1. Parmenides’ successors seemed to be concerned with these five central Parmenidean doctrines:
   
   
   1. Monism: there is no plurality.
   2. There is no motion.
   3. There is no generation or destruction.
   4. There is no qualitative change or differentiation.
   5. There is no void.
      
      
2. All of the pluralistic responses to Parmenides (Empedocles, Anaxagoras, and the Atomists) were influenced by him, but rejected his extreme monism. They sought to reconcile, as much as possible, Parmenideanism with common sense.
   
   
3. They all disagreed with Parmenides about (1) and (2): all maintained plurality and motion. But they all accepted (3): there is no coming into existence or ceasing to exist. Where they differ among themselves is over (4) and (5): the reality of qualitative differences and the existence of the void.
   
   
4. Empedocles and Anaxagoras broke ranks with Parmenides over (4), but toed the line on (5). The atomists agreed with Parmenides that there is no genuine qualitative change, but claimed that there was empty space - a void.  These points are all summarized in the table below:
   
   

   Pluralists’ Scorecard

   	Parmenides	Empedocles & Anaxagoras	The Atomists Leucippus & Democritus
   Plurality	-	+	+
   Motion	-	+	+
   Generation & Destruction	-	-	-
   Qualitative Difference & Change	-	+	- ?
   Void	-	-	+

5. It is also instructive to compare the ways different pluralists responded to Zeno. Zeno’s argument against plurality makes this explicit assumption:

   a. Whatever has size has parts.

   It also assumes implicitly (as we saw) that:

   b. There is a smallest size part.

   Here’s how two pluralists, Anaxagoras and Democritus, responded.

   Anaxagoras

   Accepts (a), but denies (b): “Of the small, there is no smallest,” he says.

   Democritus

   Accepts (b), but denies (a): Atoms have size, but don’t have parts (cf. 11=A13).

1. Areas of agreement with Parmenides

   1. No generation/destruction:

      Fools. For their thoughts are not far-reaching, who expect that there comes to be what previously was not, or that anything perishes and is completely destroyed. (36=B11)

      For it is impossible to come to be from what in no way is, and it is not to be accomplished and is unheard of that what is perishes absolutely. (39=B12)

      ...There is coming to be of not a single one of all mortal things, nor is there any end of deadly death .... (35=B8)
      
      

   2. No void:

      None of the whole is either empty or over-full. (40=B13)

2. Areas of disagreement with Parmenides

   1. Pluralism - the four elements:

      Hear first the four roots of all things: Shining Zeus [fire] and life-bringing Hera [air] and Aidoneus [earth] and Nestis [water] who with her tears moistens mortal Springs. (34=B6)
      
      

   2. Qualitative difference:

      ... For these [the four elements] are all equal and of the same age, but each rules in its own province and possesses its own individual character, but they dominate in turn as time revolves. (43=B17, line 27)
      
      

   3. Motion:

      And these [sc. the elements] never cease continually interchanging, at one time all coming together into one by Love, and at another each being borne apart by the hatred of Strife. (43=B17, line 6)

      ...For there are just these things [i.e., the four elements], and running through one another they come to be both humans and the tribes of other beasts at one time coming together into a single cosmos by Love and at another each being borne apart by the hatred of Strife .... (48=B26)

      Note that Empedocles not only accepts the existence of motion, but offers an explanation of it, in terms of two primitive forces, Love (which moves things together) and Strife (which separates them).

    

3. Generation and Change

   Apparent generation and apparent change are explained away in terms of the activity of the underlying elements, under the control of the motivating forces of Love and Strife.

   ... Thus in that they have learned to grow to be one out of many and in that they again spring apart as many when the one grows apart, in that way they come to be and their life is not lasting .... (43=B17, line 9)

   Whenever they [sc. the elements] arrive in the aither mixed so as to form a man or one of the wild beasts or bushes or birds, that is when <people> speak of coming into being; and whenever they are separated, that <is what they call> the ill-starred fate of death. They do not call it as is right, but I myself too assent to their convention. (37=B9).

   There is ... only mixture, and separation of what is mixed, and nature [or, birth, phusis] is the name given to them by humans. (35=B8)

4. 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. (45=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. (79=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.

5. 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.

6. Problems for Empedocles

   1. Motion: how is motion possible if there is no empty space? How do things have room to move?
      
      
   2. Mixture: how do the elements mix? How do they “run through one another” (48=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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