Much, then, of what I have said of difference in the course of this chapter will apply, with a simple change of language, to resemblance as well. We go through the world, carrying on the two functions abreast, discovering differences in the like, and likenesses in the different. To abstract the ground of either difference or likeness (where it is not ultimate) demands an analysis of the given objects into their parts. So that all that was said of the dependence of analysis upon a preliminary separate acquaintance with the character to be abstracted, and upon its having varied concomitants, finds a place in the psychology of resemblance as well as in that of difference.
But when all is said and done about the conditions which favor our perception of resemblance and our abstraction of its ground, the crude fact remains, that some people are far more sensitive to resemblances, and far more ready to point out wherein they consist, than others are. They are the wits, the poets, the inventors, the scientific men, the practical geniuses. A native talent for perceiving analogies is reckoned by Prof. Bain, and by others before and after him, as the leading fact in genius of every order. But as this chapter is already long, and as the question of genius had better wait till Chapter XXII, where its practical consequences can be discussed at the same time, I will say nothing more at present either about it or about the faculty of noting resemblances. If the reader feels that this faculty is having small justice done it at my hands, and that it ought to be wondered at and made much more of than has been done in these last few pages, he will perhaps find some compensation when that later chapter is reached. I think I emphasize it enough when I call it one of the ultimate foundation-pillars of the intellectual life, the others being Discrimination, Retentiveness, and Association.
THE MAGNITUDE OF DIFFERENCES.
On [page 489] I spoke of differences being greater or less, and of certain groups of them being susceptible of a linear arrangement exhibiting serial increase. A series whose terms grow more and more different from the starting point is one whose terms grow less and less like it. They grow more and more like it if you read them the other way. So that likeness and unlikeness to the starting point are functions inverse to each other, of the position of any term in such a series.
Professor Stumpf introduces the word distance to denote the position of a term in any such series. The less like is the term, the more distant it is from the starting point. The ideally regular series of this sort would be one in which the distances—the steps of resemblance or difference—between all pairs of adjacent terms were equal. This would be an evenly gradated series. And it is an interesting fact in psychology that we are able, in many departments of our sensibility, to arrange the terms without difficulty in this evenly gradated way. Differences, in other words, between diverse pairs of terms, a and b, for example, on the one hand, and c and d on the other,[442] can be judged equal or diverse in amount. The distances from one term to another in the series are equal. Linear magnitudes and musical notes are perhaps the impressions which we easiest arrange in this way. Next come shades of light or color, which we have little difficulty in arranging by steps of difference of sensibly equal value. Messrs. Plateau and Delbœuf have found it fairly easy to determine what shade of gray will be judged by every one to hit the exact middle between a darker and a lighter shade.[443]
How now do we so readily recognize the equality of two differences between different pairs of terms? or, more briefly, how do we recognize the magnitude of a difference at all? Prof. Stumpf discusses this question in an interesting way;[444] and comes to the conclusion that our feeling for the size of a difference, and our perception that the terms of two diverse pairs are equally or unequally distant from each other, can be explained by no simpler mental process, but, like the shock of difference itself, must be regarded as for the present an unanalyzable endowment of the mind. This acute author rejects in particular the notion which would make our judgment of the distance between two sensations depend upon our mentally traversing the intermediary steps. We may of course do so, and may often find it useful to do so, as in musical intervals, or figured lines, But we need not do so; and nothing more is really required for a comparative judgment of the amount of a 'distance' than three or four impressions belonging to a common kind.
The vanishing of all perceptible difference between two numerically distinct things makes them qualitatively the same or equal. Equality, or qualitative (as distinguished from numerical) identity, is thus nothing but the extreme degree of likeness.[445]
We saw above ([p. 492]) that some persons consider that the difference between two objects is constituted of two things, viz., their absolute identity in certain respects, plus their absolute non-identity in others. We saw that this theory would not apply to all cases ([p. 493]). So here any theory which would base likeness on identity, and not rather identity on likeness, must fail. It is supposed perhaps, by most people, that two resembling things owe their resemblance to their absolute identity in respect of some attribute or attributes, combined with the absolute non-identity of the rest of their being. This, which may be true of compound things, breaks down when we come to simple impressions.
"When we compare a deep, a middle, and a high note, e.g. C, f sharp, a''', we remark immediately that the first is less like the third than the second is. The same would be true of c d e in the same region of the scale. Our very calling one of the notes a 'middle' note is the expression of a judgment of this sort. But where here is the identical and where the non-identical part? We cannot think of the overtones; for the first-named three notes have none in common, at least not on musical instruments. Moreover, we might take simple tones, and still our judgment would be unhesitatingly the same, provided the tones were not chosen too close together.... Neither can it be said that the identity consists in their all being sounds, and not a sound, a smell, and a color, respectively. For this identical attribute comes to each of them in equal measure, whereas the first, being less like the third than the second is, ought, on the terms of the theory we are criticising, to have less of the identical quality.... It thus appears impracticable to define all possible cases of likeness as partial identity plus partial disparity; and it is vain to seek in all cases for identical elements."[446]
And as all compound resemblances are based on simple ones like these, it follows that likeness überhaupt must not be conceived as a special complication of identity, but rather that identity must be conceived as a special degree of likeness, according to the proposition expressed at the outset of the paragraph that precedes. Likeness and difference are ultimate relations perceived. As a matter of fact, no two sensations, no two objects of all those we know, are in scientific rigor identical. We call those of them identical whose difference is unperceived. Over and above this we have a conception of absolute sameness, it is true, but this, like so many of our conceptions (cf. [p. 508]), is an ideal construction got by following a certain direction of serial increase to its maximum supposable extreme. It plays an important part, among other permanent meanings possessed by us, in our ideal intellectual constructions. But it plays no part whatever in explaining psychologically how we perceive likenesses between simple things.