Ability, relevant possibilities, and the fixity of the past

In several writings, John Martin Fischer has argued that those who deny a principle about abilities that he calls ‘the Fixity of the Past’ are committed to absurd conclusions concerning practical reasoning. I argue that Fischer’s ‘practical rationality’ argument does not succeed. First, Fischer’s argument may be vulnerable to the charge that it relies on an equivocation concerning the notion of an ‘accessible’ possible world. Secondly, even if Fischer’s argument can be absolved of that charge, I maintain that it can be defeated by appeal to an independently plausible principle about practical reasoning that I call ‘the Knowledge Principle’. In addition, I point out that Fischer’s own presentation of his argument is flawed by the fact that the principle that he labels ‘the Fixity of the Past’ does not, in fact, succeed in representing the intuitive idea that it is intended to capture. Instead, the debate (including Fischer’s practical rationality argument) should be recast in terms of a different (and stronger) principle, which I call ‘the Principle of Past-Limited Abilities’. The principal contribution of my paper is thus twofold: to clarify the terms of the debate about the fixity of the past, and to undermine Fischer’s ‘practical rationality’ argument for the fixity of the past.


Introduction
In several writings, John Martin Fischer has argued that those who deny a principle about abilities that he calls 'the Fixity of the Past' are committed to absurd conclusions concerning practical reasoning. In this paper, I argue that Fischer's 'practical rationality' argument does not succeed. In addition, I point out that Fischer's own presentation of his argument is flawed by the fact that the principle that he labels 'the Fixity of the Past' does not, in fact, succeed in representing the intuitive idea that it is intended to capture. Instead, the debate (including Fischer's practical rationality argument) should be recast in terms of a different principle: 'the Principle of Past-Limited Abilities'.
The plan of my paper is as follows. In Sect. 2, I present a general and uncontroversial principle, which I call 'the Ability Principle', and which can be used to frame the debate about whether the past puts limitations on the abilities of agents of the type that Fischer's principle of the Fixity of the Past ('Fixity Principle') is intended to capture. In Sect. 3, I present Fischer's Fixity Principle. In Sect. 4, I argue that the debate that Fischer presents as concerning the Fixity Principle needs to be recast as a debate about the truth of a stronger principle that I call 'the Principle of Past-Limited Abilities' (PLA). In Sect. 5, I present Fischer's 'practical rationality' argument, recast as an argument for the truth of (PLA). In Sect. 6, I consider an objection to Fischer's argument based on the suspicion that it trades on an ambiguity in the notion of an 'accessible' possible world. In Sect. 7, I argue that, even if Fischer's practical rationality argument can be absolved of this charge, it can be defeated by appeal to a general principle about practical reasoning that I call 'the Knowledge Principle'. In the following sections I provide support for the Knowledge Principle, and argue that an appeal to this principle provides a convincing explanation of the evidence that Fischer appeals to in support of (PLA), while remaining neutral on the issue of the fixity of the past and the truth of (PLA).

Relevant possibilities and the ability principle
Several philosophers have suggested that some version of the following general principle holds for agential abilities 1 : 1 A clear example of an endorsement of the Ability Principle is provided by Fischer: 'very roughly, it is not unreasonable to say that an agent can do X just in case there exists a possible world suitably related to the actual world in which the agent does X ' (1994: 90). A similar general principle is suggested by Maier (2018, §4.1). Rather more specific (and hence more controversial) versions of the Ability Principle are suggested by Lehrer (1976: 253-254;quoted in Fischer & Pendergraft, 2013: 589) and by Graham (2008: 74). I should emphasize that Fischer's endorsement of (AP) is distinct from his endorsement of the Fixity of the Past Principle (FP*), to be discussed in § §3ff. below. See also note 12 below.
The plausibility of the Ability Principle rests on three considerations. One is that if I have the ability to do something, then it is in some sense possible for me to do it. The second is that a certain kind of possibility of my doing something is sufficient for me to have the ability to do it. Third, the inclusion of the 'suitably related' qualification reflects the fact that it would be inappropriate to claim that just any kind of possibility of my doing A is sufficient for my having the ability to do it. A decisive consideration here is that there are actions that it may be metaphysically possible for me to perform (for example, running a mile in under three minutes) but which it would be absurd to claim that I have the ability to perform (Beebee, 2013: 64;Maier, 2018, §2.1). A further such reason (although perhaps more controversial) is the suggestion that it might be possible for me to perform some action as a result of a fluke or stroke of luck, even if I don't have the ability to do it (Maier, 2018, §2.2).
The Ability Principle is, of course, uninformative without an account of what the 'suitable relation' is. And although the Ability Principle itself may be relatively uncontroversial, the nature of the 'suitable relation' is a highly contested matter. Many disputes between compatibilists and incompatibilists about free will and determinism concerning an agent's abilities in a certain world-for simplicity, suppose this to be the actual world-can be seen as disputes about whether worlds with a different past from the actual world prior to t*, or worlds with different laws of nature from those of the actual world, are among the 'suitably related' worlds relevant to an instance of (AP). In addition, certain debates about freedom and divine foreknowledge focus on the question whether the 'suitably related' worlds include worlds with a different past from the actual world (relative to t*). (Fischer, 2016, passim).
Let's say that a world that satisfies the 'suitable relation' condition is an abilityrelevant world; otherwise it is not. (Of course, this needs to be relativized to the particular ability and times in question.) In this terminology, the compatibilist (about free will and determinism) will typically say that a possible world may be ability-relevant even if it has a different past from that of the actual world, or has different laws of nature from those of the actual world. 3 The incompatibilist about free will and determinism will say that no such worlds are ability-relevant.
2 Throughout this paper I shall assume that t* is either identical with, or earlier (although perhaps only very slightly earlier) than t. This restriction is imposed just to keep things simple. It is not intended to prejudge the issue (which it is beyond the scope of this paper to explore) of whether it is possible to have, at some time, the ability to do something at an earlier time. For drawing my attention to the desirability of accommodating the possibility that t* is identical with t, I thank an anonymous referee. 3 Typically, but not universally, since there are compatibilists who deny that free action (at least in a sense relevant to moral responsibility) requires the ability to do otherwise, and hence will not insist that free agents under determinism have the ability to do otherwise. See McKenna and Coates (2020, §3.2). The classic source for this position is, of course, Frankfurt (1969), although Frankfurt himself explicitly applies the denial only to the conditions for moral responsibility, and not to the conditions for free action. From now on, my use of 'compatibilism' will ignore such views, unless otherwise stated.
According to the incompatibilist, '[our] freedom now is the freedom to add to the given past, holding fixed the laws of nature' (Fischer, 2013: 306, citing Ginet, 1990cf. Fischer, 1994: 88). 4 We can add a further claim. Whatever one thinks the 'suitable relation' is (and whether one is a compatibilist or an incompatibilist), one can say that if a possible world stands in the 'suitable relation' to the world in which the agent S has the ability in question, then it is a world in which S exercises that ability; otherwise it is not.
This proposal reflects the fact that, on any plausible account of these matters that accepts the Ability Principle (AP), the following may be the case: S has the ability to do A (in world w1)-and hence, according to (AP), there is a suitably related possible world in which S does A, yet there are also possible worlds in which S does A that are not suitably related (to w1) in such a way as to 'underwrite' S's ability to do A (in w1) in accordance with (AP). In those worlds, S's doing A is, in a sense, merely accidentally related to S's ability to do A (in w1). It seems to me plausible to mark this difference by saying that, in the suitably related worlds, S's doing A is an exercise of the ability to do A that S has in w1, whereas in the others, it is not. 5 Putting this together: there may be possible worlds in which S does what S actually has the ability to do, and yet which are not suitably related to the actual world to be ability-relevant, and hence in which S's doing what S (actually) has the ability to do is not an exercise of that ability. This is important to Fischer's argument for the fixity of the past, to be considered in Sect. 5 below. But two examples here will serve to illustrate the general idea.
First, and most obviously, there may be possible worlds in which S does something that S actually has the ability to do, yet in which S lacks the ability to do it, and thus does the action as a result of a fluke. It seems plausible to say that, in such a world, S does not exercise the ability that S actually has.
Secondly, a more interesting case is a possible world in which S does possess the ability to do A that S actually has, and in which S does A, but nevertheless does A as a result of a fluke. Assuming that this is coherent, it again represents a case where the agent's doing A is only 'accidentally' related to his actual possession of the ability to do A, and where his doing that which he has the ability to do is plausibly regarded as not being an exercise of that ability. 6 With these preliminaries in place, we can proceed to consider the restriction on the 'suitable relation' (and the corresponding restriction on ability-relevance) that John Martin Fischer advocates in his defence of the principle of the fixity of the past.
3 Fischer's principle of the fixity of the past In a number of writings, Fischer has defended a principle that he calls 'the Fixity of the Past' (henceforth: 'Fixity Principle'), and which can be formulated as follows: (FP*) An agent S has it in his power at t* (at or just prior to t) in possible world w1 to do A at t only if there is a possible world w2 with the same past as that of w1 up to t* in which S does A at t. (cf. Fischer, 2016: 6, 11, 17) 7 Fischer points out that a certain type of compatibilist will deny the Fixity Principle (FP*), and hold, instead, that, even if there is no 'past-matching' world in which S does A at t, an agent may have at t* the ability to do A at t in virtue of the existence of a possible world in which S does A at t against the background of a different past at t*. 8 According to this compatibilist, a possible world of this kind may be 'suitably related' to the actual world in such a way as to underwrite an ability claim (in accordance with the Ability Principle). Fischer also recognizes that the debate between the incompatibilist and a compatibilist of this type is in danger of collapsing into what he calls a 'dialectical stalemate ' (1994: 84), with incompatibilists simply insisting that the past puts a limitation on our abilities that is repudiated by the compatibilist.
However, Fischer argues that there is a positive, non-question-begging argument for the Fixity Principle (FP*), which depends on considerations of practical rationality. In Sect. 5, I shall explain Fischer's 'practical rationality' argument. In the subsequent sections, I shall argue that it does not succeed.
Footnote 6 continued his doing A is not an exercise of that specific ability, because of the element of luck involved. This, however, raises questions that space does not permit me to discuss here. For the distinction between general abilities and specific abilities, see, for example, Maier (2018, §1.3). Vihvelin (2013) employs what is essentially the same distinction, but uses 'narrow abilities' to refer to general abilities, and 'wide abilities' to refer to specific abilities (2013: 11-12). 7 This is a faithful rendition of Fischer's version of the principle, except that I have modified the variables to match those in my statement of the Ability Principle in Sect. 2 above, and introduced the distinction between t* and t to take account of the possibility of a difference between the time of the possession of the ability and the time of the action. For comparison, one version of Fischer's own formulation of (FP*) is as follows: 'An agent S has it in his power at (or just prior to) T in possible world w to do X at T only if there is a possible world w* with the same past as that of w up to T in which S does X at T.' (2016: 6) Similar formulations of this 'possible-worlds' version of Fischer's Fixity Principle can be found in many of his other papers, including many of those collected in Fischer (2016) and the coauthored Fischer and Pendergraft (2013). 8 Fischer's principal concern is with compatibilists about freedom and divine foreknowledge. However, his argument extends to 'multiple pasts' versions of compatibilism about freedom and causal determinism, as he acknowledges (e.g., Fischer & Tognazzini, 2014: 365, n. 24 To see this, first note that a compatibilist about free will and causal determinism has no reason to deny that, in every case where S actually has, at t*, the ability to do A at t, there is a possible world in with the same past up to t* in which S does A at t, and hence that the condition stated in Fischer's (FP*) is met. However,-and this is the crucial point-this compatibilist is in no way committed to the claim that the ability-relevant worlds that are relevant to S's possession at t* (in the actual world) of the ability to do A at t are restricted to those that share their past up to t* with the actual world. For (FP*) does not entail that it is only 'past-matching' worlds that stand in the 'suitable relation', according to the Ability Principle (Sect. 2 above), to the world in which the agent has an ability. 9 This compatibilist can consistently claim that an ability-relevant world may be one in which S does A against the background of a different past. But to hold that such worlds are ability-relevant is, evidently, to deny that the past puts a limitation on agents' abilities of the kind that is involved in the intuitive idea of the fixity of the past that Fischer must be intending to capture. 10 What this brings out, however, is the fact that theorists who are willing to concede that the conditions of Fischer's (FP*) may be met in all cases of the possession at t* by an agent of the ability to do A at t-and hence that (FP*) may be 9 The compatibilist about free will and determinism who accepts that there are no counterexamples to (FP*) may even hold that although, in every case where an agent has, at t*, the ability to do A at t, there is a past-matching world in which the agent does A at t, none of these worlds is ability-relevant: that is, that all the possible worlds that stand in the 'suitable relation' to the world in which the agent has the ability in question are ones with a different past up to t*. This may represent the position of those compatibilists about free will and determinism whom Horgan (1985) describes as 'altered-past compatibilists'. 10 Fischer and Pendergraft (2013) do include an acknowledgement that a compatibilist about free will and determinism need not deny (FP*) (578, n. 8). The authors note that what such compatibilists must deny is, rather, 'the Principle of the Fixity of the Past and Laws (PFPL)', a principle which, in effect, adds to (FP*) the necessary condition that w2 must have the same laws of nature as w1, as well as sharing its past up to t* with w1 (2013: 577). They argue, however, that if it is assumed that 'the relevant agent does not have access to a world with different laws of nature' (2013: 578-579), the practical rationality argument that Fischer elsewhere presents as an argument for (FP*) can be employed as an argument for (PFPL) (2013, §3). In effect, the point is that if we make the assumption that the compatibilist about free will and determinism is not permitted to treat possible worlds with different laws of nature as 'abilityrelevant' worlds, then this compatibilist must treat some possible worlds with a different past up to t* as ability-relevant, and hence will face the challenge posed by the practical rationality argument. This is, of course, correct. However, it is still the case that to treat the practical rationality argument as an argument either for Fischer's (FP*) or for Fischer and Pendergraft's (PFPL) obscures the main issue at stake in the practical rationality argument, which concerns whether ability-relevant worlds can include worlds with a different past. true 11 -may nevertheless disagree about the truth of the following principle, which I call 'the Principle of Past-Limited Abilities' (PLA): (PLA) Agent S has, in world w1, at t*, the ability to do A at t in w1 (S can in w1, at t*, do A at t in w1) only if there is some possible world w2 suitably related to w1 in which S does A at t, where a possible world w2 is suitably related to w1 only if w2 shares its past up to t* with w1. 12 Moreover, although Fischer presents his 'practical rationality' argument (to be discussed in the next section) as an argument for (FP*), I think that is a mistake. His 'practical rationality' argument is, rather, an argument for the stronger principle (PLA). 13 This does not, however, diminish the significance of the argument. For there are, indeed, compatibilists who deny (PLA), and who therefore need to respond to the challenge posed by the practical rationality argument.
Before proceeding, though, it is worth noting that not all compatibilists about free will and determinism need reject (PLA), even those who hold that free will requires the ability to do otherwise. 14 A compatibilist could accept (PLA), with its restriction on suitably related (ability-relevant) worlds, but hold that, if determinism is true, then, where the agent S in the actual world has, at t*, the ability to do A at t, the suitably related 'past-matching' worlds include ones that differ in their laws of nature from the actual world, and in which, against the background of that same past up to t*, S's doing A at t is itself a 'miracle' (in Lewis's (1981) sense), or else is preceded by a 'miracle' that occurs between t* and t. 15 The incompatibilist about free will and determinism will, of course, deny that any such world with the same past but different laws of nature can be ability-relevant. This claim, however, goes beyond the assertion of (PLA). 16 In contrast, if the debate concerns, not the 11 An anonymous referee has objected to my suggestion that the compatibilist who holds that there are no counterexamples to (FP*) should be regarded as accepting (FP*). The point, I take it, is that such a compatibilist does not accept (FP*) in the sense of accepting that it puts a constraint on the conditions for the possession of an ability: does not accept that it is necessary, for the possession at t*of the ability to do A at t, that there be a possible world with the same past up to t* in which the agent does A at t. Although I appreciate the point, I do not think that it undermines my claim that it is (PLA), and not (FP*), that lies at the heart of the dispute. 12 It should be noted that whereas the Ability Principle (AP) (Sect. 2 above) has the form of a biconditional, both (FP*) and (PLA) specify only necessary conditions for the possession of an ability, not necessary and sufficient conditions. As far as I am aware, in spite of his endorsement of a version of (AP) (cited in note 1 above), Fischer never attempts to specify sufficient conditions for the 'suitable relation' mentioned in (AP). Thanks to an anonymous referee for inviting me to clarify this point. 13 Since (PLA) entails (FP*) (although not vice versa), Fischer is, of course, correct in treating the compatibilist who denies (FP*) as committed to the denial of (PLA), and hence as incurring any untoward consequences that follow from the denial of (PLA). My point is that, since the denial of (PLA) is consistent with the acceptance that the conditions of (FP*) are always met, Fischer's presentation of the practical rationality argument as an argument for (FP*) obscures the crux of the debate. 14 Concerning the qualification, see note 3 above. 15 Lewis (1981) denies himself the option of claiming that the performance of A at t could itself be a miracle. For a version of 'local miracle compatibilism' that disagrees with Lewis on this point, see Beebee (2003). 16 As indicated in note 10 above, this point is, in effect, acknowledged in Fischer and Pendergraft (2013). compatibility of free will and determinism, but rather the compatibility of free will and God's foreknowledge (which is the context of much of Fischer's published discussion of the Fixity of the Past), then the debate between compatibilist and incompatibilist can be characterized as a debate over the truth of (PLA).

Practical reasoning and the fixity of the past
If the incompatibilist simply insists, without argument, that the past puts the limitation on agents' abilities that is represented by the principle (PLA), this may be regarded as, if not begging the question, then at least dialectically impotent in the debate against the compatibilist who rejects (PLA). However, Fischer claims that this situation can be remedied: 'it is at least plausible that rejecting [(PLA)] would lead to unacceptable consequences for practical reasoning. Thus there is a plausibility argument for accepting [(PLA)]... that does not depend on a prior acceptance of incompatibilism.' (Fischer, 2016: 18, but with '(PLA)' replacing Fischer's '(FP*)').
Fischer's 'practical rationality' argument appeals to examples of the following type (this example comes from Fischer, 1994): Consider the example of the Icy Patch. Sam saw a boy slip and fall on an icy patch on Sam's sidewalk on Monday. The boy was seriously injured, and this disturbed Sam deeply. On Tuesday, Sam must decide whether to go iceskating. Suppose that Sam's character is such that if he were to decide to go ice-skating at noon on Tuesday, then the boy would not have slipped and hurt himself on Monday. (Fischer, 2016: 18, quoting Fischer, 1994 We fill out the example so as to make it plausible that, according to both incompatibilist and compatibilist, Sam is able to decide to go, and to go, ice-skating on Tuesday. 17 And let us also assume that it is uncontroversial (and agreed by Sam himself) that it would have been a very good thing if the boy's accident had not occurred on Monday. Yet-and this is the crucial point-it would clearly be irrational, and absurd, for Sam to regard the following 'backtracking' conditional as giving him any reason to decide in favour of going ice-skating on Tuesday: (B) If Sam were to decide to go ice-skating at noon on Tuesday, the boy would not have slipped and hurt himself on Monday.
It is important that Fischer's argument is not that Sam should reject the backtracking conditional (B), and hold, instead, that even if he were to decide to go ice-skating on Tuesday, the accident would still have occurred. Fischer concedes that the backtracking conditional may be acceptable, even to the proponent of (FP*) (2016: 9-12). 18 Fischer's argument involves the claim that even if Sam accepts (B)-and thus accepts that, if he were to decide to go skating, the accident would not have occurred on Monday, and even if Sam's acceptance of (B) is legitimate, it would still obviously be irrational for Sam to treat this as a reason in favour of going skating. But this, Fischer maintains, is an embarrassment to the compatibilist who rejects (FP*) (and thus rejects (PLA)). To quote at length from Fischer, but again substituting ' ( Given a rejection of [(PLA)], nothing rules it out that in Icy Patch, Sam has access on Tuesday to a possible world in which the accident did not occur on Monday. After all, Sam can decide on Tuesday to go ice-skating that afternoon. If this can-claim is rendered true by a possible world . . . accessible to Sam, and on the assumption that we reject [(PLA)] nothing rules it out that [that possible world] will contain the accident's not happening on Monday. But if this is so, why shouldn't Sam take this as a reason to decide to go iceskating on Tuesday? If it is appropriate for Sam to take as relevant reasons that obtain in any world genuinely accessible to him at a time, then surely [if (PLA) is rejected] it is (or may well be) rational for him to decide to go iceskating on Tuesday. Fischer's argument may be summarized as follows. Although both incompatibilist and compatibilist may regard a world (call it 'the B-world') in which Sam decides on Tuesday to go skating (and does go skating) and there is no previous 18 For this reason, Fischer claims that the incompatibilist should not (or at any rate, need not) insist on what he calls 'the conditional version' of the Fixity Principle, a version that claims that an agent cannot do something such that, were the agent to do it, the past would have been different (2016: 5; cf. 1994: 78). Fischer concedes, at least for the sake of argument, that there are backtracking counterfactuals, such as (B) in Icy Patch, that refute this conditional version of the Fixity Principle. Fischer's point is that the possible worlds with different pasts that make the backtracking counterfactual true need not be what I have called 'ability-relevant' worlds (Fischer, 2016: 9-12;cf. Fischer, 1994: 89-92;Fischer and Pendergraft, 2013: 592). A similar distinction is made, although for a different purpose, by Graham (2008: 74). accident on Monday as possible, the incompatibilist regards it as 'inaccessible' to the deliberator, whereas the compatibilist who denies (PLA) seems committed to regarding it as 'accessible' to the deliberator.
Given the principle (call it 'the Accessibility Principle') that in one's practical reasoning about whether to perform an action A, it is appropriate to treat, as potentially providing reasons for or against performing A, facts that obtain in any possible world that is 'accessible' to one (cf. the quotation above), the compatibilist is in an embarrassing position, since it is manifestly inappropriate for the deliberator (Sam) to take the fact that there is no accident on Monday in the B-world as providing a reason for him to go ice-skating on Tuesday. 19 Fischer's 'practical rationality' argument rests on two crucial claims. One is the Accessibility Principle. The other is that the compatibilist who denies (PLA) is committed to accepting (or at least has no good reason to deny) that the B-world is 'accessible' to the deliberator, even though the B-world has a different past from the actual world.

Accessibility and the ability principle
Let us start with the second claim: that the compatibilist is committed to the thesis that the B-world is accessible to Sam, the deliberator. 20 There is, as I shall now demonstrate, a convincing argument that the compatibilist (unlike the incompatibilist) is committed to the claim that the B-world is one that is ability-relevant (with regard to Sam's ability to go skating on Tuesday). But why should we accept that, if a world is ability-relevant (to a deliberator's ability), it follows that it is a world that is accessible to the deliberator-a claim that plays a crucial role in Fischer's argument against the compatibilist?
It might seem that there is an obvious answer to this question. Isn't Fischer's talk of a world as 'accessible' merely a stylistic variant of the terminology of a 'suitably related' world that is involved in my formulation of the Ability Principle? 21 Although this first reaction may be a natural one, matters are by no means so simple, as I shall show in this section.
I begin by rerunning the first part of Fischer's argument using the terminology that I employed earlier in my discussion of the Ability Principle (where I did not use the expression 'accessible world'). I shall assume (uncontroversially, I take it) that both Fischer's incompatibilist and the opposing compatibilist can accept the Ability Principle as characterized in Sect. 2 above. This principle, recall, is the following: Ability Principle (AP): Agent S has, in world w1, at t*, the ability to do A at t in w1 (S can in w1, at t*, do A at t in w1) iff there is some possible world w2 suitably related to w1 in which S does A at t.
The first part of Fischer's argument, shorn of his 'accessibility' terminology, may now be rephrased as follows. (As before, I substitute '(PLA)' for Fischer's '(FP*)'.) According to the (incompatibilist) proponent of (PLA), even if the B-world is possible, and even if Sam in the actual world does have the ability at t* (noon on Tuesday) to go skating that afternoon (at t), the B-world does not satisfy the Ability Principle's conditions for being suitably related to the actual world. According to the incompatibilist, if Sam does have, at t*, the ability to go ice-skating at t, this is in virtue of the existence of possible worlds that, unlike the B-world, share their past up until t* with the actual world. 22 Thus, according to the incompatibilist, the B-world is (in my terminology) not an ability-relevant world, and not a world in which Sam exercises his ability to go ice-skating at t, even if he has that ability, and even though the B-world is one in which he goes ice-skating at t.
By contrast, the compatibilist who denies (PLA) does appear to be committed to the view that not only is the B-world a world in which Sam does something that he actually has the ability to do (which Fischer's incompatibilist accepts), but also it is a world that may bear the 'suitable relation' to the ability claim. The B-world may be one that is ability-relevant to whether Sam has the ability at t* (noon on Tuesday) to go ice-skating at (the slightly later time) t, and one in which he exercises that ability.
Fischer's own statement of his practical rationality argument clearly assumes that if a possible world is 'suitably related' to the actual world in a sense that is relevant to the Ability Principle, then that world is an accessible world-and, moreover, one that is accessible to the one who has the ability. Furthermore, Fischer's statement of his argument also assumes that if a possible world is 'accessible' in this sense, it is one that the agent can bring about. The reliance on these assumptions is evident from his wording in the passages quoted in Sect. 5 above.
Fischer's first assumption (that 'suitably related' worlds are 'accessible' worlds) is, however, capable of two interpretations. A standard use of the notion of an 'accessible world' in modal theorizing is, of course, to indicate a restriction on the range of possible worlds that are relevant to a modal claim. Thus, for example, one can say that, in certain contexts-for example, those in which it is nomological modality (a restricted type of alethic modality) that is relevant-the 'accessible' worlds are confined to those with the same laws of nature as the actual world. For other conceptions of possibility, or in other contexts, different accessibility relations may obtain. 23 In this sense of 'accessibility', it is reasonable (perhaps even trivially true) to say that a world that is suitably related to a world w1 in accordance with the Ability Principle is a world that is accessible to w1. However, for a world to be 'accessible' in this technical sense carries no implication that it is a world that can be brought about by any agent. In addition, accessibility, in this sense, is a relation between worlds, not a relation between agents and worlds. Thus, if this is what 'accessible' means, then although it is innocuous for Fischer to claim that all ability-relevant worlds are accessible worlds, this appears to provide no grounds for thinking that the worlds that are accessible in Sam's case are worlds that Sam (or anyone else) can bring about, nor even that such worlds are accessible to Sam. If so, it provides no grounds for thinking that Fischer's Accessibility Principle (Sect. 5 above) has application to the compatibilist's conception of the relation between Sam and the B-world.
On the other hand, the claim that a possible world w2 is accessible to a world in which an agent S has a certain ability may be given a different interpretation: one that entails that w2 is accessible to the agent S, in an everyday sense of 'accessible' in which to say that something is accessible to me is, roughly, to say that I can 'get to (or get at) it from where I am'. And perhaps, in this sense of 'accessible world' it is plausible to say that a world that is accessible to an agent is also a world that the agent can bring about. 24 The trouble, however, is that, in this sense of 'accessible', there is no obvious reason to accept that if a world is 'suitably related' to the actual world in accordance with the Ability Principle, it must also be an accessible world. 25 Thus, it is tempting to conclude that, insofar as Fischer's practical rationality argument in favour of (PLA) appears forceful, this is a consequence of an equivocation on the notion of accessibility. If this were so, then recognition of the equivocation would allow the compatibilist who rejects (PLA) to avoid being saddled with the absurdities concerning practical reasoning that Fischer claims to threaten the denial of (PLA).

Accessibility and the knowledge principle
There is more to be said, however. Fischer might argue that, although in general, to say that a possible world is 'accessible' implies nothing about any agents' access to that world, or about their capacity to bring such a world about, this is not so if the modality in question is the agential modality of ability. If this is correct, then Fischer's practical rationality argument could be reinstated, without any suspicion of an equivocation on the notion of accessibility. To investigate this, let me first reformulate my Ability Principle by substituting 'accessible' for 'suitably related', as follows: Ability Principle* (AP*): Agent S has, in world w1, at t*, the ability to do A at t in w1 (S can in w1, at t*, do A at t in w1) iff there is some possible world w2 accessible to w1 in which S does A at t.
In terms of (AP*), we can see Fischer as holding that, if a possible world w2 in which p is the case (in the Icy Patch example, one in which the accident did not occur) is an 'accessible' world according to (AP*) with respect to an ability to do A that an agent possesses in the actual world, then this has the following consequence. First, it follows, according to Fischer, that w2 is accessible to the agent in the actual world-that the agent has access to w2-and hence has access to a possible world in which p is the case. 26 (See the quotations from Fischer in Sect. 5 above.) In addition, it follows, according to Fischer, that: • the agent can get to w2 from the actual world (Fischer & Pendergraft, 2013: 589-592;Fischer, 1994: 101); • the agent in the actual world can actualize w2 (Fischer, 1994: e.g., 96, 97, 101, 102, 105;Fischer and Pendergraft: 589); • the agent in the actual world can bring it about that p is the case (see the quotations from Fischer in Sect. 5 above); • the agent in the actual world can (or has it open to him to) make the world contain the fact that p (Fischer, 2016: 20;Fischer & Pendergraft, 2013: 588).
According to Fischer, any of the claims in the bullet-pointed list can be exploited in an argument for his Accessibility Principle: the principle that implies that, in the case of Icy Patch, if the B-world is accessible to Sam, then Sam should take what happens in the B-world to be practically relevant to his decision whether to go iceskating, with the absurd consequences that that entails. As I have indicated (Sect. 6 above), one possible strategy for the compatibilist is to attempt to argue that all of these locutions are inappropriate. However, to defend the compatibilist against the practical rationality argument, a simpler strategy is available. This concedes, at least for the sake of argument, that all of the implications that Fischer draws, in the bullet-pointed list above, are indeed implications of w2's being accessible to the actual world in the sense involved in the Ability Principle* (AP*). The point to which the compatibilist can appeal is simply this. Even if the agent can do all these things, if p is something that was not the case in the past, and w2 is a world in which p is the case, then the agent will not do any of these things. But (crucially) if the agent knows that he will not do any of these 26 Here it may be noted that some theorists have proposed versions of the Ability Principle that (unlike (AP*)) explicitly state that the worlds relevant to an agent's possession of an ability to do A are worlds that are (not merely accessible but also) accessible to the agent (Lehrer, 1976: 253-254;quoted in Fischer & Pendergraft, 2013: 589), or contain possible actions of A-ing that are accessible to the agent (Graham, 2008: 74). things, then he can legitimately regard (indeed, should regard) a world in which he does these things as irrelevant to his aims in his practical reasoning about whether to perform a certain action. But if this is so, Fischer's Accessibility Principle is false, and his 'practical rationality' argument for incompatibilism undermined.
The compatibilist response that I have proposed (we may call it 'the knowledge response') appeals to a general principle that I call 'the Knowledge Principle' and state as follows: Knowledge Principle: In one's practical reasoning, if one knows that p is not the case, then it is not appropriate to take, as one's aim, the obtaining of a state of affairs that requires that p is the case. 27 In the following sections, I shall say more in support of the Knowledge Principle, and its application to the case in question. For the present, though, we can note that this compatibilist response exploits, and builds upon, a point that all theorists involved in this debate are likely to accept: that one can have abilities that one will not, in fact, exercise. 28 It adds to this that, with regard to some such abilities, an agent may know that he will not exercise them-in which case, according to the Knowledge Principle, it is inappropriate for him to aim at a state of affairs whose obtaining would require that he exercise them.
To amplify: this compatibilist 'knowledge response' concedes, for example, that Sam can on Tuesday, at t* (has the ability at t* to) bring about the following state of affairs: he goes ice-skating on Tuesday in a situation where there was no accident on Monday. But although he has this ability, he knows that he will not exercise it. He knows that he will not exercise that ability, even if he does exercise his ability to go ice-skating on Tuesday. In other words, even if he exercises his ability to go iceskating on Tuesday, he will not (and he knows this) exercise his (additional) ability to bring about a state of affairs in which he goes ice-skating on Tuesday against the background of a past in which the accident did not occur on Monday. But this does not imply that he lacks this additional ability. 29 27 Can't there be cases where it is appropriate to aim at something because even though one knows that one will not succeed, one will thereby get closer to success than by adopting a more modest aim? If so, that would represent an exception to my Knowledge Principle, as stated. Although I do not have space to discuss the issue here, I am untroubled by this. Even if the Knowledge Principle does need to be qualified to take account of such cases, the qualification would not affect the use that I make of the principle in this paper. 28 Some extreme versions of incompatibilism-for example, versions of fatalism-deny this assumption. But it is sufficiently uncontroversial for me to appeal to it in the context of the current debate. 29 Note that it is merely for the sake of argument that the compatibilist goes along with Fischer's gloss on the notion of accessibility (represented in the bullet-pointed list earlier in this section). It is this gloss that attributes, to the compatibilist, a conception of Sam's ability to go skating on Tuesday that appears to require that Sam has the ability to bring it about that he goes skating on Tuesday in a world in which the accident did not occur on Monday. It is not clear that the compatibilist need accept that Sam has this additional ability simply in virtue of the fact that, according to the compatibilist, Sam has an ability to go skating on Tuesday that he exercises in (among others) worlds in which the accident did not occur on Monday. However, I think that the compatibilist can concede, for the sake of argument, that Sam does have this additional ability, while still denying that attributing it to Sam leads to the problem of practical rationality that Fischer invokes.
8 The explanatory power of the knowledge principle I conclude that Fischer's practical rationality argument does not succeed in its aim of breaking the 'dialectical stalemate' between incompatibilism and those versions of compatibilism that deny that the past puts the limitation on our abilities that is expressed by the principle (PLA). 30 Even if Fischer's appeal to accessibility does not involve a fatal equivocation on the notion of accessibility (Sect. 6 above), the compatibilist can concede that the B-world is accessible to Sam, while still maintaining that Fischer's Accessibility Principle is false (Sect. 7 above).
It is worth noting that the 'knowledge response' strategy that I have proposed enables the compatibilist to provide a substantial answer to a challenge that is presented, apparently in the form of a rhetorical question, by Fischer and Pendergraft in support of the Accessibility Principle: 'Why would it be irrational to consider (bringing about) a situation that is within one's power to bring about? ' (2013: 590, n. 28). The response is that the irrationality would consist in aiming to bring about a state of affairs that, while being within one's power to bring about (such as the B-world, in Sam's case), is one that one knows will not obtain. 31 So far, however, it might seem that my compatibilist's appeal to the Knowledge Principle is a purely defensive and ad hoc move in attempting to evade Fischer's practical rationality argument. I shall now argue that that is not so. The Knowledge Principle is, I submit, an independently plausible principle. Furthermore, it is a general principle, not confined to the case where not-p represents a fact about the past as opposed to the present or future (the 'is' in the principle is to be read tenselessly). These features of the principle enable it to provide a convincing explanation of the absurdity or irrationality that would be involved in Sam's relying, in his practical reasoning concerning whether to go ice-skating, on the backtracking conditional (B) in Icy Patch.
Consider why, according to Fischer, we should accept (independently of a prior commitment to (PLA)) the claim that it would be absurd for Sam to treat what happens in the B-world as giving him a reason to go ice-skating on Tuesday. According to Fischer, the answer is this: 'given that Sam knows that the accident did in fact take place on Monday, it... seems irrational for Sam to decide to go iceskating on Tuesday on the basis of a reason flowing from the truth of the backtracker [(B)] ' (2016: 19;quoting Fischer, 1994: 95; some italics added). The compatibilist response that I have proposed, with its reliance on the Knowledge Principle, exploits 30 As noted above (at the end of Sect. 4), this does not include all compatibilists about free will and determinism (even those who hold that free will requires the ability to do otherwise), although it may include all compatibilists about free will and God's foreknowledge. 31 The compatibilist who adopts this response can agree that, if presented as a necessary condition on the topics that are suitable for deliberation, Aristotle's dictum (NE, III.3) that 'we deliberate about things that are in our power' may be accepted (although perhaps with the obvious qualification that ignorance may lead us to deliberate about things that we think are in our power although they are not). This compatibilist will hold, however, that if considered as a proposed sufficient condition, Aristotle's dictum is faulty: there are some things that are within our power, yet are not fit subjects of deliberation-namely, those that represent states of affairs that, while they are in our power to bring about, are ones that we know that we shall not bring about. the very consideration-Sam's knowledge that the accident did take place-to which Fischer appeals in order to justify the claim of absurdity or irrationality. But whereas Fischer's own explanation of why it would be irrational for Sam to defy his knowledge is that the fact that he knows is a fact about the past, my alternative explanation does not depend on that feature of the example, but on a more general principle concerning knowledge and practical rationality. Again, when Fischer amplifies his claim that it would be inappropriate for Sam to appeal to the backtracking conditional (B) in support of a decision to go ice-skating, he observes that for Sam to do so 'would seem to exemplify something akin to ''wishful thinking ''' (2016: 19;quoting Fischer, 1994: 95). Fischer's observation appears to be quite correct. But the idea that this would exemplify wishful thinking is perfectly captured by the fact that, were Sam to aim, in deciding to go skating, to bring about a world in which there was no accident on Monday, he would be adopting an aim that is prohibited by the Knowledge Principle.

The generality of the knowledge principle
In the previous sections, I have claimed that the Knowledge Principle is a plausible general principle, not confined to knowledge of the past, and also that the Knowledge Principle holds even if the agent has the ability to perform an action whose result would be the obtaining of a state of affairs that the agent knows does not in fact obtain. To provide support for these claims, I now present an example where the agent's relevant knowledge is knowledge of the future rather than the past.
Suppose that Susan is a student who would like to do well on her exam next month, but also knows that to do so she must work hard. Suppose that she also knows that she won't work hard. Susan therefore knows that her future does not include her doing well on this exam. It is then inappropriate for Susan, in her practical deliberations, to take, as her aim, the obtaining of any state of affairs that requires that she does work hard and does well on the exam. For example, suppose that she is wondering whether to make a costly and time-consuming application to a prestigious graduate programme that (as she knows) would be certain not to accept her without good results on this exam. The Knowledge Principle tells her that, if her aim in making the application would be to be accepted by the graduate programme, with all the benefits that that might bring, then that aim is inappropriate: she would not be rationally justified in making the application with that as her aim. 32 The Knowledge Principle includes, in its scope, scenarios in which although the agent knows that p will not be the case, the agent also believes that there is some action B such that, were he to do B, p would be, or would have been, the case. Suppose that Susan's working hard is not only necessary, but also sufficient, at least in ordinary circumstances, for her doing well on the exam. (The necessity and sufficiency here are not logical necessity and sufficiency, of course.) Assuming also that Susan knows this, she can reasonably believe that if she were to work hard, then she would do well on the exam. However, in spite of her acceptance of this subjunctive conditional, the Knowledge Principle still tells her that, in her practical reasoning about whether to apply to the graduate programme, she should not apply with the aim of being accepted, given that her being accepted would require her doing well on the exam.
There is yet more to be said. This instance of the Knowledge Principle is no less compelling (or so I claim) if we add, to the description of the case, the assumption that Susan has, and knows that she has, the ability to work hard. She just knows that, although she has this ability, she will not exercise it. Susan could know this of a lazy friend. So why not of herself?
There is no contradiction in the supposition that you and I have certain abilities (including abilities to do things in the future) that we do not exercise. There is no apparent contradiction in the supposition that, with regard to such an ability that you have but do not exercise, I know that you have the ability and also know that you will not exercise it. But there is also no apparent contradiction in the supposition that, in the case of such an ability that I have but do not exercise, I know that I have that ability and also know that I shall not exercise it. Given that this is possible, then, in such a situation, the Knowledge Principle implies that, in my practical reasoning, I should still not have, as my aim, the obtaining of a state of affairs that requires that I exercise that ability.
However, as we have seen (Sect. 7 above), this is precisely the situation that, according to the compatibilist 'knowledge response' to Fischer's practical rationality argument, applies to Sam and the ability to bring it about that he goes ice-skating on Tuesday in a world in which the accident did not occur on Monday that he possesses, but knows that he will not exercise.

Gallois and the fixity of reasons
In a very interesting article (Gallois, 2009), André Gallois argues that the impropriety of relying on an appeal to backtracking counterfactuals in practical reasoning is explained by the principle that he calls 'The Fixity of Reasons', and expresses as follows: Suppose that, at t, [a] deliberator D is deliberating whether to perform an action A at t' and P is the proposition that D performs A at t'. No matter how justified she is in believing it, D should (it is irrational for D not to) refrain from using as a premise in her practical reasoning about whether to perform A any conditional, P h? Q, which satisfies the following conditions. At t D is justified in believing R. Moreover, at t R is relevant to D's deliberations about whether or not to perform A. Finally, Q h? (: R). (2009: 239) This can be applied to Fischer's case of the Icy Patch. Sam (D) is, at t, deliberating about whether to perform the action of ice-skating (A) at t'. Sam is justified in believing the conditional: if he were to go ice-skating (P), the accident would not have occurred on Monday (Q). However, at t, Sam is justified in believing (indeed, knows) that R (the accident did occur on Monday). Moreover, at t R is relevant to D's deliberations about whether or not to perform A. Finally, if the accident had not occurred on Monday (Q), then (trivially) the accident would not have occurred on Monday (: R).
Gallois's principle offers a diagnosis, consistent with the denial of (PLA), of why it would be irrational for Sam to rely on the backtracking conditional in his deliberations about whether to go ice-skating on Tuesday. If the consequent of the backtracking conditional had been fulfilled (if there had been no accident on Monday), then Sam would not have been in possession of the knowledge that he has that the accident did occur on Monday-knowledge of a fact that is highly relevant to his decision, and which, according to Gallois's principle of the Fixity of Reasons, Sam is not entitled to ignore on the basis of the backtracking conditional.
Fischer and Pendergraft complain that although, if accepted, Gallois's principle of the Fixity of Reasons would explain the irrationality of Sam's reliance on the backtracking counterfactual, Gallois's principle is ad hoc (2013: 591). Their complaint is that Gallois does not explain why, given that Sam should regard the scenario in which there is no accident on Monday as one that he can bring about, he is nevertheless entitled to ignore that scenario in his practical reasoning. Without taking a stand on this issue, I claim that my appeal, on behalf of the compatibilist, to the Knowledge Principle avoids this objection.

Concluding remarks
I have argued (Sect. 4 above) that the debate about the fixity of the past that Fischer presents as a debate about the truth of the Fixity Principle (FP*) should be recast as a debate about the truth of a stronger principle: the Principle of Past-Limited Abilities (PLA). I have argued that Fischer's 'practical rationality' argument in support of (PLA) does not succeed. 33 Even if his argument avoids the charge of equivocation on the notion of 'accessibility' (Sect. 6), it is defeated (Sect. 7) by a response that relies on a plausible general principle about knowledge and practical rationality that provides an explanation of the absurdity to which Fischer appeals, yet is consistent with the denial that the past puts the limitations on our abilities that are implied by the principle (PLA). 34 My 'knowledge response' to Fischer's practical rationality argument involves a commitment to a version of a thesis that is a staple of defences of compatibilism: that agents may possess abilities that (not only will they not exercise, but also) it is 33 Of course, Fischer could attempt to fall back on an appeal to the intuitive plausibility of (PLA). But that would involve his giving up on the attempt to break the 'dialectical stalemate' by appealing to his practical rationality argument. 34 Since writing this paper, it has been drawn to my attention, by an anonymous referee, that, in a recently published paper, Helen Beebee (2021) also criticizes Fischer's practical rationality argument. Her criticisms are, however, distinct from (although I think consistent with) mine. in a sense guaranteed that they will not exercise. 35 This commitment will, of course, strike those with incompatibilist sympathies as problematic. But if this commitment really does warrant an objection to compatibilism, it is an objection that requires a defence of its own, independently of Fischer's practical rationality argument.