The Strange Paradoxes and Puzzles of Zeno of Elea

Many ancient Greek philosophers dreamed up paradoxes and puzzles to prove their worldviews and theories, but one ancient thinker stands out above the rest. That would be Zeno.

Zeno of Elea, a pre-Socratic Greek philosopher and student of Parmenides, was known for his rejection of the existence of time, space, and motion. He developed a series of paradoxes in an attempt to disprove these concepts.

Zeno’s efforts can be split into two parts. These included his arguments against plurality, or the existence of multiple objects, and those against motion.

The Paradoxes of Zeno of Elea

Perhaps his most famous paradox, the dichotomy paradox, argues that to go from any one place to another, a person must first go halfway and continue doing so into infinity. Thus, Zeno argued, motion is impossible, as reported by Constantine Vamvacas in a Springer article titled “The Founders of Western Thought.”

The paradox is supposed to show that the universe is singular, and that change, including motion, is impossible.

Another of Zeno’s motion conundrums, according to Niko Strobach’s Zeno’s Paradoxes, is known as Achilles and the tortoise. The philosopher argues that a fast runner like Achilles could never really catch up to a slow mover like a tortoise. Each time Achilles catches up to the tortoise, the tortoise will have moved ahead. When Achilles reaches the next point, the tortoise will have again moved ahead. This makes it seem as though the famous warrior could never surpass the tortoise.

Strobach also writes about another of Zeno’s paradoxes. It is called the flying arrow. This argues that all objects are motionless in space, because, if an arrow is in the air, it is stationary at any chosen instant by occupying a specific area in space.

In other words, no time passes in a single instant of time (a freeze frame), and so zero motion happens. Zeno argued that if time were made up of instances, the fact that movement doesn’t take place in any particular moment would prove that motion doesn’t happen.

Based on the article “15 Paradoxes That Will Make Your Head Explode,” published in The Independent, “The arrow paradox actually hints at modern understandings of quantum mechanics. In his book Reflections on Relativity, Kevin Brown notes that, in the context of special relativity, an object in motion is different from an object at rest. Relativity requires that objects moving at different speeds will appear different to outside observers and will themselves have different perceptions of the world around them.”

Another conundrum of Zeno’s was known as the moving rows. It is also sometimes referred to as the stadium. Strobach tell us that this paradox argues that periods of time can be simultaneously both halved and doubled. It describes a row of objects passing beside other rows of objects in a stadium.

Zeno argued that if one of the opposing rows is not moving while the other is, it will take a different amount of time for them to pass each other.