قائمة المتناقضات

تحتوي هذه المقالة على قائمة متناقضات، مرتبة حسب الموضع. علما بأن هناك العديد من هذه المتناقضات لها حلول واضحة أو تعرف بالخطأ أنها متناقضة لإحتوائها على بعض المفارقات - انظر تصنيف كواين للمتناقضات


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منطقية، غير رياضية

المقالة الرئيسية: منطق


Self-referential

Ashtray with a No Smoking symbol.

These paradoxes have in common a contradiction arising from self-reference.

  • Barber paradox: An adult male barber shaves all men who do not shave themselves, and no one else. Can he shave himself? (Russell's popularisation of his set theoretic paradox.)
  • Berry paradox: The phrase "the first number not nameable in under ten words" appears to name it in nine words.
  • Curry's paradox: "If this sentence is true, the world will end in a week."
  • Epimenides paradox: A Cretan says: "All Cretans are liars".
  • Exception paradox: "If there is an exception to every rule, then every rule must have at least one exception; the exception to this one being that it has no exception." "There's always an exception to the rule, except to the exception of the rule - which is, in of itself, an accepted exception of the rule."
  • Grelling-Nelson paradox: Is the word "heterological", meaning "not applicable to itself," a heterological word? (انظر متناقضة رسل ذات الصلة)
  • Intentionally blank page: Many documents contain pages on which the text "This page is intentionally left blank" is printed, thereby making the page not blank.
  • Liar paradox: "This sentence is false." This is the canonical self-referential paradox. Also "Is the answer to this question no?" And "I'm lying."
  • Yablo's paradox: Similar to the liar paradox, but makes the self-reference less apparent by using an infinite number of sentences.
  • Opposite Day: "It is opposite day today."
  • Paradox of the Court: A law student agrees to pay his teacher after winning his first case. The teacher then sues the student (who has not yet won a case) for payment.
  • Petronius's Paradox: "Practice moderation in all things. Including moderation."
  • Quine's paradox: "Yields a falsehood when appended to its own quotation" yields a falsehood when appended to its own quotation.
  • Richard's paradox: We appear to be able to use simple English to define a decimal expansion in a way which is self-contradictory.
  • Socratic paradox: "I know that I know nothing at all."

غموض

  • Ship of Theseus (a.k.a. George Washington's or Grandfather's old axe): It seems like you can replace any component of a ship, and it will still be the same ship. So you can replace them all, or one at a time, and it will still be the same ship. But then you can take all the original pieces, and assemble them into a ship. That, too, is the same ship with which you started.
  • Sorites paradox: One grain of sand is not a heap. If you don't have a heap, then adding only one grain of sand won't give you a heap. Then no number of grains of sand will make a heap. Similarly, one hair can't make the difference between being bald and not being bald. But then if you remove one hair at a time, you will never become bald. Also similar, one dollar will not make you rich, so if you keep this up, one dollar at a time, you will never become rich, no matter how much you obtain.

رياضية

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إحصائيات

  • قانون بنفورد: In lists of numbers from many real-life sources of data, the leading digit 1 occurs much more often than the others.
  • متناقضة بركسون: a complicating factor arising in statistical tests of proportions
  • It is quite possible to draw wrong conclusions from correlation. For example, towns with a larger number of churches generally have a higher crime rate — because both result from higher population. A professional organization once found that economists with a Ph.D. actually had a lower average salary than those with a BS — but this was found to be because those with a Ph.D. worked in academia, where salaries are generally lower. This is also called a spurious relationship.
  • Inspection paradox: Why you will wait longer for that bus than you should.
  • متناقضة لندلي: Tiny errors in the null hypothesis are magnified when large data sets are analyzed, leading to false but highly statistically significant results
  • ظاهرة ول روجر: The mathematical concept of an average, whether defined as the mean or median, leads to apparently paradoxical results — for example, it is possible that moving an entry from an encyclopedia to a dictionary would increase the average entry length on both books.

إحتمالية

The متناقضة مونتي هول: أي الأبواب تختار?
انظر أيضاً: تصنيف:متناقضات نظرية الإحتمالات

Infinity and infinitesimals

الهندسة والطوبولجيا

The Banach–Tarski paradox: A ball can be decomposed and reassembled into two balls the same size as the original.
  • Banach–Tarski paradox: Cut a ball into 5 pieces, re-assemble the pieces to get two balls, both of equal size to the first.
  • Gabriel's Horn or Torricelli's trumpet: A simple object with finite volume but infinite surface area. Also, the Mandelbrot set and various other fractals are covered by a finite shape, but have an infinite perimeter (in fact, there are no two distinct points on the boundary of the Mandelbrot set that can be reached from one another by moving a finite distance along that boundary, which also implies that in a sense you go no further if you walk "the wrong way" around the set to reach a nearby point). This can be represented by a Klein bottle
  • Hausdorff paradox: There exists a countable subset C of the sphere S such that S\C is equidecomposable with two copies of itself.
  • Coastline paradox: the perimeter of a landmass is in general ill-defined.
Smale's paradox states that it is possible to turn a sphere inside out in 3-space with possible self-intersections but without creating any crease. One such construction, a Morin surface, seen from "above".


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Decision theoretic

المقالة الرئيسية: Decision theory
  • Abilene paradox: People can make decisions based not on what they actually want to do, but on what they think that other people want to do, with the result that everybody decides to do something that nobody really wants to do, but only what they thought that everybody else wanted to do.
  • Buridan's ass: How can a rational choice be made between two outcomes of equal value?
  • Green paradox: Policies intending to reduce future CO2 emissions may lead to increased emissions in the present.
  • Kavka's toxin puzzle: Can one intend to drink the non-deadly toxin, if the intention is the only thing needed to get the reward?
  • Morton's fork: Choosing between unpalatable alternatives.
  • Navigation paradox: Increased navigational precision may result in increased collision risk.
  • Newcomb's paradox: How do you play a game against an omniscient opponent?
  • Paradox of hedonism: When one pursues happiness itself, one is miserable; but, when one pursues something else, one achieves happiness.
  • Paradox of Tolerance: Should one tolerate intolerance; if intolerance would destroy the possibility of tolerance?
  • Parrondo's paradox: It is possible to play two losing games alternately to eventually win.
  • Prevention paradox: For one person to benefit, many people have to change their behaviour—even though they receive no benefit, or even suffer, from the change.

كيميائية

  • Levinthal paradox : The length of time in which a protein chain finds its folded state is many orders of magnitude shorter than it would be if it freely searched all possible configurations.
  • SAR paradox: Exceptions to the principle that a small change in a molecule causes a small change in its chemical behavior are frequently profound.

فيزيائية

المقالة الرئيسية: متناقضة فيزيائية
Robert Boyle's self-flowing flask fills itself in this diagram, but perpetual motion machines cannot exist.

Cosmological

فلسفية

  • Fitch's paradox: If all truths are knowable, then all truths must in fact be known.
  • متناقضة الجد: You travel back in time and kill your grandfather before he conceives one of your parents, which precludes your own conception and, therefore, you couldn't go back in time and kill your grandfather.
  • Hutton's Paradox: If asking oneself "Am I dreaming?" in a dream proves that one is, what does it prove in waking life?
  • Liberal paradox: "Minimal Liberty" is incompatible with Pareto optimality.
  • Mere addition paradox: Is a large population barely tolerably living life better than a small happy population?
  • Moore's paradox: "It's raining, but I don't believe that it is."
  • Newcomb's paradox: A paradoxical game between two players, one of whom can predict the actions of the other.
  • Nihilist paradox: If truth does not exist, the statement "truth does not exist" is a truth, thereby proving itself incorrect.
  • Omnipotence paradox: Can an omnipotent being create a rock too heavy for themself to lift?
  • Paradox of hedonism: In seeking happiness, one does not find happiness.
  • Predestination paradox: A man travels back in time to discover the cause of a famous fire. While in the building where the fire started, he accidentally knocks over a kerosene lantern and causes a fire, the same fire that would inspire him, years later, to travel back in time. The ontological paradox is closely tied to this, in which as a result of time travel, information or objects appear to have no beginning.
  • Problem of evil (Epicurean paradox): The existence of evil seems to be incompatible with the existence of an omnipotent, omniscient, and morally perfect God.
  • Zeno's paradoxes: "You will never reach point B from point A as you must always get half-way there, and half of the half, and half of that half, and so on..." (This is also a paradox of the infinite)

اقتصادية

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