How did Zeno of Elea use paradoxes to challenge the idea of motion?

Zeno of Elea utilized paradoxes as a rationalist tool to defend the monistic philosophy of his teacher, Parmenides, who argued that reality is a single, motionless, and unchanging entity.123

To challenge the common-sense belief that motion is real, Zeno employed the method of reductio ad absurdum, demonstrating that the assumption of motion leads to logical contradictions. His most famous arguments include:43

• The Achilles Paradox: Zeno argued that a faster runner (Achilles) could never overtake a slower one (a tortoise) given a head start. Because Achilles must first reach the point where the tortoise began, and the tortoise will have moved forward in that interval, Achilles must traverse an infinite series of shrinking distances, rendering the completion of the race impossible.152
• The Dichotomy Paradox: This posits that an object can never reach its destination because it must first cover half the distance, then half of the remaining distance, and so on, requiring an infinite number of steps to be completed in finite time.2
• The Arrow Paradox: This suggests that at any single instant, a flying arrow occupies a space equal to its own length, meaning it is effectively at rest at every moment of its flight.2

By showing that these scenarios lead to absurd conclusions, Zeno aimed to discredit the existence of motion and plurality, reinforcing the Eleatic view of a static, indivisible reality.42