steps by which it is carried °^ ^.^ P^^ or. ?3 all very level to the powers of the fhTd'render- und standing ; for from the account gi- ed eiy and y-'-n bove, it appears that nothing more is i^itelliijible. '' ']ied in any of them th^n barely to multiply one - ;i by another. But now this easy rule of operatioa i.- v.oliy derived from the before-mentioned address c ssing our perceptions ; for to this it is owiog that • ^ ambers under consideration are distinguished into oart and that the several parts are also ciearlv repre- sent! to the mind ia the very form of notation. Now
W
■.J
200
piicand, denotes in its real value three iens^ or 30, which tlierefore taken twice, amounts to six tens or 60, And accordingly the figure 6, coming after 4 already found, is thereby thrown into the second place of the. product, and so truly expresses CO, its full and ade- quate value. The same thing happens in multiplying 4, which standing in the place of hundreds, its product by 2 is 800. But this very sum the figure 8, pro- duced from 2 and 4-, really denotes in the total pro- duct ; because, coming after 64, the two parts already, found, it is thereby determined to the third place, where it of course expresses so many hundreds, This- process, as is evident, may be continued to any length we please ; and it is remarkable, that, in like manner as in addition, though the value of the figures in the multiplicand continually rises upon us, yet we all along, proceed with them as simple units ; because the places of the several products in the total amount, represent'- the just results of multiplying the figures together, ac-; cording to their true and adequate value, ^f , J. . XIV. HavincT thus obtained the product:
Of the-disposi- , ,- r^ r i i • i-
tion of the se- by tiie lirst tigure ,oi the multiplier, we veral products next take that in the second' place, and in order to ad- p^Q^eed with it in the same manner. This- second operation gives us the effect of that figure, considered as a simple digit. But as it stood in the second place, and therefore really denoted so many tens, hence it is plain that tiie product now gain- ed must be yet multiplied by ten, in order to express: the true product sought. This is accordingly done in the operation, by placing the first figure of this second product under the second figure of the first product j for this, when they come to be added together, has the same effect as annexing a cypher, or multiplying by ten, as every one knows who is in the least acquaints! with the rules of arithmetic. In like manner, when we multiply by the figure in the third place, as this new product is placed still one figure backwards, we ^0 m effect aniKx two cyphers to it, or multiply it by
201
a!i hundred. And this we ought certainly to do ; be- cause, having considered the multiplying figure as de- noting only simple units, when it really expressed so many hundreds, the first operation gives no more than the hundredth part of the true produgt. The case is the same in multiplying by the fourth or fifth figures, because the products still running backwards, we there- by in effect annex as many cyphers to them as brings tliem up severally to their respective adequate value. By this means it happens, that though the figures of the multiplier in every advance denote still higher a,nd higher combinations, yet we all along proceed with them as simple digits; the disposition of the several products in order to addition making up for all the de- ficiencies that arise from this way of considering, them. When in this method of procedure we have obtained the product of the multiplicand into all the different parts of the multiplier, by adding these products to- gether, we obtain also the total product of the two numbers ; for since the whole is equal to all Its parts, nothing is more evident than that the product of any one number into another, must be equal to its product into, all the parts of that other : and therefore the se- veral partial products united into one sum, cannot but truly represent the real product sought.
XV. Thus we see, that m questions of Arithmetical multiplication, though the whole process operations, by is sometimes sufficiently long and tedious, being carried vet the several steps by which it is carried °" *".^ P^°"
11 111 r \ gressive me-
on are all very level to the powers or the ^hod, render- understanding ; for from the account gi- ed easy and vcn above, it appears that nothing more is intelli-^ible. required in any of them than barely to multiply one digit by another. But now this easy rule of operation is wholly derived from the before -mentioned address in classing our perceptions ; for to this it is owing that the numbers under consideration are distinguished into parts, and that the several parts are also clearly repre- sented to the mind in the very form of notation. Now
202
fis these parts have an invariable^ relation one to atio- rher, and advance in their value by an uniform law of progression, the uiiderstanding by means of such a link can easily hold them together, and carry its views from stage to suige without perplexity or confusion. Hence it happens, that however large and mighty the numbers are, so as far to exceed the immediate grasp of the mind, yet by running gradually through the several combinations of which tliey are made up, we at length comprehend them In their full extent. And because it would be impossible for the understanding to multi- ply very large numbers one into anotlier, bv a simple ciVort of thought, therefore here also it considers the parts separately, and, taking them in an orderly series, advances by a variety of successive steps. It is true indeed in the progress of the operation, the several fi- gures rise in their value : but this consideration enters not the work itself ; for there, as we have already seen, tliough the characters are taken as denoting only simple units, yet the order and disposition of the par- tial products exhibits each according to its real amount. Hence, in every step, we have only to multiply one di- git by another, which, as it is attended with scarce any dilhcultv, the whole process is carried on with won- drous dispatch : and thus by a series oi' ensy opera* tions, v>'e at length rise to discoveries, which in any o- ther method of procedure, would have been found al- together beyond the reach of the mind. The art of XVI. Since therefore by a due andorder-
cljssiug our ly disposition of our ideas we can bring perceptions ^]-^q niost Wide and extendcil objects upon nie\f/and ^ '^^"-'^ ^^'^^ ^^^ powers of the understand-
instrument of ing ; and since by this also w:e abridge invention. the fatigue and labour of the mind, and enable it to carry on its researches in a progressive me- thod, without which contrivance almost all, the more remote and distant truths of the sciences must have lain for ever hid from our knowledge, I think we may venture to aflirm, that the art of regulating and class-
203
ing our perceptions is the great mean and instrument of invention. It is for this reason that I hive endea- Youred in so p.irticular a manner to illustrate it from examples in numbers -, because we have here not only a Derfect model of the art itself, but see also in the clearest manner what helps it furnishes towards a rea- dv comprehension of objects, and a masterly investiga- tion of truth. Nor let any one find fault, as if we had insisted rather too long upon matters that are obvious and known to all ; for I am apt to think, th.n,* though very few are strangers to the received method of nota- tion, and the common rules of operation in arithme- tic,— yet it is not every one that sets himself to consi- der the address and sagacity that may be seen in the contrivance of them, or to unravel those principles of investigation which we have here so clearly deduced from them : and this I take to be the re.ison that we sometimes meet with instances of men, who though thoroughly versed in the art of invention, with record to seme particular branches of knowledge, ver, if taken out of their usual track, find themselves immediatelv at a stand, as if wholly bereft of genius and penetra- tion. With such men invention is a mere habit, car- ried on in a manner purely m.echanical, without any knowledge of tlie grounds and reasons upon which the several rules of investigation are founded. Hence they are unfurnished with those general observations which may be alike usefully applied in all sciences, with enlv some little necessary variations, suited to the nature of the subject we are upon. And indeed I know of no surer way to arrive at a fruitful and readv invention, than by attending carefully to tlie procedure of our own minds in the exercise of this distinguished facultv •, be- cause, from the particular rules relating to any one branch, we are often enabled to derive such general re-- marks as tend to by open the very foundation and principles of the art itself.
XV IT. If now we turn our thoughts The manner of from arUhfttt'tu: to algebr jy here also we F'oceeding ia
204
the resolution s^^a^^ ^^^^i that the great art of hiventioH oi algebraic lies in SO regulating and disposing our no- questions. ^.'^^^g Qf things, that we may be enabled to
proceed) gradually in the search of truth. For it is the principal aim of this science, by exhibiting the several relations of things in a kind of symbolical language, so to represent them to the imagination, as that we may carry our attention from one to another in any order we please. Hence, however numerous those relations are, yet by taking only such a number of them into consideration at once as is suited to the reach and ca- pacity of the understanding, we avoid perplexity and confusion in our researches, and never put our faculties too much upon the stretch, so as to lose ourselves amidst the multiplicity of our own thoughts. As there- fore in arithmetic, we rise to a just conception of the greatest numbers, by considering them as made up of various progressive combinations, so likewise in algcbray tliose manifold relations that often intervene between known and unknown quantities, are clearly represented to the mind, by throwing them into a series of distinct equations. And as the most difficult questions relating to numbers are managed v/ith ease, because we can l-ake the parts or figures separately, and proceed with them one after another, so also the most intricate pro- blems of algebra are in like manner readily unfolded, by examining the several equations apart, and unravel- ling them according to certain established rules of ope- ration. And here it is well worth our notice, that in very complicated problems, producing a great number of different equations, it for the most part so happens, that every one of them includes a variety of unknown quantities. When therefore we come to solve them separately, as it would too much distract and entangle the mind to engage in the pursuit of so many different objects at once, our first business is, by artfully cou- pling the several equations together, or by the various ways of multiplication, subtraction, addition, and *:ubstitution, to derive others from them more simple.
until at length by such a gradual process we arrive af
some new equation, with only one unknown quantity.
This done, we set ourselves to consider the equation
last found, and having now to do with an object suited
to the strength and capacity of the mind, easily by the
established rules of the art, discover the quantity
sought. In this manner we proceed with all the
several unknown quantities, one after another, and
having, by a series of distinct operations, traced them
separately, the question is thereby completely resolved.
XVIU. Hence it appears, that the I . r • J.- s.- I • ^ Of those other
busmess ot mvention, as practised m alge- artif^ceswhicl bra, depends entirely upon the art of a- may be consi- bridging our thoughts, reducing the num- <^ered as subsl.
ber of particulars taken under considera- f'^^^' P^ '■^
f , ^ ., , , invention.
tjon at once to the fewest possible, and
establishing that progressive method of investigation which "we have already so fully explained from exam- ples in arithmetic. I might easily shew that the same observation holds equally in other sciences ; but having already exceeded the bounds I at first prescribed to myself in- this chapter, shall only add, that besides the grand instruments of knowledge already mentioned, tliere are innumerable other artifices arising out of the particular nature of the subject we are upon, and \\ hich may be considered as subsidiary helps to inven- tion. Thus, in geometry, many demonstrations of problems and theorems, are wholly derived from the construction of the figure made use of, and the drawing of lines from one point to another. In like manner in algebra, the devising of proper equations from the conditions of the question proposed, and contriving neat expressions for the unknown quantities, contri- bute not a little to the easy solution of problems. And when we have even carried on the investigation to some single equation with only one unknown quanti- ty •, as that unknown quantity may be variously per- plexed and entangled with others that are known, so as to require a multiplicity of different operations be-
T
206
fore it can be disengaged, which cften invokes us in lon-g and intricate calculations, and brings surds and irrational quantities in our way, — algebraists, to pre- vent in Some measure these inconveniences, and shorten as much as possible the process, have fallen upon seve- ral methods of substitution, which are of great service in very complicated questions. But these and such }ike artifices of invention cannot be explained at length . in this short essay ; it is enough to have given the reader a hint of them, and .pvit him in the way of unravelling them himself, when he comes to apply his thoughts to those pnrt'.cular branches of knowledge where they are scverallv made use of. Of the ^Tcat XIX. There is one thing, however, that
advantages in a particular manner deserves to be arising from a taken notice of before we dismiss this
nappy ncta- i • ^ ^ t . • i
tion or e^pl■es- subject; and that 15, the great advantages , sion of our tivat may redound to science by a happy thoughts. notation or expression of our thoughts.
It is owing entirely to this, and the rnetiiod of denoting the several combinations of numbers by figures stand- ing in different places, tliat the mo=>t complicated ope- rations in arithmetic are managed with so much ease and dispatcji. Nor is it less apparent that tLe disco- veries made by algebra are wliolly to be imputed to that symbolical language made use of in it ; for by this means we are enabled to represent the relations of thi'^gs in the form of equations, and by variously pro- ceeding with these equations, to trace out step by step the severed particulars Vv^e are in quest of. Add to all this, that by such a notation, the eyes and imagination are also made subservient to the discovery of truth ; for the thoughts of the mind rise up and disappear, ac- cording as we set ourselves to call them into view ; and therefore, without any particular method of fixing and ascertaining them as they occur, tl;e retrieving them af^ain when out of sight, would often be no less pain- ful than the very first exercise of deducing them one from another. When therefore in the pursuit of truth
207
wo carry our attention forward from one part of tlie investigation to another, as nevertheless we have fre- quent occasion to look back upon the discoveries al- ready passed through, could these be no otherwise brought iiito view than by the same course of thinking in which they were first traced, so many different at- tentions at once must needs greatly distract the mind, and be attended with infinite trouble and fatigue. But now, the method of fixing and ascertaining our thoughts by a happy and well-chosen notation, entirely removes all these obstacles. For thus, when we have occasion to run to any former discoveries, as care is taken all along to delineate them in proper characters, we need only cast our eye upon, that part of the process wliere they stand expressed, which will lay them iM once open to the mind in their true and genuine fcrni. By this means we can at any time take a quick and ready- survey of our progress, and running over the several conclusions already gained, See more distinctly Vvdiat helps they furnish UjvrAx'ds the obtaining of those o- thers we are still in pursuit of. Nay, further, as the amount of every step of the investigation lies fairly be- fore us, by comparing them variously among them- selves, and adjusting them one to another, we come at length to discern the result of the whole, and are en- abled to form our several discoveries into an uniform and well-connected system of truths, which is the great end and aim of all our inquiries.
■ XX. Upon the whole then it appears, Recapltula- that in order to proceed successfully in the t-ion. exercise of invention, we must endeavour as much as possible to enlarge the capacity of the mind, by accus- toming it to wide and comprehensive views of things ; that we must haoituate ourselves to a strong and un- shaken attention, which carefully distinguishes all the Circumstances that come in our way, and lets nothing material slip its notice *, in fine, that we must furnish ourselves with an ample variety of intermediate ideas, and be much in the exercise of singling them out and
T 2
nppjying fhem for the discovery of truth. These pre- paratory qualifications obtained, what depends upon art lies chiefly in the manner of combining our perceptions, and classing them together with address, so as to esta- bhsh a progressive method of investigation. And here it is of great iinportance to contrive a proper no- tation or expression of our thoughts, such as may ex- liibit them according to their real appearance in the mind, and distinctly represent their several divisions, classes, and relations. This is clearly seen in the man- ner of computing by figures in arithmetic, but more particularly in that symbolical language, which hath been hitherto so successfully applied in unravelling of •Ugebraical problems. Thus furnished, we may at any time set about the investigation of truth; and if we take care to note down the several steps of the process as the mind advances from one discovery to another, such an arrangement or disposition of our thoughts constitutes what is called the Method of Invention ; for thus It is plain that v/e follow the natural procedure of the understanding, and make the truths we have un- ravelled to succeed one another, according to the order in which they present themselves to the mind, while employed in tracing and finding them out. And here again it well deserves our notice, that as by this means the whole investigation lies distinctly before us, so by comparing the several steps of it among themselves, and observing the relation they bear one to another, we are enabled to form our discoveries into a regular system of knowledge, where the truths advanced are didy linked together, and deduced in an orderly series from first principles. This other manner of combining our thoughts is distinguished by tlie name of the method of science ; which therefore now offers itself to he explained, and is accordingly ths subject of the ensuing chapter.
209
CHAP. II.
OF THE METHOD OF SCIENCE.
I. In order to give the juster idea of Ki^owledge as the rules peculiar to this species of mc- derived from thod, and establish them upon their pro- ^^^^ contem-
r 1 ^* -^ -ti u 4. plation of our
per luundation, it will be necessary . to f,,^^^ ^r ^ begin with' settling the meaning of the necessary and word science^ and shewing to what parts unchangeable of human knowledge that term may be ""'^■^^'^'v most fitiy apphed. We have already observed, in the first chapter of tlie second book, tiiat there are tliree several v/ays of coming at the knowledge of truth. Flrc^t, by contemplatmg the ideas in cur own minds. Secondly, By the information of the senses. Thirdly. By the testimony of others. When we set ourselves to consider the ideas in our own mmds, we variously compare them together, in order to judge of their a- grcement or disagreement. Now as all the truths de- duccd in this way fiow from certain connections and relatio^is discerned between the ideas themselves j and as when the same ideas are brought into comparison, the same relations must ever and invaTiably subsist^be- tvyeen them, hence it is plain that the knowledge ac- quired by t\\e contem.plation of our ideas is of a necee- sary and unchangeable nature. But farther : As these relations between our ideas are not only supposed to be real in them.seives, but also to be seen and discern- ed by the mind : and as when we clearly perceive a " connection or repugnance between any two ideas, we cannot avoid judging them to agree or disagree accord- • ingly, it evidently follows that our knowledge of this kind is attended with absolute certainty and convic- tion, insomuch that it is im.possible for us to witlihold
T3
n
10
our tissentj or entertain any doubt as to the reality of truths so offered to the understanding. The relation of equality between the whole and air its parts, is ap- parent to every one who has formed to himself a dis- tinct notion of what the words luhlc and jjart stand for. No man, therefore, who has these two ideas in his mind, can possibly doubt of the truth of this pro- position, i/iat the whole ij equal to all its parts ; for this would be only endeavouring to persuade himself that that was not, which he plainly and unavoidably per- ceives to be. So that in all cases where we discern a relation between any of our ideas, whether immediate- ly by cornparing them one with another, or by means of intermediate ideas, that lay it open distinctly to the understanding, the knowled-^^c thence arising is certain and infallible. I say infallible, because we not only perceive and own the truth of propositions so offered to the mind, but having at the same time a clear view of the ground on which our assent rests, are entirely satisfied within ourselves that we cannot possibly be deceived in this perception.
II. This second way of coming at know- As flowiRor 1 J • i_ ^1 r ^^ -r<
from the in- l^dge IS by the means or the senses, rrom formation of them we receive information of the exis- the senses, be- tence of objects without us, of the union gets undoubt- ^^^^^ conjunction of different qualities in
CO, assurance, J . . i r i • r
but excludes ' the. Same subject, and or the operation oi
rot all possibi- bodles One upon another. Thus our eves
my oi bemg ^^jj ^g^ ^j^,.^. {■];^cj-^ jg ij^ (^q universe such.
deceived. 1 , , u ^v • i .. j
a body as we call the sun : our sight and
touch, that light and heat, or at least the power of ex- citing those perceptions in us, co-exist in that body : and lastly, by the same sight we also learn, that fire has the power of dissolving metals, or of reducing wood to charcoal and ashes. But now, with regard to this kind of knowledge, we are to observe, that tho' when the organs of the body are rightly disposed and operate in a natural way, we never doubt the testimo- ny of our senses, but form mo^it of the sclien?.es of
211
life upon their information \ yet are not the truths o£ this class attended with that absokite and infaUibie assurance which belongs to those lierived from the contemplation of our own ideas. Vv''e find that the senses frequently represent' objects as really existir.g, which yet have no being but in our own imagina- tions ; as in dreams, phrenzies, and the deliriums of a fever. A disorder too in the organs, makes us often ascribe qualities to bodies entirely different from those they appear to possess at other times. Thus, a man in the jaundice shall fancy every object presented to him yellow •, and in bodily distempers, where the taste is greatly vitiated, what naturally produces the idea of svveetness, is sometimes attended with a quite contrary- sensation. It is true, these irrej^ulanties neither ought, nor indeed do they with considerate m.en in any ways tend to discredit the testimony of experi- ence. He that, av/ake, in his senses, and satisfied that his organs operated duly, should take it into his head to doubt whether fire would burn, or arsenic poison him, and therefore rashly venture, upon these objects, would soon be .convinced of his error, in a way not much to his liking. As nevertheless the senses i}iO sometimes impose upon us, there is no absolute and infallible security that they may not at others : there- fore the assurance they produce, though reasonable, . satisfying, and sufficiently well founded to determine us in the several actions and occurrences of life, is yet of such a nature as not necessarily to exclude all pos- sibility of being deceived. Hence some men go so far as to maintain, that we ought to distrust our sen- ses altogether -, nay, whole sects among the ancients, because of this bare possibility, which really extends no farther than to matters of experience and testhnony^ yet established it as a principle, that we ought to doubt of every thing. Nor are there wanting phi- losophers among the moderns, who, upon the same grounds, deny the existence of bodies, and ascribe the perceptions excited in us, not to the action of exter-
vering or dis- trust.
nal matter, but to certain established laws In nature, which operate upon us in such manner as to produce all those several effects that seem to flow from the real presence of objects variously affecting our percep- tion. It is not my design here to enter into a p irticu- lar discussion of these matters : all I aim at is to shew, that the testimony of the senses, though siilHcient to convince sober and reasonable men, yet does not so unavoidably extort our assent as to leave no room for suspicion or distrust.
^ r 11 in. The third and last wav of Comlnr?
As foi\nded i • i i i ' • '^
upon testimo- '^^ truth IS, by the report and testnnony ot
ny, is of a still others. Thls regards chiefly past facts iiioie uncertain ^^^^ transactions, vdiich haviuG: no longer nature, though . . u u i^ • i •
in many casts ^"7 existence, cannot be brought withui
embraced tlie present sphere of our observation ;. for
without w?.- 2g these could never have fallen under our cognisance but by the relations of such as Iiad sufficient opportunities of being in- formed, it is hence apparent, that all our knowledge of this kind is wholly founded upon the conveyance of testimony. But liow, although this in many cases is a sutiicient ground of assent, so as to produce a ready belief in the mind, yet is it liable to still greater object tlons than even the reports of experience. Our senses, it is true, on some occasions deceive us ; and tlierefore they may possibly on others. But this bare possibility creates little or no distrust, because there are fixed rules of judging when they operate according to na- ture, and when they are prevented or given up to ca- price. It is otherwise in matters of mere human tes- timony ; for there, besides the supposition that the persons themselves may have been deceived, there is a further possibility that they may have conspired to im- pose upon others by a false relation. This considera- tion has the greater v/eight, as we frequently meet with such instances of disingenuity among men, and know it to be their interest in some particular cases, to dissemble and misrepresent the truth. It would never^
213
tiieless be tlic height of folly to reject all human testi- mony without distinction, because of this bare possibi- lity. Who can doubt whether there ever were in the world such conquerors as Alexander and Julius Casar ? There is no absolute contradiction indeed in supposing that historians may have conspired to deceive us. But such an universal concurrence to a falsehood, without one contradicting voice, is so extremely improbable, tiid so very unlike what usually happens in the world, ahat a wise man could as soon persuade- himself to be- lieve the grossest absurdity, as to admit of a supposi- tion so remote from every appearance of truth. Hence the facts of history, when w^ell attested, are readily embraced by the mind, and though the evidence attend- ing them be not such as produces a necessary and in- fallible assurance, it is yet abundantly sufficient to jus- tify our belief, and leave those without excuse who, upon the bare ground of possibility, are for rejecting entirely the conveyance of testimony.
IV. Upon the whole then, it appears, that gdence t)e- absolute certainty, such as is attended longs entirely ' with unavoidable assent, and excludes all to that branch possibility of being deceived, is to be found ^ jjichTs de?^ only in the contemplation of our own i- rived from the deas. In matters of experience and testi- contemplation mony, men we see m-iy frame pretences o^ oii'^ i"*^'"^** for suspicion an\l distrust ; but in that part of know- ledge which regards the relations of our ideas, none such can have place ; for as all these several relations 'are either immediately discerned by the mind, or tra- ced by means ot immediate ideas, where self-evidence is supposed to accompany every step of the procedure, it is absolutely impossible for a man to persuade him- self that that is not, which he plainly and necessarily perceives to be. Now it is to knowledge attended with this last kind of evidence alone, that, in strictness and propriety of speech, w^e attribute tlie name of science ; for science implies perception and discernment, what we ourselves see 'iud cannot avoid seeing \ and therefore
214
lias place only in matters of absolute certainty, where the truths advanced are either intuitive propositions, or deduced from them in a way of strict demoru;tration^ And as this kind of certainty is nowhere to be found but in investigating the relations. of our ideas, hence it is plain that science^ properly speaking, regards wholly the first branch of human knowledge ;. that which we have said is derived from a contemplation of the ideas in- our own minds.
Ou'- know- ^ ' -^^^ ^^^'^ -^ expect it will be asked,
ledge of the if sciaice and de]?jomtraHofi heloug only to real existence the Consideration of our own ideas, what of objects not |^-j^^ ^f knowledge it is that we have reb- iutihtive. . 1 !• 1 •
tmg to bodies, then- powers, properties,
and operations one upon another ? To this I answer, that we have already distinguished it by the name of natural or experimcTttal. But that v/e may see more disf tinctly wherein the difference between scientifical and natural knowledge lies, it may not be improper to add the following observations : — When we cast our eyes towards the sun, we immediately conclude that there evists an object without us, corresponding to the idea in our minds. We are however to take notice, that this conclusion does not -arise from any necessary" and unavoidaWe connection discerned between the appear- ance of the idea in \\'\q m/md and the real existence of the object without us. We all know by experience, that ideas may be excited, and that too by a seeming operation cf objects upon our senses, when there are in fact no such objects existing ; as in dreams, and the diliriums of a fever. Upon what then is the before- mentioned conclusion properly grounded.'* W'^y evi- dently upon t'nis, that as we are satisfied our org^ms o- perate' duly, and know tl^at every effect must have a cause, nothing is more natural than to suppose, that where an idea is excited in the mind, some object ex- ists corresponding to the idea, which is tli^ cause of that appearance. But as this conclusion, by what we have seen, is no.t necessary and unavoidable, hence there
I
215
is no intuition In the case, but merely a probable con- jecture, or reasonable presumption, grounded upon an intuitive trutli.
_ VI. Again : When a piece of gold is Absolute cer- dissolved in aqua reg'iay we see indeed and tainty in na- own the effect produced, but cannot be ^^^^^ know-
• 1 . ^ • ^ J • ^ c T lecijje confined
Said m strictness and propriety ot speech, ^^ *,j,.^^ ^.^jj^ to have any perception or discernment of under our im- it. The reason is, because being unac- mediate no- quainted with the intimate nature both of ^^^^' aqua regia and gold, we cannot, from the ideas of them in our minds, deduce why the one operates upon the other in that particular manner. Hence it is that X)ur knowledge of the facts and operations cf nature ex- tends not with certainty beyond the present instance, or what falls under our immediate notice ; so that in all our researches relating to them, we nmst proceed in the way of trial and experiment, there being here no general or universal truths whereon to found scleui'ifical deductions. Because the solution of gold in aqua reg'ia'\\o\^i in one experiment, we cannot thence infallibly conclude that it will hold in another ; for not knowing upon what it is, in either of thcte bodies, that the effect here mentioned depends, we liave no absolute certainty in any new experiment we propose to make, that the objects v^ be applied one to another have that precise texture and constitution from which this solution results. Chemists know bv expe- rience, that bodies which go by t?ie same name, and have the same outward appearance, are riot alwavs •however exactly alike in their powers and operations. In vain do they often search for tho^.e properties in one piece of anlimony, which on former occasions they may have found in another ; and by this means, to their- no small mortification, find themselves frequently disap- pointed in very costly and promising experiments. Nor have we any express and positive assurance th;'.t the very bodies with which we have formerly made experiments continue so exactly the same, as to afford
216
the like appearances in any succeeding trial. A thou- sand changes happen every moment in the natural world, without our h.'^v'iu^ the least knowledp-e or perception of them. Aa alteration in our atmosphere, the approach or recess of the sun, his declination to- ward the north or south, not only vary the outward face of things, but occasion many changes in the hu- man constitution itself, which we yet perceive not wlien they happen ; nor should ever be sensible of, but by the effects and consequences resulting from them. And whether alterations analogous to these may not sometimes be produced in the frame and texture of many bodies that surround us, is what we cannot with certainty determine. Hence, from an experiment's succeeding in one instance, we cannot infallibly argue that it will succeed in another, even with the same body. The thing may indeed be probable, and that in the highest degree ; but as there is still a possibility that some change may have happened to the body, unknown to us, there can be no absolute certainty in the case.
, ^ VII. Had we such an intimate acquaint- What kind of -.u .1 i. ^ * i .u r
knowledo-e of ^"^^ ^^^" ^^^^ Structure both or aqua regia body would and gold, as to be able thence to discern deserve the -^yhy the one so operates upon the other as name of sa- j.^ occasion its dissolution •, insomivch that from the ideas of them in our own minds we could clearly deduce that bodies of such a make applied one to another, must necessarily produce the effect here mentioned, — our knowledge would then be scientific al^ and stand upon the foundation either of intuition or demonstration^ according as the perception was immediate, or attained by means of intervening ideas. In this case therefore, having two standard ideas in our minds, whose relatipns we perfectly well know, where- ever we found objects conformable to these ideas, we could then pronounce with certainty that the applica- tion of them one to another would be attended with the above effect ; because whatever is true in idea is unavoidably so also in reality of things, where things
217
exist unanswerable in these ideas. If it be true in idea that a parallelogram is the doubt of a triangle standing upon the same base, and between the same parallels, the same will be true of every real triangle and pa- rallelogram that exists with the conditions here mention- ed. We are likewise to observe, that the changes to which bodies are daily liable, could produce no confu- sion or perplexity in natural knowledge, did it stand upon the foundation here mentioned ; for in such a case, the powers and properties of objects being de- duced from the ideas of them in our own minds, would no otherwise be applied to things really existing, than as these things are found perfectly conformable to our ideas. When therefore an alteration happened in any body, as it would by this means ditter from that standard idea whence its former properties were seen to flow, we must of course be sensible that some suit- able change would follow in the properties themselves, and that its powers and operations in regard of other bodies, would not be in all respects the same.
VIII. But what is more remarkable, t
, , , , . . . , , ' Experience
we should upon tins supposition be able the only foun-
to determine the mutual action and in- dation of na- fluence of bodies, without having recourse ^,^\^^ know- to trial or experiment. Had we, tor in- ^ stance, a perfect knowledge of the intimate nature and composition of an animal body, and of the particular poison that is infused into it by the bite of a viper, so as clearly and distinctiy to discern how ti'.ey are adapted one to another, we might thence scientifically deduce, without the help of experiments, that the bite of a viper would so unhinge the human fabric, and produce such ferments and combustions in it, as must necessarily be followed by a total extinction of all the vital functions, and leave that admirable machine a mere listless lump. But as such perfect and adequate ideas of objects, and their mutual habitudes one to ano- ther, are plainly beyond the reach of our present facul- ties, it were vain for us- to think of imnrovino- natural
U
218
knowledge by abstract reasoning or scientifical deduc- tions. Experience is here the true and proper founda- tion of our judgments ; nor can we by any other means arrive at a discovery of tlie several powers'and properties of bodies. How long might a man con- template tlie nature of hemlock, examine the structure of its parts in a miscroscope, and torture and analyze it by all the processes of chemistry, before he could pronounce with certainty the effect it will have upon a human body ? One single experiment lays that open in an instant, wliich all the wit and invention of men would never of themselves have been able to trace. The same holds in all the other parts of natural philo- sophy. Our discoveries relating to electricity, the powers and properties of the loadstone, the force of gun- powder, &c. were not gained by reasoning, or the con- sideration of cur abstract ideas, but by means of ex- periments made with the bodies themselves. Hence it happened, that while the philosophy of Aristotle pre- vailed in the schools, which dealt much in metaphysical i:iotions, occult qualities, sympathies, antipathies, and such- like words witJiout m.eaning, the knowledge of nature was at a stand ; because men pretended to ar- gue abstractedly about things of which they had no perfect and adequate ideas wliereon to ground such a jnethod of reasoning. But now in the present age, ihat'we have returned to the way of trial and experi- ment, which is indeed the only true foundation of na- tural philosophy, great advances have already been made •, and the prospect of still greater lies before ys.
^rr u IX. And thus at length we may sufii-
Difference be« "^ ,
tween scienti- clently understand wherein the proper
fical and natu- differcncelles between scientifical and natu- ral knowledge. j.^j knowledge. In matters of science we argue from the ideas in our own minds, and the con- nections and relations they have one to another. And as wlien these relations are set clearly and plainly be- fore us, we cannot avoid perceiving and owning them,
219
Lence all the truths of this class produce absolute cer- tainty in the mind, and are attended with a necessary and unavoidable assent. It is otherwise in the case of natural knowledge : intuition and inward perception have here no place. We discern not the powers and properties of those objects thr-t surround us, by any views and comparison of the ideas of them one with another, but merely by experience, and the impressions they make on the senses. But now the reports of sense happening in seme instances to deceive us, we have no inf.dhble assurance that they may not in others ; which weakens not a little the evidence attcnd- infT this kind of knowledcje, and leaves room for sus- picion and distrust. Nay, what is yet more considera- , ble, as we have no perfect and adequate ideas of bodies representing their inward constitution, or iayin^^jj open the foundation upon which their qualities depend, v/e cim form no universal propositions about them, applicable with certainty in all particular instance?. Fire, we say, dissolves metals. This, though express- ed indefinitely, is however only a particular truth ; nor can be extended with absolute assurance beyond the several trials made. The reason is, that being ignorant of the inward frame and composition both of fire and metals, when objects are offered to us under that name, we have therefore no positive certainty that they are of the very make and texture requisite to the success of the experiment. The thing may indeed be probable in the highest degree, but for want of stan- dard and settled ideas, we can never arrive at a clear and absolute perception in the case*
X. As nevertheless it is certain that ^,
. . 1 ' • The manner
many general conclusions m natural pnilo- of reasonino-
sophy are embraced without doubt or hesi- in natural
tation ; nay, that we form most of the knowledge.
schemes and pursuits of life upon that foundation, it
will naturally be asked, here, how come we by thivS
assurance? I answer, not scientifically, and in the
way of strict demonstration, but bv analogy, and an
U 2
5220
induction of experiments. We distinguish fire, for instance, by such of its qualities as lie more immediately open to the notice of the senses ; among which light vmd he.'iL are the most considerable. Examining stiil farther into its nature, we fmd it likewise possessed of the power of dissolving metals. But this new property not having any necessary connection that we can trace v/ith those other qualities by which fire is distinguished, v/e cannot therefore argue with certainty that wherevex light and heat, &c. are, the pov/er of dissolving metals "co-exists with them. 'Tis not till after we have tried the thing in a variety of experiments, and found it al- ways to hold, that we begin to presume there may be really some such connection, though our views are too short ?.nd imperfect to discover it. Hence we are led to frame a general conclusion, arguing from what has rdready happened, to what will happen again in the like cases j insomuch, that where we meet with all the otlier properties of fire in any body, we have not the least doubt but that upon trial, the power above men- tioned will be found to belong to it also. This is called reasoning by analogy ; and it is, as we see, founded entirely upon induction, and experiments made with particular objects : the more precise and accurate our ideas of these objects are, and the greater the varie- ty of experiments upon which we build our reasoning, the more certain and undoubted will the conclusions be. It is in this manner we arrive at all the general truths of natural knowledge ; as that the bite of certain animals is mortal ; th.at a needle touched by a loadstone points to the north ; that gravity belongs universally to all bodies ; and innumerable others, which though not capable of strict demonstration, are nevertheless as readily embraced upon the foundation of analogy, as the most obvious ajid intuitive judgments; nay, and become fixed and steady principles of action in all the aims and pursuits of life.
How even XI. And here again it is particularly
^ciexuifical rea- remarkabicj that having ascertained the
221
general properties of things by analogy, zoning may be if we proceed next to establish these as intr&ducedinto postiilata in philosophy, we can upon this ^^• foundation build strict and mathematical demonstra- tions, and thereby introduce scientifical reasoning into natural knowledge. In this manner Sir Isaac Ncivton. having determined the laws of gravity by a variety o£ experiments, and laying it down as a principle, that it operates according to those laws through the whole system of nature, has thence in a way of strict demon- stration, deduced the whole theory of the heavenly motions. For granting once t\\\s postulation, that gravi- ty belongs universally to all bodies, and that it acts according to tlieir solid content, decreasing with the distance in a given ratio, what Sir Is-aac has determined m regard to the planetary motions, follows from the bare consideration of our own ideas ; that is, necessari- ly and scientifically. Thus likewise in opiicsj if we lay it down as a principle., that light is propagated on all sides in right lines, and that the rays of it are reflected and refracted according to certain fixed invariable laws, all which is known to be true by experience, we can upon this foundation establish mathematically the theory of vision. The same happens in mechanics^ hydrostatics^ -ptieuwatics^ &c. where from postuluta ascertained by experience, the whole theory relating to these branches of knowledge follows in a way of strict demonstration And this I take to be the reason why many parts of na- - tural philosophy are honoured with the name oi sciences. Not that they are ultimately founded upon intuition ; but that the several principles peculiar to -them beino- assumed upon the foundation of experience, the tlieory deduced from these principles is -established by scientific ■ cal reasoning.
XII. Could we indeed discern any neces- „. .,,
, • I , * <^^ still expe-
■sary connection between gravity and the Hence is the ul- ~
known essential qualities of matter, idsot timate ground
much, rhat it was inseparable from the °^ ^"^ assent.
very idea of it, the whole theory of the planetary mo« ■
U 3.
222
tions would iherx be strictly and properly scientificnl ; for seeii'g, from the notion of gravity, we can demon- stratively determine the laws that bodies will observe in their revolutions in any known circumstances, if the circumstances relating to any system of -bodies can be traced, and gravity is supposed essential to them, we can then, from the bare consideration of our own ideas, deduce all their motions and phenomena. Now this is precisely what Sir Isaac has done in regard to our planetary system. He has determined the circumstan- ces of the bodies that compose it, in respect of situation, distance, magnitude, &;c. all which being supposed, if they are essentially actuated by gravity, their several revolutions and appearances must be equally essential. But as the principle of gravitation cannot be accounted ior by the known qualities of matter, neither can this theory be immediately deduced from the idea of body ; and therefore, though our reasoning in this part of philosophy be truly scientifical, yet as the principle upon which that reasoning is grounded is derived from experience, the theory itself must needs ultimately rest upon the same foundation. And thus even the doctrine of the planetary motions, though seemingly established by mathematical reasoning, falls yet, in strictness and propriety of speech, under the head of natural know- ledge. For in this precisely consists the difference be- tween science and wh;it we call the philoscphi/ of Jiature ; that the one is grounded ultimately on intuition^ the other on experience. As the observation here made holds alike in all the other branches of natural philoso- phy, into which scientijical reasoning has been introdu- ced, it is hence apparent that they are not sciences, in the strict and proper sense of the word, but only by a certain latitude of expression common enough in all languages. What we have therefore said above, rela- ting to the impossibility of improving natural knowledge by scientifical deductions, is not contradicted by any thing advanced in this section. We there meant de- ductions grounded ultimately on intuition, and derived
223
from a consicieration of tlie abstract ideas of objects In our own minds *, not such as flow from postulata assu- med upon the foundation of experience. For these last, as we have already observed, are not truly and properly scientifical, but have obtained that name merely on account of the way of reasoning in wliich they are collected from the S2.\d postulata.
XIII. If then absolute and infaUible r^^^ nianner certainty is not to be obtained in natural of reasoning knowledge, much less can we expect it in in historical historical •, for here testimony is the only knowledge. ground of assent ; and therefore the only possibility of our being deceived is still greater than in the case of experience. Not only he who reports the fact may himself have formed a wrong judgment ; but could we €ven get over this scruple, there is still room to suspect, that he may aim at imposing upon us by a false narra- tion. In this case therefore it is plain, there can be no intuition or inward perception of truth, no strict and absolute demonstration, and consequently no science. There is however a way of reasoning even here, that begets an entire acquiescence, and leads us to embrace without wavering, the facts and reports of history. If, for instance, it appears that the historian was a man of veracity ; if he was a competent judge of what he relates ; if he had sufficient opportunities of being in- formed ; if the book that bears his nam^e was really writ by him ; if it had been handed down to us uncor- rupted ; in fine, if what he relates is probable in itself, falls in naturally with the other events of that age, and is attested by contemporary writers, — by these and such like arguments, founded partly on criticism, part- ly on probable conjecture, we judge of past transac- tions ; and though tlicy are not capable of scientijical proof, yet in many cases we arrive at an undoubted assurance of them ; for as it is absurd to demand mathematical demonstration in matters of fact, because they admit not of that kind of evidence, it is no less
so to doubt of their reality, when they are proved by the best arguments their nature and quality will bear. Scepticisms ^^^^ ^"^ ^^"^ we see, in the several
necessarily ex- divisions 01 human knowledge, both what eluded from is the ground of judging, and the manner
matters of q£ reasoning peculiar to each. In scientific science. . "^
cal knowledge, which regards wholly the
abstract ideas of the mind, and those relations and con- nections they have one with another, our judgments are grounded on intuition ; and the manner of reason- ing is by demonstration. In natural knowledge, respect- ing objects that exist without us, their powers, pro- perties, and mutual operations, we judge on the foun- dation of experience, and reason by induction and ana/ogi/; Lastly, In historical k?ioiulcdge, which is chiefly conver- sant abt^ut past facts and transactions, testimony is the ground of judgment ; and the way of reasoning is by criticistn and probable conjecture. And now I think we are able effectually to overthrow that absurd kind of scepticism maintained by some of the ancients, which brings ail propositions upon a level, and represent^ them as equally uncertain. What gave the first rise to this doctrine was, the caprice of certain philo- sophers, who observing that the reports of sense and testimony were in some instances deceitful, took thence occasion to suppose that they might be so likewise in others, and thereupon established it as a principle, that we ought to doubt of every thing. But even with re- spect to this doubting, we are to observe, that it can in fact extend no farther than to matters of experience and testimo?2yy being totally and necessarily excluded from scientijical knowledge. When ideas make their ap- pearance in the understanding, it is impossible for us to doubt of their being there : and when the relations of any of our ideas are clearly and distinctly, discerned by the mind, either immediately, which is intuition, or by means of intervening ideas, which is demonstration^ it would be in vain for. us to endeavour to persuade ourselves that that is not, which we plainly and una-
225
voidably perceive to be. In rliis case therefore we cannot withhold our assent ; truth forces its way ovcc all opposition, and breaks in with so much light upon the mind, as to beget absolute and iafaliibie cer- tainty.
XV. Indeed, in natural and historical . , , . I , , . . , , 1 And to be ad-
knowledge, scepticism may nave place, be- knitted with
cause, as we have said, there is a possibility caution in mat-
of our being deceived \ but then it is to tc^s of expe-
be observed, that a bare possibility is a '.^""'" ^"^ '"'*
111 L t:naony.
very weak ground whereon to bottom any
philosophical tenet. It is possible that Great Britain may be swallowed up by the' sea before to-morrow; but I believe no man is on this account inclined to think that it will be so. It is possible the whole hu- man race may be extinguished the next instant •, yet this possibility creates no apprehension that the thing :itseif will really happen. In a word, we ought to judge of things by the proofs brought to support them, not by bare abstract possibilities \ and when we have all the evidence they are capable of, that alone is suf- ficient to convince, though perhaps the contrary can- not be shewn to imply a contradiction. Will any wise and considerate man doubt whether there be such a place as America^ because we cannot prove by any necessary argument that it is absolutely impossible all the relations concerning it should be false ? Strict and rigorous demonstrations belong not to history, or the philosophy of nature. The way of reasoning in these branches of knowledge is by arguments drawn from experience and testimony : and when the truth of any proposition is in this manner sufficiently ascertained, insomuch that it appears with all the evidence it is capable of, and we have as great reason to believe that it is as we could possibly have, supposing it were, is' not this upon the matter as satisfactory as a demonstra- tion } It must be ov*med indeed, there is no inward perception in the case, and therefore our assent cannot be said to be necessary and unavoidable. Xv'Ien may ia
226
these matters be sceptics if they please ; Tind if they are resolved upon it, it is in vain to contend v/ith obstinacy aad perverseness. I cannot however but observe, that if they will really act up to their own principles, and treat all things in good earnest as uncertain that admit not of strict scientifical proof, their conduct must be the very madness of folly. No man can demonstrate mathematically that poison has not been conveyed into his meat or drink. And if he will be so very cautious as not to taste of either till he has i-eached this decree of certainty, I know no other remedy for him but that, in great gravity and wisdom, he must die for fear of death. The truth of it is, the most zealous patrons of scep/icism, after all their pretended doubts and scruples, find it yet convenient to behave in the several occur- rences of life, as if they gave entire credit to the re- ports of sense and testimony. They will no more venture upon a dose of arsenic, or rush into the midst of a glowing furnace, than if they verily believed death would be the consequence. And though in this it must be owned they act discreetly, yet have we hence at the same time a very convincing argument of the absurdity of those notions they effect to entertain. In reality, can any thing be more ridiculous than to givQ into a scheme of thinking, which we find ourselves ne- cessitated to contradict in almost every occurrence of life ? Opinions are not to be taken up out of caprice and fancy, but to serve as principles of action, and standing rules of behaviour. When they answer not this main purpose, they are unavailing and fruitless ; and- an obstinate adherence to them, in spite of the re- peated admonitions of experience, justily deserves to be branded for folly. We shall not therefore attempt to multiply arguments in a matter so cbvious, it suffi- ciently answering our present purpose to have shown, that doubting and uncertainty have no place in scienti- fical knowledge, and that even in matters of history and the facts of nature, an undistinguishing scepticism would be in the highest degree absurd.
227
XVI. But here perhaps It will be asked, ^^i^^^^ ^p^-. ,Why all this mighty noise about science, cable to the -when even according to the present ac- concerns of hu- count, it seems to be so very capricious ^^^^'^ and arbitrary a thing ? For seeing it is wholly confi- ned to the consideration of our ideas, and we are at liberty to frame and combine those ideas at pleasure, this indeed opens a way to castles in the air of our own building, to many chimerical and fanciful sys- tems, which men of warm and lively Imaginations love to entertain themselves with, but promises little of that knowledge which is worth a wise man's regard, and re- spects the great^ends and purposes of life. Where is the advantage of barely contemplating our ideas, and tracing their several habitudes and relations, when it is in truth the reality of things that we are chiefly con- cerned to know, and those respects they bear to us and one another ? To this I answer. That if indeed our i<leas no way regarded things themselves, the know- ledge acquired by their means would be of very little consequence to human life. But since, as we have already observed, whatever is true in idea Is unavoid- ably so also In the reality of things, where things exist answerable to these ideas, it is apparent, th^it by copy- ing our ideas with care from the real objects of nature, and framing them in a conformity to those conjunc- tures and circumstances in which we are most likely to be concerned, a way is laid open to discoveries of the greatest importance to mankind ; for in this case, our several reasonings and conclusions holding no less of the objects themselves than of the ideas by which they are represented, may be therefore applied with certain- ty to these objects, as often as they fall under our no- tice. Thus mathematicians, having formed to them- selves ideas of cones, cylinders, spheres, prisms. Sec, variously compare them together, examine their se- veral properties, and lay down rules by which to cal- culate their relative bulk and dimensions. But now as bodies answering in figure to these ideas come fre-
228
qiiently under our observation, we have by this means an opportunity of applying mathematical knowledge to the common concerns of life ; and by determining pre- cisely the quantity of extension in each body, can the better judge how far they will answer the purposes we have in view. The same thing happens in politics and morality. If we form to ourselves ideas of such com- munities, connections, actions, and conjunctures, as do or may subsist among mankind, all our reasonings and conclusions will then respect real life, and serve as steady maxims of behaviour in the several circum- stances to which it is Hable. It is not therefore enough that we set about the consideration of any ideas at random j we must further take care that those ideas truly regard things themselves ; for although knowledge is always certain when derived from the contemplation of our own ideas, yet it is then only useful and worthy our regard when it respects ideas taken from the real objects of nature, and strictly re- lated to the concerns of human life.
^, , J XVII- Having thus shewn that there is
The method i i • ^- r i i
of science be- such a thing Tusscience^ nxed and ascertam-
gins with as- ed the bounds of it, and explained its great certamxng our ^^^ ^^^^ importance in the affairs of man- * ^^^" kind, it now remains that we lay down the
rules of method peculiar to this branch of knowledge, and give some account of the manner in which that certamty and conviction which are inseparable from it, may be most naturally and effectually prcluced. Science, as we have said, regards wholly the abstract ideas of the mind, and the relations they have one to another. The great secret therefore of attaining it, lies in so managing and conducting our thoughts, as that these several relations may be laid open to the view of. the understandiiig, and become the necessary and unavoida- ble objects of our perception. In order to this we must make it our first care, distinctly to frame and settle th£ ideas about which our inquiries are to be employed. Tor as the relations subsisting between th^m can no
221^
otherwise be discerned than by comparing thcni one with another ; and as this comparison necessarily sup- poses that the ideas themselves are actually in the mind, and at that very time under our immediate in- spection, it plainly follows that all science must begin with fixing and ascertaining those ideas. Now our i- deas, as has been already observed in the first book, come all very naturally within the division of simple and comjylex. Simple ideas are excited by actual impressions made upon the understanding \ aqd as they exist under one uniform appearance, without variety or composi- tion, are in no danger of being mistaken or confounded one with another. It is otherwise in our complex con- ceptions ; for these consisting of many simple ideas joined together, great care must be taken that we ac- quaint ourselves with the true number combined, and the order and manner of their connection. By this means alone are these our most intricate notices kept distinct and invariable, insomuch that in all our several views of them, they ever have the same appearance, and exhibit the same habitudes and respects. Here therefore, properly speaking, the art of knowledge be- gins. For although we fiod it easy enough to bound and settle our ideas where they consist of but few sim- ple perceptions, yet when they grow to be very com- plicated, it often requires great address arid manage- ment to throw them into such views as may prevent that confusion which is apt to arise from the joint consideration of a multiplicity of different objects. Hence that gradation in the composition of our ideas, which we have explained at large in the last chapter of the first book •, for as they are by this means formed into different orders, and these orders arise continuaHv" one out of another, the understanding by taking them in a just succession, gradually mounts to the highest conceptions, and can at any time, with incredible ease and expedition, bring all their parts distinctly into view. To know therefore the full value of this contrivance, we must attentively consider the strict connection that
X
230
, obtains between the several classes of our perceptions when disposed in such a series. Every succeeding order is formed out of those combinations that consti- tute the rank next below it : and as in advancing from one degree to another, we are always to proportion the number of notices united, to the strength and capacity of the mind, it is apparent that by such a procedure tlie ideas will be thoroughly ascertained in every step, and, however large and bulky, II? yet fairly within our grasp. This obviously accounts for that wonderful clearness of apprehension which we often experience within ourselves, even in regard to the most complica- ted conceptions j for though the multitude of parts in many cases be great, I may say beyond belief, yet as they have been all previously formed into separate classes, and the classes themselves distinctly settled in the understanding, we find it easy, by such a series of steps, to rise to any idea how complex soever, and with a single glance of thought embrace it in its full extent.
, _ . XVITI. But it Is not enough tliat we bare- eating them ly lomi ideas m our own mmds ; we must by means of also contrlve a way to render them stable definitions. ^^j^^ permanent, that when they disappear upon calling off our attention, we may know how to retrieve them again with certainty. This is best done by words and descriptions, which serve not only to bubject them to our own review, but also to lay them open to the perception of others. And indeed as one of the main ends of reducing knowledge into the form of a science Is the easy and advantageous communica- tion of truth, it ought always to be our first care, when we set about unfolding our discoveries, to exhibit the several conceptions to which they relate, in a just and accurate series of definitions ; for till we have distinct- ly transferred our ideas into the understanding of those to whom we address ourselves, and taught their connec- tion with the appropriated sounds, all our reasonings will' evidently be without effect. If men comprehend
231
not the true import of our words, and are therefore led by them to bring wrong Ideas into comparison, they can never sure see connections and habitudes that really subsist not. But if, on the contrary, the tentis we use excite those very perceptions in others which they denote in our own minds, then, as the several re- lations pointed out will lie fairly open to view, they must needs be discerned with great readiness, and ease, and stamp the character of certainty Upon all ouf' de- ductions. '■■ XIX. Thus we seeth;it the method of science y^e names ( i begiFis- with unfolding our ideas, and com- simple i^.-^ae municatiniT them bv means of definitions, (constitute tae And ncre it is oi gre.it importance to ob- ele-nentai-r ' serve, that there must be in all languages tenns of lln- certain original anxl elementary names, g«age. whence our descriptions take their first rise, and be- yond which we cannot trace the meaning and signifi- cation of sounds *, for since our very definitions are made up of words, if we suppose not such primitive and fundamental terms, into which they all resolve themselves, and where they at last necessarily termi- nate, it is evident there would be no end of explaining. Now it is peculiar to our simple ideas, that they can- not be originally excited by words, but must always make their first entrance into the understanding by the actual operation of objects upon it. Vv^'hen therefore, in a series of definitions, we arrive at the names of these ideas, 'tis plain we can push our descriptions no farther, but are necessitated to suppose, that the per- ceptions themselves have already found admission into the mind. If they have not, definitions avail nothing; nor can they any other way be impressed upon us than by betaking ourselves to the several objects In which the power of producing them resides. Hence it ap- pears that the primary articles of speech, into which the whole of language may be ultimately resolved, are no other than the names of simple ideas : these we see admit not definitions. It is by experience and obs^r-
X2
2S2
Vation that we grow acquainted with their meaning| and furnish ourselves with the perceptions they serve to denote ; for finding that those in whose society we live, make use of certain articulate sounds to mark the various impressions of objects, we too annex these sounds to the same impressions, and thus come to un- derstand the import of their words. This way ci knowledge takes place, in regard to all our simple ideas ; but in many of those that are complex, as they are the mere creatures of the understanding, and exist nowhere out of the mind, there are of course no real objects without us, whence they n\2y be originally obtained. If therefore they could noi be communica- ted by descriptions, v/e should be left wholly without the means of transferring them into the minds of others. But happily it so falls out, that all complex conceptions whatsoever may be distinctly exhibited in definitions ; for as they are no more than different combinations of simple ideas, if these simple ideas have already got admission into the understanding, and the names serving to express them are known, it will be easy, by describing the order, number, and peculiar connection of the notices combined, to raise in the mind of another the complex notion resulting from them.
A knowledo-e ^^* Since then it is by simple ideas of these pre- and their names that we unfold all the viously sup- other conceptions of tlie mind, it mani- fint^anv sab- ' ^^stly follows, that in handling any subject ject" scienti- sctent'ificallijy we must always suppose those iically. to v/hom we address ourselves previously
furnished by experience with these first principles and elements of knowledge. Nor is this by any means an unreasonable posttdattim ; because the simple ideas that relate to the sciences being few in number, and coming very often in our way, it is hardly possible we should be unacquainted with them, or not have frequently heard their names in converse with others. What principally demands our care is, to apply those names
^33
STight, and according to the strict use and propriety of the language in which we write. 'Tis seldom allow- able to change the signification of words, especially those by which we denote simple ideas. If however such a liberty should at any time be found necessary, we may still make ourselves understood, by mention- ing the idea under its common name, and. signifying its connection with the newly-appropriated sound. In- deed it sometimes happens, that new and unusual ideas of this kind are to be taken under consideration, which we must therefore express by terms of our own invention. In this case, as the ideas themselves can- not be laid open by definitions, we refer to the seve- ral objects whence they maybe obtained; which though it excites not the perceptions immediately, yet suffi- ciently answers our purpose, by putting men in a way of being furnished with them at pleasure.
XXI. This foundation being laid, the ^he order and communication of our complex concep- connection of tions by definitions becomes both easy °"^ «istinitions. and certain ; for since the ideas themselves are formed- into different orders, and these orders arise continually one out of another, nothing more is required on our part than to observe a like method and gradation in our descriptions. As therefore the first order of our com- pound notions is formed immediately from simple ideas, so the terms appropriated to this order must be defined by the names of these ideas. And as the se- cond and all the succeeding' orders arise continually out of those combinations that constitute the classes next below them, so the definitions corresponding to these different orders gradually take in the terms by which the several inferior divisions are regularly and successively expressed. In such a series of descrip- tions, it is evident at first sight, that nothing can be obcure and unintelligible; for as it; begins with the names of simple ideas, whose meaning is supposed to be known ; and as in every order of definitions such terms only occur as have been pr-eviously. explained 'm
X 3
234
the preceding distributions, by advancing regularly from one to another, we gradually furnish ourselves with whatever is necessary towards a distinct concep- tion of all that is laid before us. Nor is it a small ad- vantage attending this disposition, that the several ideas described are hereby excited in the understanding in the very order and manner in which they are fra- med by a mind advancing uniformly from simple to the most complicated notions. Hence we see distinctly the various dependence of things, and being put inta that very train of thinking which leads directly ta science and certainty, are drawn insensibly to interest ourselves in the pursuit ; insomuch that while in fact we do no more than follow a guide and conductor, v/e can yet haidly forbear fancying ourselves engaged in the actual exercise of deducing one part of knowledge from another,
XXIL When we have thus fixed and Of the imme- .. • j -j j j- ^' xi
diate and in- ascertamed our ideas, and distmctly ex-
tuitive rela- hibited them in definitions, we then enter tions between upon the important task of tracing their our ideas. several habitudes and relations. In order
to this we set about comparing them among them- selves, and viewing them in all the variety of lights by which we can hope to arrive at a discovery of their mutual agreement or disagreement. And here it happens that some relations forwardly offer themselves to the notice of the understanding, and become the necessary objects of perception^ upon the very first appli- cation of our ideas one to another. Those are therefore immediately owned, and constitute our vrimary and intuitive judgments, being attended with the highest degree of evidence, and producing absolute certainty in the mind. But in many uses, the connection or repugnance between our ideas, even when true and real, comes not yet within our immediate view, but requires search and examination to discover it. On this occasion we have recourse to intermediate notices ; and if by means of them we can muster up a train cf
n
23j
evident and known truths, which, disposed in a regu- lar series of argumentation, lead at last to a conclu- sion expressing the relations we are in quest of, the proof thence arising is called demofistratio7u Now, as the conviction attending demonstration is no less necessary and unavoidable than that which proceeds from intuiiiony it evidently follows, that whether the relations between our ideas are immediately discerned by the mind, or whe- ther they are traced by means of intervening percep- tions, in either case we arrive at science and certainty. This however is particularly to be observed, that the more remote and distant respects being deduced from such as are obvious and self-evident, the propositions expressing these last demand our first notice, and ought to be previously established before we enter up- on higher iiiYestigations. When therefore, in the method of science^ we have finished the business of de- finitions, it must be our next care, distinctly to unfold in propositions those. immediate and intuitive relations which are necessarily seen and owned by the mind, upon the very first comparing of our ideas one with another. These propositions have obtained the name Xii first principles^ because, occurring j^j/ in the order of knowledge, and being manifest of themselves, they suppose not ?Lny prior truths in the mind whence they may be evidenced and explained. It is not needful to enlarge here upon the necessity of circumspection and care in settling these primitive and fundamental per- ceptions ; for since the whole superstructure of our knowledge rests ultimately upon them, it is evident at first sight that a mistake in this case must at once overturn and annihilate all our future reasonings. But having already explained the nature of these proposi- tions in the second book, unfolded the notion of self- evidence, and taught the manner of distinguishing be- tween the truths of this class and those that are de- monstrable, we shall for the present wave any farther Gon^deration of this subject, referring the reader to
236
wliat IS there advanced, if he desires fuller informa- tion. / . Oftheappli- XXIII. The first and more immediate cation of self- relations of our ideas being thus pointed evident truths q^^^ Q^J. next business is to investipjate in demonstra- i ^ i i- . * i r tino-sucliasare ^^*^" ^^ ^^^ remote and distant. And here remote and it is that we have occasion for intermediate distant. notices, and a skilful application of intui- tive truths. But though self-evident propositions be the ultimate foundation of our reasoning, we are not on that account to imagine that the art of improving knowledge lies in assembling at random a large and comprehensive stock of these. E,wen general pr'mclples, considered by themselves, avail but little towards the investigation of truth : they are indeed useful as media of certainty, by preserving the evidence of our reason- ings distinct, which never fail to convince, if, being pursued to their source, they are found to resolve themselves into and ultimately terminate in these prin- ciples. But when we set about the increase and en- largement of science, far other helps are required •, for here the whole secret consists in devising and singling out such intermediate ideas as, being compared with those others whose relations we inquire after, may furnish out a train of obvious and known truths, ser- ving distinctly to investigate the said relations. Euclid, in the first book of the Elements, has demonstrated, that the three inivard angles of a triangle taken togetJier^are equal to two right angles^ The reasoning by which he establishes that proposition, resolves itself into this ge- neral principle : Things equal to one and the same thing, are equal to one another. Will any one however pretend to say, that a bare consideration of the principle itself led him to that discovery .'* The merest novice in ma- thematics would upon this supposition be equally qua- lified for the business of invention, with one that had made the greatest progress ; inasmuch as these general principles of the science are commonly, alike known to both. But the truth of it is, Euclid having found out
t37
-angles, to which the three angles of a triangle, and two
right angles, heing comp ured, were found severally e-
qual, thereby ascertained the proposition m question,
by shewing it to terminate in the above axiom, though
perhaps the axiom itself was never once thought of
during the whole course of the investigation.
XXIV. And here it may not be impro- o^,,„„- „ , , - / . , Y • Reasoning,
per to observe, that though it be usual m though resol-
reasoiiing, when we arrive at any particu- vable into ge-
lar self-evident proposition, to refer to the neral triuhs,
•^ , '^ , . , . . rests immedi-
general axiom under which it is compre- ^^^ly yp^j^
hended, yet is not this done out of abso- particular self- lute necessity, or for the sake of any addi- evident prepo- tional confirmation. All intuitive truths, ^^ ^°" ' whether general or particular, standing upon the same foundation of immediate perception, are necessarily embraced for their own sake, and require no mutual illustration one from another. When therefore we have found, that the three angles of a triangle, and two right angles, are severally equal to the angles formed by one right line standing upon another, we thence im- mediately discern their equality between themselves, independent of the general axiom into which this truth may be resolved. Nor do we in reality refer to that a;ciom by way of evidence and proof, but merely to shew the coincidence of the example under notice, with a previously established general principle. The same thing happens in all other demonstrations what- soever, which terminating thus in particular self-evi- dent truths are therefore of themselves suflicient to certainty, and acquire not any new force by being ul- timately referred to general maxims. This I mention here, to obviate a common prejudice, whence many are led to imagine, that particular intuitive propositions de- rive their evidence from those that are general, as being necessarily included in them. But since they both stand upon the same foundation of certainty, and are admitted in consequence of immediate perception, they
238
have therefore nn equal claim to self-evidence, and can- , not be made plainer by any mutual appeal. Particular XXV. As however it is usual in the me-
self-evident thod of Science to lay down certain gene- propositu)ns ^^j principles by way of foundation for our
so called here, r ^ . •' ^ , mi i
in opposition i^-^f"^^ rcasonings, some perhaps will ob- to general ject that this seems to be a needlcss pre- principles. caution, since demonstrations may subsist without them, and commonly terminate in particular self-evident truths, peculiarly connected with the sub- ject under consideration. In order therefore to give a distinct idea of the true design of this previous step, wi shall begin with observing, that by the particular propositions in which demonstrations terminate, must not be understood such as are so according to the strict definition of the word, or in opposition to universals ; but only confined and limited truths, when compared with others that are more general. Thus the proposi- tion. Circles equal to one and the same circle^ are equal he- taveen themselves.^ is in strictness and propriety of speech universal, because the subject is taken in its full ex- tent, and the predicate agrees to all the individuals comprehended under It. We here notwithstanding consider it as only a particular truth, because it is of a very limited nature, when compared with the general axiom mentioned above ; Things equal to one and the same thing., are equal to one another ; tor this not only ex* tends to all the various species of figures, but takes in every object without exception, that comes under the denomination of Quantity.
General prln- XXVI. This point Settled, It will easily ciples serve appear that the method of premising general first to contract principles in the sciences, answers these
the bottom of j.^^ /rreat and valuable purposes : first, To
our reasonino^. '^ , , ^^ * -'. .
contract the pottom oi our reasonmg, and
bring it within such bounds as are sufficiently accom- modated to the capacity of the mind ; for demonstra- tions being carried on by means of intermediate ideas, which must always have some peculiar connection with
239
the matter hi hand, the particular self-evident propo- sitions in wliich they terminate, are almost as various as the subjects to which they relate. Tiius in investiga- ting the equality of different objects, whether angles, triangles, circles, squares, &c. the intuitive truths on which the proofs rest, always regard the particular spe- cies, and may be therefore multiplied /;/ infinitum as w^ell as the species themselves. But now it is remark-^ able that all these several truths, numerous as they may appear, are yet reducible to this one general principle already mentioned ; Th'uigs equal to one and the same things are equal to otie another. The same observation will be found to hold in other parts of human know- ledge ; insomuch that though the particular truths on which we bottom our reasonings are really innumera- ble, yet may they be all without exception resolved into a very few general maxims, and thereby brought readi- ly within the compass of the understanding. When therefore we begin with premising these general truths, and as we advance in science, take care universally to resolve our demonstrations into them, this must needs add a wonderful clearness and perspicuity to our rea- sonings ; and by establishing them upon a foundation previously admitted, and of whose strength and firm- ness we are abundantly satisfied, give them that irre- sistible force and influence, which serves to produce absolute certainty. Nor can we possibly imagine any thing more elegant and beautiful, than thus to behold knowledge rising from a firm and fathomable root, bearing its head aloft, and spreading forth into innu- merable branches of science j which though variously implicated and entangled, and stretching to avast extent, yet by their union in one common stock, derive thence so sure and stable a support, that all the assaults of ca- vil and scepticism are not able to destroy or lessen their connection.
, XXVII. But,, Secondliji Another purpose secondly, To served by general principles is, that they ascertain 'the enable us with less fatigue and labour, j^istness of it
240
with more ^"^^ less hazard of miscarriage, to satisfy case and less ourselves as to the justness of those^reason- hazard of itigs by which science IS established. For miscarriage. g^jice demonstrations, when pursued to their source, terminate always in particular intuitive truths, which are therefore the ultimate foundation of cer- tainty, it greatly imports us to beware that we receive not any propositions under this name until we have distinctly settled them in our own minds, and attained a full and clear perception of that self-evidence, on ac- count of which they are admitted without proof. But now these propositions being many in number, and differing according to the nature of the subject about which our researches are employed. It must greatly perplex and retard our reasonings, were we to check, ourselves every time they occur, in order to examine them by the rules of first principles. Nor is it a mat- ter of slight consideration, that in the heat and hurry of demonstrating, while the mind is advancing eagerly from one discovery to another, we should be often tempted to pass them over hastily, and without that at- tention their importance requires *, which must expose us to many errors and mistakes. These inconveniences are effectually prevented by the method of premising general truths, because, upon referring particular pro- positions to them, as the connection is obvious at first sight, and cannot possibly escape our notice, the evidence is discerned to be the very same with that of the principles to which they belong ; and thus by a bare reference, without the trouble of particular ex- periments, the grounds of reasoning are ascertained, and our demonstrations found ultimately to rest on maxims previously established.
^- , XXVIII. Having exnlained the use of
Of the man- . . , ^ , • , i_ v
ner of linking general prmciples, shewn them to be the
propositions great 7nedia of certainty, and found, that
together, in -^^ order to enlarge the bounds of science, order to the , ° ^ • ^ i- .
forming of le- we must have recourse to mtermediate
gitimate de- ideas, as by means of them we are furnish-
aaonstrations. ^^ ^j^i^ ^j^^ several previous truths of
241
which reasoning consists, it now remains that we in- quire in what manner these truths are to be disposed and linked together, towards the forming of just and legitimate dcmonstratiotu. We have seen aheady in the preceding book, that syllog'ums drawn up according to the rules there established, lead to a certain and infalli- ble conclusion. If therefore evident and allowed truths are disposed in a syllogistic order, so as to offer a regular conclusion, that conclusioti is necessarily true and valid j and since in every genuine syllogism, if the premises are true, the conclusion must needs be true, it manifestly follows, that the conclusion already gain- ed being now a known and established truth, may be admitted as one of the premises of any succeeding .syllogism, and thereby contribute towards tlie ob- taining a new conclusion. In this manner may syllo- gisms foliOw one another in train, and lead to a suc- ces.-ive discovery of truth, care being always taken th'cit the premises in every step are either self-evident propositions, or conclusions previously established. And i: deed the whole art of demonstrating lies in this due and orderly combination of our syllogisms *, for as by this means all the several premises made use of are ' manifestly true, all the several conclusions must be so too, and consequently the very last conclusion of the scries, wliich is therefore said to be demonstrated. The same order is to be observed in the disposition of the demonstrations themselves : that is, those pre- positions are always first to be demonstrated which furnish principles of reasoning in others ; it being upon the certainty of the principles m.ade use of, that ■ the certainty of the truths deduced from them de- pends. And since even the different branches and divisions of science have a near connection among themselves, insomuch that the knowledge of one is often pre- supposed in another, great care must be taken to adjust the several parts with an eye to this dependence, that those may always come first in order,
y
24^
whence the postnlata of demonstration in others are borrowed.
,^, , ^ XXIX. In this way of putting together
thod here ex- our thoughts, it is evident at first sight, plained is "call- that however far we carry our researches, ed the method j^j^^j^^ .^^d certainU/ will still attend us. 01 science. ^ , . • i i i i
But what is particularly elegant and
happy in the method now explained^ we hereby see knowledge rising out of its first elements, and discern distinctly how those elements are combined and inter- woven, in order to the erecting a goodly structure of truth. Experience furnishes us with simple ideas and their names, which are ihe jjr unary materials cf think- ing and communication. DeJi?iitions teach how to unite and bind these ideas together, so as to form them into complex notions of various orders and degrees. The general principles premised in science exhibit to the understanding such intuitive and funda- mental truths to express the immediate relations between our ideas, and constitute the ultimate ground of certainty. Demonstrations link known and esta- blished truths together in such manner, that they ne- cessarily lead to others which are unknown and re- mote. In fine, the duly adjusting the several branches of science, and the demonstrations in every branch, lays knowledge so open to the mind, that we see the parts of it growing one out of another, and embrace them with full conviction and assurance. Thus we are gradually led from simple ideas, through all the windings and labyrinths of truth, until we at length reach the highest and most exalted discoveries of hu- man reason. It is true, the method here laid down hath hitherto been observed strictly only among ma- thematicians •, and is therefore by many thought to be peculiar to number and magnitude. But it appears evidently from what we have said above, that it may be equally applied in all such other part's of knowledge as regard the abstract ideas of the mind, and the rela-
24
tr>
tions subsisting between them : — and since, wherever It is applied, it necessarily begets science and certainty^ we have hence chosen to denominate it the method of science ^ the better to intimate its true nature and extent.
THE END,
I
'
BC 101 D7 1307
Duncan, William
The elements of logic
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