Some remarks on a book on the philosophy of probability

Balkanization of Probability").She also focuses on "the peculiar traits and epistemological implications of the various interpretations of probability."Even the "common sense probability" and the "complex pattern of ordinary uses of probability" require substantial amounts of mental agility and are intrinsically connected with the concepts of human fallibility as well as with the elusive concept of rationality.Actually, according to the exalted Pierre Simon de Laplace, "the most important questions in life are usually those of probability."Chapter 1 provides a well-organized and lucid description of the history of probability, and is successful in sketching various forerunners of the "modern probability" such as G. W. Leibniz (1646-1716), J. Bernoulli (1634-1705) and other members of the Bernoulli family, Thomas Bayes (1701-1761), Condorcet (1743-1794), and a more contemporary A. Quetelet (1796-1874).Finally the fathers of statistics: F. Galton, K. Pearson, R. A. Fisher, F. Y. Edgeworth and (very briefly) the nineteenth-and twentieth-century physicists (including Maxwell, Heisenberg, and Bohr).The last section, which deals with "Probability and Induction", includes succinct surveys of F. Bacon's, D. Hume's, J. S. Mill's, and Herschel's contributions that the present author found to be illuminating.A large number of footnotes in this chapter constitute a minor distraction from the continuous exposition.The author does not mention that scholars in the early eighteenth century, as a rule, rejected the notion of randomness (chance), emphasizing "necessity" instead (e.g.John Toland (1704), Anthony Collins (1715)).A short Chapter 2 contains the standard material of the laws and fundamental properties of probability, including conditional probabilities, Bayes' rule and a brief elementary description of Kolmogorov's axioms.Possibly the material on pp.42-46 could have been shortened -the avalanche of names may overwhelm an uninitiated reader.Chapter 3 describes "The Classical Interpretation" of probability and discusses P. S. de Laplace's groundbreaking contribution and his two famous essays: Théorie analytique des probabilités (1812) and Essai philosophique sur les probabilités (1814).The cornerstones of Laplace's theory are that causality is the overall rule governing the universe.This leads him to the embrace of empiricism, determinism, the principle of insufficient reason, equiprobability assumptions, the rule of succession, and the emphasis that probability is useful in all fields of knowledge.All this is presented in an attractive, fluent manner and the problems and objections to Laplace's position (the invalidating Bertrand's paradox) are also delineated.The author refers to Stigler's, Gillies', and P. Suppes' published remarks and comments.Possibly S. Zabell's several contributions could have been mentioned.The objection to the classical definition is that it can be used only in very simple and comparatively unimportant cases like games of chance.This objection was originally made by G. W. Leibniz in 1704 against J. Bernoulli's views and was stressed by von Mises.(Proponents of this definition claim that it is not the fault of the definition but rather our ignorance of the innermost mechanism that, apart from chance, contributes to the materialization or non-materialization of contingent events.)Classical probability is described in a scholarly and vivid manner in the

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