Zeno's paradoxes

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Zeno's paradoxes are a set of problems generally thought to have been devised by Zeno of Elea to support Parmenides's doctrine that "all is one" and that, contrary to the evidence of our senses, the belief in plurality and change is mistaken, and in particular that motion is nothing but an illusion. It is usually assumed, based on Plato's Parmenides 128c-d, that Zeno took on the project of creating these paradoxes because other philosophers had created paradoxes against Parmenides's view. Thus Zeno can be interpreted as saying that to assume there is plurality is even more absurd than assuming there is only "the One" (Parmenides 128d). Plato makes Socrates claim that Zeno and Parmenides were essentially arguing exactly the same point (Parmenides 128a-b).

Several of Zeno's nine surviving paradoxes (preserved in Aristotle's Physics[1] and Simplicius's commentary thereon) are essentially equivalent to one another; and most of them were regarded, even in ancient times, as very easy to refute.[1] Three of the strongest and most famous—that of Achilles and the tortoise, the Dichotomy argument, and that of an arrow in flight—are presented in detail below.

Zeno's arguments are perhaps the first examples of a method of proof called reductio ad absurdum also known as proof by contradiction. They are also credited as a source of the dialectic method used by Socrates.[2]

While there are those who believe that modern calculus has solved the paradox through mathematics,[3] the fact is that Zeno's paradoxes continue to be a relevant problem for philosophers.[4][5][6] The paradoxes and variations on them (see Thomson's lamp) continue to produce philosophical problems.

The origins of the paradoxes are somewhat unclear. Diogenes Laertius, citing Favorinus, says that Zeno's teacher Parmenides, was the first to introduce the Achilles and the Tortoise Argument. But in a later passage, Laertius attributes the origin of the paradox to Zeno, explaining that Favorinus disagrees.[7]

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