### Abstract

Original language | English |
---|---|

Title of host publication | Paraconsistency |

Subtitle of host publication | Logic and Applications |

Editors | K. Tanaka, F. Berto, E. Mares, F. Paoli |

Publisher | Springer |

Pages | 257-276 |

Number of pages | 20 |

Volume | 26 |

ISBN (Electronic) | 978-94-007-4438-7 |

ISBN (Print) | 978-94-007-4437-0 |

DOIs | |

Publication status | Published - 2012 |

### Publication series

Name | Logic, Epistemology, and the Unity of Science |
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Publisher | Springer |

Volume | 26 |

### Fingerprint

### Cite this

*Paraconsistency: Logic and Applications*(Vol. 26, pp. 257-276). (Logic, Epistemology, and the Unity of Science; Vol. 26). Springer . https://doi.org/10.1007/978-94-007-4438-7_14

**Wittgenstein on Incompleteness Makes Paraconsistent Sense.** / Berto, Francesco.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Paraconsistency: Logic and Applications.*vol. 26, Logic, Epistemology, and the Unity of Science, vol. 26, Springer , pp. 257-276. https://doi.org/10.1007/978-94-007-4438-7_14

}

TY - CHAP

T1 - Wittgenstein on Incompleteness Makes Paraconsistent Sense

AU - Berto, Francesco

N1 - Acknowledgements The non-technical parts of this work draw on a paper published in Philosophia Mathematica, 17: 208–219, with the title “The Gödel Paradox and Wittgenstein’s Reasons”. I am grateful to Oxford University Press and to the Editors of Philosophia Mathematica for permission to reuse that material. I am also grateful to an anonymous referee for helpful comments on this expanded version

PY - 2012

Y1 - 2012

N2 - I provide an interpretation of Wittgenstein’s much criticised remarks on Gödel’s First Incompleteness Theorem in a paraconsistent framework: in taking Gödel’s proof as a paradoxical derivation, Wittgenstein was consequent upon 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. I show that the model-theoretic features of paraconsistent arithmetics match with many intuitions underlying Wittgenstein’s philosophy of mathematics, such as its strict finitism and the insistence on the decidability of any mathematical question.

AB - I provide an interpretation of Wittgenstein’s much criticised remarks on Gödel’s First Incompleteness Theorem in a paraconsistent framework: in taking Gödel’s proof as a paradoxical derivation, Wittgenstein was consequent upon 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. I show that the model-theoretic features of paraconsistent arithmetics match with many intuitions underlying Wittgenstein’s philosophy of mathematics, such as its strict finitism and the insistence on the decidability of any mathematical question.

U2 - 10.1007/978-94-007-4438-7_14

DO - 10.1007/978-94-007-4438-7_14

M3 - Chapter

SN - 978-94-007-4437-0

VL - 26

T3 - Logic, Epistemology, and the Unity of Science

SP - 257

EP - 276

BT - Paraconsistency

A2 - Tanaka, K.

A2 - Berto, F.

A2 - Mares, E.

A2 - Paoli, F.

PB - Springer

ER -