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PROBABILISTIC CONDITIONALS ARE ALMOST MONOTONIC

Published online by Cambridge University Press:  01 June 2008

MATTHEW P. JOHNSON  and
ROHIT PARIKH
MATTHEW P. JOHNSON*
Affiliation:
City University of New York
ROHIT PARIKH*
Affiliation:
City University of New York
*
*DEPARTMENT OF COMPUTER SCIENCE, CUNY GRADUATE CENTER, NEW YORK, NY 10016, USA. E-mail: [email protected]
†DEPARTMENTS OF COMPUTER SCIENCE, MATHEMATICS, AND PHILOSOPHY, CUNY GRADUATE CENTER, NEW YORK, NY 10016, USA. E-mail: [email protected]
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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.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 1 , Issue 1 , June 2008 , pp. 73 - 80
Copyright
Copyright © Association for Symbolic Logic 2008

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References

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