Notre Dame Journal of Formal Logic

A New Conditional for Naive Truth Theory

Andrew Bacon

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In this paper a logic suitable for reasoning disquotationally about truth, TJK+, is presented and shown to have a standard model. This work improves on Hartry Field’s recent results establishing consistency and ω-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.

Article information

Notre Dame J. Formal Logic, Volume 54, Number 1 (2013), 87-104.

First available in Project Euclid: 14 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03B20: Subsystems of classical logic (including intuitionistic logic)
Secondary: 03B50: Many-valued logic 03B47: Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics) {For proof-theoretic aspects see 03F52} 03Axx: Philosophical aspects of logic and foundations

liar paradox contractionless logic nonclassical logic Curry’s paradox semantic paradoxes fixed point theorem


Bacon, Andrew. A New Conditional for Naive Truth Theory. Notre Dame J. Formal Logic 54 (2013), no. 1, 87--104. doi:10.1215/00294527-1731407.

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