## The Logical Syntax of LanguageAvailable 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. |

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### Contents

INTRODUCTION 1 What is Logical Syntax? o I | 1 |

Languages as Calculi s o | 4 |

THE DEFINITE LANGUAGE I | 11 |

PAGE | 15 |

4 Syntactical Gothic Symbols o s I5 5 The Junction Symbols s | 18 |

6 Universal and Existential Sentences o | 21 |

7 The KOperator s | 22 |

8 The Definitions | 23 |

41 On Syntactical Designations o s I53 42 On the Necessity of Distinguishing between an Expression and its Designation s | 156 |

43 On the Admissibility of Indefinite Terms | 160 |

44 On the Admissibility of Impredicative Terms | 162 |

45 Indefinite Terms in Syntax | 165 |

B THE SYNTAx OF ANY LANGUAGE a General Considerations 46 Formation Rules | 167 |

47 Transformation Rules dTerms | 171 |

48 cTerms | 172 |

49 Content s | 175 |

9 Sentences and Numerical Expressions o s | 25 |

B RULES OF TRANSFORMATION FOR LANGUAGE I | 27 |

The Primitive Sentences of Language I | 29 |

The Rules of Inference of Language I | 32 |

Derivations and Proofs in Language I s | 33 |

35 Syntactical Sentences which Refer to Themselves | 35 |

36 Irresoluble Sentences | 36 |

Rules of Consequence for Language I | 37 |

REMARKS ON THE DEFINITE FORM OF LANGUAGE 15 Definite and Indefinite s e s | 44 |

On Intuitionism s | 46 |

a Identity s | 49 |

The Principle of Tolerance in Syntax o 5 I | 51 |

THE FORMAL CONSTRUCTION OF THE SYNTAX OF LANGUAGE I | 53 |

The Arithmetization of Syntax s | 54 |

20 General Terms s s s | 58 |

THE INDEFINITE LANGUAGE II | 83 |

B RULES OF TRANSFORMATION FOR LANGUAGE II | 90 |

RULES OF CONSEQUENCE FOR LANGUAGE II | 98 |

FURTHER DEVELOPMENT OF LANGUAGE II | 134 |

37 Predicates as ClassSymbols | 135 |

The Elimination of Classes | 136 |

a On Existence Assumptions in Logic | 140 |

38b Cardinal Numbers | 142 |

38c Descriptions | 144 |

39 Real Numbers | 149 |

40 The Language of Physics | 151 |

GENERAL SYNTAX A OBJECTLANGUAGE AND SYNTAxLANGUAGE | 153 |

Logical and Descriptive Expressions SubLan guage 8 | 177 |

Logical and Physical Rules d | 180 |

52 LTerms Analytic and Contradictory | 182 |

b Variables 53 Systems of Levels Predicates and Functors | 186 |

54 Substitution Variables and Constants | 189 |

55 Universal and Existential Operators | 196 |

Range | 199 |

57 Sentential Junctions s | 201 |

c Arithmetic NonContradictoriness the Antinomies | 205 |

a The Antinomies 2 II | 212 |

d Translation and Interpretation | 222 |

e Extensionality | 233 |

65 Extensionality in Relation to Partial Sentences | 240 |

Intensional Sentences of the Autonymous Mode | 247 |

70 The QuasiSyntactical and the Syntactical Methods | 256 |

71 b Syntactical Terms of Relational Theory | 262 |

e The Axiomatic Method o | 271 |

PHILOSOPHY AND SYNTAX | 277 |

74 PseudoObjectSentences | 284 |

76 Universal Words s s | 292 |

78 Confusion in Philosophy Caused by the Material | 298 |

80 The Dangers of the Material Mode of Speech | 308 |

B THE LOGIC OF SCIENCE AS SYNTAX | 315 |

Special Sciences | 328 |

BIBLIOGRAPHY AND INDEx OF AUTHORS | 334 |

347 | |

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### Common terms and phrases

according analogous analytic sentences arguments arithmetic autonymous axiomatic axiomatic system axioms belongs called complete induction concepts consequence constructed contains contradictory contravalid correlated corresponding defined symbols definiendum definiens demonstrable descriptive syntax domain equipollent equivalent in meaning example Explanation expressional extensional finite formulated free variable Frege functor Gifu hence Hilbert indefinite instance intensional Intuitionism kind language logic of science material interpretation material mode Math mathematics method mode of speech n-termed numerical expressions object object-language partial sentence philosophical physical possible predicate premisses pressions prime number primitive sentences primitive symbols proof QIrg quasi-syntactical question real numbers reihe relation respectively rules of inference Russell sentence G1 sentential calculus sentential function series-number sub-language substitution synonymous syntactical designation syntactical predicate syntactical sentence syntax-language synthetic tences term-number Theorem tion transformation translation true undefined universal operator universal word valid valuation Wittgenstein word-language