How much inconsistency is too much inconsistency?

Zach Weber (University of Otago)

Zach Weber (Otago) will present "How much inconsistency is too much inconsistency?" at 12 in Old Quad G10 on 23 November.

Abstract: A longstanding project is to investigate dialetheic paraconsistent theories (of sets, semantics, and more). Recent, and not so recent, results make clear that there are some very substantial problems for any would-be-inconsistent theorist [e.g. Field, Lederman, and {\O}gaard 2017; unpublished work by Young, Batens, others]---casting the future for this project as ``dim, at best". In this talk I will discuss two such problems, around two questions: (1) how much inconsistency is too much inconsistency? and (2) how much extensionality is too much extensionality? These questions put the focus on what accounts of negation and implication are viable for (this version of) the paraconsistent project. We will look at some concrete examples, including the looming spectre that *every argument is invalid*, with the aim of formulating some constraints on answers to the title question.