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A Structural Justification of Probabilism: From Partition Invariance to Subjective Probability

Published online by Cambridge University Press:  01 January 2022

Hannes Leitgeb
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Abstract

A new justification of probabilism is developed that pays close attention to the structure of the underlying space of possibilities. Its central assumption is that rational numerical degrees of belief ought to be partition invariant. By means of a representation theorem, one can prove that if graded belief satisfies the resulting set of postulates, rational degrees of belief may be identified with probabilities.

Type
Research Article
Information
Philosophy of Science , Volume 88 , Issue 2 , April 2021 , pp. 341 - 365
Copyright
Copyright © The Philosophy of Science Association

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References

Carnap, Rudolf. 1967. The Logical Structure of the World. Berkeley: University of California Press.Google Scholar
Cox, Richard T. 1946. “Probability, Frequency and Reasonable Expectation.” American Journal of Physics 14:1–13.CrossRefGoogle Scholar
Cox, Richard T. 1961. The Algebra of Probable Inference. Baltimore: Johns Hopkins University Press.Google Scholar
Groenendijk, Jeroen, and Stokhof, Martin. 1984. “Studies on the Semantics of Questions and the Pragmatics of Answers.” Joint PhD diss., University of Amsterdam.Google Scholar
Hájek, Alan. 2008a. “Arguments For- or Against-Probabilism?” British Journal for the Philosophy of Science 59:793–819.CrossRefGoogle Scholar
Hájek, Alan. 2008b. “Dutch Book Arguments.” In The Oxford Handbook of Rational and Social Choice, ed. Anand, P., Pattanaik, P., and Puppe, C., 173–95. Oxford: Oxford University Press.Google Scholar
Halpern, Joseph Y. 2003. Reasoning about Uncertainty. Cambridge, MA: MIT Press.Google Scholar
Howson, Colin. 2008. “De Finetti, Countable Additivity, Consistency and Coherence.” British Journal for the Philosophy of Science 59:1–23.CrossRefGoogle Scholar
Huttegger, Simon M. 2017. The Probabilistic Foundations of Rational Learning. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Jeffrey, Richard. 1983. The Logic of Decision. 2nd ed. Chicago: University of Chicago Press.Google Scholar
Jeffrey, Richard. 1992. “Probability and the Art of Judgment.” In Probability and the Art of Judgment, 44–76. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Joyce, James M. 1998. “A Nonpragmatic Vindication of Probabilism.” Philosophy of Science 65:575–603.CrossRefGoogle Scholar
Joyce, James M. 1999. The Foundations of Causal Decision Theory. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Krantz, David H., Luce, R. Duncan, Suppes, Patrick, and Tversky, Amos. 1971. Foundations of Measurement. Vol. 1, Additive and Polynomial Representations. Mineola, NY: Dover.Google Scholar
Leitgeb, Hannes. 2014. “The Stability Theory of Belief.” Philosophical Review 123:131–71.CrossRefGoogle Scholar
Leitgeb, Hannes. 2017. The Stability of Belief: How Rational Belief Coheres with Probability. Oxford: Oxford University Press.CrossRefGoogle Scholar
Lewis, David. 1988. “Statements Partly about Observation.” In Papers in Philosophical Logic, 125–55. Cambridge: Cambridge University Press.Google Scholar
Lin, Hanti, and Kelly, Kevin T.. 2012a. “A Geo-Logical Solution to the Lottery Paradox.” Synthese 186:531–75.CrossRefGoogle Scholar
Lin, Hanti, and Kelly, Kevin T.. 2012b. “Propositional Reasoning That Tracks Probabilistic Reasoning.” Journal of Philosophical Logic 41:957–81.CrossRefGoogle Scholar
Narens, Louis. 2007. Theories of Probability: An Examination of Logical and Qualitative Foundations. Hackensack, NJ: World Scientific.CrossRefGoogle Scholar
Paris, Jeffrey B. 1994. The Uncertain Reasoner’s Companion: A Mathematical Perspective. Cambridge: Cambridge University Press.Google Scholar
Pettigrew, Richard. 2016. Accuracy and the Laws of Credence. Oxford: Oxford University Press.CrossRefGoogle Scholar
Schurz, Gerhard. 2019. “Impossibility Results for Rational Belief.” Noûs 53 (10):134–59.CrossRefGoogle Scholar
Skyrms, Brian. 1977. “Resiliency, Propensities, and Causal Necessity.” Journal of Philosophy 74 (11): 704–13.CrossRefGoogle Scholar
Skyrms, Brian. 1980. Causal Necessity: A Pragmatic Investigation of the Necessity of Laws. New Haven, CT: Yale University Press.Google Scholar
Skyrms, Brian, Bell, Gary D., and Woodruff, Peter. 1999. “Theories of Counter-Factual and Subjunctive Conditionals in Contexts of Strategic Interaction.” Research in Economics 53:275–91.CrossRefGoogle Scholar
Suppes, Patrick. 2002. Representation and Invariance of Scientific Structures. Stanford, CA: CSLI.Google Scholar
Suppes, Patrick. 2016. “Qualitative Axioms of Uncertainty as a Foundation for Probability and Decision-Making.” Minds and Machines 26:185–202.CrossRefGoogle Scholar
Windschitl, Paul D., and Wells, Gary L.. 1998. “The Alternative-Outcomes Effect.” Journal of Personality and Social Psychology 75 (6): 1411–23.CrossRefGoogle Scholar
Yalcin, Seth. 2018. “Belief as Question-Sensitive.” Philosophy and Phenomenological Research 97 (1): 23–47.CrossRefGoogle Scholar
Zynda, Lyle. 2000. “Representation Theorems and Realism about Degrees of Belief.” Philosophy of Science 67:45–69.CrossRefGoogle Scholar