Abstract

In the Appendix I of his "Remarks on the Foundations of Mathematics", Wittgenstein elaborates a different interpretation of Gödel’s First Incompleteness Theorem, which we have come to refer to as "Gödel’s Theorem" or "Incompleteness Theorem". This nomenclature arises from the recognition that the so-called "Second Incompleteness Theorem" is essentially a corollary of the primary theorem. Wittgenstein aims to reassess Gödel’s conclusion that there exist true formulas not demonstrable within formal systems capable of representing a sufficient amount of arithmetic theory. Gödel’s initial reaction, as well as other commentators, was that Wittgenstein had not understood the proof. Nevertheless, recent commentators view worthy commentaries in wittgensteinian writings: some commentators, such as Juliet Floyd and Hilary Putnam, distinguish between mathematical proof and philosophical prose that surrounds the theorem, making it possible to understand Wittgenstein’s remarks. Ultimately, Wittgenstein’s observations serve as a lens through which Gödel’s theorem can be reconsidered within the realm of non-classical logics, such as paraconsistent logic.