David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
Grazer Philosophische Studien 71 (1):57-86 (2006)
In Part III of his Remarks on the Foundations of Mathematics Wittgenstein deals with what he calls the surveyability of proofs. By this he means that mathematical proofs can be reproduced with certainty and in the manner in which we reproduce pictures. There are remarkable similarities between Wittgenstein's view of proofs and Hilbert's, but Wittgenstein, unlike Hilbert, uses his view mainly in critical intent. He tries to undermine foundational systems in mathematics, like logicist or set theoretic ones, by stressing the unsurveyability of the proof-patterns occurring in them. Wittgenstein presents two main arguments against foundational endeavours of this sort. First, he shows that there are problems with the criteria of identity for the unsurveyable proof-patterns, and second, he points out that by making these patterns surveyable, we rely on concepts and procedures which go beyond the foundational frameworks. When we take these concepts and procedures seriously, mathematics does not appear as a uniform system, but as a mixture of different techniques.
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
Felix Mühlhölzer (2010). Mathematical Intuition and Natural Numbers: A Critical Discussion. [REVIEW] Erkenntnis 73 (2):265–292.
Ryan Dawson (2014). Wittgenstein on Pure and Applied Mathematics. Synthese 191 (17):4131-4148.
Ryan Dawson (2015). Wittgenstein on Set Theory and the Enormously Big. Philosophical Investigations 39 (3):n/a-n/a.
Felix Mühlhölzer (2010). Mathematical Intuition and Natural Numbers: A Critical Discussion. Erkenntnis 73 (2):265-292.
Similar books and articles
Wenceslao J. Gonzalez (1991). Intuitionistic Mathematics and Wittgenstein. History and Philosophy of Logic 12 (2):167-183.
Felix Mühlhölzer (2001). Wittgenstein and the Regular Heptagon. Grazer Philosophische Studien 62 (1):215-247.
Cyrus Panjvani (2006). Wittgenstein and Strong Mathematical Verificationism. Philosophical Quarterly 56 (224):406–425.
Francesco Berto (2009). The Gödel Paradox and Wittgenstein's Reasons. Philosophia Mathematica 17 (2):208-219.
Mark Addis (1995). Surveyability and the Sorites Paradox. Philosophia Mathematica 3 (2):157-165.
James Robert Brown (1999). Philosophy of Mathematics: An Introduction to the World of Proofs and Pictures. Routledge.
Mark Steiner (2001). Wittgenstein as His Own Worst Enemy: The Case of Gödel's Theorem. Philosophia Mathematica 9 (3):257-279.
Cesare Cozzo (2004). Rule-Following and the Objectivity of Proof. In Annalisa Coliva & Eva Picardi (eds.), Wittgenstein Today. Il Poligrafo 185--200.
James Robert Brown (2008). Philosophy of Mathematics: A Contemporary Introduction to the World of Proofs and Pictures. Routledge.
Edwin Coleman (2009). The Surveyability of Long Proofs. Foundations of Science 14 (1-2):27-43.
Added to index2009-01-28
Total downloads136 ( #27,675 of 1,906,981 )
Recent downloads (6 months)7 ( #109,456 of 1,906,981 )
How can I increase my downloads?