Games, Beliefs and Credences

theory of belief. This paper continues the defence. I have four aims. 1. To offer a new kind of reason for being unsatisfied with the simple Lockean reduction of belief to credence. 2. To defend the legitimacy of appealing to credences in a theory of belief. 3. To illustrate the importance of theoretical, as well as practical, interests in an interest-relative account of belief. 4. To have another try at extending my basic account of belief to cover propo-sitions that are practically and theoretically irrelevant to the agent. You’re probably familiar with the following dialectic. We want there to be some systematic connection between credences and beliefs. At first blush, saying that a person believes p and has a very low credence in p isn’t just an accusation of irrationality, it is literally incoherent. The simplest such connection would be a reduction of beliefs to credences. But the simplest reductions don’t work. If we identify beliefs with credence 1, and take credences to support betting dispositions, then a rational agent will have very few beliefs. There are lots o