Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-19T23:12:13.859Z Has data issue: false hasContentIssue false
  • English
  • Français

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]
Get access Rights & Permissions [Opens in a new window]

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
Check for updates
Copyright
© Association for Symbolic Logic, 2020

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Brady, R. (1983). The simple consistency of a set theory based on the logic CSQ. Notre Dame Journal of Formal Logic, 24, 431–149.CrossRefGoogle Scholar
Burgess, J. (2014). Friedman and the axiomatization of Kripke’s theory of truth. In Tennant, N., editor. Foundational Adventures: Essays in Honor of Harvey M. Friedman. London: College Publications, pp. 125–148.Google Scholar
Feferman, S. (1991). Reflecting on incompleteness. Journal of Symbolic Logic, 56, 1–49.10.2307/2274902CrossRefGoogle Scholar
Feferman, S. (2008). Axioms for determinateness and truth. Review of Symbolic Logic, 1, 204–217.CrossRefGoogle Scholar
Feferman, S. (2012). Axiomatizing truth: Why and how? In U. Berger, H. Diener, P. Schuster, and M. Seisenberger editors. Logic, Construction, Computation. Frankfurt: Ontos Verlag, pp. 185–200.10.1515/9783110324921.185CrossRefGoogle Scholar
Field, H. (2008). Saving Truth from Paradox. Oxford: Oxford University Press.CrossRefGoogle Scholar
Field, H. (2016). Indicative conditionals, restricted quantification and naive truth. Review of Symbolic Logic, 9, 181–208.10.1017/S1755020315000301CrossRefGoogle Scholar
Field, H. (2020a) Properties, propositions and conditionals. Australasian Philosophical Review, 4.CrossRefGoogle Scholar
Field, H. (2020b) Reply to Zach Weber. Australasian Philosophical Review, 4.CrossRefGoogle Scholar
Fischer, M., Nicolai, C., & Horsten, L. (2018). Iterated reflection over full disquotational truth. Journal of Logic and Computation, 27, 2631–2651.10.1093/logcom/exx023CrossRefGoogle Scholar
Gupta, A. & Martin, R. (1984). A fixed point theorem for the weak kleene valuation scheme. Journal of Philosophical Logic, 13, 131–135.CrossRefGoogle Scholar
Halbach, V. (2011). Axiomatic Theories of Truth. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Halbach, V. & Fujimoto, K. (n.d.) Classical Determinate Truth I, in preparation.Google Scholar
Halbach, V. & Horsten, L. (2006). Axiomatizing Kripke’s theory of truth. Journal of Symbolic Logic, 71, 677–712.CrossRefGoogle Scholar
Halbach, V. & Nicolai, C. (2018). On the costs of nonclassical logic. Journal of Philosophical Logic, 47, 227–257.CrossRefGoogle Scholar
Hinman, P. (1978). Recursion-Theoretic Hierarchies. Berlin: Springer.CrossRefGoogle Scholar
Kripke, S. (1975). Outline of a theory of truth. Journal of Philosophy, 72, 690–716.CrossRefGoogle Scholar
Nicolai, C. (2018). Provably true sentences across axiomatizations of Kripke’s theory of truth. Studia Logica, 106, 101–130.CrossRefGoogle Scholar
Picollo, L. (2018). Truth in a logic of formal inconsistency: How classical can it get? Logic Journal of the IGPL, jzy059. doi.org/10.1093/jigpal/jzy059.Google Scholar
Priest, G. (1998). What’s so bad about contradictions? Journal of Philosophy, 95, 410–426.CrossRefGoogle Scholar
Wang, H. (1961). The calculus of partial predicates and its extension to set theory. Mathematical Logic Quarterly, 7, 283–288.10.1002/malq.19610071705CrossRefGoogle Scholar