Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-05T12:46:56.805Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

References

Burks, A. (1977), Chance, Cause, and Reason: An Inquiry into the Nature of Scientific Evidence, Chicago: University of Chicago Press.Google Scholar
Jeffrey, R.C. (1983), The Logic of Decision, Second Edition. Chicago: University of Chicago Press.Google Scholar
Jeffrey, R.C. (1985), “Probability and the Art of Judgment,” in Observation, Experiment, and Hypotheses in Modern Physical Science, Achinstein, P. and Hannaway, O. (eds.). Cambridge, Mass: MIT Press, pp. 95–126.Google Scholar
Lewis, D. (1976), “Probabilities of Conditionals and Conditional Probabilities,” Philosophical Review 85: 297–315.CrossRefGoogle Scholar
Skyrms, B. (1986), Choice and Chance: An Introduction to Inductive Logic, Third Edition, Belmont, Calif.: Wadsworth Publishing Company.Google Scholar
Sobel, J. H. (1987), “Self-Doubts and Dutch Strategies,” Australian Journal of Philosophy 65: 56–81.CrossRefGoogle Scholar
Weirich, P. (1979), “Conditionalization and Evidence,” The Journal of Critical Analysis 8: 15–18.CrossRefGoogle Scholar