What is a Paradox?
A paradox is a sophisticated kind of riddle that intrigues philosophers, logicians, mathematicians and writers. Every paradox describes a seeming impossibility by juxtaposing two ideas that contradict each other even though they are both true. Paradoxes can embody wisdom and they can be powerful tools of communication. They also make great brain teasers.
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Identification
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The word paradox comes from two Greek words, para and doxon. Para means beyond and doxon means opinion. This clarifies the meaning of paradox as something that is beyond belief, incredible or even impossible. Famous paradoxes have endured since ancient times that continue to delight puzzlers, philosophers, mathematicians and logicians who often revise their contexts to be relevant in new times and cultures.
History
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The Paradox of Zeno, first described by Zeno of Elea in the fifth century B.C., is one of the most famous. It is a mathematical riddle expressed in a story about a race between Achilles and a tortoise. Since there are an infinite number of half-way points between two other points, mathematically, the paradox demonstrates that a slower runner can never be overtaken by a faster one. Obviously, this does not hold true in actual fact on a racetrack, but in its abstract mathematical form, it can be proved. There are many riddles based on derivations of this paradox.
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Features
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Another famous paradox was described by Nicolas of Cusa, who lived during the fifteenth century. His paradox, the Infinite Circle, is based on the relationship between the size of a circle and its curvature. The larger the circle, the straighter its circumference seems to be. Like looking at the horizon--a straight-seeming line--the circumference of an infinitely large circle will be a straight line.
Considerations
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A third famous paradox is called the Arrow in Flight. Again, this paradox juxtaposes what we know to be true about how things operate in space with how it seems from an abstract logical point of view. When an arrow is traveling, it fully occupies as much space as its length. There is no more space available for it to take up at any one very miniscule point in time. So, the paradox concludes, an arrow in flight is always "at rest."
Function
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Paradoxes appear in poetry and literature also. When a paradox is expressed as a two-word phrase like "living death," it is an oxymoron. The two words have meanings that conflict. Combining them in one phrase like this produces a rich intuitive understanding that is full of tension. Paradoxes always express the seeming contradiction between two facts.
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