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The Logical Syntax of Language

by Rudolf Carnap

English translation by Amethe Smeaton

Content Listing Only
but see also: The Philosophy of Rudolf Carnap
and: Carnap's Syntactical Method

Introduction	§1	What is Logical Syntax?
	§2	Languages as calculi
THE DEFINITE LANGUAGE I
Rules of Formation for Language I	§3	Predicates and Functors.
	§4	Syntactical Gothic Symbols.
	§5	The Junction Symbols.
	§6	Universal and Existential Sentences.
	§7	The K-Operator.
	§8	The Definitions.
	§9	Sentences and Numerical Expressions.
Rules of Transformation for Language I	§10	General Remarks concerning Transformation Rules.
	§11	The Primitive Sentences of Language I.
	§12	The Rules of Inference of Language I.
	§13	Derivations and Proofs in Language I.
	§14	Rules of Consequence for Language I.
Remarks on the Definite Form of Language	§15	Definite and Indefinite.
	§16	On Intuitionism.
	§16a	Identity.
	§17	The Principle of Tolerance in Syntax.
THE FORMAL CONSTRUCTION OF THE SYNTAX OF LANGUAGE I
	§18	The Syntax of I Can Be Formulated in I.
	§19	The Arithmetization of Syntax.
	§20	General Terms.
	§21	Rules of Formation; 1, Numerical Expressions and Sentences.
	§22	Rules of Formation; 2, Definitions.
	§23	Rules of Transformation.
	§24	Descriptive Syntax.
	§25	Arithmetical, Axiomatic and Physical Syntax.
THE INDEFINITE LANGUAGE II
Rules of Formation for Language II	§26	The Symbolic Apparatus of Language II.
	§27	The Classification of Types.
	§28	Formation Rules for Numerical Expressions and Sentences.
	§29	Formation Rules for Definitions.
Rules of Transformation for Language II	§30	The Primitive Sentences of Language II.
	§31	The Rules of Inference of Language II.
	§32	Derivations and Proofs in Language II.
	§33	Comparison of the Primitive Sentences and Rules of Language II with Those of Other Systems.
Rules of Consequence for Language II	§34a	Incomplete and Complete Criteria of Validity.
	§34b	Reduction.
	§34c	Evaluation.
	§34d	Definition of 'Analytic in II' and 'Contradictory in II'.
	§34e	On Analytic and Contradictory Sentences of Language II.
	§34f	Consequence in Language II.
	§34g	Logical Content.
	§34h	The Principles of Induction and Selection Are Analytic.
	§34i	Language II Is Non-Contradictory.
	§35	Syntactical Sentences Which Refer to Themselves.
	§36	Irresoluble Sentences.
Further Development of Language II	§37	Predicates as Class-Symbols.
	§38	The Elimination of Classes.
	§38a	On Existence Assumptions in Logic.
	§38b	Cardinal Numbers.
	§38c	Descriptions.
	§39	Real Numbers.
	§40	The Language of Physics.
GENERAL SYNTAX
Object-Language and Syntax-Language	§41	On Syntactical Designations.
	§42	On the Necessity of Distinguishing between an Expression and Its Designation.
	§43	On the Admissibility of Indefinite Terms.
	§44	On the Admissibility of Impredicative Terms.
	§45	Indefinite Terms in Syntax.
The Syntax of Any Language.
(a) General Considerations	§46	Formation Rules.
	§47	Transformation Rules; d-Terms.
	§48	c-Terms.
	§49	Content.
	§50	Logical and Descriptive Expressions; Sub-Languages.
	§51	Logical and Physical Rules.
	§52	L-Terms; 'Analytic' and 'Condradictory'.
(b) Variables	§53	Systems of Levels; Predicates and Functors.
	§54	Substitution; Variables and Constants.
	§55	Universal and Existential Operators.
	§56	Range.
	§57	Sentential Junctions.
(c) Arithmetic; Non-Contradictoriness; the Antinomies	§58	Arithmetic.
	§59	The Non-Contradictoriness and Completeness of a Language.
	§60a	The Antinomies.
	§60b	The Concepts 'True' and 'False'.
	§60c	The Syntactical Antinomies.
	§60d	Every Arithmetic Is Defective.
(d) Translation and Interpretation	§61	Translation from One Language into Another.
	§62	The Interpretation of a Language.
(e) Extensionality	§63	Quasi-Syntactical Sentences.
	§64	The Two Interpretations of Quasi-Syntactical Sentences.
	§65	Extensionality in Relation to Partial Sentences.
	§66	Extensionality in Relation to Partial Expressions.
	§67	The Thesis of Extensionality.
	§68	Intensional Sentences of the Autonymous Mode of Speech.
	§69	Intensional Sentences of the Logic of Modalities.
	§70	The Quasi-Syntactical and the Syntactical Methods in the Logic of Modalities.
	§71	Is an Intensional Logic Necessary?
(f) Relational Theory and Axiomatics	§71a	Relational Theory.
	§71b	Syntactical Terms of Relational Theory.
	§71c	Isomorphism.
	§71d	The Non-Denumerable Cardinal Numbers.
	§71e	The Axiomatic Method.
PHILOSOPHY AND SYNTAX
On the Form of the Sentences Belonging to the Logic of Science	§72	Philosophy Replaced by the Logic of Science.
	§73	The Logic of Science Is the Syntax of the Language of Science.
	§74	Pseudo-Object Sentences.
	§75	Sentences about Meaning.
	§76	Universal Words.
	§77	Universal Words in the Material Mode of Speech.
	§78	Confusion in Philosophy Caused by the Material Mode of Speech.
	§79	Philosophical Sentences in the Material and in the Formal Mode of Speech.
	§80	The Dangers of the Material Mode of Speech.
	§81	The Admissibility of the Material Mode of Speech.
The Logic of Science as Syntax	§82	The Physical Language.
	§83	The So-Called Foundations of the Sciences.
	§84	The Problem of the Foundation of Mathematics.
	§85	Syntactical Sentences in the Literature of the Special Sciences.
	§86	The Logic of Science Is Syntax.
Bibliography and Index of Authors.
Index of Subjects.