Paradox of Zeno

The Paradox of Zeno is a famous philosophical riddle by the Greek philosopher Zeno.

It is an example of how strict logical thinking can completely fail to do justice to a trivial truth of reality.

The paradox

Picture this scene:

• Imagine a running contest between Achilles (the Greek hero) and a Tortoise;
• Now, since Achilles is the hero, the Tortoise gets a lead at the start.

The race starts! According to Zeno, strict logical thinking now may reason as follows:

• In order for Achilles to win, he needs to overtake the Tortoise;
• In order to overtake the Tortoise, Achilles will need to first level with the Tortoise;
• In order to level with the Tortoise, Achilles will need to reach the spot where the Tortoise is at the very moment Achilles starts running towards it;
• When Achilles reaches the spot where the Tortoise was when Achilles started running towards this spot, the Tortoise will have advanced;
• Always when Achilles reaches the spot where the Tortoise was when Achilles started running towards this spot, the Tortoise will have advanced;
• Achilles will need to reach this spot in order to level with the Tortoise;
• Achilles will need to level first before being able to overtake the Tortoise;
• However, always the Tortoise will have advanced once Achilles reaches the spot where the Tortoise was when Achilles started running towards the spot where the Tortoise was when Achilles started running.

Hence by strict logical law, not matter how fast he runs, Achilles can never overtake the Tortoise.

Time

Problems with logical thinking occur when an essential part of the reality analyzed is ignored, which is in this case: time. When reasoning about movement, time simply cannot be ignored by talking only about the geometry of the situation. Hence the paradox, which has both baffled and entertained many people for centuries.

See also

See also dot for an explanation about the presence of this paragraph in the context of this website.