David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Philosophy of Science 37 (1):64-80 (1970)
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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Alan Hájek (2012). The Fall of “Adams' Thesis”? Journal of Logic, Language and Information 21 (2):145-161.
Robert C. Stalnaker & Richmond H. Thomason (1970). A Semantic Analysis of Conditional Logic. Theoria 36 (1):23-42.
Igor Douven, Leon Horsten & Jan-Willem Romeijn (2010). Probabilist antirealism. Pacific Philosophical Quarterly 91 (1):38-63.
Chase Wrenn (2010). A Puzzle About Desire. Erkenntnis 73 (2):185-209.
Gerhard Schurz & Paul D. Thorn (2012). REWARD VERSUS RISK IN UNCERTAIN INFERENCE: THEOREMS AND SIMULATIONS. Review of Symbolic Logic 5 (4):574-612.
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