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 that scientists of the future will look back with incredulity at a period in intellectual history when it was possible be taken seriously when claiming that Bayesian updating is the solution to the problem of scientific induction.
Jack Good once claimed to identify 46,656 different kinds of Bayesians. My first priority is therefore to clarify what I think should be regarded as the orthodoxy on Bayesian decision theory—the set of foundational assumptions that offer the fewest hostages to fortune. This takes up most of the book, since I take time out to review various aspects of probability theory along the way. My reason for spending so much time offering an ultra-orthodox review of standard decision theory is that I feel the need to deny numerous misapprehensions (both positive and negative) about what the theory really says—or what I think it ought to say—before getting on to my own attempt to extend a version of Bayesian decision theory to worlds larger than those considered by Savage (chapter 9).
I don't for one moment imagine that my extension of Bayesian decision theory comes anywhere near solving the problem of scientific induction, but I do think my approach will sometimes be found useful in applications. For example, my theory allows the mixed strategies of game theory to be extended to what I call muddled strategies (much as pure strategies were extended to mixed strategies by the creators of the theory).
What is the audience for this book? I hope that it will be read not just by the economics community from which I come myself, but also by statisticians and philosophers. If it only succeeds in bridging some . . .