# Criteria of Rational Belief

# Criteria of Rational Belief

This chapter begins by providing the problem of the detachment conditions for dyadic judgements of probability. The study of criteria for rational belief is very largely the study of the detachment conditions for dyadic judgements of probability. The deductive closure condition and the logical consistency condition present difficulties for any acceptance-rule formulated in terms of mathematical probability. The proposals for dealing with these difficulties that have been put forward by Hintikka and Hilpinen, by Kyburg, by Levi, and by Lehrer, are all, for different reasons, unsatisfactory. But a rule of acceptance formulated in terms of inductive probability does not encounter any of these difficulties. Mathematical probability can provide a basis for decision-theoretic strategies, but not for rational belief.

*Keywords:*
rational belief, mathematical probability, detachment conditions, dyadic judgements, deductive closure condition, logical consistency condition, inductive probability, acceptance-rule

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