paradoxical adj : seemingly contradictory but nonetheless possibly true; "it is paradoxical that standing is more tiring than walking" [syn: self-contradictory]

English

Pronunciation

• italbrac RP /ˌpærəˈdɒksɪkəl/
• italbrac US /ˌpɛrəˈdɑːksɪkəl/

Adjective

1. Having self-contradictory properties.

Quotations

• 17?? — Edmund Burke, On Taste

  And my point in this inquiry is, to find whether there are any principles, on which the imagination is affected, so common to all, so grounded and certain, as to supply the means of reasoning satisfactorily about them. And such principles of taste I fancy there are; however paradoxical it may seem to those, who on a superficial view imagine, that there is so great a diversity of tastes, both in kind and degree, that nothing can be more indeterminate.

• 1776 — Adam Smith, An Inquiry into the Nature and Causes of the Wealth of Nations, book II, ch 2

  It is the ambiguity of language only which can make this proposition appear either doubtful or paradoxical. When properly explained and understood, it is almost self-evident.

• 1787 — Alexander Hamilton or James Madison, Federalist Papers No. 63

  I add, as a SIXTH defect the want, in some important cases, of a due responsibility in the government to the people, arising from that frequency of elections which in other cases produces this responsibility. This remark will, perhaps, appear not only new, but paradoxical. It must nevertheless be acknowledged, when explained, to be as undeniable as it is important.

• 1839 — Edgar Allan Poe, The Fall of the House of Usher

  There can be no doubt that the consciousness of the rapid increase of my superstition—for why should I not so term it?—served mainly to accelerate the increase itself. Such, I have long known, is the paradoxical law of all sentiments having terror as a basis.

• 1861 — John Stuart Mill, Utilitarianism

  I will add, that in this condition the world, paradoxical as the assertion may be, the conscious ability to do without happiness gives the best prospect of realising, such happiness as is attainable.

• 1898 — H. G. Wells, The War of the Worlds, Book 2, ch 4

  It sounds paradoxical, but I am inclined to think that the weakness and insanity of the curate warned me, braced me, and kept me a sane man.

• 1914 — Edgar Rice Burroughs, At the Earth's Core, ch XV

  The Mahars had offered fabulous rewards for the capture of any one of us alive, and at the same time had threatened to inflict the direst punishment upon whomever should harm us. The Sagoths could not understand these seemingly paradoxical instructions, though their purpose was quite evident to me.

• 1933 — H. P. Lovecraft & Hazel Heald, Out of the Aeons

  It was tightly fitted with a cap of the same substance, and bore engraved figurings of an evidently decorative and possibly symbolic nature - conventional designs which seemed to follow a peculiarly alien, paradoxical, and doubtfully describable system of geometry.

Synonyms

• oxymoronic, self-contradictory

Antonyms

• self-consistent, self-evident

Translations

• Spanish: paradójico

Related terms

• paradox
• paradoxically

A paradox can be an apparently true statement or group of statements that leads to a contradiction or a situation which defies intuition; or it can be, seemingly opposite, an apparent contradiction that actually expresses a non-dual truth (cf. Koan). 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 with contradiction. Often, mistakenly, it is used to describe situations that are ironic.

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.

Sometimes the term paradox is used for situations that are merely surprising. The birthday paradox, for instance, is unexpected but perfectly logical. The logician Willard V. O. Quine distinguishes falsidical paradoxes, which are seemingly valid, logical demonstrations of absurdities, from veridical paradoxes, such as the birthday paradox, which are seeming absurdities that are nevertheless true. Paradoxes in economics tend to be the veridical type, typically counterintuitive outcomes of economic theory. In literature a paradox can be any contradictory or obviously untrue statement, which resolves itself upon later inspection.

Logical paradox

seealso List of paradoxes Common themes in paradoxes include self-reference, the infinite, circular definitions, and confusion of levels of reasoning. Other paradoxes involve false statements or half-truths and the resulting biased assumptions.

''For example, consider a situation in which a father and son are driving down the road. The car collides with a tree and the father is killed. The boy is rushed to the nearest hospital where he is prepared for emergency surgery. On entering the surgery suite, the surgeon says, "I can't operate on this boy. He's my son."''

The apparent paradox is caused by a hasty generalization. The reader, upon seeing the word surgeon, applies a poll of their knowledge of surgeons (regardless of its depth) and reasons that since the majority of surgeons are male, the surgeon is a man, hence the contradiction: the father of the child, a man, was killed in the crash. The paradox is resolved if it is revealed that the surgeon is a woman, the boy's mother. Other assumptions whose resolution would also resolve the paradox are based on cognitive bias; the reader, reading terms like "father" and "son" and thinking of a familial relationship, may assume a traditional family (biological father, biological mother, and son) because other combinations are unknown or disregarded out of prejudicial views. The paradox would resolve itself if it were revealed that the child was adopted and therefore had a biological and adopted father, or if a divorce resulted in the boy having a father and stepfather, or if a homosexual male couple had adopted a son or entered a committed relationship after one had already fathered a son. Another solution is that the father and son in the car are indeed not related at all - the father being parent to another individual distinct to the one in the car with him. This is because most people read the words "father and son" and immediately conclude that they are referring to two people in the same family, which is not necessarily true.

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. 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.

Thought experiments can also yield interesting paradoxes. The grandfather paradox, for example, would arise if a time traveler were to kill his own grandfather before his father was conceived, thereby preventing his own birth. Under the 'traditional' definition of a paradox, the Grandfather Paradox (and other similar situations) are typically thought to cause spacetime to rip itself apart under the strain of attempting to resolve an 'unresolvable' conclusion (ie, the time traveller killed his grandfather, therefore the time traveller wouldn't be born, therefore his grandfather could not have been killed, therefore he (and the time traveller) are still alive - and so on). However, if the many worlds theory is correct, the death of the man does not cause the father of the time traveller and the time traveller to never be born because he is an alternate version of the grandfather.

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 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.

• 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. An example might be to affirm or deny the statement "John is in the room" when John is standing precisely halfway through the doorway. It is reasonable (by human thinking) to both affirm and deny it ("well, he is, but he isn't"), and it is also reasonable to say that he is neither ("he's halfway in the room, which is neither in nor out"), despite the fact that the statement is to be exclusively proven or disproven.

Paradox in literature

The paradox as a literary device has been defined as an anomalous juxtaposition of incongruous ideas for the sake of striking exposition or unexpected insight. It functions as a method of literary analysis which involves examining apparently contradictory statements and drawing conclusions either to reconcile them or to explain their presence.

Literary or rhetorical paradoxes abound in the works of Oscar Wilde and G. K. Chesterton; other literature deals with paradox of situation. Rabelais, Cervantes, Sterne, Borges, and Chesterton are all concerned with episodes and narratives designed around paradoxes. Statements such as Wilde’s “I can resist anything except temptation” and Chesterton’s “spies do not look like spies” are examples of rhetorical paradox. Further back, Polonius’ observation in Hamlet that “though this be madness, yet there is method in’t” is a memorable third.

Moral paradox

In moral philosophy, paradox in a loose sense plays a 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 armed neighbours actively trying to kill you: if they succeed, you will not be able to love them. But to preemptively attack them or restrain them is not usually understood as loving. This might be better termed an ethical dilemma rather than a paradox in the strict sense. 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 (like the character of Robin Hood). Such a conflict between two maxims is normally resolved through weakening one or the other of them, e.g. the need for survival is greater than the need to avoid harm to your neighbor). However, as maxims are added for consideration, the questions of which to weaken in the general case and by how much pose issues related to Arrow's theorem (see above); it may be impossible to formulate a single system of ethics rules with a definite order of preference in the general case, a so-called "ethical calculus". Paradoxes in a more strict sense have been relatively neglected in philosophical discussion within ethics, as compared to their role in other philosophical fields such as logic, epistemology, metaphysics or even the philosophy of science. Important book-length discussions appear in Derek Parfit's Reasons and Persons and in Saul Smilansky's 10 Moral Paradoxes.

Genetic Paradox

In zoology, a paradox albino is an animal that exhibits trait of an albino, with little melanin and albino eyes, but may have black or pigmented blotches or half albino, half normal eyes. This trait is most commonly seen with reptiles, though it is still a rare occurrence. It has been seen with boa constrictors, leopard geckos, iguanas and corn snakes as a few examples. These specimens are prized pets for collectors and prices are much higher than the average albino.

See also

• List of paradoxes
• Temporal paradox
• Anachronism
• 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.
• Derek Parfit (1984). Reasons and Persons. Oxford: Oxford University Press.
• Saul Smilansky (2007). 10 Moral Paradoxes. Malden, MA: Blackwell Publishing.

Footnotes

External links

portalpar Logic

• Some paradoxes - an anthology
• Stanford Encyclopedia of Philosophy:
  • "Paradoxes and Contemporary Logic" -- by Andrea Cantini.
  • "Insolubles" -- by Paul Vincent Spade.
• "MathPages - Zeno and the Paradox of Motion"

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