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Why did Zeno argue that a moving object must first reach infinitely many halfway points?

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Infinity — infinity Mathematical symbol representing the concept of infinity.

Zeno of Elea argued that a moving object must first reach infinitely many halfway points to demonstrate that motion is logically impossible, thereby supporting the Parmenidean doctrine that reality is a single, motionless entity.123

His argument, often referred to as the dichotomy paradox, posits that to travel any distance, an object must first reach the midpoint of that distance. However, before reaching that midpoint, it must reach the midpoint of the remaining interval, and so on, ad infinitum. Because this process involves an infinite number of tasks that must be completed in a finite amount of time, Zeno concluded that the goal can never be reached.3

By using this reductio ad absurdum, Zeno aimed to show that the common-sense belief in motion and plurality leads to fundamental contradictions. These paradoxes challenged early theories of space and time, highlighting the complexities of infinity and continuity that were not formally resolved until the development of the mathematical concept of a limit centuries later.1234