The view endorsed by David Lewis, that identical entities do not exist in different possible worlds, and that statements that appear to require that they do are evaluated by thinking of a counterpart in other worlds. Thus ‘if you had touched the wire you would have been electrocuted’ will be true if, in a possible world like this in virtually every respect, except that you touch the wire, you are electrocuted. But ‘you’ as it occurs in this analysis no longer refers to you, but to a ‘counterpart you’ who touches the wire. The doctrine bears some resemblance to the metaphysicallybased view of Leibniz that if a person had any other attributes than the ones he has, he would not have been the same person. Leibniz thought that when I ask what would have happened if Peter had not denied Christ, I am asking what would have happened if Peter had not been Peter, for denying Christ is contained in the complete notion of Peter. But he allowed that by the name ‘Peter’ might be understood ‘what is involved in those attributes [of Peter] from which the denial does not follow’. A controversial argument against counterpart theory associated with Kripke asks why it should matter to me not to have touched the wire, if all you can tell me is that if I had done so, a counterpart of me would have been electrocuted.