This essay was written a couple years ago, and perhaps I will update it, but I thought it worth sharing:
What, precisely, is the “Problem of Parmenides,” and how does Aristotle solve it?
The problem of the one and the many has been part of philosophy as long as men have been pondering reality. Until the time of Parmenides, a major focus of philosophy was trying to understand the changes occurring in the world. Given our experience, it seemed only obvious that change is a reality, and some, like Heraclites, would go so far as to say that nothing could really be said of anything, since it was all in constant flux.
Parmenides, however, would say that our senses must not be the authority we look to, since reason shows necessarily that change is an illusion, and cannot actually be possible. He says that being is being, and non being is not being, and that being cannot come from non being, and likewise, non being cannot come from being. Therefore, all change is an illusion, since something cannot become something it is not. For example, this rock is not “there,” and so, it cannot become “there” from “not there.” Parmenides thus defends the reality of being, that it is, and his doctrine, seemingly of very sound logic, creates quite a difficulty for those who would try to explain change, as we perceive it.
Aristotle, of course, will say that our knowledge starts with our sense perception, and that we reason from there. He certainly agrees with Parmenides in that non being does not come from being, nor being from non being. However, it is the manner of being, of the subject which has things incidental to it, by which things can change. If white and rock are both said to be in the same way, then a white rock cannot become red, since white cannot become red. However, a rock can become red, and no longer be white, and it is not the white that changed, but the rock.
Below, a relevant passage (Physics i. 3 ; 186 a 24 – 186 b 3) of Aristotle’s is commented upon. Aristotle is addressing an assumption of Parmenides:
His assumption that one is used in a single sense only is false, because it is used
in several. His conclusion does not follow, because if we take only
white things, and if ‘white’ has a single meaning, none the less what
is white will be many and not one. For what is white will not be one
either in the sense that it is continuous or in the sense that it
must be defined in only one way. ‘Whiteness’ will be different from
‘what has whiteness’. Nor does this mean that there is anything that
can exist separately, over and above what is white. For ‘whiteness’
and ‘that which is white’ differ in definition, not in the sense that
they are things which can exist apart from each other. But Parmenides
had not come in sight of this distinction.
Here, Aristotle begins to define the difference between what “is” white and the “whiteness” that it has. It is in this distinction of the subject of the change from the change that takes place in, of, or to it, that we are to understand that change is not being coming from non being, or vice versa.
It is necessary for him, then, to assume not only that ‘being’ has
the same meaning, of whatever it is predicated, but further that it
means (1) what just is and (2) what is just one.
Parmenides did not recognize the difference, in speaking of being, between the thing that “is” and an attribute of it. For instance, the rock “is” and “is white,” and even though “is” can be used to speak of both of these things, they are not speaking of “being” in the same way, and this is the error of Parmenides reasoning.
It must be so, for (1) an attribute is predicated of some subject,
so that the subject to which ‘being’ is attributed will not be, as
it is something different from ‘being’. Something, therefore, which
is not will be. Hence ‘substance’ will not be a predicate of anything
else. For the subject cannot be a being, unless ‘being’ means several
things, in such a way that each is something. But ex hypothesi ‘being’
means only one thing.
As part of Aristotle’s logic, a term cannot be ambiguous, and the term “being” or “is,” as used by Parmenides, is not one and the same when he reasons that something cannot come to be from what it is not. The rock comes to be red from white, but it is false to say that the white comes to be red. Once again, it is the rock that comes to be red, and the rock was white.
Aristotle thus demonstrates that we are not thereby deceived when our senses show us that there is change in the world. Aristotle’s massive contribution to logical reasoning itself allows him to find the fault in Parmenides’ reasoning and expose it. The error now refuted, philosophy was free to continue to seek to understand the changes occurring in the world around us.