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Zeno of Elea: Biography & Paradoxes

Chapter 6 /  Lesson 32
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Instructor: Erica Cummings

Erica teaches college Humanities, Literature, and Writing classes and has a Master's degree in Humanities.

In this lesson, we'll be looking at Zeno of Elea, the ancient Greek philosopher who still manages to stump us in modern times. Learn about the man, his paradoxes, and test your knowledge with a quiz!

Biography

Is motion possible? Does a fast runner outrun a slow runner? The answers to these questions may seem obvious, but Zeno of Elea, an ancient Greek philosopher, presents us with a series of paradoxes that makes us question all of this.

Zeno of Elea was a Greek philosopher from the 5th century BCE who posed a series of paradoxes that continue to stump thinkers to this day. We don't know much about Zeno, so we have to rely on the accounts of Plato, Aristotle, and a couple other ancient writers. We do know Zeno visited Athens where he shared his book of paradoxes (which has not survived) with others, including the ancient Greek philosopher Socrates.

Zeno of Elea shows Youths the Doors to Truth and False, 16th century Spanish fresco
Zeno of Elea shows Youths the Doors to Truth and False, 16th century Spanish fresco

Zeno was a member of Paremenides's Eleatic school of Pre-Socratic philosophy. The Eleatics thought motion was impossible, believed that there are not multiple things but only one thing that exists, and doubted sense experience could reveal truth. It's thought that Zeno's paradoxes are meant to defend these Eleatic principles. These paradoxes were perhaps the first examples of the reduction ad absurdum technique, which deconstructed commonly held beliefs until all that was left was an absurd conclusion. The most famous and perplexing of his paradoxes are examined in more detail below.

The Paradox of Place

Zeno's first Paradox of Place makes us question how many things compose the universe. Zeno begins by stating that everything that exists--a dog, a chair, even a grain of sand--takes up space. If it takes up space, it must be in a place. Well that implies that place is also a thing that takes up space, which must also be in its own place that takes up space… and on and on we go. Therefore, according to Zeno, there must be an infinite number of things, spaces, and places. This concept of infinity was difficult for the ancient Greek world to comprehend, so the idea that there are infinite things in the universe was considered an absurd paradox.

The Achilles Paradox

Zeno's Achilles Paradox attempts to show that motion is impossible. Let's say a tortoise and the Greek hero Achilles were racing. Based on our experiences of how a man and a tortoise move, we would naturally assume that Achilles would win. But consider this: the tortoise has a head start and is constantly moving toward the finish line (Time 1, pictured). Before Achilles can pass the tortoise, Achilles has to reach the spot where the tortoise started, right (A2, Time 2, pictured)? But by the time Achilles reaches the tortoise's starting point, the tortoise has moved on to another location further down the track (T2, Time 2, pictured). So now Achilles has to reach the spot where the tortoise currently is. But by the time Achilles does that, the tortoise has yet again moved on (Time 3, pictured). So, the paradox is that Achilles will always be behind the tortoise and will lose the race.

Illustration of Achilles Paradox
Illustration of Achilles Paradox

The Dichotomy Paradox

The Dichotomy Paradox also shows that motion is an illusion. Let's say you were running a race. You see the finish line ahead. In order to get to the finish line, you know you first have to get to the halfway point. But before you can get to the halfway point, you have to get halfway to that halfway point. But before you get there, you have to get halfway to the halfway of the halfway point. And on it goes for eternity. Essentially, Zeno asserts that there are an infinite number of halfway points between any two locations. Before you can ever reach one location, you have to reach the halfway point first. But if there are an infinite number of halfway points, how can we possibly traverse an infinite number of locations?! 'That's absurd!' says Zeno. Therefore, motion is impossible, and you will never reach the finish line.

The Arrow Paradox

The goal of the Arrow Paradox is to show that what we think is motion is actually rest. Let's say you shoot an arrow at a target. The arrow then moves through the air, right? Not really, says Zeno. Zeno posited that time was a series of individual moments. In any given moment, the arrow can only be in one specific spot (because an object cannot be in two spots at once). But if the arrow is in one spot at any particular moment, that means the arrow is at rest at that moment, according to Zeno. So, if the arrow can only be in one spot at one time, how could it ever move? Therefore, the arrow must be at rest the whole time.

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