Belief, probability and lottery

An introduction to formal epistemology of belief

Authors

DOI:

https://doi.org/10.47456/sofia.v15i1.52545

Keywords:

epistemology, belief, rationality, bayesianism, probability

Abstract

The aim of this article is to present how the notions of belief and subjective probability appear in the contemporary epistemological debate on rationality. The main way of analyzing this relationship is through what we call a “bridge principle”: a formal principle capable of connecting the rationality of belief with the rationality of subjective probability. The central challenge in constructing a bridge principle lies in the difficulty of linking qualitative and quantitative models without generating a paradox, such as the well-known Lottery Paradox. We present here some possible alternatives to this paradoxical situation, as well as a proposal for a bridge principle that takes the concept of belief to be context-dependent: the Humean theory of belief.

Downloads

Download data is not yet available.

Author Biography

  • Matheus de Lima Rui, Universidade Federal de Santa Catarina

    Atualmente realiza estágio de pós-doutorado no Programa de Pós-Graduação em Filosofia na Universidade Federal de Santa Catarina. Foi professor substituto na área de Lógica e Epistemologia do departamento de Filosofia na Universidade Federal de Santa Catarina (UFSC), entre 2024 e 2025. Doutor em Filosofia pela Universidade Federal de Santa Catarina (UFSC). Mestre em Filosofia pela Universidade Federal de Pelotas (UFPel). Tem experiência na área de Filosofia, com ênfase em Epistemologia Formal, Bayesianismo, Lógica, Teoria da Ação e da Escolha Racional. Bolsista CAPES, sob orientação do prof. Dr. Alexandre Meyer Luz, e coorientação do prof. Dr. Jonas Becker Arenhart. Foi membro de corpo editorial do periódico Seara Filosófica (UFPel).

References

ALCHOURRÓN, C.; GÄRDENFORS, P.; MAKINSON, D. On the logic of theory change: Partial meet contraction and revision functions. In: Journal of Symbolic Logic, v. 50, p. 510–530, 1985.

BROOME, J. Rationality Through Reasoning. Oxford: Wiley-Blackwell, 2013.

EASWARAN, K. How I learned to stop worrying and love Bayesian probabilities. In: Nous, v. 50, p. 01–38, 2015.

FOLEY, R. The Epistemology of Belief and the Epistemology of Degrees of Belief. In: American Philosophical Quaterly. v. 29, p. 111–121, 1992/2009.

FRANKISH, K. Partial belief and flat-out belief. In: HUBER, F.; SCHMIDT-PETRI, C. (Org.). Degrees of belief: An anthology. Oxford: Oxford University Press, 2009. p. 75-93.

GRECO, D. How I Learned to Stop Worrying and Love Probability 1. In: Philosophical Perspectives, v. 29, p. 179 - 201, 2015.

HÁJEK, A. Is Strict Coherence Coherent?. In: Dialectica, v. 66, n. 3, p. 411-424, 2012.

HARMAN, G. Change in View. Cambridge: MIT Press, 1986.

HINTIKKA, J. Knowledge and Belief: An Introduction to the Logic of the Two Notions. Ithaca, NY: Cornell University Press, 1961.

JACKSON, E. Belief and credence: Why the attitude-type matters. In: Philosophical Studies, v. 176, n. 9, p. 2477-2496, 2019.

JEFFREY, R. The Logic of Decision. 1. ed. New York: McGrawHill, 1965.

JEFFREY, R. Dracula Meets Wolfman: Acceptance vs. Partial Belief. In: SWAIN, M. (Org.). Induction, Acceptance, and Rational Belief. Dordrecht: Reidel, 1970. p. 157–185.

KYBURG, H. Probability and the logic of rational belief. Middletown: Wesleyan University Press, 1961.

KOLMOGOROV, A. Foundations of the Theory of Probability, 2 ed. New York: Chelsea Publishing Company, 1956.

KOLODNY, N. Why be rational?. In: Mind, v. 114, n. 455, p. 509-563, 2005.

LEITGEB, H. The Review Paradox: On The Diachronic Costs of Not Closing Rational Belief Under Conjunction. In: NOUS, v.48, n. 4, p. 781–793, 2014a.

LEITGEB, H. The Stability Theory of Belief. In: Philosophical Review, v. 123, n. 02, p. 131-71, 2014b.

LEITGEB, H. The Humean Thesis on Belief. In: Aristotelian society, v. 89, n. 1, p. 143–185, 2015.

LEITGEB, H. The Stability of Belief: How Rational Belief Coheres with Probability. New York: Oxford University Press, 2017.

LEVI, I. Acceptance revisited. In: BOGDAN, R. (Org.) Local Induction. Dordrecht: Springer, 1976, p. 01-71.

LIN, H; KELLY, K. Propositional Reasoning that Tracks Probabilistic Reasoning. In: J Philos Logic, v. 41, p. 957–981, 2012.

LYON, A. Philosophy of Probability. In: ALLHOFF, Fritz (Org), Philosophies of the Sciences: A Guide. Malden, MA: Wiley-Blackwell, 2010. p. 92-125.

PARIKH, R. Sentences, Belief and Logical Omniscience, or What Does Deduction Tell Us?. In: ARLÓ-COSTA, H.; HENDRICKS, V.; VAN BENTHEM, J. (Org.). Readings in Formal Epistemology. New York: Springer, 2016, p. 627-647.

PETTIGREW, R. II—Pluralism About Belief States. In: Aristotelian Society, Supplementary Volume, p. 187-204, 2015.

RAMSEY, F. Truth and probability (1926). In: ARLÓ-COSTA, H.; HENDRICKS, V.; VAN BENTHEM, J. (Org.). Readings in Formal Epistemology. New York: Springer, 2016, p. 21-45.

ROOT, H. Stability and Scepticism in the Modelling of Doxastic States: Probabilities and Plain Beliefs. In: Minds & Machines, v. 27, p. 167–197, 2017.

SAVAGE, L. The foundations of statistics, 2ª ed. New York: Dover Publications, 1972.

SHAFER, G. Perspectives on the theory and practice of belief functions. In: International Journal of Approximate Reasoning, v. 4, n. 5-6, p. 323-362, 1990.

STAFFEL, J. Beliefs, Buses and Lotteries. In: Philosophical Studies, v. 173, n. 7, p. 1721 -1734, 2016.

TITELBAUM, M. Quitting certainties: A Bayesian Framework Modeling Degrees of Belief. Oxford University Press, 2013.

VAN FRAASSEN, Bas C. Fine-grained opinion, probability, and the logic of full belief. In: Journal of Philosophical logic, v. 24, n. 4, p. 349-377, 1995.

YAP, A. Idealization, Epistemic Logic, and Epistemology. In: Synthese, v. 191, n. 14, p. 3351-3366, 2014.

Published

2026-10-27

How to Cite

RUI, M. DE L. Belief, probability and lottery: An introduction to formal epistemology of belief. Sofia, v. 15, n. 2, p. e15252545, 27 Oct.2026.