The Indivisible Line Coincides with the Platonic Intelligible Being

Stelios Negrepontis
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Stelios Negrepontis: Athens University, Department of Mathematics

A chapter in Handbook of the History and Philosophy of Mathematical Practice, 2024, pp 599-644 from Springer

Abstract: Abstract In the present chapter, we provide a novel interpretation of the concept of Plato’s and Xenocrates’ indivisible line, in fact, we show that indivisibility is just another description of the Platonic intelligible true Being. Our claim and arguments are based on our earlier interpretation of Plato’s intelligible Being as the philosophic analogue of a dyad of opposite kinds in periodic anthyphairesis (as revealed primarily in the Meno, the second hypothesis of the One in the Parmenides, and the Sophist), and take into account the ancient sources on the indivisible by Plato (Sophist, Phaedrus, Republic, Philebus), Aristotle (Metaphysics), Proclus, and Simplicius. Additional arguments, based on Zeno (Dichotomy Paradox), and Aristotle (Physics, and the pseudo-Aristotelian On Indivisible Lines), establish that Zeno’s true Being is also indivisible. Earlier attempts by modern Platonists were not successful, mainly because these have not taken into account the geometric/anthyphairetic nature of a true Being.

Keywords: Plato; Zeno; Theaetetus; Aristotle; Proclus; Simplicius; Intelligible being; Indivisible line; Anthyphairesis; Logos Criterion; Already infinite; Dialectical infinite; Eristic infinite; Active infinite; Potential infinite; Self-moving Soul; Dichotomy Paradox; 00A30; 01A20 (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-40846-5_139

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DOI: 10.1007/978-3-031-40846-5_139

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