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CONSERVATIVELY EXTENDING CLASSICAL LOGIC WITH TRANSPARENT TRUTH

Published online by Cambridge University Press:  26 March 2012

DAVID RIPLEY*
Affiliation:
Department of Philosophy, University of Connecticut and School of Historical and Philosophical Studies, University of Melbourne
*
*DEPARTMENT OF PHILOSOPHY, 101 MANCHESTER HALL 344 MANSFIELD RD., UNIVERSITY OF CONNECTICUT STORRS, CT 06269-2054, USA AND SCHOOL OF HISTORICAL AND PHILOSOPHICAL STUDIES, OLD QUAD, UNIVERSITY OF MELBOURNE PARKVILLE, VIC 3010 AUSTRALIA E-mail: davewripley@gmail.com

Abstract

This paper shows how to conservatively extend a 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 features admissible Cut, but the other does not.)

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2012

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