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Does rationality demand higher-order certainty?

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Abstract

Should you always be certain about what you should believe? In other words, does rationality demand higher-order certainty? First answer: Yes! Higher-order uncertainty can’t be rational, since it breeds at least a mild form of epistemic akrasia. Second answer: No! Higher-order certainty can’t be rational, since it licenses a dogmatic kind of insensitivity to higher-order evidence. Which answer wins out? The first, I argue. Once we get clearer about what higher-order certainty is, a view emerges on which higher-order certainty does not, in fact, license any kind of insensitivity to higher-order evidence. The view as I will describe it has plenty of intuitive appeal. But it is not without substantive commitments: it implies a strong form of internalism about epistemic rationality, and forces us to reconsider standard ways of thinking about the nature of evidential support. Yet, the view put forth promises a simple and elegant solution to a surprisingly difficult problem in our understanding of rational belief.

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Notes

  1. I say “on pain of contradiction” although, strictly speaking, it is logically possible for both conclusions to be true at the same time. This would be the case if it were neither rational to be higher-order certain nor rational to be higher-order uncertain. Some epistemologists have expressed sympathy for views on which such “epistemic dilemmas” are possible—e.g., Christensen (2007b, 2010a) and Hughes (2019). However, it is usually assumed that they are not, and I’ll proceed on this assumption here.

  2. E.g., Titelbaum (2015), Smithies (2019), Tal (2020) and Weatherson (2019).

  3. See, e.g., Greco (2014) and Horowitz (2014). See also Smithies (2012) for a related discussion of Moore’s Paradox.

  4. So-called because of its affinity with van Fraassen’s (1984) “Reflection Principle,” which says (roughly) that you should defer to your own future credences.

  5. Here and throughout, I’ll assume that P is an ideally rational credence function, not a non-ideally (or “boundedly”) rational credence function that is sensitive to human cognitive limitations. In doing so, I’m not making any substantive assumptions about what it takes for an agent’s credences to be ideally rational. In particular, I’m not assuming that P obeys the probability axioms.

  6. As usual, the mathematical expectation of a discrete random variable, X, calculated with respect to a probability function, P, is defined as follows: \( {\mathbb{E}}_{P} \)(X) = ∑xP(X = x)x.

  7. E.g., Christensen (2010b), Sliwa and Horowitz (2015), and Dorst (2019a, b).

  8. For those interested in the technical details, Dorst (2019a, b) provides an excellent formal characterization of the result. Elga’s own formulation of the proof goes as follows: let P’ be any credence function that the agent thinks might be ideally rational. By Rational Reflection, then, P(q | P′ is ideal) = P′(q). Letting q be the proposition “P′ is ideal,” we have: P(P′ is ideal | P′ is ideal) = P′(P′ is ideal). And since P(P′ is ideal | P′ is ideal) = 1, it follows that P′ (P′ is ideal) = 1. That is, P′ is certain that it itself is the ideally rational credence function.

  9. It is perhaps easier to see this implication from Elga’s own (equivalent) formulation of rational reflection, stated in terms of conditional probabilities instead of expectations: P(q | P′ is ideal) = P′(q).

  10. This is not, to be sure, to say that Cr(·|P is rational) and Cr(·) must assign different values to every proposition. The implication is just that Cr(·|P is rational) and Cr(·) must assign different values to at least one proposition.

  11. E.g., Lasonen-Aarnio (2015, 2020) and Williamson (2014).

  12. E.g., Dorst (2019b). I would include Elga (2013) in this camp as well, although, as Dorst (2019a, §3.2) shows, the “New Rational Reflection” principle allows for some rather blatant instances of epistemic akrasia.

  13. I say “runs the risk” to leave open the possibility that there is, on closer inspection, a principled way to distinguish between those instances of epistemic akrasia that are too blatant to be rational, and those that are not. Dorst (2019b) has recently offered an interesting proposal along these lines, which, if correct, would allow us to deny Rational Reflection while maintaining that there is something importantly right about the Enkratic Intuition.

  14. Similar cases can be found in many other places; e.g., Christensen (2010a), Elga (2005), Horowitz (2014), and Skipper (2019a, b).

  15. E.g., Tal (2018, 2020), Titelbaum (2015), and Weatherson (2019).

  16. Although not “dogmatic” in the traditional sense of the term, which is associated with the dogmatism puzzle (Kripke 2011). A detailed comparison would take us too far astray, but interested readers are referred to Christensen (2010a, 2011), who offers an illuminating discussion of how the present kind of dogmatism differs from the kind of dogmatism exhibited by someone who ignores a body of evidence merely on the grounds that it speaks against his or her prior opinions.

  17. What would count as a suitably “independent” reason here? This turns out to be a difficult question. To a first approximation, we can think of the “independence” requirement as ruling out considerations that are produced by the very kind of reasoning whose reliability is called into question by the relevant higher-order evidence. For a more careful treatment of the issue, see Christensen (2019).

  18. Different versions of this view have been defended by Lasonen-Aarnio (2014), Tal (2018, 2020), Titelbaum (2015), and Weatherson (2019).

  19. To say that rational certainty is indefeasible is to say, roughly, that someone who is rationally certain of a given proposition should remain certain of that proposition no matter what evidence is received in the future. In Bayesian parlance: if the prior probability of q is 1, the posterior probability of q is also 1, conditional on any new evidence. This “certainty preservation” principle is an immediate consequence of the ratio formula for conditional probabilities (cf. Joyce 2019).

  20. Why not? Briefly put, even if rational certainty is defeasible in some contexts—say, contexts involving memory loss—this does little to show that rational certainty is defeasible in the present context. Indeed, I see no independent reason to think that rational certainty is defeasible in contexts involving higher-order evidence. In any case, however, I will eventually offer a way to resist The Anti-Dogmatism, which does not rely on any controversial assumptions about the defeasibility of rational certainty.

  21. For other, similar ways of characterizing the distinction between first-order evidence and higher-order evidence, see Christensen (2010a), Lasonen-Aarnio (2014), and Schoenfield (2015, 2016).

  22. Thanks to Jack Spencer for suggesting this example. See also Christensen (2019) for a similar kind of example.

  23. For discussions of Precision, see White (2009) and Elga (2010). For discussions of Uniqueness, see Schoenfield (2013) and Schultheis (2018).

  24. See, e.g., Kelly (2014).

  25. Assuming that rational certainty is indefeasible; cf. our discussion in Sect. 3.

  26. Examples of such norms include “Calibration” (White 2009), “Guess Calibration” (Sliwa and Horowitz 2015), and “Judgment Calibration” (Schoenfield 2015). See also Kelly’s (2010) bootstrapping worry about the Equal Weight View of peer disagreement, as defended by Christensen (2007a) and Elga (2007).

  27. Discussions of this kind of norm go back as far as to Aristotle’s ethics, but have recently seen a revival due to the work of Broome (1999, 2007), Kolodny (2005), and others.

  28. For further discussion of this general issue, see Broome (1999), Kolodny (2005), and Kiesewetter (2017).

  29. Assuming that ‘should’ distributes over the material conditional (as in standard deontic logic): if you should ‘ψ, if ϕ’, then you should ψ, if you should ϕ.

  30. Notice the difference between (a) having uncertainty about what your first-order evidence in fact supports, and (b) having uncertainty about what you should expect your first-order evidence to support. Top–Down Guidance allows for both kinds of uncertainty, but it is only the latter kind of uncertainty that creates trouble for Top–Down Guidance.

  31. Williamson (2000, 2014, 2019). See also Lasonen-Aarnio (2014, 2019), Worsnip (2018), and Salow (2019).

  32. Thanks to an anonymous reviewer for raising this worry.

  33. I also take these considerations to answer a related worry that is sometimes raised against broadly “conciliatory” views of higher-order evidence; see, e.g., Kelly (2005, 2010) for an influential development of this worry. The worry starts from an intuitive, albeit somewhat vague, idea, namely that you should “respect all the evidence” (cf. Sliwa and Horowitz 2015). In particular, you should respect both your first-order evidence and your higher-order evidence. Otherwise, you effectively ignore or “throw away” part of your evidence, which seems patently irrational. But how, exactly, should you respect both the first-order evidence and the higher-order evidence? I say: by treating both your first-order evidence and your higher-order evidence as “truth-guides.” More specifically, you should treat your first-order evidence as a guide to the truth, and you should treat your higher-order evidence as a guide to the truth about what your first-order evidence supports.

  34. This is not, to be sure, to deny that we have a kind of default “entitlement” to trust our own cognitive faculties (Dretske 2000; Pryor 2000; Wright 2004). The claim is just that this sort of default justification, if we have it, does not entitle us to be certain that our cognitive faculties are infallible.

  35. Something like this principle is what Schoenfield (2015, p. 439) calls “Inclusion.”

  36. Although it might we worth emphasizing what the assumption is not: the assumption is not that, whenever you form an opinion on the basis of having judged some evidence, the fact that you have judged the evidence will be at the forefront of your mind. Nor is the assumption that you will be aware of how you went about judging the evidence. The assumption is merely that, when you form an opinion on the basis of having judged some evidence, the fact that you have judged the evidence will be part of your evidence.

  37. In brief, she argues that, if we treat higher-order evidence as a kind of self-locating evidence, then (given certain background assumptions) the update procedure that maximizes expected accuracy says that we should not be sensitive to higher-order evidence.

  38. An anonymous reviewer raises the worry that, in the absence of probabilism, Elga’s result discussed in Sect. 2 no longer goes through, thereby undermining the Anti-Akrasia Argument, which was a crucial part of the motivation behind the Top-Down View. However, as can be seen from the proof stated in footnote 8, Elga’s result in fact doesn’t presuppose probabilism, but only something much weaker, namely that the conditional probability of a proposition given itself is 1. This is what allows us to say that P(P′ is ideal | P′ is ideal) = 1, which, when combined with Rational Reflection, implies that P′ (P′ is ideal) = 1. Thus, the move to non-probabilism does not undermine the motivation behind the Top-Down View.

  39. See, e.g., Williamson (2000, 2014, 2019), Dorst (2019a, b), and Lasonen-Aarnio (2015).

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Acknowledgements

Earlier versions of this paper were presented at Cologne University, Aarhus University, and the “MATTI” seminar at MIT. I’d like to thank the audiences on those occasions for helpful comments and questions. A special thanks to David Christensen, Kevin Dorst, Mikkel Gerken, Jack Spencer, Eyal Tal, two anonymous reviewers at The Philosophical Review, and two anonymous reviewers at Synthese for feedback that greatly improved the paper.

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    Mattias Skipper

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Skipper, M. Does rationality demand higher-order certainty?. Synthese 198, 11561–11585 (2021). https://doi.org/10.1007/s11229-020-02814-w

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