The poem of Parmenides as it has come down to us consists of a prologue and then the way of seeming and the way of being. In the prologue Parmenides establishes his credentials as someone to listen to. He tells of being swept up in a chariot to heaven where the way of truth was revealed to him. What is the way of truth? Being is being and not-being is not-being. That seems fairly clear, but what Parmenides takes this to mean is that change and multiplicity are impossible. If there were two beings, A and B, A as being A would not be B, and of course vice versa. But this is to say that what is is not, and that is an abomination, a violation of the way of truth. So, too, with change. That which changes would be what it is but not what it becomes; thus being would become non-being.
On these rather abstract bases, Parmenides denies the reality of multiplicity and change. Being is one and changeless. He likens it to an utterly homogeneous sphere. It is easier to grasp the Parmenidean doctrine in the abstract than to try to visualize it. And, of course, students will soon feel uneasy about the relation between themselves and Being. There would seem to be an inescapable duality between Parmenides talking about it and the being he is talking about. But it is the negative consequences of this austere doctrine that are crystal clear. If it is true it makes nonsense of pre-Parmenidean philosophy which, if Aristotle is right, is characterized by the search for the cause or causes of change.
Parmenides is perhaps the first philosopher to draw a firm line between being and appearance. Of course the world seems to be a place of multiplicity and continual change. In the Way of Seeming, Parmenides sketches a natural philosophy which makes the same assumptions as did his predecessors. But the truth is that the world as it appears to us is not an accurate grasp of what really is. Being is. Non-being is not. Those two propositions sum up the truth of the matter.
The reverence in which Parmenides was held is captured by Plato in the dialogue named for his great predecessor. When Parmenides arrives in Athens he is greeted like the prophet he claims to be. Is this simply dramatic licence? It does not seem so when we consider post-Parmenidean philosophers. But before considering the role Parmenides plays in the development of Plato's thought, it is important to see his effect on the development of natural philosophy.
The discussion of Parmenides in the Physics does not really belong there, Aristotle tells us, because Parmenides denies the very starting point of natural science -- that there is motion -- and it is not the task of any science to defend its own principles. How could it, since to do so it would have to appeal to those principles. It is the task of metaphysics to deal with denials as sweeping as that of Parmenides.
No one can read the acccount in Book One of the Physics without sensing that Aristotle, like Plato, holds Parmenides in high esteem. He is concerned to show that Parmenides made an rather elementary mistake, but at the same time he says it is a plausible one. Parmenides stands athwart the path of natural philosophy calling a halt to it. Those who have been giving one account or another of the way things come to be are one and all engaged in a pointless exercise. The assumption of these explanations is false, namely that motion exists. Parmenides asserts that motion does not exist because it cannot. Why not? Let us examine the position in the formulation Aristotle gave it.
Motion or change depends upon the assumption that a being comes to be. The question is, is this tenable? There are two possible antecedents to the alleged new being.
Being comes from being.
Being comes from non-being.
These can be converted into:
1. Being becomes being.
2. Non-being becomes being.
As soon as the assumption is spelled out in this way, Parmenides thinks we will see the impossibility of the claim. To say that being becomes being is to say that there is exactly the same thing before the change and after, that is, no change occurs. To say that non-being becomes being is to identify non-being and being, which is clearly absurd. Since these exhaust the possibilities, there is no way in which motion and change can be regarded as real.
Aristotle agrees that 1 and 2 above are on the face of it false. In both propositions, a change is attributed to a subject. If the subject of  means the same thing as that which it is said to become, no change occurs, whereas if the being that comes to be is not the being from which it comes, yet the change is attributed to the antecedent being, the claim seems to be that something becomes what it is not. This identification of being and non-being is even more patent in  -- non-being is said to become being.
When we are confronted with such an objection, we are sure there is something wrong with it, since if there were not, we would have to deny the evidence of our senses. That is just what Parmenides advises us to do, of course, but it is advice one is reluctant to follow. What then is to be made of Parmenides' analysis.
Aristotle reminds us of a distinction we frequently make between attributing an activity or attribute to someone essentially or doing so incidentally. For example
The philosopher does the tango
may be a perfectly true proposition but Mario who tangos does not engage in this wholesome activity precisely as a philosopher. There are, one hears, philosophers who do not tango. It is not part of the job description of the philosopher, so such lead-footed thinkers are not deficient as philosophers. It just happens that Mario is both a philosopher and a tango dancer, so to attribute dancing to him as a philosopher, while true, is only incidentally true.
On the other hand
The tango dancer tangos
is an activity true of the subject as designated. This is something essential to, part of the job description of a tango dancer. Whereas
The tango dancer is a philosopher
would be, if true, only incidentally true of someone insofar as he is a tango dancer.
There is, of course, nothing at all arcane about this distinction. Once it is articulated we realized we knew it all along, have been employing it since who knows when. It is this commonplace distinction that forms the background of Aristotle's critique of Parmenides.
In  and  above 'becomes being' is attributed to being and to not-being respectively. Parmenides understands these as essential attributions, or as Thomas will say, per se predications. So understood, Parmenides is right to say that they make no sense. What must be done is to see that these are incidental attributions.
Aristotle offers his analysis of Parmenides after he has looked into what change entails and what it means to say that something has come to be.
Take the most ordinary change imaginable. Willie is whittling wood. The wood he begins with has a shape but it does not have the shape it has as a result of Willie's whittling. A number of things are involved here: the wood and the shapes it has. Let us say that Willie is whittling an unflattering likeness of his mother-in-law, Sheila. When he begins, the wood does not have the shape of Sheila; when he is done, the wood has the shape of Sheila. Let us call its antecedent shape Block. Then we can formulate these true sentences about the process.
Block shape becomes Sheila shape.
Non-Sheila-shape becomes Sheila shape.
These are both true sentences, but how are they true? These are not essential attributions. The block shape does not become the Sheila shape as if the two then coexisted, with Block shape a constituent of Sheila shape. No more does the privation of Sheila-shape become Sheila-shape as if the latter and its opposite are one. It is because he took these to be essential attributions that Parmenides bristled and quite rightly said that can't be.
Aristotle observes that if Parmenides had recognized these as incidental attributions, his difficulties would have been over. The sentences can be rephrased as follows:
Block shape becomes Sheila shape = Wood insofar as it has the shape of block comes to have the shape of Sheila.
Non-Sheila-shape becomes Sheila shape = Wood that lacks the shape of Sheila comes to have the shape of Sheila.
The change is not attributed essentially to either block shape or non-Sheila-shape; it is attributed essentially to the wood. It is wood that having a given shape and lacking another, comes to have that other shape. It is only incidentally true that block shape becomes Sheila-shape or that non-Sheila-shape becomes Sheila shape.
Aristotle offers this definition of the subject of a change, that is, that to which the change is essentially attributed: The subject of a change is that to which the change is attributed and which is a constituent of the result. The result of Willie's whittling is Sheila-shaped-wood. Clearly neither block-shaped nor non-Sheila-shaped save this account of the subject of a change.
It can also be said that wood when it is actually block-shaped is potentially Sheila-shaped.
Thus it was that Aristotle showed that the roadblock Parmenides had erected can be removed by a simple distinction, one that Parmenides knew as well as anyone else, but which he had not applied here, with unfortunate results.
Writing assignment: Write a brief essay on one of the following:
1. What, precisely, is the Problem of Parmenides?
2. How, precisely, does Aristotle solve it?