Benardete's paradox

proper noun

A philosophical problem whereby a man intends to walk a mile from a particular point, but an infinity of gods separately plan to obstruct him. One of them will raise a barrier to stop his further advance if he reaches the half-mile point, a second if he reaches the quarter-mile point, a third if he goes one-eighth of a mile, and so on ad infinitum. The paradox involves the fact that (i) the man cannot begin walking, because a barrier will stop him even at the shortest distance, but (ii) if he does not begin walking, no barrier will rise.