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Conditional Probabilities, Conditionalization, and Dutch Books

Published online by Cambridge University Press:  31 January 2023

Jordan Howard Sobel
Jordan Howard Sobel*
Affiliation:
University of Toronto
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Extract

Relations between conditional probabilities, revisions of probabilities in the light of new information, and conditions of ideal rationality are discussed herein. The formal character of conditional probabilities, and their significance for epistemic states of agents is taken up. Then principles are considered that would, under certain conditions, equate rationally revised probabilities on new information with probabilities reached by conditionalizing on this information. And lastly the possibility of kinds of ‘books’ against known non-conditionalizers is explored, and the question is taken up, What, if anything, would be wrong with a person against whom such a book could be made?

1. The standard mathematical treatment takes probability functions as basic, and conditional probabilities defined. If P(-) is a probability function, then is its conditional probability function if and only if P(h/e) is defined only for e such that P(e) > 0, and is then equal to P(e & h)/P(e).

Type
Part IX. Belief, Cause and Induction
Information
PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association , Volume 1990 , Issue 1: Volume One: Contributed Papers 1990 , 1990 , pp. 502 - 515
Copyright
Copyright © Philosophy of Science Association 1990

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