Belief, credence, and evidence


I explore how rational belief and rational credence relate to evidence. I begin by looking at three cases where rational belief and credence seem to respond differently to evidence: cases of naked statistical evidence, lotteries, and hedged assertions. I consider an explanation for these cases, namely, that one ought not form beliefs on the basis of statistical evidence alone, and raise worries for this view. Then, I suggest another view that explains how belief and credence relate to evidence. My view focuses on the possibilities that the evidence makes salient. I argue that this makes better sense of the difference between rational credence and rational belief than other accounts.

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  1. 1.

    See Jackson (forthcominga) for why the relationship between belief and credence is an important epistemological question.

  2. 2.

    Buchak (2014), Staffel (2015), Smith (2010).

  3. 3.

    Buchak (2014). See also Cohen (1977), Thomson (1986), Colyvan et al. (2001).

  4. 4.

    Kyburg (1961), Nelkin (2000), Hawthrone (2003), Collins (2006), Staffel (2015), Kelp (2017), Horgan (2017).

  5. 5.

    See Cohen (2010: p. 663) and Plantinga (1993a: pp. vii–viii, 1993b: pp. 132–161).

  6. 6.

    A note on terminology: people often use the phrase “degrees of belief” to refer to a mental state that comes in degrees and in some sense, represents the world. I think such a mental state exists, but for our purposes, I call that “credence,” which I contrast with belief, a categorical state. One might prefer to use phrases like “partial belief” or “degrees of belief” instead of credence, and then call what I call belief “categorical belief.” I am not necessarily opposed to this, but given that some have argued that beliefs do not come in degrees (see Moon (2017)), my terminology is more ecumenical.

  7. 7.

    Schwitzgebel (2015).

  8. 8.

    Buchak (2014: p. 286). See also Holton (2014), Greco (2015).

  9. 9.

    Weatherson (2005), Wedgwood (2012), Ross and Schroeder (2014), and Locke (2014) all have views on which some kind of treating-as-true condition is necessary for belief.

  10. 10.

    See Nagel (2010: p. 418), Ross and Schroder (2014: pp. 275–277). One worry for this claim is that this is inconsistent with the threshold view of belief, on which belief that p is a high credence in p above some threshold (less than 1). However, those who hold to the threshold view could embrace this claim by maintaining that a credence’s meeting the threshold gives the attitude additional properties, which makes it function like a belief and causes the agent to close off possibilities (see Weisberg forthcoming: p. 22). Nonetheless, those sympathetic to the threshold view of belief will almost certainly disagree with my verdicts about the cases in section III, as in those cases, one’s credence in p can get arbitrarily close to one, yet one ought not believe p. In this, my assumptions about belief and credence may be inconsistent with a threshold view of belief.

  11. 11.

    See Ramsey (1926), Jeffrey (1965), de Finetti (1990).

  12. 12.

    Jeffrey (1965: p. 60).

  13. 13.

    For objections to the view that credences are reducible to and/or measurable by betting behavior, see Foley (1993: ch. 4), Plantinga (1993b: ch. 6), Christensen (2004: 5.2), Hajek and Eriksson (2007), and Steffánson (2017).

  14. 14.

    For more on the view that belief is credence 1, see Levi (1991), Roorda (1995), Wedgwood (2012), Clarke (2013), Greco (2015), Dodd (2016).

  15. 15.

    See Enoch et al. (2012), Bloom-Tillmann (2015, 2017), and Di Bello (Forthcoming).

  16. 16.

    Buchak (2014). For earlier discussions of similar cases, see Thomson (1986) and Schauer (2003); this case originated with a real civil case from the 1940 s. Thanks to an anonymous referee.

  17. 17.

    See Thomson (1986), Kaplan (1996), Smith (2010, 2016, forthcoming), Nelkin (2000), Enoch et al. (2012), Staffel (2015), Pasnau (2018).

  18. 18.

    One might worry that the reason it seems impermissible to form such beliefs is not because of the nature of one’s evidence, but because of the moral stakes involved. See Bolinger (forthcoming). Thanks to Wes Siscoe. However, consider a case where I know either a man or a woman is wearing a hat, and I know that men are 10 × more likely to wear hats than women. It still seems like I shouldn't believe the man is wearing the hat merely on the basis of the statistic alone, even though nothing is at stake morally. Further, there aren’t high moral stakes in many versions of the lottery and hedged assertions, but those cases also don’t justify belief.

  19. 19.

    See Staffel (2015). Horgan (2017) also maintains one ought not believe lottery propositions: “outright belief that one’s lottery ticket will lose does not seem epistemically justified, no matter how high are the odds against winning.” For other discussions of the lottery paradox, especially with respect to the relationship between belief and credence, see Kyburg (1961), Foley (1993: ch. 4), Christensen (2004: ch. 2), Sturgeon (2008), Nelkin (2000), Collins (2006), Kelp (2017).

  20. 20.

    Hawthorne (2003: ch. 1).

  21. 21.

    Staffel (2015). See Williamson (2000: p. 255).

  22. 22.

    See Kelp (2017) for an additional argument that it is irrational to believe lottery propositions.

  23. 23.

    Smith (2010: pp. 13–14).

  24. 24.

    Smith does not explicitly note this because his focus is not on credence, but I take this to be uncontroversial. He does note that “the probability of P given E can reach any level (short, perhaps, of one) without one having justification for believing P” (17).

  25. 25.

    Adler (2002: p. 42).

  26. 26.

    Thanks to an anonymous referee.

  27. 27.

    For discussion, see Enoch et al. (2012), Enoch and Fisher (2015), Bloom-Tillman (2015).

  28. 28.

    Smith (2010, 2016, forthcoming).

  29. 29.

    Smith (2010: pp. 15–19).

  30. 30.

    Ibid, 17.

  31. 31.

    Thanks to an anonymous referee.

  32. 32.

    However, for a recent criticism of Smith, see Backes (forthcoming).

  33. 33.

    See Buchak (2014), Thomson (1986), Kaplan (1996), Nelkin (2000).

  34. 34.

    Staffel (2015: p. 1725).

  35. 35.

    Thanks to John Keller.

  36. 36.

    Thanks to an anonymous referee.

  37. 37.

    For a discussion of related cases, see Smith (2016: pp. 109–120).

  38. 38.

    However, it is plausible that the fact that you shouldn’t withhold belief here is because the statistical evidence is trumped by the testimonial evidence, so this case may not draw any sort of interesting contrast between belief and credence. Thanks to an anonymous referee.

  39. 39.

    Thomson (1986), Kaplan (1996), Nelkin (2000).

  40. 40.

    Thanks to an anonymous referee.

  41. 41.

    For a similar criticism of the statistical evidence view, see Enoch and Fisher (2015: Part I). One might worry that ‘statistics’ in the limit are not merely statistical evidence, because they posit a necessary connection between two things. However, it is unclear why evidence’s drawing a necessary connection between two things precludes that evidence’s being statistical. For example, suppose someone claims that having blue hair causes cancer. You ask for some statistical evidence to support their claim, and they say “100% of people with blue hair have cancer.” This seems like an apt response. It would be odd to complain that this isn’t mere statistical evidence because the correlation is too tight; it is unclear that a perfect correlation precludes that connection’s being statistical. I am grateful to an anonymous referee for raising this objection.

  42. 42.

    Thanks to Daniel Rubio and an anonymous referee.

  43. 43.

    Thanks to an anonymous referee.

  44. 44.

    See Buchak (2014: p. 301).

  45. 45.

    Ibid, 295.

  46. 46.

    Thanks to an anonymous referee.

  47. 47.

    See Buchak (2014: p. 301) on the problem of defining statistical evidence.

  48. 48.

    Thanks to Blake Roeber. See Ross and Schroder (2014: p. 276).

  49. 49.

    However, there are exceptions to this. Someone uttering “That is a zebra, not a cleverly painted mule” may make salient the possibility it is not a zebra, and thus count as C-evidence, and thus not justify belief. Thanks to an anonymous referee.

  50. 50.

    For this reason, agents who fail to alter their beliefs on the basis of C-evidence will not be susceptible to the base rate fallacy. They will alter their credences in accord with the base rates, and bet accordingly. For more on the base rate fallacy see Kahneman (2011: ch. 14); for a response to Kahneman, see Feldman (1988: pp. 85–86).

  51. 51.

    Thanks to Lara Buchak. See Locke (2014), Tang (2015), Moon (2018).

  52. 52.

    Lewis (1996: p. 559). See especially Lewis’s “Rule of Attention.” See also Stalnaker (2002), Fantl and McGrath (2010: pp. 55–58).

  53. 53.

    Thanks to Alan Hajek.

  54. 54.

    Thanks to Ben Lennertz and Andrew Moon.

  55. 55.

    This raises an interesting question: given your irrational paranoia, should you believe your partner is at the store? A larger project that involved both rational and irrational agents would say something about this question. More generally, it would discuss agents who respond to their evidence in less-than-ideal ways, either because they fail to consider possibilities they ought to pay attention to (someone being careless or thoughtless), or because they consider possibilities they ought not consider (an overly neurotic, anxious person). It might be the case that the neurotic person ought not to form as many beliefs as the person who is responding normally to evidence, because the anxious person’s evidence would make the possibility they are wrong more salient. However, what doxastic attitudes irrational agents ought to form in response to their evidence is ultimately beyond the scope of this paper.

  56. 56.

    Thanks to Fritz Warfield.

  57. 57.

    Note also that if pragmatic encroachment occurs, then a change in stakes might cause a change is what possibilities ought to be salient for an agent, and thus affect what that agent should believe. However, I remain neutral on whether stakes affect what is salient for rational agents.

  58. 58.

    Collins (2006) also argues that the salience of the possibility of error does important work in the lottery paradox, but his application is to knowledge, rather than rational belief. He suggests the following necessary condition on knowledge to explain lottery cases, which nicely complements my account: “If there is some possibility that is very close to actuality that p is false, and to which S assigns a non-zero probability, then no matter how subjectively improbable this possibility is, S doesn’t know that p.” For a related discussion about the relationship between lotteries, statistical evidence, and knowledge, see Nelkin (2000).

  59. 59.

    Staffel (2015: pp. 5–7). See also Hawthorne (2003: ch. 1).

  60. 60.

    For instance: suppose we are trying to figure out what time it is, and there is a far-away, blurry clock (with hands), that makes it look roughly like it is 5:30 but it could also be 4:30 or 6:30. This would be some evidence that it is 5:30, but the nature of the perception should cause us to pay attention to the fact that we might be wrong; it would be natural to classify a blurry perception of this clock as C-evidence. For more on how perception might probabilistic, see Wedgwood (forthcoming).

  61. 61.

    See DeRose (1995: p. 24), Schaffer (2004).

  62. 62.

    Buchak (2014: p. 292).

  63. 63.

    Thanks to Fritz Warfield.

  64. 64.

    See especially Staffel (2017, Forthcominga), and also Lin (2013), Lin and Kelly (2012), Wedgwood (2012), Smithies (2012: p. 278), Tang (2015), Weatherson (2016), Staffel (Forthcomingb).

  65. 65.

    See Ross and Schroeder (2014), especially the last section, “Historical Postscript.”

  66. 66.

    I apply this view to questions about the rationality of faith in Jackson (forthcomingb).

  67. 67.

    Thanks to Andrew Moon, Blake Roeber, Fritz Warfield, John Keller, Martin Smith, Renee Bolinger, Greta Turnbull, Wes Siscoe, Calum Miller, Lara Buchak, Alan Hajek, Jeff Tolly, Ben Lennertz, Ting Lau, Anne Jeffery, Nevin Climenhaga, Dustin Crummett, Ross Jensen, Rebecca Chan, Julia Staffel, Robert Audi, Lizzie Fricker, Daniel Nolan, the Doxastic Voluntarism seminar and the epistemology reading group at Notre Dame, and audiences at the 2016 St. Thomas Summer Seminar, 2016 Society for Christian Philosophers Eastern Regional Meeting, the 2016 Indiana Philosophical Association, the 2017 Philosopher’s Cocoon Conference, and three anonymous referees from this journal for helpful comments that improved this paper in many ways.


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Jackson, E. Belief, credence, and evidence. Synthese (2018).

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  • Belief
  • Credence
  • Evidence
  • Rationality
  • Lottery paradox
  • Statistical evidence
  • Salience