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ABSTRACT
While pragmatic arguments are traditionally seen as supporting decision theory, recent discussions suggest the possibility of pragmatic arguments against this theory. I respond to two such arguments, and clarify what it would take for arguments of this sort to succeed.
Disclosure Statement
No potential conflict of interest was reported by the author.
Notes
1 I focus on a normative reading of decision theory and on the deliberative conception (which treats credences and utilities as psychologically real: see Pettigrew [Citation2015]). However, with minor variations, my discussion also applies to the preference-first conception.
2 Instead of knowledge, we might spell this out in terms of belief or available information. These distinctions are unimportant for my purposes.
3 Arntzenius et al. [Citation2004] don’t take this case to undermine CDT. However, it’s natural to read the case as posing such a threat, and so worth exploring whether it truly does so. Note that I’m not alone in reading the case in this way: Meacham [Citation2010] also sees it as threatening CDT, and Peterson [Citation2016: 170–1] raises the possibility that it underpins a pragmatic argument against decision theory.
4 She will be offered the first slice in one minute, the second thirty seconds later, the third fifteen seconds later, and so on.
5 There’s disagreement over whether evidential decision theory (EDT), a prominent alternative theory, provides this same guidance (Meacham [Citation2010: 54–5] says ‘yes’; Arntzenius et al. [Citation2004: 268] suggest ‘no’). I deny that EDT does so, given a natural reading of Satan’s Apple (because, on this reading, taking one slice provides strong evidence to Eve that she will take others). However, a more contrived reading of the scenario will lead EDT to endorse taking each slice (but at the cost of the contrivance’s threatening the reliability of our intuitions in the case). There are also versions of decision theory that clearly don’t endorse taking each slice (see Meacham [Citation2010: 68–9] and Greene [Citation2018]). As CDT faces the clearest challenge from Satan’s Apple, it’s this theory on which I focus (although the defence that I provide could be extended to EDT).
6 Bartha et al. [Citation2014] argue that CDT endorses refusing some pieces in some versions of Satan’s Apple. However, as they note, it’s unclear whether their discussion applies to all versions of this scenario. So, I’ll assume that CDT does offer the specified guidance, and will argue that, even if it does, a pragmatic argument, based on Satan’s Apple fails.
7 Some have argued that Eve is rationally required to take each slice [Arntzenius et al. Citation2004: 267, Bartha et al. Citation2014: 639–40]. If so, then her loss is avoidable only if she acts irrationally. This doesn’t violate Weak Avoidability but might appear to undermine the sense in which the pragmatic argument is avoidable. Indeed, we might be tempted to adopt what we could call Rational Avoidability, a variant on Weak Avoidability where every choice in the alternative sequence must be rational. If so, and if we accept that Eve is rationally required to take each slice, then Satan’s Apple fails as a pragmatic argument. In any case, I’ll assume that this response fails, and will show that CDT can be defended, even so. (Thanks to a reviewer for their thoughts here.)
8 There are other ways in which we might defend CDT. For example, on one reading, Arntzenius et al. [Citation2004] argue that (a) Eve would avoid problematic behaviour if she could bind herself to future actions, and (b) pragmatic arguments lack force under such circumstances. However, it has been argued elsewhere that this defence fails [Meacham Citation2010; Bartha et al. Citation2014: 645–7]. I’ll show that Satan’s Apple poses no challenge to CDT even if so.
9 Alternatively, perhaps CDT applies in infinite cases but pragmatic arguments don’t (see Arntzenius et al. [Citation2004: 278–9] and Bartha et al. [Citation2014: 644]).
10 This assumes that at least one decision is rational in such cases. If these cases are dilemmas, where no decision is rational [Slote Citation1989: ch. 5], then CDT gets things exactly right: no decision maximises EU, and so CDT (correctly) takes all decisions to be irrational.
11 In Bernoulli’s game, a fair coin is tossed until it first lands heads. You receive a payout of , where n is the number of tosses.
12 These cases reveal that CDT cannot be correctly applied in all situations. One response would be to reject CDT; another would be to restrict its scope. I take the second path. Shortly, I’ll discuss why this move isn’t ad hoc.
13 See also Arntzenius et al. [Citation2004: 260] and Bartha et al. [Citation2014: 635, 644].
14 Depending on the role that we take CDT to play, reduction might not be necessary. It might be enough that CDT’s guidance is, in finite cases, coextensive with the guidance provided by the complete theory.
15 This is true of the diachronic version of Satan’s Apple considered here. Arntzenius et al. [Citation2004: 264–5] also discuss a synchronic version of the case.
16 This relies on sequences being, in some sense, assessable for rationality. This is a safe assumption in the current context, because pragmatic arguments rely on this same assumption. So, if this assumption were rejected, the pragmatic argument would collapse (see Hedden [Citation2015]). Further, the (second framing of the) argument in section 6.3 doesn’t rely on sequences being rationally evaluable, and so it applies even if we reject the evaluability assumption.
17 One might instead argue that a sequence is irrational only if it leaves the agent (foreseeably, avoidably) worse-off than at the outset. On such a view, what matters isn’t loss compared to just any alternative, but, specifically, loss compared to the status quo. However, this seems to be an instance of the well-known human tendency to overemphasise the relevance of the status quo (see Samuelson [Citation1988]). There’s no reason to think that only loss relative to the status quo is irrational and that otherwise it’s fine to knowingly make yourself worse-off than you could be. So, there’s no reason to accept this more-restricted justification for pragmatic arguments, while rejecting the preferred-alternative claim.
18 Bartha et al. [Citation2014] reach the same conclusion, but their argument has a different shape from mine. They introduce a principle, show that this entails the rationality of taking each apple piece, and argue that this reveals that Satan’s Apple cannot underpin a pragmatic argument.
19 Peterson’s pragmatic argument against CDT is part of a larger argument. Ultimately, Peterson concludes, not that we should reject CDT, but that we should reappraise the force of pragmatic arguments. However, not everyone will agree with this move; many will continue to think that pragmatic arguments represent a serious threat. As such, a pragmatic argument against CDT calls for a response on its own terms.
20 This argument assumes that if Jacob refuses one bet then he’s offered no further bets. I’ll return to this issue shortly.
21 Perhaps we can avoid this by (a) stipulating that Jacob wins only finitely often, and (b) basing the value of x not just on the coin tosses but also on a perfect prediction of when Jacob will bet. Yet now the case relies on spookily perfect predictions of a free agent’s actions (Newcomb’s Problem can’t be appealed to as precedent here, as it doesn’t, despite standard presentations, rely on a predictor with unerring accuracy).
22 Plausibly, this would lead Jacob to become less confident that he would take all future bets (see note 24 for a discussion).
23 Jacob knows that if he bets indefinitely, he will lose his stake with probability 1. However, he is ignorant of the antecedent and hence of the consequent. This sort of failure of Foreseeability suffices to sink the pragmatic argument: it’s hardly news that a rational agent might choose poorly if they’re ignorant of crucial features of the future (and, in Jacob’s case, his own future decisions are just such a feature). Note that if Jacob’s future actions are treated as chance events then he could believe accurately about his future actions while remaining uncertain whether he will take all future bets. Yet we then have a failure of Uncompensated: there’s now a chance of gain to justify Jacob’s accepting the chance of loss.
24 The same reasoning applies to the form of CDT developed by Skyrms [Citation1990], on which agents first calculate EUs, but then reassess their beliefs in the light of these calculations, and recalculate the EU in the light of these new beliefs, and so on. The process continues until an equilibrium is reached, where the agent’s latest beliefs do not lead to a shift in the EUs. For my purposes, what matters is that, at the process’s end, Jacob’s credence function will either (a) assign credence 1 that he will take all future bets (in which case, CDT won’t endorse taking the current bet) or (b) assign a credence of less than 1 to this possibility (in which case, Foreseeability is violated). Again, the pragmatic argument fails in either case. But there might appear to be a loophole: if Jacob is initially certain that he will take future bets but ends by being unsure of this in equilibrium, it might be thought that the former fact ensures that Foreseeability is satisfied, while the latter leads CDT to endorse taking each bet. However, Foreseeability cannot be satisfied in this way. What matters in assessing this requirement is what Jacob believes when he makes his decision, not what he believed at some earlier point when he hadn’t finished accounting for evidence. Foreseeability must be satisfied by the same belief state that justifies Jacob’s decision. So, there is no loophole. (Further, it’s not clear that Skyrm’s approach really involves the distinction between initial and final beliefs that gave rise to the apparent loophole. Instead, it might be thought that the ideal agents that CDT addresses should simply start in equilibrium (see Joyce [Citation2012: 128]). Perhaps the dynamic process is just a useful tool for identifying equilibria.)
25 Arguably, the case is also a sequence-dilemma, as no sequence of actions in Jacob’s Ladder is optimal from Jacob’s own perspective (even if some sequence is objectively optimal). As rationality is a subjective notion, the case is plausibly a sequence-dilemma in the sense that matters (and so, plausibly, falls afoul of the discussion in section 6).
26 Peterson [Citation2016: 171] speaks about what Jacob will do, but I assume that the intended claim relates to what he should do.
27 See Hitchcock [Citation2004: 412] and Briggs [Citation2010: 13].
28 For feedback, thanks to Johan Gustafsson. Thanks also to a number of reviewers for detailed and insightful comments; the paper is substantially better for their assistance.