Philosophia Mathematica 17 (2):208-219 (2009)

Franz Berto
University of St. Andrews
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

Introduction to Mathematical Logic.Alonzo Church - 1956 - Princeton: Princeton University Press.
The Logic of Paradox.Graham Priest - 1979 - Journal of Philosophical Logic 8 (1):219 - 241.
Philosophy of Mathematics.Paul Benacerraf - 1964 - Englewood Cliffs, N.J., Prentice-Hall.

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Citations of this work BETA

Logic is a Moral Science.Hartley Slater - 2015 - Philosophy 90 (4):581-591.
A Note on Gödel, Priest and Naïve Proof.Massimiliano Carrara - forthcoming - Logic and Logical Philosophy:1.
Gödel's and Other Paradoxes.Hartley Slater - 2016 - Philosophical Investigations 39 (4):353-361.

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