Axiomatic Theories of Truth

Summary

At the centre of the traditional discussion of truth is the question of how truth is defined. Recent research, especially with the development of deflationist accounts of truth, has tended to take truth as an undefined primitive notion governed by axioms, while the liar paradox and cognate paradoxes pose problems for certain seemingly natural axioms for truth. 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. In particular, he shows that the discussion on topics such as deflationism about truth depends on the solution of the paradoxes. His book is an invaluable survey of the logical background to the philosophical discussion of truth, and will be indispensable reading for any graduate or professional philosopher in theories of truth.

Preface	p. viii
Foundations	p. 1
Definitional and axiomatic theories of truth	p. 3
Objects of truth	p. 9
Tarski	p. 15
Truth and set theory	p. 25
Definitions and axiomatizations	p. 25
Paradoxes and typing	p. 27
Technical preliminaries	p. 29
Peano arithmetic	p. 29
Truth and satisfaction	p. 35
Translations and the recursion theorem	p. 36
Comparing axiomatic theories of truth	p. 39
Typed truth	p. 49
Disquotation	p. 53
Classical compositional truth	p. 63
The conservativity of compositional truth	p. 68
Conservativity and model theory	p. 82
Nonstandard models	p. 83
Lachlan's theorem	p. 89
Satisfaction classes and axiomatic theories of truth	p. 98
Compositional truth and elementary comprehension	p. 101
Positive truth	p. 116
Hierarchies	p. 123
Tarski's hierarchy axiomatized	p. 125
Illfounded hierarchies	p. 129
Type-free truth	p. 135
Typed and type-free theories of truth	p. 140
Reasons against typing	p. 146
Axioms and rules	p. 149
Axioms for type-free truth	p. 152
Classical symmetric truth	p. 159
The Friedman-Sheard theory and revision semantics	p. 162
Proof theory of the Friedman-Sheard theory	p. 175
The Friedman-Sheard axiomatization	p. 185
Expressing necessitation via reflection	p. 188
Without satisfaction	p. 192
Kripke-Feferman	p. 195
Fixed-point semantics	p. 202
Completeness and consistency	p. 212
Proof theory of the Kripke-Feferman system	p. 217
Extensions	p. 225
Axiomatizing Kripke's theory in partial logic	p. 228
Partial Kripke-Feferman	p. 231
Proof-theoretic analysis of partial Kripke-Feferman	p. 244
Grounded truth	p. 257
Alternative evaluation schemata	p. 263
Disquotation	p. 267
Maximal consistent sets of disquotation sentences	p. 267
Maximal conservative sets of disquotation sentences	p. 272
Positive disquotation	p. 274
The semantics of positive disquotation	p. 277
Proof theory of positive disquotation	p. 280
Ways to the truth	p. 287
Classical logic	p. 289
The costs of nonclassical logic	p. 291
The internal logic of the Kripke-Feferman theory	p. 295
Expressive power in nonclassical logic	p. 300
Containing nonclassical logic	p. 303
Deflationism	p. 306
Disquotationalism	p. 307
Conservativity	p. 312
Reflection	p. 322
Reflection principles	p. 322
Reflective closure	p. 326
Ontological reduction	p. 330
Applying theories of truth	p. 333
Truth in natural language	p. 333
Extending schemata	p. 335
Index of systems	p. 343
Bibliography	p. 345
Index	p. 357
Table of Contents provided by Ingram. All Rights Reserved.

Supplemental Materials

What is included with this book?

The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.

The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.