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  1. Towards a Non-classical Meta-theory for Substructural Approaches to Paradox.Lucas Rosenblatt - 2021 - Journal of Philosophical Logic 50 (5):1007-1055.
    In the literature on self-referential paradoxes one of the hardest and most challenging problems is that of revenge. This problem can take many shapes, but, typically, it besets non-classical accounts of some semantic notion, such as truth, that depend on a set of classically defined meta-theoretic concepts, like validity, consistency, and so on. A particularly troubling form of revenge that has received a lot of attention lately involves the concept of validity. The difficulty lies in that the non-classical logician cannot (...)
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  • On Zardini’s Rules for Multiplicative Quantification as the Source of Contra(di)Ctions.Uwe Petersen - 2023 - Review of Symbolic Logic 16 (4):1110-1119.
    Certain instances of contraction are provable in Zardini’s system $\mathbf {IK}^\omega $ which causes triviality once a truth predicate and suitable fixed points are available.
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  • A Note on the Cut-Elimination Proof in “Truth Without Contra(di)Ction”.Andreas Fjellstad - 2020 - Review of Symbolic Logic 13 (4):882-886.
    This note shows that the permutation instructions presented by Zardini (2011) for eliminating cuts on universally quantified formulas in the sequent calculus for the noncontractive theory of truth IKTωare inadequate. To that purpose the note presents a derivation in the sequent calculus for IKTωending with an application of cut on a universally quantified formula which the permutation instructions cannot deal with. The counterexample is of the kind that leaves open the question whether cut can be shown to be eliminable in (...)
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