Notre Dame Journal of Formal Logic

A New Conditional for Naive Truth Theory

Andrew Bacon

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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.

Article information

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

Dates
First available: 14 December 2012

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

Subjects
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

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

Citation

Bacon, Andrew. A New Conditional for Naive Truth Theory. Notre Dame Journal of Formal Logic 54 (2013), no. 1, 87--104. doi:10.1215/00294527-1731407. http://projecteuclid.org/euclid.ndjfl/1355494525.


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References

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