The dispute between the Lviv-Warsaw and Krakow schools in the interwar period about the nature of mathematical knowledge

15.04.2024 | 15.04.2024

Andrew Schumann (University of Information Technology and Management in Rzeszow,
Poland), andrew.schumann@gmail.com

Since 1916, a heated discussion began between representatives of the Lviv-Warsaw school
and the Krakow school of mathematics. The debate touched on the topic of whether it is
possible to reduce mathematics to logic and set theory. On the one hand, Stanisław Zaremba
was a strong opponent of basing mathematics on set theory. He considered logic and set
theory to be auxiliary disciplines of mathematics, and not the main ones, as was the case
according to the approach of Zygmunt Janiszewski and within the framework of the Warsaw
school of Wacław Sierpiński and Stefan Banach. This debate is still relevant today, since the
possibility of such a reduction is not obvious even now. In this debate, Zaremba, and not Jan
Łukasiewicz, first expressed the idea of the three-valuedness in mathematics. The debate itself
is of great importance, especially by studying what arguments were used.

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