Probability, coherent belief and coherent belief changes

Abstract

This paper is about the statics and dynamics of belief states that are represented by pairs consisting of an agent’s credences (represented by a subjective probability measure) and her categorical beliefs (represented by a set of possible worlds). Regarding the static side, we argue that the latter proposition should be coherent with respect to the probability measure and that its probability should reach a certain threshold value. On the dynamic side, we advocate Jeffrey conditionalisation as the principal mode of changing one’s belief state. This updating method fits the idea of the Lockean Thesis better than plain Bayesian conditionalisation, and it affords a flexible method for adding and withdrawing categorical beliefs. We show that it fails to satisfy the traditional principles of Inclusion and Preservation for belief revision and the principle of Recovery for belief withdrawals, as well as the Levi and Harper identities. We take this to be a problem for the latter principles rather than for the idea of coherent belief change.