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The article in the issue 9:3/4:

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Andrew Schumann, Roman Murawski, Jean-Yves Beziau, Kazimierz Trzęsicki, Alexandre Costa-Leite, Edelcio G. de Souza, Fabien Schang, Jens Lemanski, Michał Dobrzański, Tomasz Jarmużek, Mateusz Klonowski, Rafał Palczewski, Jerzy Pogonowski, Janusz Kaczmarek, Stanisław Krajewski, Marcin Trepczyński, Wojciech Krysztofiak, Marek Zirk-Sadowski,

Stanislaw Krajewski is a professor at the Faculty of Philosophy of the University of Warsaw. He has been involved in research in the field of logic and philosophy of mathematics as well as philosophy of dialogue, philosophy of religion and interfaith dialogue. He also co-authored the post-World War II section of the core exhibition in Polin, the Museum of the History of Polish Jews.


Anti-foundationalist Philosophy of Mathematics
and Mathematical Proofs

The Euclidean ideal of mathematics as well as all the foundational schools in
the philosophy of mathematics have been contested by the new approach,
called the “maverick” trend in the philosophy of mathematics. Several points
made by its main representatives are mentioned – from the revisability of
actual proofs to the stress on real mathematical practice as opposed to its
idealized reconstruction. Main features of real proofs are then mentioned; for
example, whether they are convincing, understandable, and/or explanatory.
Therefore, the new approach questions Hilbert’s Thesis, according to which a
correct mathematical proof is in principle reducible to a formal proof, based on
explicit axioms and logic.


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