MoL-2017-31: The paradoxes of self-negation

MoL-2017-31: Janzen, Albert (2017) The paradoxes of self-negation. [Report]

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In Beyond the Limits of Thought Graham Priest presents the Inclosure Schema as the underlying structure of the paradoxes of self-reference. I argue that while the paradoxes fit the Inclosure Schema, (i) in case of Burali-Forti, Mirimanoff, 5th Antinomy, Richard, König and Berry one premise of the schema is not true and (ii) in case of the Liar, Russell and Grelling the schema does not capture what is essential to the paradoxes. For the Liar, Russell and Grelling I construct a new schema that reveals their highly analogous structure and proof of contradiction. At the heart of this schema is the notion of self-negation, a statement of the form A iff ¬ A. By classical logic, self-negation always leads to contradiction and therefore describes a structure that can be found only in paradoxical cases. In this respect, the schema describes what is essential to the paradoxes. As a result, if one were to give up self-negation to solve the paradoxes one would not give up non-paradoxical cases. Finally, I provide an analysis of No-no and Yablo that also involves self-negation. Based on this analysis, I establish a second schema involving self-negation that captures Nono and Yablo.

Item Type: Report
Report Nr: MoL-2017-31
Series Name: Master of Logic Thesis (MoL) Series
Year: 2017
Subjects: Logic
Depositing User: Dr Marco Vervoort
Date Deposited: 21 Dec 2017 15:46
Last Modified: 18 Jan 2018 14:27

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