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
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
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

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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?

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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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