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An Objective Justification of Bayesianism I: Measuring 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 sequel, we derive Bayesianism from the following norm: Accuracy—an agent ought to minimize the inaccuracy of her partial beliefs. In this article, we make this norm mathematically precise. We describe epistemic dilemmas an agent might face if she attempts to follow Accuracy and show that the only measures of inaccuracy that do not create these dilemmas are the quadratic inaccuracy measures. In the sequel, we derive Bayesianism from Accuracy and show that Jeffrey Conditionalization violates Accuracy unless Rigidity is assumed. 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. 201 - 235
Copyright
Copyright © The Philosophy of Science Association

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Footnotes

‡

We would like to thank F. Arntzenius, F. Dietrich, K. Easwaran, B. Fitelson (and his Berkeley reading group), A. Hájek, L. Horsten, F. Huber, J. Joyce, T. Kuipers, W. Myrvold, S. Okasha, G. Schurz, T. Seidenfeld, 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

Aczél, J., and Dhombres, J. 1989. Functional Equations in Several Variables. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Brier, G. W. 1950. “Verification of Forecasts Expressed in Terms of Probability.” Monthly Weather Review 78:1–3.2.0.CO;2>CrossRefGoogle 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
Huber, F. 2006. “The Consistency Argument for Ranking Functions.” Studia Logica 82:1–28.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
Kierland, B., and Monton, B. 1999. “Minimizing Inaccuracy for Self-Locating Beliefs.” Philosophy and Phenomenological Research 70 (2): 384–95..Google Scholar
Leitgeb, H., and Pettigrew, R. 2010. “An Objective Justification of Bayesianism II: The Consequences of Minimizing Inaccuracy.” Philosophy of Science, in this issue.CrossRefGoogle Scholar
Miller, D. W. 1974. “Popper's Qualitative Theory of Verisimilitude.” British Journal for the Philosophy of Science 25:166–77.CrossRefGoogle Scholar
Niiniluoto, I. 1987. Truthlikeness. Dordrecht: Reidel.CrossRefGoogle Scholar
Pettit, P. 2001. “Deliberative Democracy and the Discursive Dilemma.” Philosophical Issues (Supp. Noûs) 11:268–99.Google Scholar
Popper, K. R. 1968. The Logic of Scientific Discovery, rev. ed. London: Hutchinson.Google Scholar
Popper, K. R. 1972. Objective Knowledge: An Evolutionary Approach. Oxford: Clarendon.Google Scholar
Rosenkrantz, R. D. 1981. Foundations and Applications of Inductive Probability. Atascadero, CA: Ridgeview.Google Scholar
Selten, R. 1998. “Axiomatic Characterization of the Quadratic Scoring Rule.” Experimental Economics 1 (1): 43–61..CrossRefGoogle Scholar
Tichý, P. 1974. “On Popper's Definition of Verisimilitude.” British Journal for the Philosophy of Science 25:155–60.CrossRefGoogle Scholar
Williamson, J. forthcoming. “Objective Bayesianism, Bayesian Conditionalization, and Voluntarism.” Synthese.Google Scholar