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EQUIVALENCES FOR TRUTH PREDICATES

Published online by Cambridge University Press:  19 January 2017

CARLO NICOLAI
CARLO NICOLAI*
Affiliation:
Munich Center for Mathematical Philosophy, LMU Munich
*
*MUNICH CENTER FOR MATHEMATICAL PHILOSOPHY GESCHWISTER-SCHOLL PLATZ 1, MUNICH GERMANY E-mail: Carlo.Nicolai@lrz.uni-muenchen.de
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Abstract

One way to study and understand the notion of truth is to examine principles that we are willing to associate with truth, often because they conform to a pre-theoretical or to a semi-formal characterization of this concept. In comparing different collections of such principles, one requires formally precise notions of inter-theoretic reduction that are also adequate to compare these conceptual aspects. In this work I study possible ways to make precise the relation of conceptual equivalence between notions of truth associated with collections of principles of truth. In doing so, I will consider refinements and strengthenings of the notion of relative truth-definability proposed by Fujimoto (2010): in particular I employ suitable variants of notions of equivalence of theories considered in Visser (2006) and Friedman & Visser (2014) to show that there are better candidates than mutual truth-definability for the role of sufficient condition for conceptual equivalence between the semantic notions associated with the theories. In the concluding part of the paper, I extend the techniques introduced in the first and show that there is a precise sense in which ramified truth (either disquotational or compositional) does not correspond to iterations of comprehension.

Keywords

03F2503F3003F3503A05Formal Theories of Truthinterpretabilitysameness of theoriesarithmetical comprehension
Type
Research Article
Information
The Review of Symbolic Logic , Volume 10 , Issue 2 , June 2017 , pp. 322 - 356
Copyright
Copyright © Association for Symbolic Logic 2017 

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