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The Law of Non-Contradiction$
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Graham Priest, JC Beall, and Bradley Armour-Garb

Print publication date: 2004

Print ISBN-13: 9780199265176

Published to Oxford Scholarship Online: May 2010

DOI: 10.1093/acprof:oso/9780199265176.001.0001

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The Barber, Russell's Paradox, Catch-22, God and More: A Defence of a Wittgensteinian Conception of Contradiction

The Barber, Russell's Paradox, Catch-22, God and More: A Defence of a Wittgensteinian Conception of Contradiction

Chapter:
(p.295) 18 The Barber, Russell's Paradox, Catch-22, God and More: A Defence of a Wittgensteinian Conception of Contradiction
Source:
The Law of Non-Contradiction
Author(s):

Laurence Goldstein

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199265176.003.0019

Although he toyed with the idea that contradictions in mathematics are harmless, Wittgenstein did not subscribe to the claim that they are true. He took the highly distinctive line that contradictions are neither true nor false, a view he defended early and late. He argued that contradictions are not statements and hence are not in the true/false game; this appears to be Aristotle's view too. This chapter considers a variety of paradoxes, including the Barber, Russell's paradox, Catch-22, the lawyer paradox involving Protagoras and Euathlus, the paradox of the stone, the Liar and Yablo's paradox. What the examination of these paradoxes reveals is that a satisfyingly unified treatment of them can be had if we have in place a principled denial of the assumption that contradictions and biconditionals of the form p, if and only if not-p are necessarily false. It is the latter that Wittgenstein supplies.

Keywords:   Aristotle, Barber, Catch-22, Wittgenstein

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