Zeno of Elea

Greek philosopher

• Born: c. 490 b.c.e.
• Birthplace: Elea (now Velia, Italy)
• Died: c. 440 b.c.e.
• Place of death: Elea (now Velia, Italy)

Although Zeno cannot be said to have succeeded in defending Paramenides’ doctrine of the one, his paradoxes are still remembered, and his method of argument influenced all later philosophy.

Early Life

Little is known of the life of Zeno (ZEE-noh). In the early fifth century, when he was young, Greek philosophy was still in its cruder, experimental form, sometimes mythological, even borrowing from Oriental lore, sometimes resembling primitive science by trying to explain the physical world and basing its conclusions on observation if not on experiment. One tendency was to try to explain all material phenomena as variations on one particular element. Thus, Thales of Miletus taught that all material things were derived from water; Anaximenes of Miletus taught that all things were derived from air; and Heraclitus of Ephesus, though his philosophy was by no means as simple as those of his predecessors, thought that all things were derived from fire. Empedocles, on the other hand, rejected the idea of any single element as the source of all and saw the material world as the result of the mixture and separation of four elements: earth, air, fire, and water.

Zeno’s master, Parmenides, rejected this notion of multiplicity in favor of a fundamental unity. His arguments, which were placed in a mythological setting and expressed in hexameter verse, have survived only in fragments; they are exceedingly involved and hard to follow but perhaps can best be summarized as saying that multiplicity is illogical, self-contradictory, or merely unthinkable. This leaves the one, which is not water or air or fire but simply is “being”—“individual, changeless, featureless, motionless, rock-solid being.” Multiplicity, however, if contrary to logic, is nevertheless a fact of experience, and Parmenides apparently undertook to give a systematic account of it. A modern thinker might say that the world of reason and the world of experience were mutually exclusive and could never be reconciled.

Life’s Work

Despite the paucity of biographical information about Zeno, Plato’s dialogue Parmenides (c. 360 b.c.e.) reports the conversation of Socrates—then a young man—and the visiting Parmenides and Zeno. In that account, Zeno is described as “nearly forty years of age, tall and fair to look upon; in the days of his youth he was reported to have been beloved by Parmenides.” In the dialogue, having finished reading aloud from his works, written in his youth, Zeno frankly explains their origin and his motive:

The truth is, that these writings of mine were meant to protect the arguments of Parmenides against those who make fun of him and seek to show the many ridiculous and contradictory results which they suppose to follow from the affirmation of the one. My answer is addressed to partisans of the many, whose attack I return with interest by retorting on them that their hypothesis of the being of many, if carried out, appears to be still more ridiculous than the hypothesis of the being of one.

After Zeno confesses that his arguments were motivated not by “the ambition of an older man, but the pugnacity of a young one,” Socrates endeavors to summarize Zeno’s arguments:

Do you maintain that if being is many, it must be both like and unlike, and that this is impossible, for neither can the like be unlike, nor the unlike like. . . . And if the unlike cannot be like, or the like unlike, then according to you, being could not be many, for this would involve an impossibility. In all that you say have you any other purpose except to disprove the being of the many? And is not each division of your treatise intended to furnish a separate proof of this, there being as many proofs of the not-being of the many, as you have composed arguments?

In the dialogue, Zeno acknowledges that Socrates has correctly understood him. Zeno’s defense of Parmenides thus consists not of evidence supporting Parmenides’ position nor even of positive arguments; rather, Zeno demonstrates that the opposite position is self-contradictory.

These proofs of the being of the one by proving the not-being of the many might not seem relevant in a scientific age, but some have survived and are known to those who are not otherwise learned in pre-Socratic philosophy. Aristotle summarized the most famous of Zeno’s arguments, called the “Achilles”: “In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point where the pursued started, so that the slower must always hold a lead.” Almost as famous is the paradox of the arrow, which can never reach its target. According to Zeno’s argument, at each point of its flight, the arrow must be at that point and at rest at that point. Thus, all motion, and therefore all change, is illusory.

Zeno’s famed pugnacity was not limited to philosophy. After a plot in which he was involved against the tyrant Nearchus of Elea was discovered, the philosopher died under torture, and his death became the subject of various anecdotes. Some claim that he revealed the names of the tyrant’s own friends as conspirators. Another story states that Zeno bit off his tongue and spit it out at the tyrant; in another, he bit off the tyrant’s ear or nose.

Significance

Plato recognized in Sophistēs (365-361 b.c.e.; Sophist, 1804) that there is something futile about such arguments as those of Zeno and that those who make them may simply be showing off:

Thus we provide a rich feast for tyros, whether young or old; for there is nothing easier than to argue that the one cannot be many, or the many one: and great is their delight in denying that a man is good; for man, they insist, is man and good is good. I dare say that you have met with persons who take an interest in such matters—they are often elderly men, whose meagre sense is thrown into amazement by these discoveries of theirs, which they believe to be the height of wisdom.

Zeno can be defended in a number of ways. One could argue that his motives were good—that he wanted only to defend Parmenides. In doing so, he simply showed that trait of loyalty that brought about his death. More seriously, one could argue that his position in the history of philosophy excuses his failures and could praise him for raising issues and developing methods of argument that Aristotle took seriously. In Zeno’s arguments a recurring theme in philosophy can be seen: the conflict of reason and common sense. Periodically in philosophy, thinkers prove by logic things that ordinary people cannot accept. The British empiricists—John Locke, George Berkeley, and David Hume—did this by stripping away the qualities of objects until the real world had to be defended as an illusion. More recently, the poststructuralists have denounced the logocentric view of the world and have written sous rature—the world may be described rationally, but that analysis must be voided, since any logocentric analysis of the world by definition must be faulty. Periodically, it seems, logic and common sense must be at odds.

Nevertheless, in the twentieth century, Zeno found one eminent and eloquent defender, Bertrand Russell. Zeno, he said, for two thousand years had been pronounced an ingenious juggler, and his arguments had been considered sophisms, when “these sophisms were reinstated, and made the foundations of a mathematical renaissance, by a German professor,” Karl Weierstrass. Russell concludes, “The only point where Zeno probably erred was in inferring (if he did infer) that, because there is no change, therefore the world must be in the same state at one time as at another.” Thus, at the dawn of philosophy, when philosophers sometimes wrote in hexameters and were executed for their politics, Zeno expressed certain philosophical problems in a form that still amuses ordinary people and that still occasions profound debates among professional philosophers.

Bibliography

Aristotle. The Physics. Translated by Robin Waterfield. New York: Oxford University Press, 1999. Contains an analysis of Zeno’s arguments. Important because Zeno’s extant texts are so fragmentary. Introduction and notes by David Bostock. Includes bibliographical references.

Freeman, Kathleen. The Pre-Socratic Philosophers: A Companion to Diels’s “Fragmente der Vorsokratiker.” Cambridge, Mass.: Harvard University Press, 1959. Freeman’s work contains translations of the extant fragments of Zeno’s work, interspersed with analysis and commentary.

Hussey, Edward. The Pre-Socratics. 1972. Reprint. Indianapolis: Hackett, 1995. This volume contains a sympathetic analysis of Parmenides and Zeno. According to Hussey, “What is historically most important here is the logical analysis of such concepts as time, change, diversity, separation, completeness.”

Plato. Parmenides. Translated with introduction and commentary by Samuel Scolnicov. Berkeley: University of California Press, 2003. Plato provides a glimpse of Zeno as a person as well as some idea of the thought of Parmenides. It is not certain that the dialogue form Plato favors was actually employed by Zeno. An “Eleatic stranger,” said to be a disciple of Parmenides and Zeno, takes part in two of the dialogues, but it is not certain whether he expresses their thoughts.

Salmon, Wesley C., ed. Zeno’s Paradoxes. Indianapolis: Bobbs-Merrill, 1970. Twelve essays by noted thinkers that take a modern look and interpretation of Zeno’s puzzling concepts.

West, Martin. “Early Greek Philosophy.” In The Oxford History of the Classical World, edited by John Boardman, Jasper Griffin, and Oswyn Murray. New York: Oxford University Press, 1986. Although this essay does not give much detail on Zeno, it is nevertheless useful in placing him in his historical and cultural context. The volume itself is illustrated and includes an index and bibliographies.