Being fooled by experience: Parmenides, Zeno, and Socrates

The way that Socrates uses logic reminds me of the way Zeno argues for the paradoxes of motion (i'm taking ancient greek philosophy right now). The basic argument that Zeno makes when he's defending Parmenides claim that everything is one motionless being, is that motion requires an impossibility so there must be no motion. He uses various arguments to defend this claim, and when you read them, it makes sense...sort of. However, it seems to me that the ancient greek logic is flawed when it comes to connotation because there is none. I do understand that the ancient greeks didn't have the concept of a word meaning more than one thing (according to our textbooks) and this creates a problem. Piousness, to an ancient greek, is the exact opposite of impiousness, there is no gray area.

"Socrates: Then teach me what that characteristic itself is, in order that by concentrating on it and using it as a model, I may call pious any action of yours or anyone else's that is such as it, and may deny to be pious whatever isn't such as it."

Socrates wants a clear definition of what piousness is and isn't, there is no relativity. When you use logic that is black and white like that you run into impossibilities, which is how you you decipher what is true and what is not true. Like Socrates, Zeno has certain black and white logic that determines that motion is impossible. For example:
If you start the logic stream with -Nothing can come from nothing.- then you can assume that everything that is always was and always will be. If x doesn't exist, then x can't exist. Which means that "nothing" is impossible, and their is no "void". If you look at an object, the object must fit exactly in the space in which it is, so therefore it must be still. If movement were possible then during flight the arrow would always have to occupy a space that fits it exactly which means it would have to be at rest which creates an impossibility, therefore No Movement. Of course modern science fixes all those problems but it illustrates how cold, non-experience based, logic/reasoning can create impossibilities that may/may not exist.

Parmenides or Zeno would say that people should not be fooled by experience. But it seems to me that people can easily be fooled by logic. I think this has relevance to Socrates because in some cases, he's pulling the same trick.