In the history of Western thought, the possibility (or impossibility) of change was a question that pushed early thinkers to some of the most important philosophical distinctions of their time period and ours. These distinctions would leave their mark on philosophical inquiry and would not be fully taken up until the Modern era. Some of the most important distinctions were defined by the Eleatics (led by Parmenides), Plato, and Aristotle. While all three theories of change did not grow out of a vacuum, Parmenides more or less followed the force of his own logic, Plato kept Parmenides’ conclusions close at hand, and Aristotle’s theory grew in direct response to both of them. All three also used reason as the primary gateway to knowledge. But in their responses to the problem of change, each one integrates the material world more than the last. This integration allows more satisfactory models, but poses significant problems in itself. Parmenides never runs into these problems because he rejects the material world outright as an illusion. So to address these problems in Plato and Aristotle we must first identify Parmenides’ answer to the problem of change and its consequences: to both change and to the use of reason.
Parmenides’ argument is easily constructed in an analysis of the statement “A becomes B.” In this statement, it can be seen that A is not B because if A=B then there would be no need for change: A is already B. As it is, A is not B and so “A” can be replaced by “not B”. The statement “not B becomes B”, though, does not make sense to Parmenides. A cannot become B unless A has some of B already in it, but for Parmenides this would violate its essential not-Bness: A cannot have any of B in it because A is not B. It is through this kind of argument and logic that Parmenides says that change is impossible and that A does equal B, which equals C ad infinitum. As David C. Lindberg, in his magisterial history of Western science, says,
“What does one do if experience suggests the reality of change, while careful argumentation (with due attention to the rules of logic) unambiguously teaches its impossibility? For Parmenides and Zeno, the answer was clear: the rational process must prevail.”And so Parmenides declares that all change is merely an elaborate illusion and the underlying reality is a completely stable, unchanging monism.
Enter Plato. The force of Parmenides’ argument, taken to its logical conclusion, is truly stunning, but not quite satisfactory. Plato agrees that the underlying reality must be unchanging, but disagrees that this must be all that reality is. It is here that Plato enunciates the first great metaphysical distinction, between appearance and reality, which Parmenides had used, but not in a systematic way. It is encapsulated in Plato’s divided line, which he elaborates in The Republic. Plato designates the underlying reality as the Realm of Forms. The Realm of Forms is incorporeal, perfect, eternal, insensible, and changeless. In contrast to the Realm of Forms is the material world. It is everything that the Realm of Forms is not: corporeal, imperfect, transitory, sensible, and changing. The divided line separates the two. Plato says that the material world is a reflection of the Realm of Forms and that while the Realm of Forms is completely stable and unchanging, the material world, the reflection, does change as can be plainly seen in everyday life. In this way Plato supplies a rational, fixed underlying reality while still allowing the material world some relevance.
One challenge to this argument would be to question how the Realm of Forms interacts with the material world. How can things that are corporeal interact with things that are insensible? Plato answers this in two ways. First, through a series of arguments, Plato shows that, while we cannot sense the Forms now, our souls were in the Realm of Forms before they were placed in material bodies. We can gain access to the Forms, then, by a process of anamnesis or recollection. Through contemplation we are able to recall the Forms. (Plato does this notably in the Meno by showing how he can teach even a slave the basic mathematics: something that clearly only could be done if a Realm of Forms existed.)
Plato also answered this challenge in the form of the Allegory of the Cave. In summary, the Allegory describes people whose only known reality is the back wall of a cave where they can make shadow puppets. One day, one person ventures outside and discovers that the cave and the shadow puppets are not all that exists. In fact, he realizes that the shadows are really only reflections of the sun. It is through this analogy that Plato shows that the Forms (specifically the Form of the Good) represented by the sun, “illuminates” the material world. Without the Forms, the material world would not, could not exist.
It is important to notice here that Plato is continuing with Parmenides’ placement of reason as the pinnacle of knowledge. The process of anamnesis can also be called “reason.” It is through reason, which Plato made into a method called the “dialectic,” that we can reach the Forms. Plato merely adds a material world to account for the change of our senses. The change is real, but not as important as the unchanging, reason begotten by the Forms.
There is one other important distinction to make before we move to Aristotle. It is the distinction between the General and the Particular. The distinction has actually already been made. The General can be equated to the Realm of Forms and the Particular to the material world. This is important because the difference between Plato and Aristotle can be termed a difference in orientation to the General and the Particular. Plato believes and argues that what is real is the Forms or the General and statements about what is real are found in the material world or the Particular. Aristotle, on the other hand, is just the reverse. What is real is the Particular and statements about what is real is the General. With this distinction in hand we can turn to Aristotle.
Aristotle believes that what is real is the material world and all that the material world is contingent upon. To Aristotle, the Realm of Forms are really just properties possessed by the material Particular, or substance. And like Plato and Parmenides, Aristotle designates that the ultimate reality be unchanging. But how do we account for change now, if the material world, represented as substance and properties, is now unchanging?
To account for change, Aristotle goes back to Parmenides. Parmenides made a distinction between Being and non-Being. Aristotle sees this and says that Being can split into two different types of Being: Potential and Actual Being. So Aristotle agrees with Parmenides that a thing cannot move from non-Being to Being. However, when change occurs, Aristotle says that it is Potential Being changing into Actual Being. Take an acorn and a tree for example. In Parmenides’ model, an acorn (non-tree) cannot change into a tree. In Aristotle’s model, however, an acorn (potential tree) can change into a tree (actual tree) because the acorn houses tree-ness in the form of potentiality. So Aristotle also accounts for change and places an even greater emphasis on the material world than Plato.
What is important about these three philosophers is their use of reason. Each one placed reason on the highest pedestal, but Plato and Aristotle each successively put more and more emphasis on the material world and the senses. The question that arises then is why didn’t they question the use of reason? Parmenides used only reason and he found that change was impossible. He stuck to his guns and followed his own argument to its logical conclusion. But instead of looking around himself and seeing the fallacy of his conclusions, he declared that his use of reason had detected a flaw in the senses and that all the “evidence” to the contrary is illusory. But why does the flaw exist in the senses? Nothing in logic dictates that the flaw be placed upon the senses. It's just as logical to think that the flaw exists in the instrument of argumentation used: reason itself. Parmenides doesn’t think so and neither do Plato or Aristotle. Plato and Aristotle add the senses back into reality to some degree, but the philosophical question that arises out of the problem of change is “How much do the senses and reason play in reality?” Once you let a little in, who’s to say how much? And so the philosophical lines between the Rationalists and Empiricists of the Modern era, who would drag “reality” between these two polar points of reason and the senses, were drawn 2,000 years before the culmination point during the 17th century.
 David C. Lindberg, The Beginnnings of Western Science, University of Chicago Press: 1992, p. 33