You’re right that this argument doesn’t go through quite as cleanly as I suggest with the Stalnaker conditional. I’m going to try to write something else covering these cases. (Short version: ‘May’ and ‘Probably’ are still problems.)

And I wasn’t really trying to give another reason to believe the equivocation story as opposed to the wide scope story or the logical revisionary story. (I really should have been clearer on this.) Rather, I was worried that disjunctions were a problem for the equivocation story. And I think positing a (sometimes hidden) “if not” has two advantages. One, it reduces the problem to the previous problem. Two, both the wide-scope story and the logical revision story need to make much the same move.

Short version of previous paragraph: I was trying to defend the equivocation story from a challenge, not really trying to argue for it or against alternatives.

Heath,

It might be the case that the modals have different scope behaviour. But I’m rather sceptical of starting there. My impression was that the argument for the wide-scope view was that (a) it works, and (b) nothing else does. Since the equivocation view also works, and the wide scope view requires some ad hockery (i.e. not applying with all modals) I think it is hard to motivate the wide-scope view. But it certainly isn’t impossible that different modals behave differently here.

I don’t have strong convictions here, but that at least seems like an option worth ruling out.

Just in virtue of introducing the conditional element into the second disjunct, it looks to me that you’ve already got an equivocation between the second disjunct and (2). What we have, partially regimented, is:

(2’) not Must(Under sofa)
(11’) (Under desk) or (if not under desk, it must be under sofa).

Now however we analyze the second disjunct, it’s already clear that it doesn’t express the proposition that (2) denies—-in fact, it expresses an intuitively true prop.

If that’s right, then we don’t need to get into the partially bound stuff, or take a stance on the interaction of modals and conditionals, to get out of the puzzle with disjunctions. The response is equally available, for example, to one who thinks that modals scope over conditionals.

So, while the parallel forms you give the conditional and disjunctive puzzles seem suggestive, but I’m not as yet seeing anything uncomfortable with giving different responses in the two cases: going with the wide-scoped response to the conditional case, and the equivocation response in the disjunction case.

If there was some sort of uniform diagnosis of the problems in the offing, I’d feel some theoretical pressure towards adopting it. But it looks to me that at the moment the solutions are only superficially similar: equivocation in both cases, but for very different reasons (partially bound variables in one case, tacit conditional material in the other).

(I know you think the wide-scoped response to the conditional puzzle is independently objectionable—-I’m not so sold on that, if we follow the Stalnaker analysis closely. So I’m interested whether you’re thinking of your responses as independent, or as a package-deal).