Apeiron

Notion of Anaximander

The "Apeiron aspect'' of reality is named as such in homage to Anaximander. We read from Aristotle and his student Theophrastus, the following regarding the notion of the "Apeiron'' in the manner it has been conceived by Anaximander:

The apeiron does not have a first principle, but this seems to be the first principle, and to contain all things and steer all things, ... For it is indestructible, as Anaximander says.

Anaximander said that the apeiron was the first principle and element of things that are, and he was the first to introduce this name for the first principle [i.e., he was the first to call the first principle apeiron], ...

But some other nature which is apeiron, out of which come to be all the heavens and the worlds in them. The things that are perish into the things out of which they come to be, according to necessity, for they pay penalty and retribution to each other for their injustice against the ordering of time.

Interpretation

According to the above fragments, the "apeiron aspect'' of reality does not refer to any type of boundless spatial infinity, as the majority of the modern commentators interpret this notion. On the contrary, it pertains to the non-reversible ordering of temporal actions. More precisely, the "apeiron aspect'' is characterized by the non-directly experiential, and thus boundless, nature pertaining to the non-reversible concatenation ordering of temporal actions.

We conceive of a temporal action as an unfolding action to be thought of metaphorically as a chord in relation to the act of representation. Since the apeiron is conceptualized as a first principle by Anaximander, such distinct and non-reversible concatenation orderings of temporal actions give rise to ``temporal bonds'' out of which the manifestation of emergent entities becomes possible.

A temporal bond refers to an indirectly linked constellation of unfolding actions in parataxis, which are capable of entering into an ordered irreversible composition forming this bond. More concretely, the constellatory self-unfolding of these actions can potentially enter into an ordered intertwining composition that is not directly experiential in its totality, and thus it is boundless in this primordial temporal sense. According to necessity, a temporal bond can be only manifested on an "epiphaneia'' in "statu-nascendi'', by which we mean a pre-factual ontophainetic platform that is constitutive of representation in the "time-space of the present''.

In turn, the latter enunciates an "instantiation'' of this temporal bond, in the sense that it can reveal a "shadow'' of the bond at the corresponding present through the bounding means of representation on the apeiron. In the poetic expression of Anaximander, this is a form of "injustice'' against the ordering of these temporal actions, providing in this way an ingenious hint about the relation between the apeiron and the "epiphaneia" of manifestation in the time-space of the present.

The Necessity of Distinct Categorial Frameworks

The essential qualification of the ``apeiron aspect'' of reality in relation to the distinct ``categorial frameworks'' characterizing the "factual'' and "statu-nascendi'' aspects correspondingly, according to the above, is also stressed in the following excerpt of Weyl's "Philosophy of Mathematics and Natural Science'', in relation to his discussion of the "space continuum'' on p.41:

The continuum is not composed of discrete elements which are "separated from one another as though chopped off by a hatchet". Space is infinite not only in the sense that it never comes to an end; but at every place it is, so to speak, inwardly infinite, inasmuch as a point can only be fixed step-by-step by a process of subdivision which progresses ad infinitum. This is in contrast with the resting and complete existence that intuition ascribes to space. The "open'' character is communicated by the continuous space and the continuously graded qualities to the things of the external world. A real thing can never be given adequately, its "inner horizon'' is unfolded by an infinitely continued process of ever new and more exact experiences; ... For this reason it is impossible to posit the real thing as existing, closed and complete in itself.