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A Characterization of Imaging in Terms of Popper Functions

Published online by Cambridge University Press:  01 April 2022

Charles B. Cross
Charles B. Cross*
Affiliation:
Department of Philosophy, University of Georgia
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Abstract

Despite the results of David Lewis, Peter Gärdenfors, and others, showing that imaging and classical conditionalization coincide only in the most trivial probabilistic models of belief revision, it turns out that imaging on a proposition A can always be described via Popper function conditionalization on a proposition that entails A. This result generalizes to any method of belief revision meeting certain minimal requirements. The proof is illustrated by an application of imaging in the context of the Monty Hall Problem.

Type
Research Article
Information
Philosophy of Science , Volume 67 , Issue 2 , June 2000 , pp. 316 - 338
Copyright
Copyright © 2000 by the Philosophy of Science Association

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Footnotes

†

Send requests for reprints to the author, Department of Philosophy, University of Georgia, Athens, GA 30602-1627.

‡

For their comments on previous versions of this paper I would like to thank Horacio Arló Costa, Jim Joyce, Susan Vineberg, Don Nute, Brad Bassler, Fabrizio Sebastiani, audience members at the 1994 annual meeting of the Society for Exact Philosophy and the 1994 meeting of the Eastern Division of the APA, and especially Alan Hájek, my commentator at the 1994 Eastern Division. This research was supported in part by a grant from the University of Georgia Research Foundation.

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