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.

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)