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On Characterizing Unary Probability Functions and Truth-Value Functions

Published online by Cambridge University Press:  01 January 2020

Hugues Leblanc
Hugues Leblanc*
Affiliation:
Temple University, PhiladelphiaPA19122, U.S.A.
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Extract

Consider a language SL having as its primitive signs one or more atomic statements, the two connectives ‘∼’ and ‘&,’ and the two parentheses ‘(’ and ‘)’; and presume the extra connectives ‘V’ and ‘≡’ defined in the customary manner. With the statements of SL substituting for sets, and the three connectives ‘∼,’ ‘&,’and ‘V’ substituting for the complementation, intersection, and union signs, the constraints that Kolmogorov places in [1] on (unary) probability functions come to read:

K1. 0 ≤ P(A),

K2. P(∼(A & ∼A)) = 1,

K3. If ⊦ ∼(A & B), then P(A ∨ B) = P(A) + P(B),

K4. If ⊦ A ≡ B, then P(A) = P(B).2

Type
Research Article
Information
Canadian Journal of Philosophy , Volume 15 , Issue 1 , March 1985 , pp. 19 - 24
Copyright
Copyright © The Authors 1985

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References

[1]Kolmogorov, Andrei N. Foundations of Probability (New York: Chelsea Publishing Company 1950)Google Scholar
[2]Leblanc, Hugues ‘Popper's 1955 Axiomatization of Absolute Probability,’ Pacific Philosophical Quarterly, 63 (1982) 133–45CrossRefGoogle Scholar
[3]Leblanc, Hugues ‘Probability Functions and their Assumption Sets: The Singulary Case,’ Journal of Philosophical Logic, 12 (1983) 379–402CrossRefGoogle Scholar
[4]Popper, Karl R. ‘Two Autonomous Axiom Systems for the Calculus of Probability,’ The British Journal for the Philosophy of Science, 6 (1955) 51–7Google Scholar
[5]Popper, Karl R. The Logic of Scientific Discovery (New York: Basic Books 1959)Google Scholar
[6]Rescher, Nicholas ‘A Probabilistic Approach to Modal Logic,’ Modal and Many Valued Logics, Acta Philosophica Fennica, 16 (1963) 215–26Google Scholar