# The Consistency of Peano Arithmetic. A Defeasible Perspective

Title | The Consistency of Peano Arithmetic. A Defeasible Perspective |

Publication Type | Book Chapter (with title) |

Year of Publication | 2014 |

Authors | Batens, D |

Secondary Authors | Allo, P, Van Kerkhove, B |

Book Title | Modestly Radical or Radically Modest. Festschrift for Jean Paul Van Bendegem on the Occasion of His 60th Birthday |

Pages | 11–59 |

Publisher | College Publications |

Abstract | This paper proposes to replace \sys{PA}, Peano Arithmetic, by a theory \sys{APA} defined in terms of (i) a set of axioms that is classically equivalent to the Peano axioms and (ii) a defeasible logic that minimizes inconsistency, viz.\ an inconsistency-adaptive logic. If \sys{PA} is consistent, its set of theorems coincides with the set of \sys{APA}-theorems. If \sys{PA} is inconsistent, \sys{APA} is non-trivial and has the following remarkable property: there is a unique non-standard number that is its own successor and every `desirable' \sys{PA}-theorem is retained if restricted to the other numbers. The restriction can be expressed in the language of arithmetic. And there is much more. |

Citation Key | D:JP |

UGent Biblio Link | http://hdl.handle.net/1854/LU-5675576 |
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