Apeiron

Apeiron (ἄπειρον) means the boundless, the unlimited, the indefinite. The word joins the negating a- to peras (πέρας), 'limit' or 'boundary' — that which has no limit, no edge, no determinate character. It was made famous by Anaximander of Miletus, the pupil and associate of Thales, who held that the archē of all things is not any one familiar substance like water but the apeiron: an inexhaustible, ageless, encompassing source out of which all the worlds and all opposites come to be, and back into which they pass away.

His single surviving sentence — preserved, as it happens, by the late commentator Simplicius — says that things pay one another penalty and recompense for their injustice according to the ordinance of time. In it the play of opposites, hot against cold, wet against dry, is figured as a kind of cosmic justice, each excess corrected in turn, all of it arising from and returning to the boundless. It is among the earliest abstract conceptions in Western thought, a first principle defined not by what it is but by its very lack of limit.

Limit and the unlimited

The apeiron lives on as one pole of the Pythagorean and Platonic opposition of limit (peras) and the unlimited — the formless, indeterminate stuff on which limit and measure must be imposed to make a determinate world. In this guise it stands close to the Indefinite Dyad and to the moment of indeterminacy in the procession from the One, where an unbounded power must be turned back and given form to become Intellect.