Doc

Zeno's Paradoxes are actually quite well-formed in both philosophical and mathematical terms. They were not mathematically resoluble (your reservations about velocity included) until the development of calculus and the understanding of the notion of a limit. At least this is my understanding.

As to velocity, you are right - it seems intuitively obvious to us that that is the Gordian knot requiring cutting - but Zeno takes the philosophical position that we cannot assume we know what velocity is. He makes us question our understanding of the idea of movement itself - and that's what his paradoxes are about - not the mathematics of physics, but the philosophy behind our notions of time, space and motion.

Ask yourself this:

If an object is 'moving', then presumable at one time (p) it is in spot A, and at another time (q) it is in spot B. What happens in between A and B. Does the object fill all the spece between them? Can you chop up time such that the distance between p and q can be truly infintesimal? What does it mean to say you can have a period of time that is infinitely small?

These are the sorts of things Zeno is asking us to think about. Even today we have no perfect answers for them. (By the way, some people, particularly those who have just started college, seem to think that Zeno is a 'proof' of some sort or another that can be thrown at any philosophy to mock it. This is not a useful or clever idea either.)

Hope this helps.

cheer

the sunshine warrior