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  1. Faithfulness for Naive Validity.Ulf Hlobil - 2019 - Synthese 196 (11):4759-4774.
    Nontransitive responses to the validity Curry paradox face a dilemma that was recently formulated by Barrio, Rosenblatt and Tajer. It seems that, in the nontransitive logic ST enriched with a validity predicate, either you cannot prove that all derivable metarules preserve validity, or you can prove that instances of Cut that are not admissible in the logic preserve validity. I respond on behalf of the nontransitive approach. The paper argues, first, that we should reject the detachment principle for naive validity. (...)
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  • Non-Representational Mathematical Realism.Maria Jose Frapolli - 2015 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 30 (3):331-348.
    This paper is an attempt to convince anti-realists that their correct intuitions against the metaphysical inflationism derived from some versions of mathematical realism do not force them to embrace non-standard, epistemic approaches to truth and existence. It is also an attempt to convince mathematical realists that they do not need to implement their perfectly sound and judicious intuitions with the anti-intuitive developments that render full-blown mathematical realism into a view which even Gödel considered objectionable. I will argue for the following (...)
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  • Infinitary Contraction‐Free Revenge.Andreas Fjellstad - 2018 - Thought: A Journal of Philosophy 7 (3):179-189.
    How robust is a contraction-free approach to the semantic paradoxes? This paper aims to show some limitations with the approach based on multiplicative rules by presenting and discussing the significance of a revenge paradox using a predicate representing an alethic modality defined with infinitary rules.
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  • Expressing logical disagreement from within.Andreas Fjellstad - 2022 - Synthese 200 (2):1-33.
    Against the backdrop of the frequent comparison of theories of truth in the literature on semantic paradoxes with regard to which inferences and metainferences are deemed valid, this paper develops a novel approach to defining a binary predicate for representing the valid inferences and metainferences of a theory within the theory itself under the assumption that the theory is defined with a classical meta-theory. The aim with the approach is to obtain a tool which facilitates the comparison between a theory (...)
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  • Non-reflexivity and Revenge.Julien Murzi & Lorenzo Rossi - 2022 - Journal of Philosophical Logic 51 (1):201-218.
    We present a revenge argument for non-reflexive theories of semantic notions – theories which restrict the rule of assumption, or initial sequents of the form φ ⊩ φ. Our strategy follows the general template articulated in Murzi and Rossi [21]: we proceed via the definition of a notion of paradoxicality for non-reflexive theories which in turn breeds paradoxes that standard non-reflexive theories are unable to block.
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  • Substructural approaches to paradox: an introduction to the special issue.Elia Zardini - 2021 - Synthese 199 (3):493-525.
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  • Naïve Validity.Julien Murzi & Lorenzo Rossi - 2017 - Synthese 199 (Suppl 3):819-841.
    Beall and Murzi :143–165, 2013) introduce an object-linguistic predicate for naïve validity, governed by intuitive principles that are inconsistent with the classical structural rules. As a consequence, they suggest that revisionary approaches to semantic paradox must be substructural. In response to Beall and Murzi, Field :1–19, 2017) has argued that naïve validity principles do not admit of a coherent reading and that, for this reason, a non-classical solution to the semantic paradoxes need not be substructural. The aim of this paper (...)
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  • The Very Idea of a Substructural Approach to Paradox.Lionel Shapiro - 2016 - Synthese 199 (Suppl 3):767-786.
    This paper aims to call into question the customary division of logically revisionary responses to the truth-theoretic paradoxes into those that are “substructural” and those that are “ structural.” I proceed by examining, as a case study, Beall’s recent proposal based on the paraconsistent logic LP. Beall formulates his response to paradox in terms of a consequence relation that obeys all standard structural rules, though at the price of the language’s lacking a detaching conditional. I argue that the same response (...)
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  • 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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  • Paradox and Logical Revision. A Short Introduction.Julien Murzi & Massimiliano Carrara - 2015 - Topoi 34 (1):7-14.
    Logical orthodoxy has it that classical first-order logic, or some extension thereof, provides the right extension of the logical consequence relation. However, together with naïve but intuitive principles about semantic notions such as truth, denotation, satisfaction, and possibly validity and other naïve logical properties, classical logic quickly leads to inconsistency, and indeed triviality. At least since the publication of Kripke’s Outline of a theory of truth , an increasingly popular diagnosis has been to restore consistency, or at least non-triviality, by (...)
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  • Expressing Validity: Towards a Self-Sufficient Inferentialism.Ulf Hlobil - 2020 - In Martin Blicha & Igor Sedlár (eds.), The Logica Yearbook 2019. London: College Publications. pp. 67-82.
    For semantic inferentialists, the basic semantic concept is validity. An inferentialist theory of meaning should offer an account of the meaning of "valid." If one tries to add a validity predicate to one's object language, however, one runs into problems like the v-Curry paradox. In previous work, I presented a validity predicate for a non-transitive logic that can adequately capture its own meta-inferences. Unfortunately, in that system, one cannot show of any inference that it is invalid. Here I extend the (...)
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  • Generalized Revenge.Julien Murzi & Lorenzo Rossi - 2020 - Australasian Journal of Philosophy 98 (1):153-177.
    Since Saul Kripke’s influential work in the 1970s, the revisionary approach to semantic paradox—the idea that semantic paradoxes must be solved by weakening classical logic—has been increasingly popular. In this paper, we present a new revenge argument to the effect that the main revisionary approaches breed new paradoxes that they are unable to block.
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  • Logical Partisanhood.Jack Woods - 2019 - Philosophical Studies 176 (5):1203-1224.
    A natural suggestion and increasingly popular account of how to revise our logical beliefs treats revision of logic analogously to the revision of scientific theories. I investigate this approach and argue that simple applications of abductive methodology to logic result in revision-cycles, developing a detailed case study of an actual dispute with this property. This is problematic if we take abductive methodology to provide justification for revising our logical framework. I then generalize the case study, pointing to similarities with more (...)
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  • Principles for Object-Linguistic Consequence: From Logical to Irreflexive.Carlo Nicolai & Lorenzo Rossi - 2018 - Journal of Philosophical Logic 47 (3):549-577.
    We discuss the principles for a primitive, object-linguistic notion of consequence proposed by ) that yield a version of Curry’s paradox. We propose and study several strategies to weaken these principles and overcome paradox: all these strategies are based on the intuition that the object-linguistic consequence predicate internalizes whichever meta-linguistic notion of consequence we accept in the first place. To these solutions will correspond different conceptions of consequence. In one possible reading of these principles, they give rise to a notion (...)
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