The elements of logic

BOOK I Of the original of our ideas

their various divisions, and the manner in which they contribute to the increase of knowledge ; with a philosophical account of the rise, progress, and nature of human language.

BOOK II Of the grounds of human

judgment, the doctrine of propositions, their use in reasoning, and division into self-evident and demonstrable.

BOOK III Of reasoning and demonstra

tion, with their application to the investigation of knowledge, and the comm»n affairs of life.

BOOK IV..~.Of the methods of invention and science, where the several degrees of evidence are examined, the notion of certainty is fixed and stated, and the parts of knowledge in which it may be attained, demonstrated at large.

DESIGNED PARTICULARLY FOR

AND TO PREPARE THE WAY TO THE STUDY OF PHILOSOPHY AND THE MATHEMATICS.

BY WILLIAM DUNCAN,

NEW-YORK:

NO. 68, WATER-STREET.

J

TO THE

RIGHT HONORABLE

STEPHEN POYNTZ, ESa

Sir,

If I take this opportunity of publishing to the world the esteem I have for a character to which learning is so greatly indebted, I hope you will not think yourself injured by such a declaration from a man that honors you, and who looks upon the liberty of putting the following work under your patronage, as one of the happy incidents of his life.

From the 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 ambitious of inscribing a treatise upon the elements of philosophy, to one, w^ho has so eminently distinguished himself by his extensive knowledge in that, as well as all the other branches of human learning ?

Your great abilities in every kind, have deservedly recommended you to the notice of your king and country, and occasioned your being courted and importuned to accept of those high offices of state, which others pursue with so much eagerness, and find it often difficult to obtain, by all the arts and endeavors of ambition. Nor have your talents been confined to the view of your country alone. Foreign nations have seen and admired you, and still speak with the greatest applauses of your wise and able conduct, when it was your province to act as a British minister abroad.

4 DEDICATION.

But the qualities of a great statesman are not those alone by which you have rendered yourself illustrious. The virtues of private life no less actuate and adorn your whole behavior, and add a new dignity to the high station to which your merit has raised you. Affability, complacency of manners, and, above all, an extensive humanity and benevolence, which takes pleasure in doing good, are distinguishing parts of your character, and have contributed no less than your other extraordinary endowments, to that universal acknowledgment which is paid you by your country.

That you may long live to be an ornament and blessing to the nation, and to enjoy the pleasure which arises frnm a consciousness of the esteera and approbation of all good mefl, is the sincere and hearty prayer of.

Sir, Your most obliged, and most obedient Humble Sei^s^ant,

W. DUNCAN.

INTRODUCTION,

Sec. I.... Importance of the Knowledge o^ Ourselves.

Of all the human sciences, that concerning man is certainly the most worth}'- of man, and the most necessary part of knowledge. We find ourselves in this world surrounded with a variety of objects : we have powers and faculties fitted to deal with them, and are happy or miserable in proportion as we know how to frame a right judgment of things, and shape our actions agreeably to the circumstances in which we are placed. No study, therefore, is more important than that which introduces us to the knowledge of ourselves. Hereby we become acquainted with the extent and capacity of the human mind ; and learning to distinguish what objects it is suited to, and in what manner it must proceed in order to compass its ends, we arrive by degrees, at that justness and truth of understanding, which is the great perfection of a rational being.

Sec. ii.... Different gradations of Perfection in Things,

If we look attentively into things, and survey them in their full extent, we see them rising one above another in various degrees of eminence. Among the inanimate parts of matter, some exhibit nothing worthy our attention : their parts seem as it were jumbled together by mere chance, nor can we discover any beauty, order, or regularity in their composition. In others, we discern the finest arrangement, and a certain elegance of contexture, that makes us affix to them a notion of worth and excellence. Thus metals, and precious stones, are conceived as far surpassing those unformed masses of earth, that lie every where exposed to view. If we trace nature onward, and pursue her through the vegetable and animal kingdoms, we find her still multiplying her perfections, and rising, by a just gradation, from mere mechanism to perception, and 'from perception, in all its various degrees, to reason and understanding.

A 2 e INTRODUCTION.

Sec. III.,.. Usefulness of Culture ^ and particularly of the Study of Logic,

But though reason be the boundary by which man is distinguished from the other creatures that surround him, yet we are far from finding it the same in all. Nor is this inequality to be wholly ascribed to the original make of men's minds, or the difference of their natural 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 remarkable, 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 powers of our minds, that we increase their capacity, and carry human reason to perfection. Where this method is followed, knowledge and strength of understanding never fail to ensue ; where it is neglected, we remain ignorant of our own worth ; and those latent qualities of the soul, by which she is fitted to survey this vast fabric of the world, to scan the heavens, and search into the causes of things, lie buried in darkness and obscurity. No part of knowledge, therefore, yields a fairer prospect of improvement, than that which takes account of the understanding, examines its powers and faculties, and shows, the ways by which it comes to attain its various notions of things. This is properly the design oi Logic, which may be justly styled the history of the human mind, inasmuch as it traces the progress of our knowledge, from our first and simple perceptions, through all their different combinations, and all those numerous deductions that result from variously comparing them one with another. It is thus that we are let into the natural frame and contexture of our own minds, and learn in what manner we ought to conduct our thoughts, in order to arrive at truth, and avoid error. We see how to build one discovery upon another, and, by preserving the chain of reasonings 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 of light and conviction.

Sec. IV.... Operations of the Mind,

But as the understanding, in advancing from one part af knowledge to another, proceeds by a just gradation. and exerts various acts, according to the different prO'

Introduction

gress it has made, logicians have been careful to note these several steps, and have distinguished them in their writings by the name of the operations of the mind. These they make four in number, and agreeably to that have divided the whole system of logic into four parts, in which these acts are severally explained, and the conduct and procedure of the mind, in its diflferent stages of improvement, regulated by proper rules and observations. Now, in order to judge how far logicians have followed nature, in this distinction of the powers of the miderstanding, 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.

Sec. y ....Perception.

First, then, we find ourselves surrounded with a variety of objects, which, acting differently on our senses, convey distinct impressions into the mind, and thereby rouse the attention and notice of the understanding. By reflecting, too, on what passes within us, we become sensible 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 present themselves one after another. This attention of the understanding to the objects acting upon it, whereby it becomes sensible of the impressions they make, is called, by logicians, j^^'^ception ; and the notices themselves, as they exist in the mind, and are there treasured up to be the materials of thinking and knowledge, are distinguished by the name oi ideas.

Sec. \i... .Judgment.

But the mind does not always rest satisfied in the bare view and contemplation of its ideas. It is of a more active and busy nature, and likes to be assembling them together, and comparing them one with another. In this complicated view oi things it readily discerns, that some agree and others disagree, and joins or separates them according to this perception. Thus, upon comparing the idea of two added to two, with the idea of four, we, at first glance, perceive their agreement, and thereupon pronounce that two and two are equal to four» Again, that white is not black, that five is less than se-

8 INTROOTCTIOK.

ven, 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 relation 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 ideas together, and joining, or disjoining them, aocording to the result of its perceptions, is what logicians term judgment.

Sec. vu.... Reasoning.

Intuition affords the highest degree of certainty ; 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 immediate application one to another ; and then it becomes necessary to find out some other ideas that will admit of this application, that by means of them we may discover the agreement or disagreement we search for. Thus the mind wanting to know the agreement or disagreement in extent between two enclosed fields, which it cannot so put together as to discover their equality or inequality by an immediate comparison, casts about for some intermediate idea, which, by being applied first to the one, and then to the other, will discover the relation it is in quest of. Accordingly it assumes some staled length, as a yard, &c. and measuring the fields one after the other, comes by that means to the knowledge of the agreement or disagreement 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 the truths it is in search of, is what we term reasoning. And here let it be observed, that the knowledge gained by reasoning is a deduction from our intuitive perceptions, and ultimately founded on them. Thus in the case before mentioned, having found l^y measuring, that one of the fields make three-score square yards, and the other only fifty-five, we thence conclude, that the first field is larger than the second. Here the 1 wo first perceptions are plainly intuitive, and gained

INTRODUCTION. 9

by an immediate application of the measure of a yard to the two fields, one after another. The conclusion, though it produces no less certain knowledge, yet differs from the others in this, that it is not obtained by an immediate comparison of the ideas contained in it, one with another, but is a deduction 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 gained, and implj'ing the various comparisons of them one with another. This is the great exercise of the human faculties, and the chief instrument by which we push on our discoveries, and enlarge our knowledge. A quickness of mind to find out intermediate ideas, and apply them skilfully in determining the relations of things, is one of the principal distinctions among men, and that which give some so remarkable a superiority over others, that we are apt to look upon them as creatures of another species.

Sec. viu..., Method,

Thus far we have traced the progress of the mind in thinking, and seen it rising by natural and easy steps from its first and simple perceptions, to the exercise of its highest and most distinguishing faculty. Let us now view it in another light, as enriched with knowledge, and stored with a variety of discoveries, acquired by a due application of its natural powers. It is obvious to consider it in these circumstances, as taking a general survey of its whole stock of intellectual acquisitions, disposing them under certain heads and classes, and tying them together, according to those connexions and dependencies it discerns between them. It often happens, in carrying on our inquiries from subject to subject, that we stumble upon unexpected truths, and are encountered by discoveries which our present train of thinking gave no prospect of bringing in our way. A man of clear apprehension, and distinct reason, who, after due search and examinatio/i, has mastered any part of knowledge, and even made important discoveries in it, beyond what he at first expected, will not sufifer his thoughts to lie jumbled together in the same confused manner as chance offered them • he will be for combining them into a regular system, wnere their mutual dependence may be easily traced, and the parts

1^ INTRODUCTION.

^eem to grow one out of another. This is that opeya-

tion of the mind, known by the name of disposition or

y,, method, and comes in the last in order, according to the

■^^ division of the logicians, as presupposing some tolera-

' ' ble measure of knowledge, before it can have an oppor-

, tunity of exerting itself in any extensive degree.

'/ Sec. IX.... Perception and Judgment terms of a -nery e.x-

tensive signification.

VVe see, then, that this fourfold distinction of the powers of the mind, in perception, judgment, reasoning, and disposition, as well as the order in which they are placed, have a real foundation in 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, ^i as believing, doubting, assenting, &c. but these are all

' *5 ; implied in the act of reasoning, in the like manner, as

> <^ comprehending, abstracting, remembering, may be re-

ferred to the first operation of the mind, or perception. N r This will appear more fully in the sequel, when we

s^ Gome to handle the several parts of logic separately : at

present we shall content ourselves with this general account of things ; only it seems necessary to observe, that perce2ytion and judgment, in the propriety of the ^- English tongue, have a much more extensive significa-

^ tion than logicians commonly allow them. We not on-

ly perceive the ideas in our own minds, but we are said also to perceive their agreement or disagreement ; and 5^ ^ hence arise the common phrases of intuitive percep-

v^' '''' tions, perceptions of truth, and of the justness of argu-

ments or proofs ; where it is manifest, that the word is applied not only to our judgments, but also to our rea- .-, ,_ sonings. In a word, whatever comes under the view of

P^; ' the mind, so as to be distinctly represented and taken

" "^ notice of, whether an idea, proposition, chain of rea-

soning, or the order and connexion of things, is thereby rendered an object of perception, and gives employment to this first and most simple of our faculties. In like manner, the wovdi, judgment, is seldom, in com- '^, mon discourse, conaued to obvious and self-evident

^ trutlis.^ It rather signifies those conjectures and guesses

7^ '' that we form, in cases which admit not of undoubted

certainty, and where we are left to determine by com- N paring the various probabilities of things. Thus a man

r^ of sagacity and penetration, who sees far into the hu-

mours and passions of mankind, and seldom mistakes

INTRODUCTION. « H

ia 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 express their nature, and the manner in which they are conversant about their several objects. This accuracy of distinguishing, where there is any the least difference, is in a peculiar manner necessary in a treatise of logic, as it is the professed design of that science, to teach us how to form clear and distinct notions of things, and thereby avoid being misled by their similitude or resemblance.

Sec. X,.. .Logic divided into Four Paris. Its usefulness and Excellency.

Having thus given a general idea of the four operations of the mind, and traced their connexion and dependence upon one another, I would next observe, that in consequence of this division of the powers of the understanding, logic is also divided into four parts, which treat severally of these acts, and give rules and directions for their due conduct and regulation. The operations themselves we have from nature ; but how to exert them justly, and employ them with advantage in the search of truth, is a knowledoe 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 thinking, and a happy talent of unravelling and throwing light upon the most obscure and intricate subjects. Others confound the easiest speculations ; their understandings seem to be formed awry, and they are incapable of either conceiving clearl}^ themselves, or making their thoughts intelligible to others. If then we set ourselves carefully to observe what it is that makes the one succeed so well, and how the others come to miscarry, these remarks will furnish us with an art of the highest use and excellency in the conduct of life. Now this is the precise business of logic — to explain the nature of the human mind, and the proper manner of conducting its several powers, in order to the attainment of truth and knowledge. It lays open those errors and mistakes we are apt through inattentions to run into, and teaches us how to distinguish between truth, and what carries only the appearance of it. By this means, we gro^^ acquainted with the nature and force of the understanding, see what things lie with-

IE , INTRODUCTION.

in its reach, where we may attain certainty and demonstration, and when we must be contented with bare probability. These considerations sufficiently evince the usefulness and benefit of this science, which ought to be established as the foundation and ground- work of all our other knowledge, if we really wish to succeed in our inquiries. But we shall now proceed to treat pf its parts separately, according to the division given of Itiem above.

ELEMENTS OF LOGtC.

CHAP. I. OF THE Or.IGIXAL OF OUR IDEAS

— 040—

Sec I Simple Aijpi'ehensioii and Ideas.

The Hist thing we observe, when we take a view of what passes within us, is that we are capable of receving impressions 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 apprehension^ 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 ideas about which our thoughts are employed. For being sensible of the impressions made upon us, and attending to the perceptions they bring, v/e can renew them again upon occasion, even v/hen the objects that first produced them are removed. Now, our are nothing else but these renewed representations of what we have at any time perceived and felt, by means of which things are again brought under the view of the mind, and seem to have a kind of existence in it. It is true, we can upon many occasions combine our ideas variously together, and thereby form to ourselves representations of things that never had an existence in nature, as wheii we fancy a centaur, or a golden mountain ; 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 in^pressions, B

It remains therefore to inquire how we come by our first notions and perceptions of things. Wh^ce does the understanding derive these original impressions and characters, which it can combine 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.

Sec. n,,.,Jlll our original Ideas derived either fiom Sensation i

First, outward objects, acting upon our senses^ rouse in us a variety of perceptions, according to the different manner in which they affect us. It is thus, that we acquire ideas of light and darkness, heat and cold, sweet and bitter, and all those other impressions which we term sensible qualities. This great source and inlet of knowledge is commonly distinguished by the name of sensation, as comprehending all the notices conveyed into the mind, by impulse made upon the organs of sense.

Sec. III.. ..Or Reflection.

But these ideas, numerous as they are, are wholly derived to us from without : there is therefore yet another source of impressions, arising from the minds 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 ideas furnished by the senses, give the mind an opportunity of exerting its several powers ; and as all our thoughts, under whatever form they appear, are attended with consciousness, hence the impressions they leave, when we come to turn the eye of the soul upon them, enrich the understanding with a new set of perceptions, no less distinct than those conveyed in by the senses. Thus it is that we get ideas of thinking, doubting, believing, willing, &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 rc^ec^«07i, and evidently presup-

ELEMENTS OF LOGIC. lo

.poses sensation ; as the impressions it furnishes are only of the various powers of the understanding, employed about perceptions already in the mind.

Sec. IV Rise cmd Progress of Human Knowledge.

These considerations, if we duly attend to them, will give us a clear and 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 evi. dently the perceptions of sense, it is plain, that all our knowledge must begin here. This, then, is the first capacity of the human mind, that it is fitted to receive the impressions made upon it by outward objects affecting the senses ; which impressions, thus derived into the understanding, and there lodged, for the view of the soul, employ it in various acts of perceiving, remembering, considering, &c. all which are attended with an internal feeling and 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 operations, 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 things, has a power of combining, modifying, and examining them in an infinite variety of lights, by which means it is enabled to enlarge the objects of its perception, and finds itself possessed of an inexhaustible stock of -materials. It is in the various comparison of these ideas, according to such combinations of them as seen» 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 extends its thoughts beyond the utmost bounds of the universe. Thus we see, as it were, at one glance, the v/hole progress of the soul, from the very first dawnings of perlt» ELEMENTS or LOGIC.

ception, till it reaches the perfection of human knowledge ; nor shall we, among all its vast stock of discoveries, or that infinite variety of conceptions 'whereof the3^consist, be able to find one original idea which is riot derived from sensation or reflection, or one complex idea v^-^hich is not made up of those original ones.

Sec. v....Diiision of our Ideas into Simple and Complex. Having thus shown how the mind comes to be first furnished with ideas, we shall next proceed to the consideration of the ideas themselves, and endeavour to give such an account of them, as will best serve to explain their several appearances, and the manner in which they are formed. It is evident, from what has been said above, that they all fall naturally under these two heads : first, those original impressions that are conveyed into the mind by sensation and reflection, and which exist there, simple, uniform, and without any shadow of variety. Secondly, those more complex notions of things, that result from the various combinations 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 nnd purposes of knowledge. These two classes comprehend our whole stock of ideas : and, when considered separately, in that order wherein they most naturally seem to offer themselves to our thoughts, will, I hope, give such a view of the conduct and manner of the mind, as may contlibute not a little to introduce us to an acquaintance with ourselves, and make uz sensible of the capacity and extent of the human intellect. We proceed, therefore, to a more particular account of this divition of our icTeaSo

Chap. II. Of Simple Ideas

Sec. I.... Simple Ideas what.

The first class of our. ideas are those which I di^- ■in<TiiiL-:h by the name of simp-e pf:rc<^ption : be cause they exist in the mind under one uniform appearance without variety or composition. For though external objects convey at once into the understanding many different ideas, all united together, and making as it were one whole ; yet the impressions themselves are evidentl}' 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 same time, from the same body ; j'et these three perceptions are as distinct in themselves, as if they all proceeded from different objects, or were exhibited to our notice at different times. We are therefore carefully to distinguish ^ij^tween our simple and primitive conceptions, and those aifferent combinations of them, which are often suggested to the mind by single objects acting upon it. The first constitute our original notices of things, and are not distinguishable into different ideas, but enter by the senses simple and unmixed. They are also the materials, out of which all the others, how complex and complicated soever, are formed ; and therefore ought deservedly to be looked on as the foundation and groundwork of our knowledge.

Sec. h Simple Ideas of Sensation.

Now if we take a survey' of these ideas, and their several divisions and classes, we shall find them all suggested to us,'^fther by our senses, or the attention of the mind to what passes within itself. Thus our notices of the different qualities 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. Colours, &c. and sounds, are conveyed in by the eyes and ears ; tastes and smells by the nose and palate ; and heat, cold, solidity, &c. by 'the touch. Besides these, there are others which make impressions on several of our senses, as extension, figure, rest, and motion, &c, the ideas of which we receive into our minds both by seeing and feeling.