Some ability statements sound wrong when affirmed but also when denied. Santorio (2024) proposes a new semantics that's built around this observation.
Suppose Ava is a mediocre dart player, and it's her turn. In this context, people often reject (1):
(1)Ava is able to hit the bullseye [on her next throw].
It's obviously possible that Ava gets lucky and hits the bullseye. But ability seems to require more than mere possibility of success. A common idea, which Santorio endorses, is that ability comes with a no-luck condition, something like this:
Propositional attitudes have an attitude type (belief, desire, etc.), and a content. A popular idea in the literature on intentionality is that attitude type is determined by functional role and content in some other way. One can find this view, for example, in Fodor (1987, 17), Dretske (1995, 83), or Loewer (2017, 716). I don't see how it could be correct.
Standard decision theory studies one-shot decisions, where an agent faces a single choice. Real decision problems, one might think, are more complex. To find the way out of a maze, or to win a game of chess, the agent needs to make a series of choices, each dependent on the others. Dynamic decision theory (aka sequential decision theory) studies such problems.
There are two ways to model a dynamic decision problem. On one approach, the agent realizes some utility at each stage of the problem. Think of the chess example. A chess player may get a large amount of utility at the point when she wins the game, but she plausibly also prefers some plays to others, even if they both lead to victory. Perhaps she enjoys a novel situation in move 23, or having surprised her opponent in move 38. We can model this by assuming that the agent receives some utility for each stage of the game. The total utility of a play is the sum of the utilities of its stages.
Suppose there are no objective moral facts. It's tempting to think that this calls for a special semantics for moral language. Perhaps moral statements somehow express moral attitudes rather than describe the world. The trouble is that moral statements seem to behave like ordinary descriptive statements. Not only can we freely conjoin moral and descriptive statements. We can even use the same words – say, 'you ought to leave' – to express a moral attitude but also to report the implications of some contextually salient norms. It would be nice if we could use a standard descriptivist semantics for 'ought' statements even if we don't believe in objective normative facts.
A common worry about mathematical platonism is how we could know about an independent realm of mathematical facts. The same kind of worry arises for moral realism: if there are irreducible moral facts, how could we have access to them?
Benacerraf (1973) put the problem in terms of causation. Knowledge of maths, he suggested, would require some kind of causal connection between the mathematical facts and our mathematical beliefs, but modern platonists typically don't believe in such a connection.
Ability modals have a "specific" and a "general" reading. If a pianist is locked in a piano-free cell, they can play the piano in the general sense, but not in the specific sense. Roughly, an agent has the "general ability" to φ if they have the internal constitution required to φ. They have the "specific ability" to φ if, in addition, the external circumstances make it possible for them to φ.
What is the connection between the two notions? Some, e.g. Mandelkern, Schultheis, and Boylan (2017), hold that 'S can φ' expresses specific ability, and that the general reading results from the application of a tacit genericity operator 'Gen'. This is a natural idea, given that general abilities are often called 'general'. (Mandelkern, Schultheis, and Boylan (2017) even call them 'generic'!) The proposal is also tempting for accounts of ability that only directly capture the specific reading. (The locked-in pianist, for example, clearly wouldn't succeed to play the piano if they tried.)