Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-12-02T23:41:51.792Z Has data issue: false hasContentIssue false
  • English
  • Français

Bayesian Convergence to the Truth and the Metaphysics of Possible Worlds

Published online by Cambridge University Press:  01 January 2022

Simon M. Huttegger
Get access Rights & Permissions [Opens in a new window]

Abstract

In a recent paper, Belot argues that Bayesians are epistemologically flawed because they believe with probability 1 that they will learn the truth about observational propositions in the limit. While Belot’s considerations suggest that this result should be interpreted with some care, the concerns he raises can largely be defused by putting convergence to the truth in the context of learning from an arbitrarily large but finite number of observations.

Type
Research Article
Information
Philosophy of Science , Volume 82 , Issue 4 , October 2015 , pp. 587 - 601
Copyright
Copyright © The Philosophy of Science Association

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

†

I would like to thank Jeff Barrett, Gordon Belot, Kenny Easwaran, Teddy Seidenfeld, and Kevin Zollman for helpful comments. I am especially grateful to Jim Joyce for providing a detailed written commentary. Special thanks also go to Brian Skyrms for a finite but very large number of discussions, extending back many years, on the nuances of convergence theorems in probability theory.

References

Ash, Robert B. 2000. Probability and Measure Theory. San Diego, CA: Academic Press.Google Scholar
Belot, Gordon. 2013. “Bayesian Orgulity.” Philosophy of Science 80:483–503.CrossRefGoogle Scholar
Blackwell, David, and Dubins, Lester. 1962. “Merging of Opinions with Increasing Information.” Annals of Mathematical Statistics 33:882–86.CrossRefGoogle Scholar
Carathéodory, Constantin. 1956. Mass und Integral und ihre Algebraisierung. Stuttgart: Birkäuser.CrossRefGoogle Scholar
Elga, Adam. 2015. “Bayesian Humility.” Unpublished manuscript, Princeton University.Google Scholar
Halmos, Paul R. 1944. “The Foundations of Probability.” American Mathematical Monthly 51:497–510.CrossRefGoogle Scholar
Joyce, James M. 2010. “The Development of Subjective Bayesianism.” In Handbook of the History of Logic, Vol. 10, Inductive Logic, ed. Gabbay, Dov M., Hartmann, Stephan, and Woods, John, 415–76. Amsterdam: Elsevier.Google Scholar
Kolmogorov, Andrey N. 1933. Grundbegriffe der Wahrscheinlichkeitsrechnung. Berlin: Springer.CrossRefGoogle Scholar
Kolmogorov, Andrey N. 1948. “Algèbres de Boole métriques complètes.” Zjazd Matematyków Polskich 20:21–30. Trans. Richard Jeffrey in Kolmogorov 1995.Google Scholar
Kolmogorov, Andrey N. 1995. “Complete Metric Boolean Algebras.” Philosophical Studies 77:57–66.CrossRefGoogle Scholar
Loomis, Lynn H. 1947. “On the Representation of a σ Complete Boolean Algebra.” Bulletin of the American Mathematical Society 53:757–60.CrossRefGoogle Scholar
Łoś, Jerzy. 1955. “On the Axiomatic Treatment of Probability.” Colloquium Mathematicum 3:125–37.CrossRefGoogle Scholar
Purves, Roger A., and Sudderth, William D.. 1976. “Some Finitely Additive Probability.” Annals of Probability 4:259–76.CrossRefGoogle Scholar
Schervish, Mark J., and Seidenfeld, Teddy. 1990. “An Approach to Consensus and Certainty with Increasing Information.” Journal of Statistical Planning and Inference 25:401–14.CrossRefGoogle Scholar
Sikorski, R. 1948. “On the Representations of Boolean Algebras as Fields of Sets.” Fundamenta Mathematica 35:247–56.Google Scholar
Sikorski, R. 1949. “The Integral in a Boolean Algebra.” Colloquium Mathematicum 2:20–26.CrossRefGoogle Scholar
Skyrms, Brian. 1993. “Logical Atoms and Combinatorial Possibility.” Journal of Philosophy 90:219–32.CrossRefGoogle Scholar
Skyrms, Brian 1995. “Strict Coherence, Sigma Coherence and the Metaphysics of Quantity.” Philosophical Studies 77:39–55.CrossRefGoogle Scholar
Stone, Marshall H. 1936. “The Theory of Representations for Boolean Algebras.” Transactions of the American Mathematical Society 40:37–111.Google Scholar
Zabell, Sandy L. 2002. “It All Adds Up: The Dynamic Coherence of Radical Probabilism.” Philosophy of Science 69:98–103.CrossRefGoogle Scholar