Zeno of Elea (c. 490 – 430 B.C.) was an important Pre-Socratic Greek philosopher from the Greek colony of Elea in southern Italy. He was a prominent member of the Eleatic School of ancient Greek philosophy, which had been founded by Parmenides, and he subscribed to and defended the Monist beliefs of Parmenides.
Arguably he did not really attempt to add anything positive to the teachings of his master, Parmenides, and he is best known today for his paradoxes of motion. But Aristotle has called him the inventor of the dialectic, and no less a logician and historian than Bertrand Russell has credited him with having laid the foundations of modern Logic.
Zeno was born around 490 B.C. in the Greek colony of Elea in southern Italy. The date is an estimate based on Plato’s report of a visit to Athens by Zeno and his teacher Parmenides when Socrates was “a very young man”, and Zeno being about 25 years younger than Parmenides.
Little is known for certain about Zeno’s life. The 3rd Century A.D. biographer of the ancient Greek philosophers, Diogenes Laërtius, reported that Zeno was the son of Teleutagoras, but was adopted by Parmenides. Plato tells us that Zeno was “tall and fair to look upon” and was reported to have been “beloved” by Parmenides in his youth, so he may have been Parmenides’ eromenos (or adolescent lover, a common tradition of ancient Greece).
He was around forty years old when he accompanied Parmenides to Athens and met the young Socrates. He appears to have lived for at least some time at Athens, and to have explained his doctrines to prominent Athenian statesmen like Pericles (c. 495 – 429 B.C.) and Callias. He was praised as a “universal critic”, skilled in arguing both sides of any question. He devoted all his energies to explaining and developing Parmenides’ philosophical system.
According to some reports, Zeno was arrested and perhaps killed at the hands of a tyrant of Elea. According to the historian Plutarch (c. A.D. 46 – 120), Zeno attempted to kill the tyrant Demylus, and having failed to do so, he bit off his tongue and spit it in the tyrant’s face. However, these details may well be pure inventions, and we can only assume that he died around 430 B.C., although with little or no evidence.
Although several ancient writers refer to the “writings” of Zeno, none of his them have survive intact, and the few fragments of his philosophy we do have mainly come down to us through Aristotle (who was a major detractor of Zeno’s ideas). He did not really add anything positive to the teachings of Parmenides, but devoted himself to refuting the views of his opponents.
Like Parmenides, he taught that the world of sense, with its apparent motion (or change) and plurality (or multiplicity), is merely an illusion. The “true being” behind the illusion is absolutely one and has no plurality (Monism), and furthermore it is static and unchangeable. However, because common sense tells us that there is both motion and plurality (as in the Pythagorean notion of reality), Zeno developed arguments to show that the common sense notion of reality leads to consequences at least as paradoxical as those of Parmenides.underlying intention was to affirm that everything was One (as Monism asserted), that all belief in plurality and change is mistaken, and in particular that motion is nothing but an illusion. To do this he considered what would happen if something was divided into infinitely small amounts, showing that this inevitably resulted in a situation which made no sense, and so must be wrong.
Zeno’s paradoxes were one of the first examples of a method of proof called reductio ad absurdum (or epicheirema in Greek), a kind of dialectical syllogism or proof by contradiction. Although Parmenides himself may actually have been the first to use this style of argument, Zeno became the most famous. He devised arguments against both multiplicity and against motion, although both are really variations of one argument that applies equally to space or time. Essentially, he argued that any quantity of space (or time) must either be composed of ultimate indivisible units or it must be divisible ad infinitum. If it is composed of indivisible units, then these must have magnitude and we are faced with the contradiction of a magnitude which cannot be divided. If, however, it is divisible ad infinitum, then we are faced with the different contradiction of supposing that an infinite number of parts can be added up to make a merely finite sum.
Of Zeno’s original 40 versions of the paradox (of which 8 have come down to us through Aristotle), three in particular have become quite well known:
- The Paradox of Achilles and the Tortoise: If Achilles allows the tortoise a head start in a race, then by the time Achilles has arrived at the tortoise’s starting point, the tortoise has already run on a shorter distance. By the time Achilles reaches that second point, the tortoise has moved on again, etc, etc. So Achilles can never catch the tortoise.
- The Arrow Paradox: If an arrow is fired from a bow, then at any moment in time, the arrow either is where it is, or it is where it is not. If it moves where it is, then it must be standing still, and if it moves where it is not, then it cannot be there. Thus, it cannot move at all.
- The Dichotomy Paradox: Before a moving object can travel a certain distance (e.g. a person crossing a room), it must get halfway there. Before it can get halfway there, it must get a quarter of the way there. Before travelling a quarter, it must travel one-eighth; before an eighth, one-sixteenth; and so on. As this sequence goes on forever, an infinite number of points must be crossed, which is logically impossible in a finite period of time, so the distance will never be covered (the room crossed, etc).
Aristotle vehemently disagreed with Zeno’s ideas, calling them fallacies, and claiming to have disproved them by pointing out that, as the distance decreases, the time needed to cover those distances also decreases, becoming increasingly small. Various other possible solutions have been offered to the paradoxes over the centuries, ranging from Kant, Hume and Hegel, to Newton and Leibniz (who invented mathematical calculus as a method of handling infinite sequences). It is generally held nowadays that the paradox stems from the false assumption that it is impossible to complete an infinite number of discrete tasks in a finite time, but Zeno’s paradoxes have continued to tease and stimulate thinkers, and there is still some debate over whether they have been fully disproved even today.