
Apeiron (ἄπειρον) is a Greek word meaning "(that which is) unlimited," "boundless", "infinite", or "indefinite" from ἀ- a-, "without" and πεῖραρ peirar, "end, limit", "boundary", the Ionic Greek form of πέρας peras, "end, limit, boundary". Akin to Persian, piramon, "boundary, circumference, surrounding."
The apeiron is central to the cosmological theory created by Anaximander, a 6th-century BC pre-Socratic Greek philosopher whose work is mostly lost. From the few existing fragments, we learn that he believed the beginning or ultimate reality (arche) is eternal and infinite, or boundless (apeiron), subject to neither old age nor decay, which perpetually yields fresh materials from which everything we can perceive is derived. Apeiron generated the opposites, hot-cold, wet-dry etc., which acted on the creation of the world. Everything is generated from apeiron and then it is destroyed by going back to apeiron, according to necessity. He believed that infinite worlds are generated from apeiron and then they are destroyed there again.
His ideas were influenced by the Greek mythical tradition and by his teacher Thales (7th-6th century BC). Searching for some universal principle, Anaximander retained the traditional religious assumption that there was a cosmic order and tried to explain it rationally, using the old mythical language which ascribed divine control on various spheres of reality. This language was more suitable for a society which could see gods everywhere; therefore the first glimmerings of laws of nature were themselves derived from divine laws. The Greeks believed that the universal principles could also be applied to human societies. The word nomos (law) may originally have meant natural law and used later to mean man-made law.
Roots
In the mythical Greek cosmogony of Hesiod (8th-7th century BC) the first primordial god is Chaos, which is a void or gap. Chaos is described as a gap either between Tartarusand the earth's surface (Miller's interpretation) or between earth's surface and the sky (Cornford's interpretation). One can name it also abyss (having no bottom).
Alternately, Greek philosopher Thales believed that the origin or first principle was water. Pherecydes of Syros (6th century BC) probably called the water also Chaos and this is not placed at the very beginning.
In the creation stories of Near East the primordial world is described formless and empty. The only existing thing prior to creation was the water abyss. The Babylonian cosmology Enuma Elish describes the earliest stage of the universe as one of watery chaos and something similar is described in Genesis. In the Hindu cosmogony which is similar to the Vedic (Hiranyagarbha) the initial state of the universe was an absolute darkness.
Hesiod made an abstraction, because his original chaos is a void, something completely indefinite. In his opinion the origin should be indefinite and indeterminate. The indefiniteness is spatial in early usages as in Homer (indefinite sea). A fragment from Xenophanes (6th century BC) shows the transition from chaos to apeiron: "The upper limit of earth borders on air. The lower limit reaches down to the unlimited. (i.e. the Apeiron)". Either apeiron meant the 'spatial indefinite' and was implied to be indefinite in kind, or Anaximander intended it primarily 'that which is indefinite in kind' but assumed it also to be of unlimited extent and duration. His ideas may have been influenced by the Pythagoreans:
for they [the Pythagoreans] plainly say that when the one had been constructed, whether out of planes or of surface or of seed or of elements which they cannot express, immediately the nearest part of the unlimited began to be drawn in and limited by the limit.