What Are Zeno Paradoxes?
Merriam-Webster Online defines a paradox as a statement contrary to popular opinion, or an argument that utilizes seemingly acceptable premises and valid deductions to come to a contradictory conclusion.
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Etymology
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"Paradox" is derived from the Greek "paradoxon," meaning "contrary to expectation." It comes from combining the prefix "para-," meaning "contrary to," and the word "doxa," meaning "opinion."
Purpose of Zeno's Paradoxes
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Zeno's Paradoxes are a group of about nine surviving arguments devised by the Greek philosopher Zeno of Elea to support the tenets of his beleaguered teacher, Parmenides. Parmenides denied the prevailing belief in plurality---that reality was made up of many substances---in favor of unity---that reality is permanent and unchanging.
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Execution of the Paradoxes
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The arguments utilized a strategy called "reductio ad absurdum"---proof by contradiction. Zeno sought to disprove the criticisms of Parmenides' opponents. He demonstrated that, if their arguments were indeed true, then they led to even more absurd conclusions than Parmenides' own when thought through logically and completely.
The Arguments: In Brief
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The surviving arguments can be divided so:
A. The Paradoxes of Plurality
1) The Argument from Denseness
2) The Argument from Finite Size
3) The Argument from Complete DivisibilityB. The Paradoxes of Motion
1) The Dichotomy
2) Achilles and the Tortoise
3) The Arrow
4) The StadiumC. The Other Paradoxes
1) The Paradox of Place
2) The Grain of Millet
Curious Fact
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These paradoxes---though refutable even in ancient times and essentially "solved" by 19th century advances in mathematics---still pose intriguing problems to philosophers and quantum physicists today. And they remain excellent fodder for storytellers such as Lewis Carroll, Jorge Luis Borges and Ursula K. Le Guin.
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References
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- Photo Credit Image by Flickr.com, courtesy of Peter Gnas
