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Radical anti-realism, Wittgenstein and the length of proofs
Synthese 171 (3):419 - 432 (2009)
Abstract
After sketching an argument for radical anti-realism that does not appeal to human limitations but polynomial-time computability in its definition of feasibility, I revisit an argument by Wittgenstein on the surveyability of proofs, and then examine the consequences of its application to the notion of canonical proof in contemporary proof-theoretical-semantics.Author's Profile
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Citations of this work
Philosophical pictures about mathematics: Wittgenstein and contradiction.Hiroshi Ohtani - 2018 - Synthese 195 (5):2039-2063.
The later Wittgenstein’s guide to contradictions.Alessio Persichetti - 2019 - Synthese 198 (4):3783-3799.
Wittgenstein et la preuve mathématique comme vérifacteur.Mathieu Marion - 2011 - Philosophiques 38 (1):137-156.
Depth and Clarity * Felix Muhlholzer. Braucht die Mathematik eine Grundlegung? Eine Kommentar des Teils III von Wittgensteins Bemerkungen uber die Grundlagen der Mathematik [Does Mathematics need a Foundation? A Commentary on Part III of Wittgenstein's Remarks on the Foundations of Mathematics]. Frankfurt: Vittorio Klostermann, 2010. ISBN: 978-3-465-03667-8. Pp. xiv + 602. [REVIEW]Juliet Floyd - 2015 - Philosophia Mathematica 23 (2):255-276.
References found in this work
Natural deduction: a proof-theoretical study.Dag Prawitz - 1965 - Mineola, N.Y.: Dover Publications.
On Computable Numbers, with an Application to the Entscheidungsproblem.Alan Turing - 1936 - Proceedings of the London Mathematical Society 42 (1):230-265.
Computers and Intractability. A Guide to the Theory of NP-Completeness.Michael R. Garey & David S. Johnson - 1983 - Journal of Symbolic Logic 48 (2):498-500.
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