Conservatively extending classical logic with transparent truth

Review of Symbolic Logic 5 (2):354-378 (2012)
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
Saul A. Kripke (1975). Outline of a Theory of Truth. Journal of Philosophy 72 (19):690-716.
Gaisi Takeuti (1987). Proof Theory. Sole Distributors for the U.S.A. And Canada, Elsevier Science Pub. Co..

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Citations of this work BETA
David Ripley (2013). Paradoxes and Failures of Cut. Australasian Journal of Philosophy 91 (1):139 - 164.
Elia Zardini (2013). Naive Modus Ponens. Journal of Philosophical Logic 42 (4):575-593.

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