Book Chapter

Two negations are more than one

G Restall

Outstanding Contributions to Logic | Springer | Published : 2019

Abstract

© Springer Nature Switzerland AG 2019. In models for paraconsistent logics, the semantic values of sentences and their negations are less tightly connected than in classical logic. In ‘American Plan’ logics for negation, truth and falsity are, to some degree, independent. The truth of ~ p is given by the falsity of p, and the falsity of ~ p is given by the truth of p. Since truth and falsity are only loosely connected, p and ~ p can both hold, or both fail to hold. In ‘Australian Plan’ logics for negation, negation is treated rather like a modal operator, where the truth of ~ in a situation amounts to p failing in certain other situations. Since those situations can be different from this on..

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