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Modus tollens probabilized. (English) Zbl 1062.03015
Summary: We establish a probabilized version of modus tollens, deriving from \(p(E\mid H)=a\) and \(p(\overline E)=b\) the best possible bounds on \(p(\overline H)\). In particular, we show that \(p(\overline H)\to 1\) as \(a,b\to 1\), and also as \(a,b\to 0\).

MSC:
03A05 Philosophical and critical aspects of logic and foundations
03B48 Probability and inductive logic
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