Stephen Read: Liar Paradox | WSB #41

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Stephen Read

“This sentence is false”. Is that sentence true or false? If it’s true, then what it says must hold; but what it says is that it’s false, so it must be false. But if it’s false, then what it says must not hold; but what it says is that it’s false, so it must not be false. But if it’s not false, it must be true. So if the sentence is true, it is false, and if it is false, it is true. The sentence, therefore, seems to be both true and false, which seems absurd.

Philosopher and logician Stephen Read is one of the preeminent scholars on this “liar paradox”. He is known, in large part, for rediscovering and defending a long forgotten solution to the paradox first proposed by the medieval philosopher Thomas Bradwardine. In this first half of our conversation, Read covers the paradox’s rich and influential history. It was first discovered, in its full form, in the 4th century BCE by Eubulides (who also first set down the sorites paradox). It became a central problem in the 20th century via its association with Russell’s Paradox, a major problem in the foundations of mathematics. Later in the century, two thinkers – Alfred Tarski and Saul Kripke – proposed monumentally influential theories of language and truth motivated, largely, by the paradox. But even after their contributions, the consensus is that the paradox remains unsolved. …

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Intro to the Liar, Part 2: Structure and Inclosure Schema | Who Shaves the Barber? #3

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, 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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Intro to the Liar, Part 1: Variations | Who Shaves the Barber? #2

Logic Philosophy Podcast

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

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“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 and Inclosure Schema

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

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