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The philosophy of mathematics and logic in the 1920s and 1930s in Poland. Translated from the Polish by Maria Kantor. (English) Zbl 1329.00127
Science Networks. Historical Studies 48. Basel: Birkhäuser/Springer (ISBN 978-3-0348-0830-9/hbk; 978-3-0348-0831-6/ebook). xi, 228 p. (2014).
The interwar period in Poland was a time of dynamic development of mathematics, logic and philosophy, mainly of analytical character. The term Lvov-Warsaw School is commonly used to cover all these contributions, although not all important thinkers ot this time in Poland were directly connected with Kazimierz Twardowski and his pupils. The book of Roman Murawski provides a valuable source of information on the most important scholars and their main achievements. Is is an extended version of a monograph previously published in Polish; in the new version one can find a presentation of some additional figures like B. Bornstein, M. Kokoszyńska or J. Salamucha,
In the first chapter the author presents the views of some, rather forgotten, predecessors of the later development of Polish mathematical and logical thought. The list includes six individuals representing different backgrounds and styles of thinking: Śniadecki, Hoene-Wroński, Struve, Biegański, Dickstein and Stamm. In the second chapter one can find a concise description of the most importantant representatives of two branches of the Polish School of Mathematics: Warsaw branch (Sierpiński, Janiszewski, Mazurkiewicz) and Lvov branch (Steinhaus, Banach, Żyliński and Chwistek). More than one hundred pages is devoted to the presentation of the Lvov-Warsaw School of Philosophy. Except 8 persons presented in the Polish version of the monograph (Łukasiewicz, Zawirski, Leśniewski, Kotarbiński, Ajdukiewicz, Tarski, Mostowski and Mehlberg) Murawski decided to add a presentation of views of the founder of the School, Kazimierz Twardowski, as well as Maria Kokoszyńska, and the views of so called Cracow Circle (Bocheński, Drewnowski, Salamucha) which focused on the application of formal tools to theological and philosophical analyses in the Thomist tradition. Short chapter 4 introduces original conceptions of Benedykt Bornstein who was rather an outsider. Finally, in chapter five, a Cracow Centre (Sleszyński, Zaremba, Wilkosz) is presented.
The book is clearly written and provides a lot of well documented (numerous quotes with Polish originals in the footnotes) information on one of the most interesting European school of analytical thinking. Additionally one can find bibliographical notes, extensive references and index. Provided descriptions and analyses of views of presented scholars are deep but readable. There are some drawbacks however: 1) some terminological decisions may seem doubtful, e.g. ‘argumentation’ as a translation of Polish ‘dowodzenie’; 2) despite substantial extension of the Polish version it seems that still some persons are missing, e.g. A. Lindenbaum.
This book is indispensable for anyone interested in the history of Polish mathematics and philosophy, as well as those who are interested in the general tradition of analytic thought in Europe.

MSC:
00A30 Philosophy of mathematics
03-02 Research exposition (monographs, survey articles) pertaining to mathematical logic and foundations
03A05 Philosophical and critical aspects of logic and foundations
03-03 History of mathematical logic and foundations
01A60 History of mathematics in the 20th century
01A72 Schools of mathematics
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