Strict-tolerant logic Metainferences Proof theory Internal vs external logic Paradoxes
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Cobreros-Bordenave, P. (Pablo); Egré, P. (Paul); Ripley, D. (David); et al. "Inferences and Metainferences in ST". Journal of Philosophical Logic. 49, 2020, 1057 - 1077
In a recent paper, Barrio, Tajer and Rosenblatt establish a correspondence between
metainferences holding in the strict-tolerant logic of transparent truth ST+ and inferences holding in the logic of paradox LP+. They argue that LP+ is ST+’s external
logic and they question whether ST+’s solution to the semantic paradoxes is fundamentally different from LP+’s. Here we establish that by parity of reasoning, ST+ can
be related to LP+’s dual logic K3+. We clarify the distinction between internal and
external logic and argue that while ST+’s nonclassicality can be granted, its self-dual
character does not tie it to LP+ more closely than to K3+.