In one form or another the problem known as that of the One (Hen) and the Many (Polla) pervades the whole history of Greek philosophy. According to Aristotle (Physics I, 2–3), it arose first in the pre-Socratic inquiry into whether there is one first principle or source—for example, water alone, or air alone—for things, or whether there is more than one first principle. If we are to avoid "coming into being out of nothing," we must either deny with Parmenides that there is any multiplicity arising from the first principle, or else we must suppose that somehow or other multiplicity is already present within the unitary first principle. If we choose the second supposition, we are faced with a problem that is no longer purely physical, namely, how one thing can also be many.

In the period after Parmenides it became clear that this problem...