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Proof and the evolution of mathematics

Synthese 111 (2):133-146 (1997)

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  1. A Critique of a Formalist-Mechanist Version of the Justification of Arguments in Mathematicians' Proof Practices.Yehuda Rav - 2007 - Philosophia Mathematica 15 (3):291-320.
    In a recent article, Azzouni has argued in favor of a version of formalism according to which ordinary mathematical proofs indicate mechanically checkable derivations. This is taken to account for the quasi-universal agreement among mathematicians on the validity of their proofs. Here, the author subjects these claims to a critical examination, recalls the technical details about formalization and mechanical checking of proofs, and illustrates the main argument with aanalysis of examples. In the author's view, much of mathematical reasoning presents genuine (...)
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  • Church's Thesis: Prelude to a Proof.Janet Folina - 1998 - Philosophia Mathematica 6 (3):302-323.
  • The Origins of Eternal Truth in Modern Mathematics: Hilbert to Bourbaki and Beyond.Leo Corry - 1997 - Science in Context 10 (2):253-296.