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The Indivisible Line Coincides with the Platonic Intelligible Being

In: Handbook of the History and Philosophy of Mathematical Practice

Author

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  • Stelios Negrepontis

    (Athens University, Department of Mathematics)

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.

Suggested Citation

  • Stelios Negrepontis, 2024. "The Indivisible Line Coincides with the Platonic Intelligible Being," Springer Books, in: Bharath Sriraman (ed.), Handbook of the History and Philosophy of Mathematical Practice, pages 599-644, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-40846-5_139
    DOI: 10.1007/978-3-031-40846-5_139
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