Greg Restall: Objections to Logical Pluralism and the Preface and Liar Paradoxes | Who Shaves the Barber? #17

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Greg Restall

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.

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Next week: Tomasz Kaye, Pt. 1: Foundations for Political Philosophy

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Special thanks to Jackie Blum for the podcast art, and The Tin Box for the theme music.

Topics discussed

0:38 – Logical pluralism recap
1:00 – Why admit inconsistent situations?
15:24 – Relationship between logic, reasoning, and normativity
21:50 – Preface paradox and normativity
34:10 – Dialetheism
38:15 – Bradwardine on the Liar
42:15 – Becoming a logician
44:30 – Proof theory and philosophy

Sources

Logical Pluralism by Jc Beall and Greg Restall
consequently.org – Greg Restall’s website
Proof Theory and Philosophy by Greg Restall (book manuscript in progress)
The Liar Paradox from John Buridan to Thomas Bradwardine” by Stephen Read
Models of Liars in Bradwardine’s Theory of Truth” by Greg Restall
Normativity of Logic and the Preface Paradox” by William Nava…

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Normativity of Logic and the Preface Paradox

normativity logic

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.

The Preface

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.…

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