Wittgenstein and Gödel: An Attempt to Make ‘Wittgenstein’s Objection’ Reasonable†

Philosophia Mathematica 26 (3):324-345 (2018)
Authors
Timm Lampert
Humboldt-University, Berlin
Abstract
According to some scholars, such as Rodych and Steiner, Wittgenstein objects to Gödel’s undecidability proof of his formula $$G$$, arguing that given a proof of $$G$$, one could relinquish the meta-mathematical interpretation of $$G$$ instead of relinquishing the assumption that Principia Mathematica is correct. Most scholars agree that such an objection, be it Wittgenstein’s or not, rests on an inadequate understanding of Gödel’s proof. In this paper, I argue that there is a possible reading of such an objection that is, in fact, reasonable and related to Gödel’s proof.
Keywords Gödel  Wittgenstein  undecidability  Peano Arithmetic
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DOI 10.1093/philmat/nkx017
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References found in this work BETA

Tractatus logico-philosophicus.Ludwig Wittgenstein - 2004 - Filosoficky Casopis 52:336-341.
Wittgenstein's Philosophy of Mathematics.Michael Dummett - 1997 - Journal of Philosophy 94 (7):166--85.
The Gödel Paradox and Wittgenstein's Reasons.Francesco Berto - 2009 - Philosophia Mathematica 17 (2):208-219.
Philosophical Grammar.Ludwig Wittgenstein, Rush Rhees & Anthony Kenny - 1975 - Philosophy and Rhetoric 8 (4):260-262.
Philosophical Remarks.Ludwig Wittgenstein, R. Hargreaves & R. White - 1976 - Philosophical Quarterly 26 (103):178-180.

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