THE DISSIMILARITY OF THE DIVERSE
In Chap. X of the Nature of Existence McTaggart discusses the question whether there could be two or more particulars which were exactly similar to each other, and comes to the conclusion that this is impossible. This principle he calls "The Dissimilarity of the Diverse".
What would be meant by saying that two particulars A and B were "exactly alike"? According to McTaggart it would mean that every quality of either is a quality of both. But agreement of "primary qualities", in McTaggart's technical sense of that phrase, would entail agreement of all derived qualities. So it is enough to say that every primary quality of either is a primary quality of both. Now primary qualities are either original qualities, e.g., redness, or are the immediate derivatives of original relationships, e.g., the quality of loving C. (The reader should refer back to Chap. V, Section 1, of the present work, if he wants to remind himself of the definitions of these technical terms.) For A and B to be exactly alike it would then be necessary and sufficient that every original quality, and every quality which isimmediately derived from an original relationship, which belongs to either should belong to both.
It seems to me that if we admit that a particular can be related to itself, there are difficulties in this definition, even if we waive our objections to McTaggart's theory of relational qualities. Suppose that A and B were two selves, and that A respects A and does not respect B. whilst B respects A and does not respect B. Then both A and B have the positive relational quality of respecting A. And they both have the negative relational quality of not respecting B. Nevertheless they would not be exactly alike. For A respects himself, whilst B does not respect himself; and this is an important point of dissimilarity between thern. It seems plain then that we must add that, in order for two particulars to be exactly alike, any relation which relates either to itself must relate each to itself.
The amended definition of exact likeness would run as follows. Two particulars A and B would be exactly alike if and only if the following three conditions were fulfilled.
Now McTaggart holds that it is evident on careful inspection that no two particulars could be exactly alike. They might, for all we know, be exactly alike in all their original qualities, but they could not possibly be alike in all respects. This principle he calls the "Dissimilarity of the Diverse", and he thinks that it is what Leibniz meant by the "Identity of Indiscernibles".
If there were any relation which every particular must have to itself, and which no particular could have to another, the Dissimilarity of the Diverse would follow at once. For A would have this relation to A, and would not have it to B, whatever A and B might be. Now McTaggart regards identity as a relation which every term must have to itself and which no term could have to any other. But he is not content to rest the principle on the relation of identity. He states his reasons for this very obscurely in § 94. I think that his position is the following. If A and B be two particulars, there must be some dissimilarity between them which is not a mere analytic consequence of the fact that they are two. Now the dissimilarity which consists in the fact that A has the relation of identity to A whilst B does not have this relation to A is as mere analytic consequence of the fact that A and B are two. We see then that the complete statement of the Dissimilarity of the Diverse is that any two particulars must be dissimilar in some respect which is not a mere analytic consequence of the fact that they are two. If this is what McTaggart means, I agree that it is only when the principle is so interpreted that it is of interest and importance. And, in any case, I could not accept the argument based on the so-called "relation of identity" which relates each particular to itself; for I do not believe that there is any relation answering to this description.
Is the principle, in its amended and interesting form, true? I shall try to show that it is not. When a proposition asserts necessity, as this one does, there is no need to produce an actual exception to it in order to refute it. It is enough to show that exceptions are conceivable. Can we do so? We must remember that McTaggart counts as "substances" both what most people call "Things" or "Continuants", and what most people call "Events" or "Processes" or "Occurrents". I have discussed the question whether it is necessary to hold that there are two fundamentally different kinds of particular, and hate tentatively suggested that probably statements which are verbally about Things can be replaced without loss of meaning by more complicated statements which are about Processes. Here, however, I propose to admit, for the sake of argument, that there are two fundamentally different kinds of particular, and to deal with each in turn.
I will begin with sensibilia, which McTaggart rightly regards as particulars, and which are almost certainly of the nature of Processes. It is, I think, obvious that any two sensibilia which are sensed by the same mind must be dissimilar in sensible quality, or be spatially separated, or be temporally separated. Now either spatial or temporal separation involves dissimilarity. For A cannot stand in either of these relations to A; whilst B, if it is another sensibile sensed by the mind which senses A, must stand in one or other of these relations to A. Two such sensibilia then must be dissimilar, and their dissimilarity will not be a mere analytic consequence of the fact that they are two.
But now consider two sensibilia which are sensed by different minds, e.g., two noises. Plainly they might be exactly alike in sensible quality, viz., in pitch, loudness and tone-quality. As regards their temporal relations, it might be held either that they stand in no temporal relation to each other or that they do. On the first alternative they cannot have temporal dissimilarity. On the second alternative there is no reason why they should not be simultaneous, i.e. have temporal similarity. As regards their spatial relations, it seems clear that they would have none to each other. There is no ground for saying that a noise heard by me and a noise heard by you are themselves either spatially coincident or spatially separated. If anyone thinks otherwise he is probably confusing the sensibilia with certain physical events of which they are believed to be manifestations. It is then logically possible that there should be two sensibilia which were exactly alike in sensible quality; which either had no temporal relations or were simultaneous; and which had no spatial relations, and therefore could not have spatial dissimilarity. It is also logically possible that these should have been the only sensibilia that there ever were, and therefore that they were not dissimilar in the relationships in which they stand to other sensibilia. The only dissimilarity left between them is that one is sensed by the mind X and not by the mind Y, whilst the other is sensed by the mind Y but not by the mind X.
Now, unless it be logically impossible for there to be unsensed sensibilia, it is logically possible that neither of these sensibilia should have been sensed by any mind. If so, it is logically possible that there should have been no dissimilarity of any kind between them. Now, although there may be good reasons for doubting whether there are in fact any unsensed sensibility it cannot reasonably be held that the occurrence of an unheard squeaky noise or an unseen red flash is logically impossible. It seems to me then to be logically possible that there should have been two sensibilia which had no kind of dissimilarity except such as are analytical consequences of their diversity. If so, McTaggart's principle that there could not be two such particulars is false, though it may be true that there are not and never have been and never will be.
One objection to this conclusion presents itself. It might be said that, if A and B have parts, there must be some parts of A which are not parts of B and some parts of B which are not parts of A. Now MeTaggart holds that every particular has parts which are themselves particulars. Would it not follow that A must always be dissimilar to B at least in the respect that it contained a part P which B did not contain or that B contained a part Q which A did not contain? Undoubtedly the premise that every particular has parts does entail that any two particulars must be dissimilar in this respect. But does this help McTaggart? I do not think that it does. For this kind of dissimilarity is simply an analytic consequence of the fact that A and B are two particulars, whilst he maintains that there must be some dissimilarity which is not inferable from this fact.
Let us next consider particulars which most people would count as Continuants. Continuants have states, and most people distinguish states from parts, though McTaggart holds that the states of anything are parts of it. Now it is evident that, even if two continuants could have some states in common, they could not have all states in common. It is therefore true that any two continuants, A and B. must be dissimilar in the respect that A has some state S which is not a state of B. or that B has some state T which is not a state of A. But this kind of dissimilarity would appear to be an analytic consequence of the fact that A and B are two continuants, and it is therefore irrelevant to McTaggart's principle. The question then comes to this: "Is it possible that there should be two continuants which were dissimilar in no respect except that there were states of one which were not states of both or that there were parts of one which were not parts of both?"
It seems clear to me that this is logically possible. It is logically possible that there should have been just two minds, A and B, and no bodies, and that there should have been no other conlinuants except these two minds. Now is there any logical impossibility in supposing that these two minds should have existed through exactly the same period of time, and that every state of the one should have been exactly like the contemporary state of the other in every respect except that of occurring in a different mind? We could imagine each of them to be wholly occupied in following precisely the same chain of argument, e.g., Lindemann's proof that π is a transcendental number, at exactly the same rate and in exactly the same order. And we can imagine that the emotions of A at any stage of the process are exactly like the emotions of B at the corresponding stage of the process. I can see nothing logically impossible in this supposition. It is, then, possible that there should have been two continuants, A and B, such that the only dissimilarity between them is that A has states which are not states of B, and that B has states which are not states of A. And it is possible that the only dissimilarity between the contemporary states of A and of B should be that one occurs in A and not in B whilst the other occurs in B and not in A.
Now McTaggart asserts that two particulars must be dissimilar in some respect which is not inferable from the mere fact that they are two. We have now seen that this is false both for occurrents and for continuants. Nevertheless, it may well be true that every pair of particulars which there have been, are, or will be, are in fact dissimilar in other respects beside those which are analytical consequences of their diversity.
I am inclined to think that the Dissimilarity of the Diverse has seemed plausible because those who tried to envisage the possibility of exceptions, and failed to do so, unwittingly restricted their field of view in two respects. In the first place, they confined their attention to physical events and things, and forgot about sensibilia, experiences, and minds. Secondly, they assumed uncritically that there must be a single spatio-temporal system in which every particular has its place and date. Now, even if this be in fact true, there is, so far as I can see, no kind of necessity about it. It might be, as Bradley suggested in the chapter on "Nature " in Appearance and Reality that, whilst every particular has its place and date in some spatio-temporal systern, there is a plurality of such systems, and a particular in one has no spatio-temporal relation whatever to a particular in another.
In § 95 of the Nature of Existence McTaggart argues that the denial of the Dissimilarity of the Diverse is closely connected with an invalid distinction, which many people try to make, between the "individuality" of a particular and its "nature". It is not at all clear to me that there is any close connexion between the two. A person who denies the Dissimilarity of the Diverse is saying that it is logically possible for the same nature N to be the nature of several particulars, P1, P2, etc.; e.g., that it is logically possible that there should be several noises or minds which were precisely alike in every respect that is not a mere analytic consequence of their diversity. A person who tries to distinguish the "individuality" of a particular P from its nature N presumably means that it is logically possible that P, which in fact has the nature N, should instead have had some other nature N'; e.g., that I might have been born in Rome in 55 B.C., or that the Albert Memorial might have been a volcano in South America. Now it is obvious that the first proposition does not imply the second, and therefore is not refuted by the fact that the second is almost certainly false. And the second does not imply the first; for, even if every particular might have had a different nature from that which it in fact has, it might still be the case that no two particulars could have precisely the same nature. I do not wish to deny that some people may have believed the second proposition, and may have thought that the first followed from it. If so, they were almost certainly mistaken in their premises and they were quite certainlv committing a fallacy in their argument. But my reason for denying the Dissimilarity of the Diverse is simply that it is a proposition which claims to be necessary and that I can see on inspection that exceptions to it are conceivable.