It would seem that Geach's claim is that the relation expressed by 'is identical with' is like the relation expressed by 'is better than', at least in one respect. If x and y are people, it may turn out that x is a better golfer than y, while y is a better poet than x. If we merely say that x is better than y, we fail to specify the respect in which we hold x to be the better. Another (...) way to put this is to say that we have not made clear "in relation to what" x is the better. We can call the relation expressed by 'is better than' a "relative relation," since an ordered pair of things may stand in that relation relative to one thing but not relative to another thing. Geach seems to think that identity is a relative relation. (shrink)

Since Geach did not give any account of what is to be considered the same form of relative identity, I assumed that 'x is the same A as y' expresses the same form of relative identity as 'x is the same B as y' if and only if 'A' means the same as 'B'. If this is an incorrect assumption, then I must ask what is the criterion of identity for forms of relative identity?

On his very first page Feldman ascribes to me a claim about the relation expressed by 'is identical with'. Feldman's way of speaking is, as Ryle might say, systematically misleading: for of course I deny that any one relation, even a relative relation, is the relation expressed by 'is identical with'. My whole thesis was that 'is identical with' expressed now one, now another, relation, according to the context of utterance.

We can best begin from Wilson's "simple little puzzle" about Caesar and Antony: "What would the world be like if Julius Caesar had all the properties of Mark Antony and Mark Antony had all the properties of Julius Caesar?" Wilson's own approach to an answer is indirect--he begins by telling us not what such a world would be like but what it would look like. "Clearly the world would look exactly the same under our supposition." But this assumes that the (...) question "What would such a world look like?" is a proper one; which it surely is not. For his answer to it is meaningless until he specifies to whom this supposed world would look as he says it would. It would look exactly the same to him or to me; but would it have looked the same to Caesar or to Antony? In fact Julius Caesar had the experiences of being called "Julius Caesar," being murdered on the Ides of March, and so on, and these are very different experiences from being called "Mark Antony," dallying on the Nile with Cleopatra, and so on; so I don't see how this alternative course of events could possibly have looked the same to Julius Caesar; or--using a similar line of argument--to Mark Antony. So I cannot agree that, as Wilson goes on to say, "our attempt to describe a distinct possible world has produced just the same old world all over again." I am not, indeed, convinced that even a world which looked to everyone just as the actual one does would necessarily be the same world ; but even putting this doubt aside, since the world mentioned wouldn't look to everyone as the actual world does, it wouldn't be the same even by Wilson's own standards. (shrink)

Absolute identity seems at first sight to be presupposed in the branch of formal logic called identity theory. Classical identity theory may be obtained by adjoining a single schema to ordinary quantification theory.