Coherence, Probability and Induction

Abstract

Induction has to do with how our beliefs should change under the pressure of evidence. How should we represent our beliefs and how should we model the process of belief change? To begin with we would like our beliefs to be coherent. We don't, for instance, want to believe both that it is more likely than not that it will rain tomorrow and that it is more likely than not that it will not rain tomorrow. (At least most of us don't want to have belief systems which trip over their own feet in this way.) If we ask what is required for coherence, the answer -at the same level of precision as the questionturns out to be that coherence requires that (de-