Clotho’ Spindle: Xenocrates’ Doctrine of Indivisibles

Abstract

Abstract This paper offers a reconstruction of Xenocrates’ theory of indivisibles which would not commit him to the idea of ‘jerky motion’ criticized by Aristotle in Physica VI, yet would perfectly square with Plato’s Timaeus, the basis of Xenocrates’ canon. Relying on Alexander’s, Porphyry’s, and Themistius’s accounts of his theory, as well on a detailed analysis of De lineis insecabilibus, I suggest that Xenocrates’ minima, contrary to what Aristotle implies, are not to be understood as more or less stable particulars, like tiny chunks of matter, moving about or leaping in physical space from point A to point B. Yet Xenocrates’ minima do remain ‘physical’ and ‘corporeal’ in a more Platonic sense of these words, not presupposing any kind of leaping, jumping, or jerking. This explains why Xenocrates associated the sensible realm with one of the three Fates, namely Clotho.