In the first half of my interview with Professor Greg Restall, he laid out logical pluralism: the view that there is more than one correct logical consequence relation. In this second half, he responds to objections. Specifically, he explains why it makes sense to admit inconsistent situations even if one believes, as he does, that all possible worlds are consistent. He also touches on the relationship between notions of deductive validity and reasoning norms. We then take an extended detour into the Preface paradox, the Liar paradox, dialetheism, and the relationship between proof theory and philosophy.
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.…
I recently came across a surprising claim: that logic is normative. That is, it is in some sense wrong to deny logic. The claim isn’t surprising because it’s controversial; instead, it’s so obvious that it’s initially jarring to see it spelled out explicitly. What is controversial is the claim that followed: that logic’s normativity isn’t universal. In other words, that it is sometimes rational to accept a deductive argument as valid, accept all its premises as true, and yet still deny its conclusion. Let’s see why this might be and whether it holds up.
A well-known paradox, the Preface, goes as follows: I assert each thing I state in this post. After all, if there were something here I did not wish to assert, I would not state it. However, I also assert that I’m wrong about at least one thing I say here. Write anything long enough, and chances are, no matter how thoroughly you check yourself, you’ll get at least one thing wrong. (This post isn’t very long, but as an amateur writing on a complex topic, the post needn’t be very long for me to feel confident that there’s at least one mistake in it.)
So far so good. Here’s the trouble. Let’s label my assertions in this post p0, p1, p2, … pn. I’m apparently asserting that each of those is true, but also denying that their conjunction – (p0 & p1 & p2 & … & pn) – is true.…