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Contents 6 List of Illustrations 8 Acknowledgements 12 Introduction: Thinking the Parthenon and Liberal Arts Education Together 14 1. The Parthenon as an Institution of Liberal Arts Education 15 2. The Parthenon and the Historiography of Greek Mathematics 20 Part I: Plato on Dialectic and the Problem-Based Study of Mathematics 36 Chapter 1: Dialectic and the Mathematical Arts in Republic (9.587b–588a): Philolaus’s Scale and the Final Bout between the Just and Unjust Souls 38 1. The Two Interpretive Principles We Bring to Plato’s Dialogues 41 Leaving Things Out 41 2. Why 729? The Positive Absence of Harmony in Resp. 9.587b–588a 46 From the Five Regimes to Philolaus’s Great Year 48 The Unspoken Resonance of 729 for Philolaus 53 Chapter 2: Dialectic and the Mathematical Arts in Timaeus (35b–36c): Philolaus’s Scale in the Construction of the World-Soul 58 1. Our Interpretive Principles as Applied to Timaeus 58 2. Dialectic and the Debt to Philolaus 64 Chapter 3: Platonic Dialectic, Pythagorean Harmonics, and Liberal Arts Education 74 1. Pythagorean Harmonics and Plato’s Subordination of Mathematics to Dialectic in Resp. 7 75 2. Plato and the Liberal Arts: Epistemic Closure in Mathemati
- Author
- Lehman, Geoff
- Language
- EN
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