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Modern Czech Logic within the Philosophy of Mathematics

Standard - GACR GA25-16489S [Registered results] 2025 - 2027

Principal Investigator: RNDr. Zuzana Haniková, Ph.D.

Rieger, Vopěnka, and Hájek are pioneering figures in Czech formal logic. Their paradigmshifting works span roughly the second half of the twentieth century. Vopěnka and Hájek promoted new axiomatic theories with foundational ambitions.

This project targets the examination of the body of their work from the present-day, pluralist position in the philosophy of mathematics, which we claim they instantiate. Vopěnka's contribution to foundations of mathematics is an opportunity to critically assess the possibility of combining the tradition represented by Frege, Dedekind and Cantor and the phenomenological tradition to which Vopěnka made claims under an indirect influence of Patočka.

The project will focus on several key areas such as set-theoretic ontology or finitism and the notion of infinity. Individual works will be consistently explicated within regional and historical contexts.

The comprehensive aim of the project is exposition, assessment, and development of concrete topics in the philosophy of mathematics, featured in modern Czech logic, emphasizing the work of Vopěnka, Rieger, and Hájek. Mapping out transfer between relevant researchers, in Czechia and abroad.