The gödel paradox and Wittgenstein's reasons

Philosophia Mathematica 17 (2):208-219 (2009)
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.
Keywords Gödel's Incompleteness Theorems  Wittgenstein's philosophy of mathematics  Paraconsistency
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DOI 10.1093/philmat/nkp001
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References found in this work BETA
Graham Priest (1984). Logic of Paradox Revisited. Journal of Philosophical Logic 13 (2):153 - 179.

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Hartley Slater (2016). Gödel's and Other Paradoxes. Philosophical Investigations 39 (4):353-361.

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