Reducing Belief Simpliciter to Degrees of Belief

Leitgeb, Hannes (2013): Reducing Belief Simpliciter to Degrees of Belief. In: Annals of Pure and Applied Logic, Vol. 164, No. 12: 1338 - 1389

Abstract

Is it possible to give an explicit definition of belief (simpliciter) 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 that involve a contextual “cautiousness” threshold, there is but one way of determining the extension of the concept of belief that does the job. The qualitative concept of belief is not to be eliminated from scientific or philosophical discourse, rather, by reducing qualitative belief to assignments of resiliently high degrees of belief and a “cautiousness” threshold, qualitative and quantitative belief 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.

• Item Type: Journal article
• Keywords: Subjective probability; Doxastic logic; Belief revision; Formal epistemology
• Faculties: Philosophy, Philosophy of Science and Religious Science > Munich Center for Mathematical Philosophy (MCMP); Philosophy, Philosophy of Science and Religious Science > Munich Center for Mathematical Philosophy (MCMP) > Logic; Philosophy, Philosophy of Science and Religious Science > Munich Center for Mathematical Philosophy (MCMP) > Epistemology
• Subjects: 100 Philosophy and Psychology > 100 Philosophy; 100 Philosophy and Psychology > 120 Epistemology
• ISSN: 0168-0072
• Language: English