I agree with Kai that Daniel Rothschild’s paper on definite descriptions and NPIs looks very interesting, and worth much consideration. Two quick related comments on it.
(UPDATE: Daniel has posted a longer version of the paper which interested parties should look at. And see the comments for several corrections to misstatements I make in the post.)
First, there’s no discussion of any theory of negative polarity licencing apart from Ladusaw’s. Now Lawdusaw’s theory is very good, but it isn’t the only theory on the market, but it does face difficulties, and back when I looked at NPIs seriously (around 1996 I believe) it didn’t even seem to be the majority view. (That is, it didn’t seem to be the majority view of people actively writing on it. That’s consistent with being the majority view of most linguists. Active workers in a field usually oversubscribe to fringe theories.)
Second, one of the difficulties for Ladusaw’s view is handling negative polarity in the antecedents of conditionals, as in (1) or (2).
(1) If John thinks about the puzzle at all, he will solve it.
(2) If John had thought about the puzzle at all, he would have solved it. (See below for second thoughts on this one.)
These aren’t downward entailing, but as we see they are NPI licencing. In many respects conditionals behave semantically like Russellian definite descriptions. (1) is similar (if not identical) to the claim “In the nearest possibility that John thinks about the puzzle at all, he will solve it.”. So the worry for Rothschild’s objection is that a story about NPIs that explains what they do in conditionals might, somehow, help the Russellian.
Two big on the other hands…
Since the problem with indicatives is that they suggest the Ladusaw account is too restrictive, and the problem for the Russellian is that Russellian theories make Ladusaw’s account too permissive, it isn’t clear how fixing the account to get conditionals to work is going to help. But it might help.
There’s of course a simple explanation for why NPIs are licenced in the antecedents of subjunctives – subjunctives implicate the negations of their antecedents. If I wasn’t so lazy I’d find a dozen references of people making this simple explanation. I always thought there was a simple reason that didn’t work – subjunctives don’t in general implicate the negations of their antecedents. Just as I was writing this up, I noticed that reply won’t work. It won’t work because when the implication from “Had p, would q” to not p is blocked, so is the licencing of NPIs in p. Compare (2) and (3).
(2) If John had thought about the puzzle at all, he would have solved it.
(3) If John had thought about the puzzle at all, things would be exactly as they are.
(3) is a ‘forensic’ counterfactual of the sort discussed in Alan Ross Anderson’s 1951 Analysis paper. (I think it’s 1951, I don’t have the reference in front of me.) It’s exactly the kind of conditional that shows the (pragmatic) inference from Had p, would q” to not p is not universal. And it doesn’t licence NPIs. Maybe the simple explanation, which is of course consistent with Ladusaw’s theory, is right after all.
Final point. Rothschild is entirely right that a theory of DDs should take NPIs very seriously, though I don’t think his evidence (that Ladusaw’s seminal paper turns up in anthologies) provides great reason to believe that. NPIs are basically gifts from God to the semanticist – they provide non-trivial non-obvious tests of semantic hypotheses that probably weren’t what theories were originally designed to capture, but which can’t easily be explained away. There’s not many of those in semantics. Compare the long-running disputes over what Russellians can say about “The table is covered in books”, where there are (fittingly) too many rather than too few “explanations away”. NPI tests are (relatively speaking) good clean tests for whether a semantic theory works, and if Russellian theories of definite descriptions don’t, then those theories are wrong.