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An Objective Justification of Bayesianism II: The Consequences of Minimizing Inaccuracy

Published online by Cambridge University Press:  01 January 2022

Hannes Leitgeb  and
Richard Pettigrew
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Abstract

In this article and its prequel, we derive Bayesianism from the following norm: Accuracy—an agent ought to minimize the inaccuracy of her partial beliefs. In the prequel, we make the norm mathematically precise; in this article, we derive its consequences. We show that the two core tenets of Bayesianism follow from Accuracy, while the characteristic claim of Objective Bayesianism follows from Accuracy together with an extra assumption. Finally, we show that Jeffrey Conditionalization violates Accuracy unless Rigidity is assumed, and we describe the alternative updating rule that Accuracy mandates in the absence of Rigidity.

Type
Research Article
Information
Philosophy of Science , Volume 77 , Issue 2 , April 2010 , pp. 236 - 272
Copyright
Copyright © The Philosophy of Science Association

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Footnotes

‡

We would like to thank F. Arntzenius, L. Bayón, R. Bradley, F. Dietrich, K. Easwaran, D. Edgington, B. Fitelson (and his Berkeley reading group), A. Hájek, L. Horsten, F. Huber, J. Joyce, W. Myrvold, S. Okasha, G. Schurz, T. Seidenfeld, B. Skyrms, C. Wagner, R. Williams, J. Williamson, and B. van Fraassen for their comments on earlier versions of this article. Hannes Leitgeb would like to thank the Leverhulme Trust and the Alexander von Humboldt Foundation for their generous support of this work. Richard Pettigrew would like to thank the British Academy with whom he was a postdoctoral fellow during work on this article.

References

Berger, J. O. 1985. Statistical Decision Theory and Bayesian Analysis. New York: Springer.CrossRefGoogle Scholar
Bradley, R. 2005. “Radical Probabilism and Bayesian Conditioning.” Philosophy of Science 72:342–64.CrossRefGoogle Scholar
de Finetti, B. 1931. “Sul significato soggettivo della probabilita.” Fundamenta Mathematicae 17:298–329.CrossRefGoogle Scholar
Diaconis, P., and Zabell, S. L. 1982. “Updating Subjective Probability.” Journal of the American Statistical Association 77 (380): 822–30..CrossRefGoogle Scholar
Döring, F. 1999. “Why Bayesian Psychology Is Incomplete.” Philosophy of Science 66 (Proceedings): S379–S389.CrossRefGoogle Scholar
Field, H. 1978. “A Note on Jeffrey Conditionalization.” Philosophy of Science 45:361–67.CrossRefGoogle Scholar
Foley, R. 1992. “The Epistemology of Belief and the Epistemology of Degrees of Belief.” American Philosophical Quarterly 29:111–24.Google Scholar
Gibbard, A. 2008. “Rational Credence and the Value of Truth.” In Oxford Studies in Epistemology, Vol. 2, ed. T. Gendler and J. Hawthorne, 143–64. Oxford: Oxford University Press.Google Scholar
Greaves, H., and Wallace, D. 2006. “Justifying Conditionalization: Conditionalization Maximizes Expected Epistemic Utility.” Mind 115 (459): 607–32..CrossRefGoogle Scholar
Hájek, A. 2008. “Arguments for—or against—Probabilism?” British Journal for the Philosophy of Science 59 (4): 793–819..CrossRefGoogle Scholar
Harman, G. 1986. Change in View: Principles of Reasoning. Cambridge, MA: MIT Press.Google Scholar
Jaynes, E. T. 2003. Probability Theory: The Logic of Science. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Jeffrey, R. 1965. Logic of Decision. New York: McGraw-Hill.Google Scholar
Jeffreys, H. 1998. Theory of Probability. Oxford: Oxford University Press.Google Scholar
Joyce, J. M. 1998. “A Nonpragmatic Vindication of Probabilism.” Philosophy of Science 65 (4): 575–603..CrossRefGoogle Scholar
Joyce, J. M. 2009. “Accuracy and Coherence: Prospects for an Alethic Epistemology of Partial Belief.” In Degrees of Belief, ed. Huber, F. and Schmidt-Petri, C., 263–97. Synthese Library 342. Dordrecht: Springer.Google Scholar
Lange, M. 1999. “Calibration and the Epistemological Role of Bayesian Conditionalization.” Journal of Philosophy 96 (6): 294–324..CrossRefGoogle Scholar
Lange, M. 2000. “Is Jeffrey Conditionalization Defective by Virtue of Being Non-commutative? Remarks on the Sameness of Experience.” Synthese 123:393–403.CrossRefGoogle Scholar
Leitgeb, H., and Pettigrew, R. 2010. “An Objective Justification of Bayesianism I: Measuring Inaccuracy.” Philosophy of Science, in this issue.CrossRefGoogle Scholar
Lewis, D. K. 1999. “Why Conditionalize?” In Papers in Metaphysics and Epistemology, 403–7. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Pedregal, P. 2003. Introduction to Optimization. New York: Springer.Google Scholar
Popper, K. R. 1968. The Logic of Scientific Discovery, rev. ed. London: Hutchinson.Google Scholar
Ramsey, F. P. 1931. “Truth and Probability.” In The Foundations of Mathematics and Other Logical Essays, 156–98.Google Scholar
Schurz, G., and Leitgeb, H. 2008. “Finitistic and Frequentistic Approximation of Probability Measures with or without σ-Additivity.” Studia Logica 89 (2): 257–83..CrossRefGoogle Scholar
Skyrms, B. 1986. Choice and Chance. 3rd ed. Belmont, CA: Wadsworth.Google Scholar
van Fraassen, B. C. 1981. “A Problem for Relative Information Minimizers.” British Journal for the Philosophy of Science 32 (4): 375–79..CrossRefGoogle Scholar
van Fraassen, B. C. 1986. “A Demonstration of the Jeffrey Conditionalization Rule.” Erkenntnis 24 (1): 17–24..CrossRefGoogle Scholar
van Fraassen, B. C. 1989. Laws and Symmetry. Oxford: Oxford University Press.CrossRefGoogle Scholar
Wagner, C. G. 2002. “Probability Kinematics and Commutativity.” Philosophy of Science 69:266–78.CrossRefGoogle Scholar
Williams, P. M. 1980. “Bayesian Conditionalization and the Principle of Minimum Information.” British Journal for the Philosophy of Science 31:131–44.CrossRefGoogle Scholar
Williamson, J. 2007. “Motivating Objective Bayesianism: From Empirical Constraints to Objective Probabilities.” In Probability and Inference: Essays in Honor of Henry E. Kyburg Jr., ed. Harper, W. L. and Wheeler, G. R., 155–83. London: College.Google Scholar