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
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. 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 call