ility to perform that act. One way of challenging this claim is to deny the necessity claim: that is, to argue that it is sometimes the case that an agent is able to perform an act that she does not perform at any possible world.
This is an argument that has in fact been made by several authors. Descartes, for one, appears to have argued that God is such an agent (Curley 1984). A genuinely omnipotent being, one might argue, should be able to perform any act whatsoever, even the impossible ones. This view of omnipotence is contentious, but it is not clear that it should be ruled out formally, by the very analysis of ability, as (MA) does. Spencer (2017) argues that even non-omnipotent agents may sometimes have the ability to perform acts that they do not perform at any possible world.
Let us grant, however, that the possibility of performing an act is a necessary condition for performing that act, and that in this sense an attribution of ability entails a possibility claim. One might nonetheless resist the view that ability admits of a modal analysis in the manner suggested by (MA).
That is the kind of argument developed in a prescient discussion by Anthony Kenny (Kenny 1975; the presentation of Kenny here is indebted to the discussion in Brown 1988). Kenny argues that, if something like (MA) is indeed true, then ability should obey the principles that govern the possibility operator in standard modal logics. Kenny claims that ability fails to satisfy the following two principles:
(1) \(A \to \Diamond A.\)
Informally, (1) expresses the principle that if an agent performs an action, then she has the ability to perform this action. This is, Kenny argues, false of ability.
(2) \(\Diamond(A \lor B) \to (\Diamond A \lor \Diamond B).\)
Informally, (2) expresses the principle that if an agent has the ability to perform one of two actions, then she has the ability to perform either the first action or the second action. This is, Kenny argues, false of ability.
Let us begin with (1). Kenny claims that this principle is false 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 throug