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Conditional Probability and Dutch Books

Published online by Cambridge University Press:  01 April 2022

Frank Döring
Frank Döring*
Affiliation:
Department of Philosophy University of Cincinnati
*
†Send requests for reprints to the author, Department of Philosophy, University of Cincinnati, Cincinnati, OH 45221-0374, [email protected].
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Abstract

There is no set Δ of probability axioms that meets the following three desiderata:

  • (1) Δ is vindicated by a Dutch book theorem;

  • (2) Δ does not imply regularity (and thus allows, among other things, updating by conditionalization);

  • (3) Δ constrains the conditional probability q(·, z) even when the unconditional probability p(z) (= q(z, T)) equals 0.

  • This has significant consequences for Bayesian epistemology, some of which are discussed.

Type
Research Article
Information
Philosophy of Science , Volume 67 , Issue 3 , September 2000 , pp. 391 - 409
Copyright
Copyright © 2000 by the Philosophy of Science Association

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Footnotes

‡

For their criticism and encouragement, as well as for their patience with half-baked ideas, I wish to thank Richard Bradley, Chris Gauker, Dick Jeffrey, Jim Joyce, Isaac Levi, John Martin, Rob Rynasiewicz, and two anonymous referees.

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