Wittgenstein et le lien entre la signification d’un énoncé mathématique et sa preuve

Philosophiques 39 (1):101-124 (2012)
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Abstract

The thesis according to which the meaning of a mathematical sentence is given by its proof was held by both Wittgenstein and the intuitionists, following Heyting and Dummett. In this paper, we clarify the meaning of this thesis for Wittgenstein, showing how his position differs from that of the intuitionists. We show how the thesis originates in his thoughts, from the middle period, about proofs by induction, and we sketch his answers to a number of objections, including the idea that, given the particular meaning he gives to this thesis, he cannot account for mathematical conjectures. We conclude by showing how his views find a favourable echo today in the paradigm of “proposition-as-type” and extensions of the Curry-Howard isomorphism from which this paradigm originates.

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Author Profiles

Mathieu Marion
Université du Québec à Montréal

Citations of this work

Intuition, Iteration, Induction.Mark van Atten - 2024 - Philosophia Mathematica 32 (1):34-81.

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References found in this work

Mathematical proof.G. H. Hardy - 1929 - Mind 38 (149):1-25.
Typed lambda-calculus in classical Zermelo-Frænkel set theory.Jean-Louis Krivine - 2001 - Archive for Mathematical Logic 40 (3):189-205.
On Wittgenstein's Philosophy of Mathematics.Hilary Putnam & James Conant - 1996 - Aristotelian Society Supplementary Volume 70 (1):243-266.
On Wittgenstein's philosophy of mathematics.Hilary Putnam - 1996 - Aristotelian Society Supplementary Volume 70:243-264.

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