“Motion is not possible.” Explain how Zeno argued to prove his thesis.

Zeno of Elea, an ancient Greek philosopher, proposed several paradoxes to argue against the possibility of motion, one of which is known as the Dichotomy Paradox. Zeno's goal was to challenge the concept of change and motion by highlighting apparent logical contradictions.

The Dichotomy Paradox is presented as follows: In order to reach a destination, one must first cover half the distance, then half the remaining distance, and so on ad infinitum. Since there is an infinite number of steps or distances to cover, Zeno argued that an infinite number of tasks would need to be completed to achieve motion. Consequently, he concluded that motion is impossible.

To illustrate, consider the scenario of walking to a nearby wall. Before reaching the wall, one must first traverse half the distance. Upon reaching the midpoint, another half-distance remains. According to Zeno, this process continues infinitely, with the traveler covering an infinite number of smaller distances. Since completing an infinite number of tasks is deemed impossible, Zeno contended that motion itself must be impossible.

Zeno's argument relies on the paradoxical nature of infinite divisibility. While each individual step in the journey becomes progressively smaller, the infinite sum of these steps raises questions about whether the journey can ever be completed. The Dichotomy Paradox serves as a conceptual challenge to the intuitive understanding of motion and continuity.

It's essential to note that Zeno's paradoxes were later addressed and resolved through advancements in mathematical understanding, particularly with the development of calculus. Mathematicians like Aristotle, Archimedes, and later thinkers provided solutions by introducing the concept of convergent infinite series, demonstrating that an infinite sum of decreasing values can indeed have a finite total. Despite Zeno's paradoxes challenging early philosophical thinking about motion, subsequent mathematical developments clarified the compatibility of motion with logical reasoning.