Here’s a cute little factoid I found out about from Ben Russell, a PhD student at Brown who is working on (among other things) the relationship between implicatures and NPI licencing. One issue that arises with NPIs is how they behave in complex sentences inside the scope of a ‘negative’ modifier. It turns out there are some surprising generalisations in the area. For instance, it seems NPIs are not licenced inside conjunctions, unless something that licences them appears in the same conjunct. So even though (1) is OK, (2) is bad.
(1) I doubt that he ate any beans.
(2) *I doubt that he ate some potatoes and any beans.
We get a similar result with NPIs inside universal quantifiers.
(3) I doubt that he lifted a finger to help.
(4) *I doubt that everyone lifted a finger to help.
(Note, by the way, that the NPIs in (2) and (4) are in downward-entailing environments.)
Those results are fairly well known, but it doesn’t seem there’s been much work on how far these results can be extended. It seems we don’t get a similar result with modals. (5) isn’t a great sentence, but it seems like it could be a reasonable way to express a certain kind of anti-essentialist view.
(5) He doesn’t necessarily have any parents.
On the other hand, we do (it seems to me) get a similar result for temporal modifiers.
(6) ??He didn’t always have any children.
(7) *He doesn’t always give a red cent to the Christmas charity appeal.
Compare
(8) He always doesn’t give a red cent to the Christmas charity appeal.
(8) isn’t perfect, but it’s nowhere near as bad as (7).
The real news, to me, was the difference between (5) and (6). I would have thought that both modifers like always which are quantifiers across times, and modifiers like necessarily which are (I thought) quantifiers across worlds would be syntactically similar. But they behave quite differently here. (By the way, I put the emphasis on any in both (5) and (6) deliberately. Apparently stressed any is a stronger NPI than unstressed any, and it certainly helps to bring out the contrast.)