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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.

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