Lewis, David On the Plurality of Worlds
Saul Kripke criticizes Lewis’s paper in N&N in footnote 13 like this: “David K. Lewis, ‘Counterpart Theory and Quantified Modal Logic’, Journal of Philosophy 6S (1968), II3-I26. Lewis’s elegant paper also suffers from a purely formal difficulty : on his interpretation of quantified modality, the familiar law (y) ((x)A(x) � A(y» falls, if A(x) is allowed to contain modal operators. (For example, (3y) ((x) 0 (x =F y» is satisfiable but (3y) 0 (y =F y) is not.) Since Lewis’s formal model follows rather naturally from his philosophical views on counterparts, and since the failure of universal instantiation for modal properties is intuitively bizarre, it seems to me that this failure constitutes an additional argument against the plausibility of his philosophical views. There are other, lesser, formal difficulties as well. I cannot elaborate here. Strictly speaking, Lewis’s view is not a view of ‘ transworld identification‘.
Rather, he thinks that similarities across possible worlds determine a counterpart relation which need be neither symmetric nor transitive. The counterpart of something in another possible world is never identical with the thing itself. Thus if we say ‘Humphrey might have won the election (if only he had done such-and-such), we are not talking about something that might have happened to Humphrey but to someone else, a “counterpart”” Probably, however, Humphrey could not care less whether someone else, no matter how much resembling him, would have been victorious in another possible world. Thus, Lewis’s view seems to me even more bizarre than the usual notions of transworld identification that it replaces. The important issues, however, are common to the two views : the supposition that other possible worlds are like other dimensions of a more inclusive universe, that they can be given only by purely qualitative descriptions, and that therefore either the identity relation or the counterpart relation must be established in terms of qualitative resemblance. Many have pointed out to me that the father of counterpart theory is probably Leibnitz. I will not go into such a historical question here. It would also be interesting to compare Lewis’s views with the Wheeler-Everett Interpretation of quantum mechanics. I suspect that this view of physics may suffer from philosophical problems analogous to Lewis’s counterpart theory; It is certainly very similar in spirit.”