Review of Symbolic Logic:1-37 (forthcoming)

Bruno Whittle
University of Wisconsin, Madison
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 rules  Semantic paradox  Classical logic
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DOI 10.1017/s1755020320000210
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References found in this work BETA

Outline of a Theory of Truth.Saul Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
Paradox Without Self-Reference.Stephen Yablo - 1993 - Analysis 53 (4):251.
Semantical Paradox.Tyler Burge - 1979 - Journal of Philosophy 76 (4):169-198.
The Liar Paradox.Charles Parsons - 1974 - Journal of Philosophical Logic 3 (4):381 - 412.
The Liar in Context.Michael Glanzberg - 2001 - Philosophical Studies 103 (3):217 - 251.

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