The Paradoxes of Zeno of Elea
Does an arrow really fly?
There are only a small number of ancient philosophers who still manage to occupy and fascinate us today, more than two and a half thousand years later. Zeno of Elea certainly is one of them.
There are actually two famous Zenos: Zeno of Elea (490-430 BC), the one with the paradoxes we will talk about here, and then another man, Zeno of Citium, who was probably the founder of Stoicism.
Both have in common that none of their works survived, except in the tales that others told about them (a fate they share with most so-called “Presocratic” philosophers, like Thales). Sometimes, these others would be their students (as in the case of Plato, who tells us about the philosophy of his teacher, Socrates). But more often, we find the only reference to some philosophers in the works of their enemies who are trying to discredit and to refute them. This is also what happened to Zeno: most of what we know about him comes from Aristotle, who was trying to show how Zeno’s paradoxes don’t actually work and are far less interesting than people thought. Under these circumstances, it’s almost a wonder that we’re still able to reconstruct some of Zeno’s paradoxes.
What Is a Stoic Person?
A Stoic is an adherent of Stoicism, an ancient Greek and Roman philosophy of life. Stoics thought that, in order to be happy, we must learn to distinguish between what we can control and what we cannot.
Zeno’s flying arrow
Perhaps the easiest one to begin with is “the arrow”: imagine an arrow flying horizontally across your field of vision, say, from the left to the right, and out of view. If you were fast enough, you could photograph that arrow at various points along its path, as it crosses in front of you. What would every one of these photographs show? Well, it would show an arrow. But would it show the arrow actually moving? This depends on the shutter speed of your camera. Assuming you really manage to photograph one single moment of the arrow’s flight, then the arrow would always appear to be hanging in the air, unmoving, still.
But then, Zeno says, where does the movement of the arrow come in? I can photograph the arrow at any moment, and at any other moment that is in between two moments, and I can document every single point along its way with a photograph like that, and the arrow will never be seen moving. This proves, says Zeno, that the arrow cannot possibly be moving. In reality, it stands still. Movement is an illusion. Nothing can possibly move, for the same reason.
Even children get it that something must be horribly wrong with this argument, but it’s surprisingly difficult to say precisely what is wrong and why. Zeno seems to be right in saying that there is no point in time at which we would be able to see the arrow moving. At every single moment, the arrow is standing still. So how (and when) does it actually move?
Many philosophers, up to the present, have thought about this problem. One of the more promising approaches is to understand “movement” as something that can happen only over time. “Movement at one point in time” is a notion that does not make any sense, and so Zeno’s paradox is not really a paradox, but just a confirmation of that assumption that movement can only be defined as the difference in location of one thing at two different points in time.
Bertrand Russell (1892-1970)
Bertrand Russell (1872-1970) was a British philosopher and writer, one of the most important analytic philosophers of the 20th century.
The hero and the turtle
Achilles was, for the ancient Greeks, the most well-known example of a hero: a strong, fearless soldier, invincible in battle as much as in any kind of sport. If Achilles decided to run in a race against you, you had no chance. He’d always win.
Zeno could not resist such a target. No, he said. Achilles will never win a single race, not even against a turtle. Of course, he said, the turtle being in a slight disadvantage, we must let it start just a little bit ahead of the great hero. Ten paces will be enough. Now they both start running. A few seconds after the race begins, Achilles will have reached the starting point of the turtle. But by then, the turtle will have moved on from there. Let’s say, it’s now only one pace ahead. Achilles will easily cover that distance, but until he does, the turtle will again have moved a little bit further ahead. In almost no time, Achilles will have covered even this distance, but then the turtle will again be ahead by a tiny bit… and so on. Clearly, Zeno says, Achilles will never be able to reach the turtle, which must always stay ahead of the great hero, even if it is only by the tiniest distance.
Here is a wonderful book by Douglas Hofstadter on paradoxes, logic, computer programming and Bach’s music. Since 1979, when it was written, “Godel, Escher, Bach” has become a classic of nerd culture. A hugely inspiring book!
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Perhaps surprisingly for such a playful logician, Zeno seemed to be a hardcore revolutionary. He was arrested in an uprising against the tyrant (today we’d probably say dictator) of Elea, Zeno’s home town. The dictator Nearchus came to interrogate Zeno and make him reveal the names of his fellow revolutionaries. But Zeno endured the torture and did not give Nearchus any names. But right at the end of the interrogation, he called the dictator to come closer. “I’ll tell you something important,” he whispered. “But I can only whisper. Come closer to hear what I have to say.” The tyrant came so close to Zeno’s face that the philosopher could bite Nearchus' ear. He didn’t let go until, so the ancient source, Zeno had lost his life and Nearchus his ear.
Looking around the world today, we could use some more philosophers like that. Too many ears attached to the wrong heads, for sure.
Thanks for reading! Do you find Zeno’s paradoxes interesting or boring? Tell me in the comments! Image source: Wikipedia.