[4] 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.
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.
[10] In the mythical Greek cosmogony of Hesiod (8th to 7th century BC) the first primordial god is Chaos, which is a void or gap.
A fragment from Xenophanes (6th century BC)[17] shows the transition from chaos to apeiron: "The upper limit of earth borders on air.
The basic elements of nature, water, air, fire, earth, which the first Greek philosophers believed composed the world, represent in fact the mythical primordial forces.
It acts as the substratum supporting opposites such as hot and cold, wet and dry, and directed the movement of things, by which there grew up all of the host of shapes and differences which are found in the world.
In the commentary of Simplicius on Aristotle's Physics the following fragment is attributed direct to Anaximander: Whence things have their origin, there their destruction happens as it is ordained [Greek: kata to chreon means 'according to the debt'].
For they give justice and compensation to one another for their injustice according to the ordering of time.This fragment remains a mystery because it can be translated in different ways.
Simplicius comments that Anaximander noticed the mutual changes between the four elements (earth, air, water, fire), therefore he did not choose one of them as an origin, but something else which generates the opposites without experiencing any decay.
The word dike (justice) was probably originally derived from the boundaries of a man's land and transmits metaphorically the notion that somebody must remain in his own sphere, respecting the one of his neighbour.
[34] Arrogance was considered very dangerous because it could break the balance and lead to political instability and finally to the destruction of a city-state.
Because only then genesis and decay will never stop.Therefore, it seems that Anaximander argued about apeiron and this is also noticed by Aristotle: The belief that there is something apeiron stems from the idea that only then genesis and decay will never stop, when that from which is taken what is generated is apeiron.Friedrich Nietzsche[36] claimed that Anaximander was a pessimist and that he viewed all coming to be as an illegitimate emancipation from the eternal being, a wrong for which destruction is the only penance.
[37] Scholars in other fields, e.g. Bertrand Russell[38] and Maurice Bowra,[39] did not deny that Anaximander was the first who used the term apeiron, but claimed that the mysterious fragment is dealing with the balance of opposite forces as central to reality being closer to the quotation transmitted by Simplicius.
[40] The idea that the fact of existence by itself carries along an incurable guilt is Greek (Theognis 327) and anybody claims that surpasses it, commits arrogance and therefore he becomes guilty.
The first half of the 6th century is a period of great social instability in Miletus, the city state where Anaximander lives.
Arrogance is an expression of the chaotic element of human existence and in a way a part of the rebounding mechanism of order, because pushing it to exertions causes destruction which is also a reestablishment.
The Greeks believed that each individual had unlimitable potentialities both in brain and in heart, an outlook which called a man to live at the top of his powers.
[44] Philolaus (5th century BC) mentions that nature constituted and is organized with the world from unlimitable (Ancient Greek: ἄπειρα apeira, plural of apeiron) and limitable.
[46] Some doctrines existing in Western thought still transmit some of the original ideas: "God ordained that all men shall die", "Death is a common debt".
The relative English word arrogance (claim as one's own without justification; Latin: arrogare), is very close to the original meaning of the aphorism: "Nothing in excess."
For the Pythagoreans (in particular, Philolaus), the universe had begun as an apeiron, but at some point it inhaled the void from outside, filling the cosmos with vacuous bubbles that split the world into many different parts.