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paradox

 
Dictionary: par·a·dox   (păr'ə-dŏks') pronunciation
n.
  1. A seemingly contradictory statement that may nonetheless be true: the paradox that standing is more tiring than walking.
  2. One exhibiting inexplicable or contradictory aspects: "The silence of midnight, to speak truly, though apparently a paradox, rung in my ears" (Mary Shelley).
  3. An assertion that is essentially self-contradictory, though based on a valid deduction from acceptable premises.
  4. A statement contrary to received opinion.

[Latin paradoxum, from Greek paradoxon, from neuter sing. of paradoxos, conflicting with expectation : para-, beyond; see para-1 + doxa, opinion (from dokein, to think).]

paradoxical par'a·dox'i·cal adj.
paradoxically par'a·dox'i·cal·ly adv.
paradoxicalness par'a·dox'i·cal·ness n.

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Wordsmith Words: paradox
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(PAR-uh-doks)
noun

1. A statement that appears contradictory or absurd yet in fact may be true.

2. A self-contradictory statement that appears true or is derived from true statements.

3. A statement that contradicts commonly accepted opinion.

[From Latin paradoxum, from Greek paradoxon, from paradoxos (contrary to opinion), from para- (beyond) + doxa (opinion), from dokein (to think).]

Usage:

"Assuming that the engineering problems could be overcome, the production of a time machine could open up a Pandora's box of causal paradoxes. Consider, for example, the time traveler who visits the past and murders his mother when she was a young girl. How do we make sense of this? If the girl dies, she cannot become the time traveler's mother. But if the time traveler was never born, he could not go back and murder his mother." — Paul Davies, How to Build a Time Machine, Scientific American (New York), Sep 1, 2002.

"Latest figures from the Property Council highlight the paradox faced by commercial property investors, with most sectors offering good returns while suffering declining capital values." — Greg Ninness, Property Investors' Paradox, Sunday Star Times (New Zealand), Jul 28, 2002. Ruth: "A most ingenious paradox! We've quips and quibbles heard in flocks, But none to beat this paradox! A paradox, a paradox, A most ingenious paradox!" — Frederic (who was born on Feb 29): "How quaint the ways of Paradox! At common sense she gaily mocks! Though counting in the usual way, Years twenty-one I've been alive, Yet, reck'ning by my natal day, Yet, reck'ning by my natal day, I am a little boy of five!" — Gilbert and Sullivan, The Pirates of Penzance, 1880.



Literary Dictionary: paradox
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paradox, a statement or expression so surprisingly self‐contradictory as to provoke us into seeking another sense or context in which it would be true (although some paradoxes cannot be resolved into truths, remaining flatly self‐contradictory, e.g. Everything I say is a lie). Wordsworth's line ‘The Child is father of the Man’ and Shakespeare's ‘the truest poetry is the most feigning’ are notable literary examples. Ancient theorists of rhetoric described paradox as a figure of speech, but 20th‐century critics have given it a higher importance as a mode of understanding by which poetry challenges our habits of thought. Paradox was cultivated especially by poets of the 17th century, often in the verbally compressed form of oxymoron. It is also found in the prose epigram; and is pervasive in the literature of Christianity, a notoriously paradoxical religion. In a wider sense, the term may also be applied to a person or situation characterized by striking contradictions. A person who utters paradoxes is a paradoxer.


Apparently self-contradictory statement whose underlying meaning is revealed only by careful scrutiny. Its purpose is to arrest attention and provoke fresh thought, as in the statement "Less is more." In poetry, paradox functions as a device encompassing the tensions of error and truth simultaneously, not necessarily by startling juxtapositions but by subtle and continuous qualifications of the ordinary meanings of words. When a paradox is compressed into two words, as in "living death," it is called an oxymoron.

For more information on paradox, visit Britannica.com.

A paradox arises when a set of apparently incontrovertible premises gives unacceptable or contradictory conclusions. To solve a paradox will involve either showing that there is a hidden flaw in the premises, or that the reasoning is erroneous, or that the apparently unacceptable conclusion can, in fact, be tolerated. Paradoxes are therefore important in philosophy, for until one is solved it shows that there is something about our reasonings and our concepts that we do not understand. Famous families of paradoxes include the semantic paradoxes and Zeno's paradoxes. At the beginning of the 20th century, Russell's paradox and other set-theoretic paradoxes led to the complete overhaul of the foundations of set theory, whilst the Sorites paradox has led to the investigation of the semantics of vagueness, and fuzzy logics. Paradoxes are indexed under their other titles: See analysis, paradox of; lottery paradox; Moore's paradox; omnipotence, paradox of; prediction paradox; St Petersburg paradox, two-envelope paradox.

A person or thing exhibiting apparently contradictory features, as in Lombard's paradox; or a phenomenon, such as a medical symptom, in conflict with what is expected.

 
paradox, statement that appears self-contradictory but actually has a basis in truth, e.g., Oscar Wilde's "Ignorance is like a delicate fruit; touch it and the bloom is gone." Many New Critics maintained that paradox is not just a rhetorical or illustrative device but a basic aspect of all poetic language.


Psychoanalysis: Paradox
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A paradox is defined, according to Paul-Claude Racamier, as a "mental formation that indissolubly binds two propositions or directives that are irreconcilable and yet not contradictory."

This character of non-contradiction is essential. According to transactionalists, it is associated with the fact that irreconcilable prohibitions are not part of the same logical class, or, more simply, are not part of the same class (gesture and verb or affect and speech, for example). However, these irreconcilable directives can sometimes belong to the same class. In all cases the paradox results in infinite oscillations between two utterances of opposite meaning that are not contradictory but antagonistic—which is what accounts for its remarkable indeterminacy. The implicit conclusion of a paradox is that A = not-A. In 1952 Gregory Bateson and his colleagues began investigating the paradoxes of communication in men and animals.

We distinguish two kinds of paradox: logical paradox and pragmatic paradox. The most famous example of logical paradox, first formulated in antiquity by the Greek sophists, is attributed to Epimenides: "Epimenides the Cretan claims that all Cretans are liars. But Epimenides is a Cretan. Therefore he is lying when he says that Cretans are liars. But if Cretans are not liars, Epimenides is telling the truth." Pragmatic paradoxes are practical paradoxes. We distinguish paradoxical forecasts from paradoxical prohibitions. The "double bind" is a sophisticated version of the paradoxical prohibition.

The introduction of the concept of paradox into psychoanalytic theory and clinical practice occurred during the 1970s, from several different sources simultaneously. In France it is largely the result of Didier Anzieu's article "Transfert paradoxal" (Paradoxical transference; 1975) and Paul-Claude Racamier's "Humour et la folie" (Humor and insanity; 1973) and "Paradoxes des schizophrènes" (Paradoxes of schizophrenics); 1976, 1978, 1980). Anzieu insisted on the fact that paradoxical transference assumes, in individual or group psychotherapy, two forms: the paradoxical prohibition and disqualification, both of which are uttered by an individual or group in order to force psychoanalysts to contradict themselves and prevent the work of psychoanalysis from being accomplished. Paradoxical transference is thus one of the manifestations of the work of the negative. Paradoxical transference is accompanied by paradoxical resistance and paradoxical counter-transference.

Racamier extended the class of paradox to a type of mental and rational defensive organization—"paradoxicality"—which is found in schizophrenics, in whom it is both generalized and eroticized in particular ways. René Rousillon has investigated the formal nature of the paradox while contrasting it with the transitional class. Jean-Pierre Caillot used the concept of paradoxicality, applying it to interactive behavior and the psychoanalytic treatment of families engaged in psychotic transactions (1982). He described the paradoxical narcissistic position, where defense, through the oscillation of narcissistic and anti-narcissistic cathexes (Francis Pasche), against catastrophic, claustrophobic, and agoraphobic sensations or anxieties, characterizes the paradoxical narcissistic object relation. This position is comprised by the paranoid-schizoid position elaborated by Melanie Klein, where defense entails splitting and idealization. Caillot has defined paradoxical transference, whether individual, group, or familial, as a transference act or fantasy that indissolubly binds, self-referentially, two aspects of transference with opposite meanings, irreconcilable and yet non-contradictory. For example, Didier Anzieu has described the transference dream of a patient, in which he is simultaneously forced to remain at home and enjoined not to do so. This patient cannot remain in the analyst's office, nor can he leave it. Caillot and Gérard Decherf (1982) have described a paradoxical family transference where "living together kills and living apart is fatal."

According to Racamier, paradoxical behavior is obviously part of the general possibilities of the ego and the avatars of human relations. But its prevalence as a clinically close-knit system is associated with an overwhelming defensive organization designed to fend off intrapsychic and group conflict, the risks of individuation and separation, the internal or collective movements of fantasies of desire and death, as well as dream images and feelings of mourning or disillusionment. It is used to foster feelings of omnipotence and is active in the denial of desire, of mourning, and of the difference between the sexes and generations.

Bibliography

Anzieu, Didier. (1975). Le transfert paradoxal. Nouvelle Revue de Psychanalyse, 12, 49-72.

Caillot, Jean-Pierre, and Decherf, Gérard. (1982). Paradoxalité et thérapie familiale psychanalytique. Paris: Clancier-Guénaud.

Racamier, Paul-Claude. (1980). Les schizophrènes. Paris: Payot.

——. (1998). Paradoxalité et ambiguïté. In S. Decobert, J.-P. Caillot, C. Pigott (Eds.), Vocabulaire de psychanalyse groupale et familiale, v. 1. Paris:Éditions du Collège de Psychanalyse Groupale et Familiale.

Watzlawick, Paul; Beavin, Janet Helmick; and Jackson, Don D. (1967). Pragmatics of human communication. New York: W.W. Norton.

Further Reading

Pizer, Stuart A. (1992). The negotiation of paradox in the analytic process. Psychoanalytic Dialogues, 2, 215-240.

—JEAN-PIERRE CAILLOT

Grammar Dictionary: paradox
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A statement that seems contradictory or absurd but is actually valid or true. According to one proverbial paradox, we must sometimes be cruel in order to be kind. Another form of paradox is a statement that truly is contradictory and yet follows logically from other statements that do not seem open to objection. If someone says, “I am lying,” for example, and we assume that his statement is true, it must be false. The paradox is that the statement “I am lying” is false if it is true.

Veterinary Dictionary: paradoxical
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Different from what is expected; at variance with the established laws.

  • p. motion — see paradoxical respiration (below).
  • p. respiration — a type of breathing in which all or part of a lung inflates during inspiration and balloons out during expiration; the opposite of normal chest motion. Called also paradoxical motion. The condition seriously inhibits the movement of gases during respiration and can produce severe and even fatal cardiovascular disturbances and respiratory insufficiency if not quickly relieved by emergency treatment.
  • — Paradoxical respiration or paradoxical motion of the lung usually results from traumatic injury to the thorax (flail chest) in which several ribs are fractured in two or more places and are no longer attached by bony cartilage to the rest of the rib cage. The condition can also be seen following surgical removal of several ribs and in paralysis of the diaphragm.
  • p. septal motion — in echocardiography, the interventricular septum moves away from the left ventricular free wall during systole. Normally, it would move towards the wall. It is seen in right ventricular hypertrophy.
Poetry Glossary: Paradox
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A statement which contains seemingly contradictory elements or appears contrary to common sense, yet can be seen as perhaps, or indeed, true when viewed from another angle.

Word Tutor: paradox
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pronunciation

IN BRIEF: A statement or doctrine seemingly in contradiction to the received belief. Also: A statement that seems to contradict itself or seems false, but that may be true in fact.

pronunciation It is the paradox of life that the way to miss pleasure is to seek it first. — Hugo LaFayette Black (18741-1971), U.S. Lawyer, senator, associate justice of the U.S. Supreme Court.

Quotes About: Paradox
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Quotes:

"Play not with paradoxes. That caustic which you handle in order to scorch others may happen to sear your own fingers and make them dead to the quality of things." - George Eliot

"The paradox is really the pathos of intellectual life and just as only great souls are exposed to passions it is only the great thinker who is exposed to what I call paradoxes, which are nothing else than grandiose thoughts in embryo." - Soren Kierkegaard

"The paradoxes of today are the prejudices of tomorrow, since the most benighted and the most deplorable prejudices have had their moment of novelty when fashion lent them its fragile grace." - Marcel Proust

"The way of paradoxes is the way of truth. To test Reality we must see it on the tight-rope. When the Verities become acrobats we can judge them." - Oscar Wilde

Wikipedia: Paradox
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A paradox is a statement or group of statements that leads to a contradiction or a situation which defies intuition. The term is also used for an apparent contradiction that actually expresses a non-dual truth (cf. kōan, Catuskoti). 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.[1] 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, circular definitions, and confusion of levels of reasoning.

Patrick Hughes outlines three laws of the paradox:

  • Self reference - all Cretans are liars, said the Cretan, is self referential, because the Cretan describes all Cretans;
  • Contradiction - Cretans are liars, said the Cretan, is contradictory because the Cretan is saying that Cretans are liars;
  • Vicious circularity or infinite regress - so if all Cretans are liars, and the Cretan told us so, then it cannot be true, but if it is not true that ALL Cretans are liars, then SOME Cretan must be a liar, and if there is only one Cretan, the statement stands, but then it is true that all Cretans are liars, so it must be a lie... and so on ad infinitum[2] This is not necessarily a paradox: If there exists a Cretan other than the Cretan making the claim, and this Cretan is not a liar, then the Cretan making the claim is a liar: He is saying that ALL Cretans are liars when there is in fact a Cretan who is not. A better example of vicious circularity is the statement:
          "The statement below is false."
          "The statement above is true."

Other paradoxes involve false statements or half-truths and the resulting biased assumptions.

For example, consider a situation in which a father and his 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; if the surgeon is the boy's father, the statement cannot be true. The paradox is resolved if it is revealed that the surgeon is a woman, the boy's mother.

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 known to be false then it is known that it must be true, and if it is known to be true then it is known that it must be false. Therefore, it can be concluded that it is unknowable. 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. This paradox can be resolved by postulating that time travel leads to parallel or bifurcating universes, or that only contradiction-free timelines are stable.

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 twenty-one-year-old would have had only five birthdays, if he was born on a leap day. Likewise, Arrow's impossibility theorem demonstrates difficulties in mapping voting results to the will of the people.
  • A falsidical paradox establishes a result that not only appears false but actually is false due to a fallacy in the supposed demonstration. The various invalid mathematical proofs (e.g. that 1 = 2) are classic examples, generally relying on a hidden division by zero. Another example is the inductive form of the Horse paradox, falsely generalizes from true specific statements.
  • 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 described 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 unorthodox 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.[3]

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.[3]

A taste for paradox is central to the philosophies of Laozi, Heraclitus, Meister Eckhart, Kierkegaard, Nietzsche, and Tom Robbins, among many others.

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 neighbors actively intending murder. If the hostile neighbors succeed, it is impossible to follow the dictum. On the other hand, to attack, fight back, or restrain them is also not usually considered loving. This might be better termed an ethical dilemma rather than a paradox in the strict sense. However, for this to be a true example of a moral paradox, it must be assumed that "loving" and restraint cannot co-exist. In reality, this situation occurs often, notably when parents punish children out of love.

Another example is the conflict between a moral injunction and a duty that cannot be fulfilled without violating that injunction. For example, take the situation of a parent with children who must be fed (the duty), but cannot afford to do so without stealing, which would be wrong (the injunction). Such a conflict between two maxims is normally resolved through weakening one or the other of them: the need for survival is greater than the need to abide by the law. 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 impossibility theorem; it may not be possible to formulate a consistent 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.

See also

Footnotes

  1. ^ Van Orman Quine, Willard (1966). "The Ways of Paradox". The Ways of Paradox and Other Essays. Random House. p. 5. 
  2. ^ Patrick Hughes and George Brecht, Vicious Circles and Infinity, New York, 1975
  3. ^ a b Rescher, Nicholas (2001). Paradoxes: Their Roots, Range, and Resolution. Chicago: Open Court. ISBN 0812694368. .

External links

Wikisource-logo.svg "Paradox". Encyclopædia Britannica (11th ed.). 1911. 


Translations: Paradox
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Dansk (Danish)
n. - paradoks

Nederlands (Dutch)
paradox

Français (French)
n. - paradoxe

Deutsch (German)
n. - Paradox

Ελληνική (Greek)
n. - παράδοξο, παραδοξολογία

Italiano (Italian)
paradosso

Português (Portuguese)
n. - paradoxo (m)

Русский (Russian)
парадокс

Español (Spanish)
n. - paradoja

Svenska (Swedish)
n. - paradox

中文(简体)(Chinese (Simplified))
似非而是的论点, 自相矛盾的话, 逆说, 悖论

中文(繁體)(Chinese (Traditional))
n. - 似非而是的論點, 自相矛盾的話, 逆說, 悖論

한국어 (Korean)
n. - 역설, 자기 모순된 말, 앞뒤가 맞지 않는 일

日本語 (Japanese)
n. - 逆説, パラドックス, 矛盾したこと

العربيه (Arabic)
‏(الاسم) العبارة الموهمه للتناقض, العبارة الموهمه للصحه, تناقض, مغالطه‏

עברית (Hebrew)
n. - ‮היגד הנראה מופרך או סותר את עצמו, אפילו כאשר יש לו בסיס הגיוני, אדם או דבר המתנגשים עם מושג קודם על מה שהוא הגיוני או אפשרי, תמיהה, חידה, תפריך, פרדוקס‬


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