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Logical Syntax of Language

Logical Syntax of Language

by Rudolf Carnap

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ISBN-10: 0415225531

ISBN-13: 9780415225533

Pub. Date: 11/28/2001

Publisher: Taylor & Francis

First published in 2000. Routledge is an imprint of Taylor & Francis, an informa company.


First published in 2000. Routledge is an imprint of Taylor & Francis, an informa company.

Product Details

Taylor & Francis
Publication date:
International Library of Philosophy Series
Product dimensions:
5.50(w) x 8.50(h) x 1.00(d)

Table of Contents

Preface to the English Editionxi
1.What is Logical Syntax?1
2.Languages as Calculi4
Part I.The Definite Language I
A.Rules of Formation for Language I
3.Predicates and Functors11
4.Syntactical Gothic Symbols15
5.The Junction Symbols18
6.Universal and Existential Sentences20
7.The K-Operator22
8.The Definitions23
9.Sentences and Numerical Expressions25
B.Rules of Transformation for Language I
10.General Remarks Concerning Transformation Rules27
11.The Primitive Sentences of Language I29
12.The Rules of Inference of Language I32
13.Derivations and Proofs in Language I33
14.Rules of Consequence for Language I37
C.Remarks on the Definite Form of Language
15.Definite and Indefinite44
16.On Intuitionism46
17.The Principle of Tolerance in Syntax51
Part II.The Formal Construction of the Syntax of Language I
18.The Syntax of I can be Formulated in I53
19.The Arithmetization of Syntax54
20.General Terms58
21.Rules of Formation: 1. Numerical Expressions and Sentences62
22.Rules of Formation: 2. Definitions66
23.Rules of Transformation73
24.Descriptive Syntax76
25.Arithmetical, Axiomatic, and Physical Syntax78
Part III.The Indefinite Language II
A.Rules of Formation for Language II
26.The Symbolic Apparatus of Language II83
27.The Classification of Types84
28.Formation Rules for Numerical Expressions and Sentences87
29.Formation Rules for Definitions88
B.Rules of Transformation for Language II
30.The Primitive Sentences of Language II90
31.The Rules of Inference of Language II94
32.Derivations and Proofs in Language II95
33.Comparison of the Primitive Sentences and Rules of II with those of other Systems96
C.Rules of Consequence for Language II
34a.Incomplete and Complete Criteria of Validity98
34d.Definition of 'Analytic in II' and 'Contradictory in II'110
34e.On Analytic and Contradictory Sentences of Language II115
34f.Consequence in Language II117
34g.Logical Content120
34h.The Principles of Induction and Selection are Analytic121
34i.Language II is Non-Contradictory124
35.Syntactical Sentences which Refer to Themselves129
36.Irresoluble Sentences131
D.Further Development of Language II
37.Predicates as Class-Symbols134
38.The Elimination of Classes136
38a.On Existence Assumptions in Logic140
38b.Cardinal Numbers142
39.Real Numbers147
40.The Language of Physics149
Part IV.General Syntax
A.Object-Language and Syntax-Language
41.On Syntactical Designations153
42.On the Necessity of Distinguishing between an Expression and its Designation156
43.On the Admissibility of Indefinite Terms160
44.On the Admissibility of Impredicative Terms162
45.Indefinite Terms in Syntax165
B.The Syntax of any Language
(a)General Considerations
46.Formation Rules167
47.Transformation Rules; d-Terms170
50.Logical and Descriptive Expressions; Sub-Language177
51.Logical and Physical Rules180
52.L-Terms; 'Analytic' and 'Contradictory'182
53.Systems of Levels; Predicates and Functors186
54.Substitution; Variables and Constants189
55.Universal and Existential Operators196
57.Sentential Junctions200
(c)Arithmetic; Non-Contradictoriness; the Antinomies
59.The Non-Contradictoriness and Completeness of a Language207
60a.The Antinomies211
60b.The Concepts 'True' and 'False'214
60c.The Syntactical Antinomies217
60d.Every Arithmetic is Defective220
(d)Translation and Interpretation
61.Translation from One Language into Another222
62.The Interpretation of a Language227
63.Quasi-Syntactical Sentences233
64.The Two Interpretations of Quasi-Syntactical Sentences237
65.Extensionality in Relation to Partial Sentences240
66.Extensionality in Relation to Partial Expressions243
67.The Thesis of Extensionality245
68.Intensional Sentences of the Autonymous Mode of Speech247
69.Intensional Sentences of the Logic of Modalities250
70.The Quasi-Syntactical and the Syntactical Methods in the Logic of Modalities256
71.Is an Intensional Logic necessary?257
(f)Relational Theory and Axiomatics
71a.Relational Theory260
71b.Syntactical Terms of Relational Theory262
71d.The Non-Denumerable Cardinal Numbers267
71e.The Axiomatic Method271
Part V.Philosophy and Syntax
A.On the Form of the Sentences Belonging to the Logic of Science
72.Philosophy Replaced by the Logic of Science277
73.The Logic of Science is the Syntax of the Language of Science281
75.Sentences about Meaning288
76.Universal Words292
77.Universal Words in the Material Mode of Speech297
78.Confusion in Philosophy Caused by the Material Mode of Speech298
79.Philosophical Sentences in the Material and in the Formal Mode of Speech302
80.The Dangers of the Material Mode of Speech308
81.The Admissibility of the Material Mode of Speech312
B.The Logic of Science as Syntax
82.The Physical Language315
83.The so-called Foundations of the Sciences322
84.The Problem of the Foundation of Mathematics325
85.Syntactical Sentences in the Literature of the Special Sciences328
86.The Logic of Science is Syntax331
Bibliography and Index of Authors334
Index of Subjects347

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