So, I began by making a strong case for the pragmatic implicature reading. I then felt a little stuck: I had made *such* a good case for the Ross entailment's being pragmatic, that another, semantic version seemed unnecessary. I'll now to try to say (more clearly than I did then) just what needs to be said next.
First, the LF in which disjunction takes narrow scope has independent interest. It seems to be allowed by our syntax, so there is a question of what the semantics is for it.
Secondly, it is hard to claim that all claims with Surface Form MIGHT(A v B) are really wide-scope disjunctions: Zimmermann doesn't even try. (He just claims that it is the syntactic "sine qua non" of his solution. Presumably his evidence for the syntactic claim is only as good as the claim that, the LF must be a wide-scope disjunction in order to validate the free choice inference. But this is exactly what Simons and I dispute; if we CAN give a semantics for the narrow LF on which the entailment still holds, the evidence for taking the surface form to really be a wide-scope disjunction *because the Ross's entailment is felt* evaporates.)
Thirdly, there is a good set-centric generalization of our current semantics for MIGHT and MUST which suggests the interpretation for narrow-scope disjunction I'd like to give....since it is intuitively the function of MIGHT and MUST to characterize SETS, it is prima facie plausible that they could predicate irreducibly setwise properties of these sets. (We lack an argument, at least, that they cannot or shouldn't.)
Fourthly, the generalization I have suggested is supported on independent grounds found at the semantics-pragmatics interface. There is good reason to believe, for example, that what is merely a good inference at the level of unembedded assertion is a semantic entailment at the level of belief ascription. Why is *this*? Well, it relates to the idea that belief contexts are intensional (or even hyperintensional).
Consider, for example, a philosopher who (like nearly everyone) accepts that
"Hesperus is Phosphorus is nec. true" is true iff "Phosphorus is Phosphorus is nec. true" is true.
but nonetheless denies that
"Joe believes Hesperus is Phosphorus is nec. true" is true iff "Joe believes Phosphorus is Phosphorus is nec. true" is true. (Compare: "Joe believes Hesperus might not be Phosphorus" is true iff "Joe believes that Phosphorus might not be Phosphorus" is true.)
As for belief ascription, so for epistemic modal statements (which characterize information).
Compare, also the general maxim that belief ascriptions attribute diagonalized propositions, which comes directly from the maxim, "don't say "Joe believes p" unless Joe would assert "p."" This enables a (hyperintensional) account of belief ascription to piggyback on Stalnaker's diagonalization strategy in "Assertion." [which was originally a theory of communicative content.] If we do this, then we can get an account of why you shouldn't say e.g. "Joe believes that p or q" unless Joe would assert "p or q"--which, for Gricean reasons, he probably wouldn't assert unless both disjuncts were epistemically possible for him. Depending on the semantics we give for belief assertion [and the formalization diagonalization provides], it could be positively FALSE to ascribe to Joe the belief that p or q unless both disjuncts are epistemically possible for him.
Another route to (possibly?) the same point: we can associate with a sentence at a context both (a) a semantic value and (b) the characteristic effect the assertion of the sentence has on the context. When we get into belief contexts, we are characterizing an agent's state of mind; when we say "a believes p," we ascribe to him a state of mind which is the state of the context brought about by a felicitous assertion of p. Thus, we can connect the pragmatic effects of unmodalized disjunction with the semantic effects of modalized disjunction.
Lastly, and relatedly, the "mixed info-state" semantics I suggest for embedded disjunctions can help us account for puzzles like MacFarlane and Kolodny's miners puzzle.
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