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AXIOMS FOR TYPE-FREE SUBJECTIVE PROBABILITY

Part of: Foundations of probability theory Philosophical aspects of logic and foundations

Published online by Cambridge University Press:  27 February 2023

CEZARY CIEŚLIŃSKI ,
LEON HORSTEN Open the ORCID record for LEON HORSTEN [Opens in a new window]  and
HANNES LEITGEB
CEZARY CIEŚLIŃSKI
Affiliation:
FACULTY OF PHILOSOPHY UNIVERSITY OF WARSAW WARSAW, POLAND E-mail: [email protected]
LEON HORSTEN
Affiliation:
FACHBEREICH PHILOSOPHIE UNIVERSITÄT KONSTANZ UNIVERSITAETSSTRASSE 10 78464 KONSTANZ, GERMANY E-mail: [email protected]
HANNES LEITGEB
Affiliation:
FAKULTÄT FÜR PHILOSOPHIE WISSENSCHAFTSTHEORIE UND RELIGIONSWISSENSCHAFT LUDWIG-MAXIMILIANS-UNIVERSITÄT MÜNCHEN D-80539 MUNICH, GERMANY E-mail: [email protected]
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Abstract

We formulate and explore two basic axiomatic systems of type-free subjective probability. One of them explicates a notion of finitely additive probability. The other explicates a concept of infinitely additive probability. It is argued that the first of these systems is a suitable background theory for formally investigating controversial principles about type-free subjective probability.

Keywords

probabilityself-reference

MSC classification

Primary: 03A05: Philosophical and critical 60A05: Axioms; other general questions
Type
Research Article
Information
The Review of Symbolic Logic , Volume 17 , Issue 2 , June 2024 , pp. 493 - 508
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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References

BIBLIOGRAPHY

Benci, V., Horsten, L., & Wenmackers, S. (2018). Infinitesimal probabilities. British Journal for the Philosophy of Science, 69, 509–552.CrossRefGoogle ScholarPubMed
Campbell-Moore, C. (2016). Self-Referential Probability. Ph.D. Thesis, Ludwig-Maximilans-Universität München.Google Scholar
Campbell-Moore, C., Horsten, L., & Leitgeb, H. (2019). Probability for the revision theory of truth. Journal of Philosophical Logic, 48, 87–112.CrossRefGoogle Scholar
Christensen, D. (2007). Epistemic self-respect. Proceedings of the Aristotelian Society, 107, 319–337.CrossRefGoogle Scholar
Christiano, P., Yudkowski, E., Herreshof, M., & Barasz, M. (2014). Definability in probabilistic logic. Unpublished manuscript.Google Scholar
Cieśliński, C. (2017). The Epistemic Lightness of Truth: Deflationism and its Logic. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Cieśliński, C. Believability Theories: Corrigendum to the Epistemic Lightness of Truth. Deflationism and its Logic. Unpublished manuscript. Available from: http://cieslinski.filozofia.uw.edu.pl/Corrigendum.pdf.Google Scholar
de Finetti, B. (1972). Probability Induction and Statistics. London: Wiley.Google Scholar
De Howson, C. (2008). Finetti, countable additivity, consistency and coherence. British Journal for Philosophy of Science, 59, 1–23.CrossRefGoogle Scholar
Friedman, H., & Sheard, M. (1987). Axiomatic theories of self-referential truth. Annals of Pure and Applied Logic, 33, 1–21.CrossRefGoogle Scholar
Fujimoto, K. (2012). Classes and truths in set theory. Annals of Pure and Applied Logic, 163, 1484–1523.CrossRefGoogle Scholar
Hajek, A. Staying regular? Unpublished manuscript.Google Scholar
Halbach, V. (1994). A system of complete and consistent truth. Notre Dame Journal of Formal Logic, 35, 311–327.CrossRefGoogle Scholar
Halbach, V. (2014). Axiomatic Theories of Truth (second edition). Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Kaplan, D., & Montague, R. (1960). A paradox regained. Notre Dame Journal of Formal Logic, 1, 79–90.CrossRefGoogle Scholar
Kolmogorov, A. (1933). Grundbegriffe der Wahrscheinlichkeitsrechnung. Ergebnisse der Mathematik. Translated by N. Morrison, Foundations of the Theory of Probability. New York: Chelsea Publishing Company, 1956 (second edition).CrossRefGoogle Scholar
Leitgeb, H. (2008). On the probabilistic convention T. Review of Symbolic Logic, 1, 218–224.CrossRefGoogle Scholar
Leitgeb, H. (2012). From type-free truth to type-free probability. In Restall, G. and Russell, G., editors. New Waves in Philosophical Logic. London: Palgrave Macmillan, pp. 84–94.CrossRefGoogle Scholar
Leitgeb, H. (2014). Probabilistic theories of type-free truth and probability. Talk given at the Conference in Honour of the 60th Birthday of Philip Welch. University of Bristol, March 22nd 2014.Google Scholar
Leitgeb, H., & Schurz, G. (2008). Finitistic and frequentistic approximation of probability measures with or without $\sigma$ -additivity. Studia Logica, 85, 257–283 Google Scholar
Schuster, D., & Horsten, L. (2022). On the pure logic of justified belief. Synthese, 200, https://doi.org/10.1007/s11229-022-03905-6.CrossRefGoogle Scholar
Sheard, M. (2001). Weak and strong theories of truth. Studia Logica, 68, 89–101.CrossRefGoogle Scholar
van Fraassen, B. (1984). Belief and the will. Journal of Philosophy, 81, 235–256.CrossRefGoogle Scholar
van Fraassen, B. (1995). Belief and the problem of Ulysses and the sirens. Philosophical Studies, 77, 7–37.CrossRefGoogle Scholar
Weisberg, J. (2007). Conditionalisation, reflection, and self-knowledge. Philosophical Studies, 135, 179–197.CrossRefGoogle Scholar
Williamson, T. (2000). Knowledge and its Limits. Oxford: Oxford University Press.Google Scholar
Zhou, C. (2014). Probability logic for Harsanyi type spaces. Logical Methods in Computer Science, 10, 1–23.Google Scholar