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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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  • (Meta)Inferential Levels of Entailment Beyond the Tarskian Paradigm.Eduardo Alejandro Barrio, Federico Pailos & Damian Szmuc - 2019 - Synthese 198 (S22):5265-5289.
    In this paper we discuss the extent to which the very existence of substructural logics puts the Tarskian conception of logical systems in jeopardy. In order to do this, we highlight the importance of the presence of different levels of entailment in a given logic, looking not only at inferences between collections of formulae but also at inferences between collections of inferences—and more. We discuss appropriate refinements or modifications of the usual Tarskian identity criterion for logical systems, and propose an (...)
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  • (I Can’T Get No) Antisatisfaction.Pablo Cobreros, Elio La Rosa & Luca Tranchini - 2020 - Synthese 198 (9):8251-8265.
    Substructural approaches to paradoxes have attracted much attention from the philosophical community in the last decade. In this paper we focus on two substructural logics, named ST and TS, along with two structural cousins, LP and K3. It is well known that LP and K3 are duals in the sense that an inference is valid in one logic just in case the contrapositive is valid in the other logic. As a consequence of this duality, theories based on either logic are (...)
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  • On Structural Contraction and Why It Fails.Lucas Rosenblatt - 2019 - Synthese 198 (3):2695-2720.
    The goal of the paper is to discuss whether substructural non-contractive accounts of the truth-theoretic paradoxes can be philosophically motivated. First, I consider a number of explanations that have been offered to justify the failure of contraction and I argue that they are not entirely compelling. I then present a non-contractive theory of truth that I’ve proposed elsewhere. After looking at some of its formal properties, I suggest an explanation of the failure of structural contraction that is compatible with it.
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  • Paradoxicality Without Paradox.Lucas Rosenblatt - forthcoming - Erkenntnis:1-20.
    It is not uncommon among theorists favoring a deviant logic on account of the semantic paradoxes to subscribe to an idea that has come to be known as ‘classical recapture’. The main thought underpinning it is that non-classical logicians are justified in endorsing many instances of the classically valid principles that they reject. Classical recapture promises to yield an appealing pair of views: one can attain naivety for semantic concepts while retaining classicality in ordinary domains such as mathematics. However, Julien (...)
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  • Semidisquotation and the Infinitary Function of Truth.Camillo Fiore - forthcoming - Erkenntnis:1-16.
    The infinitary function of the truth predicate consists in its ability to express infinite conjunctions and disjunctions. A transparency principle for truth states the equivalence between a sentence and its truth predication; it requires an introduction principle---which allows the inference from "snow is white" to "the sentence 'snow is white' is true"---and an elimination principle---which allows the inference from "the sentence 'snow is white' is true" to "snow is white". It is commonly assumed that a theory of truth needs to (...)
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  • Theories of Truth and the Maxim of Minimal Mutilation.Ole Thomassen Hjortland - forthcoming - Synthese:1-32.
    Nonclassical theories of truth have in common that they reject principles of classical logic to accommodate an unrestricted truth predicate. However, different nonclassical strategies give up different classical principles. The paper discusses one criterion we might use in theory choice when considering nonclassical rivals: the maxim of minimal mutilation.
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  • A Hierarchy of Classical and Paraconsistent Logics.Eduardo Alejandro Barrio, Federico Pailos & Damian Szmuc - 2020 - Journal of Philosophical Logic 49 (1):93-120.
    In this article, we will present a number of technical results concerning Classical Logic, ST and related systems. Our main contribution consists in offering a novel identity criterion for logics in general and, therefore, for Classical Logic. In particular, we will firstly generalize the ST phenomenon, thereby obtaining a recursively defined hierarchy of strict-tolerant systems. Secondly, we will prove that the logics in this hierarchy are progressively more classical, although not entirely classical. We will claim that a logic is to (...)
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