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The British Journal for the Philosophy of Science 2004 55(4):747-753; doi:10.1093/bjps/55.4.747
© 2004 by British Society for the Philosophy of Science
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Modus Tollens Probabilized

Carl G. Wagner

Mathematics Department, University of Tennessee, Knoxville, TN 37996-1300, USA, wagner{at}math.utk.edu

We establish a probabilized version of modus tollens, deriving from p(E|H)=a and p(E)=b the best possible bounds on p(). In particular, we show that p() -> 1 as a, b -> 1, and also as a, b -> 0.

  1. Introduction
  2. Probabilities of conditionals
  3. Conditional probabilities
    3.1 Adams' thesis
    3.2 Modus ponens for conditional probabilities
    3.3 Modus tollens for conditional probabilities


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