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Lógos and Máthēma 2

Studies in the Philosophy of Logic and Mathematics

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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 Warsaw School of Mathematical Logic

Philosophy of Logic and Mathematics in the Warsaw School of Mathematical Logic

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The Warsaw School of Mathematical Logic was a part of the Lvov–Warsaw School of Philosophy. It belonged to the most important centres of mathematical logic between the wars. It is natural to ask what were the philosophical views and attitudes of logicians in Warsaw towards mathematics and logic itself. One can also ask whether and to what extent those views influenced formal and technical research, whether that research had its source in philosophical considerations or was it independent of any philosophical presuppositions. Did the philosophical views bound the technical investigations or were they without meaning for them?

The attitude of Polish logicians and mathematicians towards the philosophy of mathematics can be shortly characterized as follows: they saw the mathematical and philosophical foundations of mathematics as independent although connected in a way and indispensable for understanding logical and mathematical activity. With two exceptions (Chwistek and Leśniewski) they represented a view guided by the following two principles:

What were the sources of such an attitude? One can indicate two of them. The first one can be exemplified by Sierpiński’s work on the axiom of choice (AC) and its applications in mathematics. In his paper (1918) on the role of AC, Sierpiński distinguished two independent questions:

According to Sierpiński, the second issue should be investigated independently of philosophical inclinations concerning the problem whether the AC is to be accepted or not. This opinion was included in all editions of Sierpiński’s textbook...

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