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Alfred Tarski: Philosophy of Language and Logic

Overview

This study looks to the work of Tarski's mentors Stanislaw Lesniewski and Tadeusz Kotarbinski, and reconsiders all of the major issues in Tarski scholarship in light of the conception of Intuitionistic Formalism developed: semantics, truth, paradox, logical consequence.

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Alfred Tarski: Philosophy of Language and Logic

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Overview

This study looks to the work of Tarski's mentors Stanislaw Lesniewski and Tadeusz Kotarbinski, and reconsiders all of the major issues in Tarski scholarship in light of the conception of Intuitionistic Formalism developed: semantics, truth, paradox, logical consequence.

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Product Details

Meet the Author

DOUGLAS PATTERSON is Associate Professor of Philosophy at Kansas State University, USA.

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Table of Contents

Series Editor's Foreword viii

Introduction 1

Expressive and representational semantics 1

The received view 4

Themes 7

1 Intuitionistic Formalism 12

1.1 What was Intuitionistic Formalism? 12

1.1.1 A puzzle about concepts and definitions 12

1.1.2 Tarski, Lesniewski and Intuitionistic Formalism 16

1.1.3 Formalism 19

1.2 Lesniewski 20

1.2.1 Lesniewski's early work 20

1.2.2 Lesniewski's later work 25

1.3 Kotarbinski 31

1.4 Tarski in context 37

1.4.1 The axiomatic method 37

1.4.2 Monism vs tolerance 41

1.4.3 Five doctrines 43

1.4.4 Tarski's project 49

2 Tarski as Intuitionistic Formalist 53

2.1 The early metamathematical works 53

2.1.1 Axiomatizing consequence 53

2.1.2 Relativization to a deductive science 55

2.2 Explicit definition 62

2.2.1 Defining definition 63

2.2.2 Two conceptions of definition 65

2.2.3 Padoa's method 67

2.3 Categoricity and completeness of terms 70

2.3.1 Provable monotransformability 70

2.3.2 Absolute monotransformability 76

2.4 Theory and concept 80

3 Semantics 84

3.1 Philosophical resistance 85

3.1.1 The quantifier 86

3.1.2 Paradox 89

3.2 Mathematical acceptance 91

3.3 Intuitionistic Formalism in "On Definable Sets" 94

3.3.1 The intuitive notion of definability 95

3.3.2 Defining definable sets vs defining "Defines" 100

4 Truth 108

4.1 Convention T 109

4.1.1 Terminological notes 109

4.1.2 Truth in the Lvov-Warsaw school 111

4.1.3 Semantic concepts in a mathematical theory 114

4.1.4 T-sentences 117

4.2 Tarski's definitions 122

4.2.1 Truth for the language of the calculus of classes 122

4.2.2 Higher order and polyadicity 124

4.2.3 Domain relativization and consequence 128

4.3 Evaluating Tarski's account 129

4.3.1 Familiar questions 129

4.3.2 Tarskian definitions and Tarski's "theory" 133

4.3.3 Reduction and physicalism 138

4.3.4 Correspondence and deflationism 140

5 Indefinability and Inconsistency 144

5.1 Indefinability 145

5.1.1 Indefinability before 1931 145

5.1.2 Theorem I: textual issues 147

5.1.3 Theorem I and Intuitionistic Formalism 155

5.1.4 Axiomatic semantics 158

5.2 Inconsistency in everyday language 160

5.2.1 Inconsistent Kotarbinskian conventions 162

5.2.2 Tarski after Kotarbinski 166

6 Transitions: 1933-1935 169

6.1 The 1935 postscript 170

6.2 Carnap on analyticity and truth 174

6.3 The establishment of scientific semantics 179

7 Logical Consequence 181

7.1 Tarski's definition 182

7.1.1 Synopsis 182

7.1.2 Objections to Tarski's account 185

7.2 Consequence in Logical Syntax 187

7.2.1 L-consequence and condition F 187

7.2.2 Tractarianism in the Vienna circle 191

7.3 The overgeneration problem and domain variation 194

7.3.1 Domain variation 194

7.3.2 Consequence in Gödel's completeness theorem 198

7.3.3 Tarski's fixed domain 201

7.4 The modality problem and "Tarski's Fallacy" 203

7.4.1 Modalities 204

7.4.2 Consequence and truth 206

7.4.3 Tarski's "must" 208

7.5 The formality problem and the logical constants 209

7.5.1 Constant and consequence 209

7.5.2 Anachronistic readings 211

7.5.3 Carnap on formality 213

7.5.4 The ω-rule and Gödel sentences 214

7.5.5 Antitractarianism and the nature of logic 215

7.6 Evaluating Tarski's account 219

7.6.1 The analytic problem 219

7.6.2 Eliminating transformation rules 221

7.6.3 Epistemic and generality conceptions of logic 223

8 Conclusion 227

8.1 Paris 1935 and the reception of semantics 227

8.2 Final remarks 232

Notes 234

Bibliography 249

Index 260

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