A Graded Bayesian Coherence Notion

Abstract

Coherence is a key concept in many accounts of epistemic justification within ‘traditional’ analytic epistemology. Within formal epistemology, too, there is a substantial body of research on coherence measures. However, there has been surprisingly little interaction between the two bodies of literature. The reason is that the existing formal literature on coherence measure operates with a notion of belief system that is very different from—what we argue is—a natural Bayesian formalisation of the concept of belief system from traditional epistemology. Therefore, formal epistemology has so far only been concerned with one particular—arguably not even very natural—way of formalising coherence of belief systems; it has by no means refuted the viability of coherentism. In contrast to the existing literature, we formalise belief systems as families of assignments of (conditional) degrees of belief (which may be compatible with several subjective probability measures). Within this framework, we propose a Bayesian formalisation of the thrust of BonJour’s coherence concept in The structure of empirical knowledge (Harvard University Press, Cambridge, 1985), using a combination of Bayesian confirmation theory and basic graph theory. In excursions, we introduce graded notions for both logical and probabilistic consistency of belief systems—the latter being based on certain geometrical structures induced by probabilistic belief systems. For illustration, we reconsider BonJour’s “ravens” challenge (op. cit., p. 95f.). Finally, potential objections to our proposed formal coherence notion are explored.