Notes by RBJ on

The Logical Syntax of Language

by Rudolf Carnap

English translation by Amethe Smeaton

Countess von Zeppelin.
International Library of Psychology, Philosophy and Scientific Method,
gen. ed., C. K. Ogden.
London: Kegan Paul Trench, Trubner & Co., 1937. xvi, 352 pp.

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

Introduction1What is Logical Syntax?
2Languages as calculi
Rules of Formation for Language I3Predicates and Functors.
4Syntactical Gothic Symbols.
5The Junction Symbols.
6Universal and Existential Sentences.
7The K-Operator.
8The Definitions.
9Sentences and Numerical Expressions.
Rules of Transformation for Language I10General Remarks concerning Transformation Rules.
11The Primitive Sentences of Language I.
12The Rules of Inference of Language I.
13Derivations and Proofs in Language I.
14Rules of Consequence for Language I.
Remarks on the Definite Form of Language15Definite and Indefinite.
16On Intuitionism.
17The Principle of Tolerance in Syntax.
18The Syntax of I Can Be Formulated in I.
19The Arithmetization of Syntax.
20General Terms.
21Rules of Formation; 1, Numerical Expressions and Sentences.
22Rules of Formation; 2, Definitions.
23Rules of Transformation.
24Descriptive Syntax.
25Arithmetical, Axiomatic and Physical Syntax.
Rules of Formation for Language II26The Symbolic Apparatus of Language II.
27The Classification of Types.
28Formation Rules for Numerical Expressions and Sentences.
29Formation Rules for Definitions.
Rules of Transformation for Language II30The Primitive Sentences of Language II.
31The Rules of Inference of Language II.
32Derivations and Proofs in Language II.
33Comparison of the Primitive Sentences and Rules of Language II with Those of Other Systems.
Rules of Consequence for Language II34aIncomplete and Complete Criteria of Validity.
34dDefinition of 'Analytic in II' and 'Contradictory in II'.
34eOn Analytic and Contradictory Sentences of Language II.
34fConsequence in Language II.
34gLogical Content.
34hThe Principles of Induction and Selection Are Analytic.
34iLanguage II Is Non-Contradictory.
35Syntactical Sentences Which Refer to Themselves.
36Irresoluble Sentences.
Further Development of Language II37Predicates as Class-Symbols.
38The Elimination of Classes.
38aOn Existence Assumptions in Logic.
38bCardinal Numbers.
39Real Numbers.
40The Language of Physics.
Object-Language and Syntax-Language41On Syntactical Designations.
42On the Necessity of Distinguishing between an Expression and Its Designation.
43On the Admissibility of Indefinite Terms.
44On the Admissibility of Impredicative Terms.
45Indefinite Terms in Syntax.
The Syntax of Any Language.
(a) General Considerations46Formation Rules.
47Transformation Rules; d-Terms.
48 c-Terms.
50Logical and Descriptive Expressions; Sub-Languages.
51Logical and Physical Rules.
52L-Terms; 'Analytic' and 'Condradictory'.
(b) Variables53Systems of Levels; Predicates and Functors.
54Substitution; Variables and Constants.
55Universal and Existential Operators.
57Sentential Junctions.
(c) Arithmetic; Non-Contradictoriness; the Antinomies58Arithmetic.
59The Non-Contradictoriness and Completeness of a Language.
60aThe Antinomies.
60bThe Concepts 'True' and 'False'.
60cThe Syntactical Antinomies.
60dEvery Arithmetic Is Defective.
(d) Translation and Interpretation61Translation from One Language into Another.
62The Interpretation of a Language.
(e) Extensionality63Quasi-Syntactical Sentences.
64The Two Interpretations of Quasi-Syntactical Sentences.
65Extensionality in Relation to Partial Sentences.
66Extensionality in Relation to Partial Expressions.
67The Thesis of Extensionality.
68Intensional Sentences of the Autonymous Mode of Speech.
69Intensional Sentences of the Logic of Modalities.
70The Quasi-Syntactical and the Syntactical Methods in the Logic of Modalities.
71Is an Intensional Logic Necessary?
(f) Relational Theory and Axiomatics71aRelational Theory.
71bSyntactical Terms of Relational Theory.
71dThe Non-Denumerable Cardinal Numbers.
71eThe Axiomatic Method.
On the Form of the Sentences Belonging to the Logic of Science72Philosophy Replaced by the Logic of Science.
73The Logic of Science Is the Syntax of the Language of Science.
74Pseudo-Object Sentences.
75Sentences about Meaning.
76Universal Words.
77Universal Words in the Material Mode of Speech.
78Confusion in Philosophy Caused by the Material Mode of Speech.
79Philosophical Sentences in the Material and in the Formal Mode of Speech.
80The Dangers of the Material Mode of Speech.
81The Admissibility of the Material Mode of Speech.
The Logic of Science as Syntax82The Physical Language.
83The So-Called Foundations of the Sciences.
84The Problem of the Foundation of Mathematics.
85Syntactical Sentences in the Literature of the Special Sciences.
86The Logic of Science Is Syntax.
Bibliography and Index of Authors.  
Index of Subjects.  

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