Journal of Logic, Language and Information 15 (1-2):65-81 (2006)
AbstractAdams' famous thesis that the probabilities of conditionals are conditional probabilities is incompatible with standard probability theory. Indeed it is incompatible with any system of monotonic conditional probability satisfying the usual multiplication rule for conditional probabilities. This paper explores the possibility of accommodating Adams' thesis in systems of non-monotonic probability of varying strength. It shows that such systems impose many familiar lattice theoretic properties on their models as well as yielding interesting logics of conditionals, but that a standard complementation operation cannot be defined within them, on pain of collapsing probability into bivalence.
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References found in this work
The Logic of Conditionals: An Application of Probability to Deductive Logic.Ernest Wilcox Adams - 1996 - Dordrecht, Netherland: D. Reidel Pub. Co..
Probabilities of Conditionals and Conditional Probabilities.David Lewis - 1976 - Philosophical Review 85 (3):297-315.
Erratum: Probabilities of Conditionals and Conditional Probabilities.David Lewis - 1976 - Philosophical Review 85 (4):561.