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The logic of paradox

The logic of paradox GRAHAM PRIEST ‘Indeed, even at this stage, I predict a time when there will be mathematical investigations of calculi containing contradictions, and people wilI actually be proud of having emancipated themselves.from consistency.’ WITTGENSTEIN 1930, Philosophical Remarks, p. 332. 0. INTRODUCTION The purpose of the present paper is to suggest a new way of handling the logical paradoxes. Instead of trying to dissolve them, or explain what has gone wrong, we should accept them and learn to come to live with them. This is argued in Sections I and II. For obvious reasons this will require the abandonment, or at least modification, of ‘classical’ logic. A way to do this is suggested in Section III. Sections IV and V discuss some implications of this approach to paradoxes. I. PARADOXES 1.1. The logical paradoxes (which are normally subdivided into the set theoretic ones such as Russell’s and the semantic ones such as the liar) have been around for a long time now. Yet no solution has been found. Admittedly, the liar paradox, which has been known for over 2000 years, has often been ignored as a triviality unworthy of serious consideration. (Though medieval logicians such as Buridan by no means regarded http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Philosophical Logic Springer Journals

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References (11)

Publisher
Springer Journals
Copyright
Copyright
Subject
Philosophy; Logic
ISSN
0022-3611
eISSN
1573-0433
DOI
10.1007/BF00258428
Publisher site
See Article on Publisher Site

Abstract

GRAHAM PRIEST ‘Indeed, even at this stage, I predict a time when there will be mathematical investigations of calculi containing contradictions, and people wilI actually be proud of having emancipated themselves.from consistency.’ WITTGENSTEIN 1930, Philosophical Remarks, p. 332. 0. INTRODUCTION The purpose of the present paper is to suggest a new way of handling the logical paradoxes. Instead of trying to dissolve them, or explain what has gone wrong, we should accept them and learn to come to live with them. This is argued in Sections I and II. For obvious reasons this will require the abandonment, or at least modification, of ‘classical’ logic. A way to do this is suggested in Section III. Sections IV and V discuss some implications of this approach to paradoxes. I. PARADOXES 1.1. The logical paradoxes (which are normally subdivided into the set theoretic ones such as Russell’s and the semantic ones such as the liar) have been around for a long time now. Yet no solution has been found. Admittedly, the liar paradox, which has been known for over 2000 years, has often been ignored as a triviality unworthy of serious consideration. (Though medieval logicians such as Buridan by no means regarded

Journal

Journal of Philosophical LogicSpringer Journals

Published: Aug 7, 2004

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