Speaker:  Assoc. Prof. Zach Weber 

Could the world be inconsistent? Could mathematics? A paraconsistent logic makes it possible to have some inconsistency without total collapse. For over 60 years logicians have developed formal, rigorous approaches to paraconsistency and applied them to many areas, including mathematics. In this talk I will present a brief overview of this area, including its motivations and history (especially in Australasia), to show how there are two countervailing tendencies in paraconsistency: one, a more conservative “classical recapture” project, and the other a more radical and revisionary “truth glut” project. I will argue that the latter project is riskier but more philosophically coherent—and leaves us better prepared for the future in an inconsistent world. 

This talk is based in part on the work-in-porgress volume Paraconsistency in Mathematics in the Cambridge Elements series (Cambridge University Press), due out in 2022.