The Logical Syntax of Language

Available for the first time in 20 years, here is the Rudolf Carnap's famous “principle of tolerance” by which everyone is free to mix and match the rules of language and logic. In The Logical Syntax of Language, Carnap explains how his entire theory of language structure came to him like a vision when he was ill. He postulates that concepts of the theory of logic are purely syntactical and therefore can be formulated in logical syntax.

Preface to the English Edition

xi

Foreword

xiii

Introduction

What is Logical Syntax?

1

(3)

Languages as Calculi

4

(7)

PART I. THE DEFINITE LANGUAGE I

Rules of Formation for Language I

Predicates and Functors

11

(4)

Syntactical Gothic Symbols

15

(3)

The Junction Symbols

18

(2)

Universal and Existential Sentences

20

(2)

The K-Operator

22

(1)

The Definitions

23

(2)

Sentences and Numerical Expressions

25

(2)

Rules of Transformation for Language I

General Remarks Concerning Transformation Rules

27

(2)

The Primitive Sentences of Language I

29

(3)

The Rules of Inference of Language I

32

(1)

Derivations and Proofs in Language I

33

(4)

Rules of Consequence for Language I

37

(7)

Remarks on the Definite Form of Language

Definite and Indefinite

44

(2)

On Intuitionism

46

(3)

Identity

49

(2)

The Principle of Tolerance in Syntax

51

(2)

PART II. THE FORMAL CONSTRUCTION OF THE SYNTAX OF LANGUAGE I

The Syntax of I can be Formulated in I

53

(1)

The Arithmetization of Syntax

54

(4)

General Terms

58

(4)

Rules of Formation: 1. Numerical Expressions and Sentences

62

(4)

Rules of Formation: 2. Definitions

66

(7)

Rules of Transformation

73

(3)

Descriptive Syntax

76

(2)

Arithmetical, Axiomatic, and Physical Syntax

78

(5)

PART III. THE INDEFINITE LANGUAGE II

Rules of Formation for Language II

The Symbolic Apparatus of Language II

83

(1)

The Classification of Types

84

(3)

Formation Rules for Numerical Expressions and Sentences

87

(1)

Formation Rules for Definitions

88

(2)

Rules of Transformation for Language II

The Primitive Sentences of Language II

90

(4)

The Rules of Inference of Language II

94

(1)

Derivations and Proofs in Language II

95

(1)

Comparison of the Primitive Sentences and Rules of II with those of other Systems

96

(2)

Rules of Consequence for Language II

Incomplete and Complete Criteria of Validity

98

(4)

Reduction

102

(4)

Evaluation

106

(4)

Definition of `Analytic in II' and `Contradictory in II'

110

(5)

On Analytic and Contradictory Sentences of Language II

115

(2)

Consequence in Language II

117

(3)

Logical Content

120

(1)

The Principles of Induction and Selection are Analytic

121

(3)

Language II is Non-Contradictory

124

(5)

Syntactical Sentences which Refer to Themselves

129

(2)

Irresoluble Sentences

131

(3)

Further Development of Language II

Predicates as Class-Symbols

134

(2)

The Elimination of Classes

136

(4)

On Existence Assumptions in Logic

140

(2)

Cardinal Numbers

142

(2)

Descriptions

144

(3)

Real Numbers

147

(2)

The Language of Physics

149

(4)

PART IV. GENERAL SYNTAX

Object-Language and Syntax-Language

On Syntactical Designations

153

(3)

On the Necessity of Distinguishing between an Expression and its Designation

156

(4)

On the Admissibility of Indefinite Terms

160

(2)

On the Admissibility of Impredicative Terms

162

(3)

Indefinite Terms in Syntax

165

(2)

The Syntax of any Language

General Considerations

Formation Rules

167

(3)

Transformation Rules; d-Terms

170

(2)

c-Terms

172

(3)

Content

175

(2)

Logical and Descriptive Expressions; Sub-Language

177

(3)

Logical and Physical Rules

180

(2)

L-Terms; `Analytic' and `Contradictory'

182

(4)

Variables

Systems of Levels; Predicates and Functors

186

(3)

Substitution; Variables and Constants

189

(7)

Universal and Existential Operators

196

(3)

Range

199

(1)

Sentential Junctions

200

(5)

Arithmetic; Non-Contradictoriness; the Antinomies

Arithmetic

205

(2)

The Non-Contradictoriness and Completeness of a Language

207

(4)

The Antinomies

211

(3)

The Concepts `True' and `False'

214

(3)

The Syntactical Antinomies

217

(3)

Every Arithmetic is Defective

220

(2)

Translation and Interpretation

Translation from One Language into Another

222

(5)

The Interpretation of a Language

227

(6)

Extensionality

Quasi-Syntactical Sentences

233

(4)

The Two Interpretations of Quasi-Syntactical Sentences

237

(3)

Extensionality in Relation to Partial Sentences

240

(3)

Extensionality in Relation to Partial Expressions

243

(2)

The Thesis of Extensionality

245

(2)

Intensional Sentences of the Autonymous Mode of Speech

247

(3)

Intensional Sentences of the Logic of Modalities

250

(6)

The Quasi-Syntactical and the Syntactical Methods in the Logic of Modalities

256

(1)

Is an Intensional Logic necessary?

257

(3)

Relational Theory and Axiomatics

Relational Theory

260

(2)

Syntactical Terms of Relational Theory

262

(2)

Isomorphism

264

(3)

The Non-Denumerable Cardinal Numbers

267

(4)

The Axiomatic Method

271

(6)

PART V. PHILOSOPHY AND SYNTAX

On the Form of the Sentences Belonging to the Logic of Science

Philosophy Replaced by the Logic of Science

277

(4)

The Logic of Science is the Syntax of the Language of Science

281

(3)

Pseudo-Object-Sentences

284

(4)

Sentences about Meaning

288

(4)

Universal Words

292

(5)

Universal Words in the Material Mode of Speech

297

(1)

Confusion in Philosophy Caused by the Material Mode of Speech

298

(4)

Philosophical Sentences in the Material and in the Formal Mode of Speech

302

(6)

The Dangers of the Material Mode of Speech

308

(4)

The Admissibility of the Material Mode of Speech

312

(3)

The Logic of Science as Syntax

The Physical Language

315

(7)

The so-called Foundations of the Sciences

322

(3)

The Problem of the Foundation of Mathematics

325

(3)

Syntactical Sentences in the Literature of the Special Sciences

328

(3)

The Logic of Science is Syntax

331

(3)

Bibliography and Index of Authors

334

(13)

Index of Subjects

347

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The Logical Syntax of Language

Summary

Table of Contents

Supplemental Materials