## Notre Dame Journal of Formal Logic

### A Propositional Theory of Truth

Yannis Stephanou

#### Abstract

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: $$\mathbf{S}\mbox{ is true iff }p,\vspace*{12pt}$$ where the letter $p$ is to be replaced with a sentence and the letter $\mathbf{S}$ 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.

#### Article information

Source
Notre Dame J. Formal Logic, Volume 59, Number 4 (2018), 503-545.

Dates
Received: 5 June 2014
Accepted: 11 May 2016
First available in Project Euclid: 13 October 2018

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1539396036

Digital Object Identifier
doi:10.1215/00294527-2018-0013

Mathematical Reviews number (MathSciNet)
MR3871899

Zentralblatt MATH identifier
06996542

#### Citation

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

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