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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.

References

Eells, Ellery and Skyrms, Brian (eds.) (1994), Probability and Conditionals: Belief Revision and Rational Decision. Cambridge: Cambridge University Press.Google Scholar
Gärdenfors, Peter (1982), “Imaging and Conditionalization”, Journal of Philosophy 79: 747–760.10.2307/2026039CrossRefGoogle Scholar
Gärdenfors, Peter. (1988), Knowledge in Flux. Cambridge, MA: MIT Press.Google Scholar
Hájek, Alan (1989), “Probabilities of Conditionals—Revisited”, Journal of Philosophical Logic 18: 423–428.10.1007/BF00262944CrossRefGoogle Scholar
Hájek, Alan. (1994), “Triviality on the Cheap?” in Eells and Skyrms 1994, 113–140.Google Scholar
Hájek, Alan and Hall, Ned (1994), “The Hypothesis of the Conditional Construal of Conditional Probability”, in Eells and Skyrms 1994, 75–111.Google Scholar
Hall, Ned (1994), “Back in the CCCP”, in Eells and Skyrms 1994, 141–160.Google Scholar
Harper, William (1976), “Rational Belief Change, Popper Functions and Counterfactuals”, in Harper and Hooker 1976, 73–115.10.1007/978-94-010-1853-1_5CrossRefGoogle Scholar
Harper, William and Hooker, Clifford A. (eds.) (1976), Foundations and Philosophy of Epistemic Applications of Probability Theory. Dordrecht: D. Reidel.Google Scholar
Lewis, David (1973), Counterfactuals. Cambridge, MA: Harvard University Press.Google Scholar
Lewis, David. (1976), “Probabilities of Conditionals and Conditional Probabilities”, Philosophical Review 85: 297–315. Reprinted with postscript in Lewis 1986a, 133–156. (Page references are to the reprinting.)10.2307/2184045CrossRefGoogle Scholar
Lewis, David. (1986a), Philosophical Papers, vol. 2. Oxford: Oxford University Press.Google Scholar
Lewis, David. (1986b), “Probabilities of Conditionals and Conditional Probabilities II”, Philosophical Review 95: 581–589.10.2307/2185051CrossRefGoogle Scholar
Nute, Donald (1980), Topics in Conditional Logic. Dordrecht: D. Reidel.10.1007/978-94-009-8966-5CrossRefGoogle Scholar
Rescher, Nicholas (ed.) (1968), Studies in Logical Theory. Oxford: Blackwell.Google Scholar
Skyrms, Brian (1986), Choice and Chance: an Introduction to Inductive Logic, 3rd ed. Belmont: Wadsworth Publishing Company.Google Scholar
Spohn, Wolfgang (1986), “The Representation of Popper Measures”, Topoi 5: 69–74.10.1007/BF00137831CrossRefGoogle Scholar
Stalnaker, Robert (1968), “A Theory of Conditionals”, in Rescher 1968, 98–112.10.1007/978-94-009-9117-0_2CrossRefGoogle Scholar
Stalnaker, Robert. (1970), “Probability and Conditionals”, Philosophy of Science 37: 64–80.10.1086/288280CrossRefGoogle Scholar
van Fraassen, Bas C. (1976a), “Probabilities of Conditionals”, in Harper and Hooker 1976, 261–308.10.1007/978-94-010-1853-1_10CrossRefGoogle Scholar
van Fraassen, Bas C. (1976b), “Representation of Conditional Probabilities”, Journal of Philosophical Logic 5: 417–430.10.1007/BF00649400CrossRefGoogle Scholar
van Fraassen, Bas C. (1989), Laws and Symmetry. Oxford: Clarendon Press.10.1093/0198248601.001.0001CrossRefGoogle Scholar