ARTICLES:
Anti-foundationalist Philosophy of Mathematics and Mathematical Proofs
Issue: 9:3/4 (the thirty fifth/sixth issue)
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.
Issue: ()