Anti-foundationalist Philosophy of Mathematics and Mathematical Proofs

Stanisław Krajewski 1
  • 1 University of Warsaw, , Krakowskie Przedmieście 3 Street, 00-927, Warszawa, Poland

Abstract

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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