Modus TollensProbabilized

We establish a probabilized version of modus tollens, deriving from p(E|H)=a and p(Ē)=b the best possible bounds on p(H̄). In particular, we show that p(H̄) → 1 as a, b → 1, and also as a, b → 0. 1. Introduction2. Probabilities of conditionals3. Conditional probabilities 3.1 Adams' thesis 3.2 Modus ponens for conditional probabilities 3.3 Modus tollens for conditional probabilities Introduction Probabilities of conditionals Conditional probabilities 3.1 Adams' thesis 3.2 Modus ponens for conditional probabilities 3.3 Modus tollens for conditional probabilities 3.1 Adams' thesis 3.2 Modus ponens for conditional probabilities 3.3 Modus tollens for conditional probabilities