Zeno of Elea

Zeno of Elea was born in Elea, Italy, in 490 B.C. He died there in 430 B.C., in an

attempt to oust the city's tyrant. He was a noted pupil of Parmenides, from whom he

learned most of his doctrines and political ideas. He believed that what exists is one,

permanent, and unchanging. Zeno argued against multiplicity and motion. He did so by

showing the contradictions that result from assuming that they were real. His argument

against multiplicity stated that if the many exists, it must be both infinitely large and

infinitely small, and it must be both limited and unlimited in number. His argument

against motion is characterized by two famous illustrations: the flying arrow, and the

runner in the race. It is the illustration with the runner that is associated the first part of

the assignment. In this illustration, Zeno argued that a runner can never reach the end of a

race course.

Created by Jim Bergquist using Mathcad 11 //German...

English: Zeno of Elea shows Youths the Doors to Tr...

Zeno of Elea

He stated that the runner first completes half of the race course, and then half

of the remaining distance, and will continue to do so for infinity. In this way, the runner

can never reach the end of the course, as it would be infinitely long, much as the semester

would be infinitely long if we completed half, and then half the remainder, ad infinitum.

This interval will shrink infinitely, but never quite disappear. This type of argument may

be called the antinonomy of infinite divisibilty, and was part of the dialectic which Zeno

invented.

These are only a small part of Zeno's arguments, however. He is believed to have

devised at least forty arguments, eight of which have survived until the present. While

these arguments seems simple, they have managed to raise a number of profound

philosophical and scientific questions about space, time, and...