Notre Dame Journal of Formal Logic
- Notre Dame J. Formal Logic
- Volume 59, Number 4 (2018), 503-545.
A Propositional Theory of Truth
The liar and kindred paradoxes show that we can derive contradictions if our language possesses sentences lending themselves to paradox and we reason classically from schema (T) about truth: where the letter is to be replaced with a sentence and the letter with a name of that sentence. This article presents a theory of truth that keeps (T) at the expense of classical logic. The theory is couched in a language that possesses paradoxical sentences. It incorporates all the instances of the analogue of (T) for that language and also includes other platitudes about truth. The theory avoids contradiction because its logical framework is an appropriately constructed nonclassical propositional logic. The logic and the theory are different from others that have been proposed for keeping (T), and the methods used in the main proofs are novel.
Notre Dame J. Formal Logic, Volume 59, Number 4 (2018), 503-545.
Received: 5 June 2014
Accepted: 11 May 2016
First available in Project Euclid: 13 October 2018
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 03B20: Subsystems of classical logic (including intuitionistic logic)
Secondary: 03B50: Many-valued logic 03B80: Other applications of logic 03A99: None of the above, but in this section
Stephanou, Yannis. A Propositional Theory of Truth. Notre Dame J. Formal Logic 59 (2018), no. 4, 503--545. doi:10.1215/00294527-2018-0013. https://projecteuclid.org/euclid.ndjfl/1539396036