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An Argument for Minimal Logic

Research output: Contribution to journalArticle

Original languageEnglish
Pages (from-to)31-63
Number of pages33
JournalDIALECTICA
Volume73
Issue number1-2
Early online date21 Jul 2019
DOIs
Accepted/In press1 May 2019
E-pub ahead of print21 Jul 2019

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Abstract

The problem of negative truth is the problem of how, if everything in the world is positive, we can speak truly about the world using negative propositions. A prominent solution is to explain negation in terms of a primitive notion of metaphysical incompatibility. I argue that if this account is correct, then minimal logic is the correct logic. The negation of a proposition A is characterised as the minimal incompatible of A composed of it and the logical constant ¬. A rule based account of the meanings of logical constants that appeals to the notion of incompatibility in the introduction rule for negation ensures the existence and uniqueness of the negation of every proposition. But it endows the negation operator with no more formal properties than those it has in minimal logic.

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