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.

Audio

Video

Next week: The Epistemological Skyhook w/ Prof. Jim Slagle
Visit http://williamnava.com for more info!
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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WSB #2 – Intro to the Liar: Variations

Logic Philosophy Podcast

Episode 2: Intro to the Liar Paradox, Part 1: Variations

Download this episode / Watch on YouTube / RSS Feed / iTunes

“This sentence is false.” More ink has been spilled over the meaning of these four words than almost any other paradox in the history of philosophy. Why? What makes the Liar’s loopy reasoning more than just a party trick? How does the Liar challenge basic laws of logic and the meaning of truth? To understand the problems the Liar poses, we need to dive into its structure. What makes the Liar tick? Is it self-reference? What does it share with related paradoxes, like Russell’s paradox and the truth-teller paradox? What do the phenomena of “strengthened liars” and “circular liars” tell us about what’s at stake with this family of paradoxes?

Audio


Video

Topics discussed

0:04 – Intro
1:37 – Liar reasoning
2:40 – History of the Liar (Epimenides, Eubulides, Russell)
7:27 – Why it matters: excluded middle, non-contradiction, t-schema, self-reference
11:56 – 3 ways out
13:39 – “I am hereby lying”
14:57 – Circular liar
16:30 – Strengthened (revenge) liars
20:33 – Structure of the Liar
24:21 – Set theory disclaimer
25:57 – Russell’s paradox
28:30 – Properties
29:40 – Truth teller paradox
31:54 – Principle of uniform solution

Next week: Intro to the Liar, Part 2: Structure

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

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A Quick Note on the “It’s Meaningless” Solution to the Liar Paradox

In an earlier post, I discuss one good reason to reject the solution to the Liar paradox that says that it’s meaningless: it means calling some other sentences, like “This sentence is in Japanese” and “This sentence has five words” meaningless, though they seem to be obviously meaningful.

Anyone who defends this solution has to bite the bullet on these sentences. It’s a tough bullet to bite, but at first it doesn’t seem implausible. Maybe those sentences only seem to be meaningful, though they aren’t really.

I came across three sentences today that convince me that rejecting all self-referential sentences is, in fact, utterly ridiculous. I found them in Tim Urban’s newest amazing article on Elon Musks’ newest mind-blowing venture, Neuralink. (By the way: go read it. Now. Elon Musk is turning humanity into the Starchild from the end of 2001 and you’re reading about loopy sentences? Get out of here!)

Here are the three sentences:

That’s why we still communicate using technology Bok invented, it’s why I’m typing this sentence at about a 20th of the speed that I’m thinking it, and it’s why brain-related ailments still leave so many lives badly impaired or lost altogether.

And

Right now, your eyes are making a specific set of horizontal movements that allow you to read this sentence.

And

None of this stuff will take any effort or thought—we’ll all get very good at it and it’ll feel as automatic and subconscious as moving your eyes to read this sentence does to you now.

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