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AXIOMATIC TRUTH, SYNTAX AND METATHEORETIC REASONING

Published online by Cambridge University Press:  28 August 2013

GRAHAM E. LEIGH
Affiliation:
Faculty of Philosophy, University of Oxford
CARLO NICOLAI
Affiliation:
Somerville College, University of Oxford

Abstract

Following recent developments in the literature on axiomatic theories of truth, we investigate an alternative to the widespread habit of formalizing the syntax of the object-language into the object-language itself. We first argue for the proposed revision, elaborating philosophical evidences in favor of it. Secondly, we present a general framework for axiomatic theories of truth with ‘disentangled’ theories of syntax. Different choices of the object theory O will be considered. Moreover, some strengthenings of these theories will be introduced: we will consider extending the theories by the addition of coding axioms or by extending the schemas of O, if present, to the entire vocabulary of our theory of truth. Finally, we touch on the philosophical consequences that the theories described can have on the debate about the metaphysical status of the truth predicate and on the formalization of our informal metatheoretic reasoning.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2013 

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