Zeno of Elea was a disciple of Parmenides and lived in the fourth century B.C. He set forth a series of paradoxes, logical arguments leading to absurd or impossible conclusions proving that actions taken every day are actually not possible at all. Philosophers who followed had to cope with the logical ramifications of this sort of argument, a form of logic known as reductio ad absurdum. The paradoxes of Zeno differentiate between reason and experience, between what we know to be true through logic and what we know to be true from experience. Aristotle offered solutions to the paradoxes of Zeno in his Physics.
One of Zeno's primary paradoxes can be stated as follows:
Zeno argued that, even granting motion, one could never arrive anywhere, not even to such a simple goal as a door. Before you can get to the door, you must go halfway, but before you can go halfway, you must go halfway to the remaining halfway, but before you can do that, you must go halfway of halfway, but before you can go halfway, you must go halfway. Where does this argument end? Never! It goes on to infinity. Therefore, motion would be impossible even if it were possible (Palmer 27).
One of his more famous paradoxes involves a race between Achilles and a tortoise. If Achilles were to give the tortoise a head start, he could never overtake the tortoise:
This is because, before Achilles can pass the tortoise, he must arrive at the point where the tortoise used to be; but given the hypothesis of motion, the tortoise will never still be there. He will have moved on. This will forever be the case. When Achilles arrives at a point where the tortoise was, the tortoise will have progressed. Achilles can never catch him (Palmer 28).
Zeno was not merely creating clever contradictions or toying with language in these paradoxes. He derived the basis for his philosophy and the rationale for the questions he asked from the work of his mentor, Pa...