This Theory, That Belongs to Me, Goes As Follows

"You may well ask, 'What is it, that it is, this theory of mine on Anaximander?' My theory, that belongs to me, is as follows. This is how it goes. This theory goes as follows, and begins now."

(Here's the link, if you haven't seen that hilarious Monty Python skit, of Anne Elk's theory of the brontosaurus, 3 min 36 sec.)

Actually, I don't have much of a theory, or much that I'd wish to stake anything on, but more like a hunch. This hunch, which is mine, is as follows...

What is meant to have prominence, I think, in the highlighted sentence below, is the notion of destruction or perishing. The sentence, in the context, introduces that notion for the first time in the passage, after, so far, only talk of origins and coming to be:

Of those who say that it is one, moving, and infinite, Anaximander, son of Praxiades, a Milesian, the successor and pupil of Thales, said that the principle and element of existing things was infinite, being the first to introduce this name to the material principle. He says that it is neither water nor any other of the so-called elements, but some other infinite nature, from which come into being all the heavens and the worlds in them. And the source of coming-to-be for existing things is that into which destruction, too, happens by necessity. (ἐξ ὧν δὲ ἡ γένεσίς ἐστι τοῖς οὖσι, καὶ τὴν φθορὰν εἰς ταῦτα γίνεσθαι.) For they pay penalty and compensation to each other for injustice according to the order of time. It is clear that he, seeing the changing of the elements into each other, thought it right to make none of these the substratum, but something else beside these. And he produces coming-to-be not through the alteration of the element, but by the separation off of the opposites through the eternal motion.

Exactly what thought about perishing the sentence is meant to convey, is difficult to say. At least: whatever comes to be also perishes. From this Anaximander might have reasoned, intuitively:

1. Coming-to-be and perishing are corresponding processes.
2. Thus, end points of perishings and starting points of comings-to-be have the same status.
3. Thus, end points of perishings are as likely candidates for the most basic principle (archē) and element (stoicheon), as are starting points of comings-to-be.
4. But everything (or: every putative element) may be seen either among starting points or among end points. (Indeed, since the seas are drying up, dryness is an end point, as much as wateriness is a starting point.)
   
5. Thus, there is no reason to pick any one thing rather than another to be the most basic principle and element.
6. Thus, the most basic principle and element is something different and apeiron.

This gives an argument for why the archē and stoicheon is something apeiron (which is what was needed at that point in the passage from Simplicius); it does so by drawing out implications from the fact and necessity of perishing (which is what is stressed in the relevant sentence); and it is at bottom an indifference argument (step 5), a type of argument which we have reason to think Anaximander favored.

Furthermore, a line of thought such as this would have been a natural development from the position of Thales, because, whatever we think of Aristotle's reconstruction of Thales' reasons for positing water as the archē, it seems likely that Thales looked simply to the origins of things to justify his view -- and then Anaximander would be offering a significant correction in insisting that the end points of processes of perishing (especially the drying up of the earth) have parity.

Moreover, the view leads naturally to Heraclitus, because it is a short step from holding that coming-to-be and perishing are corresponding processes, to holding that, in fact, anything that counts as the one is, at the same time, an instance of the other -- which perplexes Plato in the Phaedo ("When a pair is separated, is that the phthora of the pair or the genesis of each individual?"), and Aristotle in de Gen et Corr.

As for the famous 'fragment'-- "they pay penalty and compensation to each other for injustice"--its function, on this interpretation, would be to give a reason, figuratively, for why everything that comes to be also perishes. Since its language is figurative, we should not, I think, place much weight on on the fragment; and, indeed, the subject matter is inherently difficult. (Exactly why, indeed, must everything that comes to be also perish?)

The intuition of Plato on this point was that a 'becoming' was between being and nothingness and therefore was inherently unstable. Other philosophers have held that anything that comes to be must be composite, and every composite is potentially divided, but any real potential must become realized in an indefinite length of time.

Anaximander's intuition, judging from the fragment, is that whatever comes to be is, to that extent, somehow 'in debt'--perhaps because the 'cost' of its existing is that something else that it excludes cannot exist--and that this debt must eventually be 'repaid', which is its perishing.

I am inclined to explain the 'debt' owed by any generated thing through an indifference argument: that something of one sort exist, rather than something of some other sort that it excludes, is, so far, irrational given the fact of an initial or background apeiron element--this irrationality becoming corrected through the perishing. (Note that such a debt might still be spoken of as a debt of one thing to something else, rather than to the apeiron, because the 'debt' is created by one thing's excluding something else.)

"And that is my theory. It is mine."