Mathematics as a cultural system:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford u.a.
Pergamon Pr.
1981
|
| Ausgabe: | 1. ed. |
| Schriftenreihe: | Foundations and philosophy of science and technology series.
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 182 S. |
| ISBN: | 0080257968 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804118043626831872 |
|---|---|
| adam_text | Contents
Chapter I. The nature of Culture and Cultural Systems 1
1. Evolution of a cultural artifact 3
2. The things that make up a culture 6
3. Culture as a collection of elements in a communications
network 8
4. Mathematics as a cultural system 14
5. Cultural and conceptual evolution 17
Chapter II. Examples of Cultural Patterns Observable in the
Evolution of Mathematics 21
1. Multiples 22
2. Clustering of genius 23
3. The before his time phenomenon 24
4. The operation of cultural lag in mathematics 25
5. Patterns of thought. Mathematical reality and
mathematical existence 27
6. Evolution of greater abstraction 30
7. Forced origins of new concepts 33
8. Selection in mathematics 35
9. The effect of the occurrence of paradox, or the discovery
of inconsistency 37
10. The relativity of mathematical rigor 39
11. Growth patterns of fields of mathematics 41
12. A problem 45
Chapter III. Historical Episodes; a Laboratory for the Study of
Cultural Change 47
1. The great diffusions 48
2. Symbolic achievements 49
ix
X MATHEMATICS AS A CULTURAL SYSTEM
3. Pressure from the environment; environmental stress 54
4. Motivation for multiple invention; exceptions to the rule 55
5. The great consolidations 58
6. Leaps in abstraction 60
7. Great generalizations 64
Chapter IV. Potential of a Theory or Field; Hereditary Stress 66
1. Hereditary stress 67
2. Components of hereditary stress 68
(i) Capacity 68
(ii) Significance 70
(iii) Challenge 72
(iv) Conceptual stress 73
(1) Symbolic stress 73
(2) Problems whose solution requires new concepts 75
(3) Stress for creating order among alternative
theories 76
(4) New attitudes toward mathematical existence 77
(v) Status 80
(vi) Paradox and/or inconsistency 81
3. General remarks 82
Chapter V. Consolidation: Force and Process 84
Part I. General theory 85
la. Consolidation as a social or cultural phenomenon 88
Ib. Effects of diffusion 89
Part II. The consolidation process in mathematics 91
Part Ha. Examples 91
lib. Cultural lag and cultural resistance in the
consolidation process 100
He. Analysis 102
Part III. Concluding remarks 103
Chapter VI. The Exceptional Individual; Singularities in the
Evolution of Mathematics 105
1. General remarks. Mendel, Bolzano, Desargues 105
2. Historical background of Desargues work 108
2a.Girard Desargues and PG 17 109
CONTENTS Xi
3. Why was PG17 not developed into a field? 112
3a. The mathematical environment of the 17th century 113
3b. The internal nature of PG17 115
4. Avenues of possible survival 117
5. The success of projective geometry in the 19th century 118
6. General characteristics of the before-his-time
phenomenon 121
6a. The premat as a loner 122
6b. Tendency of the premat to create a vocabulary that
repels possible readers 123
6c. The capacity and significance of the new concepts
embodied in the prematurity not recognized 123
6d. The culture not ready to incorporate and extend the
new concepts embodied in the prematurity 124
6e. Lack of personal status of the premat in the scientific
community 124
6f. Insufficient diffusion of the new ideas presented
by the prematurity 124
6g. An unusual combination of interests on the part of
the premat 125
7. Comment 125
Chapter VII. Laws Governing the Evolution of Mathematics 126
1. Law governing multiple discovery 127
la. Law governing first proof of a theorem 127
2. Law re. acceptance of a new concept 127
3. Law re. evolution of new concepts 128
4. Law re. the status of creator of a new concept 129
5. Law re. continued importance of a concept 129
6. Law re. the solution of an important problem 130
7. Law re. the occurrence of consolidation 131
7a. Law of consolidation 132
8. Law re. interpretation of unreal concepts 132
9. Law re. the cultural intuition 133
10. Law re. diffusion 135
11. Law re. environmental stresses 138
12. Law re. great advances or breakthroughs 140
Xii MATHEMATICS AS A CULTURAL SYSTEM
13. Law re. inadequacies of a conceptual structure 141
14. Law re. revolutions in mathematics 142
15. Law re. mathematical rigor 144
16. Law re. evolution of a mathematical system 145
17. Law re. the individual and mathematics 145
18. Law re. mathematics becoming worked out 146
19. Law re. beginnings 146
20. Law re. ultimate foundation of mathematics 147
21. Law re. hidden assumptions 147
22. Law re. emergence of periods of great activity 148
23. Law re. absolutes in mathematics 148
Chapter VIII. Mathematics in the 20th Century; Role and Future 149
1. The place of mathematics in 20th-century culture 149
2. Future dark ages? 150
3. The role of mathematics in the 20th century 152
4. The uses of mathematics in the natural and social sciences 156
5. Relevance to historiography 160
Appendix: Footnote for the Aspiring Mathematician 164
Bibliography 167
Index 173
|
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| dewey-ones | 303 - Social processes 306 - Culture and institutions |
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| dewey-search | 303.4/83 306/.4 |
| dewey-sort | 3303.4 283 |
| dewey-tens | 300 - Social sciences |
| discipline | Soziologie Mathematik |
| edition | 1. ed. |
| era | Geschichte gnd |
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| spelling | Wilder, Raymond Louis 1896-1982 Verfasser (DE-588)118632809 aut Mathematics as a cultural system 1. ed. Oxford u.a. Pergamon Pr. 1981 XII, 182 S. txt rdacontent n rdamedia nc rdacarrier Foundations and philosophy of science and technology series. Geschichte gnd rswk-swf Mathématiques - Aspect social Mathématiques - Aspect social ram Mathématiques - Histoire Mathématiques - Histoire ram Sociale aspecten gtt Wiskunde gtt Geschichte Gesellschaft Mathematik Mathematics History Mathematics Social aspects Philosophie (DE-588)4045791-6 gnd rswk-swf Wissenschaftssoziologie (DE-588)4066611-6 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Mathematik (DE-588)4037944-9 s Wissenschaftssoziologie (DE-588)4066611-6 s DE-604 Philosophie (DE-588)4045791-6 s 1\p DE-604 Geschichte z 2\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002354297&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 |
| spellingShingle | Wilder, Raymond Louis 1896-1982 Mathematics as a cultural system Mathématiques - Aspect social Mathématiques - Aspect social ram Mathématiques - Histoire Mathématiques - Histoire ram Sociale aspecten gtt Wiskunde gtt Geschichte Gesellschaft Mathematik Mathematics History Mathematics Social aspects Philosophie (DE-588)4045791-6 gnd Wissenschaftssoziologie (DE-588)4066611-6 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4045791-6 (DE-588)4066611-6 (DE-588)4037944-9 |
| title | Mathematics as a cultural system |
| title_auth | Mathematics as a cultural system |
| title_exact_search | Mathematics as a cultural system |
| title_full | Mathematics as a cultural system |
| title_fullStr | Mathematics as a cultural system |
| title_full_unstemmed | Mathematics as a cultural system |
| title_short | Mathematics as a cultural system |
| title_sort | mathematics as a cultural system |
| topic | Mathématiques - Aspect social Mathématiques - Aspect social ram Mathématiques - Histoire Mathématiques - Histoire ram Sociale aspecten gtt Wiskunde gtt Geschichte Gesellschaft Mathematik Mathematics History Mathematics Social aspects Philosophie (DE-588)4045791-6 gnd Wissenschaftssoziologie (DE-588)4066611-6 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Mathématiques - Aspect social Mathématiques - Histoire Sociale aspecten Wiskunde Geschichte Gesellschaft Mathematik Mathematics History Mathematics Social aspects Philosophie Wissenschaftssoziologie |
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