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Probability and Conditionals

Published online by Cambridge University Press:  14 March 2022

Robert C. Stalnaker
Robert C. Stalnaker*
Affiliation:
University of Illinois
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Abstract

The aim of the paper is to draw a connection between a semantical theory of conditional statements and the theory of conditional probability. First, the probability calculus is interpreted as a semantics for truth functional logic. Absolute probabilities are treated as degrees of rational belief. Conditional probabilities are explicitly defined in terms of absolute probabilities in the familiar way. Second, the probability calculus is extended in order to provide an interpretation for counter-factual probabilities—conditional probabilities where the condition has zero probability. Third, conditional propositions are introduced as propositions whose absolute probability is equal to the conditional probability of the consequent on the antecedent. An axiom system for this conditional connective is recovered from the probabilistic definition. Finally, the primary semantics for this axiom system, presented elsewhere, is related to the probabilistic interpretation.

Type
Research Article
Information
Philosophy of Science , Volume 37 , Issue 1 , March 1970 , pp. 64 - 80
Copyright
Copyright © 1970 The Philosophy of Science Association

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Footnotes

1

The preparation of this paper was supported under National Science Foundation Grant, GS-1567.

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