Richard: Kripke proposes that…
Richard: Kripke proposes that we simply stipulate that we’re talking about the possibility in which this very man wins the election, or whatever.
This is a common way of putting Kripke’s view in a nutshell. But I think that his point is actually directed at a more fundamental target than you suggest.
When Kripke talks about stipulating identity across worlds he’s explicitly criticizing the whole Lewisian view on which we are given a set of possible worlds ahead of time, and then strike out to find where a particular object of interest happens to be in them. The idea is not that you have these possible worlds and just stipulate that that man over there is Nixon; it’s that you don’t even have a cognitive grasp on the possible world except by way of starting with considerations about (for example) Nixon and how he might have been. Thus:
“A possible world isn’t a distant country that we are coming across, or viewing through a telescope. Generally speaking, another possible world is too far away. Even if we travel faster than light, we won’t get to it. A possible world is given by the descriptive conditions we associate with it. What do we mean when we say ‘In some other possible world I would not have given this lecture today?’ We just imagine the situation where I didn’t decide to give this lecture or decided to give it on some other day. Of course, we don’t imagine everything that is true or false, but only those things relevant to my giving the lecture; but, in theory, everything needs to be decided to make a total description of the world. We can’t really imaigne that except in part; that, then, is a ‘possible world’. …. ‘Possible worlds’ are stipulated, not discovered by powerful telescopes.” (44)
“Most important, even when we can replace questions about an object by questions about its parts, we need not do so. We can refer to the object and ask what might have happened to it. So, we do not begin with worlds (which are supposed somehow to be real, and whose qualities, but not whose objects, are perceptible to us), and then ask about criteria of transworld identification; on the contrary, we begin with the objects, which we have, and can identify, in the actual world. We can then ask whether certain things might have been true of the objects.” (53)
Of course, it’s a separate question whether Kripke is right or wrong about this; but I do think it’s important to keep in mind that he’s just not starting from the same problem that you are. In fact he’s trying to undermine the idea that there is such a problem at all. If you begin with things (Nixon, the die in front of you, etc.), or with stuff (water, gold, etc.), and then spin out possible worlds around them, then a lot of the problems that exercise accounts of transworld identification simply dissolve. (That doesn’t rule out the anti-essentialist view. You might hold that the range of possible worlds you can successfully spin out around the thing you have in mind is context-relative. But the view becomes much less compelling once you’re no longer worried about haecceities or counterpart relations r the like.