Traversing the Infinite

A very interesting discussion of whether the infinite can be traversed is going on at Philosophy, etc. I'm inclined to agree with some of the commentators that the common 'calculus' resolution of Zeno's paradox isn't a resolution of the paradox at all -- it's simply a restatement of the situation (that there is a finite interval whose traversal would take an infinite series). It's true that such situations really do exist; but that's the whole point of the original paradox, which Zeno directed against claims that a real, physical infinite divisibility was possible. As Hallq says in the comments, we don't seem to be able to get the claim that we can traverse an infinite; just that we can traverse any arbitrarily large finite series. But there are arguments that might be raised against this conclusion. Go and check out the discussion.