Ludwig Wittgenstein’s Critique of Gödel’s First Incompleteness Theorem
Abstract
Wittgenstein’s RFM remarks on Gödel’s First Incompleteness Theorem have been widely criticized, ridiculed or dismissed out of hand. The principal reason for this is negative evaluation of Wittgenstein’s critique is not Wittgenstein rejection of the standard interpretation of Gödel’s result but rather an exaggerated reaction to a alleged “mistake” Wittgenstein makes while discussing GIT. The aim of my paper, which due to Wittgenstein’s method is merely a draft, is to pull apart the different and the very distinct strands in these remarks to understand them in the context of Wittgenstein’s own philosophy of mathematics, and to determine what merit they have.
To understand Wittgenstein’s attitude I will point out his hostility towards mathematical realism, hostility based on the “rule-following considerations” and his conventionalism. As I shall show, the aim of Wittgenstein’s critique is not a proof itself but it’s certain philosophical interpretation (prose). On a number of occasions this leads Wittgenstein to say that we should simply ‘withdraw’ or ‘give up’ this interpretation as if the contradiction goes away with the natural language interpretation.
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