ZENO OF ELEA, ancient Greek phikrso pher: b. Ele (Vella). Lucania, southern Ita:s. about 488 s.c. He was the favorite disc.:;.e of Parmcndies, whose opinions he defended. and whose ethico-political schemes be shared. He appears to have lived for a considerable time in Athens, where he taught for re munerations, and had distinguished pupas. as Pericles and Callias. He is said. on un satisfactory evidence, to have engaged in an etiterprise on behalf of his native land sepias: the tyrant Nearchus. Whether he perished .a this attempt or survived is not known. Name of his writings are extant, but his opinions are referred to by Aristotle, who attempted to con fute some of them, and who had distin guished him as the inventor of dialectic. As a defender of the Eleatic doctrine of the mazy of the existent, he was the first to lay down the problems of skepticism in regard us else real existence of the phenomenal worid. and has thus exercised an important influence on philosophy. He is said to have directed ions arguments against the reality of motion_ There all are very similar to one another; the run most famous are those of the flying arrow and of Achilles and the tortoise The firs: finds a contradiction in the properties of the arrow, which cannot be where it is not, but is at rest if it remain where it is. That 11, al though a body in motion is in motion through out Its course, if any instant of the existence of the body be considered in itself, there is no distinguishable property of the body which can be called motion. Bergson considers that the paradox, which was stated by Zeno in order to prove the specious character of motion and change, is insoluble on any view which analyzes motion into a series of states. An answer to the paradox which is more in favor among scientists follows outlines that had already been indicated by Aristotle, and depends upon the fact that the velocity or measure of motion of a body is a limit — the limit of the ratio of the distance traversed by a body, divided by the time which it takes the body to traverse the distance, as this time grows smaller and smaller. The distinction between a property
of a body at an instant, and the limit of a property of a body in the neighborhood of that instant, is all-essential for the explanation of the paradox. This distinction was only ren dered clear in the last century by the develop ment of the theories of assemblages and of the functions of a real variable, which made clear the nature of continua and of continuous functions. It will he seen, then, bow incorrect is the often-repeated statement that the para doxes of Zeno were dialectical puerilities which were completely refuted by Aristotle.
The other famous paradox of Zeno is that of Achilles and the tortoise. Achilles, the swiftest of mortals, can never catch up with the tortoise, because when be reaches the tor toise's former position, the animal is no longer there, so that he has to traverse an infinite iiumber of distances to overtake it. This argument is completely dependent on a clear distinction between the measure of an interval and the number of points it contains—a dis tinction whose true import has only been under stood within the past 50 years. Zeno, in his arguments against motion, exhibits a truer ap preciation of the nature of this process than is evinced by many moderns in their support of it.
In another argument, designed to establish the fallacious nature of sense-perception, Zeno shows his knowledge of the existence of sen sory limina (sec WEBER'S Law). He points out the difficulty of unders•anding how, if the fall of one grain of wheat makes no audible noise, the fall of a bushel can be heard. See TI ME ; SPACE; ASSEMBLAGES, GENERAL THEORY or; REAL VARIABLE, TII DAY OF FUNCTIONS OF TUG Bibliography.— Bery son, H., 'Time and Free Will' (tr., London 1910) ; Burnet, J., 'Greek Philosophy (part i, London 1014); Die's, H. 'Die Fragmente der Vorsokratikcr' (Berlin 190(s-07); Russell, B. A. 'Princi ples of Mathematics' (Cambridge 1903).