## Lore and Science in Ancient PythagoreanismFor this first English edition of his distinguished study of Pythagoreanism, Weisheit und Wissenschajt: Studien zu Pythagoras, Philolaos, und Platon, Walter Burkert has carefully revised text and notes, taking account of additional literature on the subject which appeared between 1962 and 1969. By a thorough critical sifting of all the available evidence, the author lays a new foundation for the understanding of ancient Pythagoreanism and in particular of the relationship within it of "lore" and "science." He shows that in the twilight zone when the Greeks were discovering the rational interpretation of the world and quantitative natural science, Pythagoras represented not the origin of the new, but the survival or revival of ancient, pre-scientific lore or wisdom, based on superhuman authority and expressed in ritual obligation. |

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### Contents

Platonic and Pythagorean Number Theory | 15 |

The Philosophy of the Pythagoreans according to Aristotle | 28 |

The Later NonAristotelian Tradition and Its Sources | 53 |

Pythagoreanism in Plato and the Origin in Platonism of the | 83 |

Pythagoras in the Earliest Tradition | 97 |

Metempsychosis and Shamanism | 120 |

Acusmata | 166 |

Acusmatici and Mathematici | 197 |

The Cosmos of Philolaus | 337 |

Harmony of the Spheres and Astral Immortality | 350 |

Pythagorean Musical Theory | 369 |

Number Symbolism and Calculation of Proportions in | 386 |

Pythagorean Number Theory and Greek Mathematics | 401 |

Pythagorean Arithmetic | 427 |

Pythagorean Geometry and Mathematical Secrets | 447 |

Number and Cosmos | 465 |

Philolaus | 218 |

The Spurious and the Genuine in the Philolaus Fragments | 238 |

Reflections of Pythagorean Philosophy in the Fifth | 277 |

Astronomy and Pythagoreanism | 299 |

The Theory of Planetary Movements | 322 |

Abbreviations | 485 |

509 | |

528 | |

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### Common terms and phrases

according acusmata Alcmaeon Anaxagoras Anaximander ancient Anst Archytas Arist Aristotle Aristotle's Aristox Aristoxenus astronomy attested attributed Becker Boyance Burkert Burnet century B.C. Cherniss cited concept connection cosmos Croton Delatte Democritus Dicaearchus Diels Diogenes earth Empedocles Eucl Euclid Eudemus Eudoxus expression fact FGrHist fragments Frank Fritz geometry Greek harmony Heath Heraclides Heraclitus Hermes Herodotus Hippasus Hippocrates idea Indefinite Dyad interpretation lamblichus later Math mathematics mentioned Metapontum metempsychosis Mondolfo moon music theory Nicom Nicomachus number theory oreans origin Parmenides passage Philolaus philosophy Phys planets Plato Plut Posidonius presupposes Procl Ptol Pythag Pythagoras Pythagorean Pythagorean doctrine reference reports Rohde says Schol soul speaks Speusippus stars Tannery Theo Sm Thesleff thought Timaeus tone tradition Unlimited van der Waerden Waerden Wehrli Wilamowitz word Xenocrates Zeller Zeno