Wittgenstein and Gödel: An attempt to make 'Wittgenstein's Objection' reasonable

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 (or ω- consistent). 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.