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Encyclopedia > Paradox
Look up paradox in Wiktionary, the free dictionary.

A paradox is an apparently true statement or group of statements that leads to a contradiction or a situation which defies intuition. Typically, either the statements in question do not really imply the contradiction, the puzzling result is not really a contradiction, or the 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. Wikipedia does not have an article with this exact name. ... Wiktionary (a portmanteau of wiki and dictionary) is a multilingual, Web-based project to create a free content dictionary, available in over 150 languages. ... A common dictionary definition of truth is agreement with fact or reality.[1] There is no single definition of truth about which the majority of philosophers agree. ... This article is about the word proposition as it is used in logic, philosophy, and linguistics. ... Broadly speaking, a contradiction is an incompatibility between two or more statements, ideas, or actions. ... Intuition is an unconscious form of knowledge. ... In discourse, a premise (also premiss in British usage) is a claim which is part of a reason or objection. ... Broadly speaking, a contradiction is an incompatibility between two or more statements, ideas, or actions. ...


The recognition of ambiguities, equivocations, and unstated assumptions 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. Look up ambiguity in Wiktionary, the free dictionary. ... Equivocation is a logical fallacy. ... Look up assumption in Wiktionary, the free dictionary. ... Part of a scientific laboratory at the University of Cologne. ... The philosopher Socrates about to take poison hemlock as ordered by the court. ... Euclid, Greek mathematician, 3rd century BC, as imagined by by Raphael in this detail from The School of Athens. ... Currys paradox is a paradox that occurs in naive set theory or naive logics, and allows the derivation of an arbitrary sentence from a self-referring sentence and some apparently innocuous logical deduction rules. ...


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 contradictory or obviously untrue statement, which resolves itself upon later inspection. In probability theory, the birthday paradox states that in a group of 23 (or more) randomly chosen people, there is more than 50% probability that some pair of them will have the same birthday. ... This article needs additional references or sources for verification. ... Old book bindings at the Merton College library. ... Broadly speaking, a contradiction is an incompatibility between two or more statements, ideas, or actions. ...

Contents

Logical paradox

See also: List of paradoxes

Common themes in paradoxes include direct and indirect self-reference, infinity, circular definitions, and confusion of levels of reasoning. Paradoxes which are not based on a hidden error generally happen at the fringes of context or language, and require extending the context or language to lose their paradoxical quality. This is a list of paradoxes, grouped thematically. ... A self-reference occurs when an object refers to itself. ... The infinity symbol ∞ in several typefaces. ... This article needs additional references or sources for verification. ... For other uses, see Reason (disambiguation). ...


Paradoxes that arise from apparently intelligible uses of language are often of interest to logicians and philosophers. 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. Logic (from Classical Greek λόγος logos; meaning word, thought, idea, argument, account, reason or principle) is the study of the principles and criteria of valid inference and demonstration. ... A philosopher is a person who thinks deeply regarding people, society, the world, and/or the universe. ... In philosophy and logic, the liar paradox encompasses paradoxical statements such as: These statements are paradoxical because there is no way to assign them a consistent truth value. ... Part of the foundation of mathematics, Russells paradox (also known as Russells antinomy), discovered by Bertrand Russell in 1901, showed that the naive set theory of Frege leads to a contradiction. ... In mathematics, a set can be thought of as any collection of distinct objects considered as a whole. ... Set theory is the mathematical theory of sets, which represent collections of abstract objects. ...


Thought experiments can also yield interesting paradoxes. The grandfather paradox, for example, would arise if a time traveler were to kill his own grandfather, thereby preventing his own birth. In philosophy, physics, and other fields, a thought experiment (from the German Gedankenexperiment) is an attempt to solve a problem using the power of human imagination. ... The grandfather paradox is a paradox of time travel, first described by the science fiction writer René Barjavel in his 1943 book Le Voyageur Imprudent (The Imprudent Traveller).[1] The paradox is this: Suppose a man traveled back in time and killed his biological grandfather before the latter met the... Time travel is a concept that has long fascinated humanity—whether it is Merlin experiencing time backwards, or religious traditions like Mohammeds trip to Jerusalem and ascent to heaven, returning before a glass knocked over had spilt its contents. ...


W. V. Quine (1962) distinguished between three classes of paradoxes. W. V. Quine Willard Van Orman Quine (June 25, 1908 - December 25, 2000) was one of the most influential American philosophers and logicians of the 20th century. ...

  • 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 proofs (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. Poster announcing the copyright performance at the Bijou Theatre, Paignton The Pirates of Penzance, or The Slave of Duty, is a comic opera in two acts, with music by Arthur Sullivan and libretto by W. S. Gilbert. ... A leap year (or intercalary year) is a year containing an extra day or month in order to keep the calendar year in sync with an astronomical or seasonal year. ... In voting systems, Arrow’s impossibility theorem, or Arrow’s paradox, demonstrates that no voting system can possibly meet a certain set of reasonable criteria when there are three or more options to choose from. ... In mathematics, there are a variety of spurious proofs of obvious contradictions. ... In mathematics, a division is called a division by zero if the divisor is zero. ... All horses are not necessarily the same colour as Julian The horse paradox is the following (invalid) proof of the statement All horses are the same colour: We use the principle of mathematical induction. ... Antinomy (Greek anti-, against, plus nomos, law) is a term used in logic and epistemology, which, loosely, means a paradox or unresolvable contradiction. ... The Grelling-Nelson paradox is a semantic paradox formulated in 1908 by Kurt Grelling and Leonard Nelson and sometimes mistakenly attributed to German philosopher and mathematician Hermann Weyl. ...

  • A paradox which is both true and false at the same time in the same sense is called a 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 logics.

Dialetheism is a paraconsistent logic typified by its tolerance of at least some contradictions. ... Aristotle (Greek: Aristotélēs) (384 BC – 322 BC) was a Greek philosopher, a student of Plato and teacher of Alexander the Great. ... A paraconsistent logic is a logical system that attempts to deal nontrivially with contradictions. ...

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. Ethics is a general term for what is often described as the science (study) of morality. In philosophy, ethical behavior is that which is good or right. ... Ethics (via Latin from the Ancient Greek moral philosophy, from the adjective of Ä“thos custom, habit), a major branch of philosophy, is the study of values and customs of a person or group. ... An ethical dilemma is a situation that will often involve an apparent conflict between moral imperatives, in which to obey one would result in transgressing another. ... The term steal can mean either: To commit theft In baseball, to gain a stolen base In basketball, stealing the ball from the opponents team This is a disambiguation page — a navigational aid which lists other pages that might otherwise share the same title. ...


In the rocknroll greaser subculture, The Diminishing Marginal Square Pardadox (DMSP) presented by famed rocknroll pulp philospher Prof. Mcgloff pertains to the notion of the inevitable mortality of the world's supply of squares. That is, despite the fact that one of the most well known hobbies of greasers involves savage beatings of those whom they deem to be squares, the overarching fact remains that one day all squares will be dead or otherwise incapicitated. Will the overall enjoyment gained by beating up squares be diminshed over time when the realization that they will one day have no more squares to maim sets in? Further complicating the paradox is the fact that squares are the "eternal enemy" of the greaser, and therefore their misfortune should theoretically be proportionate to the pleasure gained by these cladestine rocknrollers. Wikipedia does not yet have an article with this exact name. ... A Greaser is a type of person that is familiar with the greasyness of of human culture. ... In sociology, anthropology and cultural studies, a subculture is a set of people with a set of behaviors and beliefs, culture, which could be distinct or hidden, that differentiate them from the larger culture to which they belong. ... Pulp can refer to: Soft shapeless substances in general. ... During the swing era, the late 1920s to 1947, jazz musicians and their followers were called hepcats, and hep was used to describe people who were in the know, about music, night life, drugs, sex, etc. ...


See also

This is a list of paradoxes, grouped thematically. ... Paradox is a relational database management system currently published by Corel Corporation. ... Two famous undecidable figures, the Penrose triangle and devils pitchfork. ... In philosophy, the term logical fallacy properly refers to a formal fallacy : a flaw in the structure of a deductive argument which renders the argument invalid. ... Look up Dilemma in Wiktionary, the free dictionary For the Nelly song, see Dilemma (song). ... A puzzle is a problem or enigma that challenges ingenuity. ... “Arrow paradox” redirects here. ... Self-refuting ideas are ideas or statements whose falsehood is a direct logical consequence of holding that they are true. ... This article contains a discussion of paradoxes of set theory. ...

References

R. Mark Sainsbury (born 1943) is a philosopher from the United Kingdom who has worked in the areas of philosophical logic, philosophy of language, reference, and the philosophies of Bertrand Russell and Gottlob Frege. ... W. V. Quine Willard Van Orman Quine (June 25, 1908 - December 25, 2000) was one of the most influential American philosophers and logicians of the 20th century. ... Scientific American is a popular-science magazine, published (first weekly and later monthly) since August 28, 1845, making it the oldest continuously published magazine in the United States. ... Michael Clarke may refer to: Michael Clarke (cricketer) Michael Clarke (musician) Michael Clarke Duncan, U.S. actor This is a disambiguation page — a navigational aid which lists other pages that might otherwise share the same title. ...

External links

Logic Portal

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Paradox Interactive (1023 words)
We are licensing the game for all European territories and release on Gamers Gate in September.
Paradox just signed UFO: Extraterrestrials for European release.
Release is scheduled for the end of June with a sneak release on Gamers Gate May 4.
PlanetMath: paradox (101 words)
Paradoxes typically lead to a reevaluation of the axioms of mathematics.
Cross-references: Zeno's paradox, Simpson's paradox, Russell's paradox, Hausdorff paradox, Cantor's paradox, Burali-Forti paradox, Banach-Tarski paradox, axioms
This is version 6 of paradox, born on 2006-07-30, modified 2006-08-23.
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