Ancient Philosophers: The Eliatic School, Zeno of Elea

Classic Philosophers: The Great Thinkers of Western Philosophy

Ancient Philosophers: The Philosophy of the Early Greek Naturalists, by Jonathan Dolhenty

I. The Eliatic School: Zeno of Elea

 Zeno (picture), chosen disciple of Parmenides, was born in Elea about the year 500 B.C. He is called by Aristotle the first dialectician because he assumed the task of proving with arguments (Sophistic) how much of paradox there was in the doctrine of his master.Parmenides had reduced becoming to non-being and to illusion. Zeno attempted to prove just what exactly is becoming. To understand the arguments of Zeno it is necessary to remember that becoming signifies movement. If the movement were not real but illusory, it would follow that becoming also has no other consistency save that of illusion. This is the task which Zeno assumed.His argument are four, but they follow the same pattern; for they all begin with the supposition that space (the line) is composed of infinite parts, and that it is impossible to cross these infinite parts of which space is composed. As a consequence, all that to us seems to move does not move in reality, for movement is an illusion.

Take, for example, the so-called argument of Achilles. The hero of the winged foot can never overtake the turtle — symbol of slowness — because the hero gives the turtle the handicap of space. Let us supposed that this interval between Achilles and the turtle is twenty feet, and while the hero runs twenty feet, the turtle advances one foot. Achilles cannot reach his running mate, because while he runs twenty feet the animal moves one foot, and while runs a foot, his rival will run one-twentieth of a foot, and successively, while Achilles run one-twentieth of a foot, the animal will have traveled one-twentieth of a twentieth of a foot, and so on, ad infinitum.

The same is to be said of the arrow which will never reach its target. Before striking the target, the arrow must traverse half the distance, and before it reaches half this space it must traverse one-half of this half, ad infinitum. Thus the arrow remains ever at the same place, no matter how much it may seem to be displaced. Such Sophistic arguments, as Aristotle noted well, are based on a false prejudgment that space is made up of an infinite number of parts.

The late Dr. Jonathan Dolhenty was the Founder and President of The Center for Applied Philosophy and the Radical Academy, and is Honorary Philosophy Editor at Self-Educated American. Self-Educated American has adopted these projects beginning with a republishing and preserving of all of Dr. Dolhenty’s work. “Classic Philosophers: The Great Thinkers of the Western World” was designed and organized by Jonathan Dolhenty, Ph.D. Copyright ©1992 -2011 The Radical Academy. Copyright renewed in © 2011 -2013 The Radical Academy (a project of Self-Educated American).

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