The philosophical concepts of probability in the works of Czech thinkers (Q2865027)

It is a common wisdom that probability theory played only a minor role in the research of Czech mathematicians before World War I, with the sole exception of Emanuel Czuber, who however left for Vienna relatively early. Althought this is not completely misleading as far as the mathematics of probability theory is concerned, the present monograph shows convincingly that the problems of the philosophical foundations of probability theory and/or of the applications of the calculus of probabilities in philosohical investigations were addressed quite often, some of the contributions being of an indisputable importance. (``Czech'' is interpreted in the book consequently in the territorial -- not the language -- sense which corresponds to the nature of the studied problem.)NEWLINENEWLINE The book is divided into eight chapters. The first is introductory, the core of it being the explanation of the philosophical approaches to probability that are relevant in the subsequent chapters, namely two epistemic interpretations (logical and subjective) and the frequentist one. The chapter also contains an interesting excursus on probabilistic topics included in secondary-school textbooks used in Czech lands in the second half of the 19th century. Chapter 2 treats the work of Bernard Bolzano. It has been already noted in the literature that Bolzano studied probability in his famous logical treatise \textit{Wissenschaftslehre} and used probabilistic reasoning in his textbook on the science of religion, but the author presents Bolzano's contribution much more thoroughly and traces its influence on later philosophical theories. Chapter 3 is devoted to T.\,G. Masaryk, a politician and philosopher whose interests were seemingly far from the natural sciences. The author shows, however, that Masaryk competently used probability theory in his effort to defend inductive reasoning agains Humean scepticism. The fourth chapter treats an almost forgotten early attempt of Václav Šimerka, a priest and secondary-school mathematics teacher, to develop a subjective approach to probability based on a notion of a ``strength of conviction''. The next chapter is about Karel Vorovka, a mathematician who turned to pure philosophy and became a professor of the philosophy of exact sciences at the Charles University in Prague in 1921. Chapter 6 is only loosely connected with the rest of the book, being devoted to a brief description of the early history of the theory of geometric probabilities. Particular attention is paid to contributions of E. Czuber, B. Hostinský and J. Baťa, so this is in a sense an introduction to the next chapter, which deals with the work of Emanuel Czuber. This author had a deep interest in all aspects of probability theory and the chapter shows that a further study of his books and papers on probability from both a mathematical and philosophical point of view is desirable and promising. The last chapter discusses the work of Otomar Pankraz, a private associate professor of actuarial mathematics at the Charles University in the thirties of the 20th century, who had a profound interest in the logical foundations of probability theory and, in particular, proposed (unfortunately, in papers written in Czech) an axiomatization of the concept of conditional probability almost identical with a later well known approach of A. Rényi.NEWLINENEWLINE The book is amended with a name index and an extensive bibliography.NEWLINENEWLINE The book is published in a series which addresses mainly mathematicians and mathematics teachers with a modest knowledge of the history of mathematics, so the author carefully and in detail explains the wider context in which the studied papers and books originated.NEWLINENEWLINE Many of the topics covered by the book have been already discussed in the literature, but Magdalena Hykšová's monograph is much more detailed and systematic and presents many new facts. For example, up to my knowledge, the chapter on O. Pankraz is the first publication about this interesting personality.