## 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

### Keywords:

philosophy of science; conditional probabilities
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