[note: I lost much of this post (in my text editor) and tried to reconsruct along the same lines. That stuff never quite works. It is not possible to write things again. So, here are the notes.]

I haven't been reading as much as I want lately (sort of comes along with "not doing as much in general as I'd like to lately") though I have been scanflipping through many of the books I've acquired in the last month or two. I keep Jonathan Barnes' outstanding The Presocratic Philosophers handy because it is a topic that I am really looking forward to learning more about.

A good scanflip resulted in (pp252-3):

(c) Fractured atoms?

Atoms, though indivisible, may have parts: we may not be able, physically, to split an atom; but we can, theoretically, divide it into notional parts: 'the half nearer to b', 'the part with the point on', and so on. And if we take a large Democritean atom we may even be able to measure it, to mark it into parts, to draw a design upon it; the only thing we cannot do is cut it along our marks or carve it to the drawn design. The doxographers say nothing about the notional parts of Abderite atoms; but both Alexander (in Met 36. 25-7) and Simplicius (in Phys 82. 1-3) mention them casually.

Epicurus said more about sub-atomic particles (§§58-9). His views are controversial; but an orthodox interpretation runs thus: every atom is theoretically, but not of course physically, divisible; but just as physical splitting eventually reaches atoms or physical indivisibles, so too theoretical division ultimately reaches minima or theoretical indivisibles; and an atom is thus composed of a finite set of theoretically indivisible minima, conjoined by a physically indissoluble bond. Epicurus is a second-hand thinker; and it is proper to wonder if his theory was not taken from Democritus, along with the other trappings of atomism. Alexander implies that it was:

I [Leucippus and Democritus] do not say whence the weight in the atoms comes; for the partless items (ta amerê) conceptually present in (epinooumena) the atoms and parts of them are, they say, weightless: but how could weight come from weightless components? (255: in Met 36.25-7)

I gave a one-off lecture in grad school called "A Being a Part and Coming Apart" which I would say was about just these sort of "notional" parts if I believed that there are such things as "notional parts" at all. I mean, what bunk! Imagine a room with a large block or marble in it: are there also untold trillions of overlapping Davids in that room? You may be able to make the chunk of marble into a David, but you are not merely exposing one of the many Davids which was already there all along.

And yet there is something to the intuition that those things are parts which can come apart: and if we can take the a David-shaped block away from the David-complement (the rest of the chunk of marble), why aren't those (the) two parts of the whole block? You decide for yourself: my answer is very long and complicated and may not be convincing to you.

The important thing is that we understand that separability-in-principle is often perceived to be a necessary condition for saying that x is a part of y (and even sufficient by some, dummies). But it doesn't much help: chickens and eggs, eggs and chickens — they all come to roost in matters of mereology. Recall that "atom" comes from the negative "a" + "tomos", verbal adjective of temnein (to cut). A no-cutter. A no-cuttabler. A non-cuttable thing. At "atom" is by definition something that is whole and simple.

And who could mention "whole and simple" without the first six propositions of the Monadology smashing into one's head? Not me!

  1. The Monad, of which we will speak here, is nothing else than a simple substance, which goes to make up composites; by simple, we mean without parts.
  2. There must be simple substances because there are composites; for a composite is nothing else than a collection or aggregatum of simple substances.
  3. Now, where there are no constituent parts there is possible neither extension, nor form, nor divisibility. These Monads are the true Atoms of nature, and, in fact, the Elements of things.
  4. Their dissolution, therefore, is not to be feared and there is no way conceivable by which a simple substance can perish through natural means.
  5. For the same reason there is no way conceivable by which a simple substance might, through natural means, come into existence, since it can not be formed by composition.
  6. We may say then, that the existence of Monads can begin or end only all at once, that is to say, the Monad can begin only through creation and end only through annihilation. Composites, however, be in or end gradually

On one side we have atoms that are extended, having a form and a mass but which you cannot actually cut, because they are atoms. And in the other corner, we have atoms which cannot be cut because they are not extended, do not have any form nor any mass. In arguments like this, it is best to break out the sword since you can't get anywhere.

So, lose your Democritean hooks and crannies, and your Lucretian weight. You can't cut this. Simple. But put the simple things together and you are on your way to a whole sublunary spehere of generation and corruption. Including — and you knew where this was going all along, didn't you? — the more human affairs.

E.g., near the beginning of Aristophanes speech in the Symposium:

In the first place, let me treat of the nature of man and what has happened to it; for the original human nature was not like the present, but different. [189e] The sexes were not two as they are now, but originally three in number; there was man, woman, and the union of the two, having a name corresponding to this double nature, which had once a real existence, but is now lost, and the word "Androgynous" is only preserved as a term of reproach. In the second place, the primeval man was round, his back and sides forming a circle; and he had four hands and four feet, one head with two faces, looking opposite ways, [190a] set on a round neck and precisely alike; also four ears, two privy members, and the remainder to correspond. He could walk upright as men now do, backwards or forwards as he pleased, and he could also roll over and over at a great pace, turning on his four hands and four feet, eight in all, like tumblers going over and over with their legs in the air; this was when he wanted [190b] to run fast.

Aristophanes' "men" were two of our workaday normal human beings stuck together, back to back. The three flavours were man-man, woman-woman and man-woman. Perhaps you know the rest of the story: pesky people are too powerful in this form. They anger the Gods and Zeus decides that they must be split into two. Gay men decended from the old double-males, lesbians from the double-females and straight people from the mixed ones.

But we are all of us cruelly separated from ourselves, made into mere parts, and constantly seeking our other halves, to be made whole again. And that's what love is (according to the Platonic Aristophanes anyway). (Cf. the idea of wholeness-as-an-end for living things in The Critique of Teleological Judgement)