Simplicius has Zeno saying "it is impossible to traverse an infinite number of things in a finite time". However, none of the original ancient sources has Zeno discussing the sum of any infinite series. For example, Zeno is often said to have argued that the sum of an infinite number of terms must itself be infinite–with the result that not only the time, but also the distance to be travelled, become infinite. Popular literature often misrepresents Zeno's arguments. Aristotle offered a response to some of them. Some of Zeno's nine surviving paradoxes (preserved in Aristotle's Physics and Simplicius's commentary thereon) are essentially equivalent to one another. They are also credited as a source of the dialectic method used by Socrates.
Thus Plato has Zeno say the purpose of the paradoxes "is to show that their hypothesis that existences are many, if properly followed up, leads to still more absurd results than the hypothesis that they are one." Plato has Socrates claim that Zeno and Parmenides were essentially arguing exactly the same point. Zeno's arguments may then be early examples of a method of proof called reductio ad absurdum, also known as proof by contradiction. In Plato's Parmenides (128a–d), Zeno is characterized as taking on the project of creating these paradoxes because other philosophers claimed paradoxes arise when considering Parmenides' view. Many of these paradoxes argue that contrary to the evidence of one's senses, motion is nothing but an illusion.
But in a later passage, Laërtius attributes the origin of the paradox to Zeno, explaining that Favorinus disagrees. Diogenes Laërtius, citing Favorinus, says that Zeno's teacher Parmenides was the first to introduce the paradox of Achilles and the tortoise. The origins of the paradoxes are somewhat unclear, but they are generally thought to have been developed to support Parmenides' doctrine of monism, that all of reality is one, and that all change is impossible. Zeno's paradoxes are a set of philosophical problems devised by the Eleatic Greek philosopher Zeno of Elea (c. ( Learn how and when to remove this template message) Please consider expanding the lead to provide an accessible overview of all important aspects of the article. This article's lead section may be too short to adequately summarize the key points.
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