Zeno of Elea

Zeno of Elea (flourished 5th century bc), Greek mathematician and philosopher of the Eleatic school, known for his philosophical paradoxes.

Zeno was born in Elea, in southwestern Italy. He became a favorite disciple of the Greek philosopher Parmenides and accompanied him to Athens at the age of about 40. In Athens, Zeno taught philosophy for some years, concentrating on the Eleatic system of metaphysics. The Athenian statesmen Pericles and Callias (flourished 5th century bc) studied under him. Zeno later returned to Elea and, according to traditional accounts, joined a conspiracy to rid his native town of the tyrant Nearchus; the conspiracy failed and Zeno was severely tortured, but he refused to betray his accomplices. Further circumstances of his life are not known.

Only a few fragments of Zeno's works remain, but the writings of Plato and Aristotle provide textual references to Zeno's writings. Philosophically, Zeno accepted Parmenides' belief that the universe, or being, is a single, undifferentiated substance, a oneness, although it may appear diversified to the senses. Zeno's intention was to discredit the senses, which he sought to do through a brilliant series of arguments, or paradoxes, on time and space that have remained complex intellectual puzzles to this day. A typical paradox asserts that a runner cannot reach a goal because, in order to do so, he must traverse a distance; but he cannot traverse that distance without first traversing half of it, and so on, ad infinitum. Because an infinite number of bisections exist in a spatial distance, one cannot travel any distance in finite time, however short the distance or great the speed. This argument, like several others of Zeno, is intended to demonstrate the logical impossibility of motion. In that the senses lead us to believe in the existence of motion, the senses are illusory and therefore no obstacle to accepting the otherwise implausible theories of Parmenides. Zeno is noted not only for his paradoxes, but for inventing the type of philosophical argument they exemplify. Thus Aristotle named him the inventor of dialectical reasoning.