THE POWER OF NAIVE TRUTH

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.

[1]  Hartry Field Reply to Zach Weber , 2020 .

[2]  Hartry Field Properties, Propositions and Conditionals , 2020 .

[3]  Lavinia Picollo Truth in a Logic of Formal Inconsistency: How classical can it get? , 2020, Log. J. IGPL.

[4]  Carlo Nicolai,et al.  On the Costs of Nonclassical Logic , 2018, J. Philos. Log..

[5]  Carlo Nicolai,et al.  Provably True Sentences Across Axiomatizations of Kripke’s Theory of Truth , 2017, Studia Logica.

[6]  Carlo Nicolai,et al.  Iterated reflection over full disquotational truth , 2017, J. Log. Comput..

[7]  Peter G. Hinman,et al.  Recursion-Theoretic Hierarchies , 2017, Perspectives in Logic.

[8]  Hartry Field,et al.  INDICATIVE CONDITIONALS, RESTRICTED QUANTIFICATION, AND NAIVE TRUTH , 2015, The Review of Symbolic Logic.

[9]  Volker Halbach,et al.  Axiomatic Theories of Truth , 2014 .

[10]  S. Feferman Axiomatizing Truth: Why and How? , 2012 .

[11]  J. Burgess FRIEDMAN AND THE AXIOMATIZATION OF KRIPKE ' S THEORY OF TRUTH , 2010 .

[12]  Solomon Feferman,et al.  AXIOMS FOR DETERMINATENESS AND TRUTH , 2008, The Review of Symbolic Logic.

[13]  Hartry Field Saving Truth From Paradox , 2008 .

[14]  Leon Horsten,et al.  Axiomatizing Kripke's theory of truth , 2006, Journal of Symbolic Logic.

[15]  G. Priest What is so bad about contradictions , 1998 .

[16]  Solomon Feferman,et al.  Reflecting on incompleteness , 1991, Journal of Symbolic Logic.

[17]  Robert L. Martin,et al.  A fixed point theorem for the Weak Kleene valuation scheme , 1984, J. Philos. Log..

[18]  Ross T. Brady The simple consistency of a set theory based on the logic CSQ , 1983, Notre Dame J. Formal Log..

[19]  Saul A. Kripke,et al.  Outline of a Theory of Truth , 1975 .

[20]  Hao Wang,et al.  The Calculus of Partial Predicates and Its Extension to Set Theory I , 1961 .