I seem to spend loads of time thinking how to defend supervaluationism these days. That's reasonably peculiar, since I don't defend its application in many areas: not to vagueness, especially not as a cure-all to the problem of the many (I'm a many-man myself: there are *billions* of mountains around Kilimanjaro). I'm not particularly chuffed with it as a way of handling the inscrutability of reference, either. So basically we're down to a few bits and pieces: perhaps partially defined predicates, perhaps theoretical terms (though even there I have my doubts).
I do like the spirit of the thing, though, and some relatives of supervaluationism appeal to me as a way of thinking about vagueness (e.g. Edgington-style degree theory).I also like something isomorphic to supervaluationism as a way of thinking about ontic indeterminacy and the like. So I've got some investment in it. (continued below the fold)
I've recently had a go at defending supervaluationism from the charge that it's logically revisionary. My line, in affect, is that the arguments that it's revisionary (most famously pushed by Tim Williamson in the marvelous "Vagueness" book) work only if you think "definitely" is a logical operator. And I can't see any reason to believe that. (A draft is available here).
Because of this, I was intrigued to find an argument that supervaluationists are (and should be!) logically revisionary in a recent paper by Delia Graff (it's in the JC Beall "Liars and Heaps" volume). The idea is the following. Suppose that we have a sorites series on the predicate F, and R is an "adjacency" relation along the series. Then from Fa and ~Fb, it should follow for the supervaluationist that ~Rab. For the whole supervaluationist thing is that if there's a gap between the last F's and the first ~F's. But the contrapositive principle (simplifying) is that from Rab you can get ~(Fa v~Fb). That gives you all you need for a negated-conjunction "long sorites" argument.
I think that defender of non-revisionary supervaluation should say that *in no sense* does ~Rab follow from Fa and ~Fb. Yet *intuitively* it does follow (just repeat it to yourself!). But we've come against this sort of situation before: the answer is going to be that we *confuse* the inference from Fa and ~Fb to ~Rab with the inference from Def[Fa] and Def[~Fb] to Def[~Rab]. That inference may well be in goodstanding in some sense (it's obviously not logically valid, but still...) but we won't get in trouble if we take the contrapositive to be in equal goodstanding. (My moves here are independently motivated because I'm basically replaying the Fine/Keefe "confusion hypothesis" moves that the supervaluationist (and others) need in order to account for the seductiveness of the sorites (there's a brief presentation of this here).)
So *I think* the Graff thing doesn't force us to be revisionists any more than the Williamson arguments. But there's lots of rich stuff around here: plenty more things to think about.