The Logical Syntax of Language

by Rudolf Carnap, Amethe Smeaton (Translator)

Overview

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.

Product Details

ISBN-13:	9780812695243
Publisher:	Open Court Publishing Company
Publication date:	12/11/2002
Edition description:	Special ed.
Pages:	180
Product dimensions:	6.00(w) x 9.00(h) x (d)

About the Author

Rudolf Carnap

Table of Contents

	Preface to the English Edition	xi
	Foreword	xiii
	Introduction
1.	What is Logical Syntax?	1
2.	Languages as Calculi	4
Part I.	The Definite Language I
A.	Rules of Formation for Language I
3.	Predicates and Functors	11
4.	Syntactical Gothic Symbols	15
5.	The Junction Symbols	18
6.	Universal and Existential Sentences	20
7.	The K-Operator	22
8.	The Definitions	23
9.	Sentences and Numerical Expressions	25
B.	Rules of Transformation for Language I
10.	General Remarks Concerning Transformation Rules	27
11.	The Primitive Sentences of Language I	29
12.	The Rules of Inference of Language I	32
13.	Derivations and Proofs in Language I	33
14.	Rules of Consequence for Language I	37
C.	Remarks on the Definite Form of Language
15.	Definite and Indefinite	44
16.	On Intuitionism	46
16a.	Identity	49
17.	The Principle of Tolerance in Syntax	51
Part II.	The Formal Construction of the Syntax of Language I
18.	The Syntax of I can be Formulated in I	53
19.	The Arithmetization of Syntax	54
20.	General Terms	58
21.	Rules of Formation: 1. Numerical Expressions and Sentences	62
22.	Rules of Formation: 2. Definitions	66
23.	Rules of Transformation	73
24.	Descriptive Syntax	76
25.	Arithmetical, Axiomatic, and Physical Syntax	78
Part III.	The Indefinite Language II
A.	Rules of Formation for Language II
26.	The Symbolic Apparatus of Language II	83
27.	The Classification of Types	84
28.	Formation Rules for Numerical Expressions and Sentences	87
29.	Formation Rules for Definitions	88
B.	Rules of Transformation for Language II
30.	The Primitive Sentences of Language II	90
31.	The Rules of Inference of Language II	94
32.	Derivations and Proofs in Language II	95
33.	Comparison of the Primitive Sentences and Rules of II with those of other Systems	96
C.	Rules of Consequence for Language II
34a.	Incomplete and Complete Criteria of Validity	98
34b.	Reduction	102
34c.	Evaluation	106
34d.	Definition of 'Analytic in II' and 'Contradictory in II'	110
34e.	On Analytic and Contradictory Sentences of Language II	115
34f.	Consequence in Language II	117
34g.	Logical Content	120
34h.	The Principles of Induction and Selection are Analytic	121
34i.	Language II is Non-Contradictory	124
35.	Syntactical Sentences which Refer to Themselves	129
36.	Irresoluble Sentences	131
D.	Further Development of Language II
37.	Predicates as Class-Symbols	134
38.	The Elimination of Classes	136
38a.	On Existence Assumptions in Logic	140
38b.	Cardinal Numbers	142
38c.	Descriptions	144
39.	Real Numbers	147
40.	The Language of Physics	149
Part IV.	General Syntax
A.	Object-Language and Syntax-Language
41.	On Syntactical Designations	153
42.	On the Necessity of Distinguishing between an Expression and its Designation	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; d-Terms	170
48.	c-Terms	172
49.	Content	175
50.	Logical and Descriptive Expressions; Sub-Language	177
51.	Logical and Physical Rules	180
52.	L-Terms; '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
56.	Range	199
57.	Sentential Junctions	200
(c)	Arithmetic; Non-Contradictoriness; the Antinomies
58.	Arithmetic	205
59.	The Non-Contradictoriness and Completeness of a Language	207
60a.	The Antinomies	211
60b.	The Concepts 'True' and 'False'	214
60c.	The Syntactical Antinomies	217
60d.	Every Arithmetic is Defective	220
(d)	Translation and Interpretation
61.	Translation from One Language into Another	222
62.	The Interpretation of a Language	227
(e)	Extensionality
63.	Quasi-Syntactical Sentences	233
64.	The Two Interpretations of Quasi-Syntactical Sentences	237
65.	Extensionality in Relation to Partial Sentences	240
66.	Extensionality in Relation to Partial Expressions	243
67.	The Thesis of Extensionality	245
68.	Intensional Sentences of the Autonymous Mode of Speech	247
69.	Intensional Sentences of the Logic of Modalities	250
70.	The Quasi-Syntactical and the Syntactical Methods in the Logic of Modalities	256
71.	Is an Intensional Logic necessary?	257
(f)	Relational Theory and Axiomatics
71a.	Relational Theory	260
71b.	Syntactical Terms of Relational Theory	262
71c.	Isomorphism	264
71d.	The Non-Denumerable Cardinal Numbers	267
71e.	The Axiomatic Method	271
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 Science	277
73.	The Logic of Science is the Syntax of the Language of Science	281
74.	Pseudo-Object-Sentences	284
75.	Sentences about Meaning	288
76.	Universal Words	292
77.	Universal Words in the Material Mode of Speech	297
78.	Confusion in Philosophy Caused by the Material Mode of Speech	298
79.	Philosophical Sentences in the Material and in the Formal Mode of Speech	302
80.	The Dangers of the Material Mode of Speech	308
81.	The Admissibility of the Material Mode of Speech	312
B.	The Logic of Science as Syntax
82.	The Physical Language	315
83.	The so-called Foundations of the Sciences	322
84.	The Problem of the Foundation of Mathematics	325
85.	Syntactical Sentences in the Literature of the Special Sciences	328
86.	The Logic of Science is Syntax	331
	Bibliography and Index of Authors	334
	Index of Subjects	347