Zeno of Elea (zē`nō, ē`lēə), c.490–c.430 B.C., Greek philosopher of the Eleatic school Eleatic school (ēlēăt`ĭk), Greek pre-Socratic philosophical school at Elea, a Greek colony in Lucania, Italy.
..... Click the link for more information. . He undertook to support in his only known work, fragments of which are extant, the doctrine of Parmenides Parmenides (pärmĕn`ĭdēz), b. c.515 B.C., Greek philosopher of Elea, leading figure of the Eleatic school .
..... Click the link for more information. by demonstrating that motion and multiplicity are logically impossible. The substance of his argument against multiplicity was that a whole must be composed of ultimate indivisible units, or it must be divisible ad infinitum. If the whole is divisible ad infinitum, there is a contradiction involved in the assumption that an infinite number of parts can be added up to a finite total. The essence of his argument against motion was that a moving body can never come to the end of a line, as it must first cover half the line, then half the remainder, and so on ad infinitum. The thrust of these arguments was to demonstrate, through logical reasoning, the error of common-sense notions of time and space. According to Aristotle, Zeno was the first to employ the dialectical method. Contemporary philosophers and mathematicians have taken renewed interest in Zeno's problems.

Bibliography

See A. Grunbaum, Modern Science and Zeno's Paradoxes (1967).

Zeno of Elea

(born c. 495—died c. 430 BC) Greek philosopher and mathematician. He was called by Aristotle the inventor of dialectic. He is best known for his paradoxes (see paradoxes of Zeno). As a pupil and friend of Parmenides, he took it upon himself to reply to those who asserted that his master's doctrine of “the one” (i.e., indivisible reality) was inconsistent (see monism); he tried to show that the assumption of the existence of “the many” (i.e., a plurality of things in time and space) carried with it more serious inconsistencies.