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Lógos and Máthēma 2

Studies in the Philosophy of Logic and Mathematics


Roman Murawski

The volume consists of thirteen papers devoted to various problems of the philosophy of logic and mathematics. They can be divided into two groups. The first group contains papers devoted to some general problems of the philosophy of mathematics whereas the second group – papers devoted to the history of logic in Poland and to the work of Polish logicians and math-ematicians in the philosophy of mathematics and logic. Among considered problems are: meaning of reverse mathematics, proof in mathematics, the status of Church’s Thesis, phenomenology in the philosophy of mathematics, mathematics vs. theology, the problem of truth, philosophy of logic and mathematics in the interwar Poland.
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Philosophy of Logic and Mathematics in the Lvov School of Mathematics

Philosophy of Logic and Mathematics in the Lvov School of Mathematics


The aim of this chapter is to consider philosophical ideas concerning logic and mathematics developed in Lvov School of Mathematics. Views of Hugo Steinhaus (1887–1972), Stefan Banach (1892–1945), Eustachy Żyliński (1889–1954) and Leon Chwistek (1884–1944) will be analysed. In the case of the first three of them, there is no room for doubt that they belonged to this school. There may be some doubts in the case of Chwistek. We have included him into the Lvov school because since 1930 he was the chairman of the chair of mathematical logic at the faculty of mathematics and natural sciences of the Jan Kazimierz University in Lvov – though some part of his scientific career was connected with Cracow, he developed his main philosophical ideas just in Lvov.

Lvov School of Mathematics, accepting main ideas of Janiszewski’s program (1917), developed another specialization than the Warsaw school. In Warsaw, mainly set theory, topology and mathematical logic were developed. In Lvov, functional analysis dominated, which was initiated by Stefan Banach (his mathematical talent has been discovered by Steinhaus) and developed by Steinhaus, Stanisław Mazur, Władysław Orlicz, Juliusz Schauder, Stefan Kaczmarz, Stanisław Ulam and Władysław Nikliborc. It did not demand deeper studies of logic and foundations of mathematics as it was the case in Warsaw. Consequently, it is rather difficult to find philosophical remarks concerning mathematics in works of Lvov mathematicians. It could be also the result of the fact that logic as...

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