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:For other meanings of "Paradox", see Paradox (disambiguation).thumb Robert Boyle's self-flowing flask fills itself in this diagram, but perpetual motion machines don't exist.
A paradox is an apparently true statement or group of statements that seems to lead to a contradiction or to a situation that defies intuition. Typically, either the statements in question do not really imply the contradiction; or the puzzling result is not really a contradiction; or the premisses themselves are not all really true (or, cannot all be true together). The recognition of ambiguities, equivocations, and unstated assumptions underlying known paradoxes has often led to significant advances in science, philosophy and mathematics.
The word paradox is often used indifferently with contradiction; but where a contradiction by definition cannot be true, many paradoxes do allow of resolution, though many remain unresolved or only contentiously resolved (such as Curry's paradox).. Still more casually, the term is sometimes used for situations that are merely surprising (albeit in a distinctly "logical" manner) such as the Birthday Paradox.
The etymology of paradox can be traced back to the early Renaissance. Early forms of the word appeared in the late Latin paradoxum and the related GreekThe Greek language ( /Elini'k{/) is an Indo-European language which has existed from around the 14th century BC in the Cretan inscriptions called Linear B. Mycenaean Greek of this period is distinguished from later Classical or Ancient Greek of the 8th ce paradoxon. The word is composed of the preposition para which means "by way of", or "according to" conjoined to the noun stem doxa, meaning "what is received." Compare orthodox (literally, "straight teaching") and heterodox (literally, "different teaching"). The liar paradox and other paradoxes were studied in medieval times under the heading insolubiliaIn the Middle Ages, variations on the liar paradox were studied under the name of insolubilia (insolubles). Although the liar paradox was well known in antiquity, interest seems to have lapsed until the twelfth century, when it appears to have been reinve.
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 contextSee also ConTeXt, a macro package for the TeX typesetting system. Context includes the circumstances and conditions which "surround" an event. Within specific academic disciplines, it has the following meanings: In archaeology, the context (physical locat or languageAs with any complex, emergent concept, language is somewhat resistant to definition; however, most would agree that language is a system of communication or reasoning using representation along with metaphor and some manner of logical grammar. Many langua, and require extending the context (or language) to lose their paradox quality.
In moral philosophy, paradox plays a particularly central role in debates on ethicsEthics is a general term for what is often described as the " science of morality". In philosophy, ethical behavior is that which is " good". The Western tradition of ethics is sometimes called moral philosophy . This is one of the three major branches of. For instance, an ethical admonition to "love thy neighbor" is not just in contrast with, but in contradiction to an armed neighbor actively trying to kill you: if he or she succeeds, then, you will not be able to love them. But to preemptively attack them or restrain them is not usually understood as very 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.
1 Types of paradoxes
W. V. Quine (1962) distinguished three classes of paradox:
- 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 may be more than N years old on his Nth birthday. Likewise, Arrow's impossibility theorem involves behavior of voting systems that is surprising but all too 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 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.
