Mathematics and the image of reason:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London u.a.
Routledge
1991
|
| Edition: | 1. publ. |
| Series: | Philosophical issues in science
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 188 S. graph. Darst. |
| ISBN: | 0415033187 |
Staff View
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| 245 | 1 | 0 | |a Mathematics and the image of reason |c Mary Tiles |
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| 600 | 1 | 4 | |a Hilbert, David <1862-1943> |
| 600 | 1 | 4 | |a Russell, Bertrand <1872-1970> |
| 600 | 1 | 4 | |a Frege, Gottlob <1848-1925> |
| 600 | 1 | 4 | |a Hilbert, David <1862-1943> |
| 600 | 1 | 4 | |a Russell, Bertrand <1872-1970> |
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Record in the Search Index
| _version_ | 1804118857526280192 |
|---|---|
| adam_text | CONTENTS
Acknowledgements xi
Introduction 1
1 AXIOMATIZATION, RIGOUR AND REASON 7
Rigour and Proof 7
Deserting Euclidean Standards 10
The Return to Euclidean Standards 25
2 FREGE: ARITHMETIC AS LOGIC 33
Calculation and Reasoning 33
Numbers and the Nature of Arithmetical Truths 38
Numbers as Objects 42
The Natural Numbers 49
Word Games? 54
3 RUSSELL: MATHEMATICS AS LOGIC 59
Geometry and Relational Structures 60
Paradoxes and Logical Types 70
Empiricism, Logical Positivism and the Sterility of Reason 78
4 HILBERT: MATHEMATICS AS A FORMULA GAME? 89
Formalism and Hilbert s Programme 90
Geometrical Rigour 92
Forging the Formal Chains of Reason 103
Successes and Failures 110
Logic and its Limitations 123
Appendix — Recursive Functions 128
5 IDEAL ELEMENTS AND RATIONAL IDEALS 129
Formulae, Symbols and Forms 130
Ideal Elements and Ideals 138
ix
CONTENTS
Geometry: Diagrams and Rigour 142
Pragmatism, Axiomatization and Ideals 147
Logic and the Objects of Mathematical Knowledge 154
Lack of Closure and the Power of Reason 166
Glossary of Symbols 175
Further Reading 176
Bibliography 178
Index 184
|
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| discipline | Mathematik Philosophie |
| edition | 1. publ. |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T16:16:58Z |
| institution | BVB |
| isbn | 0415033187 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002915154 |
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| physical | XI, 188 S. graph. Darst. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | Routledge |
| record_format | marc |
| series2 | Philosophical issues in science |
| spelling | Tiles, Mary 1946- Verfasser (DE-588)1059945274 aut Mathematics and the image of reason Mary Tiles 1. publ. London u.a. Routledge 1991 XI, 188 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Philosophical issues in science Frege, Gottlob <1848-1925> Hilbert, David <1862-1943> Russell, Bertrand <1872-1970> Logica gtt Mathématiques - Philosophie Wiskunde gtt Logik Mathematik Philosophie Mathematics Philosophy Philosophie (DE-588)4045791-6 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Mathematik (DE-588)4037944-9 s Philosophie (DE-588)4045791-6 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002915154&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Tiles, Mary 1946- Mathematics and the image of reason Frege, Gottlob <1848-1925> Hilbert, David <1862-1943> Russell, Bertrand <1872-1970> Logica gtt Mathématiques - Philosophie Wiskunde gtt Logik Mathematik Philosophie Mathematics Philosophy Philosophie (DE-588)4045791-6 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4045791-6 (DE-588)4037944-9 |
| title | Mathematics and the image of reason |
| title_auth | Mathematics and the image of reason |
| title_exact_search | Mathematics and the image of reason |
| title_full | Mathematics and the image of reason Mary Tiles |
| title_fullStr | Mathematics and the image of reason Mary Tiles |
| title_full_unstemmed | Mathematics and the image of reason Mary Tiles |
| title_short | Mathematics and the image of reason |
| title_sort | mathematics and the image of reason |
| topic | Frege, Gottlob <1848-1925> Hilbert, David <1862-1943> Russell, Bertrand <1872-1970> Logica gtt Mathématiques - Philosophie Wiskunde gtt Logik Mathematik Philosophie Mathematics Philosophy Philosophie (DE-588)4045791-6 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Frege, Gottlob <1848-1925> Hilbert, David <1862-1943> Russell, Bertrand <1872-1970> Logica Mathématiques - Philosophie Wiskunde Logik Mathematik Philosophie Mathematics Philosophy |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002915154&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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