Paraconsistent Reasoning in Science and Mathematics

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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.

The great variety of paraconsistent logics gives rise to various, interrelated questions:

  1. What are the desiderata a paraconsistent logic should satisfy?
  2. Which paraconsistent logics score well given certain desiderata?
  3. Is there prospect of a universal approach to paraconsistent reasoning with axiomatic theories?
  4. Comparison of paraconsistent approaches in terms of inferential power.
  5. To what extent is reasoning about sets structurally analogous to reasoning about truth?
  6. To what extent is reasoning about sets structurally analogous to reasoning with inconsistent axiomatic theories in the natural sciences?
  7. Is paraconsistent logic a normative or descriptive discipline, or intermediate between these two options?
  8. Which inconsistent but non-trivial axiomatic theories are well understood by which types of paraconsistent approaches?

This conference aims to address these questions from different perspectives in order

  1. to obtain a representative overview of the state of the art in paraconsistent logics,
  2. to come up with fresh ideas for the future of paraconsistency, and
  3. to facilitate debate and collaboration beyond the borders of the different schools of paraconsistency.


Holger Andreas (, LMU Munich, Germany
Peter Verdée (, Ghent University, Belgium


Here you learn more about the submission.