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Bayesian Inference with Indeterminate Probabilities

Published online by Cambridge University Press:  28 February 2022

Stephen Spielman
Stephen Spielman*
Affiliation:
Lehman College of the City Universityof , New York
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Extract

There is an increasing recognition by friends of personal probability that the standard systems of personal probability do not provide a fully adequate basis for the theories of scientific inference and rational decision making. This recognition has methodological and formal components. On the methodological side, Jeffrey [8] and Spielman [16], [17] have suggested that personal probabilities should be interpreted as judgments about the credibility of propositions, i.e., as appraisals of the degrees of confidence that are warranted by the information available to the appraiser. The idea behind this interpretation is that there are criteria for appraising degrees of confidence as rational, plausible, silly or unwarranted. They have not been canonized, with the exception of the traditional informal fallacies of insufficient evidence, and if they were, would be highly vague and subject to revision as knowledge advances.

Type
Part VI. Induction and Probability
Information
PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association , Volume 1976 , Issue 1: Volume One: Contributed Papers 1976 , 1976 , pp. 184 - 196
Copyright
Copyright © 1976 by the Philosophy of Science Association

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References

Adams, E.W. “Elements of a Theory of Inexact Measurement.” Philosophy of Science 32 (1965): 205-228.CrossRefGoogle Scholar
Boole, G. An Investigation of the Laws of Thought. London: Macmillan, 1854.Google Scholar
Fine, T. Theories of Probability. New York: Academic Press, 1973.Google Scholar
Fishburn, P. “Weak Qualitative Probability on Finite Sets.” Annals of Mathematical Statistics 40 (1969): 2118-2126.Google Scholar
Fishburn, P. Utility Theory for Decision Making. New York: Wiley, 1970.CrossRefGoogle Scholar
Good, I.J. “Subjective Probability as the Measure of a Non-Measurable Set.” In Logic, Methodology and Philosophy of Science. Edited by Nagel, E., Suppes, P. and Tarski, A.. Stanford: Stanford University Press, 1962. Pages 319-329.Google Scholar
Hacking, I. Logic of Statistical Inference. Cambridge: Cambridge University Press, 1965.CrossRefGoogle Scholar
R., Jeffrey “Replies.” Synthese 30 (1975): 149-157.Google Scholar
Koopman, B.O. “The Axioms and Algebra of Intuitive Probability.” Annals of Mathematics 41 (1940): 269-292.CrossRefGoogle Scholar
Kraft, C.H., Pratt, J.W. and Seidenberg, A. “Intuitive Probability on Finite Sets.” Annals of Mathematical Statistics 30 (1959): 408-419.CrossRefGoogle Scholar
Levi, I. “On Indeterminate Probabilities.” Journal of Philosophy LXXI (1974): 391-418.CrossRefGoogle Scholar
Scott, D. “Measurement Structures and Linear Inequalities.” Journal of Mathematical Psychology 1 (1964): 233-247.CrossRefGoogle Scholar
Smith, C.A.B. “Consistency in Statistical Inference and Decision.” Journal of the Royal Statistical Society Ser. B,23 (1961): 1-25.Google Scholar
Spielman, S. The Logical Structure of Probability. Unpublished Ph.D. dissertation, University of Pennsylvania, 1967. Xerox University Microfilm Publication Number 68-09242.Google Scholar
Smith, C.A.B. “Assuming, Ascertaining and Inductive Probability.” American Philosophical Quarterly Monograph #3 (1969): 143-161.Google Scholar
Smith, C.A.B. “Levi on Personal ism and Revisionism.” Journal of Philosophy LXXII (1975): 785-793.Google Scholar
Smith, C.A.B. “Comments on Joseph Agassi.” Synthese 30 (1975): 15-23.Google Scholar
Villegas, C. “On Qualitative Probability σ - Algebras.” Annals of Mathematical Statistics 35 (1960: 1787-1796.Google Scholar