Logical foundations of probability:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Chicago
Univ. of Chicago Press
1971
London Routledge & Kegan Paul |
| Ausgabe: | 2. ed., 4. impr. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXVII, 613 S. 24 cm |
| ISBN: | 0226093433 |
Internformat
MARC
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| 245 | 1 | 0 | |a Logical foundations of probability |c Rudolf Carnap |
| 250 | |a 2. ed., 4. impr. | ||
| 264 | 1 | |a Chicago |b Univ. of Chicago Press |c 1971 | |
| 264 | 1 | |a London |b Routledge & Kegan Paul | |
| 300 | |a XXVII, 613 S. |c 24 cm | ||
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| 650 | 4 | |a INDUCTION (Logic) | |
| 650 | 4 | |a PROBABILITY | |
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Datensatz im Suchindex
| _version_ | 1804119882609983488 |
|---|---|
| adam_text | CONTENTS
I. On Explication i
1. Introduction: Our Problems i
2. On the Clarification of an Explicandum 3
3. Requirements for an Explicatum 5
4. Classificatory, Comparative, and Quantitative Concepts ... 8
5. Comparative and Quantitative Concepts as Explicata .... 11
6. Formalization and Interpretation 15
II. The Two Concepts of Probability 19
8. The Semantical Concepts of Confirmation 19
9. The Two Concepts of Probability 23
10. The Logical Nature of the Two Probability Concepts .... 29
A. Probability,, Degree of Confirmation (29)—B. Probability,,, Rela¬
tive Frequency (33)
11. Psychologism in Deductive Logic 37
12. Psychologism in Inductive Logic 42
A. Probability as a Logical Relation (43)—B. The Classical Theory
of Probability (47)
III. Deductive Logic 52
14. Preliminary Explanations 53
15. The Signs of the Systems 8 58
A. The Signs Occurring in Our Systems (58)—B. On the Possibility
of an Ordered System (62)
16. The Rules of Formation 65
17. Rules of Truth 68
18. State Descriptions (3) and Ranges (5R) 70
A. State Descriptions (70)—B. The Requirements of Logical Inde¬
pendence and Completeness (72)—C. Families of Related Proper¬
ties (76)—D. The Range of a Sentence (78)
19. Theorems on State Descriptions and Ranges 80
20. L Concepts 82
21. Theorems of Propositional Logic 89
A. Elementary Theorems of Propositional Logic (89)—B. Theorems
on Truth Tables (93)—C. Normal Forms (94)
22. Theorems on General Sentences 96
23. Theorems on Replacements 100
24. Theorems on Identity 101
25. On Predicate Expressions and Divisions 104
xxiii
xxiv CONTENTS
26. Isomorphic Sentences; Individual and Statistical Distributions . 108
A. Individual Correlations and Isomorphism (108)—B. Individual
and Statistical Distributions (in)
27. Structure Descriptions (@tr) 114
28. Correlations for Basic Matrices 118
29. Some Numbers Connected with the Systems 8 121
31. The Systems ?*; the ^ Predicates 122
32. Logical Width 126
33. The Q Normal Form 130
34. The ^ Numbers 134
35. Some Numbers Connected with the Systems 8T 138
37. Simple Laws 141
38. Simple Laws of Conditional Form 144
40. Some Mathematical Definitions and Theorems 148
A. Some Mathematical Functions (149)—B. Limit (154)—C. Infinite
Cardinal Numbers (155)—D. Combinatorics (156)
IV. The Problem of Inductive Logic 161
41. The Logical Concept of Probability 162
A. Probability, as a Measure of Evidential Support (164)—B. Prob¬
ability, as a Fair Betting Quotient (165)—C. Probability, and Rela¬
tive Frequency (167)—D. Probability, as an Estimate of Relative
Frequency (168)—E. Some Comments on Other Conceptions (175)—
F. Presuppositions of Induction (177)
42. Probability, and Probability 1 182
A. The Shift in the Meaning of the Word Probability (182)— B. On
the Interpretation of Given Probability Statements (187)
43. Inductive and Deductive Logic 192
A. On the Possibility of Exact Rules of Induction (192)—B. The
Relation between Deductive and Inductive Logic (199)
44. Logical and Methodological Problems 202
A. Methodological Problems (202)—B. Inductive Inferences (205)
45. Abstraction in Inductive Logic 208
A. Abstraction in Deductive and Inductive Logic (208)—B. The Re¬
quirement of Total Evidence (211)—C. The Applicability of Induc¬
tive Logic (213)—D. Dangers and Usefulness of Abstraction (215)
46. Is a Quantitative Inductive Logic Impossible? 219
47. Some Difficulties Involved in the Problem of Degree of Confirmation 226
A. Singular Prediction (226)—B. Confirming Cases for a Law (228)
—C. More Complex Evidence (229)—D. Disconfirming Cases (229)
—E. The Variety of Instances (230)—F. The Task before Us (231)
48. Is Probability, Used as a Quantitative Concept? 233
A. Probability, Is Used as a Comparative Concept (233)—B. Prob¬
ability, and Games of Chance (234)—C. Probability, and Direct In
CONTENTS xxv
ference (235)—!). Probability! and Betting Behavior (235)—E.
Probability, Is Used as an Objective Concept (238)
49. The Question of the Usefulness of Inductive Logic 241
A. Theoretical Usefulness of Inductive Logic in Science (242)—B.
Practical Usefulness of Inductive Logic: Probability as a Guide of
Life (246)
50. The Problem of a Rule for Determining Decisions 252
A. The Problem (253)—B. The Rule of High Probability (254)—
C. The Rule of Maximum Probability (255)—/). The Rule of the
Use of Estimates (257)—E. The Rule of Maximizing the Estimated
Gain (260)
51. The Rule of Maximizing the Estimated Utility 264
A. The Rule of Maximizing the Estimated Utility (265)—B. Daniel
Bernoulli s Law of Utility (270)—C. Consequences of Bernoulli s
Law (273)
52. On the Arguments of Degree of Confirmation 279
53. Some Conventions on Degree of Confirmation 284
54. Reduction of the Problem of Degree of Confirmation 287
A. Degree of Confirmation in the Infinite System (288)—B. The Null
Confirmation (289)—C. Reduction to State Descriptions (289)—
D. Null Confirmation for the State Descriptions (289)—E. The Re¬
quirement of Fitting Together (290)
V. The Foundation of Quantitative Inductive Logic: The Regular
c Functions 293
55. Regular m and c Functions for Finite Systems 293
A. Regular m and c Functions (294)—B. Deductive and Inductive
Logic (296)—C. Probability! and Probability,, (300)
56. Regular Functions for the Infinite System 302
57. Null Confirmation; Fitting Sequences 305
A. Theorems on Regular m Functions (305)—B. Null Confirmation
(307)—C. Fitting Sequences (309)
58. Almost L True Sentences 311
59. Theorems on Regular c Functions 315
60. Confirmation of Hypotheses by Observations; Bayes s Theorem . 326
61. Confirmation of a Hypothesis by a Predictable Observation . . 333
62. On Some Axiom Systems by Other Authors 337
VI. Relevance and Irrelevance 346
65. The Concepts of Relevance and Irrelevance 346
66. The Relevance Quotient 356
67. The Relevance Measure 360
68. Relevance Measures for Two Observations and Their Connections . 366
69. The Possible Relevance Situations for Two Observations and Their
Connections 374
xxvi CONTENTS
70. Relevance Measures for Two Hypotheses and Their Connections . 386
71. The Possible Relevance Situations for Two Hypotheses and Their
Connections 391
72. Relevance Measures of State Descriptions; First Method: Disjunc¬
tive Analysis 397
73. Second Method: Conjunctive Analysis 404
74. Extreme Relevance 409
75. Complete Relevance 4J4
76. Relations between Extreme and Complete Relevance . . . . 421
VII. Comparative Inductive Logic 428
79. The Problem of a Comparative Concept of Confirmation . . . 428
80. Requirements of Adequacy 43°
81. Definition of the Comparative Concept of Confirmation 3KE . . 435
82. Some Concepts Based on 3KE 441
83. Further Theorems on Comparative Concepts 445
A. Theorems (445)—B. Koopman s Axiom System (450)
84. Maximum and Minimum Confirmation 454
85. Correspondence between Comparative and Quantitative Theorems 456
86. The Concept of Confirming Evidence 462
87. Hempel s Analysis of the Concept of Confirming Evidence . . . 468
88. Hempel s Definition of Confirming Evidence 478
VIII. The Symmetrical c Functions 483
90. Symmetrical tn Functions 483
91. Symmetrical c Functions 486
92. Theorems on Symmetrical c Functions 489
94. The Direct Inductive Inference 492
95. The Binomial Law 498
96. Bernoulli s Theorem 503
IX. Estimation 511
98. The Problem of Estimation 511
99. A General Estimate Function 520
100. Definition of the c Mean Estimate Function 524
A. Definition of the c Mean Estimate Function (525)—B. Some Ter¬
minological Remarks (528)—C. The Paradox of Estimation (530)
102. The Problem of the Reliability of an Estimate 533
103. The Estimated Square Error of an Estimate 537
104. Estimation of Frequencies 540
105. Direct Estimation of Frequencies 546
106. Predictive Estimation of Frequencies 550
A. Theorems on Predictive Estimation of Frequencies (550)—B. The
CONTENTS xxvii
Limit of Relative Frequency in an Infinite Class (552)—C. The
Problem of the Reliability of a Value of Degree of Confirmation (554)
107. Further Theorems on Predictive Estimation of Relative Frequency 555
A. Frequencies of (^ Properties (556)—B. The Problem of the Null
Evidence (557)—C. Further Theorems on the Estimate of Relative
Frequency (559)—D. The Inverse Estimation of Frequency (560)
Appendix 562
no. Outline of a Quantitative System of Inductive Logic .... 562
A. The Function c* (562)— B. The Direct Inference (567)— C. The
Predictive Inference (567)—D. The Inference by Analogy (569)—
E. The Inverse Inference (570)—F. The Universal Inference (570)
—G. The Instance Confirmation of a Law (571)—H. Are Laws Need¬
ed for Making Predictions? (574)—/. The Variety of Instances (575)
—/. Inductive Logic as a Rational Reconstruction (576)
Glossary 578
Bibliography 583
Index 605
|
| any_adam_object | 1 |
| author | Carnap, Rudolf 1891-1970 |
| author_GND | (DE-588)118519158 |
| author_facet | Carnap, Rudolf 1891-1970 |
| author_role | aut |
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| building | Verbundindex |
| bvnumber | BV005695431 |
| callnumber-first | B - Philosophy, Psychology, Religion |
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| callnumber-raw | BC141 |
| callnumber-search | BC141 |
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| callnumber-subject | BC - Logic |
| classification_rvk | CI 1804 SK 130 SK 800 |
| ctrlnum | (OCoLC)225032526 (DE-599)BVBBV005695431 |
| discipline | Mathematik Philosophie |
| edition | 2. ed., 4. impr. |
| format | Book |
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| id | DE-604.BV005695431 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:33:15Z |
| institution | BVB |
| isbn | 0226093433 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003557352 |
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| physical | XXVII, 613 S. 24 cm |
| publishDate | 1971 |
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| publisher | Univ. of Chicago Press Routledge & Kegan Paul |
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| spelling | Carnap, Rudolf 1891-1970 Verfasser (DE-588)118519158 aut Logical foundations of probability Rudolf Carnap 2. ed., 4. impr. Chicago Univ. of Chicago Press 1971 London Routledge & Kegan Paul XXVII, 613 S. 24 cm txt rdacontent n rdamedia nc rdacarrier INDUCTION (Logic) PROBABILITY Logik (DE-588)4036202-4 gnd rswk-swf Induktion (DE-588)4026765-9 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf Wahrscheinlichkeit (DE-588)4137007-7 gnd rswk-swf Induktive Logik (DE-588)4161594-3 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s Logik (DE-588)4036202-4 s DE-604 Wahrscheinlichkeit (DE-588)4137007-7 s 1\p DE-604 Induktive Logik (DE-588)4161594-3 s 2\p DE-604 Induktion (DE-588)4026765-9 s 3\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003557352&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Carnap, Rudolf 1891-1970 Logical foundations of probability INDUCTION (Logic) PROBABILITY Logik (DE-588)4036202-4 gnd Induktion (DE-588)4026765-9 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Wahrscheinlichkeit (DE-588)4137007-7 gnd Induktive Logik (DE-588)4161594-3 gnd |
| subject_GND | (DE-588)4036202-4 (DE-588)4026765-9 (DE-588)4064324-4 (DE-588)4137007-7 (DE-588)4161594-3 |
| title | Logical foundations of probability |
| title_auth | Logical foundations of probability |
| title_exact_search | Logical foundations of probability |
| title_full | Logical foundations of probability Rudolf Carnap |
| title_fullStr | Logical foundations of probability Rudolf Carnap |
| title_full_unstemmed | Logical foundations of probability Rudolf Carnap |
| title_short | Logical foundations of probability |
| title_sort | logical foundations of probability |
| topic | INDUCTION (Logic) PROBABILITY Logik (DE-588)4036202-4 gnd Induktion (DE-588)4026765-9 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Wahrscheinlichkeit (DE-588)4137007-7 gnd Induktive Logik (DE-588)4161594-3 gnd |
| topic_facet | INDUCTION (Logic) PROBABILITY Logik Induktion Wahrscheinlichkeitsrechnung Wahrscheinlichkeit Induktive Logik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003557352&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT carnaprudolf logicalfoundationsofprobability |