Lore and Science in Ancient Pythagoreanism

Introduction ......Page 8
1.  The Platonic Theory of Ideal Numbers ......Page 22
2.  The Philosophy of the Pythagoreans according to Aristotle ......Page 35
3.  The Later Non-Aristotelian Tradition and Its Sources, Speusippus, Xenocrates, and Heraclides Ponticus ......Page 60
4.  Pythagoreanism in Plato and the Origin in Platonism of the Pythagorean Tradition ......Page 90
1.  Source Problems ......Page 104
2.  Historical Background ......Page 116
3.  Metempsychosis and \"Shamanism\" ......Page 127
4.  Acusmata ......Page 173
5.  Acusmatici and Mathematici ......Page 199
6.  Early Evidence for Pythagoras as a Scientist? ......Page 215
1.  The Special Position of Philolaus\' Book in the Pythagorean Tradition ......Page 225
2.  The Spurious and the Genuine in the Philolaus Fragments ......Page 245
3.  Reflections of Pythagorean Philosophy in the Fifth Century B.C.? ......Page 284
1.  The Structure of the World and the Planetary System ......Page 306
2.  The Theory of Planetary Movements ......Page 329
3.  The Cosmos of Philolaus ......Page 344
4.  Harmony of the Spheres and Astral Immortality ......Page 357
1.  Speculation, Experimentation, and Fiction ......Page 376
2.  Number Symbolism and Calculation of Proportions in Philolaus ......Page 393
1.  Did the Pythagoreans Lay the Foundations of Greek Mathematics?- ......Page 408
2.  Pythagorean Arithmetic ......Page 434
3.  Pythagorean Geometry and Mathematical Secrets ......Page 454
4.  Number and Cosmos ......Page 472
Abbreviations ......Page 492
Bibliography ......Page 500
Greek Words Discussed ......Page 516
Index of Passages ......Page 517
General Index ......Page 535