AbstractWhile non-classical theories of truth that take truth to be transparent have some obvious advantages over any classical theory that evidently must take it as non-transparent, several authors have recently argued that there's also a big disadvantage of non-classical 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 should seem preferable to their external counterparts.
Similar books and articles
Axiomatizing Kripke’s Theory of Truth.Volker Halbach & Leon Horsten - 2006 - Journal of Symbolic Logic 71 (2):677 - 712.
On the Costs of Nonclassical Logic.Volker Halbach & Carlo Nicolai - 2018 - Journal of Philosophical Logic 47 (2):227-257.
A Proof-Theoretic Account of Classical Principles of Truth.Graham E. Leigh - 2013 - Annals of Pure and Applied Logic 164 (10):1009-1024.
Provably True Sentences Across Axiomatizations of Kripke’s Theory of Truth.Carlo Nicolai - 2018 - Studia Logica 106 (1):101-130.
Truth, Partial Logic and Infinitary Proof Systems.Martin Fischer & Norbert Gratzl - 2017 - Studia Logica 106 (3):1-26.
Deflationary Truth and the Ontology of Expressions.Carlo Nicolai - 2015 - Synthese 192 (12):4031-4055.
S. Feferman. Reflecting on Incompleteness. The Journal of Symbolic Logic, Vol. 56 , No. 1, Pp. 1–49. - W. N. Reinhardt. Some Remarks on Extending and Interpreting Theories with a Partial Predicate for Truth. Journal of Philosophical Logic, Vol. 15 , No. 2, Pp. 219–251. - V. Halbach and L. Horsten. Axiomatizing Kripke’s Theory of Truth. The Journal of Symbolic Logic, Vol. 71 , No. 2, Pp. 667–712 - H. Friedman and M. Sheard. An Axiomatic Approach to Self-Referential Truth.Annals of Pure and Applied Logic, Vol. 33 , No. 1, Pp. 1–21. - V. Halbach. A System of Complete and Consistent Truth. Notre Dame Journal of Formal Logic, Vol. 35 , No. 3, Pp. 311–327. [REVIEW]Graham E. Leigh - 2010 - Bulletin of Symbolic Logic 16 (3):424-428.
Norms for Theories of Reflexive Truth.Leon Horsten & Volker Halbach - 2015 - In Kentaro Fujimoto, José Martínez Fernández, Henri Galinon & Theodora Achourioti (eds.), Unifying the Philosophy of Truth. Springer Verlag.
An Ordinal Analysis for Theories of Self-Referential Truth.Graham Emil Leigh & Michael Rathjen - 2010 - Archive for Mathematical Logic 49 (2):213-247.
Relative Truth Definability of Axiomatic Truth Theories.Kentaro Fujimoto - 2010 - Bulletin of Symbolic Logic 16 (3):305-344.
Added to PP
Historical graph of downloads
Citations of this work
Nonclassical Truth with Classical Strength. A Proof-Theoretic Analysis of Compositional Truth Over Hype.Martin Fischer, Carlo Nicolai & Pablo Dopico - 2021 - Review of Symbolic Logic:1-24.
References found in this work
No references found.