Zeno of Elea

Biography of Zeno of Elea

Zeno was a pre-Socratic philosopher born in Elia in the late 6th century B.C., around 490-485. He sought to demonstrate, as did Parmenides, the impossibility of motion and multiplicity.

He opposed those who tried to refute Parmenides’ ideas by demonstrating that their refutations were contradictory.

The philosophical thesis that denies motion has traditionally become known as the Eleatic School, or Eleaticism: Parmenides, Zeno, Xenophanes, and Melissus of Samos.

Zeno had a rather eventful political life, and was even imprisoned by a tyrant. He was tortured into handing over his political companions, but he refused and was killed by the tyrant.

Of his work, written in his youth, only a few fragments remain.

Zeno had a peculiar way of arguing, he apparently agreed with the ideas of his opponents and then showed that they led to various contradictions and absurdities, this kind of argument is known as Reductio ad absurdum.

Because of his ability to construct arguments and deductions, Aristotle called Zeno the father of dialectics.

To understand Zeno’s main ideas, we will now look at his famous paradoxes and theses.

SEE ALSO: What is movement according to Aristotle?

The Paradoxes of Zeno of Elea

To prove the impossibility of motion, Zeno elaborated some paradoxes, that is, arguments which are apparently true, but which lead to contradictory and absurd conclusions. Let us now look at Zeno’s main paradoxes.

Dichotomy Paradox

To prove the impossibility of movement, Zeno proposes the following reasoning:

To get from one particular place to another we need to go halfway. But in order to reach the halfway point, we must travel halfway along the halfway point, and so on to infinity. But since it is impossible to go to infinity, Zeno concludes that movement doesn’t exist, and that it is nothing more than an illusion of our senses.

Achilles and the Tortoise

Another famous paradox of Zeno’s is that of Achilles and the tortoise.

In Greek tradition, Achilles is known as “the swift foot,” in contrast to the tortoise, an animal known to be very slow. Zeno argues that no matter how much faster Achilles is, he will never catch up with the tortoise.

Zeno imagines the following situation: Achilles and the tortoise will compete in a race. Because he is faster, Achilles allows the tortoise to get a certain advantage by letting it overtake him by a few meters. Zeno says that Achilles will never overtake the tortoise, because when he has covered a certain distance in a certain time, the tortoise will be covering another distance, and so on indefinitely. The space that separates Achilles and the slow animal is infinite.

However much we may observe with our own eyes that Achilles outran the tortoise, we should not trust our senses, because they make us believe in illusions.

The Arrow Paradox

Zeno, to demonstrate once again the unreality of movement, proposes the paradox of the arrow.

When we see an arrow being shot to hit a certain target, we realize that it is moving. But for Zeno, this is an illusion. In fact, the arrow occupies a certain space in each of the moments it travels. At each of these moments the arrow is at rest.

Zeno against the multiplicity of things

For Zeno, just as there is no movement, there is no multiplicity. If there were multiplicity, we would have to say that there are many units, since multiplicity is precisely the multiplicity of units. But these units are, for Zeno, unthinkable, since they lead to absurd consequences.

If many things exist, we have to affirm that they exist in a limited way in number, that is, in units. But if many things exist, then they are numerically unlimited. Now, this is a contradiction.