Gillian Russell: Logical Nihilism | Who Shaves the Barber? #53

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Gillian Russell

In recent years, philosophers have debated the question of logical pluralism: the view that there is more than one correct logic (see my interview with Greg Restall on this very issue). The idea, roughly, is that which putative logical laws hold depends on what sorts of “cases” we take logic to be about; different kinds of cases yield different (but equally legitimate) logics. A common logical monist objection is to say that a form of argument is only a logical law if it applies in all cases. If this is true, it raises the question: what argument forms do hold in all cases? At this point in the debate, a third position becomes viable, defined by the answer: none.

Gillian Russell, a philosopher of language and logic, argues both that applying in all cases is necessary for qualifying as a logical law; and that no argument form applies in all cases. As such, she believes there are no logical laws. Much of our discussion surrounds her claim that no argument form applies to all cases. Is this really true even of the law of non-contradiction, the “law” that says that ‘A and not-A’ can never be true? Of conjunction elimination (‘A and B’ entails ‘A’)? Of identity (‘A’ entails ‘A’)? Russell runs through purported counterexamples to these laws; what’s more, she illustrates a method for conjuring counterexamples to any proposed “law”.

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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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Greg Restall: Logical Pluralism | WSB #16

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Greg Restall

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.

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Next week: Greg Restall: Objections to Logical Pluralism, and the Preface and Liar Paradoxes

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.…

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