Inferences and metainferences in ST

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⁺.