Eleatic philosophy created a difficult problem for the Presocratics that came afterward: that is, how to conceive of the sensible world in a logical way, after Parmenides had shown that the things perceived by senses are illusory and false. Parmenides and his successors held fast to the doctrine that "being" (i.e. everything that is) is a unity, unchanging and eternal. A necessary consequence of this is that things like change, creation, and destruction become altogether unthinkable. In light of the fact that things we see seem to be changing all the time, this philosophy is complicated to understand; but both Parmenides and his followers, like Zeno, made it a very difficult position to refute.
Though it is rarely accurate or fair to speak of Presocratic philosophers as though each followed after his predecessors in logical succession, it is occasionally evident that this is precisely what happened. The Pluralist school is just such an example; it was comprised of philosophers who addressed Eleatic philosophy head-on. Anaxagoras of Clazomenae, in Asia Minor (500-428 BCE), and Empedocles of Agrigentum, in Silicy (c. 495-435 BCE), both classified as Pluralists, proposed different solutions to the Eleatic problem. Anaxagoras suggested that everything was contained within everything else, in varying amounts; Empedocles proposed the existence of four elements that could be combined and recombined in different ways to "create" new substances, without actually making any fundamental changes. Both philosophers attempt to hold on to the Eleatic position -- that is, the unity of being -- but at the same time allow for the reality of the changes that we see happening around us, things like birth and death and creation and destruction. Arguably, they succeeded to a certain extent in saving the sensible world from logical non-existence; but neither really replaced the Eleatic aporia with anything more concrete than new and more varied problems.
The Eleatic problem, as conceived of by Parmenides, starts and finishes with the idea that "being" is necessarily a unity -- that all things that exist are one and the same, by virtue of their existence. Since "being" is the property of all things that are, it is possible to say that being is; and logically it is also possible to say the opposite, that not-being is not. Beyond that, however, there is nothing more that we can say without contradicting ourselves: all we can say truthfully is that the nature of "the one [is] that it is and that it is not possible for it not to be", and "neither may [one] know that which is not [...]/nor may [one] declare it" (Presocratics Reader, 45-6, no. 2).
Zeno's paradoxes are an especially illustrative example of this. For instance, his first paradox states "that there can be no motion because that which is moving must reach the midpoint before the end" (75, no.6). But this is not an argument against the possibility of motion so much as an argument against the way that we think of motion, as though it involves change. If we concede that any distance can be divided into halves, then halves again, and on ad infinitum, then any movement between the points we've defined becomes impossible -- there will always be another halfway distance to traverse. But if we disagree with this proposition, and argue that the distance to be travelled cannot be divided, then suddenly the movement is no longer impossible -- there are no halfway points to stumble over, only a beginning and an endpoint that are connected to each other, such that "motion" is still contained within a unity.
That being is a unity, as demonstrated, must also mean that it is eternal. Not only is imposing temporal constraints upon anything necessarily a divisive process (dividing up a time period into hours, minutes, seconds, and so on, for instance), but to say that being is not eternal implies that it has a beginning, and it will have an end -- that is, that somehow it came to be out of nothing, and will someday be destroyed. According to the Eleatic doctrine, this is unacceptable, because comings-to-be and passings-away are changes, beyond a shadow of a doubt, and change is not possible.
Thus the logical position of Parmenides and the rest of the Eleatics is that since being is a unity, there can be no creation or destruction; in fact, there can be no change at all. Being is, not-being is not, and anything else is unthinkable. But how can an argument like this have any value, since it seems evident that things around us are changing all the time? In fact it is this idea that Parmenides sought to discard; that our senses can be relied upon to give us a true account of the world around us.
We can think of the Eleatic doctrine as stemming from the desire to express that nature as a whole is continuous, even though when we attempt to confront it head-on it appears to us as a collection of individuals. From this angle the Eleatic argument becomes more readily understandable. It is not a negation of the natural world and its apparent changes, but a way to reconcile the fact that nature seems to persist -- like being born of like, and the continuation of species, for instance -- with the similarly obvious fact that all living things come to be and subsequently pass away, replaced by other things of their kind.
As Parmenides saw it, the natural world is continuous and discontinuous at the same time (in the same way that a species carries on even as members of it are dying all the time). These two poles are so opposed that it seems impossible to reconcile them; so one of them must be untrue. Parmenides says that it is the discontinuous, sensual experience of nature that it false; he deprecates it, calling it "opinion" or doxa, and suggests that the only true way to understand the world is to conceive of it as the unity described above -- not in terms of what we experience, but in terms of what we think. It is in thinking rationally, rather than experiencing sensually, that we can come to an understanding of the nature of the one, the unity, of being: "such, unchanging, is that for which as a whole the name is 'to be' " (51, no. 19). This is where the aporia appears. Parmenides has effectively discarded the world we sense and replaced it by one we can only think of, not experience. But what, then, are we supposed to do with our senses and what they tell us?
This problem is what the Pluralists, Anaxagoras and Empedocles, attempted to solve: how can the sensible world be saved from negation, without violating any of the tenets of the Eleatic philosophy? Logically, the Eleatic position is sound -- and it is evidently correct, at least in part; for it is true that species do persist, and nature does seem continuous; and following Zeno's paradoxes, if we impose divisions upon things we condemn ourselves to think nonsense. But surely ignoring sensory perception altogether is not the answer, either.
Empedocles' effort to resolve sense perception into something more than unreality without contradicting Eleaticism hinged upon the idea that within its unity, the natural world is actually composed of four different elements: "fire and water and earth and the immense height of air" (62, no. 32). These four combine, with varying amounts of each, to form substances that seem different to our senses; and just as they can be combined, they can be torn apart and recombined in different ratios to form different things. (Incidentally, these four are remarkably similar to the single elements from which all things spring proposed by earlier philosophers who held a cosmological view of material monism: Thales' water, Anaximander's air, Anaximenes' boundless apeiron, not unlike fire in its indeterminate nature, and Xenophanes' earth.) The forces responsible for this apparent change are Love and Strife, which respectively bring the elements together and move them apart. The four elements do not undergo change themselves; nothing is added to them, and nothing is taken away. It is only the way in which they are arranged that changes. This makes them not precisely contrary to the Eleatic position, which demands a static universe; they are even more compatible with Parmenides' philosophy when we take into consideration that they are co-eternal as well as immutable, neither coming to be nor passing away. Empedocles describes them thus:
For [they] 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.
And nothing is added to them, nor do they leave off,
For if they were perishing continuously, they would no longer be.
But what could increase this totality? And where would it come from?
And how could it perish, since nothing is empty of these?
But there are just these very things, and running through one another
at different times they come to be different things and yet are always and continuously the same. (64, no. 32)
Analogically speaking, the elements are like atoms combining and recombining to make molecules; the bonds between them can be broken and reformed, and they can be rearranged into substances with entirely different properties from the way they started out, but despite the apparent change they remain fundamentally the same. (That is not to say that Empedocles' position ought to be conflated with that of the Atomists, Democritus and Leucippus; but it is a useful example nonetheless.) Thus any process of "creation" or "destruction" is in fact illusory; comings-to-be and passings-away are rearrangements of the elements, all of which are conserved in their entirety throughout the process. Moreover, just as elements are being forced apart by Strife, they are already being pulled into new configurations by Love; nothing has time to be "born" or to "die", because all of its elements are always already being recycled into "new" things, comprised of the old. Thus even as creation and destruction seem to occur, each negates the other, and we are left once more with an immutable world.
According to Parmenides, all of being must be held together as a unity; the four elements seem to be distinct from each other, at least insofar as they can be drawn together and pulled apart. But Empedocles' elements are a unity: "at one time they grow to be only one/out of many", he says, "but at another they grow apart to be many out of one" (63, no. 32). This opposition is similar to the one that arises from apparent creative and destructive processes -- even as it takes place, it is always already negating itself and becoming its opposite again; even as the unity is dividing itself into many, it is coming together to reform into the one.
Anaxagoras' position is similar to Empedocles', in that it involves an account of the perceptible world given in Eleatic terms. But it differs in its application; where Empedocles had four elements to make up the totality of the world, Anaxagoras held that everything was contained within everything else, like "seeds" of specific things; these were combined much like Empedocles' elements in different ratios, and any given thing's defining characteristics were based on the "seeds" that made up its bulk. (For instance, flesh appears to us as flesh because the majority of the seeds it contains are flesh; it also contains some of every other thing imaginable, but in lesser quantity.) The logic behind this is simple: as Anaxagoras says, "how could hair come to be from not hair, or flesh from not flesh?" (56, no. 11) But Anaxagoras' comings-to-be and passings-away are still in accordance with Eleatic doctrine, in a similar fashion as are Empedocles'; all things already are, just not necessarily in the configuration in which they will end up. And the fact that everything contains some small measure of everything else means that simply by virtue of being, it is participating in the unity of being-again, a legacy inherited from Parmenides.
Another important difference to note between Anaxagoras and Empedocles is that where Empedocles invented the forces of Love and Strife to account for movement within the unity of being, Anaxagoras held that it was the force of mind, or nous, that was responsible. (He is widely credited with being the first philosopher to conceive of mind; and perhaps he is also the one we can blame for the mind/body problem that has haunted philosophy ever since.) What he meant by this is debatable; it could mean that there is some divine Mind that moves all things without interrupting the continuity of being. But if we are considering Anaxagoras in terms of how his philosophy followed after that of Parmenides, it makes more sense to conceive of his nous as being the mind of the thinker himself -- if we can conceive of a movement, from place to place or in the form of an apparent creative or destructive gesture, and it is logically sound, then it is valid.
To demonstrate what this means, we might consider Zeno's first paradox a second time. If we think of it in strictly Parmenidean terms, with no change at all being allowed, then of course nothing can ever move; there is always another halfway distance to cross in order to reach a previously-defined endpoint. But as soon as we think of the distance to be crossed as a totality that cannot logically be divided, we've already crossed it and achieved the goal. This, then, is the power of nous: and it applies to other fields as well, specifically to apparent creations and destructions as above.
It seems that Empedocles and Anaxagoras both have succeeded in preserving the sensible world, the former with the elements arranged and rearranged by Love and Strife, and the latter with the seeds of all things contained in all else and manipulated by nous. But neither of them can truly be said to have been successful, because each of their theories presents more problems even as it provides a solution for the problem it set out to solve. The unresolved problem with Empedocles lies in the exact nature of Love and Strife in relation to the elements: evidently they are above being arranged by some higher power, as they themselves do the arranging of the subordinate elements. But whether they actually partake in divinity is left unexplained, and we are left to suppose that they are materially different without knowing how or why. Conversely, the difficulty with Anaxagoras' theory of seeds is a material one: what precisely are these "seeds" that make up all things? Perhaps these apparent inadequacies of philosophy are a result of some of Anaxagoras' and Empedocles' work being lost to posterity. But regardless of the reason why, these sticking points at the tail ends of solutions to the Eleatic aporia are enough to seriously hamper the efforts of their respective philosophers, and indeed stand in the way of a single definitive solution to the original problem.
Curd, Patricia, ed. A Presocratics Reader. Indianapolis: Hackett Publishing Company, 1995.