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

Philosophia Mathematica 26 (3):324-345 (2018)
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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.

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Timm Lampert
Humboldt-University, Berlin

Citations of this work

Wittgenstein on Proof and Concept-Formation.Sorin Bangu - forthcoming - Philosophical Quarterly.

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References found in this work

The Principles of Mathematics.Bertrand Russell - 1903 - Cambridge, England: Allen & Unwin.
Tractatus logico-philosophicus.Ludwig Wittgenstein - 1922 - Filosoficky Casopis 52:336-341.
Introduction to mathematical logic.Alonzo Church - 1944 - Princeton,: Princeton University Press. Edited by C. Truesdell.
Remarks on the Foundations of Mathematics.Ludwig Wittgenstein - 1956 - Oxford: Macmillan. Edited by G. E. M. Anscombe, Rush Rhees & G. H. von Wright.
The Principles of Mathematics.Bertrand Russell - 1903 - Revue de Métaphysique et de Morale 11 (4):11-12.

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