On the matter of logic and the world One class of paradoxes is of particular interest to me because it seems to drive a giant wedge between rationalism and empiricism.
Zeno has a couple, one being the a priori impossibility of motion and the a posteriori actuality of motion (the dichotomy paradox).
Up until Zeno, the Parmenidean luminary, discovered these paradoxes, (Greek) thinkers must've been completely convinced of the power of lumen naturale (the light of reason) to make sense of the world - in every case, reason merely served to confirm observation or if ever the two were in conflict, reason would come out on top, an doublechecking empirical data would reveal errors, subtle and egregious.
This, however, wasn't/isn't possible with the dichotomy paradox. Logic clearly demonstrates motion is impossible; observation, to our dismay, shows that motion is not only possible but actual (ambulando solvitur).
As you can see, a pre-Zeno reconciliation of rationalism and empiricism is impossible. We have to make a choice: believe our minds or believe our legs, but not both! We all know Zeno's preference: motion, in the Parmenidean umiverse, is an illusion. I guess this means Zeno, Parmenideans, were true blue rationalists.
That said, Zeno clearly wasn't as mathematically talented as Archimedes who had used the method of exhaustion (limits) to calculate the value of , presaging the advent of calculus by roughly 1.8 k years. Calculus in its full glory took off with Newton and Leibniz and it could be said that calculus (differentiation and integration) could one day bridge the rationalism vs. empiricism gulf.
Aside: Actual may not imply possible.