Zeno of Elea (c. 495 – c. 430 BC) was a pre-Socratic Greek philosopher, notable as a member of the Eleatic School founded by Parmenides. His biographical details are largely sourced from Plato's "Parmenides" and Aristotle's "Physics." Plato suggests Zeno was a contemporary of Socrates, and describes him as tall, handsome, and a former beloved of Parmenides. Additional, potentially less reliable, details from Diogenes Laërtius suggest Zeno was a political activist, who was eventually arrested and killed for his attempts to overthrow tyrannical rule.
Zeno's works do not survive in their original form; what we know about his arguments on motion primarily comes from Aristotle and Simplicius of Cilicia. Plato suggests Zeno's works were designed to support the arguments of Parmenides and mentions a specific work wherein Zeno argues against the idea of being as many. Proclus, in his commentary on Plato's "Parmenides," mentions that Zeno produced over forty arguments showcasing contradictions, but only nine are currently known.
Zeno is recognized for his method of reductio ad absurdum, which can be traced back to Parmenides. This style of argument, designed to reduce an opponent's position to absurdity, became known as the epicheirema. His effective use of this approach had profound impact, to the point where Seneca the Younger commented that Zeno's arguments could deconstruct even the concept of the One.
Furthermore, Zeno is considered a pioneer in dealing with mathematical infinity. Some scholars, like Sir William Smith, link Zeno and Parmenides to the Pythagorean school, attributing them high-mindedness and veneration.
Zeno is perhaps most famous for his paradoxes, which have stirred a wide range of reactions, from puzzlement to amusement, among philosophers, mathematicians, and physicists for over two thousand years. The most well-known of these paradoxes, as described by Aristotle in his "Physics," include "Achilles and the Tortoise," "The Dichotomy," "The Arrow," and "The Moving Rows." These paradoxes interrogate the notions of motion and infinity in profound and challenging ways.