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Finite Circular Definitions

In Thomas Bolander, Vincent F. Hendricks & Stig Andur Andersen (eds.), Self-Reference. CSLI Publications. pp. 79-93 (2006)

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  1. Vagueness and Revision Sequences.C. M. Asmus - 2013 - Synthese 190 (6):953-974.
    Theories of truth and vagueness are closely connected; in this article, I draw another connection between these areas of research. Gupta and Belnap’s Revision Theory of Truth is converted into an approach to vagueness. I show how revision sequences from a general theory of definitions can be used to understand the nature of vague predicates. The revision sequences show how the meaning of vague predicates are interconnected with each other. The approach is contrasted with the similar supervaluationist approach.
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  • In Praise of a Logic of Definitions That Tolerates Ω‐Inconsistency.Anil Gupta - 2018 - Philosophical Issues 28 (1):176-195.
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  • Guest Editors’ Introduction.Riccardo Bruni & Shawn Standefer - 2019 - Journal of Philosophical Logic 48 (1):1-9.
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  • Solovay-Type Theorems for Circular Definitions.Shawn Standefer - 2015 - Review of Symbolic Logic 8 (3):467-487.
    We present an extension of the basic revision theory of circular definitions with a unary operator, □. We present a Fitch-style proof system that is sound and complete with respect to the extended semantics. The logic of the box gives rise to a simple modal logic, and we relate provability in the extended proof system to this modal logic via a completeness theorem, using interpretations over circular definitions, analogous to Solovay’s completeness theorem forGLusing arithmetical interpretations. We adapt our proof to (...)
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  • Conditionals in Theories of Truth.Anil Gupta & Shawn Standefer - 2017 - Journal of Philosophical Logic 46 (1):27-63.
    We argue that distinct conditionals—conditionals that are governed by different logics—are needed to formalize the rules of Truth Introduction and Truth Elimination. We show that revision theory, when enriched with the new conditionals, yields an attractive theory of truth. We go on to compare this theory with one recently proposed by Hartry Field.
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  • Definitions.Anil Gupta - 2008 - Stanford Encyclopedia of Philosophy.
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