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date: 15 May 2021

Abstract and Keywords

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

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