# Paraconsistent Reasoning in Science and Mathematics (June 11 - 13, 2014)

## Idea and Motivation

Paraconsistent logics restrict the inferential power of logics that trivialize inconsistent sets, such as Classical Logic. A large number of different paraconsistent logics have been developed in the previous and present century. They attempt to formalize reasoning from inconsistent premises, with the intent to explain how theories may be inconsistent, and yet meaningful and useful. Such non-trivial inconsistent theories definitely exist: this is abundantly shown in the history of science. There are moreover prototypical non-empirical cases among which naive set theory and naive truth theories are the most prominent ones.

## Program

### 11 June

Time | Topic |
---|---|

09:00 - 09:15 | Opening speech by Holger Andreas and Peter Verdée |

09:15 - 10:15 | Diderik Batens: “Transitory and Permanent Applications of Paraconsistency” |

10:15 - 10:30 | Coffee Break |

10:30 - 11.30 | Heinrich Wansing: “On the methodology of paraconsistent logic” |

11:30 - 11:45 | Coffee Break |

11:45 - 12:45 | Andreas Kapsner: “Why designate gluts?” |

12:45 - 14:30 | Lunch Break |

14:30 - 15:00 | Hitoshi Omori: “From paraconsistent logic to dialetheic logic ” |

15:00 - 15:30 | Cian Chartier: “Revision-Theoretic Truth and Degrees of Paradoxicality” |

15:30 - 16:00 | Coffee Break |

16:00 - 17:00 | Franz Berto: “Inconsistent Thinking, Fast and Slow” |

### 12 June

Time | Topic |
---|---|

09:15 - 10:15 | Graham Priest: “Models of Naive Set Theory Validating ZF” |

10:15 - 10:30 | Coffee Break |

10:30 - 11:30 | Itala Maria Loffredo D’Ottaviano: “Can a paraconsistent differential calculus extend the classical calculus?” |

11:30 - 11:45 | Coffee Break |

11:45 - 12:15 | Zach Weber: “Recursive functions for paraconsistent reasoners" |

12:15 - 12:45 | João Marcos: “What makes for a good paraconsistent negation?” |

12:45 - 14:30 | Lunch Break |

14:30 - 15:00 | Luis Estrada-González: “Prospects for triviality” |

15:00 - 15:30 | Nick Thomas: “On the interpretation of classical mathematics in naïve set theory.” |

15:30 - 16:00 | Coffee Break |

16:00 - 17.00 | Maarten McKubre-Jordens: “Doing Mathematics Paraconsistently. A manifesto.” |

17:00 - 17:30 | Fenner Tanswell: “Saving Proof from Paradox: Against the Inconsistency of Informal Mathematics” |

19:00 | Conference dinner in Restaurant “Schlosswirtschaft Schwaige” Address: Schloss Nymphenburg 30, 80638 München |

### 13 June

Time | Topic |
---|---|

09:15 - 10:15 | Bryson Brown: “On the Preservation of Reliability” |

10:15 - 10:30 | Coffee Break |

10:30 - 11:30 | Holger Andreas: “A Paraconsistent Generalization of Carnap’s Logic of Theoretical Terms” |

11:30 - 11:45 | Coffee Break |

11:45 - 12:15 | Corry Shores: “Instantaneous Contradiction in Motion and Perception: Modeling the Phenomenal Present with a Dialetheic Logic of Time” |

12:15 - 12:45 | David Ripley: “Confusion and contradiction” |

12:45 - 14:30 | Lunch Break |

14:30 - 15:00 | Maria Martinez: “Inconsistent and Functional Theories: A Classification” |

15:00 - 15:30 | Diego Tajer: “Revenge for Berto’s Law of Non-Contradiction” |

15:30 - 16:00 | Coffee Break |

16:00 - 17.00 | Otávio Bueno: “Inconsistent Scientific Theories: A Framework” |

## Acknowledgement:

Paraconsistent Reasoning in Science and Mathematics is supported by the Alexander von Humboldt Foundation and the Carl Friedrich von Siemens Stiftung.