Zimmermann basics

Zimmermann is interested in analyzing (unembedded) disjunctions as "lists of epistemic possibilities." Here, what "list" crucially involves is closure: a list of items is closed when nothing else can be added to the list: (intuitively, the list items union to and *cover* the contextually determined set over which we are quantifying--so nothing can be added to the list except a set which is a union of subsets the sets that are already in it). Various "closure operators" which may be added to "open" lists are discussed (and many of them involve Montague type-lifting the items in the list.)

What this involves for choice sentences, syntactically speaking, is that all choice sentences are analyzed as wide disjunctions (the contrast here with Simons couldn't be greater.) So the following inference does follow for Zimmermann:

Might(A)

Therefore, Might (A v B)

...it's just that the conclusion is not a parse that occurs in natural language. As far as I can tell, this gives [[or]] quite a complicated semantic entry. It is going to be a recursive, raised-type thing, but the basis for the recursion will be:

[[or]] = \lambda p . \lambda q . might p and might q.

In order to figure out how the recursion goes, I'll need to learn more about Montague lifts.