Authors
Richard Bradley
London School of Economics
Abstract
Adams' 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.
Keywords Conditionals  non-monotonic logic  axiomatic probability theory  Adams' Thesis
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DOI 10.1007/s10849-005-9007-5
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Indicative Conditionals.Robert Stalnaker - 1975 - Philosophia 5 (3):269-286.
Conditionals.Frank Jackson - 1992 - Philosophical Quarterly 42 (167):266.

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