Intensions, Referents and Counterparts
Yesterday, I said that it doesn't really matter whether we regard identity simpliciter as identity-at-our world -- individuationg referents extensionally -- or as identity-at-every-world -- individuating referents intensionally. Suppose we want to do the latter, so that the referent of "the amazon" determines a function from worlds to world-bound individuals, that is, an intension. So on the present account, we identify the amazon with something that completely determines the intension of "the amazon". The intension? What if, as two-dimensionalists argue, "the amazon" has two intensions? Which one is the one we want extensions to determine?
Let's call the individuals in the range of "the amazon"'s intension the counterparts of the amazon. (If the amazon is a trans-world fusion, these counterparts are its maximal spatiotemporal parts.) Corresponding to the two intensions, we get two sets of counterparts, A-counterparts and C-counterparts. Which, if any, of these are the traditional counterparts? The C-counterparts. (Almost. The traditional counterpart relation allows for several counterparts in one world. The functionality of intensions rules this out. But since C-intensions are supposed do exactly the job of counterparts I think we should simply drop the functionality requirement.) For consider the interpretation of an ordinary ("counterfactual") modal statement like
The amazon is not essentially longer than 500 km.
Using C-intensions, we can say that this is true iff not every element in the range of the C-intension of "the amazon" is longer than 500 km. And in counterpart theory, we say that it is true iff not every counterpart of the amazon is longer than 500 km.
At least in my idiolect, there are also modal contexts that operate on A-intensions, for example contexts in which it is true to say "water could not have been H2O". (I assume here that the C-intensions of "water" and "H2O" are identical. I hope I'll get back to that in the next part of this monologue.) To treat these contexts counterpart-theoretically, we would have to use A-counterparts. But I'm not sure if it's very illuminating to treat them counterpart-theoretically.
Now back to the question which intension is the one we might just as well include into the extension. It's the C-intension. For the A-intension registers context-dependence, and even if we don't care much about the folk theory of reference it would be very odd to say that the referent of "the amazon" contains information on that. Compare the temporal analogue: The C-intension of my current utterance of "the prime minister" determines a function that assigns to every time (at our world) the stage of Tony Blair located at that time. (C-intensions are often presented as having non-centered worlds in their domains. But we need the C-intension of my utterance to tell us which of the things that existed an hour ago is the one I refered to just now. So if the domain of C-intensions isn't centered, its range must contain temporally extended individuals. And every temporally extended individual determines a function from times to stages of that individual.) It is reasonable to call the fusion of all these stages the referent of my utterance. On the other hand, the A-intension of my utterance determines a function that assigns to every time (at our world) the thing that is prime minister at that time. (It is not clear to me whether these things in the range of the A-intension are stages or persons. I think they ought to be stages, but often they are treated like persons. To arrive at persons, I would employ two-dimensional intensions.) It would obviously be very strange to call the fusion of all of those (stages or persons) the refent of my utterance.