Interpretations
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 = 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. He mentions also that Anaximander said all these in poetic terms, meaning that he used the old mythical language. The Goddess Justice (Dike), appears to keep the order. The quotation is close to the original meanings of the relevant Greek words. 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 into his own sphere, respecting the one of his neighbour. The word adikia (injustice) means that someone has operated outside of his own sphere, something that could disturb "law and order" (eunomia). In Homer's Odyssey eunomia is contrasted with hybris (arrogance). 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.
Aetius (1st century BC) transmits a different quotation:
Everything is generated from apeiron and there its destruction happens. Infinite worlds are generated and they are destructed there again. And he says (Anaximander) why this is apeiron. 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 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. In accordance to this the world of the individual definite objects should perish into the indefinite since anything definite has to eventually return to the indefinite. His ideas had a great influence on many scholars.
Werner Heisenberg, noted for the creation of quantum mechanics, arrived at the idea that the elementary particles are to be seen as different manifestations, different quantum states, of one and the same “primordial substance.” Because of its similarity to the primordial substance hypothesized by Anaximander, his colleague Max Born called this substance apeiron.
Scholars in other fileds, e.g. Bertrand Russell and Maurice Bowra, didn't 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.
There are also other interpretations which try to match both the previous aspects. Apeiron is an abstract, void, something that cannot be described according to the Greek pessimistic belief for death. Death indeed meant "nothingless". The dead live like shadows and there is no return to the real world. Everything generated from apeiron must return there according to the principle genesis-decay. There is a polar attraction between the opposites genesis-decay, arrogance-justice. The existence itself carries a guilt.
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. Any attempt of excess leads to exaggerations and each exaggeration must be corrected. All these have to be paid according to the debt. The things give justice to one another with the process of time.
Justice has to destroy everything which is born. There is no external limit that can restrict the activities of men, except the destruction. 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.
Read more about this topic: Apeiron (cosmology)