Ability and Possibility
My paper "Ability and Possibility" has been published in Philosophers' Imprint. Here's the abstract:
According to the classical quantificational analysis of modals, an agent has the ability to perform an act iff (roughly) relevant facts about the agent and her environment are compatible with her performing the act. The analysis faces a number of problems, many of which can be traced to the fact that it takes even accidental performance of an act as proof of the relevant ability. I argue that ability statements are systematically ambiguous: on one reading, accidental performance really is enough; on another, more is required. The stronger notion of ability plays a central role in normative contexts. Both readings, I argue, can be captured within the classical quantificational framework, provided we allow conversational context to impose restrictions not just on the "accessible worlds" (the facts that are held fixed), but also on what counts as a performance of the relevant act among these worlds.
So, even though it is not the main motivation, you do have an account of the Kenny-type puzzles with ability modals. E.g. Sam is not very good at throwing darts, but at least usually hits the board. Then talking about her next throw: 0a seems true, but neither 0b nor 0c seems true.
0a. Sam can hit the dart board.
0b. Sam can hit the top half of the dart board.
0c. Sam can hit the lower half of the dart board.
So its seems that ability "can" doesn't distribute over disjunction. That's weird. And so people think it shows that this "can" is not a possibility modal, or should get a totally different sort of analysis.
But on your account "can" is essentially ambiguous between two different possibility modals: effective and transparent. Effective "can" does distribute over disjunction, that is, 1a entails (1b v 1c). But transparent "can" doesn't distribute over disjunction.
1a. Sam can (effectively) hit the dart board.
1b. Sam can (effectively) hit the top half of the dart board.
1c. Sam can (effectively) hit the lower half of the dart board.
2a. Sam can (transparently) hit the dart board.
2b. Sam can (transparently) hit the top half of the dart board.
2c. Sam can (transparently) hit the lower half of the dart board.
And the Kenny-type puzzles have to do with the transparent readings in 2. Is that basically right, on that aspect of the view? No objection. Somehow I hadn't really noticed this last time I read this paper.