Episode 3: Intro to the Liar Paradox, Part 2: Structure and the Inclosure Schema
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.
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.
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?
“The Structure of the Paradoxes of Self-Reference” by Graham Priest
“Dialetheic Vagueness” by Graham Priest
“This Proposition Is Not True: C.S. Peirce and the Liar Paradox” by Richard Kenneth Atkins
Paradoxes by R. M Sainsbury