Minds and Machines

, Volume 27, Issue 1, pp 167–197 | Cite as

Stability and Scepticism in the Modelling of Doxastic States: Probabilities and Plain Beliefs

  • Hans RottEmail author


There are two prominent ways of formally modelling human belief. One is in terms of plain beliefs (yes-or-no beliefs, beliefs simpliciter), i.e., sets of propositions. The second one is in terms of degrees of beliefs, which are commonly taken to be representable by subjective probability functions. In relating these two ways of modelling human belief, the most natural idea is a thesis frequently attributed to John Locke: a proposition is or ought to be believed (accepted) just in case its subjective probability exceeds a contextually fixed probability threshold \(t<1\). This idea is known to have two serious drawbacks: first, it denies that beliefs are closed under conjunction, and second, it may easily lead to sets of beliefs that are logically inconsistent. In this paper I present two recent accounts of aligning plain belief with subjective probability: the Stability Theory of Leitgeb (Ann Pure Appl Log 164(12):1338–1389, 2013; Philos Rev 123(2):131–171, 2014; Proc Aristot Soc Suppl Vol 89(1):143–185, 2015a; The stability of belief: an essay on rationality and coherence. Oxford University Press, Oxford, 2015b) and the Probalogical Theory (or Tracking Theory) of Lin and Kelly (Synthese 186(2):531–575, 2012a; J Philos Log 41(6):957–981, 2012b). I argue that Leitgeb’s theory may be too sceptical for the purposes of real life.


Plain belief Subjective probability Formal epistemology Lockean thesis Stability Theory of belief Leitgeb Lin Kelly 



I am grateful to audiences in Etelsen, Regensburg, Patras, Uppsala and Maastricht, to John Cantwell, Paul Égré, Tim Kraft, an anonymous referee of this journal, and most of all to Hannes Leitgeb for valuable discussions of various versions of this paper. I have checked the correctness of my calculations for the space of four possibilities (Sect. 5) by determining the values for particular thresholds in numerous special cases. In doing this, I have made extensive use of the websites and I am grateful to the people running these sites.


  1. Benferhat, S., Dubois, D., & Prade, H. (1997). Possibilistic and standard probabilistic semantics of conditional knowledge. Journal of Logic and Computation, 9(6), 873–895.MathSciNetCrossRefzbMATHGoogle Scholar
  2. Cohen, L. J. (1992). An essay on belief and acceptance. Oxford: Clarendon Press.Google Scholar
  3. Easwaran, K. (2016). Dr. Truthlove or: How I learned to stop worrying and love Bayesian probabilities. Noûs, 50(4), 816–853.MathSciNetCrossRefzbMATHGoogle Scholar
  4. Leitgeb, H. (2013). Reducing belief simpliciter to degrees of belief. Annals of Pure and Applied Logic, 164(12), 1338–1389.MathSciNetCrossRefzbMATHGoogle Scholar
  5. Leitgeb, H. (2014). The stability theory of belief. Philosophical Review, 123(2), 131–171.CrossRefGoogle Scholar
  6. Leitgeb, H. (2015a). The Humean thesis on belief. Proceedings of the Aristotelian Society, Supplementary Volume, 89(1), 143–185.CrossRefGoogle Scholar
  7. Leitgeb, H. (2015b). The stability of belief: An essay on rationality and coherence. Oxford: Oxford University Press. (Draft of 3 March 2015, retrieved from Scholar
  8. Levi, I. (1996). For the sake of argument: Ramsey test conditionals, inductive inference, and nonmonotonic reasoning. Cambridge: Cambridge University Press.CrossRefzbMATHGoogle Scholar
  9. Lin, H., & Kelly, K. T. (2012a). A geo-logical solution to the lottery paradox, with applications to conditional logic. Synthese, 186(2), 531–575.MathSciNetCrossRefzbMATHGoogle Scholar
  10. Lin, H., & Kelly, K. T. (2012b). Propositional reasoning that tracks probabilistic reasoning. Journal of Philosophical Logic, 41(6), 957–981.MathSciNetCrossRefzbMATHGoogle Scholar
  11. Makinson, D. (2015). The scarcity of stable belief sets. Last revised 22 February 2015, scheduled for a volume on the stability theory of beliefs, retrieved from
  12. Ross, J., & Schroeder, M. (2014). Belief, credence and pragmatic encroachment. Philosophy and Phenomenological Research, 88(2), 259–288.CrossRefGoogle Scholar
  13. Rott, H. (2009). Degrees all the way down: Beliefs, non-beliefs and disbeliefs. In F. Huber & C. Schmidt-Petri (Eds.), Degrees of belief (pp. 301–339). Dordrecht: Springer.CrossRefGoogle Scholar
  14. Rott, H. (2016). Unstable knowledge, unstable belief. Unpublished manuscript, August 2016.Google Scholar

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© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.Department of PhilosophyUniversity of RegensburgRegensburgGermany

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