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The emergence of probability. A philosophical study of early ideas about probability, induction and statistical inference. 2nd ed. (English) Zbl 1140.01007

Cambridge: Cambridge University Press (ISBN 978-0-521-68557-3/pbk; 978-0-521-86655-2/hbk). 209 p. (2007).
A review of the first edition (1975) of this book is given in Zbl 0311.01004.
This edition is its reprint with additional 23 unnumbered pages of “Introduction 2006” mentioning the usual set of related new books (a few of them unworthy and one undeservedly praised to the skies and notorious for slandering the memory of Gauss).
The book is written by a well-read author endowed with a good style. As stated in the earlier review, it describes the rapid growth of the (future) theory of probability since mid-17th century, the development, of the dual concept of probability (statistical and subjective) beginning from signs and opinion and of the method of induction.
Reviewer’s remarks: There is no generally accepted definition of philosophy, but in any case it reinterprets (at least discusses) concepts and principles, which the author had not even attempted. Then, “emergence” is not history, but he had to describe the history of his subject, although abandoning Aristotle (p. 17) and forgetting Levi den Gerson (to whom the appearance of the method of induction is due) and Oresme (who discussed probability without defining it).
The missing philosophical and historical issues of considerable philosophical interest, some of which even belong to probability and/or statistics proper, include: hypotheses (and their discussion by Laplace); moral aspects of stochastic applications (only Pascal’s wager is described; but not the Petersburg paradox and the moral expectation, or the somewhat dangerous inoculation of small-pox, including religious objections to it); correlation; the Bayesian approach in statistics; true value of a measured constant; transition from mean values to frequencies; axiomatization versus frequentist theory; randomness; relevant problems posed by natural sciences.
Then, the history of probability is not separated into stages and its place in mathematics (pure or applied) is not discussed. De Moivre’s attempt to apply Newton’s philosophy for separating necessity from randomness (the initial aim of the theory of probability) is omitted, but life annuities (although not the related moral problems) are for some reason treated (non-mathematically) in detail.
Jakob (called Jacques!) Bernoulli’s law of large numbers is not adequately described and he is wrongly named as the last author to consider non-additive probabilities (p. 144) whereas the medieval doctrine of probabilism is not mentioned in this connection. Süssmilch is wrongly dismissed (p. 113). A mathematically mistaken proof of a conclusion made by Graunt is offered (p. 108), and the dates of publication of the memoirs of Arbuthnot, Daniel Bernoulli and Bayes are wrong (pp. 169, 125, 129).

MSC:

01A45 History of mathematics in the 17th century
60-03 History of probability theory
62-03 History of statistics
00A30 Philosophy of mathematics
01-02 Research exposition (monographs, survey articles) pertaining to history and biography

Citations:

Zbl 0311.01004
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