We have seen that there are fundamental problems with the standard account of early Greek philosophy.  The alleged Material Monists seem not be Monists but Pluralists.  They allow their original, generating substance, such as water for Thales, air for Anaximenes, to change into other substances.  Heraclitus accepts their general picture, but rejects their conclusions: if the generating substance turns into other substances and they turn back into the generating substance, then no substance is permanent, or ultimately real. What is real in one sense is constant change.  But this does not entail that there is no order or permanence in nature.  There is: the structure, the pattern of change remains permanent, and so does the overall word-order, the cosmos itself. 

But this picture seems disturbing, particularly since Heraclitus delights in paradox.  He seems to say that there is no order, only change and discontinuity.  His philosophy seems to invite objections based on the apparently order of the world.  How could radical flux produce order?  Here there seems to be room for a significant objection to this theory.  Enter Parmenides, the famous philosopher from Elea, in southern Italy.

He tells a story, in dactylic hexameter verse, the verse of epic poetry, of a youth who travels to the ends of the earth, where he meets a goddess who instructs him.  She offers a foundational principle:

Come now, and I shall tell, and do you receive through hearing the tale,

which are the only two ways of inquiry for thinking:

the one: that it is and that it is not possible not to be,

is the path of Persuasion (for she attends on Truth);

the other: that is is not and that it is right that it should not be,

this I declare to you is an utterly inscrutable track,

for neither could you know that is not (for it cannot be accomplished),

nor could you declare it.  (fr. 2)

There are only two ways of investigating something: either by assuming that it is, or by assuming that it is not.  But the latter approach is surely doomed from the outset.  For if it is not, you cannot know it or even think it.  Accordingly, “It is right to say that what-is is, for being is/ and nothing is not” (fr. 6. 1-2).  So the goddess rejects the second approach, and also a third one

which mortals knowing nothing

wander, two-headed.  For helplessness in their

breasts directs a wandering mind; and they are borne

both deaf and blind, dazed, undiscerning tribes,

by whom to-be and not-to-be are thought to be the same

and not the same, and the path of all is backward-turning.  (fr. 6. 4-9)

Perhaps no one would make the mistake of trying to study nothing.  But ignorant mortals try to combine being with not-being in their theories, thus undermining their theories.  In this passage there seem to be several echoes of Heraclitean language, including the term “backward-turning,” which is an extremely rare term in the Greek lexicon.  Heraclitus speaks of a backward-turning bow and lyre in one of his statements (fr. 51).  In all likelihood Heraclitus wrote before Parmenides, because when he strongly disagreed with one of his predecessors or contemporaries, he lambasted him in his statements.  Parmenides, by contrast, names (or has his goddess name) none of his opponents.  (It would be beneath the goddess to get down and dirty with mortals.)  But here and elsewhere, I believe, he leaves some literary hints as to who he has in mind. 

The goddess goes on to develop an extended argument as to what we can know of what-is.  Having dismissed the study of what-is-not and of the conflation of what-is and what-is-not, she concludes:

Only one tale is left of the way:

that it is; and on this are posted

very many signs, that [1] what-is is ungenerated and imperishable,

[2] a whole of one kind, [3] unperturbed and [4] complete.  (fr. 8. 1-4)

Parmenides of Elea identifies four traits that what-is has, which I like to call his Eleatic properties (he is revered as the founder of the Eleatic “school” or tradition): what-is is (1) without coming-to-be or perishing; (2) all alike in quality; (3) unmoved; and (4) complete.  He gives an extended argument for these properties, as part of his extended defense of his ideas, in what is the first detailed argument in Greek philosophy.  In each case, he argues that to say anything else would be to introduce not-being back into the discussion.  For instance, if what-is comes to be, it must come-to-be after not being.  It must, then, come-to-be either from what-is-not or from what-is.  But if it comes to be from what-is, it already is; and it cannot come from what-is-not, for that is unsayable and unthinkable. 

So what-is must be unchanging and all alike.  This sounds like a radical Monism.  Not a Material Monism, for what-is is not necessarily material (if so, it would probably not be changeless and complete).  Indeed, it must be a more austere Monism than that of the (alleged) Material Monists, for each one of them allows his ultimate reality to take on different appearances, and hence to not be all alike, at least in its sensible qualities. 

So who is Parmenides arguing against?  Not, it would seem, against the Material Monists, at least in the first place, because he is ruling out coming-to-be and perishing in his first argument.  For Material Monists don’t allow coming-to-be and perishing, but only more limited kinds of change.  We might want to say he is arguing against “mortals” in general, ordinary people who think things coming into being and perish.  Perhaps.  But haven’t the Material Monists already done that—if there really are Material Monists before Parmenides? 

If, however, there have been no Material Monists, and all the early philosophers have been saying (Heraclitus), or at least implying (the other earlier Ionians), that everything is changing all the time, wouldn’t that provide the kind of target Parmenides’ goddess needs?  And Heraclitus, as we have seen, comes very close to saying that what-is and what-is-not are interconnected when he says, for instance, that the death of one element is the birth of another (fr. 36, fr. 76).  What-is comes-to-be from what-is-not and vice versa. 

So we end up with a story like this:

1. Every (derivative) stuff comes-to-be from and perishes back into some original stuff.  (Generating Substance Theory)
2. If (1), then every stuff changes into every other stuff, and no portion of stuff stays the same; only the pattern of change is constant.  (Heraclitus)
3. If (2), then what-is comes-to-be from what-is-not; but what-is-not is-not; so there is no change and no differentiation.  (Parmenides)

Parmenides offers what seems to be the ultimate refutation, not only to some philosophies, but to all philosophy that seeks to explain how the world works.  He challenges philosophers to answer a simple but profound question:

How can what-is come-to-be from what-is-not?

Call this the Eleatic Challenge.  It becomes the challenge that confronts all philosophy from Parmenides to Aristotle.  Yet Parmenides does not destroy philosophy of nature and cosmology.  That continues to flourish after him.  So how can we reconcile the philosophy of nature with the Eleatic Challenge?