The imprecise impermissivist’s dilemma


Impermissivists hold that an agent with a given body of evidence has at most one rationally permitted attitude that she should adopt towards any particular proposition. Permissivists deny this, often motivating permissivism by describing scenarios that pump our intuitions that the agent could reasonably take one of several attitudes toward some proposition. We criticize the following impermissivist response: while it seems like any of that range of attitudes is permissible, what is actually required is the single broad attitude that encompasses all of these single attitudes. While this might seem like an easy way to win over permissivists, we argue that this impermissivist response leads to an indefensible epistemology; permissive intuitions are not so easily co-opted.

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  1. 1.

    There are many formulations of uniqueness in the literature. What unites these formulations is a commitment to the general idea that there is a unique rational response to a given body of evidence (cf. Kopec and Titelbaum 2016). The careful reader might want to be alive to our reasons for choosing the formulation of uniqueness that we give here. Three points are relevant here. First, on our formulation the evidence justifies at most one attitude. In this regard it resembles Feldman’s (2007) statement of uniqueness. One might alternatively hold that, \(\grave{a}\) la White (2005), the evidence justifies exactly one attitude. Note that the at most one formulation is logically weaker than the exactly one formulation. We will argue that certain moves are not open to the impermissivist. For this reason, we think that charity favors using the weaker formulation, as it leaves more logical space for defenders of impermissvism. Second, discussions of uniqueness often distinguish between inter and intrapersonal uniqueness (e.g. Kelly 2013; Meacham 2013; Kopec and Titelbaum 2016). On the intrapersonal interpretation, given an agent, body of total evidence, and proposition, the evidence justifies at most one doxastic attitude towards the proposition, but the attitude the evidence justifies is not necessarily the same for every agent. On the interpersonal interpretation, the attitude the evidence justifies is the same for every agent. Our formulation is a statement of interpersonal uniqueness. We have chosen this formulation because this is where the heart of the debate over impermissivism lies. Many avowed permissivists, e.g. Kelly (2013) and Meacham (2013), endorse intrapersonal uniqueness. Lastly, our formulation states that the evidence justifies attitudes as opposed to propositions. We do not think that anything interesting hangs on this choice. Our arguments work for both doxastic and propositional uniqueness.

  2. 2.

    Versions of this principle can be found in Hedden (2015), “In the absence of any evidence, you ought to be in a course-grained doxastic state represented by a set of probability functions ([\(\ldots \)] your representor), in particular the set S resulting from all the different permissible weights to the various competing epistemic values. And if your present total evidence is E, your representor ought to be the set consiting of each member of S conditionalized on E” (Hedden 2015, pp. 135–136; Kelly 2013), “It’s not really that there is some range of permissible options. Rather, the uniquely reasonable thing [\(\ldots \)] to do is to go vague over the ostensibly permissible range. On this way of thinking about it, one way of falling short of perfect reasonableness is to have overly precise degrees of belief: that amounts to treating your evidence as though it carries information that it doesn’t carry” (Kelly 2013, pp. 300–301; Christensen 2007),“[I]n situations in which the evidence bearing on some proposition P is relatively meager, it does not seem that one unique number could possibly be singled out as the uniquely rational degree of belief in P. But rejecting permissive conceptions of rationality need not commit one to representing the rational response to every evidential situation with a single probability function.[\(\ldots \)] One can hold that the uniquely rational response to an evidential situation is representable by a particular set of probability assignments, and the uniquely rational attitude toward proposition P is represented by a particular range of values between 0 and 1” (Christensen 2007, p. 195 (fn. 8)). NB: Hedden and Christensen are sympathetic to impermissivism and the IC strategy; Kelly, on the other hand, is a permissivist who thinks IC is a promising strategy for impermissivists.

  3. 3.

    See White (2010).

  4. 4.

    We can really cash this out in either diachronic (how the credences should change over time) or synchronic (how conditional credences should be) terms.

  5. 5.

    Note that our argument relies on the imperissivist accepting either of these two principles. So, our paper is not an indictment of all conceivable forms of imprecise impermissivism, as there’s logical space for a view that maintains an imprecise impermissivism but rejects Strict Evidentialism and No Arbitrary Credences. Rather, our target is narrower. We are interested here in addressing the most pervasive forms of imprecise impermissivism, which are motivated by some version of Strict Evidentialism or No Abritrary Credences.

  6. 6.

    See White (2005) for arguments in favor of these two points, and Meacham (2013) for a critical response.

  7. 7.

    In what immediately follows we will restrict our discussion to a view that takes endpoints of the range to be determinable. Later we consider a view that avails itself to epistemiscism about the endpoints of ranges. That strategy warrants its own treatment.

  8. 8.

    cf. Joyce (2010, pp. 283–284).

  9. 9.

    We’re labeling the credence function \(Pr(\cdot )\), assuming that it is rationally required to have a probability function satisfying Kolmogorov’s axioms.

  10. 10.

    This has been noted in Walley (1991), Weatherson (2007), Joyce (2010) and Rinard (2013).

  11. 11.

    There are some special cases where a (0, 1) collapses, and we will see such an example in Sect. 4.

  12. 12.

    Thanks to a referee for pointing out just how exceptional such a case would be. For, in most cases where one is entertaining a wide range of probability functions, the probability functions will disagree about how to process the evidence. Still, our point here is that even if one were to find a case where every credal committee member moved closer to .6 upon learning some piece of evidence, it does not follow that that piece of evidence would narrow one’s ranged credence.

  13. 13.

    For instance, see Lyon (2015). Lyon, however, takes a very different interpretive tack in cases of the priors or situations with no evidence: he thinks such cases do not warrant any credence at all. Nevertheless, his framework may give some formal tools to help in this general project.

  14. 14.

    It’s worth noting that IC Narratives motivated by not going beyond one’s evidence might have a greater conflict with this approach. As Joyce notes, once we pick a density function for our credence range, this commits us to very precise claims about probabilities.

  15. 15.

    This list isn’t meant to be exhaustive.

  16. 16.

    For different numbers of balls in the urn, this ordered n-tuple will contain more or less elements. There will always be \(n + 1\) places, where n is the number of balls in the urn.

  17. 17.

    Following Meacham (2013), we understand an extreme permissive Bayesian as a Bayesian who maintains that any probabilistic priors function is rationally permissiable.

  18. 18.

    This is because drawing any pattern of white and black balls with replacement will be consistent with those two members of the partition taking any value. If you were to look into the urn and learn the exact proportion of white and black balls, then one could narrow the credences to precise values, and hence set one’s credence in W to the precise chance that a white ball will be drawn when randomly selected. But, this doesn’t pose a serious challenge to the objection that (0, 1) is sticky.

  19. 19.

    Where 0 means that W is always false, 1 means that W is always true, and, say, .4 means that W is 40% likely to be true.

  20. 20.

    In this case there may not be infinitely many biases, since perhaps one can set a reasonable cap on how many crayons would fit in the bucket.

  21. 21.

    You can think of this a number of ways. The prior might be an idealized agent’s credence function at the beginning of her epistemic life. Or, the prior might be the result taking a perfectly rational informed credence function and reverse engineering it to extract its initial prior.

  22. 22.

    You might think that we’re being unfair here; sense perception, especially calibration of our senses, is tricky for everyone. And yet, we indicate that sense perception poses a particularly trick problem for ranged impermissivists. The long response to this objection appears later in this paper, in Sect. 4.4, The Permissivist’s Dilemma?. The short response is this: Molly’s situation in Bird Watching is isomorphic to the situation described in Urn of Unknown Distribution. Since imprecise impermissivists have a unique problem in the latter, they will have a unique problem in the former.

  23. 23.

    Many thanks to Jennifer Carr for this way of putting the issue.

  24. 24.

    Technically there are more than three values, since the extreme ranges can have hard or soft brackets on either side, making it a six-value epistemology. Despite this, “three-value” epistemology seems more apt.

  25. 25.

    See Herron et al. (1994), White (2009) and Hart and Titelbaum (2015).

  26. 26.

    NB: Joyce (2010) identifies \(C^*\) as the subset of C whose members satisfy \(c(X) = c(Y)\); this is a typographical error (verified through personal communication).

  27. 27.

    \({C}(X) = {C}(Y) = {C}^*(X) = {C}^*(Y) = (0, {1}/{2}).\)

  28. 28.

    Many thanks to Brian Hedden and an anonymous reviewer for pressing us on this.


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We are grateful to Jennifer Carr, Kenny Easwaran, Brian Hedden, James Joyce, Ben Schwan, Reuben Stern, Olav Vassend, participants at the 2016 meeting of the Wisconsin Philosophical Association, the 2016 meeting of the Society for Exact Philosophy, and the 2017 Central Division Meeting of the American Philosophical Association, and two anonymous referees. We are especially grateful to William Roche and Michael Titelbaum for extensive feedback.

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Correspondence to Clinton Castro.

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Castro, C., Hart, C. The imprecise impermissivist’s dilemma. Synthese 196, 1623–1640 (2019).

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  • Uniqueness
  • Permissivism
  • Bayesianism
  • Ranged credence