First of all, there are two of Zeno's Paradoxes: the Dichotomy and the Achilles, both of which are critiques of continuous motion in infinite space and time. Ultimately, this is seemingly best understood as the paradox of Zeno's Maze.
(Image from MathPages.)
If space, time, and motion (mass and energy) are all infinitely divisible then one can construct an infinite sequence of mirrors, the separation between which decreases geometrically, such that, if the first mirror is 1 unit from the second, the second is 1/2 unit from the third, the third is 1/4 unit from the fourth, etc..Therefore, after a finite amount of time, a point-particle goes a finite distance, and therefore must exit the maze; but the maze is infinite, therefore there is no last mirror, which means that it cannot exit the maze. This is a contradiction; therefore, space, time, and motion (mass and energy) must be only finitely divisible.
Next, there is Hilbert's Paradox of the Grand Hotel. If you have an infinite number of rooms in a hotel, you can always accommodate one more room of guests by moving each room to the next. Or, you can accommodate countably infinitely more guests by moving room one to room two, room two to room four, room three to room six, etc.. There more paradoxes of physical infinitude like this, all of which we owe to Hilbert.
Interestingly, there is an argument against the possibility of finitely-divisible, such that, if within each instant there is no motion, then there can be no motion regardless of how many more you add to it. In order for motion to be possible within an instant, space, time, energy, and mass must interrelate in such a way as to create motion in spacetime. That is, they must be relative to each other.
Zeno's last famous paradox considers the implications of a finite upper limit on velocity and is also ultimately an argument for the relativity of motion in spacetime. Clocks that are in motion relative to each other run slower or faster than clocks which are not in motion relative to each other. Does this require that the past, present, and future are all on the same ontological footing?
I do not believe that they are: the past is fixed, the present fixes, and the future can be fixed. That is, the future is a field of probability, possible futures with various probabilities; the present is the eternally changing Now, the flux of physical actuality (actualization); and the past is the eternally expanding sequence of events that have transpired.
