The mathematical philosophy of Bertrand Russell: origins and development
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Basel [u.a.]
Birkhäuser
1991
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Bibliographie B. Russell S. 227 - 236 |
| Beschreibung: | XIV, 236 S. 24 cm |
| ISBN: | 3764326565 0817626565 |
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Datensatz im Suchindex
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| adam_text | Contents
Keys to Russell s works and Cross references x
Acknowledgements xi
Preface by Ivor Grattan Guinness xiii
Introduction 1
1. Methodological and logicist background 5
1.1. Boole and Peirce 5
1.2. Dedekind and Cantor 13
1.3. Couturat and Whitehead 19
1.4. Bradley and Moore 27
1.5. Foundations of geometry 36
2. The unpublished mathematical philosophy: 1898 1900 44
2.1. The genesis of the 1898 1900 manuscripts 44
2.2. Logic, mathematics and ontology 49
2.3. The evolution of the main concepts 57
2.4. Concepts, axioms, presupposition and implication 62
2.5. The contradiction and the infinite 69
2.6. Relations and the principle of abstraction 72
2.7. The method of definition 77
2.8. The gradual approach to Cantor 81
2.8.1. The first contacts and opinions 81
2.8.2. The reasons for the rejection 86
viii The mathematical philosophy of Bertrand Russell
3. The contribution of Peano and his school 91
3.1. Logic 92
3.1.1. Objective and stages 92
3.1.2. Primitives, logical order and interdefinability 93
3.1.3. Implication, inclusion and membership 97
3.1.4. Classes, propositions and individuals 99
3.1.5. Mathematical propositions and quantification 101
3.1.6. Relations, functions, classes, properties and propositions 103
3.2. Arithmetic 105
3.2.1. The axioms and their interpretation: Dedekind 105
3.2.2. The definability of number 107
3.2.3. Real numbers: construction and definition 108
3.2.4. The logicist arithmetic: Cantor 110
3.3. Geometry 113
3.3.1. The geometric calculus and the principles of geometry 113
3.3.2. The logicist geometry 117
3.4. The method 119
3.4.1. Axiomatics 119
3.4.2. Definitions 121
3.4.3. The definition by abstraction 124
3.4.4. Simplicity, analysis and intuition 125
3.5. Peano s followers and their contributions 127
3.5.1. The various improvements 127
3.5.2. The transformation of definitions by abstraction into nominal ones 131
4. The principles of mathematics 135
4.1. The reaction to the Congress of 1900 135
4.1.1. The notes to the manuscripts: from Moore to Peano 135
4.1.2. The first writings 138
4.1.3. The acceptance of Cantor 141
4.2. Logic 144
4.2.1. The indefinables and the prepositional function 144
4.2.2. Relations 151
Contents ix^
4.3. Arithmetic 155
4.3.1. The definition of cardinal number 155
4.3.2. Finite and infinite 162
4.3.3. Quantity 164
4.3.4. Order 166
4.3.5. Ordinal numbers 169
4.3.6. Real numbers 173
4.4. Geometry 175
4.5. What Russell learned from Peano 181
5. Philosophical and methodological problems 185
5.1. Origin and evolution of Russell s logicism 185
5.2. The principle of abstraction 189
5.2.1. Origin and evolution 189
5.2.2. Assumptions and implications 194
5.3. The constructive definition 205
5.3.1. Nominal definitions 205
5.3.2. Mathematical and philosophical definitions 208
5.3.3. Analysis and ordinary language 211
5.4. Relational logic and ontology 215
Bibliography 224
B.I. Works by Russell 224
B. 1.1. Unpublished manuscripts 224
B. 1.2. Published or unpublished correspondence 225
B.1.3. Published works 225
B.2. Works by other authors 227
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| isbn | 3764326565 0817626565 |
| language | English |
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| spelling | Rodríguez-Consuegra, Francisco A. Verfasser aut The mathematical philosophy of Bertrand Russell origins and development Francisco A. Rodriguez-Consuegra Basel [u.a.] Birkhäuser 1991 XIV, 236 S. 24 cm txt rdacontent n rdamedia nc rdacarrier Bibliographie B. Russell S. 227 - 236 Russell, Bertrand - 1898 / 1903 rero Russell, Bertrand 1872-1970 (DE-588)118604287 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Grundlage (DE-588)4158388-7 gnd rswk-swf Analytische Philosophie (DE-588)4001869-6 gnd rswk-swf Philosophie (DE-588)4045791-6 gnd rswk-swf Russell, Bertrand 1872-1970 (DE-588)118604287 p Analytische Philosophie (DE-588)4001869-6 s DE-604 Mathematik (DE-588)4037944-9 s Grundlage (DE-588)4158388-7 s Philosophie (DE-588)4045791-6 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002803756&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rodríguez-Consuegra, Francisco A. The mathematical philosophy of Bertrand Russell origins and development Russell, Bertrand - 1898 / 1903 rero Russell, Bertrand 1872-1970 (DE-588)118604287 gnd Mathematik (DE-588)4037944-9 gnd Grundlage (DE-588)4158388-7 gnd Analytische Philosophie (DE-588)4001869-6 gnd Philosophie (DE-588)4045791-6 gnd |
| subject_GND | (DE-588)118604287 (DE-588)4037944-9 (DE-588)4158388-7 (DE-588)4001869-6 (DE-588)4045791-6 |
| title | The mathematical philosophy of Bertrand Russell origins and development |
| title_auth | The mathematical philosophy of Bertrand Russell origins and development |
| title_exact_search | The mathematical philosophy of Bertrand Russell origins and development |
| title_full | The mathematical philosophy of Bertrand Russell origins and development Francisco A. Rodriguez-Consuegra |
| title_fullStr | The mathematical philosophy of Bertrand Russell origins and development Francisco A. Rodriguez-Consuegra |
| title_full_unstemmed | The mathematical philosophy of Bertrand Russell origins and development Francisco A. Rodriguez-Consuegra |
| title_short | The mathematical philosophy of Bertrand Russell |
| title_sort | the mathematical philosophy of bertrand russell origins and development |
| title_sub | origins and development |
| topic | Russell, Bertrand - 1898 / 1903 rero Russell, Bertrand 1872-1970 (DE-588)118604287 gnd Mathematik (DE-588)4037944-9 gnd Grundlage (DE-588)4158388-7 gnd Analytische Philosophie (DE-588)4001869-6 gnd Philosophie (DE-588)4045791-6 gnd |
| topic_facet | Russell, Bertrand - 1898 / 1903 Russell, Bertrand 1872-1970 Mathematik Grundlage Analytische Philosophie Philosophie |
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