Mathematisches Kolloquium

Zusammenfassung: Is it possible to give an explicit definition of belief (or acceptance) in terms of subjective probability, such that believed propositions are guaranteed to have a sufficiently high probability, and yet it is neither the case that belief is stripped of any of its usual logical properties, nor is it the case that believed propositions are bound to have probability 1? We prove the answer is 'yes', and that given some plausible logical postulates on belief, there is but one way of determining the extension of the concept of belief that does the job. The concept of belief is not to be eliminated from scientific or philosophical discourse, rather, by reducing belief to assignments of consistently high probability, belief and probability turn out to be governed by one unified theory that offers the prospects of a huge range of applications. Within that theory, logic and probability theory are not opposed to each other but go hand in hand.

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