The Logical Syntax of Language

by Carnap, Rudolf; Smeaton, Amethe

• ISBN13: 9780812695243
• ISBN10: 0812695240
• Format: Paperback
• Copyright: 2002-12-11
• Publisher: Open Court

Summary

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.

Table of Contents

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