Semantic Apparatus – Naïve validity

Cited by Lee Sonogan

Why do the Chinese love to call the person 'naive' or 'not suitable' as  long as he has a different view from the CCP? - Quora

Abstract by Julien Murzi1,2 and Lorenzo Rossi1

Beall and Murzi (J Philos 110(3):143–165, 2013) introduce an object-linguistic predicate for naïve validity, governed by intuitive principles that are inconsistent with the classical structural rules (over sufficiently expressive base theories). As a consequence, they suggest that revisionary approaches to semantic paradox must be substructural. In response to Beall and Murzi, Field (Notre Dame J Form Log 58(1):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 (J Philos Log. doi:10.1007/s10992-017-9438-x, 2017), is a generalisation of Kripke’s notion of grounded truth (J Philos 72:690–716, 1975), and yields an irreflexive logic. While we do not advocate the adoption of a substructural logic (nor, more generally, of a revisionary approach to semantic paradox), we take the notion of naïve validity to be a legitimate semantic notion that points to genuine expressive limitations of fully structural revisionary approaches.

Publication: Synthese

Pub Date: 2021 Doi: 10.1007/s11229-017-1541-6

Keywords: Curry’s paradox, Naïve validity, Substructural logics, Grounded validity (Plenty more sections and references in this research article)

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