x. But here the difficulty meets us that, if we are really talking

about only the one x, we have said quite all we have to say in merely saying x; while if, to complete our thought, we must add the second x, we have not an identical proposition, in any strict sense of the word, but a synthetic one. It is easy enough in words to divide a "thing" from "itself," since the words "thing" and "itself" are two, and may readily be distinguished. In the same way it is easy in words to affirm a thing to be and not to be at the one time. There is no law to prevent one's stringing sounds together as he may please. But if one is interested not in the mere symbols, but in that which they are supposed to represent, one must see that the expression "x is x," to be a significant proposition, must have a subject and a predicate, and affirm a relation between them. Here we have, by hypothesis, strictly one thing for subject and predicate. The proposition "x is x" must then consist of one thing and a relation between it--which is about as significant as the statement that a door may consist of one side and a relation between it. Between what? One side.[29] Every form of proposition employed to give expression to the law of identity implies this difficulty. Whether we say "x is x," or "whatever is is," or "everything is identical with itself," our proposition, taken literally, is either useless (since we have said all we have to say in mentioning the subject alone), or untrue (since we add a new element in adding the predicate).

[29] This abnormal door has its parallel in the now discredited _causa sui_. Note the following from Descartes: "De même, lorsque nous disons que Dieu est par soi, nous pouvons aussi à la vérité entendre cela négativement, comme voulant dire qu'il n'a point de cause; mais si nous avons auparavant recherché la cause pourquoi il est ou pourquoi il ne cesse point d'être, et que, considérant l'immense et incompréhensible puissance qui est contenue dans son idée, nous l'ayons reconnue si pleine et si abondante qu'en effet elle soit la vraie cause pourquoi il est, et pourquoi il continue ainsi toujours d'être, et qu'il n'y en puisse avoir d'autre que celle-là, nous disons que Dieu est _par soi_, non plus négativement, mais au contraire très positivement. Car, encore qu'il n'est pas besoin de dire qu'il est la cause efficiente de soi-même, de peur que peut-être on n'entre en dispute du mot; néanmoins, parce que nous< voyons que ce qui fait qu'il est par soi, ou qu'il n'a point de cause différente de soi-même, ne procède pas du néant, mais de la réelle et véritable immensité de sa puissance, il nous est tout a fait loisible de penser qu'il fait en quelque façon la même chose a l'égard de soi-même que la cause efficiente à l'égard de son effet, et partant qu'il est par soi positivement."--Réponses aux Premières Objections.

It is then sufficiently evident that the forms used to express the logical law of identity do not, taken strictly, express at all the kind of sameness with which we are now concerned, but, on the contrary, something very different. We are considering a sameness in which there is no duality whatever, but our expressions would seem to have no meaning except as indicating a relation between two. They are then significant, not as _expressing_ sameness of the first kind, but as _suggesting_ it, and this they certainly serve to do. The reason for this I shall try to give in a moment.

It has been said that in the other kinds of sameness we always find the notion of similarity. When, however, we distinguish two things as two and yet recognize them as similar, we must have what I may call a mixed experience of likeness and unlikeness. In any two things compared, the degrees of likeness and unlikeness may vary, and we may fix attention upon similarities or differences. In proportion to the attention given to dissimilar elements will the two objects be clearly distinguished from each other and discriminated as two. If the purpose in hand does not require a careful attention to differences, and if what is prominent in mind is the likeness of the two objects, the sense of duality may fall into the background, and the man pass readily from one object to the other with little consciousness that he has made a change. As I now look at the two ink-stands on my desk, I clearly recognize them as two and yet as of the one kind. Here I am as distinctly aware that they are two as I am that they are in some respects the same. But in some of the kinds of sameness I have described this sense of duality falls more into the shade. When I speak of seeing the same ink-stand twice, or when I call up in memory an ink-stand once seen, I am likely, unless I take particular pains to reflect upon my mental operation, to have but a dim realization of the fact that I have two distinct things to deal with. How those who distinguish between the immediate and the mediate objects of knowledge have a tendency to forget their distinction, and to pass unconsciously from one to the other, I have dwelt upon sufficiently.

Suppose, now, that from two objects which we recognize as similar and yet distinct, we abstract one by one the elements which differ. So long as there is any difference left, we still have "identity in diversity"--similarity in the ordinary sense of the term, which implies a recognition of two things as two. When, however, the last difference disappears, all sense of duality must disappear with it, for any division or distinction within what remains is inadmissible. Things which are distinguished are distinguished through some difference. A sense of duality implies a discrimination between two, and where it is impossible to discriminate duality vanishes. Similarity, as we commonly use the word, must then disappear with the disappearance of all dissimilarity between two objects. I say "between two objects" in default of a better expression, for, of course, we have at this point no longer two objects. My meaning is, however, sufficiently plain. A sense of duality implies difference, and similarity, as commonly understood, implies duality. The similarity will then take itself off with the last difference.

It may be objected that _a consciousness of duality_ and _a consciousness of similarity_ are only possible on the ground that I mention, but that duality and similarity themselves may really obtain when no difference between two is perceptible. But a moment's reflection will make it plain that one who speaks thus is simply supplying in himself the elements that he is supposing absent in the case of another. If he uses the words "duality" and "similarity," and they really mean anything to him, they imply all that I have said. He cannot represent to himself two things at all without distinguishing them from each other, and he can not distinguish them from each other unless they differ in some way. If, then, he speak of two things as being two and yet completely indistinguishable, he is, taken literally, talking nonsense. He may, of course, mean the misleading phrase to be understood as indicating something not actually expressed by the words. He may mean to point out that, under certain circumstances, in which he has an experience which he calls a recognition of two objects as two and as similar, he has reason to think another mind has an experience partly like and partly unlike his own--like in as much as it contains what corresponds to that which is _common_ to the two objects he has in mind; unlike in as much as it contains nothing which corresponds to the elements which make it possible for him to recognize two objects. It is this that is in his mind when he speaks of thinking of two objects as really two and yet indistinguishable to this man or that. If, however, the expression "two things may be indistinguishable" is used to indicate this experience, it should be carefully borne in mind that the proposition must not be taken literally, for the good reason that the subject and predicate are not in the one consciousness. The "two objects" are in the mind of Smith, and the "indistinguishable" element in the mind of Jones. When we speak of two men as seeing the same thing, I have shown that we are using the word same in a looser sense which should never be confounded with the stricter sense. Strictly speaking, then, the "two things" are never indistinguishable, but that which corresponds to the two things in a consciousness from which all recognition of duality is absent. That one man may have a consciousness of duality while another man has not, and that these two experiences may be related as the experiences of different minds are related when we say they are experiencing the same thing, no one would care to dispute. Should a man say that he can think of himself as unable to distinguish two things which are nevertheless two, the case, would not be materially different. The man cannot, of course, think of _the two things_ as indistinguishable, but he may think of two things and connect with this thought the thought of himself as having an experience in which there is no consciousness of duality.

But, it may be insisted, we are still only talking about consciousness; let us come to "real" things. Suppose no one able to distinguish between them, abstract all consciousness of difference, would not two "real" things remain two, however we might confound them? Can a thing in one place be a thing in another place, however closely it may resemble it, or however ignorant we may be?

To this I answer that when one speaks of _two_ "real" things the words only mean something to him because he has present in mind what I have said must be present if one is to have a consciousness of duality. A "thing in one place" and a "thing in another place" are to him two simply because he thinks them as differing--in place. When one has come to the conclusion that he must duplicate his experience, distinguish between the world of immediate and the world of mediate objects, and place the latter in a region "outside," there is nothing to prevent him from thinking of two "real" things as two, although all distinctions within the field of immediate objects have been obliterated. Still, in thinking these "real" things as two, he does just what he does in thinking two immediate objects as two--he recognizes difference. The twoness depends upon difference as much in the one case as in the other, and to speak of two objects in a "real" world as two and yet having no differing element would be to use words without meaning. In talking about a "real" world, if we are really to talk and not merely to utter a series of sounds, our words must be significant. To say "this or that may be in a 'real' world, though we may not be able to conceive it," would, if "this" or "that" implies a contradiction, be to say nothing. The fact is that this "external" world, as we think it, implies the notions of before and after, in this place and that, all the distinctions and differences which make it to us a world of distinct objects. Of course it follows that things in the "external" world are thought as distinct from each other, but this does not affect my statement that distinction is impossible without difference.

We may, then, have a series of experiences, beginning with one in which two objects are recognized as similar and yet are very clearly distinguished as two objects, continued in others in which the sense of duality falls more and more into the background, and ending in one in which there is no consciousness of duality at all. The last of these experiences is not wholly different from the others. There is in it no experience of similarity in so far as this word is used to express identity in difference, or a relation between two. There can be no such relation unless there are two, and here there are not two. But it should be marked that this experience differs from the others, not in the element which has led us to declare two objects similar--the element which they have in common--but in that which has led us to declare them two and different. It is by adding to this last experience, so to speak, that we get the others. They contain it and more. Usage will not allow us to apply the term similarity in speaking of an experience in which two things are not distinguished, and this is proper enough; but it should never be forgotten that this experience is at the bottom of all our experiences of similarity--is, so to speak, their common core. When, therefore, I said some pages back that all the kinds of sameness under discussion contain the idea of similarity, I was using the word in a certain broad sense to indicate that which is the ground of all our experiences of similarity, and is also found in the first kind of sameness on the list. I preferred to use there the word similarity, because it was easy to show that this notion is really contained in six of the seven uses of the word same, and it was convenient afterward to show the connection between the first kind of sameness and the notion of similarity.

And now it is not difficult to guess why we employ such expressions as we do to indicate strict identity. If I habitually use the proposition "x is y" to indicate a relation between two things having similar elements and yet regarded as distinct, and look upon the proposition as justified by the similar elements, observing that, these remaining unchanged, the dissimilar elements may be very variable without affecting the truth of the proposition, what more natural than that I should go on using the propositional form when the dissimilar elements have diminished to zero--when the proposition has become "x is x"? To be sure, no one can take such a proposition literally, any more than one can soberly believe that one divided by zero results in infinity. Such expressions have their use and value, but they must be properly understood. If one uses the expression "x is x" to emphasize the fact that one is not to pass from x to any y or z--that one is to rule out all distinction or sense of difference, the use cannot be harmful. And the use of the propositional form has this great convenience: it puts a period, so to speak, to one's thinking, and prevents one from casting about for a completion of the thought. If one merely say to me "x," I shall probably take it as a subject and busy myself to find a predicate. If he say "x is x," he says really no more than x, but he makes me fix my thoughts upon x alone.

SEC. 20. In the foregoing search for the element that the kinds of sameness have in common, I have had in mind chiefly the samenesses of things immediately known. It is not necessary to repeat the search in the field of the "external." We have but the seven kinds of sameness, and whatever may be the things that are the same in these several ways, the elements I have indicated must be present if our words are to be significant. But one thing remains for me to do in this part of my monograph, and that will not detain me long. I must distinguish between sameness and identity, or rather point out to what kinds of sameness this latter word is commonly applied.

The word is often used quite loosely, but where the attempt is made to distinguish between identity and sameness in a looser sense, and to use terms with some precision, the former word serves to indicate sameness in which there is no consciousness of duality, or in which the consciousness of duality has fallen into the background and may easily be overlooked. Sameness of the first kind, for example, is spoken of as identity. This is the only kind of sameness in which there is no element of duality at all. The use of the word identity is not, however, restricted to this. Locke's inquiry concerning the identity of masses of inorganic matter, of vegetables, of animals, and of persons, has to do with sameness of the third kind on the list. In this kind of sameness there is no clear consciousness that one is dealing with more than one thing, and Locke's discussion is conducted throughout as though one were not.

It may be objected that in certain other kinds there is often no clear consciousness of duality, and yet one does not think of using the term identity. This is quite true. The two kinds mentioned have been thought worthy of special discussion by logician and philosopher, and have been given a technical name. The others have not. Still, although the word is not commonly used in such cases, it would, I fancy, seem natural to use it in a direct ratio to the degree in which the sense of duality falls into the background. Dr. Johnson would probably have been willing to say that the stone he saw himself kick was identical with the one the existence of which he wanted to prove. Bishop Berkeley could have felt only disgust at such a use of the term. Scarcely anyone, I suppose, would regard himself as speaking strictly if he called the fourth kind of sameness identity. The co-existence of the two things compared would prevent their being confounded. Without, then, attempting to assign any very exact limits to the application of a somewhat loosely used word, I may repeat my former statement that men use the word identity to mark certain kinds of sameness in which there is little or no consciousness of duality, and they are not inclined to use it to mark samenesses in which things are recognized as similar but clearly distinct.

With this I end the first part of my discussion, and I confess I draw a long breath in doing so. When I sat down to write it was with the impression that I could say all that was necessary about the kinds of sameness in a much smaller number of pages; but finding it impossible to avoid misunderstandings without being more explicit and detailed, I have had to change my plan. Now, that I am through, I must confess to myself that most persons will find this hair-splitting anything but entertaining--which would be held by the inconsiderate to furnish a presumption against the truth it contains, if ancient adages go for anything. It should be remembered, however, that the old saw which puts truth in a well does not indicate that the well may not be a dry one. With this consolatory reflection I turn to the second part of my task.