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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?