Journal of Philosophical Logic

, Volume 44, Issue 6, pp 817–834 | Cite as

You’ve Come a Long Way, Bayesians

  • Jonathan Weisberg

Forty years ago, Bayesian philosophers were just catching a new wave of technical innovation, ushering in an era of scoring rules, imprecise credences, and infinitesimal probabilities. Meanwhile, down the hall, Gettier’s 1963 paper [28] was shaping a literature with little obvious interest in the formal programs of Reichenbach, Hempel, and Carnap, or their successors like Jeffrey, Levi, Skyrms, van Fraassen, and Lewis. And how Bayesians might accommodate the discourses of full belief and knowledge was but a glimmer in the eye of Isaac Levi.

Forty years later, scoring rules, imprecise credences, and infinitesimal probabilities are all the rage. And the formal and “informal” traditions are increasingly coming together as Bayesian arguments spill over into debates about the foundations of empirical knowledge, skepticism, and more. Relatedly, Bayesian interest in full belief and knowledge has never been greater.

Much more besides has happened in the last forty years of Bayesian philosophy,...


Bayesianism Probability Epistemic utility Justification Knowledge Foundationalism Imprecise probability Indeterminate probability Representor theory Decision theory Expected utility theory Infinitesimal probabilities Full belief Partial belief 


  1. 1.
    Bernstein, A.R., & Wattenberg, F. (1969). Non-standard measure theory. In W.A.J. Luxemberg (Ed.), Applications of model theory of algebra, analysis, and probability, Holt. New York: Rinehart and Winston.Google Scholar
  2. 2.
    Bradley, S., & Steele, K. (2014). Should subjective probabilities be sharp? Episteme, 11(3), 277–289.CrossRefGoogle Scholar
  3. 3.
    Brier, G.W. (1950). Verification of forecasts expressed in terms of probability. Monthly Weather Review, 78(1), 1–3.CrossRefGoogle Scholar
  4. 4.
    Briggs, R.A. (2009). Distorted reflection. The Philosophical Review, 118(1), 59–85.CrossRefGoogle Scholar
  5. 5.
    Buchak, L. (2014). Belief, credence, and norms. Philosophical Studies, 169 (2), 285–311.CrossRefGoogle Scholar
  6. 6.
    Carr, J. (2013). Justifying bayesianism Massachusetts Institute of Technology dissertation.Google Scholar
  7. 7.
    Carr, J. manuscript. Epistemic utility theory and the aim of belief.Google Scholar
  8. 8.
    Chandler, J. (2010). The lottery paradox generalized? British Journal for the Philosophy of Science, 61(3), 667–679.CrossRefGoogle Scholar
  9. 9.
    Chandler, J. forthcoming. Subjective probabilities need not be sharp. Erkenntnis.Google Scholar
  10. 10.
    de Finetti, B. (1937). Foresight, its logical laws, its subjective sources. In H.E. Kyburg, & H.E. Smokler (Eds.), Studies in subjective probability. NY 2nd: Krieger Huntington.Google Scholar
  11. 11.
    de Finetti, B. (1974). Theory of probability. WileyGoogle Scholar
  12. 12.
    Douven, I. (2002). A new solution to the paradoxes of rational acceptability. British Journal for the Philosophy of Science, 53(3), 391–410.CrossRefGoogle Scholar
  13. 13.
    Douven, I. (2011). Further results on the intransitivity of evidential support. The Review of Symbolic Logic, 4(4), 487–97.CrossRefGoogle Scholar
  14. 14.
    Douven, I., & Kelp, C. (2013). Proper bootstrapping. Synthese, 190(1), 171–185.CrossRefGoogle Scholar
  15. 15.
    Douven, I., & Williamson, T. (2006). Generalizing the lottery paradox. British Journal for the. British Journal for the Philosophy of Science, 57(4), 755–779.CrossRefGoogle Scholar
  16. 16.
    Dubins, L.E. (1975). Finitely additive conditional probabilities, conglomerability and disintegrations. Annals of Probability, 3(1), 89–99.CrossRefGoogle Scholar
  17. 17.
    Easwaran, K. this volume. Formal epistemology. Journal of Philosophical Logic.Google Scholar
  18. 18.
    Easwaran K., & Branden F. (2012). An ‘evidentialist’ worry about joyce’s argument for probabilism. Dialectica, 66(3), 425–433.CrossRefGoogle Scholar
  19. 19.
    Elga, A. (2010). Subjective probabilities should be sharp. Philosophers’ Imprint, 10(5), 1–11.Google Scholar
  20. 20.
    Ellsberg, D. (1961). Risk, ambiguity, and the savage axioms. Quarterly Journal of Economics, 75(4), 643–649.CrossRefGoogle Scholar
  21. 21.
    Fitelson, B. (2012). Joyce’s argument for probabilism. Philosophy of Science, 79(1), 167–174.CrossRefGoogle Scholar
  22. 22.
    Fitelson, B., & Hájek, A. manuscript. Declarations of independence.Google Scholar
  23. 23.
    Foley, R. (1993). Working without a net A study of egocentric epistemology. Oxford University Press.Google Scholar
  24. 24.
    Foley, R. (2009). Beliefs, degrees of belief, and the lockean thesis. In H. Franz & C. Schmidt-Petri (Eds.), Degrees of belief (Vol. 342, pp. 37–47). Synthese Library, Springer.Google Scholar
  25. 25.
    Frankish, K. (2009). Partial belief and flat-out belief. In H. Franz & C. Schmidt-Petri (Eds.), Degrees of belief (Vol. 342). Synthese Library, Springer.Google Scholar
  26. 26.
    Fumerton, R. (1995). Metaepistemology and skepticism. Rowman & Littlefield.Google Scholar
  27. 27.
    Gallow, J.D. (2014). How to learn from theory-dependent evidence; or commutativity and holism A solution for conditionalizers. British Journal for the Philosophy of Science, 65(3), 493–519.CrossRefGoogle Scholar
  28. 28.
    Gettier, E.L. (1963). Is justified true belief knowledge. Analysis, 23, 121–3.CrossRefGoogle Scholar
  29. 29.
    Gibbard, A. (2008). Rational credence and the value of truth. In T.S. Gendler & J. Hawthorne (Eds.), Oxford studies in epistemology (Vol. 2). Oxford University Press.Google Scholar
  30. 30.
    Greaves, H., & Wallace, D. (2006). Justifying conditionalization conditionalization maximizes expected epistemic utility. Mind, 115, 607–632.CrossRefGoogle Scholar
  31. 31.
    Hájek, A. (2009). Arguments for—or against—probabilism? In F. Huber, & C. Schmidt-Petri (Eds.), Degrees of belief. (pp. 229–252). Springer.Google Scholar
  32. 32.
    Hájek, A. manuscript. Staying regular.Google Scholar
  33. 33.
    Jeffrey, R.C. (1987). Indefinite probability judgment: A reply to Levi. Philosophy of Science, 54(4), 586–591.CrossRefGoogle Scholar
  34. 34.
    Joyce, J. (1998). A nonpragmatic vindication of probabilism. Philosophy of Science, 65(4), 575–603.CrossRefGoogle Scholar
  35. 35.
    Joyce, J. (1999). The foundations of causal decision theory. Cambridge University Press.Google Scholar
  36. 36.
    Joyce, J. (2009). Accuracy and coherence: Prospects for an alethic epistemology of partial belief. In Huber, F., & Schmidt-Petri, C. (Eds.), Degrees of belief (Vol. 342, pp. 263–297). Synthese Library, Synthese.Google Scholar
  37. 37.
    Joyce, J. (2010). A defense of imprecise credences in inference and decision making. Philosophical Perspectives, 24(1), 281–323.CrossRefGoogle Scholar
  38. 38.
    Kaplan, M. (1996). Decision theory as philosophy. Cambridge University Press.Google Scholar
  39. 39.
    Korb, K. B. (1992). The collapse of collective defeat: Lessons from the lottery paradox. In: Psa: Proceedings of the biennial meeting of the philosophy of science association (Vol. 1, pp. 230–236).Google Scholar
  40. 40.
    Kyburg, H.E. (1970). Conjunctivitis. In M. Swain Induction, acceptance, and rational belief. D. Reidel.Google Scholar
  41. 41.
    Lee, M.D., & Cummins, T.R. (2004). Evidence accumulation in decision making Unifying the “take the best” and the “rational” models. Psychonomic Bulletin & Review, 11(2), 343–52.CrossRefGoogle Scholar
  42. 42.
    Leitgeb, H., & Pettigrew, R. (2010). An objective justification of bayesianism i: Measuring inaccuracy. Philosophy of Science, 77(2), 201–235.CrossRefGoogle Scholar
  43. 43.
    Leitgeb, H., & Pettigrew, R. (2010). An objective justification of bayesianism ii: The consequences of minimizing inaccuracy. Philosophy of Science, 77(2), 2010.Google Scholar
  44. 44.
    Levi, I. (1967). Gambling with truth. A. Knopf.Google Scholar
  45. 45.
    Levi, I. (1974). On indeterminate probabilities. Journal of Philosophy, 71, 391–418.CrossRefGoogle Scholar
  46. 46.
    Levi, I. (1980). The enterprise of knowledge, An essay on knowledge, credal probability, and chance. The MIT Press.Google Scholar
  47. 47.
    Lewis, D. (1980). A subjectivist’s guide to objective chance. In R.C. Jeffrey (Ed.), Studies in inductive logic and probability, vol. II. University of California Press.Google Scholar
  48. 48.
    Lewis, D. (1986). On the plurality of worlds. Malden MA: Blackwell Publishing.Google Scholar
  49. 49.
    Maher, P. (1993). Betting on theories. Cambridge University Press.Google Scholar
  50. 50.
    Maher, P. (2002). Joyce’s argument for probabilism. Philosophy of Science, 69, 73–81.CrossRefGoogle Scholar
  51. 51.
    Makinson, D.C. (1965). The paradox of the preface. Analysis, 25, 205–7.CrossRefGoogle Scholar
  52. 52.
    Moss, S. (2011). Scoring rules and epistemic compromise. Mind, 120(480), 1053–1069.CrossRefGoogle Scholar
  53. 53.
    Moss, S. forthcoming. Credal dilemmas. Noûs.Google Scholar
  54. 54.
    Nelkin, D.K. (2000). The lottery paradox, knowledge, and rationality. The Philosophical Review, 109(3), 373–408.CrossRefGoogle Scholar
  55. 55.
    Neta, R. (2008). What evidence do you have. British Journal for the Philosophy of Science, 59(1), 89–119.CrossRefGoogle Scholar
  56. 56.
    Newell, B.R., & Lee, M.D. (2011). The right tool for the job? Comparing an evidence accumulation and a naïve strategy selection model of decision making. Journal of Behavioral Decision Making, 24(5), 456–481.CrossRefGoogle Scholar
  57. 57.
    Pettigrew, R. (2012). Accuracy, chance, and the principal principle. The Philosophical Review, 121(2), 241–275.CrossRefGoogle Scholar
  58. 58.
    Pettigrew, R. (2013). A new epistemic utility argument for the principal principle. Episteme, 10(1), 19–35.CrossRefGoogle Scholar
  59. 59.
    Pettigrew, R. forthcoming. Accuracy, risk, and the principle of indifference. Philosophy and Phenomenological Research.Google Scholar
  60. 60.
    Pollock, J.L. (1971). Perceptual knowledge. The Philosophical Review, 80 (2), 287–319.CrossRefGoogle Scholar
  61. 61.
    Pollock, J.L. (1974). Knowledge and justification. Princeton University Press.Google Scholar
  62. 62.
    Pollock, J.L. (1995). Cognitive carpentry. Cambridge: MIT Press.Google Scholar
  63. 63.
    Popper, K. (1959). The logic of scientific discovery. London: Hutchinson & Co.Google Scholar
  64. 64.
    Pruss, A.R. (2012). Infinite lotteries, perfectly thin darts, and infinitesimals. Thought, 1(2), 81–9.Google Scholar
  65. 65.
    Pruss, A.R. (2013). Probability, regularity, and cardinality. Philosophy of Science, 80(2), 231–240.CrossRefGoogle Scholar
  66. 66.
    Pryor, J. (2000). The skeptic and the dogmatist. Noûs, 34(4), 517–549.CrossRefGoogle Scholar
  67. 67.
    Pryor, J. (2005). There is immediate justification. In M. Steup & E. Sosa (Eds.), Contemporary debates in epistemology. Blackwell.Google Scholar
  68. 68.
    Pryor, J. (2013). Problems for credulism. In C. Tucker (Ed.), Seemings and justification, New essays on dogmatism and phenomenal conservatism. Oxford University Press.Google Scholar
  69. 69.
    Rényi, A. (1970). Foundations of probability. San Francisco: Holden-Day, In.Google Scholar
  70. 70.
    Ross, J., & Schroeder, M. (2014). Belief, credence, and pragmatic encroachment. Philosophy and Phenomenological Research, 88(2), 259–288.CrossRefGoogle Scholar
  71. 71.
    Roush, S. (2005). Tracking truth knowledge, evidence, and science. Oxford University Press.Google Scholar
  72. 72.
    Ryan, S. (1996). The epistemic virtues of consistency. Synthese, 109(22), 121–141.CrossRefGoogle Scholar
  73. 73.
    Savage, L.J. (336). Elicitation of personal probabilities and expectations. Journal of American Statistical Association, 66, 783–801.Google Scholar
  74. 74.
    Seidenfeld, T. (2004). A contrast between two decision rules for use with (convex) sets of probabilities: γ-maximin versus e-admissibility. Synthese, 140(1–2), 69–88.CrossRefGoogle Scholar
  75. 75.
    Shafer, G. (1976). A mathematical theory of evidence. Princeton University Press.Google Scholar
  76. 76.
    Silins, N. (2008). Basic justification and the moorean response to the skeptic. In Oxford studies in epistemology (vol. 2). Oxford University Press.Google Scholar
  77. 77.
    Skyrms, B. (1980). Causal necessity. New Haven: Yale University Press.Google Scholar
  78. 78.
    Smith, M. (2010). A generalized lottery paradox for infinite probability spaces. British Journal for the Philosophy of Science, 61(4), 821–831.CrossRefGoogle Scholar
  79. 79.
    Steele, K. (2010). What are the minimal requirements of rational choice? arguments from the sequential setting. Theory and Decision, 68(4), 463–487.CrossRefGoogle Scholar
  80. 80.
    Sturgeon, S. (2008). Reason and the grain of belief. Noûs, 42(1), 139–65.CrossRefGoogle Scholar
  81. 81.
    Titelbaum, M. (2010). Tell me you love me, Bootstrapping externalism, and no-lose epistemology. Philosophical Studies, 149(1), 119–34.CrossRefGoogle Scholar
  82. 82.
    van Fraassen, B. (1983). Calibration: A frequency justification for personal probability. In R.S Cohen & L. Laudan (Eds.), Physics, philosophy, and psychoanalysis. Reidel, D.Google Scholar
  83. 83.
    van Fraassen, B. (1984). Belief and the will. The Journal of Philosophy, 81 (5), 235–256.CrossRefGoogle Scholar
  84. 84.
    van Fraassen, B. (1990). Figures in a probability landscape. In Truth or consequences. Kluwer.Google Scholar
  85. 85.
    Vineberg, S. (2014). Dutch book arguments. Stanford Encyclopedia of Philosophy Retrieved August 27, 2014.
  86. 86.
    Vogel, J. (2000). Reliabilism leveled. Journal of Philosophy, 97(11), 602–23.CrossRefGoogle Scholar
  87. 87.
    Vogel, J. (2008). Epistemic bootstrapping. Journal of Philosophy, 105(9), 518–539.CrossRefGoogle Scholar
  88. 88.
    Wagner, C. (2013). Is conditioning really incompatible with holism? Journal of Philosophical Logic, 42(2), 409–414.CrossRefGoogle Scholar
  89. 89.
    Weatherson, B. (2012). Knowledge, bets, and interests. In J. Brown, & M. Gerken (Eds.), Knowledge ascriptions (pp. 75–103). Oxford University Press.Google Scholar
  90. 90.
    Weintraub, R. (2008). How probable is an infinite sequence of heads? A reply to williamson. Analysis, 68(3), 247–250.CrossRefGoogle Scholar
  91. 91.
    Weisberg, J. (2007). Conditionalization, reflection, and self-knowledge. Philosophical Studies, 135(2), 179–197.CrossRefGoogle Scholar
  92. 92.
    Weisberg J. (2009). Commutativity or holism A dilemma for conditionalizers. British Journal for the Philosophy of Science, 60(4), 793–812.CrossRefGoogle Scholar
  93. 93.
    Weisberg, J. (2010). Bootstrapping in general. Philosophy and Phenomenological Research, 81(3), 525–48.CrossRefGoogle Scholar
  94. 94.
    Weisberg, J. (2012). The bootstrapping problem. Philosophy Compass, 7(9), 597–610.CrossRefGoogle Scholar
  95. 95.
    Weisberg, J. (2013). Knowledge in action. Philosophers’ Imprint, 13(22), 1–23.Google Scholar
  96. 96.
    Weisberg, J. forthcoming. Updating, undermining, and independence. British Journal for the Philosophy of Science.Google Scholar
  97. 97.
    Wenmackers, S., & Horsten, L. (2013). Fair infinite lotteries. Synthese, 190 (1), 37–61.CrossRefGoogle Scholar
  98. 98.
    White, R. (2005). Epistemic permissiveness. Philosophical Perspectives, 19 (1), 445–459.CrossRefGoogle Scholar
  99. 99.
    White, R. (2006). Problems for dogmatism. Philosophical Studies, 131(3), 525–557.CrossRefGoogle Scholar
  100. 100.
    White, R. (2010). Evidential symmetry and mushy credence. In T.S. Gendler, , & J. Hawthorne (Eds.), Oxford studies in epistemology (Vol. 3, pp. 161–186). Oxford University Press.Google Scholar
  101. 101.
    Williamson, T. (2000). Knowledge and its limits. Oxford University Press.Google Scholar
  102. 102.
    Williamson, T. (2007). How probable is an infinite sequence of heads. Analysis, 67(3), 173–80.CrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.Department of PhilosophyUniversity of TorontoTorontoCanada

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