Paraconsistent logic and inconsistent mathematics
Philosophy Department University of Otago
Date: Tuesday 23 July 2019
Time: 2:00 p.m.
Place: Room 241, 2nd floor, Science III building
There are nowadays many different well-understood systems of logic: classical, intuitionistic, and paraconsistent, to name a few. This introductory talk will explain some of the motivations for studying paraconsistent logic—systems of formal logic developed since the 1970s that make it possible to have some local inconsistency without global absurdity. We will look at some of the basic details of how a paraconsistent logic works in practice, and apply it to some elementary foundational mathematics, in particular the original ‘naive’ set theory of Cantor and Dedekind, and some point-set topology. I’ll conclude with a brief discussion of the place of non-classical logic and prospects for the wider inconsistent mathematics program as it stands today.