stativity and modality

thanks to a language log post, which pointed out the irony in the following headline, a question i've had before (but haven't done any research on) is once again on my radar.

of course, what is being pointed out is that "you can't belong in Britain" is ungrammatical.  what's being taken for granted is why that should be.

to me, this seems to be a problem with 'can' and statives. the examples in (1) are all ungrammatical, but the examples in (2) are just fine:
    (1)  a. *You can't belong in Britain if you don't speak English.
         b. *He can't know Marie - they've never met.
         c. *They can't like milk if they're vegan.
         d. *I can't possibly care about what happened at work.
    (2)  a.  You won't/might not/couldn't belong in Britain if you don't speak English.
         b.  He won't/might not/couldn't know Marie - they've never met.
         c.  They won't/might not/couldn't like milk if they're vegan.
         d.  I won't/might not/couldn't possibly care about what happened at work.

why (1) should be out is not straightforward, and i have struggled with trying to explain it to non-native speakers learning english.  moreover, it's not as simple as "stative verbs cannot appear with 'can'" because sometimes 'can' with a stative verb is possible:
    (3)  a.  You can't have personal belongings as a monk.
         b.  Four people can't live in a one-bedroom apartment.

though i can't quite put my finger on what the analysis would be, i have a feeling it's related to the fact that stative verbs often get a generic/habitual interpretation when in the present tense.

...thoughts?

'singular they'

when facebook doesn't know the gender of one of its users, it "panics" when it needs to refer to them with a pronoun.  what to do?  "he/she"?  "this person"?  well, what facebook does is use the pronoun otherwise used for third person plural.

this is actually a reasonable choice. if you go back to the first sentence of this post, you'll see that's actually what i did as well (without even thinking).  people have been using they/them/their in these situations for quite some time[1], as randall munroe points out in an old xkcd:

indeed --there are situations in which they/them/their is often the only felicitous option.  for example, if you're driving down the highway, and you notice someone's taillight is out, (1b) or (1c) would seem to indicate something about the speaker's knowledge/beliefs on the gender of the driver, whereas (1a) remains happily agnostic about the issue of gender:
     (1)  a.  That person probably doesn't know their taillight is out.
          b.  That person probably doesn't know his taillight is out.
          c.  That person probably doesn't know her taillight is out.

but! can you just use they/them/their as "gender-free" (or even "number free" -- "No matter whether 1 student takes the class or 20 students take the class, they'll be surprised") in any situation you like?

this seems to be the assumption facebook makes (or, if they're not assuming so, they're willfully ignoring grammar and using "they" as in a "it's the best option we've got" way).  for example, i have a friend, shannon (even this person's name is ungendered!) who prefers that facebook not know his/her gender.  whenever shannon changes profile pictures, facebook reports it as:
     (2)  Shannon changed their profile picture. 
then, when i read this, i do a double-take.  it doesn't seem felicitous.  but why not?  if "they" were really gender/number-free, (2) should be, in principle, grammatical.  similarly, (3a) should be as grammatical as (3b):
     (3)  a. #Matthew₁ is a good student. They₁ always do their₁ homework.
          b.  [Sara and Jane]₁ are good students. They₁ always do their₁ homeworks. 

perhaps, then, (2) and (3a) *are* grammatical -- in the narrowest sense.  they are ruled out for independent pragmatic reasons: "you have the information that matthew is male, so you should use the appropriately gendered pronoun".

or maybe they are ungrammatical for reasons of grammatical features: "the gender/number-free they is additionally marked as indefinite".  this has been proposed by Pinker [2],  but it raises a new question.  how many "they"s are there?  is there one with features [3rd, pl, def] and another with the features [3rd, indef]?  alternatively, could it be that there is exactly one "they" whose features are [3rd] and its being infelicitous in (2) and (3a) is a non-featural (perhaps pragmatic) one?

one last alternative.  perhaps this has to do with grammatical plurality.  that is, 'they' really is [3rd, pl] in cases like (1a), and it's just that grammatical plurality would be the elsewhere case, and singular is used only when the speaker believes there is exactly 1. for example, in the phrase "___ books" i can use literally any number, except "1". i could use "1.4", "0", "232", etc.  and when i ask the question of "how many", you have to use the plural noun, as in "how many books".  this is the case even if i am biased into thinking there is actually only 1 (for example if i only see the outline of 1 book in your shopping bag), i cannot ask "how many book".

the main question we're left to chew on: why does 'they' get used in situations like (1a) and what restricts it against appearing in (3a)?  is it the issue pragmatic, lexico-featural, or part of the larger issue of plurality?