Rooij, R. (Robert) van

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    Inferences and Metainferences in ST
    (2020) Rooij, R. (Robert) van; Egré, P. (Paul); Cobreros-Bordenave, P. (Pablo); Ripley, D. (David)
    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+.
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    Tolerant reasoning: nontransitive or nonmonotonic?
    (Springer, 2021) Cobreros-Bordenave, P. (Pablo); Egré, P. (Paul); Ripley, D. (David); Rooij, R. (Robert) van
    The principle of tolerance characteristic of vague predicates is sometimes presented as a soft rule, namely as a default which we can use in ordinary reasoning, but which requires care in order to avoid paradoxes. We focus on two ways in which the tolerance principle can be modeled in that spirit, using special consequence relations. The first approach relates tolerant reasoning to nontransitive reasoning; the second relates tolerant reasoning to nonmonotonic reasoning. We compare the two approaches and examine three specific consequence relations in relation to those, which we call: strict-to-tolerant entailment, pragmatic-to-tolerant entailment, and pragmatic-to-pragmatic entailment. The first two are nontransitive, whereas the latter two are nonmonotonic.