The Eleatics' continuum

This chapter examines the Eleatic continuum by distinguishing the different approaches of Parmenides, Zeno, and Melissus. Parmenides is examined in light of the Pythagorean one-many dualism, as well as Heraclitus’ reduction of the many to the one and the concept of one presented by Xenophanes. The unity of Parmenidean being coincides with its wholeness and continuity, demonstrated through its spatiotemporal homogeneity and indivisibility. Indivisibility, as a distinctive feature of the continuity of being, underlies Zeno’s interpretation of the unity of being. Through a discussion of Zeno’s arguments and some Neoplatonic sources, it is shown how Zeno makes explicit, at least from Aristotle’s perspective, reasoning that foreshadows atomism, insofar as it seems to dialectically examine the hypothesis of an infinite in act once division is admitted. The unity of being re-emerges powerfully in Melissus’ philosophy, particularly in the denial that the being can have a beginning, middle, or end. However, these parts are what Aristotle attributes, in potency, to the whole and the continuum, relating this doctrine to the Pythagoreans in De Caelo I 1. For Aristotle, Melissus’ discussions of the void confirm that for the Eleatics, multiplicity and movement are possible only in a reality that is contiguous but noncontinuous.