Sam also asked:
Why do Parmenides and Zeno think that change/ flux/ motion are impossible?
Answer by Helier Robinson
Parmenides took one side in the problem of identity and change. This is a problem that is largely ignored today, although it should not be. It begins with the logical fact that qualitative difference entails quantitative difference. This is easily proved: whatever A and B may be, if there is a qualitative difference between them then there is some quality, Q, such that A is Q and B is not-Q (or vice versa); if A and B are one and the same (that is, identical) then one thing is at once Q and not-Q, which is impossible; therefore A and B are two. Hence qualitative difference entails quantitative difference. Secondly, change is defined as any qualitative difference over time. Thirdly, one thing cannot change and remain the same one thing — remain identical; because if it did then the thing before the change would be qualitatively different from the thing after the change, by the definition of change, and therefore they would be two.
Heraclitus famously claimed that you cannot step into the same river twice (because both you and the river have changed) and that nothing is permanent except the fact of change. In other words, there is no identity, only change. Parmenides took the opposite view: all change is illusion, only the One is. In other words, there is no change, only identity. A particular case of this problem is the problem of personal identity: we each of us believe ourselves to be one person, changing through time — and this is logically impossible. The best solution to this is to say that between each personal change there is a numerically different person, and personal identity consists in the totality of these different momentary persons.