A New Conditional for Naive Truth Theory
Andrew Bacon
Source: Notre Dame J. Formal Logic Volume 54, Number 1
(2013), 87-104.
Abstract
In this paper a logic suitable for reasoning disquotationally about truth, $\mathsf{TJK}^{+}$, is presented and shown to have a standard model. This work improves on Hartry Field’s recent results establishing consistency and $\omega$-consistency of truth theories with strong conditional logics. A novel method utilizing the Banach fixed point theorem for contracting functions on complete metric spaces is invoked, and the resulting logic is shown to validate a number of principles which existing revision theoretic methods have so far failed to provide.
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Keywords: liar paradox; contractionless logic; nonclassical logic; Curry’s paradox; semantic paradoxes; fixed point theorem
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.ndjfl/1355494525
Digital Object Identifier: doi:10.1215/00294527-1731407
Zentralblatt MATH identifier: 06132727
Mathematical Reviews number (MathSciNet): MR3007964
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Digital Object Identifier: doi:10.1305/ndjfl/1093870447
Project Euclid: euclid.ndjfl/1093870447
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