## Plato and PythagoreanismWas Plato a Pythagorean? Plato's students and earliest critics thought so, but scholars since the 19th century have been more skeptical. In Plato and Pythagoreanism, Phillip Sidney Horky argues that a specific type of Pythagorean philosophy, called "mathematical" Pythagoreanism, exercised a decisive influence on fundamental aspects of Plato's philosophy. The progenitor of mathematical Pythagoreanism was the infamous Pythagorean heretic and political revolutionary Hippasus of Metapontum, a student of Pythagoras who is credited with experiments in harmonics that led to innovations in mathematics. The innovations of Hippasus and other mathematical Pythagoreans, including Empedocles of Agrigentum, Epicharmus of Syracuse, Philolaus of Croton, and Archytas of Tarentum, presented philosophers like Plato with new approaches to science that sought to reconcile empirical knowledge with abstract mathematical theories. Plato and Pythagoreanism shows how mathematical Pythagoreanism established many of the fundamental philosophical questions Plato dealt with in his central dialogues, including Cratylus, Phaedo, Republic, Timaeus, and Philebus. In the process, it also illuminates the historical significance of the mathematical Pythagoreans, a group whose influence over the development of philosophical and scientific methods have been obscured since late antiquity. The picture that results is one in which Plato inherits mathematical Pythagorean method only to transform it into a powerful philosophical argument concerning the essential relationships between the cosmos and the human being. |

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### Contents

1 Aristotle on Mathematical Pythagoreanism in the Fourth Century BCE | 3 |

2 Hippasus of Metapontum and Mathematical Pythagoreanism | 37 |

3 Exoterism and the History of Pythagorean Politics | 85 |

4 Mathematical Pythagoreanism and Platos Cratylus | 125 |

5 What Is Wisest? Mathematical Pythagoreanism and Platos Phaedo | 167 |

Mathematical Pythagoreanism and Discovery | 201 |

Afterword | 261 |

Bibliography | 265 |

281 | |

295 | |

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acousmatic acousmatic Pythagoreans activity appears Archytas Archytas’s argued Arist Aristotle Aristotle’s Aristoxenus associated Athenian attributes Burkert chapter chieﬂy claims classiﬁcation concerning Cratylus deﬁne deﬁnition demonstration derived described dialogue Dicaearchus difﬁcult Dillon discussion doctrines doxographical early Echecrates Empedocles Epicharmus Epicharmus’s Eurytus evidence exoteric FGrHist FGrHist 566 ﬁfth century BCE ﬁgures ﬁre ﬁrst principles ﬁrst-discoverer fourth century BCE fragments Greek Growing Argument Heraclitus Heraclitus’s heurematographical Hippasus of Metapontum Hippasus’s honorable Horky Huffman human Iambl Iamblichus Iamblichus’s inﬂuence mathematical Pythagoreans Metaph Metaphysics myth nature Nicomachus objects ofthe Palamedes Parmenides passage Peripatetic Phaedo Philebus Philolaus of Croton Philolaus’s philosophical Plato Platonists political pragmateia predication Presocratic Protagoras Pythago Pythagoras Pythagoras’s reference reﬂects Republic sciences scientiﬁc section entitled signiﬁcant so-called Socrates Socrates’s Sophists sort soul speciﬁcally Speusippus suggests Tarentum Theophrastus theory Theuth things Timaeus of Tauromenium Timaeus’s translation uniﬁed University Press unlimited Wehrli Xenocrates Zhmud