Parmenides was a pre-Socratic philosopher from Elea. He is notorious for denying that there can be any change. He believed that everything is part of a single unified and unchanging whole. All apparent change is merely illusion. His follower, Zeno, extended this idea by providing further logical paradoxes which attempted to show that motion leads to essential contradictions that are logically irreconcilable. For example, he showed that motion isn't possible because in order to travel from A to B we have to travel half the distance, and then half that distance and then half that distance, and an infinite number of halves. But if we have to cross an infinite number of halves, how can we even get started? Aristotle, simply rejected this argument on the grounds that we can observe things in motion, but this isn't very effective because Parmenides already argument that motion is an illusion. The difficuly in this paradox is that of the infinite, which Greek mathematics couldn't handle, and it would require a far more sophisticated relationship with infinity in mathematics for this problem ultimately to be solved.
Parmenides' argument for lack of motion was twofold. First, he argued that for change to occur it must progress from being to non-being, since something which was not before now is. For example, if I grow tall, I have to start from not-tall and then change to tall. But how could something possible come from nothing? How could being come from nothing, since nothing is completely nothing? After Parmenides, thinkers would recognize that this absolute change, (something from nothing) is not possible, but change is possible because things don't need to change completely. There is something that persists through the change. For example, if I grow tall, it is I who persists through the change. Tall to non-tall is not absolute change, because the I is the unchanging ground upon which the ball of change can roll.
Parmenides other argument is about the incomprehensibility of non-being. A world in which there is change requires a combination of being and non-being, but we can't possibly comprehend non-being since it is absolutely nothing. Thus, the comprehensibility of the world would be undermined by change. Parmenides here was again mistaken since the presence of change only undermines the complete comprehensibility of the world, which is an unfortunate fact which all we people who would like to know more about the world have to deal with.
I think the essential lesson to learn from Parmenides is the danger of thinking only with absolutes. Parmenides assumed that all change must be absolute change and so rejected change altogether. He assumed that for the world to be comprehensible it must be completely comprehensible. He will not be the last philosopher to make this error. For example, if one were to say, since we can't have complete access to truth, then we can't know anything.