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Probability Logic and ℱ-Coherence

Published online by Cambridge University Press:  01 April 2022

A. I. Dale
A. I. Dale*
Affiliation:
University of Natal, Durban
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Abstract

In order that a degree-of-belief function be coherent it is necessary and sufficient that it satisfy the axioms of probability theory. This theorem relies heavily for its proof on the two-valued sentential calculus, which emerges as a limiting case of a continuous scale of truth-values. In this “continuum of certainty” a theorem analogous to that instanced above is proved.

Type
Research Article
Information
Philosophy of Science , Volume 43 , Issue 2 , June 1976 , pp. 254 - 265
Copyright
Copyright © 1976 by the Philosophy of Science Association

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References

REFERENCES

Carver, W. B. “Systems of Linear Inequalities.” Annals of Mathematics 23 (1923): 212–220.CrossRefGoogle Scholar
Kemeny, J. G. “Fair Bets and Inductive Probabilities.” Journal of Symbolic Logic 20 (1955): 263–273.CrossRefGoogle Scholar
Lehman, R. S. “On Confirmation and Rational Betting.” Journal of Symbolic Logic 20 (1955): 257–262.CrossRefGoogle Scholar
Reichenbach, H. The Theory of Probability. Berkeley: University of California Press, 1949.Google Scholar
Uchii, S. “Higher Order Probabilities and Coherence.” Philosophy of Science 40 (1973): 373–381.CrossRefGoogle Scholar