Hostname: page-component-8448b6f56d-mp689 Total loading time: 0 Render date: 2024-04-23T05:23:40.080Z Has data issue: false hasContentIssue false
  • English
  • Français

Jeffrey's Rule of Conditioning

Published online by Cambridge University Press:  01 April 2022

Glenn Shafer
Glenn Shafer*
Affiliation:
Department of Mathematics, University of Kansas
Get access Rights & Permissions [Opens in a new window]

Abstract

Richard Jeffrey's generalization of Bayes' rule of conditioning follows, within the theory of belief functions, from Dempster's rule of combination and the rule of minimal extension. Both Jeffrey's rule and the theory of belief functions can and should be construed constructively, rather than normatively or descriptively. The theory of belief functions gives a more thorough analysis of how beliefs might be constructed than Jeffrey's rule does. The inadequacy of Bayesian conditioning is much more general than Jeffrey's examples of uncertain perception might suggest. The “parameter α” that Hartry Field has introduced into Jeffrey's rule corresponds to the “weight of evidence” of the theory of belief functions.

Type
Research Article
Information
Philosophy of Science , Volume 48 , Issue 3 , September 1981 , pp. 337 - 362
Copyright
Copyright © 1981 by the Philosophy of Science Association

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

de Finetti, B. (1974), Theory of Probability, Vol. 1. New York: Wiley.Google Scholar
Diaconis, P., and Zabell, S. (1979), “Updating Subjective Probability.” Unpublished.Google Scholar
Dempster, A. P. (1968), “A Generalization of Bayesian Inference.” Journal of the Royal Statistical Society, Series B 30: 205–247.Google Scholar
Jeffrey, R. (1965), The Logic of Decision. New York: McGraw-Hill.Google Scholar
Jeffrey, R. (1968), “Probable Knowledge.” In The Problem of Inductive Logic, Lakatos, I. (ed.), Netherlands: North-Holland: 166–180.CrossRefGoogle Scholar
Jeffrey, R. (1970), “Dracula Meets Wolfman.” In Induction, Acceptance and Rational Belief, Swain, M. (ed.), Dordrecht: Reidel: 157–185.CrossRefGoogle Scholar
Jeffrey, R. (1975), “Carnap's Empiricism.” In Minnesota Studies in the Philosophy of Science, Vol. VI, Maxwell, and Anderson, (eds.), University of Minnesota Press: 37–49.Google Scholar
Mosteller, F. and Wallace, D. (1964), Inference and Disputed Authorship: The Federalist. Reading, MA: Addison-Wesley.Google Scholar
Shafer, G. (1976), A Mathematical Theory of Evidence. Princeton: Princeton University Press.CrossRefGoogle Scholar
Shafer, G. (1978), “Non-Additive Probabilities in the Work of Bernoulli and Lambert.” Archive for History of Exact Sciences 19: 309–370.CrossRefGoogle Scholar
Shafer, G. (1979), “Two Theories of Probability.” In PSA 1978, Vol. 2, Philosophy of Science Association, East Lansing, Michigan.Google Scholar
Shafer, G. (1981), “Constructive Probability.” To appear in Synthese.CrossRefGoogle Scholar
Skyrms, B. (1975), Choice and Chance. 2nd ed. Belmont, CA: Wadsworth.Google Scholar
van Fraassen, B. (1980), “Rational Belief and Probability Kinematics.” Philosophy of Science 47: 165–187.CrossRefGoogle Scholar