Conservatively extending classical logic with transparent truth

Review of Symbolic Logic 5 (2):354-378 (2012)
Authors
David Ripley
Monash University
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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DOI 10.1017/S1755020312000056
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References found in this work BETA

Outline of a Theory of Truth.Saul A. Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
Proof Theory.Gaisi Takeuti - 1987 - Elsevier.
From Heaps and Gaps to Heaps of Gluts.D. Hyde - 1997 - Mind 106 (424):641-660.

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Citations of this work BETA

Paradoxes and Failures of Cut.David Ripley - 2013 - Australasian Journal of Philosophy 91 (1):139 - 164.
The Cut‐Free Approach and the Admissibility‐Curry.Ulf Hlobil - 2018 - Thought: A Journal of Philosophy 7 (1):40-48.
Contractions of Noncontractive Consequence Relations.Rohan French & David Ripley - 2015 - Review of Symbolic Logic 8 (3):506-528.

View all 23 citations / Add more citations

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