Article

Relevance in Reasoning

Neil Tennant

in The Oxford Handbook of Philosophy of Mathematics and Logic

Published in print June 2007 | ISBN: 9780195325928
Published online September 2009 | e-ISBN: 9780199892082 | DOI: http://dx.doi.org/10.1093/oxfordhb/9780195325928.003.0023

Series: Oxford Handbooks

Relevance in Reasoning

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This article advances an unabashedly partisan view of how best to “relevantize” a logic. The view is laid out as informally as possible, given the technical nature of the subject matter. Here, “relevantizing” is understood as the project of formulating a decent system of logic that does not endorse Lewis's First Paradox: A, ¬A:B. Such a system will be paraconsistent, in that it will allow for distinct inconsistent theories (within a given language). But it will not be dialetheist. That is, it will not allow for true contradictions. Dialetheism does not follow from (though, in order to avoid trivialization, it requires) a refusal to infer whatever one pleases from a contradiction.

Keywords: relevantizing; system of logic; Lewis's First Paradox; dialetheism; contradictions; reasoning

Article.  10750 words. 

Subjects: Philosophy of Mathematics and Logic

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