What is logical pluralism? Greg Restall, logician and Professor of Philosophy from the University of Melbourne joins me to answer this question.
When we study logic, we’re concerned with consequence or entailment: what follows from what. But what are the criteria for being “consequence”? Professor Restall says there are three: necessity, formality, and normativity. Given these criteria, he argues there is more than one relation worthy of the name “consequence”. In other words, there is more than one system of logic that correctly represents our informal grasp of necessary entailment. This is because logical rules operate differently depending on the sort of “case” they’re functioning in. Among various, Professor Restall highlights two types of cases: “possible worlds” and “situations”. The first fit classical logic, the second paraconsistent logic. Though they differ on what kinds of arguments are valid, they both correctly represent deductive reasoning. Professor Restall explains why this makes perfect sense.
Special thanks to Jackie Blum for the podcast art, and The Tin Box for the theme music.
0:20 – Introduction to Greg Restall
1:49 – What is logic about?
12:41 – The metaphysics of logic
21:20 – What is logical pluralism?
22:52 – The criteria for consequence
24:32 – Necessity
25:37 – Formality
27:17 – Normativity
33:15 – The role of cases: classical v. paraconsistent logics
39:10 – Possible worlds v. situations