Paradoxology

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#A statement that leads to an [[infinite]] and instant [[contradiction]].
 
#A statement that leads to an [[infinite]] and instant [[contradiction]].
 
#:''If a court ruled that common law no longer existed, then the only thing that made that ruling binding was common law, which means that the ruling instantly destroys what lets it exist, which means it no longer exists, which means common law can exist again, which means the ruling can exist again, which means common law doesnt exist anymore because of the ruling, which means the ruling doesnt exist, etc.''
 
#:''If a court ruled that common law no longer existed, then the only thing that made that ruling binding was common law, which means that the ruling instantly destroys what lets it exist, which means it no longer exists, which means common law can exist again, which means the ruling can exist again, which means common law doesnt exist anymore because of the ruling, which means the ruling doesnt exist, etc.''
A '''paradox''' is an apparently [[Truth|true]] [[Proposition|statement]] or group of statements that leads to a [[contradiction]] or a situation which defies [[intuition (knowledge)|intuition]]. Typically, either the statements in question do not really imply the contradiction, the puzzling result is not really a contradiction, or the [[Premise (argument)|premises]] themselves are not all really true or cannot all be true together. The word ''paradox'' is often used interchangeably and wrongly with ''[[contradiction]]''; but whereas a contradiction asserts its own opposite, many paradoxes do allow for resolution of some kind.
 
 
The recognition of [[ambiguity|ambiguities]], [[equivocation]]s, and unstated [[assumption]]s underlying known paradoxes has led to significant advances in [[science]], [[philosophy]] and [[mathematics]]. But many paradoxes, such as [[Curry's paradox]], do not yet have universally accepted resolutions.
 
 
Sometimes the term ''paradox'' is used for situations that are merely surprising. The [[birthday paradox]], for instance, is unexpected but perfectly logical. This is also the usage in [[economics]], where a paradox is a counterintuitive outcome of economic theory. In [[literature]] it can be any [[contradiction|contradictory]] or obviously untrue statement, which resolves itself upon later inspection.
 
 
==Logical paradox==
 
{{seealso|List of paradoxes}}
 
Common themes in paradoxes include direct and indirect [[self-reference]], [[infinity]], [[Begging the question|circular definitions]], and confusion of levels of [[Reason|reasoning]]. Paradoxes which are not based on a hidden error generally happen at the fringes of [[wiktionary:context|context]] or [[language]], and require extending the context or language to lose their paradoxical quality.
 
 
Paradoxes that arise from apparently intelligible uses of language are often of interest to [[logic]]ians and [[philosopher]]s. ''This sentence is false'' is an example of the famous [[liar paradox]]: it is a sentence which cannot be consistently interpreted as true or false, because if it is false it must be true, and if it is true it must be false. Therefore, it can be concluded the sentence is neither true nor false. [[Russell's paradox]], which shows that the notion of ''the [[set]] of all those sets that do not contain themselves'' leads to a contradiction, was instrumental in the development of modern logic and [[set theory]].
 
 
[[Thought experiment]]s can also yield interesting paradoxes. The [[grandfather paradox]], for example, would arise if a [[time travel]]er were to kill his own grandfather, thereby preventing his own birth.
 
 
[[W. V. Quine]] (1962) distinguished between three classes of paradoxes.
 
* A ''veridical paradox'' produces a result that appears absurd but is demonstrated to be true nevertheless. Thus, the paradox of Frederic's birthday in ''[[The Pirates of Penzance]]'' establishes the surprising fact that a person's fifth birthday is the day he turns twenty, if born on a [[leap day]]. Likewise, [[Arrow's impossibility theorem]] involves behaviour of voting systems that is surprising but true.
 
* A ''falsidical paradox'' establishes a result that not only appears false but actually is false; there is a fallacy in the supposed demonstration. The various [[invalid proof]]s (e.g. that 1 = 2) are classic examples, generally relying on a hidden [[division by zero]]. Another example would be the inductive form of the [[Horse paradox]].
 
* A paradox which is in neither class may be an ''[[antinomy]]'', which reaches a self-contradictory result by properly applying accepted ways of reasoning. For example, the [[Grelling-Nelson paradox]] points out genuine problems in our understanding of the ideas of truth and description.
 
 
A fourth kind has sometimes been asserted since Quine's work.
 
* A paradox which is both true and false at the same time in the same sense is called a [[dialetheism|dialetheia]]. In Western logics it is often assumed, following [[Aristotle]] that no dialetheia exist, but they are sometimes accepted in eastern traditions and in [[Paraconsistent logic]]s.
 
 
==Moral paradox==
 
In [[moral philosophy]], paradox plays a central role in [[ethics]] debates. For instance, it may be considered that an ethical admonition to "love thy neighbour" is not just in contrast with, but in contradiction to an armed neighbour actively trying to kill you: if he or she succeeds, you will not be able to love him or her. But to preemptively attack them or restrain them is not usually understood as loving. This might be termed an [[ethical dilemma]]. Another example is the conflict between an injunction not to [[steal]] and one to care for a family that you cannot afford to feed without stolen money.
 
 
==See also==
 
* '''[[List of paradoxes]]'''
 
* [[Paradox (database)]]
 
* [[Impossible object]]
 
* [[Formal fallacy]]
 
* [[Dilemma]]
 
* [[Puzzle]]
 
* [[Zeno's paradoxes]]
 
* [[Self refuting ideas]]
 
* [[Paradoxes of set theory]]
 
 
==References==
 
* [[R. M. Sainsbury]] (1988). ''Paradoxes''. Cambridge.
 
* [[W. V. Quine]] (1962). "Paradox". ''[[Scientific American]]'', April 1962, pp. 84–96.
 
* [[Michael Clarke]] (2002). ''Paradoxes from A to Z''. London: Routledge.
 
 
==External links==
 
{{Spoken Wikipedia|Paradox.ogg|2005-07-07|SubCat=}}
 
*[http://www.paradoxes.co.uk/ Some paradoxes - an anthology]
 
*{{dmoz|Society/Philosophy/Philosophy_of_Logic/Paradoxes/|Paradoxes}}
 
*[http://www.dpmms.cam.ac.uk/~wtg10/richardsparadox.html Definability paradoxes]
 
*[http://plato.stanford.edu/entries/insolubles Insolubles] ''(at the [http://plato.stanford.edu Stanford Encyclopedia of Philosophy])''
 
*[http://www.mathpages.com/rr/s3-07/3-07.htm "Zeno and the Paradox of Motion"]
 
 
 
{{wikipedia}}
 
{{wikipedia}}

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