- In the first twelve chapters of this book I am concerned with the Fregean notion of an object (the reference of a proper name) and its connection with the notion of identity. I proceed by discussing the views of Peter Geach, David Wiggins, Michael Dummett and W.V. Quine on these topics, and argue finally that the only tenable position is that of Quine.
- Geach has argued for the thesis that identity is relative, and that a proper name must be associated with a criterion of identity. In order to interpret Geach's Relative Identity1 Thesis I introduce a distinction between absolute and relative equivalence relations. Geach's thesis turns out to be the claim that (in a sense I explain) there are no absolute equivalence relations. On this interpretation Geach is not claiming that there are counterexamples to Leibniz's Law2, as he has often been taken as doing; I take this to be a good thing since, so far as I can see, any attempt to produce such counterexamples would be quite futile.
- The view that a proper name must be associated with a criterion of identity, that is, that the act of endowing a sense on such a name must involve associating it with a criterion of identity, is not peculiar to Geach; of the writers mentioned above it is shared also by Dummett and Wiggins. These writers, like Geach, regard a criterion of identity as a relation which "sustains the application of a name" (to use a neat phrase I owe to Professor Williams), but they believe that only what I call absolute equivalence relations can serve this purpose, whereas Geach, of course, is committed to holding that relative equivalence relations can so serve. I argue that the use of an absolute equivalence relation as a criterion of identity will always be tantamount to the use of a relative equivalence relation as a criterion of identity, so that Wiggins and Dummett must be wrong about this. At this stage I have already argued independently that certain relations which Wiggins and Dummett would regard as paradigm examples of relations capable of serving as criteria of identity and which it seems ought to be so regarded by anyone wishing to maintain the thesis that the introduction of a proper name requires its association with a criterion of identity, are in fact relative equivalence relations, and this, though of course not a conclusive refutation of their view, makes it clear that to maintain it involves swallowing a number of highly unintuitive consequences.
- Geach has put forward in association with arguments for his Relative Identity3 Thesis arguments against the customary reduction of restricted quantification to the unrestricted sort. He holds that "Heraclitus bathed in some river yesterday and bathed in the same river today" is not equivalent to "Something is a river and Heraclitus bathed in it yesterday and bathed in it again today". I discuss his argument for this claim and show how neither Wiggins nor Dummett have responded adequately to it.
- It can, however, be answered by someone who accepts Quine's thesis that what are ordinarily thought of as continuants are, in fact, "process-things", with temporal parts as well as spatial parts. I explain why this is so.
- But to say that someone who accepts Quine's thesis can resist Geach's argument is not to say that he ought to deny Geach's claim. I argue that, in fact, he ought to accept a certain version of Geach's claim. This version is weaker than the one Geach himself accepts, however, and does not have the consequence, as Geach's version does, that general names are a category of expression semantically distinct from the category of predicates.
- In Chapter Eleven I discuss an argument which would, if successful, establish that Geach was correct in maintaining this distinction, but show that it is not cogent.
- In Chapter Twelve I then argue that in fact only the weaker version of Geach's claim is tenable. This in fact emerges as a corollary of the refutation of the Relative Identity4 Thesis I there offer; another corollary of this refutation is that, just as Quine maintains, continuants have temporal parts. Chapter Twelve also contains a refutation of the claim that any equivalence relation can serve as a criterion of identity and a characterization of two classes of equivalence relation which can do so (not every equivalence relation which can do so falls in one of these classes, however, as I point out). At the end of Chapter Twelve I explain briefly why the argument Geach has given for the Relative Identity5 Thesis leaves me unconvinced.
- The rest of the book is devoted to a discussion of the problem of personal identity.
I conclude by suggesting that even the view that "person", thus defined, conveys a criterion of identity at all is very doubtful, and that modem discussions of "personal identity" are therefore possibly as lacking in subject matter as John Locke's discussion was.
- In Chapter Thirteen I argue that "one thing can become two", in a sense in which this is often denied.
- Using this conclusion as a premiss I argue in Chapter Fourteen that Shoemaker's notion of "quasi-memory6" cannot be used, as he wishes, to defend a mentalistic criterion of personal identity against Bishop Butler's charge of vicious circularity and that in fact only a criterion in terms of bodily continuity can suffice.
- However (I argue in Chapter Fifteen) though present-day mentalistic accounts of personal identity are vulnerable to Butler's objection, Locke's account, against which the objection was originally made, was not. This is because Locke's aim was to define the identity of persons in terms of the memory beliefs of (immaterial) thinking substances, whereas modem writers attempt to define the identity of persons in terms of the memory-beliefs of persons. Nevertheless, I argue, although Locke's discussion cannot be faulted in the way it is commonly thought, a fatal flaw still remains, namely, that Locke mistakenly assumes that "person", defined in terms of self- consciousness,; conveys a criterion of identity which cannot serve as the criterion of identity for anything except a self-conscious creature.
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