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Naïve validity
Julien Murzi1,2, Lorenzo Rossi1
1Philosophy Department (KGW), University of Salzburg, Salzburg, Austria.
Synthese
|January 24, 2022
Summary
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.
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.
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