It is said to be one of the merits of the human mind that it is capable of framing abstract ideas, and of conducting nonsensational thought. In this it is supposed to differ from the mind of animals. From Plato onward the "idea" has played a great part in the systems of idealizing philosophers. The "idea" has been, in their hands, always something noble and abstract, the apprehension and use of which by man confers upon him a quite special dignity. The thing we have to consider to-day is this: seeing that there certainly are words of which the meaning is abstract, and seeing that we can use these words intelligently, what must be assumed or inferred, or what can be discovered by observation, in the way of mental content to account for the intelligent use of abstract words?
Taken as a problem in logic, the answer is, of course, that absolutely nothing in the way of abstract mental content is inferable from the mere fact that we can use intelligently words of which the meaning is abstract. It is clear that a sufficiently ingenious person could manufacture a machine moved by olfactory stimuli which, whenever a dog appeared in its neighbourhood, would say, "There is a dog," and when a cat appeared would throw stones at it. The act of saying "There is a dog," and the act of throwing stones, would in such a case be equally mechanical. Correct speech does not of itself afford any better evidence of mental content than the performance of any other set of biologically useful movements, such as those of flight or combat. All that is inferable from language is that two instances of a universal, even when they differ very greatly, may cause the utterance of two instances of the same word which only differ very slightly. As we saw in the preceding lecture, the word "dog" is useful, partly, because two instances of this word are much more similar than (say) a pug and a great dane. The use of words is thus a method of substituting for two particulars which differ widely, in spite of being instances of the same universal, two other particulars which differ very little, and which are also instances of a universal, namely the name of the previous universal. Thus, so far as logic is concerned, we are entirely free to adopt any theory as to general ideas which empirical observation may recommend.
Berkeley and Hume made a vigorous onslaught on "abstract ideas." They meant by an idea approximately what we should call an image. Locke having maintained that he could form an idea of triangle in general, without deciding what sort of triangle it was to be, Berkeley contended that this was impossible. He says:
"Whether others, have this wonderful faculty of abstracting their ideas, they best can tell: for myself, I dare be confident I have it not. I find, indeed, I have indeed a faculty of imagining, or representing to myself, the ideas of those particular things I have perceived, and of variously compounding and dividing them. I can imagine a man with two heads, or the upper parts of a man joined to the body of a horse. I can consider the hand, the eye, the nose, each by itself abstracted or separated from the rest of the body. But, then, whatever hand or eye I imagine, it must have some particular shape and colour. Likewise the idea of a man that I frame to myself must be either of a white, or a black, or a tawny, a straight, or a crooked, a tall, or a low, or a middle-sized man. I cannot by any effort of thought conceive the abstract idea above described. And it is equally impossible for me to form the abstract idea of motion distinct from the body moving, and which is neither swift nor slow, curvilinear nor rectilinear; and the like may be said of all other abstract general ideas whatsoever. To be plain, I own myself able to abstract in one sense, as when I consider some particular parts of qualities separated from others, with which, though they are united in some object, yet it is possible they may really exist without them. But I deny that I can abstract from one another, or conceive separately, those qualities which it is impossible should exist so separated; or that I can frame a general notion, by abstracting from particulars in the manner aforesaid—which last are the two proper acceptations of ABSTRACTION. And there is ground to think most men will acknowledge themselves to be in my case. The generality of men which are simple and illiterate never pretend to ABSTRACT NOTIONS. It is said they are difficult and not to be attained without pains and study; we may therefore reasonably conclude that, if such there be, they are confined only to the learned.
"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 excellent and 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 footsteps 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," Bk. II, chap. xi, paragraphs 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," Bk. III, chap. III, paragraph 6.) But it seems that a word becomes general by being made the sign, not of an abstract general idea, but of several particular ideas, 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.
"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." *
     * Introduction to "A Treatise concerning the Principles of
     Human Knowledge," paragraphs 10, 11, and 12.
Berkeley's view in the above passage, which is essentially the same as Hume's, does not wholly agree with modern psychology, although it comes nearer to agreement than does the view of those who believe that there are in the mind single contents which can be called abstract ideas. The way in which Berkeley's view is inadequate is chiefly in the fact that images are as a rule not of one definite prototype, but of a number of related similar prototypes. On this subject Semon has written well. In "Die Mneme," pp. 217 ff., discussing the effect of repeated similar stimuli in producing and modifying our images, he says: "We choose a case of mnemic excitement whose existence we can perceive for ourselves by introspection, and seek to ekphore the bodily picture of our nearest relation in his absence, and have thus a pure mnemic excitement before us. At first it may seem to us that a determinate quite concrete picture becomes manifest in us, but just when we are concerned with a person with whom we are in constant contact, we shall find that the ekphored picture has something so to speak generalized. It is something like those American photographs which seek to display what is general about a type by combining a great number of photographs of different heads over each other on one plate. In our opinion, the generalizations happen by the homophonic working of different pictures of the same face which we have come across in the most different conditions and situations, once pale, once reddened, once cheerful, once earnest, once in this light, and once in that. As soon as we do not let the whole series of repetitions resound in us uniformly, but give our attention to one particular moment out of the many... this particular mnemic stimulus at once overbalances its simultaneously roused predecessors and successors, and we perceive the face in question with concrete definiteness in that particular situation." A little later he says: "The result is—at least in man, but probably also in the higher animals—the development of a sort of PHYSIOLOGICAL abstraction. Mnemic homophony gives us, without the addition of other processes of thought, a picture of our friend X which is in a certain sense abstract, not the concrete in any one situation, but X cut loose from any particular point of time. If the circle of ekphored engrams is drawn even more widely, abstract pictures of a higher order appear: for instance, a white man or a negro. In my opinion, the first form of abstract concepts in general is based upon such abstract pictures. The physiological abstraction which takes place in the above described manner is a predecessor of purely logical abstraction. It is by no means a monopoly of the human race, but shows itself in various ways also among the more highly organized animals." The same subject is treated in more detail in Chapter xvi of "Die mnemischen Empfindungen," but what is said there adds nothing vital to what is contained in the above quotations.
It is necessary, however, to distinguish between the vague and the general. So long as we are content with Semon's composite image, we MAY get no farther than the vague. The question whether this image takes us to the general or not depends, I think, upon the question whether, in addition to the generalized image, we have also particular images of some of the instances out of which it is compounded. Suppose, for example, that on a number of occasions you had seen one negro, and that you did not know whether this one was the same or different on the different occasions. Suppose that in the end you had an abstract memory-image of the different appearances presented by the negro on different occasions, but no memory-image of any one of the single appearances. In that case your image would be vague. If, on the other hand, you have, in addition to the generalized image, particular images of the several appearances, sufficiently clear to be recognized as different, and as instances of the generalized picture, you will then not feel the generalized picture to be adequate to any one particular appearance, and you will be able to make it function as a general idea rather than a vague idea. If this view is correct, no new general content needs to be added to the generalized image. What needs to be added is particular images compared and contrasted with the generalized image. So far as I can judge by introspection, this does occur in practice. Take for example Semon's instance of a friend's face. Unless we make some special effort of recollection, the face is likely to come before us with an average expression, very blurred and vague, but we can at will recall how our friend looked on some special occasion when he was pleased or angry or unhappy, and this enables us to realize the generalized character of the vague image.
There is, however, another way of distinguishing between the vague, the particular and the general, and this is not by their content, but by the reaction which they produce. A word, for example, may be said to be vague when it is applicable to a number of different individuals, but to each as individuals; the name Smith, for example, is vague: it is always meant to apply to one man, but there are many men to each of whom it applies.* The word "man," on the other hand, is general. We say, "This is Smith," but we do not say "This is man," but "This is a man." Thus we may say that a word embodies a vague idea when its effects are appropriate to an individual, but are the same for various similar individuals, while a word embodies a general idea when its effects are different from those appropriate to individuals. In what this difference consists it is, however, not easy to say. I am inclined to think that it consists merely in the knowledge that no one individual is represented, so that what distinguishes a general idea from a vague idea is merely th............