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.

Post-Meeting 2/19/10

--Challenge: Consider two felt entailments:

(1) (Might A) v (Might B) => (Might A) & (Might B)

(2) Might (A v B) => (Might A) & (Might B)

Considering that we will, according to Simons, need recourse to pragmatic mechanisms to explain the first felt entailment, isn't a semantics that gives us a semantic entailment in (2) redundant?

--Answer: I'm not sure. It depends on:

1) whether the first felt entailment is really that strong. I guess I don't think it is--especially not on the assumption that epistemic modal operators work in the same way that deontic and other modals do (but perhaps this is not a good assumption to make...) Even without relying on the analogy with other forms of modality, it seems like the felt entailment is NOT CANCELLED by the rider "but I don't know which", but rather forced to a reading in which the entailment was never felt in the first place!

There is Zimmerman's argument that A v B => Might A & Might B. This is a good one in most circumstances. But this is definitely pragmatic.

2) the status and viability of my/Simons's claim that epistemic modal operators by default take type-lifted arguments--that is, sets of propositions rather than bare propositions. Reply: but the Hamblin Type-shift will make it the case that bare propositions are also (singleton) sets of propositions. Counter-reply: ok, well, I was considering an alternative semantics in which the type-lift doesn't occur until the derivation hits an operator that demands it: that means that, when [[Might]] hits a set {p1, p2} of propositions, it will try to compose with the whole unit before trying to compose with the individual disjuncts. Since it CAN compose with the whole unit, that's what it will do--it will never go to the fallback step. (Simons thinks that it does, sometimes, but I don't think so.)

Q) How devastating is it, for Simons, that on her semantics [[must]] and [[might]] aren't duals?

A) It's not so good, but note that in her favor they do come out duals in the single-proposition case: that's the case about which we have the strongest prima facie intuitions.

Counter-answer) Yeah, but, those negations of the second type (``You can't take French or Spanish, you HAVE to take Spanish") sound awfully metalinguistic!

[what is the status of metalinguistic negation...?]