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Imprecision and Indeterminacy in Probability Judgment

Published online by Cambridge University Press:  01 April 2022

Isaac Levi
Isaac Levi*
Affiliation:
Department of Philosophy Columbia, University
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Abstract

Bayesians often confuse insistence that probability judgment ought to be indeterminate (which is incompatible with Bayesian ideals) with recognition of the presence of imprecision in the determination or measurement of personal probabilities (which is compatible with these ideals). The confusion is discussed and illustrated by remarks in a recent essay by R. C. Jeffrey.

Type
Research Article
Information
Philosophy of Science , Volume 52 , Issue 3 , September 1985 , pp. 390 - 409
Copyright
Copyright © 1985 by the Philosophy of Science Association

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Footnotes

†

Thanks are due to Richard Jeffrey, Henry E. Kyburg, Jr., Sidney Morgenbesser, Calvin Normore, Nils-Erik Sahlin, and especially Teddy Seidenfeld and the two referees for Philosophy of Science for helpful criticisms and comments.

References

REFERENCES

Dempster, A. P. (1967), “Upper and Lower Probabilities Induced by a Multivalued Mapping”, Annals of Mathematical Statistics 38: 325–39.CrossRefGoogle Scholar
Ellsberg, D. (1961), “Risk, Ambiguity, and the Savage Axioms”, Quarterly Journal of Economics 75: 643–69.CrossRefGoogle Scholar
Gärdenfors, P., and Sahlin, N.-E. (1982a), “Unreliable Probabilities, Risk Taking and Decision Making”, Synthese 53: 361–86.CrossRefGoogle Scholar
Gärdenfors, P., and Sahlin, N.-E. (1982b), “Reply to Levi”, Synthese 53: 433–38.CrossRefGoogle Scholar
Good, I. J. (1952), “Rational Decisions”, Journal of the Royal Statistical Society B 14: 107–14.Google Scholar
Good, I. J. (1962), “Subjective Probability as a Measure of a Non-measurable Set”, Logic, Methodology and Philosophy Science, Nagel, E., Suppes, P., and Tarski, A. (eds.). Stanford: Stanford University Press, pp. 319–29.Google Scholar
Jeffrey, R. C. (1965), The Logic of Decision. New York: McGraw-Hill. (2nd revised edition, McGraw-Hill, 1983.)Google Scholar
Jeffrey, R. C. (1975), “Replies”, Synthese 30: 149–57.CrossRefGoogle Scholar
Jeffrey, R. C. (1984), “Bayesianism with a Human Face”, in Testing Scientific Theories, Earman, John (ed.). Minnesota Studies in the Philosophy of Science, vol. 10. Minneapolis: University of Minnesota Press, pp. 133–56.Google Scholar
Koopman, B. O. (1940), “The Bases of Probability”, Bulletin of the American Mathematical Society 46: 763–74.CrossRefGoogle Scholar
Kyburg, Henry E., Jr, . (1961), Probability and the Logic of Rational Belief. Middletown, Conn.: Wesleyan University Press.Google Scholar
Kyburg, Henry E., Jr, . (1974), The Logical Foundations of Statistical Inference. Dordrecht: D. Reidel.CrossRefGoogle Scholar
Levi, I. (1974), “On Indeterminate Probabilities”, Journal of Philosophy 71: 391–418.CrossRefGoogle Scholar
Levi, I. (1980), The Enterprise of Knowledge. Cambridge: The MIT Press.Google Scholar
Levi, I. (1982a), “Conflict and Social Agency”, Journal of Philosophy 79: 231–46.CrossRefGoogle Scholar
Levi, I. (1982b), “Ignorance, Probability and Rational Choice”, Synthese 53: 387–417.CrossRefGoogle Scholar
Putnam, H. (1975), “The Refutation of Conventionalism”, in Mind, Language and Reality. Cambridge: Cambridge University Press, pp. 153–91.CrossRefGoogle Scholar
Savage, L. J. (1954), The Foundations of Statistics. New York: John Wiley and Sons. (2nd revised edition, Dover, 1972.)Google Scholar
Savage, L. J. (1971), “Elicitation of Personal Probabilities and Expectations”, Journal of the American Statistical Association 66: 783–801.CrossRefGoogle Scholar
Schick, F. (1958), Explication and Inductive Logic. Ph.D. dissertation, Columbia University.Google Scholar
Schick, F. (1984), Having Reasons. Princeton: Princeton University Press.CrossRefGoogle Scholar
Seidenfeld, T., and Schervish, M. (1983), “A Conflict between Finite Additivity and Avoiding Dutch Book”, Philosophy of Science 50: 398–412.CrossRefGoogle Scholar
Smith, C. A. B. (1961), “Consistency in Statistical Inference and Decision”, Journal of the Royal Statistical Society B 23: 1–31.Google Scholar
Williams, P. M. (1976), “Indeterminate Probabilities”, in Formal Methods in the Methodology of the Empirical Sciences, Dordrecht: D. Reidel.Google Scholar
Wolfenson, M., and Fine, T. (1982), “Bayes-like Decision Making with Upper and Lower Probabilities”, Journal of the American Statistical Association 77: 80–88.CrossRefGoogle Scholar