Zeno of Elea
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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
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ever exists as an actual infinite, for it is a successive continuum and its parts never coexist (Copleston 324).
Aristotle states that magnitude and time are both continuous, and that anything continuous is divisible into smaller parts. Looking directly to Zeno's first paradox, Aristotle states:
Hence Zeno's argument makes a false assumption in asserting that it is impossible for a thing to pass over or severally to come in contact with infinite things in a finite time. For there are two senses in which length and time and generally anything continuous are called "infinite": they are called so either in respect of divisibility or in respect of their extremities. So while a thing in a finite time cannot come in contact with things quantitatively infinite, it can come in contact with things infinite in respect of divisibility: for in this sense the time itself is also infinite: and so we find that the time occupied by the passage over the infinite is not a finite but an infinite time, and the contact with the infinite is made by means of moments not finite but infinite in number (Aristotle 320).
Passage over the infinite cannot thus occupy a finite time, and the passage over the finite cannot occupy an infinite time. This show
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Approximate Word count = 2567
Approximate Pages = 10 (250 words per page)
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