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arXiv · 1405.4186

The Anthyphairetic Revolutions of the Platonic Ideas

Stelios Negrepontis
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Abstract

In the present work it is shown, by an examination of the Platonic dialogues Theaetetus, Sophistes, Politicus, and Philebus, that (a) a Platonic Idea is the philosophic analogue of a pair of lines incommensurable in length only, (b) the Division and Collection, the method by which humans obtain knowledge of a Platonic Idea, is the philosophic analogue of the palindromically periodic anthyphairesis of this pair, and (c) a Platonic Idea is One in the sense of the self-similarity induced by periodic anthyphairesis. A byproduct of the above analysis is that (d) Theaetetus had obtained a proof of the Proposition: The anthyphairesis of a dyad of lines incommensurable in length only is palindromically periodic. It is further verified that the concepts and tools contained in the Theaetetean Book X of the Elements suffice for the proof of the Proposition.

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Stelios Negrepontis. 2014-05-16. The Anthyphairetic Revolutions of the Platonic Ideas. https://arxiv.org/abs/1405.4186

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