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pengvado comments on Rationality quotes: June 2010 - Less Wrong
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That's not true. He had perfectly good reasons for atomism in his context.
The ontological arguments of Parmenides (and as exposited by Melissus) lead to extremely unpalatable, if not outright contradictory, conclusions, such as there being no time or change or different entities. The arguments seem valid, and most of their premises are reasonable, but one of his most important and questionable premises is that void cannot exist.
Reject that premise and you are left with matter and void. How are matter and void distributed? Well, either matter can be indefinitely chopped up (continuous) or it must halt and be discrete at some point. The Pluralists like Anaxagoras take the former approach, but continuousness leads to its own issues with regard to change.* So to avoid issues with infinity, you must have discrete matter with size/divison limits - atoms.
So, Democritus and Leucippus are led to Atomism as the one safe path through a thicket of paradoxes and problems. Describing it as wild conjecture is deeply unfair, and, I hope, ignorant.
* One argument, if I remember it from Sextus Empiricus's Against the Physicists correctly, is that if matter really is infinitely divisible, then you should be able to divide it again and again, with void composing ever more of the original mass you started with; if you do division infinitely, then you must end up with nothing at all! That is a problem. Cantor dust would not have been acceptable to the ancient Greeks.
Would a conserved Lebesgue measure have been acceptable? I don't see why infinitely dividing matter has to reduce the amount of anything.
Not unless you enjoy anachronisms. The Greeks probably wouldn't have liked that either; the basic point stands: if at any point one can divide it to produce a void and 2 smaller masses, then where is the 'real' mass? Any point you pick, I can turn into void. If I can do it for any point, I can do it for every point, and if every point is void...
Unless you postulate a knife with really weird properties, cutting a continuous object in half isn't turning matter into void. It's moving some of the matter without changing its density (hence my offer of conservation of volume). You can do that to every point currently occupied by an object, but only by reserving an equal amount of space that's currently void and displacing all of the matter to there.
It's more of a conceptual knife - pointing out that by the definition of continuity, segment X is made of void and 2 smaller segments, Y and Z; but Y and Z are themselves made of void (and 2 smaller segments), and so on.
(Any conceptual knife just illustrates how motion was supposed to be possible in a continuous framework: the matter in the knife fits into the voids of what it is moving into.)
Oh, so the "made of void" thing comes from the void that the knife fits into. That wasn't at all clear - it seemed like we were just talking about separating things into parts, not about the physical process of cutting.