Zeno of Elea - Motion Is Impossible

Let me just say before we start that I don't agree with Zeno. Motion is impossible? This is some different definition of motion than the one we use in everyday life, yes? But I also have to say that, although I don't agree with him, Zeno's famous paradoxes have always held an irresistible fascination for me.

Zeno apparently did believe that all motion is impossible, and that therefore it follows that what we see or experience as motion must necessarily be an illusion. I have no idea how Zeno died, but it's just possible he died of starvation. Since motion is impossible, a trip down to the local food store would have been an adventure that was fraught with cosmic impossibility. Therefore it would hardly have been worthwhile to make the attempt. So we can thus imagine Zeno wasting away, while the steak and fries waited a short distance from his doorstep, philosophically unreachable.

Not much is known about Zeno. None of his writings have come down to us, and we only know of his existence from the writings of other philosophers, some of whom may have been opponents. He was said to be a pupil of Parmenides, who was himself a philosopher who believed the world was stuck.

Zeno's most famous paradox concerns Achilles and the Tortoise. The two agree to have a race. Because Achilles is an athlete, he gives the tortoise 100 metres start. Achilles runs 10 times as fast as the tortoise, so you would expect him to easily overtake his opponent.

But not so, says Zeno.

BANG! goes the starting gun and both runners are off. Achilles runs 100 metres, to arrive at the place where the tortoise began. But the tortoise is now 10 metres ahead. So Achilles runs 10 metres, but the tortoise is still 1 metre ahead, so Achilles runs 1 metre, only to find the tortoise is still 0.1 metre ahead.

And so on. You get the picture. This proves the athlete can never overtake the tortoise, and so we have a paradox. Therefore, motion is impossible.

I like this paradox. The great thing about it is that you know it can't be right, but you can't really fault its logic. Many have tried. Most counter-arguments fall into some absurdity or logical trap. Or, even worse, bluster! To refute it is not as easy as you might think it would be. That's one reason why I like it so much.

Once I asked a Math professor to give a refutation of Zeno's Paradox of Achilles and the Tortoise, upon which he started to drone on about infinite seqeunces with a finite limit, and Leibnizian calculus. This may indeed have been very dull, but probably it was about as close as you will ever get to a refutation of Zeno.

Ideas from Ancient Greece

Two philosophers of the past I just read about are Heraclitus and Parmenides. They both lived a long long time ago, and their writings are for the most part lost, so that all we know about them is from what other philosophers wrote about them. They both lived in ancient Greece, not far from each other, but their thinking was about as opposite as could be.

Heraclitus was a recluse because he didn't really like people very much, and he believed society was corrupt. He believed that the universe and everything in it is in a continual state of flux and change. He is believed to be the first person to say that you can never step into the same river twice. He believed that even though we see things around us that might appear to be solid and fixed, in reality this solidity is just an illusion. Everything is in a constant process of becoming something else. His ideas are said to have had a lot of influence on modern science.

Parmenides was a bit more sociable. He ran a philosophy school, called the Eleatic school, because it was in the city of Elea. He believed that the universe and everything in it is fixed and unchanging. Everything is made of the same basic stuff and it never changes. Nothing is capable of changing into anything else, because to do that, it would have to become something that doesn't exist. When we believe that we see change or movement, that is an illusion. His ideas are said to have had a lot of influence on modern science too!

Parmenides had a famous pupil at his school. This pupil was called Zeno of Elea. He wanted to prove that all movement and change were illusions, so he invented over 40 paradoxes for this purpose. One of them "proved" that you can never reach the finishing line in a race, because first you have to reach the halfway point, then the point halfway through the second half of the race, then the point halfway through the final quarter, and so on for ever. He also imagined an athlete called Achilles, racing against a tortoise. He said that Achilles can never overtake the tortoise, as he must first run to where the tortoise is, but in that time the tortoise has moved on. Every time Achilles runs to where the tortoise is, it will have moved on a little bit more, so the tortoise will always be ahead.

Of course we know that you can run a race, and Achilles can overtake the tortoise, but Zeno would say that was just an illusion. He also said that an arrow shot from a bow can never reach the target, because it can never move from where it is to where it is not. Zeno said that if the arrow moved to somewhere where it was not, it would cease to exist.

You may well be thinking that Heraclitus, Parmenides, and Zeno were a bit stupid and cracked-up, and that it would be easy to knock down their ideas and paradoxes. But the argument against them is not as obvious as you might think, and, if you are up against a real philosopher, they will easily defend them against the most obvious objections. Even if a philosopher doesn't agree with them, he or she can do that. The refutation of Zeno's paradoxes uses very technical logic, based on maths - at university entrance level - so I'm not going to try to write about that.

If you were an ancient Greek philosopher, would you be Heraclitus, would you be Parmenides, or would you be Zeno?