### Abstract

Original language | English |
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Pages (from-to) | 208-219 |

Number of pages | 12 |

Journal | Philosophia Mathematica |

Volume | 17 |

Issue number | 2 |

Early online date | 3 Feb 2009 |

DOIs | |

Publication status | Published - 1 Jun 2009 |

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### Cite this

*Philosophia Mathematica*,

*17*(2), 208-219. https://doi.org/10.1093/philmat/nkp001

**The Gödel Paradox and Wittgenstein's Reasons.** / Berto, Francesco.

Research output: Contribution to journal › Article

*Philosophia Mathematica*, vol. 17, no. 2, pp. 208-219. https://doi.org/10.1093/philmat/nkp001

}

TY - JOUR

T1 - The Gödel Paradox and Wittgenstein's Reasons

AU - Berto, Francesco

PY - 2009/6/1

Y1 - 2009/6/1

N2 - 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.

AB - 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.

U2 - 10.1093/philmat/nkp001

DO - 10.1093/philmat/nkp001

M3 - Article

VL - 17

SP - 208

EP - 219

JO - Philosophia Mathematica

JF - Philosophia Mathematica

SN - 0031-8019

IS - 2

ER -