The Gödel Paradox and Wittgenstein's Reasons

Francesco Berto

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

An interpretation of Wittgenstein's much criticized remarks on Gödel's First Incompleteness Theorem is provided in the light of paraconsistent arithmetic: in taking Gödel's proof as a paradoxical derivation, Wittgenstein was drawing the consequences of his deliberate rejection of the standard distinction between theory and metatheory. The reasoning behind the proof of the truth of the Gödel sentence is then performed within the formal system itself, which turns out to be inconsistent. It is shown that the features of paraconsistent arithmetics match with some intuitions underlying Wittgenstein's philosophy of mathematics, such as its strict finitism and the insistence on the decidability of any mathematical question.
Original languageEnglish
Pages (from-to)208-219
Number of pages12
JournalPhilosophia Mathematica
Volume17
Issue number2
Early online date3 Feb 2009
DOIs
Publication statusPublished - 1 Jun 2009

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