Paradox

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A paradox is a true statement or group of statements that leads to a contradiction or a situation which defies logic and or intuition. The term is also used for an apparent contradiction that actually expresses a non-dual truth such as two true sentences which put together seem incompatible as both being true (cf. kōan, Catuskoti). Typically however, quoted paradoxical statements do not imply a real contradiction and the puzzling results can be rectified by demonstrating that one or more of the premises themselves are not really true, a play on words, faulty and/or cannot all be true together. But many paradoxes, such as Curry's paradox, do not yet have universally accepted resolutions. The word paradox is often used interchangeably with contradiction. Literary and other artistic uses of paradoxes imply no contradiction and may be used to describe situations that are ironic.[1] Sometimes the term paradox is used for situations that are merely surprising.

The logician Willard V. O. Quine distinguishes:

Paradoxes in economics tend to be the veridical type, typically counterintuitive outcomes of economic theory, such as Simpson's paradox. In literature a paradox can be any contradictory or obviously untrue statement, which resolves itself upon later inspection.

Contents

Logical paradox

Common themes in paradoxes include self-reference, the infinite regress, circular definitions, and confusion between different levels of abstraction.

Patrick Hughes outlines three laws of the paradox:[3]

  • Self reference - An example is "This statement is false", a form of the Liar paradox. The statement is referring to itself. Another example of self reference is the question of whether the barber shaves himself in the Barber paradox. One more example would be "Is the answer to this question no?" In this case, if you replied no, you would be stating that the answer is not no. If you reply yes, you are stating that it is no, because you said yes. However you could reply "It isn't." indicating a negative response without saying the word "no".
  • Contradiction - "This statement is false"—the statement cannot be false and true at the same time.
  • Vicious circularity or infinite regress - "This statement is false"—if the statement is true, then the statement is false, thereby making the statement true. Another example of vicious circularity is the following group of statements:

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