Bayesian Epistemology

Bayesian epistemology addresses epistemological problems with the help of the mathematical theory of probability. It turns out that the probability calculus is especially suited to represent degrees of belief (credences) and to deal with questions of belief change, confirmation, evidence, justification, and coherence. Compared to the informal discussions in traditional epistemology, Bayesian epistemology allows for a more precise and fine-grained analysis which takes the gradual aspects of these central epistemological notions into account. Bayesian epistemology therefore complements traditional epistemology; it does not replace it or aim at replacing it. Bayesian epistemology can be traced back to the work of Reverend Thomas Bayes (1701-1761) who found an elementary mathematical theorem that plays a central role in Bayesian epistemology. More on this below. Later Bayesian ideas began to surface not only in philosophy, but also in statistics, formal learning theory, and other parts of science. Obviously, the probability calculus finds many applications because of its enormous flexibility, expressive power, and formal simplicity. Bayesian epistemology shares much with these endeavors, including a certain scientific attitude vis-a-vis the problems in question, but it is worth noting that Bayesian epistemology is, in the first place, a philosophical project, and that it is its ambition to further progress in philosophy. This essay is structured as follows. Section 2 introduces the probability calculus and explains why degrees of belief obey the probability calculus. Section 3 applies the formal machinery to an analysis of the notion of evidence, and highlights potential application. Section 4 discusses Bayesian models of coherence and testimony, and section 5 ends this essay with a comparison of traditional epistemology and Bayesian epistemology.