Notre Dame Journal of Formal Logic

A Propositional Theory of Truth

Yannis Stephanou

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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: Sis true iffp, where the letter p is to be replaced with a sentence and the letter 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

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

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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 03B80: Other applications of logic 03A99: None of the above, but in this section

liar paradox theories of truth nonclassical propositional logics


Stephanou, Yannis. A Propositional Theory of Truth. Notre Dame J. Formal Logic 59 (2018), no. 4, 503--545. doi:10.1215/00294527-2018-0013.

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  • [1] Aristotle, Metaphysics, edited by W. Jaeger, Scriptorum Classicorum Bibliotheca Oxoniensis, Clarendon Press, Oxford, 1957.
  • [2] Avron, A., and A. Zamansky, “Non-deterministic semantics for logical systems,” pp. 227–304 in Handbook of Philosophical Logic, Vol. 16, edited by D. Gabbay and F. Guenthner, Springer, Dordrecht, 2011.
  • [3] Beall, J. C., Spandrels of Truth, Oxford University Press, Oxford, 2009.
  • [4] Field, H., Saving Truth from Paradox, Oxford University Press, Oxford, 2008.
  • [5] Fine, K., “Prior on the construction of possible worlds and instants,” pp. 133–75 in Modality and Tense: Philosophical Papers, Oxford University Press, Oxford, 2005.
  • [6] Kripke, S., “Outline of a theory of truth,” Journal of Philosophy, vol. 72 (1975), pp. 690–716.
  • [7] Plantinga, A., “On existentialism,” Philosophical Studies, vol. 44 (1983), pp. 1–20.
  • [8] Prawitz, D., “Towards a foundation of a general proof theory,” pp. 225–50 in Logic, Methodology and Philosophy of Science, IV (Bucharest, 1971), edited by P. Suppes, L. Henkin, A. Joja, and G. Moisil, vol. 74 of Studies in Logic and the Foundations of Mathematics, North-Holland, Amsterdam, 1973.
  • [9] Prawitz, D., “On the idea of a general proof theory,” Synthese, vol. 27 (1974), pp. 63–77.
  • [10] Priest, G., In Contradiction: A Study of the Transconsistent, 2nd edition, Oxford University Press, New York, 2006.
  • [11] Sainsbury, M., Logical Forms: An Introduction to Philosophical Logic, 2nd edition, Blackwell, Oxford, 2001.
  • [12] Zardini, E., “Truth without contra(di)ction,” Review of Symbolic Logic, vol. 4 (2011), pp. 498–535.