Text #9164"Zeno of Elea", in .
Zeno of Elea (c. 490 – c. 430 BC) was a pre-Socratic Greek philosopher of Magna Graecia and a member of the Eleatic School founded by Parmenides. Aristotle called him the inventor of the dialectic. He is best known for his paradoxes, which Bertrand Russell has described as “immeasurably subtle and profound”.
Little is known for certain about Zeno’s life. Although written nearly a century after Zeno’s death, the primary source of biographical information about Zeno is Plato’s Parmenides and he is also mentioned in Aristotle’s Physics. In the dialogue of Parmenides, Plato describes a visit to Athens by Zeno and Parmenides, at a time when Parmenides is “about 65,” Zeno is “nearly 40” and Socrates is “a very young man”. Assuming an age for Socrates of around 20, and taking the date of Socrates’ birth as 469 BC gives an approximate date of birth for Zeno of 490 BC. Plato says that Zeno was “tall and fair to look upon” and was “in the days of his youth … reported to have been beloved by Parmenides.”
According to Diogenes Laertius, Zeno conspired to overthrow Nearchus the tyrant. Eventually, Zeno was arrested and tortured. According to Valerius Maximus, when he was tortured to reveal the name of his colleagues in conspiracy Zeno refused to reveal their names, although he said he did have a secret that would be advantageous for Nearchus to hear. When Nearchus leaned in to listen to the secret, Zeno bit his ear. He “did not let go until he lost his life and the tyrant lost that part of his body.” Within Men of the Same Name, Demetrius said it was the nose that was bit off instead.
Although many ancient writers refer to the writings of Zeno, none of his work survive intact. The main sources on the nature of Zeno’s arguments on motion, in fact, come from the writings of Aristotle and Simplicius of Cilicia.
Plato says that Zeno’s writings were “brought to Athens for the first time on the occasion of” the visit of Zeno and Parmenides. Plato also has Zeno say that this work, “meant to protect the arguments of Parmenides”, was written in Zeno’s youth, stolen, and published without his consent. Plato has Socrates paraphrase the “first thesis of the first argument” of Zeno’s work as follows: “if being is many, it must be both like and unlike, and this is impossible, for neither can the like be unlike, nor the unlike like.”
According to Proclus in his Commentary on Plato’s Parmenides, Zeno produced “not less than forty arguments revealing contradictions”, but only nine are now known.
Zeno’s arguments are perhaps the first examples of a method of proof called reductio ad absurdum, literally meaning to reduce to the absurd. Parmenides is said to be the first individual to implement this style of argument. This form of argument soon became known as the epicheirema (ἐπιχείρημα). In Book VII of his Topics, Aristotle says that an epicheirema is “a dialectical syllogism.” It is a connected piece of reasoning which an opponent has put forward as true. The disputant sets out to break down the dialectical syllogism. This destructive method of argument was maintained by him to such a degree that Seneca the Younger commented a few centuries later, “If I accede to Parmenides there is nothing left but the One; if I accede to Zeno, not even the One is left.”
Zeno is also regarded as the first philosopher who dealt with the earliest attestable accounts of mathematical infinity.
Jonathan Barnes The Presocratic Philosophers, 2nd edition, London: Routledge and Kegan Paul, 1982.
G. E. L. Owen. Zeno and the Mathematicians, Proceedings of the Aristotelian Society (1957-8).
Mark Sainsbury, Paradoxes. Cambridge, 1988.
Wesley C. Salmon, ed. Zeno’s Paradoxes Indianapolis, 1970.