Bill Vallicella (Maverick Philosopher) asserts that
No one has successfully answered Zeno's Paradoxes of Motion. (No, kiddies, Wesley Salmon did not successfully rebut them; the 'calculus solution' is not a definitive (philosophically dispositive) solution.)
The link in the quoted passage leads to a post from 2009 in which BV addresses Zeno's Regressive Dichotomy:
The Regressive Dichotomy is one of Zeno's paradoxes of motion. How can I get from point A, where I am, to point B, where I want to be? It seems I can't get started.
A_______1/8_______1/4_______________1/2_________________________________ B
To get from A to B, I must go halfway. But to travel halfway, I must first traverse half of the halfway distance, and thus 1/4 of the total distance. But to do this I must move 1/8 of the total distance. And so on. The sequence of runs I must complete in order to reach my goal has the form of an infinite regress with no first term:
. . . 1/16, 1/8, 1/4, 1/2, 1.
Since there is no first term, I can't get started.
Zeno's paradox rests on the assumption that a first step is an infinitesimal fraction of the distance to be traversed, a fraction that can never be resolved mathematically. But that is an obviously false and arbitrary assumption.
Zeno, had he been less provocative (though mundane), would have observed that first step in going from A to B is a random distance that depends on the stride of the traveler; it has nothing to do with the distance to be traversed.
Thus, the distance from point A to point B can be traversed in x strides, where
x = d/l
and
d = distance from A to B
l = average length of stride.
That's all f-f-folks.
See also "Achilles and the Tortoise Revisited".