Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-27T19:55:32.576Z Has data issue: false hasContentIssue false
  • English
  • Français

Bayesian Orgulity

Published online by Cambridge University Press:  01 January 2022

Gordon Belot
Get access Rights & Permissions [Opens in a new window]

Abstract

A piece of folklore enjoys some currency among philosophical Bayesians, according to which Bayesian agents who, intuitively speaking, spread their credence over the entire space of available hypotheses are certain to converge to the truth. The goals of the current discussion are to show that that kernel of truth in this folklore is in some ways fairly small and to argue that Bayesian convergence-to-the-truth results are a liability for Bayesianism as an account of rationality since they render a certain sort of arrogance rationally mandatory.

Type
Research Article
Information
Philosophy of Science , Volume 80 , Issue 4 , October 2013 , pp. 483 - 503
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

†

For helpful conversations and suggestions, thanks to Bob Geroch, Alistair Isaac, Jim Joyce, Sarah Moss, Laura Ruetsche, and two anonymous referees. This article owes a great deal to the approaches of Earman (1992, chap. 9) and Kelly (1996, chap. 13). For all those readers out there who are fans of both Stefan Banach and Sir Thomas Malory, n. 13 is for you.

References

Belot, Gordon. 2013. “Failure of Calibration Is Typical.” Statistics and Probability Letters 83:2316–18.CrossRefGoogle Scholar
Billingsley, Patrick. 1999. Convergence of Probability Measures. 2nd ed. New York: Wiley.CrossRefGoogle Scholar
Dawid, Philip. 1982. “The Well-Calibrated Bayesian.” Journal of the American Statistical Association 77:605–10.Google Scholar
Dawid, Philip 1985. “Calibration-Based Empirical Probability.” Annals of Statistics 13:1251–73.Google Scholar
Diaconis, Persi, and Freedman, David. 1986. “On the Consistency of Bayes Estimates.” Annals of Statistics 14:1–67.Google Scholar
Dieudonné, Jean. 1960. Foundations of Modern Analysis. New York: Academic Press.Google Scholar
Dubins, Lester, and Freedman, David. 1964. “Measurable Sets of Measures.” Pacific Journal of Mathematics 14:1211–22.CrossRefGoogle Scholar
Dudley, R. M. 1964. “On Sequential Convergence.” Transactions of the American Mathematical Society 112:483–507.CrossRefGoogle Scholar
Earman, John. 1992. Bayes or Bust? A Critical Examination of Bayesian Confirmation Theory. Cambridge, MA: MIT Press.Google Scholar
Edwards, Ward, Lindman, Harold, and Savage, Leonard J.. 1963. “Bayesian Statistical Inference for Psychological Research.” Psychological Review 70:193–242.CrossRefGoogle Scholar
Freedman, David. 1963. “On the Asymptotic Behavior of Bayes’ Estimates in the Discrete Case.” Annals of Mathematical Statistics 34:1386–1403.CrossRefGoogle Scholar
Freedman, David 1965. “On the Asymptotic Behavior of Bayes’ Estimates in the Discrete Case.” Pt. 2. Annals of Mathematical Statistics 36:454–56.CrossRefGoogle Scholar
Gelbaum, Bernard, and Olmsted, John. 2003. Counterexamples in Analysis. New York: Dover.Google Scholar
Ghosh, J. K., and Ramamoorthi, R. V.. 2003. Bayesian Nonparametrics. New York: Springer.Google Scholar
Glymour, Clark. 1980. Theory and Evidence. Princeton, NJ: Princeton University Press.Google Scholar
Howson, Colin. 2000. Hume’s Problem: Induction and the Justification of Belief. Oxford: Oxford University Press.CrossRefGoogle Scholar
Howson, Colin, and Urbach, Peter. 1989. Scientific Reasoning: The Bayesian Approach. 1st ed. LaSalle, IL: Open Court.Google Scholar
Howson, Colin, and Urbach, Peter 2006. Scientific Reasoning: The Bayesian Approach. 3rd ed. LaSalle, IL: Open Court.Google Scholar
Kechris, Alexander. 1995. Classical Descriptive Set Theory. New York: Springer.CrossRefGoogle Scholar
Kelly, Kevin. 1996. The Logic of Reliable Inquiry. New York: Oxford University Press.Google Scholar
Kelly, Kevin, and Glymour, Clark. 1989. “Convergence to the Truth and Nothing but the Truth.” Philosophy of Science 56:185–220.CrossRefGoogle Scholar
Kelly, Kevin, Schulte, Oliver, and Juhl, Cory. 1997. “Learning Theory and the Philosophy of Science.” Philosophy of Science 64:245–67.CrossRefGoogle Scholar
Koumoullis, George. 1996. “Baire Category in Spaces of Measures.” Advances in Mathematics 124:1–24.CrossRefGoogle Scholar
Oxtoby, John C. 1957. “The Banach-Mazur Game and the Banach Category Theorem.” In Contributions to the Theory of Games, Vol. 3, ed. Melvin Dresher, Albert Tucker, and Philip Wolfe, 159–63. Princeton, NJ: Princeton University Press.Google Scholar
Oxtoby, John C. 1980. Measure and Category: A Survey of the Analogies between Topological and Measure Spaces. 2nd ed. New York: Springer.CrossRefGoogle Scholar
Savage, Leonard J. 1954. The Foundations of Statistics. New York: Wiley.Google Scholar
Schervish, Mark J. 1995. Theory of Statistics. New York: Springer.CrossRefGoogle Scholar
Schervish, Mark J., and Seidenfeld, Teddy. 1990. “An Approach to Consensus and Certainty with Increasing Evidence.” Journal of Statistical Planning and Inference 25:401–14.CrossRefGoogle Scholar
Skyrms, Brian. 1991. “Carnapian Inductive Logic for Markov Chains.” Erkenntnis 35:469–60.Google Scholar
Skyrms, Brian 1993. “Carnapian Inductive Logic for a Value Continuum.” Midwest Studies in Philosophy 18:78–89.CrossRefGoogle Scholar
Sober, Elliott, and Steel, Michael. 2002. “Testing the Hypothesis of Common Ancestry.” Journal of Theoretical Biology 218:395–408.CrossRefGoogle ScholarPubMed
Steel, Michael, Székely, László, and Hendy, Michael. 1994. “Reconstructing Trees When Sequence Sites Evolve at Variable Rates.” Journal of Computational Biology 1:153–63.CrossRefGoogle ScholarPubMed
Wasserman, Larry. 1998. “Asymptotic Properties of Nonparametric Bayesian Procedures.” In Practical Nonparametric and Semiparametric Bayesian Statistics, ed. Dey, Dipak, Müller, Peter, and Sinha, Debajyoti, 293–304. New York: Springer.CrossRefGoogle Scholar