Lore and Science in Ancient Pythagoreanism

Lore and Science in Ancient Pythagoreanism

Philolaus, of Croton, approximately 470 B.C.-
Plato
Pythagoras and Pythagorean school

Walter Burkert

Cambridge, Mass. : Harvard University Press

1972

Translated by Edwin L. Minar, Jr

I. Platonic and Pythagorean Number Theory. -- 1. The Platonic Theory of Ideal Numbers -- 2. The philosophy of the Pythagoreans according to Aristotle -- 3. The Later Non-Aristotelian Tradition and Its Sources, Speusippus, Xenocrates, and Heraclides Ponticus -- 4. Pythagoreanism in Plato and the Origin in Platonism of the Pythagorean Tradition -- II. Pythagoras in the Earlist Tradition. -- 1. Source Problems -- 2. Historical Background -- 3. Metemphychosis and "Shamanism" -- 4. Acusmata -- 5. Acusmatici and Mathematici -- 6. Early Evidence for Pythagoras as a Scientist? -- III. Philolaus. -- 1. The Special Position of Philolaus' Book in the Pythagorean Tradition -- 2. The Spurious and the Genuine in the Philolaus Fragments -- 3. Reflection of Pythagorean Philosophy in the Fifth Century B.C.? -- IV. Astronomy and Pythagoreanism. -- 1. The Structure of the World and the Planetary System -- 2. The Theory of Planetary Movements -- 3. The Cosmos of Philolaus -- 4. Harmony of the S[heres and Astral Immortality -- V. Pythagorean Musical Theory. -- 1. Speculation, Experimentation, and Fiction -- 2. Number Symbolism and Calculation of Proportions in Philolaus -- VI. Pythagorean Number Theory and Greek Mathematics. -- 1. Did the Pythagoreans Lay the Foundations of Greek Mathematics? -- 2. Pythagorean Arithmetic -- 3. Pythagorean Geometry and Mathematical Secrets -- 4. Number and Cosmos.

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