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Concept
Zeno's paradoxes
Summary
Zeno's paradoxes are a set of philosophical problems devised by the Eleatic Greek philosopher Zeno of Elea (c. 490–430 BC).
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. Diogenes Laërtius, citing Favorinus, says that Zeno's teacher Parmenides was the first to introduce the paradox of Achilles and the tortoise. But in a later passage, Laërtius attributes the origin of the paradox to Zeno, explaining that Favorinus disagrees.
Many of these paradoxes argue that contrary to the evidence of one's senses, motion is nothing but an illusion. 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. Zeno's arguments may then be early examples of a method of proof called reductio ad absurdum, also known as proof by contradiction. 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. They are also credited as a source of the dialectic method used by Socrates.
Some of Zeno's nine surviving paradoxes (preserved in Aristotle's Physics and Simplicius's commentary thereon) are essentially equivalent to one another. Aristotle offered a response to some of them. Popular literature often misrepresents Zeno's arguments. 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. However, none of the original ancient sources has Zeno discussing the sum of any infinite series. Simplicius has Zeno saying "it is impossible to traverse an infinite number of things in a finite time".
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