The Tarskian Turn: Deflationism and Axiomatic Truth

Subject Index

Subject Index ACA, 100 ACA1, 113 ACAǫ0 , 126 ACAω, 113 ACAωω , 138 COND, 132 CONEC, 104 DIST, 88 DT, 50 DT1, 54 FACT, 88 FI, 89 FS, 104 IKF, 129 K, 88 KF, 124 NEC, 104 NP, 40 NT, 38 PA, 29 PA2, 99 PAT , 37 PKF, 132 PT−, 96 PUTB, 98 RCOND, 133 RKF, 130 S1, 114 SV, 87 SV∗, 89 TC, 71 TC1, 77 TCǫ0 , 126 TCω, 111 VF, 139 WV, 87 WV∗, 89 ZFC, 62 anti-extension, 117 anti-realist truth theory, 12 axiomatic truth theory, 3, 20 bounded truth predicate, 41 Cantor’s theorem, 7 categorical theory, 85 classes virtual, 149 closing off, 121 co-necessitation rule for truth, 104 coding, 23 coherence theory, 12 completeness truth-theoretic, 25 completeness theorem, 34 compositionality intuition, 72 compositional theory of truth, 71 comprehension scheme arithmetical, 100 full, 99 naive, 137 conceptual reducibility, 94 conditionalization, 132 restricted, 133 conservativeness, 74 arithmetical, 75, 82 generalized, 80 ideological, 82 ontological, 82 over epistemology, 86 over logic, 81 over metaphysics, 85 over science, 85 second-order, 85 semantical, 80 consistent, 31 correspondence theory, 11 Tarski on, 16 164 Subject Index Davidson’s semantic program, 92 deduction theorem, 18 deflationism, 59 derivability, 34 derivability conditions, 33 determinate truth, 146 diagonal function, 30 diagonal lemma, 30 extended, 37 strengthened, 30 strengthened extended, 37 dialetheism, 6, 24 disjunctive normal form, 41 disquotational intuition, 17, 37, 137 disquotationalism, 50, 97–99 disquotational theory of truth, 50, 63 proof-theoretic strength, 69 extension, 117 Field-biconditional, 145 first incompleteness theorem, 31 Fitch’s argument, 87 formalized modus ponens, 145 global reflection principle, 76 gödel code, 28 gödel number, 28 gödel sentence, 31 groundedness, 123 Hilbert’s program, 93 inconsistency, 24 ω-inconsistency, 109 diachronic, 107 inferential deflationism, 4, 147 inner logic, 129 iterative conception of sets, 137 Knower paradox, 40 knowledge traditional analysis of, 86 least fixed point model, 120 liar paradox, 18 diagnosis of, 50 formalized, 38 liar sentence, 36 strengthened, 58 Löb’s lemma, 34 logic multivalued, 6 partial, 5 second-order, 84 logical consequence, 34 Luxemburger Zirkel, xii material adequacy condition, 48 mathematical induction, 29 expressed in one sentence, 63 second-order, 84 meaning, 91 inferential theories of, 92 metalanguage, 47 metatheory, 48 Metawissenschaft, 48 minimalism, 4 model nice, 51 minimal, 52 partial, 118 monotonicity, 119 Montague’s theorem, 39 naive theory of truth, 38 name quotational, 48 structural-descriptive, 48 natural deduction, 143 nearly stable truth, 106 necessitation rule of modal logic, 39 for truth, 40, 104 necessity operator, 41 predicate, 41 nonconservativeness phenomenon, 84 objectlanguage, 47 paradox of informal provability, 40 paradox of necessity, 40 Peano arithmetic, 29 second-order, 99 Pilate’s question, 15 positive occurrence, 98 power game, 101, 111, 115 power set, 7 pragmatic theory, 12 predicative analysis, 148 predicative number theory, 113 predicativism, 100 prenex normal form, 41 presupposition, 73 proposition, 67 quantification objectual, 88 over everything, 21, 151 propositional, 88 redundancy theory of truth, 56 reflexive truth theory, 103 reflexivity axiom, 40 Subject Index 165 relative interpretability, 94 revision theory of truth, 105 rule-following, 147 rule of assertion, 127 Russell’s paradox, 137 satisfaction relation, 74 scheme, 64 second incompleteness theorem, 32 self-reference, 23 coherence of, 18 semantically closed truth theory, 103 semantic truth theory, 3, 20 semi-classical truth theory, 142 soundness, 24, 31 arithmetical, 52, 110 stable truth, 106 standard numeral, 28 strengthened liar problem, 124, 144 strong Kleene scheme, 118 strong verificationism, 87 substantial truth theory, 11, 59 substitution function, 43 supervaluation scheme, 123 Tarskian hierarchy, 54 Tarski-biconditionals, 3, 17, 37 Tarski’s Angels, xii restricted, 50 theory, 9, 32 total, 96 translation from object- to metalanguage, 47, 67 true of, 74 truth as a disquotational device, 63 as a logical notion, 65 as a logico-linguistic notion, 65 as a logico-mathematical notion, 65 bearer of, 2 blind ascriptions, 63 compositional nature of, 70 definition of, 19, 48 essence of, 15, 148 expressive power of, 64 function of, 63 negative, 64 positive, 63 laws of, 148 meaning of, 61 nature of, 148, 150 property, 2 redundancy of, 63 reflexive, 8 simplicity of, 62 uniformity of, 55 truth-definability, 95 truth-determinate, 96 truth-iteration, 8, 53 truthmaker, 12, 96 truth-teller sentence, 122 typed truth theory, 103 undefinability theorem, 35 strengthened, 36 strengthened extended, 38 untyped truth theory, 103 vagueness, 72, 97...