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Unformatted text preview: That is, every piece of gold contains portions of wood, flesh, hair, water, silver, etc. Anaxagoras’s principle (UM) is designed to enable him to allow for the existence of real change without allowing for real generation and destruction. , (UM) is certainly a bizarre principle, however well motivated it may be. Some critics have found it worse than bizarre. They think it flatly contradicts (H). Thus, Cornford:
Anaxagoras’s theory of matter rests on two propositions which seem flatly to contradict one another. One is the principle of homoiomereity: a natural substance such as a piece of gold consists solely of parts which are like the whole and like one another - every one of them gold and nothing else. The other is: “There is a portion of everything in everything,” understood to mean that a piece of gold . . . so far from containing nothing but gold, contains portions of every other substance in the world. Is Cornford right? Or can Anaxagoras, without contradiction, maintain that every part of a lump of gold is itself gold and still maintain that every piece of gold contains portions of all the other stuffs (including ones which are not gold)? 6 Various ways out have been proposed.
a. Guthrie: “homoiomerous” was Aristotle’s word, not Anaxagoras’s. Anaxagoras’s elements were the natural stuffs that Aristotle called homoiomerous. But Anaxagoras didn’t think they were like-parted. Rather, they contained everything. So Anaxagoras doesn’t hold (H).
b. Vlastos: what’s present in every kind of stuff is every opposite, not every kind of stuff. So (UM) doesn’t contradict (H). ° But are (H) and (UM) really incompatible? If it can be shown that they are compatible after all, we will not have to look for a way out in the manner of Guthrie or Vlastos. Let us reconsider the argument for saying that (H) and (UM) are inconsistent. Suppose we have a lump of gold, L. (UM) tells us that it is a universal mixture, and (H) tell us that all of its parts are gold. So we consider some part of it, P. (H) tells us that P is gold and that P, like L, is an instance of universal mixture - it contains every kind of stuff within it. Why not? There does not seem to be any inconsistency yet. L is both gold and contains a mixture within, and so is P. Evidently, the trouble is thought to come when we consider the parts of P. Are they also both gold and instances of universal mixture? The underlying assumption seems to be that one can maintain that the parts of L are both gold and instances of universal mixture only until one reaches some part, P*, which cannot be further broken down into parts. What can we say about P*? (H) says it is gold, and (UM) says it is a mixture. But how can it be a mixture if it has no parts? So (H) and (UM) cannot both be true about P*. But notice that this argument implicitly assumes that a process of division of L will ultimately lead us to an indivisible part, P*. And it is P* that we have shown cannot be both homoiomerous (i.e., pure gold) and a universal mixture. So our argument to show that (H) and (UM) are inconsistent has implicitly been assuming a third principle: that every process of division comes to an end - that matter is only finitely divisible. L But Anaxagoras did not assume this. Indeed, he explicitly denied it. Cf. 3=B3: For of the small there is no smallest, but always a smaller. This is Anaxagoras’s principle of Infinite Divisibility. There are no atoms. [A question that naturally arises here is the relation of Anaxagoras to Zeno. For more on this issue, see this supplementary note.] As applied to the argument at hand, the principle of Infinite Divisibility means that we will never reach a part, P*, about which we get the contradictory result that it contains no parts but still satisfies (UM). Ð But this still leaves us with a puzzle: how can L, our lump of gold, have other things (e.g., silver, lead, sugar) in it, when all of its parts are gold? If no part of L is silver, how can there be silver in the gold? Or flesh in the corn? To answer this question, we must distinguish between the (physically discriminable) parts of a substance and the portions of stuff which it contains.
ˆ Reductionism Empedocles’ theory is reductionistic. Such apparent stuffs as bone or blood, and such apparent entities as frogs and trees, are, according to his theory, reduced to complex combinations of elements. So although there appear to be more kinds of stuff than just the elements, they are not “real,” but only aggregates of the real entities (E, A, F, W): For from these [sc. the elements] come all things that were and are and will be in the future. Trees have sprouted and men and women, and beasts and birds and fishes nurtured in water, and long-lived gods highest in honors. For there are just these things [i.e., the elements], and running through one another they come to have different appearances, for mixture changes them. (35=B21) Empedocles even tries to quantify precisely the reduction of ordinary objects to compounds of elements: Pleasant earth in her well made crucibles obtained two parts of bright Nestis out of the eight, and four of Hephaestus, and white bones came into being, fitted together divinely by the glues of Harmonia. (42=B96) This gives us a kind of primitive chemistry with obvious Pythagorean overtones: Bone = 2W + 4F + 2E We’re told there are 8 parts in all, that some of them are earth, that 2 are Nestis (water) and 4 are Hephaestus (fire). So we solve for E: E = 8 - (2 + 4) = 8 - 6 = 2 The formulas Empedocles gives (like the one above for bone) are reductionistic in character. Entities in “common sense” ontology are reduced to (complexes of) the four elements - the only genuine entities in Empedocles’ ontology. Summary Only the elements are real, and the elements don’t change. Thus, the real is unchanging, just as Parmenides said. But there is some sort of change in a world without void, packed full of ungenerated and unchanging elements, when the elements mix with one another. ? Problems for Empedocles a. Motion: how is motion possible if there is no empty space? How do things have room to move? b. Mixture: how do the elements mix? How do they “run through one another” (50=B26)? Aristotle supposed that, to solve this, Empedocles would have to smuggle in a notion of a void: elements would contain “gaps” into which other elements could flow. Here is how Aristotle puts the criticism (GC 325b1):
Leucippus maintains that all alteration and all being affected comes to be in this way, the disintegration and corruption of things coming to be by way of the void - and similarly also growth, solid bodies slipping in through the gaps. Empedocles is bound to speak in more or less the same way as Leucippus does. A number of solid bodies exist, and are undivided, unless there are continuous passages everywhere. But this is impossible, because there would be nothing else solid over and above the passages, but everything would be a void. So the things which are in contact are necessarily undivided, and what is between them is a void, and this is what Empedocles calls ‘passages’. And this is how Leucippus too speaks of action and passion. ...
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This note was uploaded on 01/31/2011 for the course PHYSICS 110 taught by Professor Staff during the Spring '09 term at UC Davis.
- Spring '09