Abstract
This paper discusses a scenario borrowed from Williamson (2000) and repurposes it to argue for the possibility of conflict between two prima facie categorical norms of epistemic rationality: the norm to respect one’s evidence and the norm to be coherent. It is argued, pace Williamson, that in the conflict defining the scenario, the evidence norm overrides the coherence norm; that a rational agent with our evidence would lack evidence about some of their own credences; and that for agents whose evidence is limited in this way, incoherence fails to entail irrationality. The above possibility claim has also been defended by Worsnip (2018), albeit on a quite different premise set and in conjunction with a coherence-centered account of epistemic rationality that issues predictions incompatible with those licensed by the evidence-centered account recommended here, as illustrated towards the end of the paper.
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Notes
That is, an epistemically rational agent makes no mistakes in reasoning—where reasoning includes both assessing what follows from what deductively, and assessing what the evidence supports inductively to what degree—and performs such assessments in an infinitely short amount of time, irrespective of complexity.
One way to do avoid commitment to Uniqueness would be to prefix the second occurrence of ‘such-and-such’ with a vague modifier, such as ‘roughly’. For an overview of the Uniqueness debate, see Kopec & Titelbaum (2016).
Relativists deny that there is a binary function of evidential support defined for all pairs of an evidence set and a hypothesis, maintaining that, at least in the inductive case, E supports H to such-and-such degree only relative to a third parameter, such as an evidential standard or an inductive method. See Kopec & Titelbaum (2019). To be ecumenical in this regard, relativists are invited to interpret our talk of E’s supporting H to such-and-such degree as elliptical for talk of E’s supporting H to such-and-such degree relative to evidential standard/inductive method s.
Utilizing cases of this kind, Williamson (2007) argues against correlating probability 1 with certainty, by arguing that there are propositions that have probability 1 even though they fail to be certain. To take his simplest example, let \(H(1\ldots )\) be the proposition that x’s next series of coin tosses will be an infinite series of heads; and stipulate that x is given an infinite amount of time so that \(H(1\ldots )\) is one of the uncountably many ways that series could possibly turn out. Nevertheless, Williamson argues, the probability of \(H(1\ldots )\) is 0 (even if we permit infinitesimal probabilities), and that of \(\lnot H(1\ldots )\) is accordingly 1, however uncertain the latter proposition. Accepting both Williamson’s conclusion and unqualified (RC) commits one to holding that a rational agent with evidence reflecting the above stipulations would have maximal certainty (credence 1) in \(\lnot H(1\ldots )\), even though their evidence would not strictly rule out \(H(1\ldots )\). Arguably, that goes against the spirit of (RC). For objections to Williamson’s argument, see Weintraub (2008), Howson (2017), Benci et al. (2006); for a defense see Parker (2018).
There is a more general interpretation of ‘conditional fallacy’ that applies to variants that relate Q and R by a conditional other than a counterfactual. See Bonevac, Dever & Sosa (2006: 276). However, in the light of our purposes we may confine ourselves to the more narrow conception.
It may be worthwhile to point out that our reliance on the non-contingency of conditional probability is not incompatible with Relativism about evidential support (see fn. 3). Of course, it may be possible for evidential standards to change from one situation to the next, to the effect that H may have probability such-and-such on E in a situation governed by standard s while having probability so-and-so on the same E in a situation governed by \(s'\). But that much is compatible with the non-contingency of conditional probability which, more elaborately, states that if H has such-and-such probability on E relative to s, then it is necessarily the case that H has such-and-such probability on E relative to s.
For pure convenience, I’m speaking in terms of Stalnaker’s uniqueness assumption, claiming that for each world, there is exactly one world that is closest, or most similar. Without harming the argument, we might as well speak in terms of all the closest possible worlds v.
As an anonymous referee notes, there is a question as to how serious Williamson’s commitment to the Awareness Assumption really is. Indeed, the phrase ‘presumably’ with which he prefixes that assumption may be taken to signal a form of hedging. But since the anti-(RP) argument he offers clearly depends on the Awareness Assumption, if he isn’t serious about the latter, he can’t be serious about the former. Either way, I’m not concerned here with what Williamson personally believes but with the argument he puts on the table.
Eder (fc: 10f.): “According to Williamson, ideal agents [...] have the kind of self-awareness of their own doxastic states that prevents them from assigning high credence to a Moore-paradoxical proposition such as \(L \wedge H^{*}\) [...]. It is not entirely clear to me which kinds of abilities and belief-forming processes ideal agents have that prevent them from having high credence in [such propositions]. However, presumably the abilities involved are different to the abilities that make them logically and mathematically omniscient. Assuming this, defenders of (IAC) [\(\approx\) (RC)] could plausibly suggest we interpret the evidential probability of a proposition on an agent’s total evidence in terms of [the] credence of an ideal agent who is logically and mathematically omniscient but lacks the kind of ability that prevents the agent from assigning high credence to a Moore-paradoxical proposition such as \(L \wedge H^{*}\). [...] However, according to this way out, the ideal agent referred to in (IAC) is only ideal with respect to the domain of logic and mathematics. Consequently, (the notion of) ideal rationality would also be restricted to the domain of logic and mathematics. Instead of stopping here and considering (IAC) to have been saved, let us look for an alternative way out that is less restrictive.” (Formal notation adapted.) Contrary to the present approach, the way out Eder envisages for the (RC) proponent is still in the spirit of an analysis of evidential probability as rational credence (as indicated by her name for (RC): ‘the Ideal-Agent-Credence interpretation of evidential probability’).
An anonymous referee advises me to acknowledge that this claim of mine is contentious in the light of a venerable tradition of arguments—from Descartes through Kant to Shoemaker—aimed at showing that knowledge of one’s own mental states is categorically disanalogous to perceptual knowledge of the external world. This gives me the opportunity to stress that my position conflicts with these efforts only to the extent that they have the consequence of making self-awareness a necessary condition of rationality.
This objection also applies to Eder’s own approach (ibid: Sect. 3), centered around the suggestion that there are certain kinds of evidence sets that an agent ideally “ought” not have as their total evidence.
Noting that the present account commits us to saying that x’s having high credence in L is not probable on our evidence, an anonymous referee finds this a strange thing to say, given that x does not exist in our world and that we cannot refer to what does not exist. The oddity is explained away by distinguishing between us as protagonists of the scenario and us as those stipulating, imagining, and discussing the scenario. True, as protagonists of the scenario, we cannot refer to x. But in our capacity as story tellers, we can “refer to” x just as we can “refer to” Pegasus when telling the Pegasus story. Or more precisely, we can simulate referring to something fulfilling such-and-such description (being a rational agent with our evidence, being a winged horse, ...), as we are accustomed to doing in fictional discourse. Note that to say that x’s having high credence in L is not probable on our evidence is not to imply that it is probable on our evidence that x lacks high credence in L, nor, for that matter, that this has a middling probability on our evidence. Assuming both contingentism about existence as well as the object-dependence of singular propositions (see Stalnaker 2012), if x fails to exist in a given world, propositions about x fail to exist in that world just as well, to the effect that they can’t be probable or improbable on evidence possessed in that world.
Assume Holmes is subject to appearances that he would express in terms of ‘the butler lied to me’; Watson is subject to appearances that he would express in terms of ‘the butler lied to him’ (using ‘he’/‘him’ to refer to Holmes); and sane Heimson is subject to appearances that he would express in terms of ‘the butler lied to me’. Here, Holmes and Watson are subject to the same appearances content-wise, while Holmes and sane Heimson are subject to the same appearances character-wise.
I’m indebted to an anonymous referee for pressing me on this point.
Before moving on to the next section, allow me to remark on how the considerations offered in this section point the way to an argument against (RP) on the content interpretation, an argument that differs from Williamson’s. The argument exploits a technicality to do with the kind of indexicality characteristic of ‘actually’, understood not as a device of emphasis but as a two-dimensional modal operator affecting the truth-conditions of sentences embedding it. (As in ‘it could have happened that everyone who actually lost won’. For the logical indispensability of ‘actually’ in this and similar examples, see Hughes & Cresswell 1996: 350f.) A use of ‘actually’ rigidly refers to the world in which the expression is used, to the effect that a sentence \(\ulcorner\)actually \(P\) \(\urcorner\) as used in w is true at any world v iff P is true at w. As a consequence, \(\ulcorner\)actually \(P\)\(\urcorner\) expresses different propositions depending on the world of utterance. Now, whenever we have evidence that P, we also have evidence that actually P, and trivially so. But if there were a perfectly rational agent with evidence that P, they would not have evidence that actually P. It is true that, as a result of having P in evidence, they would also have a proposition in evidence that they would express in terms of \(\ulcorner\)actually \(P\)\(\urcorner\); but that is not the proposition we express in such terms, ‘actually’ again rigidly referring to the respective world of utterance. Since there are no perfectly rational agents, if there were, they would not use ‘actually’ to refer to the actual world but to whatever counterfactual world would then be actual. On natural assumptions, the propositions we express in terms of ‘actually’ are not even expressible in counterfactual worlds. (Unless we believe in something like transworld reference, by analogy with Edgington's (1985, 2010) notion of transworld knowledge. For a powerful critique of both ideas, see Williamson 2000: 290f.) If so, it follows that propositions of that kind cannot be elements of the evidence sets of agents in counterfactual worlds. So on the content interpretation, it is true that a perfectly rational agent could not have evidence strictly equivalent to ours, contrary to (RP).
Put more carefully, irrationality entails a disposition to make some kind of mistake in reasoning or assessing the evidence; but, we may assume, x does not even have any such disposition.
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Acknowledgements
For comments and constructive criticism, I’m indebted to André Fuhrmann, Roman Heil, Melvin Keilbar, and three anonymous referees for Erkenntnis.
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Kauss, D. A Rational Agent With Our Evidence. Erkenn (2023). https://doi.org/10.1007/s10670-022-00653-4
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DOI: https://doi.org/10.1007/s10670-022-00653-4