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THE POWER OF NAIVE TRUTH

Part of: Philosophical aspects of logic and foundations General logic

Published online by Cambridge University Press:  06 July 2020

HARTRY FIELD
HARTRY FIELD*
Affiliation:
PHILOSOPHY DEPARTMENT NEW YORK UNIVERSITY 5 WASHINGTON PLACE NEW YORK, NY10003, USA E-mail: [email protected]
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Abstract

Nonclassical theories of truth that take truth to be transparent have some obvious advantages over any classical theory of truth (which must take it as nontransparent on pain of inconsistency). But several authors have recently argued that there’s also a big disadvantage of nonclassical theories as compared to their “external” classical counterparts: proof-theoretic strength. While conceding the relevance of this, the paper argues that there is a natural way to beef up extant internal theories so as to remove their proof-theoretic disadvantage. It is suggested that the resulting internal theories are preferable to their external counterparts.

Keywords

truthfixed pointSaul KripkeKFPKFVolker HalbachLeon HorstenSolomon Fefermanproof-theoretic strengthpredicativityschematic theory

MSC classification

Primary: 03A05: Philosophical and critical
Secondary: 03B20: Subsystems of classical logic (including intuitionistic logic) 03B50: Many-valued logic
Type
Research Article
Information
The Review of Symbolic Logic , Volume 15 , Issue 1 , March 2022 , pp. 225 - 258
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Copyright
© Association for Symbolic Logic, 2020

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