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Document Details :

Title: Just True?
Subtitle: On the Metatheory for Paraconsistent Truth
Author(s): OMORI, Hitoshi , WEBER, Zach
Journal: Logique et Analyse
Volume: 248    Date: 2019   
Pages: 415-433
DOI: 10.2143/LEA.248.0.3287323

Abstract :
One alternative to Tarski’s hierarchy of metalanguages is to consider paraconsistent logics for theories of truth, to deal with paradoxical sentences. In the face of the possibility of inconsistency, critics and proponents of paraconsistency alike have then sought ‘consistency operators’, to characterize non-paradoxical sentences. For strong forms of paraconsistency—dialetheism—this is called the ‘just true’ problem. In this paper we consider various options for treatments of the issue, and follow the ‘just true’ problem to a stark divide. If a paraconsistentist uses a classical metatheory, then they can have a ‘just true’ operator, but only by accepting a paracomplete logic, and in fact ruling out any truth value gluts. If a paraconsistentist uses a paraconsistent metatheory, then the ‘just true’ problem is easily resolved, albeit not in a way that would be satisfying to a non-paraconsistentist.

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