Probabilistic conditionals are almost monotonic

Review of Symbolic Logic 1 (1):73-80 (2008)
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Abstract

One interpretation of the conditional If P then Q is as saying that the probability of Q given P is high. This is an interpretation suggested by Adams (1966) and pursued more recently by Edgington (1995). Of course, this probabilistic conditional is nonmonotonic, that is, if the probability of Q given P is high, and R implies P, it need not follow that the probability of Q given R is high. If we were confident of concluding Q from the fact that we knew P, and we have stronger information R, we can no longer be confident of Q. We show nonetheless that usually we would still be justified in concluding Q from R. In other words, probabilistic conditionals are mostly monotonic

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Rohit Parikh
CUNY Graduate Center
Matthew Johnson
Iowa State University