Plato's philosophy of mathematics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
Sankt Augustin
Academia Verl.
1995
|
| Ausgabe: | 1. Aufl. |
| Schriftenreihe: | International Plato studies
5 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 191 S. |
| ISBN: | 3883456373 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804141322582360064 |
|---|---|
| adam_text | Titel: Plato s philosophy of mathematics
Autor: Pritchard, Paul
Jahr: 1995
CONTENTS
Introduction 1
Parti On the Differences Between Greek and Modern Mathematics 7
Chapter 1. The subject matter of Greek arithmetic 9
1. The influence of Euclid s arithmetic 9
2. Euclid s definitions 11
3. Existence and definition 12
4. u.ovd ; cannot denote the number 1 12
5. The meaning of kccG rjv 13
6. Plato on arithmos 14
7. The meaning of uoväc, 15
Chapter 2. Arithmos in Pre-Euclidean Mathematics and Literature 23
1. Pythagorean pebble arithmetic 23
2. The origin of logical proof 24
3. Ancient reports of pre-Euclidean definitions 25
4. The word dpt0u.6 ; in Greek literature before Euclid 27
5. Conclusion 30
Chapter 3. The Ideas of Arithmoi and the Natural Numbers 33
Chapter 4. On the difference between ancient Greek and post-Renaissance
mathematics 39
l.Philosophicalandmathematicalreasoning 40
2. Mathematical abstraction and the imagination 43
3. Abstraction ancient and modern 46
4. The arithmetical Operations 50
5. The difference between ancient and modern mathematics 53
6. Conclusion 55
Chapter 5. The Number One 63
1. Renaissance views 63
2. Greek views 64
3. Cases where arithmos denotes a Single item 67
4. Is the notion that the first arithmos is two a philosophical dogma? 69
5. Do Plato and Aristotle use 1 as a number? 70
Appendix 1: Plato s Ideal Arithmoi and Frege s Platonism 84
Part n. Plato s Philosophy of Mathematics 87
89
89
91
98
99
100
Chapter 6. Sun, Line and Cave
1. The Sun
2. The Line
3. AXf|öeta and recollection 93
4. The objects of mathematical thought 94
5. That Aidvoia is not a separate faculty 96
6. The ratio in which the Line is divided doesn t contribute to the analogy 96
7. The Cave
8. Eikasia in the Cave
9. The bearers of the images
10. That the objects of C2 and C3 are equally unreal 101
ll.Dialectic 103
12. Education and conversion 105
13. Two differentiae of clarity: Tight and genuineness 108
14. Plato s mathematical ontology 111
Chapter 7. Repubiic 525 and Philebus 56 119
1. The problem 119
2. A refutation of Cherniss proposed Solution 120
Chapter 8. The Inadequacy of Mathematical Sensibles 127
1. The Approximation Interpretation 128
2. The Problem of Arithmetic 128
3. Exact Mathematical Sensibles in the Dialogues 129
4. The trouble with greater and less 130
5. The trouble with equal 132
6. The pattern of Plato s arguments distinguishing forms from sensibles 132
7. The Equal Sticks and the Form Equal 136
8. Protagons and the circles of Epistle VU 140
9. The Inadequacy of Mathematical Sensibles 145
Chapter 9. Ideal arithmoi and the intermediates 150
1. The problem of Aristoüe s account of Plato s views 150
2. Ideas of arithmoi 151
3. The arithmetical Operations 151
4. What are the cuu.ßXT|TOi ipiOjiof? 152
5. Aristoüe s account of arithmoi of forms 153
6. The mathematical intermediates 156
7. Aristotle on the intermediates 156
8. Intelligible matter 157
9. The objects of thought 158
VI
Appendix 2: Aristotle and Plato on Recollection 163
1. The Attack on Plato 163
2. Memory is of the pasf 167
3. Saying in the Soul 169
4. Memory, Recollection and Time 170
5. Theorems and Images 171
6. Conclusion 173
Conclusion 177
References 181
Bibliography 185
|
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| discipline | Philosophie Philologie / Byzantinistik / Neulatein |
| edition | 1. Aufl. |
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| id | DE-604.BV025868311 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:14:02Z |
| institution | BVB |
| isbn | 3883456373 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-019115710 |
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| physical | 191 S. |
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| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Academia Verl. |
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| series | International Plato studies |
| series2 | International Plato studies |
| spelling | Pritchard, Paul Verfasser aut Plato's philosophy of mathematics by Paul Pritchard 1. Aufl. Sankt Augustin Academia Verl. 1995 191 S. txt rdacontent n rdamedia nc rdacarrier International Plato studies 5 Plato v427-v347 (DE-588)118594893 gnd rswk-swf 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 Plato v427-v347 (DE-588)118594893 p International Plato studies 5 (DE-604)BV008909289 5 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019115710&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pritchard, Paul Plato's philosophy of mathematics International Plato studies Plato v427-v347 (DE-588)118594893 gnd Philosophie (DE-588)4045791-6 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)118594893 (DE-588)4045791-6 (DE-588)4037944-9 |
| title | Plato's philosophy of mathematics |
| title_auth | Plato's philosophy of mathematics |
| title_exact_search | Plato's philosophy of mathematics |
| title_full | Plato's philosophy of mathematics by Paul Pritchard |
| title_fullStr | Plato's philosophy of mathematics by Paul Pritchard |
| title_full_unstemmed | Plato's philosophy of mathematics by Paul Pritchard |
| title_short | Plato's philosophy of mathematics |
| title_sort | plato s philosophy of mathematics |
| topic | Plato v427-v347 (DE-588)118594893 gnd Philosophie (DE-588)4045791-6 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Plato v427-v347 Philosophie Mathematik |
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