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EXCEPTIONAL LOGIC

Part of: General logic Philosophical aspects of logic and foundations

Published online by Cambridge University Press:  21 July 2020

BRUNO WHITTLE
BRUNO WHITTLE*
Affiliation:
DEPARTMENT OF PHILOSOPHY UNIVERSITY OF WISCONSIN–MADISONMADISON, WI53706, USAE-mail: [email protected]
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Abstract

The aim of the paper is to argue that all—or almost all—logical rules have exceptions. In particular, it is argued that this is a moral that we should draw from the semantic paradoxes. The idea that we should respond to the paradoxes by revising logic in some way is familiar. But previous proposals advocate the replacement of classical logic with some alternative logic. That is, some alternative system of rules, where it is taken for granted that these hold without exception. The present proposal is quite different. According to this, there is no such alternative logic. Rather, classical logic retains the status of the ‘one true logic’, but this status must be reconceived so as to be compatible with (almost) all of its rules admitting of exceptions. This would seem to have significant repercussions for a range of widely held views about logic: e.g., that it is a priori, or that it is necessary. Indeed, if the arguments of the paper succeed, then such views must be given up.

Keywords

logical rulessemantic paradoxclassical logic

MSC classification

Primary: 03A05: Philosophical and critical
Secondary: 03B80: Other applications of logic
Type
Research Article
Information
The Review of Symbolic Logic , Volume 14 , Issue 1 , March 2021 , pp. 85 - 111
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Copyright
© Association for Symbolic Logic, 2020

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