<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></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.

Anti-foundationalist Philosophy of Mathematics and Mathematical Proofs

Studia Humana

This work is licensed under the Creative Commons Attribution 4.0 International License.

{"article-title":"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...

Anti-foundationalist Philosophy of Mathematics and Mathematical Proofs

Publié en ligne: 11 nov. 2020

Pages: 154 - 164

DOI: https://doi.org/10.2478/sh-2020-0034

Mots clés
mathematical proof, axiomatic proof, formal proof, philosophy of mathematics, foundations of mathematics, mathematical practice, explanatory proof, analytic proof, Hilbert’s thesis

© 2020 Stanisław Krajewski, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Anti-foundationalist Philosophy of Mathematics and Mathematical Proofs

Publié en ligne: 11 nov. 2020

Pages: 154 - 164

DOI: https://doi.org/10.2478/sh-2020-0034

Mots clésmathematical proof, axiomatic proof, formal proof, philosophy of mathematics, foundations of mathematics, mathematical practice, explanatory proof, analytic proof, Hilbert’s thesis

© 2020 Stanisław Krajewski, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Mots clés
mathematical proof, axiomatic proof, formal proof, philosophy of mathematics, foundations of mathematics, mathematical practice, explanatory proof, analytic proof, Hilbert’s thesis