Resemblance and Identity

Wehave explained general ideas as resting on the notion of resemblance. But resemblance itself and its companion, difference, are relations which have been no small stumbling-block to theories of knowledge, and therefore demand our attention.

Though the term resemblance admits of confusion, and therefore demands analysis, the facts of resemblance can only be analysed a very little way. It is simple matter of fact that I see resemblances and differences, but I cannot resolve this characteristic of the world into anything more simple. One step, however, I can sometimes take. Beginning with a vague perception of resemblance, I can analyse out a common quality in two objects presented to me, and see that while precisely alike in that quality they are different in other respects. That is to say, I can resolve likeness into identity ¹ in difference. Two architectural styles, two pictures, two faces, two landscapes, two constitutions, two historical situations resemble one another; they “impress” us as alike, we vaguely say. Then comes analysis, and points out a common quality—the same development of constructive knowledge, the same technique, pose of the head, prevalence of democratic sentiment, decay of civic morality in the presence of a spirit of faction. Now it is explained—the common quality is clear, and the slight mystery which attends vague resemblance is dispersed; the remainder is mere difference, and does not interest us.

Which, now, is the ultimate of these relations—likeness or identity? In the instances given we proceed from a knowledge of likeness to that of identity, a fact which may tell either way. We may infer that identity is an abstraction of likeness, an idea derived from reflecting on likeness and difference, seeing that most likeness involves or includes difference, and conceiving the likeness in abstraction from the difference. Or we may urge that if vague knowledge begins with likeness it rests really on identity. Likeness is always logically analysable into identity in difference, and therefore these ideas are its logical basis, that is, its ultimate basis in fact.

Both views, I believe, are too extreme, and they fail in distinguishing the perception of likeness and identity on the one side from the analysis of these ideas on the other. Both likeness and identity are matters of immediate apprehension, that is, reality presents us with both relations. If I consider the colour, shape, weight, “feel,” etc., of a number of small shot run from one mould, they are all in these respects identical to my apprehension. A minutely accurate balance might detect a difference of a milligramme, but that is no difference to my hand; or a micrometer a difference of a millimètre, but that is no difference to my eye. The relation of perfect resemblance is thus given to my apprehension whether or not the shot, regarded as something physical (i.e. as existing apart from my consciousness or for some higher consciousness), resemble one another thus perfectly. The idea of identity is generalised from these resemblances, and they are just as truly perfect resemblances of the object as given as the rheumatism of an amputated leg is really pain. Just as the idea of identity is generalised from apprehension, so is that of mere likeness. Blue or green are something alike; orange and red are something alike; those two faces, figures, sounds are nearly alike. All these are facts that I perceive long before I can analyse them; and even when I can analyse them the original likeness in general remains, ¹ i.e. the likeness though analysed into identity and difference is not analysed away. Likeness is not an unreal or even an evanescent relation of which identity in difference is the only genuine or permanent ground. Where there is likeness there is generally ² identity in difference; but the likeness does not in the least bit cease to be real because it is then analysed. Brown does not look less like Jones because you have discovered that each has a Roman nose and a receding chin.

So far our result is that relations both of identity and of likeness are matter of apprehension. Both terms will then be the names of ideas generalised from apprehension. The ideas thus formed are, as the next step, compared, and the result of the comparison, about the method of which we shall have more to say presently, is to make clear the relation between them. Thus identity becomes known as likeness without difference, and likeness as identity plus difference. These definitions or analyses of the two terms mutually involve one another, and hence make it equally plausible to argue that either is ultimate. The truth is that the given is the ultimate; that both are given, but that they are analysed and understood by comparison with one another.

General ideas rest on comparison, and comparison reveals sometimes identity and sometimes likeness. Which, then, does an idea contain? “A” is a general content suggested of reality by an idea. Then does A mean A₁ A₂ A₃ all identical with one another; or does it mean A a a and α, all resembling one another? It is reasonable to suppose that idea follows comparison, and that thus there will be two classes of general ideas to correspond with the twofold relation of comparison. Perhaps it seems difficult at first to attach any meaning to a general content which shall include not merely identical but similar facts within it. For, it may be asked, where are we to stop? If a heap is a hundred grains, “more or less,” i.e. if it refers to a hundred grains or any similar collection, do ninety-nine grains form a heap, do ninety-eight, and so on, as the puzzle goes? In short, there is nothing precise or definite in our content. But this is just what we really find. There is a complete want of precision and definiteness about the majority of our ideas; they are kinglets whose territories are very ill defined, and whose boundaries are the happy hunting-ground of the sophist, the punster, the rhetorician, and many other knaves and fools. The idea is really king only in his own capital. The centre of the territory is definite enough. This is just; but push the principles of the action a step—is that just? We are not quite sure. A step further—that is unjust—clear daylight again. Now it is night. Now it is morning: both propositions are equally certain. What was it just between times? The only lesson that so many weary controversies have left us is that ideas are not as definite as we could wish. We make them, if we are honest, as definite as we can, but that is not saying much. There are ideas definite and ideas indefinite, and one object of scientific reflection is to transfer as many as possible from the second to the first class. The definite idea suggests a content which is identical in all instances; the indefinite idea one of which all instances resemble one another. There are two sources of vagueness in the mass of our ideas. The first is that they are often generalised from contents which are not identical. Two facts, M and N, resemble one another in p, and p being asserted of reality, becomes the content of a general idea. But, now, suppose the p₁ of M and the p₂ of N are not identical, but only alike? Then the general idea p already has a loosely defined content, which, at least, may alternate between p₁ and p₂, and over all the distance between them. That is to say, the mind, in applying such an idea, will consider anything to be “a case of p” which has either of the qualities p₁ or p₂, or has any quality p which is “something between” the two. In all this the mind is probably not conscious of any difference between p₁ and p₂, the distinction being drawn by later analysis. It is not so much that we take them for identical, as that we do not at this point distinguish between identity and resemblance. And here is our second source of vagueness. Supposing p a real identity (i.e. a resemblance in which no microscopic analysis can find a difference), it does not follow that it will be made a content of a definite idea. If the mind which asserts it of reality does not distinguish between identity and resemblance, it does not remain for that mind a clear cut content, nor will its application be restricted to contents exactly alike it. It will be “loosely” applied.

A vague idea, then, is one which suggests of reality a quality more or less resembling X; or, if you prefer it, which suggests that contents more or less like X qualify reality as an indefinite number of points. A definite idea suggests that X and contents exactly like X are found in reality. Ideas ought to be definite, but mostly are indefinite. The postulates of definiteness in an idea are, first, the general condition that the mind should have arrived at the distinction between identity and likeness, or at least should not assert them indiscriminately; and second, that in the special contents concerned analysis should have arrived at a point of identity. This definiteness is not reached all at once. Just as the general condition of definiteness is reached by stages, so with the actual definiteness of any special content. If p is common to M and N, p is a temporary resting-place for the mind; but further analysis may show (as above) that M had p₁, and N p₂; that they only resembled one another, and that their resemblance was based on a common point π. The same process may or may not be repeated; but the goal is in any case a point of identity resisting further analysis, asserted with absolute definiteness, and applied always with identical meaning.

But this is not all. As we discriminate degrees or forms of likeness, we become able to make comparisons or sub-sumptions which are not identical but yet are definite, Identity is only one case of definite likeness. It is likeness without any difference at all. Substitute for it a resemblance admitting a definite degree or kind of difference, and we still get a definite assertion. Twice as loud, twice as tall, fix, or attempt to fix, relations to some given content which are definite and yet not relations of identity. But in getting definite ideas we are able to assert with precision both identity and kind or degree of resemblance, identity itself being only a special kind of resemblance, viz. the maximum up to which degrees are measured. The advance of definition thus substitutes for a vague, indiscriminate identity-or-likeness, a precise determination of resemblance, according to kinds, one of which is identity. A kind of resemblance is itself merely a general idea formed by a combination of comparisons. “This is brighter than that.” Here is first a recognition of resemblance or difference—it does not matter which we call it. Then the resemblance itself is compared with other resemblances, and a general idea “brighter” is formed, differentiated from other resemblances to the same qualitative content, such as “less bright,” or, again, “as bright, but of different colour.” Again, “brighter” breaks up by analysis into “much brighter” and “a little brighter,” and so on. How far we can carry analysis by such simple comparison depends on circumstances. We shall see later on that a mediate comparison is necessary when we require mathematical exactitude. Meanwhile there is progress in another direction. “Brighter, louder, heavier,” all involve the general relation expressed by the word“more,” and “more” and “less” have also a certain community of content, which we express by saying that they give quantitative difference as distinct from qualitative. These are the summa genera of resemblance and difference into which all our apprehensions of likeness and difference fall. Thus the conceptions of quality and quantity are simple generalisations of the various resemblances which we find given among the facts of apprehension. ¹

We can now understand that an idea may be definite and yet admit of much difference. Take a content like “green.” All greens are not identical; but green is a definite idea, for one green differs from another in certain determinate directions, e.g. in saturation or in intensity. Greens may also differ in actual greenness, in quality proper, within certain limits. Now the idea green asserts or suggests any content within these limits indiscriminately, and if you say “The sea is green,” you assert only that the colour of the sea falls within these limits, without assigning it a more definite place within them. Nevertheless, so far as this is concerned, the idea is precise. It is indefinite only so far as its limits in any direction are not precisely fixed. For example, where is the minimum saturation point below which green becomes white? or where is the line which marks it off from blue and yellow? In neither direction can the limit be fixed with absolute precision. But a very small step in either direction along the spectrum will make us at once say “blue,” or “green,” as the case may be. The idea is definite in this direction in proportion to the narrowness of this debatable ground; and, as we have already seen, the existence of such debatable ground does not in the least make green less truly green, or blue less truly blue. ¹

It may be said (and up to the present chapter we have ourselves assumed it) that what makes an idea definite is the presence of some point of identity. In all green there is an actual point of identity “which makes it green.” In all colour there is a more attenuated identity which makes it colour. This may be so, but we still require analysis to point it out. If I ask you what then is the common point in all colour, you will answer probably, “Why, it's—colour.” You will not be readily able to isolate this “colour” in the concrete colours given you, and say what part of the given is to be set down to its account. If you make a further effort to define it, you will come back to the point you started from, and say that it is precisely that in which this tint is identical with all other colours, as against those properties which it shares with some only. Meanwhile, if you have studied the matter a little, you will be able to tell me what resemblances this tint exhibits. It has its own place in the circle of colours somewhere between red and blue; it has such a degree of saturation, and so much luminosity—all of them definite points of comparison between it and other colours, and the general idea colour includes all contents differing from one another in these ways only. Now, I am not arguing against the existence of an identical quality in all colours, but I say that in the existing state of our knowledge such an identity is less definite and less easily assignable than the resemblances and differences in which all colours stand to one another; and that the colours themselves, in their analysed relations of likeness and difference, form the most definite content for the general name colour. ¹ I conclude that when you say that a thing has colour, you assert of it a content which may vary within the whole range thus specified; and the idea of colour taken by itself suggests of reality an indefinite number of facts resembling one another in certain definite ways.

To put the point in a slightly different way. Admitting an identical character in all colours, and calling it, without attempt at definition, simply colour, we must admit that in the different tints which we see this common character is itself modified. Colour itself is differently qualified in red or in green. The scalene and the equilateral differ as triangles in those very features, relations of sides and angles, on which their character as triangles depends. ² Contrast two patches of sunlight which differ only in the place on which they fall, or two notes which are distinct only in time. Here the time, place, or other characteristics qualify the whole which is given, but can scarcely be said to modify the colour or the sound, as colour or sound. We have come once more on the contrast between specific modifications on the one hand and mere differences of context on the other. The first may be said to qualify the general content itself; the second, to be further qualities of the sensible wholes to which they belong. Now we cannot draw a hard and fast line between the two cases. The merest difference of context tends to assume a specific value, and to become a modifying character. Thus the texture of the coloured object would be naturally taken as mere matter of context; but the scarlet of a smooth ivory ball and of a soldier's coat, scarcely “look” the same. Even the heat of the sun and the heat of the fire might be said to have distinguishing characteristics; and the “same” note on two differently built instruments will, of course, present distinct peculiarities. It is enough to notice that the different “cases” in which a content may be present vary in the way in which they affect the content itself; and that in proportion as this affection diminishes, the easier it becomes to get at a distinct general content of precisely similar character in all cases in which it is realised. While in the converse cases the general idea tends to mean a series of contents which, while retaining a common character, must also differ in point of that character along certain definable lines.

To sum up. Both identity and likeness (of all kinds) are relations originally given in apprehension. Ideas may be founded upon either, and so long as different forms of likeness are not distinguished, ideas are vague; that is, the mind does not discriminate their contents from any similar contents. Forms of resemblance are compared, and give rise to ideas of them, discriminating different forms with increasing accuracy, and also discerning resemblances, with the result that differences are finally grouped under the heads of quantity and quality, differences of degree coming under both. Differences in any point admit also of being classified according to the nearness or remoteness of the resemblance, and identity is distinguished as the maximum of resemblance. When these distinctions are clear, ideas also become definite; their contents are either identical in every application, or vary within known limits, which can be defined with an exactitude varying according to the nature of the subject and our knowledge of it. We thus get two great genera of definite general ideas, those with an identical content ¹ (e.g. the middle C of a piano, cobalt blue), and those admitting definitely ascertained differences (e.g. a musical note, colour). The knowledge of identical contents is the basis of measurement, and, therefore, of mathematics; the knowledge of degrees of quality, and affinities among qualities, is the basis of any systematic science of nature. And this definiteness of knowledge rests simply on further combinations of the comparative judgment applied to the comparative relation, as well as to the things compared.

The simplest instances of likeness of any kind, exact or inexact, are, of course, those which we call purely “sensible”—the taste of two sorts of jam, the matching of two colours, the “identical” pitch of two notes. We have already seen that some degree of analysis is requisite for the detection of these simple resemblances, and it is a further stage of analysis—further, because dealing with a more attenuated character of the whole—when we attend to resemblances of quantity, equality, or proportion. Yet another stage of complexity is reached where the data of comparison are themselves complex. The contents compared are then results formed either by construction or analysis, and on this the analysis which constitutes the comparison has to supervene. Thus the judgment, “In these two triangles the sides about the equal angles are reciprocally proportional,” involves attention first to each pair of sides, and then (abstracting from the actual lengths, etc., of the sides) the selection of the proportions of each pair as the point of comparison. Construction and analysis may go to any degree of complexity in affording us points of resemblance. Thus it is right to say that two systems of forces which produce the same motion have a common character. But what is this character? Not any one direction or quantity of any one force. We may have only one force in the first system and a hundred in the second, or we may have a hundred forces in each, acting at first sight in all manner of directions. There is still this one common point—that, if we sum up and consider together the totals of the forces, their directions and amounts, there will be as between all the components of each total a relation expressed by the fact that their resultant is of such an amount and direction, and this resultant will be common to the two. In cases like this we can in some degree “reconstruct” the totals, assigning their elements and the acts by which they are brought into comparison. But who can analyse resemblances of face, of personality, of style, of national character? The data here, the constructions and the analyses, are too subtle for recognition; but there is no need to regard them as fundamentally different. We may then look on analysis as an essential feature in comparison, and construction as commonly concerned in it; and calling those comparisons “sensible” which rest on the simplest and slightest analysis, we may say that resemblances become “intelligible” in proportion as the constructions and analyses involved increase in complexity.

A word must be added here as to the senses, already referred to, of the term identity. I have used it in this chapter as a synonym for precise or exact resemblance (Gleichheit), and I think that that usage is in English unavoidable. ¹ But I should be sorry to give any colour to the charge of confusing this kind of identity with that which we predicate of one thing in two relations, or of one person at different periods of his life (Identität). Quite different contents of perception or thought are before us in these cases, according to my view, which I will state, avoiding controversy as far as I can. ² We have then three relations.