Yet nothing physically infinite happens, and what motion is possible is determined by the laws of physics alone, and not by the necessary truths about an abstraction that bears the same name.
Common sense dictates that Zeno's mistake was to PRESUME that a certain mathematical notion called "infinity" is physically relevant. — tom
Zeno's intentions aside, you aren't solving the paradox by saying this. You're merely restating it. Infinite regresses appear from time to time. Philosophers usually take them as a sign that something's wrong. Consider Frege's and Quine's reactions to the regresses they discovered. No one says, "Oh that's just a fluke of the mind... I'll proceed on as if I never noticed that."
No. We pay attention to regresses because philosophy is the domain where we're free to take note of such impractical doo-dads.
If you're planning a trip to the Grand Canyon, feel free to ignore Zeno's Paradox. It has nothing to do with your trip. And by the way, why are you going this time of year? Don't you know the road to the North Rim is probably closed?