Zeno of Elea [key], c.490–c.430 b.c., Greek philosopher of the Eleatic school. He undertook to support in his only known work, fragments of which are extant, the doctrine of Parmenides 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.
See A. Grunbaum, Modern Science and Zeno's Paradoxes (1967).
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