Zeno's paradoxes  

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"According to Simplicius, Diogenes the Cynic said nothing upon hearing Zeno's arguments, but stood up and walked to and fro, in order to demonstrate the falsity of Zeno's conclusions."

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Kunstformen der Natur (1904) by Ernst Haeckel
Kunstformen der Natur (1904) by Ernst Haeckel

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 eight surviving paradoxes (preserved in Aristotle's Physics 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. 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.

Zeno's paradoxes were a major problem for ancient and medieval philosophers, who found most proposed solutions somewhat unsatisfactory. More modern methods using calculus have generally satisfied mathematicians and engineers, while developments in physics have called into question the idea that position, time, and speed can ever be exactly determined. Many philosophers still hesitate to say that all paradoxes are completely solved, while pointing out also that attempts to deal with the paradoxes have resulted in many intellectual discoveries. Variations on the paradoxes (see Thomson's lamp) continue to produce at least temporary puzzlement in elucidating what, if anything, is wrong with the argument.

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.

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