se in light of cases like the following: ‘A hopeless darts player may, once in a lifetime, hit the bull, but be unable to repeat the performance because he does not have the ability to hit the bull’ (Kenny 1975, 136). This kind of ‘fluky success’ has been extensively discussed in the philosophical literature — perhaps most famously in Austin (1956) — in order to make a variety of points. Kenny’s insight is to observe that these simple cases tell against the modal analysis of ability, as they violate an axiom of many modal logics, namely any system as strong as the system T.
A simple response to this point is to deny that T (or any stronger logic) is the correct logic for ability. To deny this is still to allow for a treatment of ability within the framework of possible worlds. Notably, the modal logic K is one that fails to validate (1). A natural response to Kenny’s first point, then, is to say that K, rather than T or some stronger system, is the correct modal logic of ability.
This response is not available, however, in response to Kenny’s second objection. Recall that objection was that (2) is true of possibility but not of ability. Here the retreat to weaker modal logics will not work, since (2) is provable on the weakest standard modal logic, namely K. Yet the parallel claim does not seem true of ability. Kenny gives the following example:
Given a pack of cards, I have the ability to pick out on request a card which is either black or red; but I don’t have the ability to pick out a red card on request nor the ability to pick out a black card on request. (Kenny 1975, 137)
This then appears to be a case where S has the ability to A or B but lacks the ability to A and lacks the ability to B. So it appears that (2) is false of ability. In light of this Kenny concludes that ‘if we regard possible worlds semantics as making explicit what is involved in being a possibility, we must say that ability is not any kind of possibility’ (Kenny 1975, 140).
To appreciate Kenny’s conclusion, it is instructive to work through 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.
