Priest, Tanaka, and Weber (2015)

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Priest, Graham; Tanaka, Koji and Weber, Zachary. (2015) Paraconsistent Logic. In Zalta (Ed.) (2016). Retrieved from http://plato.stanford.edu/archives/spr2015/entries/logic-paraconsistent/.

Title Paraconsistent Logic
Resource Type collection article
Author(s) Graham Priest, Koji Tanaka, Zachary Weber
Year 2015
URL http://plato.stanford.edu/archives/spr2015/entries/logic-paraconsistent/
Collection Zalta (Ed.) (2016)

Abstract

The contemporary logical orthodoxy has it that, from contradictory premises, anything can be inferred. Let ⊨ be a relation of logical consequence, defined either semantically or proof-theoretically. Call ⊨ explosive if it validates {A , ¬A} ⊨ B for every A and B (ex contradictionequodlibet (ECQ)). Classical logic, and most standard ‘non-classical’ logics too such as intuitionist logic, are explosive. Inconsistency, according to received wisdom, cannot be coherently reasoned about. Paraconsistent logic challenges this orthodoxy. A logical consequence relation, ⊨, is said to be paraconsistent if it is not explosive. Thus, if ⊨ is paraconsistent, then even if we are in certain circumstances where the available information is inconsistent, the inference relation does not explode into triviality. Thus, paraconsistent logic accommodates inconsistency in a sensible manner that treats inconsistent information as informative. The prefix ‘para’ in English has two meanings:‘quasi’ (or ‘similar to, modelled on’) or ‘beyond’. When the term ‘paraconsistent’ was coined by Miró Quesada at the Third Latin America Conference on Mathematical Logic in 1976, he seems to have had the first meaning in mind. Many paraconsistent logicians, however, have taken it to mean the second, which provided different reasons for the development of paraconsistent logic as we will see below. This article is not meant to be a complete survey of paraconsistent logic. The aim is to provide some aspects and features of the field that are philosophically salient.

Contributors

Paul Patton (100.0%)