Conservatively extending classical logic with transparent truth

Review of Symbolic Logic 5 (2):354-378 (2012)

Abstract

This paper shows how to conservatively extend classical logic with a transparent truth predicate, in the face of the paradoxes that arise as a consequence. All classical inferences are preserved, and indeed extended to the full (truth—involving) vocabulary. However, not all classical metainferences are preserved; in particular, the resulting logical system is nontransitive. Some limits on this nontransitivity are adumbrated, and two proof systems are presented and shown to be sound and complete. (One proof system allows for Cut—elimination, but the other does not.)

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Author's Profile

David Ripley
Monash University

References found in this work

Outline of a Theory of Truth.Saul Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
Paradoxes and Failures of Cut.David Ripley - 2013 - Australasian Journal of Philosophy 91 (1):139 - 164.
The Liar: An Essay on Truth and Circularity.Jon Barwise & John Etchemendy - 1987 - Oxford, England and New York, NY, USA: Oxford University Press USA.
Tolerant, Classical, Strict.Pablo Cobreros, Paul Egré, David Ripley & Robert van Rooij - 2012 - Journal of Philosophical Logic 41 (2):347-385.

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Citations of this work

Anti-Exceptionalism About Logic.Ole Thomassen Hjortland - 2017 - Philosophical Studies 174 (3):631-658.
Paradoxes and Failures of Cut.David Ripley - 2013 - Australasian Journal of Philosophy 91 (1):139 - 164.
Paraconsistent Logic.Graham Priest - 2008 - Stanford Encyclopedia of Philosophy.
The Laws of Thought and the Laws of Truth as Two Sides of One Coin.Ulf Hlobil - forthcoming - Journal of Philosophical Logic:1-31.

View all 92 citations / Add more citations

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