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Good thinking. The foundations of probability and its applications. (English) Zbl 0583.60001
Minneapolis: University of Minnesota Press. XVIII, 332 p. hbk: {$} 35.00; pbk: {$} 14.95 (1983).
If the quality of the index is a sure guide to the quality of the book, this must be just about the best book ever. There is an index of names, of course. There is also a partial bibliography of the author, running to a selection among some 1517 entries. (One must, after all, hold something back for the next collection!) There is a subject index to the bibliography which is almost a guided tour to the thoughts of I. J. Good. There is, of course, a subject index to the articles reprinted in the collection. (The latter contains the entry: ”Joke, as an excuse for rejecting a paper.”) And, finally, there is the usual index of works cited. (The latter is incomplete, though there is nothing referred to in the volume that the energetic student can’t track down. The difficulty is the references to ”X said so-and-so at this conference, but… ” The only way to find out what X really meant, in context, is to track down the conference proceedings. The volume is divided into five parts: Bayesian rationality (comprising four articles in defence of Baysianism); Probability, containing six articles, including the early intervalist article, ”Subjective probability as the measure of a non-measurable set;” Corroboration, hypothesis testing, induction and simplicity: five articles, all essentially on induction; Information and surprise: five papers about uncertainty; and three papers on Causality and explanation. These last papers are quite strictly philosophical, but the other sections contain papers of a spectrum of flavors from the quite technically statistical or mathematical, to the quite personally speculative, to the quite down to earth (e.g., how to measure the value of a position in chess, ”Dynamic probability, computer chess, and the measurement of knowledge”). All of these papers are thought-provoking (although some may also be provoking in the more general sense). Joking aside, this is an extraordinary collection of papers, documenting creativity in both statistics and philosophy, extending over some 35 years. There may be nothing in these papers that constitutes (as we now see it) a monumental theorem or breakthrough. But there is no paper that is not in some degree inspiring; and almost every reader concerned with the foundations of probability and statistics, or with the philosophical foundations of induction and probability, will find ideas that - even though he may have read these papers before - are of immediate current use to him. In short, this is a highly recommended book. It is recommended exactly in the sense of its title: It is valuable to watch (read?) Jack Good think; it would be quite another matter - and one I would not endorse - to suggest that one should merely attend respectfully to his conclusions.
Reviewer: H.E.Kyburg jun

60A05Axioms of probability theory
60-02Research monographs (probability theory)
62A01Foundations and philosophical topics in statistics