Under what conditions does evidence confirm a scientific hypothesis? And why under those conditions only? There is an answer to these questions that is both precise and general, and which fits well with scientific practice. I allude to the Bayesian theory of confirmation. This theory represents scientists as having subjective probabilities for hypotheses, and it uses probability theory (notably Bayes' theorem) to explain when, and why, evidence confirms scientific theories.

I think Bayesian confirmation theory is correct as far as it goes and represents a great advance in the theory of confirmation. But its foundations have sometimes been seen as shaky. Can we really say that scientists have subjective probabilities for scientific theories – or even that rationality requires this? One purpose of the present book is to address this foundational issue. In Chapter 1, I defend an interpretation of subjective probability that is in the spirit of Frank Ramsey. On this interpretation, a person has subjective probabilities if the person has preferences satisfying certain conditions. In Chapters 2 and 3 I give reasons for thinking that these conditions are requirements of rationality. It follows that rational people have (not necessarily precise) subjective probabilities. In Chapter 4, I apply this general argument to science, to conclude that rational scientists have (not necessarily precise) subjective probabilities for scientific theories.

The presupposition of Bayesian confirmation theory that I have been discussing is a synchronic principle of rationality; it says that a rational scientist at a given time has subjective probabilities.