What is rationality? What is the solution to the problem of scientific induction? I don’t think it reasonable to expect sharp answers to such questions. One might as well ask for precise definitions of life or consciousness. But we can still try to push forward the frontier of rational decision theory beyond the Bayesian paradigm that represents the current orthodoxy.

Many people see no need for such an effort. They think that Bayesianism already provides the answers to all questions that might be asked. I believe that Bayesians of this stamp fail to understand that their theory applies only in what Jimmie Savage (1951) called a small world in his famous Foundations of Statistics. But the world of scientific inquiry is large—so much so ...

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