Two-state solution to the lottery paradox

  • Artūrs LoginsEmail author


This paper elaborates a new solution to the lottery paradox, according to which the paradox arises only when we lump together two distinct states of being confident that p under one general label of ‘belief that p’. The two-state conjecture is defended on the basis of some recent work on gradable adjectives. The conjecture is supported by independent considerations from the impossibility of constructing the lottery paradox both for risk-tolerating states such as being afraid, hoping or hypothesizing, and for risk-averse, certainty-like states. The new proposal is compared to views within the increasingly popular debate opposing dualists to reductionists with respect to the relation between belief and degrees of belief.


The lottery paradox Epistemic justification Closure Emotions Justified belief Confidence Gradable adjectives Paradox Lockean thesis Belief Knowledge Certainty Risky states Absolute adjectives Credences Dualism about belief Reductionism about belief 



Many thanks to Richard Dub, Jeremy Goodman, John Hawthorne, Benjamin Kiesewetter, Thomas Kroedel, Tristram Oliver-Skuse, Edgar Phillips, Travis Timmerman, Alexis Wellwood, audiences at University of Geneva, University of Fribourg, SOPHA 2018 congress, and two anonymous referees for this journal for discussion and comments on earlier version of this paper. The research work that led to this article was supported by the Swiss National Science Foundation Grants Number 171464 and 169293.


  1. Bartsch, R., & Vennemann, T. (1972). Semantic structures: A study in the relation between semantics and syntax. Frankfurt am Main: Athenaum.Google Scholar
  2. Buchak, L. (2014). Belief, credence, and norms. Philosophical Studies, 169(2), 1–27.CrossRefGoogle Scholar
  3. Cariani, F., Santorio, P., & Wellwood, A. (2017). Comparative confidence. Unpublished Manuscript, ms.Google Scholar
  4. Christensen, D. (2004). Putting logic in its place: Formal constraints on rational belief. Oxford: Oxford University Press.CrossRefGoogle Scholar
  5. Clarke, R. (2013). Belief is credence one (in context). Philosophers’ Imprint, 13, 1–18.Google Scholar
  6. Clarke, R. (2017). Contextualism about belief ascriptions. In J. J. Ichikawa (Ed.), Routledge handbook of epistemic contextualism (pp. 400–410). London: Routledge.CrossRefGoogle Scholar
  7. Cohen, S. (1998). Contextualist solutions to epistemological problems: Scepticism, gettier, and the lottery. Australasian Journal of Philosophy, 76(2), 289–306.CrossRefGoogle Scholar
  8. Cresswell, M. J. (1976). The semantics of degree. In B. H. Partee (Ed.), Montague grammar (pp. 261–292). New York: Academic Press.CrossRefGoogle Scholar
  9. de Sousa, R. B. (2002). Emotional truth. Proceedings of the Aristotelian Society, 76(76), 247–63.CrossRefGoogle Scholar
  10. Deonna, J. A., & Teroni, F. (2012). The emotions: A philosophical introduction. London: Routledge.CrossRefGoogle Scholar
  11. Dietz, C. (2018). Reasons and factive emotions. Philosophical Studies, 175(7), 1681–1691.CrossRefGoogle Scholar
  12. Dorst, K. (2017). Lockeans maximize expected accuracy. Mind, 128, 175–211.CrossRefGoogle Scholar
  13. Douven, I., & Williamson, T. (2006). Generalizing the lottery paradox. British Journal for the Philosophy of Science, 57(4), 755–779.CrossRefGoogle Scholar
  14. Echeverri, S. (2019). Emotional justification. Philosophy and Phenomenological Research, 98, 541–566.CrossRefGoogle Scholar
  15. Engel, P. (2012). Trust and the doxastic family. Philosophical Studies, 161(1), 17–26.CrossRefGoogle Scholar
  16. Easwaran, K. (2016). Dr. Truthlove or: How i learned to stop worrying and love bayesian probabilities*. Noûs, 50(4), 816–853.CrossRefGoogle Scholar
  17. Foley, R. (1979). Justified inconsistent beliefs. American Philosophical Quarterly, 16(4), 247–257.Google Scholar
  18. Foley, R. (2009). Beliefs, degrees of belief, and the lockean thesis. In F. Huber & C. Schmidt-Petri (Eds.), Degrees of belief (pp. 37–47). Dordrecht: Springer.CrossRefGoogle Scholar
  19. Gao, J. (2019). Credal pragmatism. Philosophical Studies, 176, 1595–1617.CrossRefGoogle Scholar
  20. Gordon, R. M. (1987). The structure of emotions: Investigations in cognitive philosophy. Cambridge: Cambridge University Press.Google Scholar
  21. Greco, D. (2015). How I learned to stop worrying and love probability 1. Philosophical Perspectives, 29(1), 179–201.CrossRefGoogle Scholar
  22. Harman, G. (1986). Change in view. Cambridge: MIT Press.Google Scholar
  23. Hawthorne, J. (2003). Knowledge and lotteries. Oxford: Oxford University Press.CrossRefGoogle Scholar
  24. Hawthorne, J., Rothschild, D., & Spectre, L. (2016). Belief is weak. Philosophical Studies, 173(5), 1393–1404.CrossRefGoogle Scholar
  25. Heim, I. (1985). Notes on comparatives and related matters. Austin: University of Texas. Unpublished manuscript.Google Scholar
  26. Holton, R. (2008). Partial belief, partial intention. Mind, 117(465), 27–58.CrossRefGoogle Scholar
  27. Holton, R. (2014). Intention as a model for belief. In M. Vargas & G. Yaffe (Eds.), Rational and social agency: essays on the philosophy of Michael Bratman. Oxford University Press.Google Scholar
  28. Howthorne, J., & Logins, A. Graded epistemic justification. Unpublished Manuscript, ms.Google Scholar
  29. Jackson, E. G. (2019). Belief and credence: why the attitude-type matters. Philosophical Studies, 176(9), 2477–2496.CrossRefGoogle Scholar
  30. Jeffrey, R. (1970). Dracula meets wolfman: Acceptance vs. partial belief. In M. Swain (Ed.), Induction, acceptance, and rational belief (pp. 157–185). D. Reidel.Google Scholar
  31. Kennedy, C. (1999). Projecting the adjective: The syntax and semantics of gradability and comparison. New York: Garland.Google Scholar
  32. Kennedy, C. (2007). Vagueness and grammar: The semantics of relative and absolute gradable adjectives. Linguistics and Philosophy, 30(1), 1–45.CrossRefGoogle Scholar
  33. Kennedy, C., & McNally, L. (2005). Scale structure, degree modification, and the semantics of gradable predicates. Language, 81, 345–381.CrossRefGoogle Scholar
  34. Klein, P. (1985). The virtues of inconsistency. The Monist, 68(1), 105–135.CrossRefGoogle Scholar
  35. Kroedel, T. (2012). The lottery paradox, epistemic justification and permissibility. Analysis, 72(1), 57–60.CrossRefGoogle Scholar
  36. Kyburg, H. E. (1961). Probability and the logic of rational belief. Middletown, CT: Wesleyan University Press.Google Scholar
  37. Leffel, T., & Xiang, M., Kennedy, C. (2017). Interpreting gradable adjectives in context: Domain distribution vs. scalar representation. Unpublished Manuscript.Google Scholar
  38. Leitgeb, H. (2013). Reducing belief simpliciter to degrees of belief. Annals of Pure and Applied Logic, 164(12), 1338–1389.CrossRefGoogle Scholar
  39. Leitgeb, H. (2014). The stability theory of belief. The Philosophical Review, 123(2), 131–171.CrossRefGoogle Scholar
  40. Leitgeb, H. (2017). The stability of belief. Oxford: Oxford University Press.CrossRefGoogle Scholar
  41. Lewis, D. (1996). Elusive knowledge. Australasian Journal of Philosophy, 74(4), 549–567.CrossRefGoogle Scholar
  42. Littlejohn, C. (2013). Don’t know, don’t believe: Reply to Kroedel. Logos and Episteme, 4(2), 231–238.CrossRefGoogle Scholar
  43. Makinson, D. C. (1965). The paradox of the preface. Analysis, 25(6), 205–207.CrossRefGoogle Scholar
  44. Nelkin, D. K. (2000). The lottery paradox, knowledge, and rationality. The Philosophical Review, 109, 373–408.CrossRefGoogle Scholar
  45. Ross, J., & Schroeder, M. (2014). Belief, credence, and pragmatic encroachment. Philosophy and Phenomenological Research, 88(2), 259–288.CrossRefGoogle Scholar
  46. Rotstein, C., & Winter, Y. (2004). Total adjectives vs. partial adjectives: Scale structure and higher-order modifiers. Natural Language Semantics, 12, 259–288.CrossRefGoogle Scholar
  47. Sturgeon, S. (2008). Reason and the grain of belief. Nous, 42(1), 139–165.CrossRefGoogle Scholar
  48. Smith, M. (2010). What else justification could be. Nous, 44(1), 10–31.CrossRefGoogle Scholar
  49. Smith, M. (2016). Between probability and certainty. Oxford: Oxford University Press.CrossRefGoogle Scholar
  50. Sorensen, R. (2017). Epistemic paradoxes. In E. N. Zalta (Ed.), The Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University, fall 2017 edition.Google Scholar
  51. Staffel, J. (2016). Beliefs, buses and lotteries: Why rational belief can’t be stably high credence. Philosophical Studies, 173(7), 1721–1734.CrossRefGoogle Scholar
  52. Timmerman, T. (2013). The persistent problem of the lottery paradox: And its unwelcome consequences for contextualism. Logos & Episteme, 4(1), 85–100.CrossRefGoogle Scholar
  53. Unger, P. (1975). Ignorance. Oxford: Oxford University Press.Google Scholar
  54. Weatherson, B. J. (2016). Games, beliefs and credences. Philosophy and Phenomenological Research, 92(2), 209–236.CrossRefGoogle Scholar
  55. Weisberg, J. (2016). Belief in psyontology. Philosopher’s imprint, forthcoming.Google Scholar
  56. Williamson, T. (2000). Knowledge and its limits. Oxford: Oxford University Press.Google Scholar
  57. Williamson, T. (2017). Ambiguous rationality. Episteme, 14(3), 263–274.CrossRefGoogle Scholar
  58. Williamson, T. (forthcoming). Justifications, excuses, and sceptical scenarios. In F. Dorsch & J. Dutant (Eds.), The new evil demon. Oxford: Oxford University Press.Google Scholar
  59. Williamson, T. (forthcoming, ms). Knowledge, credence, and strength of belief. In A. Flowerree, & B. Reed (Eds.), The epistemic.Google Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of Philosophy and Swiss Center for Affective SciencesUniversity of GenevaGenevaSwitzerland

Personalised recommendations