Synthese 199 (Suppl 3):819-841 (2017)

Authors
Lorenzo Rossi
University of Salzburg
Julien Murzi
University of Salzburg
Abstract
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 is to respond to Field’s objections and to point to a coherent notion of validity which underwrites a coherent reading of Beall and Murzi’s principles: grounded validity. The notion, first introduced by Nicolai and Rossi, is a generalisation of Kripke’s notion of grounded truth, and yields an irreflexive logic. While we do not advocate the adoption of a substructural logic, we take the notion of naïve validity to be a legitimate semantic notion that points to genuine expressive limitations of fully structural revisionary approaches.
Keywords Validity  Curry's Paradox  Reflexivity  Substructural logics
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Reprint years 2021
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DOI 10.1007/s11229-017-1541-6
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References found in this work BETA

Saving Truth From Paradox.Hartry Field - 2008 - Oxford, England: Oxford University Press.
In Contradiction: A Study of the Transconsistent.Graham Priest - 1987 - Dordrecht, Netherland: Oxford University Press.
Outline of a Theory of Truth.Saul Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
Spandrels of Truth.J. C. Beall - 2009 - Oxford, England: Oxford University Press.
Understanding Truth.Scott Soames - 1998 - Oxford and New York: Oxford University Press USA.

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Citations of this work BETA

Generalized Revenge.Julien Murzi & Lorenzo Rossi - 2020 - Australasian Journal of Philosophy 98 (1):153-177.
Non-reflexivity and Revenge.Julien Murzi & Lorenzo Rossi - 2022 - Journal of Philosophical Logic 51 (1):201-218.
Logical Nihilism and the Logic of ‘Prem’.Andreas Fjellstad - forthcoming - Logic and Logical Philosophy:1.

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