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Full Belief and Probability: Comments on Van Fraassen

Published online by Cambridge University Press:  13 April 2010

William Harper  and
Alan Hajek
William Harper
Affiliation:
University of Westen Ontario
Alan Hajek
Affiliation:
California Institute of Technology
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Extract

As van Fraassen pointed out in his opening remarks, Henry Kyburg's lottery paradox has long been known to raise difficulties in attempts to represent full belief as a probability greater than or equal to p, where p is some number less than 1. Recently, Patrick Maher has pointed out that to identify full belief with probability equal to 1 presents similar difficulties. In his paper, van Fraassen investigates ways of representing full belief by personal probability which avoid the difficulties raised by Maher's measure-theoretic version of the lottery paradox. Van Fraassen's more subtle representation dissolves the simple identification of full belief with maximal personal probability. His investigation exploits the richer resources for representing opinion provided by taking conditional, rather than unconditional, personal probability as fundamental. It has interesting implications for equivalent alternative approaches based on non-Archimedean probability, as well as for equivalent approaches in which assumption contexts representing full belief relative to suppositions are taken as fundamental.

Type
Articles and Interventions/Articles et Discussions
Information
Dialogue: Canadian Philosophical Review / Revue canadienne de philosophie , Volume 36 , Issue 1 , Winter 1997 , pp. 91 - 100
Copyright
Copyright © Canadian Philosophical Association 1997

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References

Anscombe, Francis, and Aumann, Robert 1963 “A Definition of Subjective Probability.” Annals of Mathematical Statistics, 34: 199–205.CrossRefGoogle Scholar
Bume, Lawrence, Brandenburger, Adam, and Dekel, Eddie 1991 “Lexicographic Probabilities and Choice Under Uncertainty.” Econometrica, 59, 1: 61–79.Google Scholar
Gärdenfors, Peter 1988 Knowledge in Flux: Modelling the Dynamics of Epistemic States. Cambridge, MA: MIT Press.Google Scholar
Harper, William 1975 “Rational Belief Change, Popper Functions and Counterfactuals.” Synthese, 30: 221–62.CrossRefGoogle Scholar
Harper, William 1977 “Rational Conceptual Change.” PSA 1976, 2: 462–94.Google Scholar
Harper, William 1978a “Bayesian Learning Models with Revision of Evidence.” Philosophia, 7, 2: 357–67.CrossRefGoogle Scholar
Harper, William 1978b “Conceptual Change Incommensurability and Special Relativity Kinematics.” Acta Philosophica Fennica, 30, 2–4: 430–61.Google Scholar
Harper, William, Leblanc, Hugues, and van Fraassen, Bas 1983 “On Characterizing Popper and Carnap Probability Functions.” In Essays in Epistemology and Semantics. Edited by Leblanc, Hugues, Stern, Raphael, and Gumb, Raymond. New York: Haven Publications, pp. 140–52.Google Scholar
Kyburg, Henry E. Jr. 1961 Probability and the Logic of Rational Belief. Middletown, CT: Wesleyan University Press.Google Scholar
Leblanc, Hugues, Stern, Raphael, and Gumb, Raymond, eds. 1983 Essays in Epistemology and Semantics. New York: Haven Publications.Google Scholar
Maher, Patrick 1990 “Acceptance Without Belief” PSA 1990, 1: 381–92.Google Scholar
McGee, Van 1994 “Learning the Impossible.” In Probability and Conditionals. Edited by Eells, Ellery and Skyrms, Brian. Cambridge: Cambridge University Press, pp. 179–99.Google Scholar
Raiffa, Howard 1970 Decision Analysis. Reading, MA: Addison-Wesley Publishing.Google Scholar
Savage, Leonard J. 1954 The Foundations of Statistics. New York: John Wiley & Sons.Google Scholar
Skyrms, Brian 1980 Causal Necessity. New Haven, CT: Yale University Press,Google Scholar
van Fraassen, Bas C. 1976 “Representation of Conditional Probabilities.” Journal of Philosophical Logic, 5: 417–30.CrossRefGoogle Scholar
van Fraassen, Bas C. 1977 “Erratum” (to 1976) Journal of Philosophical Logic, 6: 365.Google Scholar