Maybe you should take the "paradox" of
Zeno of Elea (490BC) from a different angle.

It describes the impossibility of movement in a world where
you can take any distance and still devide it by 2, thus a world with
infinitively small distances.
Since movement in such a world is impossible, but obviously possible in the real world,
it can be a proove that the real world has distances / lenghts that can not be
devided / or split up in smaller distances.

Zeno would have thus proovesd 490BC the basic laws of quantum mechanics !
Where there are "resolutions" of the world that can not be measured more accuratly.
(Quanten-unschärfe).