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