Suppose I say (*), with respect to a particular gambling occasion.
(*) A gambler lost some of her savings. Another lost all of hers.
There is an implicature here that the first gambler, unlike the second, didn't lose all her savings. How does this implicature arise?
On the standard account of scalar implicatures, we should consider certain alternatives to the uttered sentences. In particular, I could have said 'A gambler lost all of her savings' instead of 'A gambler lost some of her savings'. If true, this alternative would have been more informative. Since I chose the weaker sentence, you can infer that I wasn't in a position to assert the stronger sentence. Assuming I am well-informed, you can further infer that the stronger sentence is false.
But in the context of (*) this explanation makes no sense. For the second sentence in (*) entails that the stronger alternative to the first sentence ('a gambler lost all of her savings') is true. So you can hardly conclude that I wasn't in a position to utter that alternative.
One might suggest that we should consider not just alternatives to the individual sentences in (*), but to (*) as a whole. If I had known that both gamblers lost all of their savings, I would have chosen 'two gamblers lost all of their savings' instead of the weaker (and more complex?) (*). Since I didn't, you can infer that only one of the gamblers lost all their savings.
That might work for (*). But I don't think it will do as a general solution. Couldn't I utter just the first sentence of (*), 'a gambler lost some of her savings', without thereby suggesting that there is no gambler who lost all of her savings?
Perhaps a more promising idea is that when we compute the implicature in (*), we hold fixed the gambler at issue. You might reason as follows:
The speaker said of some gambler that she lost some of her savings; it would have been more informative to say that she lost all of her savings; so the speaker probably doesn't think that this is true; so the gambler at issue probably didn't lose all of her savings.
This might even fit the standard account of scalar implicatures provided we treat the indefinite 'a gambler' in (*) not as a quantifier but as a referring expression, as suggested e.g. in Kamp's DRT or Heim's File Change Semantics. On these accounts, the logical form of 'a gambler lost some of her savings' is something like 'x is a gambler and x lost some of her savings', where 'x' is a free variable that gets existentially closed only on the level of discourse. When computing scalar implicatures, the alternatives should plausibly involve the same variable. In particular, since I didn't use the alternative 'x is a gambler and x lost all of her savings', you can infer 'x is a gambler and x lost some but not all of her savings'.
Unfortunately it isn't clear to me that this still works in more recent versions of dynamic semantics, where the logical form of 'a gambler' is taken to include a quantificational element.
Is there any literature on this?