h why precisely this is a counterexample to (MA). Consider an agent S who has the ability to pick a red card or a black card, but does not have the ability to pick a red card or the ability to pick a black card. According to (MA), S has the ability to A iff S does A at some world (or set of worlds) satisfying condition C. Consider the case where (MA) appeals to a single world, not a set of worlds. If S has the ability to pick a red card or pick a black card, then by (MA) there is a world w satisfying condition C where S picks a red card or black card. Then either S picks a red card at w or S picks a black card at w. Then, applying (MA) now in the other direction, S has the ability to pick a red card or S has the ability to pick a black card. But that, by assumption, is not the case. Since (MA) is the only substantive premise appealed to that argument, (MA) must be rejected.
Note that this argument turned essentially on adopting the version of (MA) which appealed to a single world, rather than a set of worlds. So one way of responding to this objection is by appealing to sets of worlds in the modal analysis of ability. This is precisely the proposal of Mark Brown, who argues that, if we take accessibility relations to hold between a world and a set of worlds, then we may capture talk of ability within a possible worlds framework that is broadly in the spirit of standard views (Brown 1988; see also Cross 1986). Alternatively, we may take this sort of point to militate in favor of a return to hypothetical theories of ability, since, at least on Lewis’s view of subjunctive conditionals, it may be that a disjunction follows from a counterfactual claim without either of its disjuncts following from that claim (Lewis 1973, 79–80). Modal accounts that appeal to sets of worlds are ‘non-normal’ in the sense that they do not satisfy the axiom K, but they remain true to the letter of (MA) as well as the spirit of modal analyses generally, insofar as they avail themselves only of possible worlds and quantification thereover.
In the material mode, the modal analysis gives an account of what it is to have an ability in terms of quantification over possible worlds. In the formal mode, it gives a semantics for the ascription of ability — paradigmatically, sentences involving ‘can’ or ‘is able to’ — in terms of quantification over possible worlds.
This formal aspect of the modal analysis has been prominent in the philosophical and linguistic literature because the standard semantics for ability ascriptions is an explicitly modal one. This is the view developed in a series of papers by Angelika Kratzer (Kratzer 2012). Kratzer treats expressions such as ‘S can A’ and ‘S is able to A’ as possibility claims. That is, ‘S is able to A’ is true just in case there is a possible world w meeting certain conditions at which S does A. The conditions are that (i) w be accessible given some contextually-specified set of facts (the modal base) and (ii) that w be at least as good, according to a contextually-specified ranking of worlds (the ordering source), as any other accessible world. The Kratzer semantics is thus an instance of the modal analysis on its semantic formulation:
(MAsemantic) ‘S is able to A’ is true iff S does A at some world (or set of worlds) satisfying condition C.
A number of objection have been brought against the modal analysis in this latter, formal, aspect.
One objection prominent in the recent literature (Mandelkern et al. 2017; Schwarz 2020) is that Kratzer’s semantics, or any analysis of the form of (MAsemantic), appears to have trouble marking an intuitive distinction between what someone is able to do and what it is possible for her to do. Let us say that an unskilled darts-player is about to throw a dart. She utters:
(3) I am able to hit the bullseye
Intuitively, what she says is false: she is not able to hit the bullseye, as she is a poor darts-player. Yet there is an accessible and perfectly good possible world w at which she hits the bullseye — which is just to say, in the object language, that it is possible for her to