Abstract

I argue for the moderate probabilist view that probability theory plays much the same role in epistemology as does logic, and so is as indispensable to epistemology as is logic; but probability theory by itself does not constitute a theory of rational degree of belief, just as deductive logic does not by itself constitute a theory of rational belief. I defend a version of Ramsey's view that degrees of belief, which are defined using the notion of mathematical expectation, must obey the laws of probability or an implicit logical error, namely preferring one thing over itself under two different but logically equivalent descriptions, will be committed. This fact is what licenses speaking of probability theory as an extension of formal logic. I also discuss how the notions of coherence and consistency are related to principles of epistemic rationality. I argue that coherence is best understood as an epistemic ideal, i.e., a quality that the opinion of an ideally rational being who makes no logical errors in forming its preferences would have. For us humans, who are not ideally rational, ideals of reason such as coherence and consistency are things towards which we should strive even though they are not things we can attain. They have substantive normative force for how we manage our opinion, however, since rationality only requires that we approximate to epistemic ideals such as coherence as much as is possible for us. To help make sense of the notion of approximation to coherence, I develop a generalized model of degree of belief and give a precise formal explication of the notion of increasing coherence within this framework. I argue that logical improvements of the sort that move a person from lesser to greater coherence cannot account for all epistemically interesting notions such as justification or warrant. In particular, I argue that there is little reason to think that the notion of scientific confirmation can be explicated wholly in terms of subjective probabilistic relations between hypotheses and evidence, even if probability theory is liberalized to allow for incoherent degrees of belief