Greek Philosopher: Zeno of Elea
Zeno of Elea, ancient Greek philosopher. The son of Teleutagoras, born in Elea (now in Italy), about 490 B.C. Died Elea, about 430 B.C.
Zeno was a philosopher of the Eleatic school and a favorite pupil and friend of Parmenides, whose doctrines he defended and whose political schemes he shared.
In about 450 BC Zeno accompanied his mentor to Athens, where he propounded the principles of the Eleatic school, of which he was one of the last important exponents.
He helped develop an early form of dialectical reasoning, which proves a point by showing that the opposite position is self-contradictory. Zeno employed a series of paradoxes to support his teacher Parmenides in opposing the Heraclitean view that change is the basis of all reality. Zeno tried to show that change does not exist and that only permanence is real. In one of his best-known paradoxes he argued that an arrow shot into the air does not move, because at each instant of its progress it occupies a still point in space. In another paradox he argued that the swift Achilles could never catch a tortoise in a race, because every time Achilles reached the point where the tortoise was, the tortoise would have already advanced to a further point. Zeno's paradoxes continue to arouse live philosophical discussion.
Of Zeno's philosophical treatises, only rare fragments remain in ancient authors' works, from which can be constructed something of his system. To support Parmenidean ontology, he proposed certain ideas about time and space. Since Parmenides had taught that the phenomenal world is illusory and false, that its essentials are alteration and multiplicity, and that true being has in it no plurality and is unchangeable, Zeno argued against multiplicity and motion and attempted to prove these to be impossible by showing that contradictory propositions follow from the assumption that they are real.
Zeno's argument against multiplicity may be summarized thus: (1) if the many exists, it must be both infinitely large and infinitely small; and (2) it must be both limited and unlimited in number. Of this fourfold argument against motion two illustrations are famous: (1) Achilles and the tortoise; (2) the flying arrow. The first assumes that Achilles, the swiftest of mortals, and the tortoise, notoriously a slow-moving reptile, run a race, in which the tortoise is given a start. Achilles never can overtake the tortoise because, when he has run to the point from which the tortoise started, he finds that the tortoise has advanced. Achilles then must run to the second point, only to find that the tortoise has reached a third point. This situation continues forever; although the interval continually diminishes, it never is eradicated entirely, and Achilles never will outrun the tortoise. This argument depends on a clear distinction between the measure of an interval and the number of points contained therein, a distinction that has been fully understood only in the 20th century.
The argument illustrated by the flying arrow states that an object cannot occupy two places at the same time. Therefore, at any particular moment during its flight the arrow is in only one place. But to be in one place is to be at rest. Therefore, the arrow is at rest at every moment of its flight. It follows that motion is impossible. This argument was not refuted until the 19th century, by application of the theory of assemblages and the theory of the functions of the real variable, which clarify the nature of space-time continua and of continuous functions.
Zeno's type of argument may be called the antinomy of infinite divisibility and is part of his dialectic, which, according to Aristotle, Zeno invented. Certainly the conception of dialectic was as important in Zeno's system as it proved to be later in the philosophy of Plato, Kant, Hegel, Henri Bergson, and Einstein, who, among others, examined the essential contradictions inherent in our ideas of space and time. Zeno's merit was that by his illustrations he was the first to pose this important problem for later philosophy.
He would return to Elea, where he later died in an attempt to oust the city's tyrant.
According to Strabo, Zeno promoted law and order in Elea. Tradition attaches to his name an heroic effort to avoid giving incriminating evidence against friends. Rather than implicate them, Zeno is said to have bitten off his tongue.