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A Disjunctive Argument Against Conjoining Belief Impermissivism and Credal Impermissivism


In this paper, I offer reasons to conclude that either belief impermissivism or credal impermissivism is false. That is to say, I argue against the conjunction of belief impermissivism and credal impermissivism. I defend this conclusion in three ways. First, I show what I take to be an implausible consequence of holding that for any rational credence in p, there is only one correlating rational belief-attitude toward p, given a body of evidence. Second, I provide thought experiments designed to support the intuition that there are at least a few credences in some cases for which more than one belief-attitude is rationally permissible. Third, I provide one possible theoretical grounding for my position by appeal to Jamesian values.

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  1. Jackson and Turnbull (forthcoming).

  2. Jackson and Turnbull (forthcoming). For another example of the distinction between credal permissivism and belief permissivism, see Sharadin 2015.

  3. Some authors have distinguished between intrapersonal and interpersonal versions of (im)permissivism. Intrapersonal permissivism posits that one and the same person sometimes has rationally open to them more than one credence or belief-attitude given a body of evidence e and proposition p. Interpersonal permissivism posits that different persons can sometimes rationally differ from one another in their credences or belief-attitudes given a body of evidence e and proposition p. I am concerned with questions about interpersonal (im)permissivism in this paper, and my definitions of Credal Impermissivism and Belief Impermissivism should be read accordingly. For more on this distinction, see Kelly 2014, 303–307 and Kopec and Titelbaum 2016, 191.

  4. Jackson and Turnbull (forthcoming). This accords with how others describe the divide between permissivism and impermissivism. For example, Scott Stapleford writes that “The extreme position, accordingly, is impermissivism: There are no permissive cases. Open the door to one, and you’re permissive on matters of evidence” (Stapleford, 2019, 342, emphasis in original). Similarly, Thomas Kelly writes that “the permissivist thinks that in at least some possible cases, there is at least a little bit of slack” (Kelly, 2014, 299), and Ru Ye writes “Can there sometimes be multiple rational responses to the same body of evidence? An impermissivist says no, while a permissivist says yes” (Ye, 2021, 1).

  5. For examples of philosophical work arguing for or relying on the distinction between credence (or “degrees of belief”) and course-grained belief attitudes see Foley 1992, Sturgeon, 2008, 2010, Buchak, 2014, Leitgeb, 2014, Pettigrew, 2015, Staffel 2015, 2018, Carter, Jaris, and Rubin 2016, Weatherson 2016, Palmira, 2017, Jackson 2019, 2020a, 2020b, 2021, and Siscoe (forthcoming).

  6. For lottery-based arguments against the view that belief is merely high credence see, for example, Nelkin 2000, Staffel, 2016, Kelp, 2017, and Jackson 2019a. For other arguments against the view that belief is merely high credence see Nelkin 2000, Smith, 2010, Buchak, 2014, Staffel 2016, and Jackson 2019a.

  7. This relationship can be represented as follows. Take a proposition p and a body of evidence e. Credal impermissivism says that for any [p, e] → c, where ‘→’ points toward all permissible credences and ‘c’ picks out a single credence. Similarly, belief impermissivism says that for any [p, e] →b, where ‘→’ points toward all permissible belief-attitudes and ‘b’ picks out a single belief-attitude. Thus, the conjunction of credal impermissivism and belief impermissivism restricts the possibly combination of credences and belief-attitudes in a given case as follows [p, e] → c, b, where ‘→’ points toward all permissible credences and belief-attitudes. What values apply to c and b can change across scenarios. For example, one can accept both credal impermissivism and belief impermissivism and think the following two scenarios are possible: [p1, e1] → c = 0.9, b = suspending judgement; [p2, e2] → c = 0.9, b = believing. This is because, absent a proposition and body of evidence, there is no fixed relationship between a given c and a given b. However, given a specified p and e, the relationship does become fixed to a single credence and belief-attitude if one accepts both credal impermissivism and belief impermissivism. Thus, the one-to-one relationship between permissible credences and permissible beliefs when one accepts credal and belief impermissivism is achieved indirectly as a result of how both credences and beliefs are restricted in a given case on credal impermissivism and belief impermissivism, respectively. That is to say, the unique rational combination of a credence and belief-attitude in any given case for the credal- and belief-impermissivist is guaranteed by the uniqueness of the fixing components (the proposition and the body of evidence) rather than by any relation between the credences and belief-attitudes themselves.

  8. This simplifying assumption is for mere convenience of exposition. Adopting this simplification does not put a thumb on the scale in favor of my arguments or conclusions. If anything, as will be shown, it makes my case more challenging.

  9. To generate a set of bodies of evidence and propositions that would make this true, consider first a jar with 100 green balls. Then consider 99 additional jars, with one red ball being added each time, and one green ball being subtracted from the original set of 100 green balls each time. Then consider what the probability would be of pulling a red ball from each of the 100 jars if you had no information other than the number of balls of each color in the jar. A natural way of thinking about this case is that you must proportion your credence that you will pull a red ball out of the jar to the probability that you will pull a red ball out of the jar.

  10. Given how I have defined belief impermissivism, anyone who thinks that the standards for holding a particular belief-attitude can shift based on pragmatic considerations (like context or stakes) and thinks that such pragmatic considerations are not part of one’s evidence will not count as a belief impermissivist. There are at least two kinds of epistemologists who may end up in the camp. The first are epistemologists who have argued directly that the credence threshold at which someone should believe a proposition can shift based on changes in context or stakes, even while the body of evidence remains fixed (see, for example, Weatherson 2005 and Ganson 2008). The second are epistemologists who accept some kind of shifting standards account of knowledge (such as pragmatic encroachment theorists like Stanley 2005 and Fantl and McGrath 2012) or of ‘knowledge’ (such as contextualists like Cohen 1999 and DeRose 2009) and who also accept that knowledge is the norm of belief (see, for example, Williamson 2005, 108, Sutton 2005, Littlejohn, 2013, and Swindlehurst 2020). Similarly, anyone holding such a view will count as a belief permissivist on Jackson and Turnbull’s definition of belief permissivism. This seems like the right result because to think that what belief-attitudes are appropriate to hold for a given proposition can change across contexts, even while the body of evidence remains fixed, is to deny both the spirit and letter of impermissivism. Cf. Ye 2021 (writing that the epistemic permissivist “thinks that rationality is slack—people with the same evidence can rationally respond differently, due to differences in factors such as epistemic standards, background beliefs, practical stakes, ways of weighing theoretical virtues, etc.) and Rubin 2015 (arguing that “[i]f the suggestion that all epistemic notions are interest-relative is viable [as Jason Stanley has recently claimed], then it seems that a certain species of epistemic permissivism must be viable as well.”).

  11. This way of describing permissivism accords with how others have described permissivism. For example, Sophie Horowitz writes that “many permissivists hold that some bodies of evidence are impermissive with respect to some propositions” (Horowitz, 2018, 273). Similarly, Thomas Kelly writes that “One respect in which permissivism is a very modest thesis, then, is that it’s compatible with there being relatively few permissive cases. Another respect in which it’s a very modest thesis is that the permissivist might think that what permissive cases there are, aren’t all that permissive” (Kelly, 2014, 299). That said, this way of describing permissivism also requires much less permissiveness than is sometimes attributed to standard permissivist accounts. See, for example, the description of epistemic permissivism in Schultheis 2018.

  12. My argument is compatible with views on which certain credences or credence ranges either entail or constitute certain belief-attitudes, so long as the view is one in which at least some credences neither entail nor constitute a particular belief-attitude.

  13. See, for example, Greco 2015 (equating belief with probability 1), Hunter 1996 (concluding that belief in its ordinary sense should not be identified with probability 1), Foley 1992 (claiming belief-talk is vague and suggesting that the threshold for belief can only be stipulated, but requiring that the stipulated threshold entail that the degree of confidence for belief must be higher than its negation), Lee 2017 (defending the view that “if you are near-maximally confident that p in a low-stakes situation, then you outright believe p”), Dorst 2019 (defending that “high credence suffices for belief” and that “your beliefs just are the things you’re sufficiently confident in”), Staffel 2016 (defending the view that “rational belief can’t be stably high credence”), Dallmann 2014 (arguing that belief can be reduced to a type of imprecise credence), and Sturgeon 2008 (defending the view that “the epistemology of binary belief falls out of the epistemology of confidence; yet norms for binary belief do not always derive from more fundamental ones for confidence”).

  14. Something analogous happens with legal standards of proof, such as the “beyond a reasonable doubt” standard employed in criminal cases in many jurisdictions. It is widely recognized that judges and scholars disagree among themselves as to what credence threshold is sufficient for a finding beyond a reasonable doubt. See, e.g., McCauliff 1982. Furthermore, there is disagreement as to whether beyond a reasonable doubt should even be defined in terms of reaching a particular credence threshold to begin with. See, e.g., Gardiner 2019. This suggests that there is no particular credence that constitutes the threshold for being “beyond a reasonable doubt.”

  15. Things are in fact much worse than this for those who reject the argument given that it is only a simplifying assumption that no rational credence goes beyond the hundredth. Consider a modified version of the scenario in footnote 3 by considering a jar with 100,000 green balls, and an additional 99,999 jars, with one red ball being added each time, and one green ball being subtracted from the original number of 100,000 green balls each time. On such a scenario there would be a situation where credence .x would require disbelief and credence .x + 0.0001 would require suspension of belief, and another scenario where credence .y would require suspension of belief and credence .y + 0.0001 would require belief.

  16. See, for example, Friedman 2019 (arguing that belief and credences “play different roles in inquiry” and that belief “should be thought of as playing a key role in our settling our inquiries”), Staffel 2019 (arguing that beliefs are “terminal attitudes” but that both suspension of belief and credence holding are “transitional attitudes”), Lee 2020 (arguing that “one cannot inquire into whether p while at the same time occurrently believing that p”), Hindriks 2007 (defending the “traditional analysis of assertion as the linguistic expression of belief”), and Bach 2008, 77 (arguing that “the only relevant rule on assertion is belief”).

  17. I also find it difficult to see how either of you could be irrational in thinking that the other one is acting rationally, but that moves beyond the main point here.

  18. Analogous scenarios can be constructed for those who think that stakes influence at what point one crosses the firm threshold from being required to have one belief-attitude to another. If one is both a credal impermissivist and a belief impermissivist, then in any particular case there will be two points at which an incremental change from .x to .x + 0.01 rationally requires a change in belief-attitude. The only difference for at least certain forms of stakes-sensitive impermissivism is that what those two points are can change between cases, depending on what is at stake.

  19. One could, of course, create an analogous case dealing with a self-identified agnostic and a self-identified theist.

  20. Schultheis 2018, 863.

  21. Schultheis 2018, 864.

  22. Schultheis 2018, 864 (emphasis in original).

  23. Schultheis 2018, 878.

  24. Schultheis 2018, 866 (emphasis in original).

  25. Schultheis 2018, 866.

  26. Schultheis 2018, 866.

  27. Schultheis 2018, 866. For an argument that Schultheis’ argument does not succeed, see Bradley (2021).

  28. Roeber 2020, for example, concludes that belief impermissivism (which he calls Doxastic Impermissive Evidentialism) is false but that this is compatible with credal impermissivism (which he calls Credal Impermissive Evidentialism) being true. I take my arguments to support such a view.

  29. James 1897, Section VII.

  30. Kelly 2014, 301–303.

  31. Kelly 2014, 301–303.

  32. This is particularly true if one adopts either a dualist perspective or a credence-first perspective about the relationship between beliefs and credences. For a discussion of these views, see Jackson 2020a, 2478-79.

  33. Kelly 2014, 302 (emphasis added).

  34. Horowitz 2018, 269.

  35. Horowitz 2018, 269 (emphasis added). Horowitz notes that there are “many subtly different ways that one could define ‘permissivism.’” She is certainly right about this, and it is worth pointing out that her definition of credal permissivism is more permissive than the one I use in this paper.

  36. Horowitz 2018, 287.

  37. Another kind of theoretical grounding one could appeal to is a permissive set of “epistemic standards.” As Miriam Schoenfield points out, there are different ways to conceptualize what epistemic standards are (Schoenfield, 2014, 199). Schoenfield describes epistemic standards as “a set of standards as a function from bodies of evidence to doxastic states which the agent takes to be truth conducive” (2014, 199). Schoenfield notes that others may describe epistemic standards as a set of rules or belief (2014, 199). Appeals to epistemic standards can be used in a variety of ways in providing a theoretical grounding for epistemic permissivism. For example, Laura Frances Callahan appeals to epistemic standards as part of her “epistemic existentialism” (2020). On Callahan’s account, “[a]ccording to the epistemic existentialist, it’s not just that what’s rational to believe on the basis of evidence can vary according to agents’ frameworks, understood as passive aspects of individuals’ psychologies. Rather, what’s rational to believe on the basis of evidence is sensitive to agents’ choices and active commitments” (2020, 539). Michael Titelbaum and Matthew Kopec also provide a theoretical grounding for permissivism based on differences in epistemic standards, which they refer to as different “methods of reasoning” (2019, 208). Any of these views could be modified to ground a rejection of just one of credal or belief impermissivism. This mirrors the strategy I offered above on which Jamesian values are used to ground belief permissivism while assuming credal impermissivism.

  38. Given how I have structured my arguments in this paper, it would be natural for one to conclude that the conjunct that I have shown to be false is belief impermissivism. I think my arguments put greater pressure on belief impermissivism compared to credal impermissivism. But given that for much of my argument, I assumed that credal impermissivism was true in order to assess what followed, I leave open the possibility that one could make a more convincing argument that credal impermissivism is the disjunct that ought to be rejected by approaching the matter from another angle.

  39. Jackson and Turnbull (forthcoming). Levinstein (2017) has argued against this view—at least for credal permissivism—while still acknowledging that “many writers think that if [credal permissivism] is true, conciliationism is wrong” (2017, 343).

  40. Arguments for such non-reductionism about belief and credence can be found in Buchak 2014, Ross & Schroeder, 2014, Pettigrew, 2015, Jackson, 2019b, and Collins 2020, among others.


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Thanks to Mike Ashfield, Liz Jackson, Eric Hiddleston, Bruce Russell, Wes Siscoe, two anonymous referees for this journal, and those in the audience at the 75th Annual Mountain-Plains Philosophy Conference for helpful comments on earlier drafts of this paper. Thanks also to Layla Saatchi for valuable discussions about epistemic permissivism during the time in which I was first thinking about this paper’s ideas.

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Satta, M. A Disjunctive Argument Against Conjoining Belief Impermissivism and Credal Impermissivism. Erkenn (2022).

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