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MINIMAL TRUTH AND INTERPRETABILITY

Published online by Cambridge University Press:  01 December 2009

MARTIN FISCHER
MARTIN FISCHER*
Affiliation:
Centre for Logic and Analytical Philosophy, University of Leuven
*
*CENTRE FOR LOGIC AND ANALYTICAL PHILOSOPHY, UNIVERSITY OF LEUVEN, LEUVEN, BELGIUM, 3000 E-mail:martin.fischer@hiw.kuleuven.be
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Abstract

In this paper we will investigate different axiomatic theories of truth that are minimal in some sense. One criterion for minimality will be conservativity over Peano Arithmetic. We will then give a more fine-grained characterization by investigating some interpretability relations. We will show that disquotational theories of truth, as well as compositional theories of truth with restricted induction are relatively interpretable in Peano Arithmetic. Furthermore, we will give an example of a theory of truth that is a conservative extension of Peano Arithmetic but not interpretable in it. We will then use stricter versions of interpretations to compare weak theories of truth to subsystems of second-order arithmetic.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 2 , Issue 4 , December 2009 , pp. 799 - 815
Copyright
Copyright © Association for Symbolic Logic 2009

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