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Naïve validity.

Julien Murzi1,2, Lorenzo Rossi1

  • 1Philosophy Department (KGW), University of Salzburg, Salzburg, Austria.

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Summary
This summary is machine-generated.

This paper introduces grounded validity, a coherent notion supporting naïve validity principles. It argues against Field's objections, suggesting naïve validity highlights limitations in revisionary approaches to semantic paradoxes.

Keywords:
Curry’s paradoxGrounded validityNaïve validitySubstructural logics

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Area of Science:

  • Philosophy of Logic
  • Formal Semantics
  • Metaphysics of Logic

Background:

  • Beall and Murzi proposed naïve validity principles inconsistent with classical logic.
  • These principles suggest semantic paradox solutions must be substructural.
  • Field contested the coherence of naïve validity, arguing against substructural logics.

Purpose of the Study:

  • To respond to Field's objections regarding naïve validity.
  • To introduce and defend grounded validity as a coherent notion.
  • To demonstrate how grounded validity supports naïve validity principles.

Main Methods:

  • Introducing the concept of grounded validity, generalizing Kripke's grounded truth.
  • Developing an irreflexive logic based on grounded validity.
  • Analyzing the implications of grounded validity for semantic paradoxes.

Main Results:

  • Grounded validity provides a coherent reading of naïve validity principles.
  • Naïve validity principles do not necessarily require substructural logics.
  • Grounded validity reveals expressive limitations in fully structural revisionary approaches.

Conclusions:

  • Naïve validity is a legitimate semantic notion.
  • Grounded validity offers a coherent framework for understanding naïve validity.
  • Revisionary approaches to semantic paradoxes may face expressive limitations.