Axiomatic theories of truth /
Volker Halbach.
- New York: Cambridge university press, 2014.
- ix, 350 p.
Includes bibliographical references and index.
Part I FOUNDATIONS; 1 Definitional and axiomatic theories of truth; 2 Objects of truth; 3 Tarski; 4 Truth and set theory; 4.1 Definitions and axiomatizations; 4.2 Paradoxes and typing; 5 Technical preliminaries; 5.1 Peano arithmetic; 5.2 Truth and satisfaction; 5.3 Translations and the recursion theorem; 6 Comparing axiomatic theories of truth; Part II TYPED TRUTH; 7 Disquotation; 8 Classical compositional truth; 8.1 The conservativity of compositional truth; 8.2 Conservativity and model theory; 8.3 Nonstandard models; 8.4 Lachlan's theorem 8.5 Satisfaction classes and axiomatic theories of truth8.6 Compositional truth and elementary comprehension; 8.7 Positive truth; 9 Hierarchies; 9.1 Tarski's hierarchy axiomatized; 9.2 Illfounded hierarchies; Part III TYPE-FREE TRUTH; 10 Typed and type-free theories of truth; 11 Reasons against typing; 12 Axioms and rules; 13 Axioms for type-free truth; 14 Classical symmetric truth; 14.1 The Friedman-Sheard theory and revision semantics; 14.2 Proof theory of the Friedman-Sheard theory; 14.3 The Friedman-Sheard axiomatization; 14.4 Expressing necessitation via reflection 14.5 Without satisfaction15 Kripke-Feferman; 15.1 Fixed-point semantics; 15.2 Completeness and consistency; 15.3 Proof theory of the Kripke-Feferman system; 15.4 Extensions; 16 Axiomatizing Kripke's theory in partial logic; 16.1 Partial Kripke-Feferman; 16.2 Proof-theoretic analysis of partial Kripke-Feferman; 17 Grounded truth; 18 Alternative evaluation schemata; 19 Disquotation; 19.1 Maximal consistent sets of disquotation sentences; 19.2 Maximal conservative sets of disquotation sentences; 19.3 Positive disquotation; 19.4 The semantics of positive disquotation 19.5 Proof theory of positive disquotationPart IV WAYS TO THE TRUTH; 20 Classical logic; 20.1 The costs of nonclassical logic; 20.2 The internal logic of the Kripke-Feferman theory; 20.3 Expressive power in nonclassical logic; 20.4 Containing nonclassical logic; 21 Deflationism; 21.1 Disquotationalism; 21.2 Conservativity; 22 Reflection; 22.1 Reflection principles; 22.2 Reflective closure; 23 Ontological reduction; 24 Applying theories of truth; 24.1 Truth in natural language; 24.2 Extending schemata
In this book, Volker Halbach examines the most important axiomatizations of truth, explores their properties and shows how the logical results impinge on the philosophical topics related to truth.