10. Bayesianism and What Is Likely
Our beliefs are not static. Ideally, our beliefs will change as new information becomes available. Otherwise, we are unreasonably stubborn. But our beliefs should not always change since the new information might not matter, or it might not be trustworthy. “A wise man proportions his belief to the evidence,” David Hume once intoned, but it does take some special sort of wisdom to know exactly how to proportion our beliefs to the evidence.
In a way, this is the central, practical problem in knowing: how should I revise my beliefs when new information comes in? When should I find new information compelling, and when should I be skeptical? When should I change my mind, and when should I hold fast? Anyone who has a good method for figuring this out would be an expert knower.
In fact, there is a method available for figuring this out—at least, in a wide range of cases—and that is what this chapter is about. The method is Bayesianism. But it is a little tricky to understand, so we will have to take some care in building up to it. We will begin by considering David Hume’s discussion of miracles and when it is rational for someone to believe the report of a miracle.