On Sameness and Identity: A Psychological Study / Being a Contribution to the Foundations of a Theory of Knowledge

by George Stuart Fullerton

In reading this extract one cannot but admire the courtesy or wonder at the simplicity of Aristoteles. He always answers just as he should to keep the ball rolling; and he is in no wise compelled to do this under the circumstances, for the argument is loose in the extreme. Briefly stated, the reasoning is as follows:

One cannot be a whole, and cannot have parts, for then it would not be one, but many. But if it has no parts it has no beginning, middle, or end, and is formless. It is then in no place, for it cannot be in itself, since the container must be different from the thing contained; nor can it be in other, for it would have to be encircled by that other, and touched in many parts, which is impossible. It follows that it can neither be at rest nor in motion. Not in motion; for it cannot have change in itself, or it would no longer be one; nor can it have motion in place, whether circular motion upon a centre or motion from place to place; the former for the reason that circular motion implies a centre and parts around the centre; and the latter because one is in no place: and as to coming into being in anything, which may be regarded as a kind of motion, while doing this it would have to be part in and part not in, which is impossible. It cannot be at rest, for one is never in the same; to be in the same, is to be in something which is the same, and one cannot be in anything. Nor, farther, can one be the same with itself or other, nor other than itself or other. If other than itself it would not be one; and if the same with other it would be that other, and not itself. On the other hand only other can be the other of other, and not one; and the one cannot be the same with itself, for the nature of the one is not the nature of the same, since that which becomes the same with the many does not become one. Finally, one cannot be like or unlike itself or other, for likeness is sameness of affections, and sameness is not oneness; one must, however, have no affection except oneness, or it becomes more than one. It cannot, then, have the same affections as itself or other. As, for the same reason, it cannot have other affections than itself or other, it cannot be unlike.

We have here one chief error, which runs through almost the whole of the argument—is, indeed, the "Kern" of the "Pudel"—and several subsidiary errors of different kinds. Some of these last are very readily discovered, as that about the coming into being in a thing. With these, however, I am not concerned. I merely remark en passant that they may all be cleared up with a little care and accuracy, and I turn to the main error, which consists in a constant confusion of two kinds of sameness. The fact is that Parmenides is always passing from "the one," or one in the abstract, mere oneness, to "a one," or one object. These are no more identical in the strict sense than "manhood" and "a man," and in overlooking their difference he is simply confounding the first and the fourth kinds of sameness. "The one" cannot have parts, for the good reason that it is a quality taken by itself, and not a thing, which is thought as a bundle of qualities. "A one," on the other hand, may have parts, and each of these parts may be "a one" too. "A one" by no means consists of a single element, oneness, but of this element combined with others; and each such group may be distinguished from each other such group, and all be recognized as similar, or the same in a true sense of the word. The question whether one can be in a place, too, evidently has to do, not with "the one," but "a one," for spacial or temporal differences are individualizing, and distinguish a thing from another thing of the same kind. To ask whether "the one" may or may not be in a place is inadmissible.

The same error is at the bottom of the argument about the one's being in motion or at rest. The question has no significance except in reference to "a one." If we speak of "the one" as in motion, we at once put this abstract element in such a relation to other elements that we have no longer "the one" but "a one." "The one" cannot have change in itself and remain "the one," but "a one" may change a good deal and still be "a one." And without admitting the justice of the argument, that what has no parts cannot be in anything, the proof of the impossibility of motion in space may be condemned merely upon the ground that it is only "the one" which cannot have parts, while it is only "a one" which is concerned in the problem of motion. The same may be said for the argument against the one's coming into being in anything. It is only "a one" which can be thought as coming into being in a thing, and "a one" may have parts. As for the impossibility of the one's being at rest, on the ground that to be at rest, a thing must be in the same, and one cannot be in anything—this is a repetition of the former error. "A one" may be in something, as has been pointed out, even on the basis established at the outset, and it is with this, and not with "the one," that we are concerned in the problem of rest and motion.

The rest of the argument is based upon errors of a different kind, and in it one may keep to "the one" throughout, if one choose. There is, of course, no reason to think that the speaker did this. He probably here, as before, carried over to "a one," one thought as an individual thing, distinctions drawn in view of "the one," one viewed in the abstract. As some of the statements made may be true or false as one is taken in this sense or that; and particularly as the antinomy rests upon a misconception as to the nature of sameness, I will continue the analysis. What is to be proved is, first, that one cannot be the same with itself or other, or other than itself or other; and second, that it cannot be like or unlike itself or other. The position that the one, if other than itself, would not be one, and if the same with other, would be that other, is somewhat ambiguous. If "a one" is in question, it may undoubtedly be "a one" and yet be other than any particular one; and it may be the same with other—another one—without ceasing to be one, if by same we mean similar. The play upon words in "other of other" it is not necessary to consider. The conclusion that one cannot be the same with itself is based upon the supposition that sameness is a quality superadded to the other qualities of a thing; but in its first sense the word does not even serve to indicate a relation; it is merely used to point out the absence of duality. Both "a one" and "the one" may be the same with themselves perfectly well, and in saying so we do not in thought endow them with any quality not already possessed. This last error serves also as a basis to the second paradoxical position, that one cannot be like or unlike itself or other. It assumes likeness and unlikeness to be qualities added to the other qualities of things which are like or unlike.

A possible objection to my use of the term "a one" I must forestall before passing on. I have used this as synonymous with "one object." One horse is one object, and so is one part of a horse. It may be said, however, that "a one" may also be used to signify a single occurrence of oneness, as distinguished from another occurrence of oneness. That any element of consciousness may be distinguished from any similar element merely by spatial or temporal differences I have argued in the first part of my monograph. Why may not then "a one" mean the oneness of this one horse, or the oneness of this part of the horse? And if it may, can "a one" of this kind have parts any more than "the one?"

I answer, it cannot; for it is then only a particular occurrence of the quality (if I may so use the word) of oneness. But, then, if we so understand the term, the argument loses all significance. We cannot call "a one" of this kind a container or a thing contained, or talk of it as encircled by anything. We do not even try to imagine it as moving on its centre, or passing from place to place, or coming into being in anything, or being at rest in anything. Such language we use only in speaking of things. It seems to me plain that the speaker is thinking of one as a thing, and it is this that gives its charm to the bundle of paradoxes. The Eleatic "one" was always a thing and not mere unity or an occurrence of unity. My criticism of the reasoning is, I think, just. And whether Plato is responsible for the Parmenides or not, we must agree that such a confusion of "the one" and "a one" (as an object) would not be foreign to his modes of thought. His world of Ideas is peopled with "the"'s turned into "a"'s, a fact which his acute pupil Aristotle was not slow to discover.[36]

Sec. 26. Aristotle has again and again discussed with his usual keenness the kinds of sameness. He saw well enough that the word is ambiguous, and may with equal right be employed in speaking of experiences which do or do not contain an element of duality. He has pointed out that the law of non-contradiction has to do with sameness of the first kind, and not with the others.[37] His question as to "Socrates" and "Socrates sitting," his treatment of "Coriscus" and "the musical Coriscus," his statement that the white and the musical are the same when they are accidents in the same subject,[38] show that he clearly understood the significance of sameness in sense third. He gives us sense fourth when he says that things may be called the same when they belong to the same species or genus.[39] In his polemic against the Protagorean doctrine of relativity,[40] senses sixth and seventh come to the surface, though they are not very clearly or exhaustively discussed. The fallacy in the apparent possibility of attributing contradictory predicates to the same subject, from the fact that the same wine may appear sweet to one taster and not sweet to another, or at one time sweet and at another not sweet to the one palate, is laid bare in the distinction between kinds of sameness. Aristotle distinguishes between the wine itself and the sensations it produces in different persons, and he recognizes the fact that one man's perception of the "same" wine need not be wholly like that of another. But this does not imply any violation of the law of non-contradiction, for each sensation is just what it is at any instant; and the statement that the same wine is sweet and not sweet at the one moment amounts only to saying that the one object can cause dissimilar sensations in two minds at one moment. As much may be said for the non-simultaneous sensations of the one man. Sensations differing in time are two, and may differ without violating any law. In marking the fact that when we say two men perceive the same thing we do not mean that the immediate object of knowledge is in the two cases strictly one, but merely that these two objects are related in a peculiar way, Aristotle draws the line between sameness in sense first and in sense sixth. As to sense seventh. He distinguishes between the apparent and the real, and yet goes on speaking, quite in modern fashion, as though one thing could serve for both. He points out, à propos of pressing upon the eyeball and doubling the visual image, that there is a distinction between the apparent and the real, and then closes the paragraph with the remark that "to those persons who do not move their organ of vision that which is one appears one."[41] This language would certainly seem to indicate that that which is appears—or that they are the same in some strict sense of the word. The sentence reads much in the style of Mr. Spencer or Sir William Hamilton.

It appears, then, that Aristotle recognized a sameness in which there is no sense of duality, and samenesses in which two things are called the same and yet distinguished as two. Our way of expressing strict identity, however, a way which, as I have shown, does not properly express it all—seems to have misled him into finding a sort of quasi duality even here, where he knows it to be really absent. In a chapter[42] devoted to sameness and diversity, he closes his list of samenesses with the remark: "It is plain that sameness is a oneness either of two or more things with reference to their essence, or of one thing treated as two; as when you say a thing is the same with itself, for then you do treat it as two." We do employ two words, undoubtedly; but if we are really thinking a thing as itself, we are not making it dual in any sense whatever. The quotation smacks just a little of Cratylus.

Sec. 27. The sceptical arguments of Pyrrho are excellent instances of a confusion of samenesses. The argument, for example, that since an apple seen by the eye as yellow seems to the taste sweet, and to the smell as fragrant, "that which is seen is just as likely to be something else as the reality;"[43] this argument gains what little plausibility it may have from the assumption that an object seen and an object tasted are (or ought to be) the same in sense first instead of sense third.