Must. Think. Harder.

I think weak conjunction is a step in the wrong direction, but I can't prove it. Grrr.

Even if we embrace weak conjunction, we are stuck with a problem with modal necessity: Must(p v q) = Must-p and Must-q

(using the entry for "must" that doesn't break the symmetry between "must" and "might")

***

In broad outline:

if you pick existential quantification, you get wide-scope, "...I can't remember which" type truth-conditions. But this seems to really be a case where the ''or'' has wide scope at LF and is subject to grammatical surface deletion. So the semantics is totally wrong--it's assigning wide-scope truth conditions to the narrow-scope LFs.

On the other hand, if you pick universal quantification, you get things easy for conjunctive readings of "or" (choice situations) but everything goes wrong in downward-entailing environments like negation,

If you try to split the difference--some existential and some universal--then, at the very least, the symmetry between "must" and "might" is broken.

...This seems to me to be an intrinsic limitation of doing Hamblin semantics for disjunction in this way. A recent grad student of Kratzer's, Alonso-Ovalle, did his dissertation on this in 2005 and, though I've only read the introduction, his work seems to bear this out. He designed his semantics so that the quantification over the disjuncts was existential--hence the choice inference isn't valid after all. Then he said it was a conversational implicature.

That seems disappointing to me...why posit so much extra complication just to give the felt inference the status of an implicature? I don't mean to denigrate the study of implicature--it's just that then a Prof. Bach-style, "why'd ya add a disjunct if it wasn't doing any work?"-type response seems good enough. Its sort of like "why'd ya say 'produced a series of sounds which corresponded closely to the score of...' instead of 'sang'?" Surely, there's an answer here, but it has nothing to do with compositionality!

...Am I totally wrong?