Chance without Credence

Abstract

It is a standard view that the concept of chance is inextricably related to the technical concept of credence. One influential version of this view is that the chance role is specified by (something in the neighborhood of) David Lewis's Principal Principle, which asserts a certain definite relation between chance and credence. If this view is right, then one cannot coherently affirm that there are chance processes in the physical world while rejecting the theoretical framework in which credence is defined, namely the Bayesian framework. This is surprising; why should adopting a theory that says there are chances at work in nature put any particular constraints on our theorizing about epistemology and rational choice? It is quite plausible that in order for anything to count as the referent of our concept chance, it would have to be related to epistemic rationality in a certain way—roughly, it is rational to have more confidence that something will happen the greater you think its chance is. But this commonsensical idea does not seem to be inherently committed to any particular theoretical approach to rationality, so why should we think that adopting the Bayesian approach is a prerequisite for thinking coherently about chance? I propose and defend a replacement for the Principal Principle which makes no use of the concept of credence. I also argue that this replacement is advantageous for the project of theorizing about the nature of chance. 1 The Entanglement of Chance with Credence2 Desiderata for a Replacement for PP3 Disentangling Chance from Credence4 What RP Demands of a Bayesian Subject5 How Narrowly RP Constrains the Chance Function6 An Objection7 An Unexpected Benefit8 ConclusionAppendix A: Any Subject with Credences who Obeys PP also Obeys RPAppendix B: Any Subject with Credences who Obeys RP also Approximately Obeys PP