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

Visit http://williamnava.com for more info!
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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Against Certainty, Pt. 2: Logic | Who Shaves the Barber? #13

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What about 2+2=4? Can we be 100% sure of that?

In this second part of my case against 100% certainty, I tackle claims to logical certainty. These include appeals to the three fundamental laws of logic: the Law of Excluded Middle, the Law of Non-Contradiction, and the Law of Identity. To call excluded middle into doubt, I discuss non-referring terms, vagueness, fuzzy logic, and Aristotle’s problem of future contingents. For contradiction, the topics are legal contradictions, the Liar paradox, and Zeno’s Arrow. To argue against certainty of the law of identity, I cover Theseus’s ship, problems with time, problems of mereology, and the universe of symmetrical spheres. I then argue that even claims like “2+2=4” and “bachelors are bachelors” can’t be fully foolproof. Finally, a quick barrage of skeptical concerns – concerns that, while they may not be enough to justify a self-defeating view like skepticism, are enough to block claims to 100% certainty.

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Next week: The Case for Anarchism, Pt. 1: Social Ontology
Special thanks for Jackie Blum for the podcast art, and The Tin Box for the theme music.

Topics discussed:

0:20 – Quick pt. 1 recap
1:21 – Introducing claims to logical certainty
2:21 – Classical logic, syllogistic logic, and the 3 laws
5:48 – Law of Excluded Middle
6:45 – Non-referring terms: the present king of France
9:16 – Vagueness and fuzzy logic
12:11 – Future contingents
13:51 – Law of Non-Contradiction – DeMorgan’s Law
15:38 – The legal case
18:22 – Liar paradox
22:09 – Zeno’s arrow
26:45 – Law of Identity – Theseus’s ship
29:26 – Content of an instant
31:17 – Mereological – Tibbles
36:06 – Symmetrical spheres
37:47 – Do we understand identity?

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WSB #3 – Intro to the Liar: Structure and Inclosure Schema

Inclosure schema

Episode 3: Intro to the Liar Paradox, Part 2: Structure and the Inclosure Schema

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How can we tell if a paradox is really of the Liar family? Bertrand Russell proposed a structure that Graham Priest has called the “inclosure schema” – a mechanism meant to identify what drives self-referential paradoxes like the Liar and Russell’s. In this episode, I break down the technical details of the inclosure schema to show how it fits the paradoxes in question and allows us to tell apart Liar-type paradoxes from those that aren’t. I also look at some problems with the schema and how they might be solved. I conclude with an overview of a solution to the Liar: one favored by C.S. Peirce.

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Next week: The Epistemological Skyhook w/ Prof. Jim Slagle, Pt. 1: Plantinga
Special thanks for Jackie Blum for the podcast art, and The Tin Box for the theme music.

Topics discussed

0:49 – Problems with the Principle of Uniform Solution
5:19 – Inclosure Schema
9:05 – Inclosure Schema: Russell’s paradox
14:46 – Inclosure Schema: The Barber
17:04 – Inclosure Schema: The Liar
19:27 – Problems with the Inclosure Schema
23:27 – Salvaging the Inclosure Schema
25:00 – Difference between the Liar and Russell’s paradox
28:34 – List of Liar/Russell variations (Infallible Seducer)
32:00 – C.S. Peirce: automatic truth assertion
36:55 – Outro: necessarily self-referential?

Sources

The Structure of the Paradoxes of Self-Reference” by Graham Priest
“Dialetheic Vagueness” by Graham Priest
“This Proposition Is Not True: C.S.…

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