You reconcile it by refuting Zeno's presumption that nature is infinitely divisible. We know that at the atomic domain, particles are defined in terms of wave functions which connect all points in spacetime by a 'probability' that a particle will be found there. We also suspect that space-time itself cannot be subdivided below a scale of 10**-33 centimeters at which point space-time becomes a quantum mechanical 'thing' lacking a definite shape. Both of these things differ from Zeno's assumption that space and motion were subdividable infinitely, and it is in the TRUE character of space, time, and motion that the mathematical paradox is resolved once and for all. We do not live in an abstract mathematical universe, but one with lots of 'dirt' and things that go bump in the night!!!