Probability and conditionals

Philosophy of Science 37 (1):64-80 (1970)
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 counterfactual 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
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DOI 10.1086/288280
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The Probabilities of Conditionals Revisited.Igor Douven & Sara Verbrugge - 2013 - Cognitive Science 37 (4):711-730.
A Ranking‐Theoretic Approach to Conditionals.Wolfgang Spohn - 2013 - Cognitive Science 37 (6):1074-1106.

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