ZENO OF ELEA

(Greek philosopher, bom about 480 ВС in Elea, died in 430 ВС)

Before reading the text answer the following questions:

1. What is a paradox?

2. Do you know the origin of this word?

Zeno belonged to the philosophical school which arose in Elea (hence the name Eleatic school) in the 6,h”5lh centuries ВС. The Eleatic school denied the usefulness of the senses as a means of attaining truth. In fact Eleat-ics attempted to demonstrate that by reasoning they could show that the message of the senses must be ignored. Zeno did precisely that to illustrate the unreality of motion. He showed mathematicians, once and for all, that the Pythagorean program of building continuous quantities out of finite series of discrete units ran into impossible inconsistencies.

Zeno is most famous for his paradoxes, all of which seemed to disprove the possibility of motion as it was sensed. The best known is that of Achilles and the tortoise. Suppose Achilles

can run ten times as fast as a tortoise. And the tortoise has a ten-yard head start. It follows then that Achilles can never overtake the tortoise because while he covers the ten yards difference, the tortoise will have moved ahead one yard. When Achilles covers that one yard, the tortoise will have moved on a tenth of a yard and so on.

Another paradox, that of the arrow, is the simplest of the four, but historically it has proven to be the most provocative. It asks, very simply, “If the flying arrow is at every instant of its flight at rest, in a space equal to its length, when does it move?” These paradoxes (the other two being those of the bisection and the three moving chariots), although all based on fallacies, were of utmost importance to science, for they stimulated thought and gave a headway to the development of mathematics and logic, as they discovered contradictions in the main concepts of space, time, multitude and motion.

Since all Zeno’s paradoxes were based on the number of assumptions, derived by him from the Pythagorean mathematics, about the divisibility of space and time and the likeness or difference in their parts, this encouraged philosophers like Democritus to avoid paradoxes. Democritus searched for indivisibility and found it in the atoms which are, as he claimed, the basic components of matter.