Creating modern probability. Its mathematics, physics and philosophy in historical perspective.
Repr.

*(English)*Zbl 0829.01012
Cambridge Studies in Probability, Induction, and Decision Theory. Cambridge: Cambridge University Press. x, 323 p. (1995).

The subject of this book is probability from 1900 onward with emphasis being laid on statistical physics, quantum theory, Mises’s frequentist theory, the measure-theoretic approach and subjective probability and exchangeability. A supplement on Oresme’s understanding of the relative frequencies of rational and irrational numbers is appended. The author looked up many sources including items in Russian and Swedish and some archival materials. The history of random processes is not studied comprehensively, chaos theory is left out and explanatory notes for non- physicists are missing. The main deficiencies, however, stem from the author’s superficial knowledge of the history of classical probability and tacit refusal to search for continuity between old and new. Then, there are many repetitions of statements, many linguistic errors and the sentences are often short and jerky. Examples of mistakes and omissions: Buffon’s needle problem “of 1777” (p. 5) is several decades older; Boole and Lomnicki are not mentioned in discussing the history of axiomatizing probability (p. 32); the notion of “true value” is not obsolete (p. 73): metrologists still use it having independently defined it (as Fourier did) as the mean of an infinitely large number of observations; the Ehrenfests’ urn model (p. 92) was first considered by D. Bernoulli, then by Laplace; Markov (pp. 132-133) had begun work on his “chains” in 1906 rather than in 1908 and the term appeared in 1926, not in the 1930’s; the probability of the next sunrise (p. 165) was first discussed by Price; an erroneous description of the Poisson theorem by Mises is repeated without comment (p. 182); normal numbers (p. 193) were intuitively anticipated by Lambert; the history of exchangeability (p. 246) should begin with Chuprov (Seneta 1987). The author avoids referring to the reviewer’s papers on Newton (p. 5) and Poincaré (p. 170), see Arch. Hist. Exact. Sci. 7, 217-243 (1971; Zbl 0236.01004) and 42, No. 2, 137-171 (1991; Zbl 0764.01008) resp., and excessively praised another author (p. 72n), cf. I. Schneider, Die Entwicklung der Wahrscheinlichkeitstheorie von den Anfängen bis 1933: Einführungen und Texte. Darmstadt (1988; Zbl 0681.01001).

Reviewer: O.B.Cheinine (Berlin)