The Ancient Greek Philosophers: Zeno’s Paradoxes

Zeno of Elea was a pupil of Parmenides, and undertook his teacher’s belief that change is an illusion by proposing arguments known as paradoxes, his most famous being Achilles and the Tortoise. In this paradox, it is said that Achilles and the tortoise are racing, but the tortoise has a head start of say, 50 metres. Even though Achilles is running much faster than the tortoise, once Achilles reaches the 50 metre mark, the tortoise would have covered another say, 10 metres, and so will be ahead. Once Achilles reaches this point, the tortoise would have covered more ground, ad infinitum, and Zeno argued that this proves that Achilles could never actually overtake the tortoise because Achilles must always reach where the tortoise has already been, at which point the tortoise will have moved ahead. Another paradox is the Dichotomy paradox, a paradox which says that if you want to walk to a certain point, you must first get halfway there, and before this a quarter of the way, and before this an eighth of the way, ad infinitum, and so one cannot actually reach any point whatsoever-change is an illusion. Many philosophers have attempted to solve these paradoxes. Hans Reichenbach argued that the paradox arises from believing time and space to be separate entities. Diogenes the Cynic simply got up and walked to a certain point instead of trying to refute the paradoxes through words. Herman Weyll proposed that there are only a finite number of distances between two points, rather than an infinite number, and so the paradox is resolved.