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Inferences and metainferences in \(\mathsf{ST}\). (English) Zbl 1485.03059

Summary: In a recent paper, E. Barrio et al. [J. Philos. Log. 44, No. 5, 551–571 (2015; Zbl 1350.03007)] establish a correspondence between metainferences holding in the strict-tolerant logic of transparent truth \(\mathsf{ST}^+\) and inferences holding in the logic of paradox \(\mathsf{LP}^+\). They argue that \(\mathsf{LP}^+\) is \(\mathsf{ST}^+\)’s external logic and they question whether \(\mathsf{ST}^+\)’s solution to the semantic paradoxes is fundamentally different from \(\mathsf{LP}^+\)’s. Here we establish that by parity of reasoning, \(\mathsf{ST}^+\) can be related to \(\mathsf{LP}^+\)’s dual logic \(\mathsf{K3}^+\). We clarify the distinction between internal and external logic and argue that while \(\mathsf{ST}^+\)’s nonclassicality can be granted, its self-dual character does not tie it to \(\mathsf{LP}^+\) more closely than to \(\mathsf{K3}^+\).

MSC:

03B53 Paraconsistent logics
03B50 Many-valued logic

Citations:

Zbl 1350.03007
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References:

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