Neg-raising through question-raising?
"Neg-raising" occurs when a negation that appears to have wide scope (over some operator) is interpreted as having narrow scope. For example, (1) conveys not only the absence of a belief that pizza is available (as one might expect), but also the presence of a belief that pizza is unavailable.
There is a large literature on this phenomenon, with many competing explanations. Foolishly, I've tried to contribute to this literature with a new proposal.
My proposal is that neg-raising is an instance of a more general phenomenon whereby negative utterances are interpreted as conveying positive information. (2), for example, tends to convey not only that Jack didn't sing Hey Jude, but also that Jack sang something else – especially if Hey Jude has intonational focus.
The effect in (2) is somewhat less well-studied, but one can find some promising conjectures. For example, Rooth 1996, 293–95, Beaver and Clark 2008, 45–49, and Simons et al. 2010, 318 suggest that it arises because (2) is taken to address the question ("qud") what did Jack sing?, which presupposes that there's something that Jack sang. This pragmatic presupposition, combined with the literal meaning of (2), entails that Jack sang something other than Hey Jude.
Suppose this is the correct account of (2). Can it be extended to (1)? Arguably, yes. The idea is that (1) is taken to address the question what I think about the availability of pizza. The question presupposes that I have an opinion on this issue: either I think that pizza is available or that it is not. This presupposition, combined with the literal meaning of (1), entails that I think that pizza is unavailable.
If this explanation is on the right track, the neg-raising interpretation of ¬φ(p) as φ(¬p) arises iff ¬φ(p) is assumed to address a question of the form "which p is such that φ(p)?", in which φ is held fixed and the complement p is varied. Can we test this? My sense is that theories of discourse structure in the tradition of Roberts 1996, Rooth 1996, and Beaver and Clark 2008 don't allow us to directly inspect the addressed question, but one can find good indirect evidence.
For example, focus marking gives a strong hint: focussed constituents generally aren't held fixed in the addressed question. On the proposed account, the neg-raising effect should therefore depend on whether the relevant predicate (e.g., "think") is focussed. This prediction seems correct.
We would also expect that comparatively weak and inconspicuous predicates are more likely to trigger neg-raising than strong and conspicuous predicates. For example, (3) doesn't convey that Jack sang a song other than Hey Jude because the unusual predicate (although more or less equivalent to "sing") draws attention to itself: the speaker plausibly wants to elaborate on how Jack moved his lips; this is varied in the qud.
By the same reasoning, we can explain why (4) doesn't trigger neg-raising: when a speaker uses "100% sure", they want to elaborate on the strength of their belief, which is varied in the qud.
So the proposal looks promising. Fleshing it out requires some care. For example, one might assume that the question addressed by (5) is what I think we'll have for dinner: pizza or pasta or curry or …
But then (5) would convey that there's a specific dish other than pizza that I think we'll have for dinner, which it doesn't.
It's also not entirely clear how the proposal deals with quantified cases like (6).
In both cases, though, there are plausible explanations, as I explain in my paper. I also think the proposal has a good chance of explaining the limited cyclicity of neg-raising and the licensing of certain negative polarity items that much of the linguistics literature has focussed on.
But I'm not a linguist, and I'm not sure how these details should be worked out.
That's why I was foolish to embark on this project. I've submitted my manuscript to Semantics & Pragmatics and (in a heavily revised form) to Meaning; the response has been polite, but uniformly negative. Linguists want to see a concrete mechanism, not a hand-wavy story. All I have is a hand-wavy story. The story still seems plausible to me. I hope one day somebody will pick it up.