Is Zeno's paradox really refuted by the fact of someone's walking? ("Solvitur ambulando" - L. Carroll)

Zeno most famous paradoxical argument seems to show that Achilles can never overtake the tortoise. Plainly, the conclusion of Zeno's argument is false: that can be shown by Achilles just walking along, overtaking the tortoise! That's why the argument -- which seems to go from true premisses via plausible reasoning to the palpably false conclusion -- is a paradox . But of course, just re-iterating that the conclusion is false doesn't solve the paradox, if that means explaining just where Zeno's reasoning goes wrong. It's perhaps not helpful, then, to talk about "refuting" the paradox, for that's ambiguous. It could mean showing the conclusion is false , or it could mean explaining where the bug is in Zeno's reasoning . Doing a bit of walking (Achilles overtaking the tortoise yet again) suffices for the first, but not for the second!