Anaximander begins his cosmogony, a description of how the current world came to exist and what elements caused that existence to occur, by stating that not any of the four Earthly elements (those being earth, air, fire, and water) were the archê. Each cosmogony has and relies upon an archê, or the beginning point, one in which all that exists in the present is in its most primary form. Anaximander was a monist, or someone who believed that the archê was a single form, and then further branched out into the many different things we have in the present.
Anaximander made clear that his archê could not be defined. This is important because if an archê existed in an indefinite state, it cannot possess any physical qualities. This would immediately exclude any substance that exists presently on Earth, including the four elements. Anaximander may have opposed the idea of any physical matter being the archê because of the different properties between physical matter that exists presently. For example, the defining characteristics of air, weightless and all-surrounding, are quite opposite those of earth, massive and fixed. Anaximander could not reconcile these differences; he could not believe that one element that possesses certain qualities could create an element that does not hold any of those qualities.
Anaximander likely refers to ‘water’ specifically in the passage because Thales, his mentor, believed that it was the archê. Since those elements had to be excluded, Anaximander had to search for a different substance to be his archê. The archê would need to be apeiron, which means limitless or ‘boundless.’ This was a way to explain the nature of the substance; it does not exist physically, but refers to a substance which created all physical matter. This was essentially a step into the metaphysical realm.
This apeiron could not be defined, as its key characteristic was that it was indefinite and enveloped all that it created. In this sense, it was a metaphysical entity; something that does not exist within the postulations of physics, yet has an affect upon them. To Anaximander, it was the apeiron which was his archê, an indefinite substance that gave birth to all that exists. This indefinite substance would not hold any defining characteristics, and therefore, not hold any characteristics that could limit what it may become.
The apeiron was not affected by the passage of time; it likely exists outside of a temporal state, as not to be subject to any definable features time may represent. It also allows for the apeiron to be ‘eternal,’ and thus, able to be the creator of all physical worlds. The apeiron existed before the universe, before time, and it itself is what allows the universe and time to continue to exist. Apeiron may ‘surround’ the entire universe as a sort of metaphysical underpinning, it being what allows the laws of physics to function, while simultaneously being the relative to all physical creations. This is somewhat reminiscent of the unmoved mover argument; before the physical world existed, there was an entity or force which caused all of that to exist, without such a need for itself to be created in that way. The apeiron is also described as being in motion, an ‘eternal’ motion, and this is what created the heavens.
By using the word heavens, Anaximander is likely referring to the celestial bodies and the sky, whether it be daytime or nighttime. The motion that he is referring most likely explains why the sun goes away at night, replaced by the moon. In this case, the eternal motion of the universe would explain that the celestial bodies revolved around Earth in a circular pattern. The observable patterns that the celestial bodies take would have been an indicator to Anaximander of the motion that occurs, motion which seems to be a property of apeiron. Never-ending motion was a property apeiron possessed and likely contributed to it being the archê. The two properties possessed by apeiron, unlimited and eternal motion, could be viewed as one and the same; the motion is an aspect of unlimitedness, namely unlimited motion or potency. It is what gave apeiron the power to create the existing world.