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.

Audio

Video

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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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Greg Restall: Logical Pluralism | WSB #16

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Greg Restall

What is logical pluralism?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.

Audio

Video

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

Topics discussed

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

Sources

Logical Pluralism by Jc Beall and Greg Restall
consequently.org – Greg Restall’s website (see his excellent and accessible recent series on “Twelve Things I Love about Philosophical Logic“)…

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