11. I proceed to examine what can be alleged in DEFENCE OF THE DOCTRINE OF ABSTRACTION, and try if I can discover what it is that inclines the men of speculation to embrace an opinion so remote from common sense as that seems to be. There has been a late deservedly esteemed philosopher who, no doubt, has given it very much countenance, by seeming to think the having abstract general ideas is what puts the widest difference in point of understanding betwixt man and beast. "The having of general ideas," saith he, "is that which puts a perfect distinction betwixt man and brutes, and is an excellency which the faculties of brutes do by no means attain unto. For, it is evident we observe no foot-steps in them of making use of general signs for universal ideas; from which we have reason to imagine that they have not the FACULTY OF ABSTRACTING, or making general ideas, since they have no use of words or any other general signs." And a little after: "Therefore, I think, we may suppose that it is in this that the species of brutes are discriminated from men, and it is that proper difference wherein they are wholly separated, and which at last widens to so wide a distance. For, if they have any ideas at all, and are not bare machines (as some would have them), we cannot deny them to have some reason. It seems as evident to me that they do, some of them, in certain instances reason as that they have sense; but it is only in particular ideas, just as they receive them from their senses. They are the best of them tied up within those narrow bounds, and have not (as I think) the faculty to enlarge them by any kind of ABSTRACTION." Essay on Human Understanding, II. xi. 10 and 11. I readily agree with this learned author, that the faculties of brutes can by no means attain to ABSTRACTION. But then if this be made the distinguishing property of that sort of animals, I fear a great many of those that pass for men must be reckoned into their number. The reason that is here assigned why we have no grounds to think brutes have abstract general ideas is, that we observe in them no use of words or any other general signs; which is built on this supposition--that the making use of words implies the having general ideas. From which it follows that men who use language are able to ABSTRACT or GENERALIZE their ideas. That this is the sense and arguing of the author will further appear by his answering the question he in another place puts: "Since all things that exist are only particulars, how come we by general terms?" His answer is: "Words become general by being made the signs of general ideas."--Essay on Human Understanding, IV. iii. 6. But [Note. 1] it seems that a word becomes general by being made the sign, not of an ABSTRACT general idea, but of several particular ideas [Note. 2], any one of which it indifferently suggests to the mind. For example, when it is said "the change of motion is proportional to the impressed force," or that "whatever has extension is divisible," these propositions are to be understood of motion and extension in general; and nevertheless it will not follow that they suggest to my thoughts an idea of motion without a body moved, or any determinate direction and velocity, or that I must conceive an abstract general idea of extension, which is neither line, surface, nor solid, neither great nor small, black, white, nor red, nor of any other determinate colour. It is only implied that whatever particular motion I consider, whether it be swift or slow, perpendicular, horizontal, or oblique, or in whatever object, the axiom concerning it holds equally true. As does the other of every particular extension, it matters not whether line, surface, or solid, whether of this or that magnitude or figure.
[Note 1: "TO THIS I CANNOT ASSENT, BEING OF OPINION," edit of 1710.]
[Note 2: Of the same sort.]
12. EXISTENCE OF GENERAL IDEAS ADMITTED.--By observing how ideas become general we may the better judge how words are made so. And here it is to be noted that I do not deny absolutely there are general ideas, but only that there are any ABSTRACT GENERAL IDEAS; for, in the passages we have quoted wherein there is mention of general ideas, it is always supposed that they are formed by ABSTRACTION, after the manner set forth in sections 8 and 9. Now, if we will annex a meaning to our words, and speak only of what we can conceive, I believe we shall acknowledge that an idea which, considered in itself, is particular, becomes general by being made to represent or stand for all other particular ideas of the SAME SORT. To make this plain by an example, suppose a geometrician is demonstrating the method of cutting a line in two equal parts. He draws, for instance, a black line of an inch in length: this, which in itself is a particular line, is nevertheless with regard to its signification general, since, as it is there used, it represents all particular lines whatsoever; so that what is demonstrated of it is demonstrated of all lines, or, in other words, of a line in general. And, as that particular line becomes general by being made a sign, so the name LINE, which taken absolutely is PARTICULAR, by being a sign is made GENERAL. And as the former owes its generality not to its being the sign of an abstract or general line, but of ALL PARTICULAR right lines that may possibly exist, so the latter must be thought to derive its generality from the same cause, namely, the VARIOUS PARTICULAR lines which it indifferently denotes. [Note.]
[Note: "I look upon this (doctrine) to be one of the greatest and most valuable discoveries that have been made of late years in the republic of letters."--Treatise of Human Nature, book i, part i, sect. 7. Also Stewart's Philosophy of the Mind, part i, chapt. iv. sect. iii. p. 99.]
13. ABSTRACT GENERAL IDEAS NECESSARY, ACCORDING TO LOCKE.--To give the reader a yet clearer view of the nature of abstract ideas, and the uses they are thought necessary to, I shall add one more passage out of the Essay on Human Understanding, (IV. vii. 9) which is as follows: "ABSTRACT IDEAS are not so obvious or easy to children or the yet unexercised mind as particular ones. If they seem so to grown men it is only because by constant and familiar use they are made so. For, when we nicely reflect upon them, we shall find that general ideas are fictions and contrivances of the mind, that carry difficulty with them, and do not so easily offer themselves as we are apt to imagine. For example, does it not require some pains and skill to form the general idea of a triangle (which is yet none of the most abstract, comprehensive, and difficult); for it must be neither oblique nor rectangle, neither equilateral, equicrural, nor scalenon, but ALL AND NONE of these at once? In effect, it is something imperfect that cannot exist, an idea wherein some parts of several different and INCONSISTENT ideas are put together. It is true the mind in this imperfect state has need of such ideas, and makes all the haste to them it can, for the CONVENIENCY OF COMMUNICATION AND ENLARGEMENT OF KNOWLEDGE, to both which it is naturally very much inclined. But yet one has reason to suspect such ideas are marks of our imperfection. At least this is enough to show that the most abstract and general ideas are not those that the mind is first and most easily acquainted with, nor such as its earliest knowledge is conversant about."--If any man has the faculty of framing in his mind such an idea of a triangle as is here described, it is in vain to pretend to dispute him out of it, nor would I go about it. All I desire is that the reader would fully and certainly inform himself whether he has such an idea or no. And this, methinks, can be no hard task for anyone to perform. What more easy than for anyone to look a little into his own thoughts, and there try whether he has, or can attain to have, an idea that shall correspond with the description that is here given of the general idea of a triangle, which is NEITHER OBLIQUE NOR RECTANGLE, EQUILATERAL, EQUICRURAL NOR SCALENON, BUT ALL AND NONE OF THESE AT ONCE?
14. BUT THEY ARE NOT NECESSARY FOR COMMUNICATION.--Much is here said of the difficulty that abstract ideas carry with them, and the pains and skill requisite to the forming them. And it is on all hands agreed that there is need of great toil and labour of the mind, to emancipate our thoughts from particular objects, and raise them to those sublime speculations that are conversant about abstract ideas. From all which the natural consequence should seem to be, that so DIFFICULT a thing as the forming abstract ideas was not necessary for COMMUNICATION, which is so EASY and familiar to ALL SORTS OF MEN. But, we are told, if they seem obvious and easy to grown men, IT IS ONLY BECAUSE BY CONSTANT AND FAMILIAR USE THEY ARE MADE SO. Now, I would fain know at what time it is men are employed in surmounting that difficulty, and furnishing themselves with those necessary helps for discourse. It cannot be when they are grown up, for then it seems they are not conscious of any such painstaking; it remains therefore to be the business of their childhood. And surely the great and multiplied labour of framing abstract notions will be found a hard task for that tender age. Is it not a hard thing to imagine that a couple of children cannot prate together of their sugar-plums and rattles and the rest of their little trinkets, till they have first tacked together numberless inconsistencies, and so framed in their minds ABSTRACT GENERAL IDEAS, and annexed them to every common name they make use of?
15. NOR FOR THE ENLARGEMENT OF KNOWLEDGE.--Nor do I think them a whit more needful for the ENLARGEMENT OF KNOWLEDGE than for COMMUNICATION. It is, I know, a point much insisted on, that all knowledge and demonstration are about universal notions, to which I fully agree: but then it doth not appear to me that those notions are formed by ABSTRACTION in the manner PREMISED--UNIVERSALITY, so far as I can comprehend, not consisting in the absolute, POSITIVE nature or conception of anything, but in the RELATION it bears to the particulars signified or represented by it; by virtue whereof it is that things, names, or notions, being in their own nature PARTICULAR, are rendered UNIVERSAL. Thus, when I demonstrate any proposition concerning triangles, it is to be supposed that I have in view the universal idea of a triangle; which ought not to be understood as if I could frame an idea of a triangle which was neither equilateral, nor scalenon, nor equicrural; but only that the particular triangle I consider, whether of this or that sort it matters not, doth equally stand for and represent all rectilinear triangles whatsoever, and is in that sense UNIVERSAL. All which seems very plain and not to include any difficulty in it.
16. OBJECTION.--ANSWER.--But here it will be demanded, HOW WE CAN KNOW ANY PROPOSITION TO BE TRUE OF ALL PARTICULAR TRIANGLES, EXCEPT we have first seen it DEMONSTRATED OF THE ABSTRACT IDEA OF A TRIANGLE which equally agrees to all? For, because a property may be demonstrated to agree to some one particular triangle, it will not thence follow that it equally belongs to any other triangle, which in all respects is not the same with it. For example, having demonstrated that the three angles of an isosceles rectangular triangle are equal to two right ones, I cannot therefore conclude this affection agrees to all other triangles which have neither a right angle nor two equal sides. It seems therefore that, to be certain this proposition is universally true, we must either make a particular demonstration for every particular triangle, which is impossible, or once for all demonstrate it of the ABSTRACT IDEA OF A TRIANGLE, in which all the particulars do indifferently partake and by which they are all equally represented. To which I answer, that, though the idea I have in view whilst I make the demonstration be, for instance, that of an isosceles rectangular triangle whose sides are of a determinate length, I may nevertheless be certain it extends to all other rectilinear triangles, of what sort or bigness soever. And that because neither the right angle, nor the equality, nor determinate length of the sides are at all concerned in the demonstration. It is true the diagram I have in view includes all these particulars, but then there is not the least mention made of them in the proof of the proposition. It is not said the three angles are equal to two right ones, because one of them is a right angle, or because the sides comprehending it are of the same length. Which sufficiently shows that the right angle might have been oblique, and the sides unequal, and for all that the demonstration have held good. And for this reason it is that I conclude that to be true of any obliquangular or scalenon which I had demonstrated of a particular right--angled equicrural triangle, and not because I demonstrated the proposition of the abstract idea of a triangle And here it must be acknowledged that a man may consider a figure merely as triangular, without attending to the particular qualities of the angles, or relations of the sides. So far he may abstract; but this will never prove that he can frame an abstract, general, inconsistent idea of a triangle. In like manner we may consider Peter so far forth as man, or so far forth as animal without framing the fore-mentioned abstract idea, either of man or of animal, inasmuch as all that is perceived is not considered.
17. ADVANTAGE OF INVESTIGATING THE DOCTRINE OF ABSTRACT GENERAL IDEAS.--It were an endless as well as an useless thing to trace the SCHOOLMEN, those great masters of abstraction, through all the manifold inextricable labyrinths of error and dispute which their doctrine of abstract natures and notions seems to have led them into. What bickerings and controversies, and what a learned dust have been raised about those matters, and what mighty advantage has been from thence derived to mankind, are things at this day too clearly known to need being insisted on. And it had been well if the ill effects of that doctrine were confined to those only who make the most avowed profession of it. When men consider the great pains, industry, and parts that have for so many ages been laid out on the cultivation and advancement of the sciences, and that notwithstanding all this the far greater part of them remains full of darkness and uncertainty, and disputes that are like never to have an end, and even those that are thought to be supported by the most clear and cogent demonstrations contain in them paradoxes which are perfectly irreconcilable to the understandings of men, and that, taking all together, a very small portion of them does supply any real benefit to mankind, otherwise than by being an innocent diversion and amusement--I say the consideration of all this is apt to throw them into a despondency and perfect contempt of all study. But this may perhaps cease upon a view of the false principles that have obtained in the world, amongst all which there is none, methinks, has a more wide and extended sway over the thoughts of speculative men than [Note.] this of abstract general ideas.