Axiomatic Theories of Truth

Cover......Page 1
Half-title......Page 3
Title......Page 5
Copyright......Page 6
Contents......Page 7
Preface......Page 10
Part I: FOUNDATIONS......Page 13
1 Definitional and axiomatic theories of truth......Page 15
2 Objects of truth......Page 21
3 Tarski......Page 27
4.1 Definitions and axiomatizations......Page 37
4.2 Paradoxes and typing......Page 39
5.1 Peano arithmetic......Page 41
5.2 Truth and satisfaction......Page 47
5.3 Translations and the recursion theorem......Page 48
6 Comparing axiomatic theories of truth......Page 51
Part II: TYPED TRUTH......Page 61
7 Disquotation......Page 65
8 Classical compositional truth......Page 75
8.1 The conservativity of compositional truth......Page 80
8.2 Conservativity and model theory......Page 94
8.3 Nonstandard models......Page 95
8.4 Lachlan’s theorem......Page 101
8.5 Satisfaction classes and axiomatic theories of truth......Page 110
8.6 Compositional truth and elementary comprehension......Page 113
8.7 Positive truth......Page 128
9 Hierarchies......Page 135
9.1 Tarski’s hierarchy axiomatized......Page 137
9.2 Illfounded hierarchies......Page 141
Part III: TYPE-FREE TRUTH......Page 147
10 Typed and type-free theories of truth......Page 152
11 Reasons against typing......Page 158
12 Axioms and rules......Page 161
13 Axioms for type-free truth......Page 164
14 Classical symmetric truth......Page 171
14.1 The Friedman–Sheard theory and revision semantics......Page 174
14.2 Proof theory of the Friedman–Sheard theory......Page 187
14.3 The Friedman–Sheard axiomatization......Page 197
14.4 Expressing necessitation via reflection......Page 200
14.5 Without satisfaction......Page 204
15 Kripke–Feferman......Page 207
15.1 Fixed-point semantics......Page 214
15.2 Completeness and consistency......Page 224
15.3 Proof theory of the Kripke–Feferman system......Page 229
15.4 Extensions......Page 237
16 Axiomatizing Kripke’s theory in partial logic......Page 240
16.1 Partial Kripke–Feferman......Page 243
16.2 Proof-theoretic analysis of partial Kripke–Feferman......Page 256
17 Grounded truth......Page 269
18 Alternative evaluation schemata......Page 275
19.1 Maximal consistent sets of disquotation sentences......Page 279
19.2 Maximal conservative sets of disquotation sentences......Page 284
19.3 Positive disquotation......Page 286
19.4 The semantics of positive disquotation......Page 289
19.5 Proof theory of positive disquotation......Page 292
Part IV: WAYS TO THE TRUTH......Page 299
20 Classical logic......Page 301
20.1 The costs of nonclassical logic......Page 303
20.2 The internal logic of the Kripke–Feferman theory......Page 307
20.3 Expressive power in nonclassical logic......Page 312
20.4 Containing nonclassical logic......Page 315
21 Deflationism......Page 318
21.1 Disquotationalism......Page 319
21.2 Conservativity......Page 324
22.1 Reflection principles......Page 334
22.2 Reflective closure......Page 338
23 Ontological reduction......Page 342
24.1 Truth in natural language......Page 345
24.2 Extending schemata......Page 347
Index of systems......Page 355
Bibliography......Page 357
Index......Page 369