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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 |
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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 |
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