Perhaps the most interesting question in metaphysics, to my mind, is whether identity facts are among the base facts; whether worlds or their constituent objects are prior; whether de dicto or de re modality is fundamental. (I take these to be different angles on the same core question.) We can illustrate the issue by way of my old example of duplicates Bob1 and Bob2 in the perfectly symmetrical universe. Although this possible world contains two of everything, presumably things could have been different. In particular, there might have been no duplication. But now we ask: how many ways are there for a world to be exactly like the mirror world, minus the duplication?
(A) The Kripkean Answer: Many. At the very least, you might have just Bob1's half of the universe, or just Bob2's half of the universe. So that's two possibilities. We might even mix and match, conceiving of a possibility containing precisely Bob2's world except that Bob1 exists in Bob2's place. To generalize: if there are n independent objects in each half of the symmetrical universe, then there will be 2^n ways to populate a possible world containing just one of each object. (Essentialists may deny that all the objects are independent in this way, though: perhaps Bob1 could not have been born to Bob2's mother. Such details needn't concern us here, though.)
(B) The Lewisian Answer: There is really just one possibility here. There is no difference between the various possibilities mentioned in the Kripkean answer. They are all describing one and the same way for a world to be. What we have imagined is a world which contains but a single Bob counterpart (and similarly for each other object in the mirror world). Whether he is really Bob1 or Bob2 is an empty question. In the strictest sense of identity, he is plainly neither. But as a counterpart, he can play a truthmaking role for counterfactual claims made about either. (E.g. "Bob1 might have existed without Bob2," and vice versa.)
I lean heavily in the Lewisian direction, since the idea that there could be any number of qualitatively identical worlds which nonetheless differ in the identities of their constituents strikes me as completely nutty. (There's nothing there to ground such a difference -- nothing in Bob's metaphysical makeup that could fix whether he is Bob1 or Bob2. Well, unless you care to introduce a 'haecceity' for just this purpose, but haecceities seem mysterious and insufficiently motivated posits.)
"That's nuts" does not, however, seem to convince the Kripkeans of my acquaintance. Can anyone suggest a better way to make progress on this issue? (Or some good papers to read? I'm not at all familiar with the literature.) I think Jack is with me on the specific case of time-points, at least, so maybe I just need a few more compelling examples to form a base from which to generalize...? More seriously, though, it seems like such a central issue that it cannot be settled on its own. Rather, we must do the hard work of exploring the implications for whole systems of Kripkean and Lewisian metaphysics, to see which approach ultimately bears fruit. What do you think?