This article does not cite any references or sources. (November 2007) Please help improve this article by adding citations to reliable sources. Unverifiable material may be challenged and removed.

Logic Portal

This is a list of paradoxes, grouped thematically. Note that many of the listed paradoxes have a clear resolution. — see Quine's Classification of Paradoxes. Image File history File links Question_book-3. ... Image File history File links Portal. ... Look up paradox in Wiktionary, the free dictionary. ... Look up paradox in Wiktionary, the free dictionary. ...

Logical (except mathematical)

Main article: Logic

• Paradox of entailment: Inconsistent premises always make an argument valid.
• Raven paradox (or Hempel's Ravens): Observing a green apple increases the likelihood of all ravens being black.
• Horse paradox: All horses are the same color.
• Unexpected hanging paradox: The day of the hanging will be a surprise, so it cannot happen at all, so it will be a surprise. The Bottle Imp paradox uses similar logic.
• Drinker paradox: In any pub there is a customer such that, if he or she drinks, everybody in the pub drinks.
• Carroll's paradox: "Whatever Logic is good enough to tell me is worth writing down..."
• Lottery paradox: it is philosophically justifiable to believe that every individual lottery ticket won't win, but not justifiable to believe that no lottery ticket will win.

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. ... The paradox of entailment is an apparent paradox derived from the observation that, in classical logic, inconsistent premises always make an argument valid; that is, inconsistent premises imply any conclusion at all. ... A black raven Non-black non-ravens The Raven paradox, also known as Hempels paradox or Hempels ravens is a paradox proposed by the German logician Carl Gustav Hempel in the 1940s to illustrate a problem where inductive logic violates intuition. ... The horse paradox is an apparent paradox which arises from the following supposed demonstration, using mathematical induction, of the statement All horses are the same colour: As the basis case, note that in a set containing a single horse, all horses are clearly the same colour. ... This article or section is in need of attention from an expert on the subject. ... Wikisource has original text related to this article: The Bottle Imp The Bottle Imp (1893) is a short story by the Scottish author Robert Louis Stevenson about a working class native of Hawaii, Keawe, who buys a strange bottle from a sad, elderly gentleman who credits the bottle with his... The drinker paradox is a tautology in predicate logic that is apparently in contrast with common intuition. ... What the Tortoise Said to Achilles is a brief dialog by Lewis Carroll which playfully problematizes the foundations of logic. ... The Lottery Paradox is a paradox studied by epistemologists interested in justification. ... Theory of justification is a part of epistemology that attempts to understand the justification of statements and beliefs. ...

Self-referential

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

• 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, excepting this one" ...is there an exception to the rule that states that there is an exception to every rule?
• Grelling-Nelson paradox: Is the word "heterological", meaning "not applicable to itself," a heterological word? (Another close relative of Russell's paradox.)
• Intentionally blank page: Many documents contain pages on which the text "This page is intentionally 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?"
• The Y combinator in the lambda calculus and combinatory logic has been called the paradoxical combinator since it is related to the self-referential antinomies.
• Petronius' paradox: "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.
• 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.
• Russell's paradox: Does the set of all those sets that do not contain themselves contain itself? Russell popularized it with the Barber paradox: The adult male barber who shaves all men who do not shave themselves, and no-one else.
• Richard's paradox: We appear to be able to use simple English to define a decimal expansion in a way which is self-contradictory.

The Berry paradox is the apparent contradiction that arises from expressions such as the following: The smallest positive integer not nameable in under eleven words. ... 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. ... The Epimenides paradox is a problem in logic. ... This article does not cite any references or sources. ... 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. ... 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. ... Intentionally blank pages at the end of a book An intentionally blank page is a page that is devoid of content, and may be unexpected. ... In philosophy and logic, the liar paradox encompasses paradoxical statements such as: I am lying now. ... Y Combinator Logo Y Combinator is a seed-stage startup funding firm, started in 2005 by Paul Graham, Robert Morris, Trevor Blackwell, and Jessica Livingston. ... The lambda calculus is a formal system designed to investigate function definition, function application, and recursion. ... Not to be confused with combinational logic, a topic in digital electronics. ... A fixed point combinator is a function which computes fixed points of other functions. ... This article is about the Roman author Petronius. ... Quines paradox is a paradox concerning truth values, attributed to W. V. O. Quine. ... The Paradox of the Court is a very old problem in logic stemming from ancient Greece. ... 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. ... The Barber paradox is a puzzle attributed to Bertrand Russell. ... Richards paradox is a fallacious paradox of mathematical mapping first described by the French mathematician Jules Richard in 1905. ...

Vagueness

• 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 you started with.
• 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.

The Ship of Theseus is a paradox also known as Theseus paradox. ... Grandfathers old axe is a colloquial expression describing something of which little original remains: its had three new heads and four new handles but its still the same old axe. ... The Sorites paradox (σωρός (sōros) being Greek for heap and σωρίτης (sōritēs) the adjective) is a paradox that arises from vague predicates. ...

Mathematical and statistical

The Monty Hall paradox: which door do you choose?

See also: Category:Mathematics paradoxes

• Apportionment paradox: Some systems of apportioning representation can have unintuitive results due to rounding
  • Alabama paradox: Increasing the total number of seats might shrink one block's seats.
  • New states paradox: Adding a new state or voting block might increase the number of votes of another.
  • Population paradox: A fast-growing state can lose votes to a slow-growing state.
• Arithmetic paradoxes: Proofs of obvious contradictions; for example, proving that 2=1 by writing a huge expression and dividing by another expression that is zero.
• Arrow's paradox/Voting paradox You can't have all the attributes of an ideal voting system at once.
• Benford's law: In lists of numbers from many real-life sources of data, the leading digit 1 occurs much more often than the others.
• Condorcet's paradox: A group of separately rational individuals may have preferences which are irrational in the aggregate.
• Elevator paradox: Elevators can seem to be mostly going in one direction, as if they were being manufactured in the middle of the building and being disassembled on the roof and basement.
• Inspection paradox: Why you will wait longer for that bus than you should.
• Interesting number paradox: The first number that can be considered "dull" rather than "interesting" becomes interesting because of that fact.
• Intransitive dice: You can have three dice, called A, B, and C, such that A is likely to win in a roll against B, B is likely to win in a roll against C, and C is likely to win in a roll against A.
• Lindley's paradox: tiny errors in the null hypothesis are magnified when large data sets are analyzed, leading to false but highly statistically significant results
• Low birth weight paradox: Low birth weight and mothers who smoke contribute to a higher mortality rate. Babies of smokers have lower average birth weight, but low birth weight babies born to smokers have a lower mortality rate than other low birth weight babies. (A special case of Simpson's paradox.)
• Missing dollar paradox: Faulty logic makes it appear as if a dollar from a restaurant bill has gone missing. Not in the same class as the others.
• Statistical paradox: 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 due to the fact that those with a Ph.D. worked in academia, where salaries are generally lower. This is also called a spurious relationship.
• Will Rogers phenomenon: 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.
• Smallest number paradox describes how a rolling object should be able to attain a velocity of the smallest positive number.

Image File history File links Monty_open_door. ... Image File history File links Monty_open_door. ... In search of a new car, the player picks door 1. ... To apportion is to divide into parts according to some rule, the rule typically being one of proportion. ... The Alabama paradox was the first of the apportionment paradoxes to be discovered today on 11/10/06. ... The new states paradox occurs when adding a new state to the United States of America causes another state to get more congressional representatives than it had before the new state was added. ... The population paradox occurs when two states of the United States of America have populations increasing at different rates and the state with the greater growth rate loses a congressional seat to the state with the lower growth rate. ... In mathematics, there are a variety of spurious proofs of obvious contradictions. ... 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. ... The voting paradox (also known as Condorcets paradox or the paradox of voting) is a situation noted by the Marquis de Condorcet in the late 18th century, in which collective preferences can be cyclic (i. ... A voting system is a means of choosing between a number of options, based on the input of a number of voters. ... A logarithmic scale bar. ... The voting paradox (also known as Condorcets paradox or the paradox of voting) is a situation noted by the Marquis de Condorcet in the late 18th century, in which collective preferences can be cyclic (i. ... The elevator paradox is an apparent paradox first noted by George Gamow and Moritz Stern, physicists who had offices on two different floors of a multi-story building. ... Renewal theory is a branch of probability theory with an interesting and varied range of applications. ... The interesting number paradox is a semi-humorous paradox that arises from attempting to classify numbers as interesting or dull. ... A set of nontransitive dice is a set of dice for which the relation is more likely to roll a higher number is not transitive. ... Lindleys paradox describes a counterintuitive situation in statistics in which the Bayesian and frequentist approaches to a hypothesis testing problem give opposite results for certain choices of the prior distribution. ... The low birth weight paradox is a certain observation relating birth weights and mortality of children born to smoking mothers. ... Simpsons paradox for continuous data: a positive trend appears for two separate groups (blue and red), a negative trend (black, dashed) appears when the data are combined. ... This article does not cite any references or sources. ... Positive linear correlations between 1000 pairs of numbers. ... Alan Greenspan, former chairman, United States Federal Reserve. ... Doctor of Philosophy, abbreviated Ph. ... B.S. redirects here. ... Doctor of Philosophy, abbreviated Ph. ... Academia is a collective term for the scientific and cultural community engaged in higher education and research, taken as a whole. ... In statistics, a spurious relationship (or, sometimes, spurious correlation) is a mathematical relationship in which two occurrences have no causal connection, yet it may be inferred that they do, due to a certain third, unseen factor (referred to as a confounding factor or lurking variable). The spurious relationship gives an... The Will Rogers phenomenon is obtained when moving an element from one set to another set raises the average values of both sets. ... In mathematics, an average or central tendency of a set (list) of data refers to a measure of the middle of the data set. ... In statistics, mean has two related meanings: the arithmetic mean (and is distinguished from the geometric mean or harmonic mean). ... This article is about the statistical concept. ... Cyclopedia redirects here. ... For other uses, see Dictionary (disambiguation). ... This article is being considered for deletion in accordance with Wikipedias deletion policy. ...

Probability

See also: Category:Probability theory paradoxes

• Berkson's paradox: a complicating factor arising in statistical tests of proportions
• Bertrand's paradox (probability): Different common-sense definitions of randomness give quite different results.
• Birthday paradox: What is the chance that two people in a room have the same birthday?
• Borel's paradox: Conditional probability density functions are not invariant under coordinate transformations.
• Boy or Girl: A two-child family has at least one boy. What is the probability that it has a girl?
• Monty Hall problem: An unintuitive consequence of conditional probability. Essentially the same as the Three Prisoners Problem.
• Necktie Paradox : A wager between two people seems to favour them both. Very similar in essence to the Two-envelope paradox.
• Simpson's paradox: An association in sub-populations may be reversed in the population. It appears that two sets of data separately support a certain hypothesis, but, when considered together, they support the opposite hypothesis.
• Sleeping Beauty problem: A probability problem that can be correctly answered as one half or one third depending on how the question is approached.
• Three cards problem: When pulling a random card, how do you determine the color of the underside?
• Two-envelope paradox: You are given two indistinguishable envelopes and you are told one contains twice as much money as the other. You may open one envelope, examine its contents, and then, without opening the other, choose which envelope to take.

Berksons paradox is a result in conditional probability and statistics which is counter-intuitive for some people, and so has been described as a paradox. ... Bertrands paradox is a problem in probability theory. ... 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. ... Borels paradox (sometimes known as the Borel-Kolmogorov paradox) is a paradox of probability theory relating to conditional probability density functions. ... The Boy or Girl problem is a well known example in probability theory. ... In search of a new car, the player picks door 1. ... The Three Prisoners Problem appeared in Martin Gardners Mathematical Games column in 1959. ... Two men are each given a necktie by their wives as a Christmas present. ... The envelope paradox is a paradox of probability. ... Simpsons paradox for continuous data: a positive trend appears for two separate groups (blue and red), a negative trend (black, dashed) appears when the data are combined. ... The sleeping beauty problem is a puzzle in probability theory: a sleeper is to be woken once or twice according to the toss of a coin, and asked her credence for the coin having come up heads. ... Three Cards is a simple but slightly counterintuitive puzzle used as a standard example in probability theory. ... The envelope paradox is a paradox of probability. ...

Infinity

• Burali-Forti paradox: If the ordinal numbers formed a set, it would be an ordinal number which is smaller than itself.
• Galileo's paradox: Though most numbers are not squares, there are no more numbers than squares. (See also Cantor, Diagonal Argument)
• Hilbert's paradox of the Grand Hotel: If a hotel with infinitely many rooms is full, it can still take in more guests.
• Skolem's paradox: Countably infinite models of set theory contain uncountably infinite sets.
• Supertasks can result in paradoxes such as the Ross-Littlewood paradox and Benardete's paradox.

In set theory, a field of mathematics, the Burali-Forti paradox demonstrates that naïvely constructing the set of all ordinal numbers leads to a contradiction and therefore shows an antinomy in a system that allows its construction. ... In set theory, ordinal, ordinal number, and transfinite ordinal number refer to a type of number introduced by Georg Cantor in 1897, to accommodate infinite sequences and to classify sets with certain kinds of order structures on them. ... In mathematics, a set can be thought of as any collection of distinct objects considered as a whole. ... Galileos paradox is a demonstration of one of the surprising properties of infinite sets. ... Georg Ferdinand Ludwig Philipp Cantor (March 3, 1845[1] – January 6, 1918) was a German mathematician. ... Cantors diagonal argument, also called the diagonalisation argument, the diagonal slash argument or the diagonal method, was published in 1891 by Georg Cantor as a proof that there are infinite sets which cannot be put into one-to-one correspondence with the infinite set of natural numbers. ... Hilberts paradox of the Grand Hotel was a mathematical paradox about infinity presented by German mathematician David Hilbert (1862 – 1943): In a hotel with a finite number of rooms, it is clear that once it is full, no more guests can be accommodated. ... Infinity is a word carrying a number of different meanings in mathematics, philosophy, theology and everyday life. ... In mathematical logic, specifically set theory, Skolems paradox is a direct result of the (downward) Löwenheim-Skolem theorem, which states that every model of a sentence of a first-order language has an elementarily equivalent countable submodel. ... In mathematics the term countable set is used to describe the size of a set, e. ... This article or section is in need of attention from an expert on the subject. ... In mathematics, an uncountable set is a set which is not countable. ... In philosophy, a supertask is a task occurring within a finite interval of time involving infinitely many steps (subtasks). ... It has been suggested that this article or section be merged into Ping-pong ball conundrum. ... In philosophy, a supertask is a task occurring within a finite interval of time involving infinitely many steps (subtasks). ...

Geometry and topology

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).
• Hausdorff paradox: There exists a countable subset C of the sphere S such that SC 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".

• Smale's paradox: A sphere can, topologically, be turned inside out.
• Missing square puzzle: Two similar figures appear to have different areas while built from the same pieces.
• No Shortcuts paradox: The length of the hypotenuse in a right triangle is not shorter then the sum of the two axis-parallel legs, i.e., the direct connection between two points (which should amount to the euclidean distance) is not shorter than a path with segments that are orthogonal to each other (which amounts to the Manhattan distance). (See this reference)

Image File history File links Banach-Tarski_Paradox. ... Image File history File links Banach-Tarski_Paradox. ... A ball can be decomposed into a finite number of pieces and reassembled into two balls identical to the original. ... A ball can be decomposed into a finite number of pieces and reassembled into two balls identical to the original. ... Gabriels Horn (also called Torricellis trumpet) is a figure invented by Evangelista Torricelli which has infinite surface area, but finite volume. ... Initial image of a Mandelbrot set zoom sequence with continuously coloured environment The Mandelbrot set is a set of points in the complex plane that forms a fractal. ... The boundary of the Mandelbrot set is a famous example of a fractal. ... In mathematics, the Hausdorff paradox, named after Felix Hausdorff, states that if you remove a certain countable subset of the sphere S², the remainder can be divided into three subsets A, B and C such that A, B, C and B ∪ C are all congruent. ... The coastline paradox is the counterintuitive observation that the coastline of a landmass does not have a well-defined length. ... Image File history File links MorinSurfaceFromTheTop. ... Image File history File links MorinSurfaceFromTheTop. ... In differential topology, Smales paradox states that it is possible to turn a sphere inside out in 3-space with possible self-intersections but without creating any crease, a process often called sphere eversion. ... The Morin surface is the half-way model of the sphere eversion discovered by Bernard Morin. ... In differential topology, Smales paradox states that it is possible to turn a sphere inside out in 3-space with possible self-intersections but without creating any crease, a process often called sphere eversion. ... The missing square puzzle is an optical illusion used in mathematics classes, to help students reason about geometrical figures. ...

Decision theoretic

Main article: 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?
• Control paradox: Man can never be free of control, for to be free of control is to be controlled by oneself.
• Morton's fork: Choosing between unpalatable alternatives.
• Paradox of hedonism: When one pursues happiness itself, one is miserable; but, when one pursues something else, one achieves happiness.
• Newcomb's paradox: How do you play a game against an omniscient opponent?
• Kavka's toxin puzzle: Can one intend to drink the deadly toxin, if the intention is the only thing needed to get the reward?

Decision theory is an area of study of discrete mathematics that models human decision-making in science, engineering and indeed all human social activities. ... The Abilene paradox is a paradox in which the limits of a particular situation force a group of people to act in a way that is directly the opposite of their actual preferences. ... Buridans ass is the common name for the paradox which states that an entirely rational ass, placed exactly in the middle between two stacks of hay of equal size and quality, will starve since it cannot make any rational decision to start eating one rather than the other. ... Rationality as a term is related to the idea of reason, a word which following Websters may be derived as much from older terms referring to thinking itself as from giving an account or an explanation. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... The control paradox states that a live or conscious human being will also be controlled either by others, or by themselves, so the idea of control will be operating on them. ... Mortons Fork is an expression that describes a choice between two equally unpleasant alternatives (in other words, a dilemma), or two lines of reasoning that lead to the same unpleasant conclusion. ... The paradox of hedonism, also called the pleasure paradox, is the idea in the study of ethics which points out on that pleasure and happiness are strange phenomena that do not obey normal principles. ... This article or section may contain original research or unverified claims. ... For the album by Swans, see Omniscience (album). ... Kavkas toxin puzzle is a thought experiment about the possibility of forming an intention to perform an act which, following from reason, it is an action one would not actually perform. ...

Chemical

• SAR paradox: Exceptions to the principle that a small change in a molecule causes a small change in its chemical behavior are frequently profound.
• The 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.

Quantitative structure-activity relationship (QSAR) is the process by which chemical structure is quantitatively correlated with a well defined process, such as biological activity or chemical reactivity. ... 3D (left and center) and 2D (right) representations of the terpenoid molecule atisane. ... The Levinthal paradox is a thought experiment in the theory of protein folding dynamics. ...

Physical

Main article: physical paradox

Robert Boyle's self-flowing flask fills itself in this diagram, but perpetual motion machines cannot exist (according to our current understanding of physics).

• Archimedes Paradox: A massive battleship can float in a few litres of water.
• Bell's spaceship paradox: concerning relativity.
• Bell's Theorem: Measurement of quantum particles do not satisfy mathematical probability theory.
• Black hole information paradox: Black holes violate a commonly assumed tenet of science — that information cannot be destroyed.
• Braess' paradox: Sometimes adding extra capacity to a network can reduce overall performance.
• Carroll's paradox: The angular momentum of a stick should be zero, but is not.
• D'Alembert's paradox: An inviscid liquid produces no drag.
• Denny's paradox: Surface-dwelling arthropods (such as the water strider) should not be able to propel themselves horizontally.
• Ehrenfest paradox: On the kinematics of a rigid, rotating disk.
• Einstein-Podolsky-Rosen paradox: Can far away events influence each other in quantum mechanics?
• Fermi paradox: If there are, as probability would suggest, many other sentient species in the Universe, then where are they? Shouldn't their presence be obvious?
• Gibbs paradox: In an ideal gas, is entropy an extensive variable?
• The GZK paradox: High-energy cosmic rays have been observed which seem to violate the Greisen-Zatsepin-Kuzmin limit which is a consequence of special relativity.
• The Irresistible force paradox: what would happen if an unstoppable force hits an immovable object?
• Ladder paradox: A classic relativity problem.
• Loschmidt's paradox: Why is there an inevitable increase in entropy when the laws of physics are invariant under time reversal? The time reversal symmetry of physical laws appears to allow the second law of thermodynamics to be broken.
• Mpemba paradox: Hot water can under certain conditions freeze faster than cold water, even though it must pass the lower temperature on the way to freezing.
• Olbers' paradox: Why is the night sky black if there is an infinity of stars?
• Ontological paradox: Can a time traveler send himself information with no outside source?
• Schrödinger's cat paradox: A quantum paradox — Is the cat alive or dead before we look?
• Supplee's paradox: the buoyancy of a relativistic object (such as a bullet) appears to change when the reference frame is changed from one in which the bullet is at rest to one in which the fluid is at rest.
• Twin paradox: When the traveling twin returns, he is younger and older than his sibling who stayed put.

A physical paradox is an apparent contradiction relating to physical descriptions of the universe. ... The figure is sometimes called Boyles perpetual motion scheme (in honor of Robert Boyle (1627-1691)), the perpetual vase or perpetual goblet. It was discussed by Denis Papin (1647-1712) in the Philosophical Transactions for 1685. ... The figure is sometimes called Boyles perpetual motion scheme (in honor of Robert Boyle (1627-1691)), the perpetual vase or perpetual goblet. It was discussed by Denis Papin (1647-1712) in the Philosophical Transactions for 1685. ... Robert Boyle (Irish: Robaird Ó Bhaoill) (25 January 1627 – 30 December 1691) was an Irish natural philosopher, chemist, physicist, inventor, and early gentleman scientist, noted for his work in physics and chemistry. ... This article or section should include material from Parallel Path See also Perpetuum mobile as a musical term Perpetual motion machines (the Latin term perpetuum mobile is not uncommon) are a class of hypothetical machines which would produce useful energy in a way science cannot explain (yet). ... A magnet levitating above a high-temperature superconductor demonstrates the Meissner effect. ... The Archimedes Paradox states that an object can float in water that has less volume than the object itself, if its average density is less than that of water. ... In relativistic physics, Bells spaceship paradox denotes any of a family of closely related thought experiments giving results which many students initially consider to be counterintuitive. ... Two-dimensional analogy of space-time curvature described in General Relativity. ... Bells theorem is the most famous legacy of the late Irish phyisicist John Bell. ... This article or section cites very few or no references or sources. ... Braess paradox, credited to the mathematician Dietrich Braess, states that adding extra capacity to a network can in some cases reduce overall performance. ... In physics, Carrolls paradox arises when considering the motion of a falling rigid rod that is specially constrained. ... // DAlemberts paradox is a contradiction reached by French mathematician Jean le Rond dAlembert in 1752 [1] using inviscid theory in the form of potential solutions of the incompressible Euler equations, to prove that the drag of a body of any shape moving through an inviscid fluid is... For other uses, see Viscosity (disambiguation). ... In the study of animal locomotion, Dennys paradox refers to the apparent impossibility of surface-dwelling animals such as the water strider generating enough propulsive force to move. ... Subphyla and Classes Subphylum Trilobitomorpha Trilobita - trilobites (extinct) Subphylum Chelicerata Arachnida - spiders,scorpions, etc. ... Genera Aquarius Gerris Halobates Limnogonus Limnoporus Metrobates Neogerris Rheumatobates Trepobates The water strider, also known as the Magic bug, pond skater, skater, skimmer, water scooter, water skater, water skeeter, water skimmer, water skipper, or water spider, is any of a number of predatory insects in the family Gerridae (Leach, 1815... In relativistic physics, the Ehrenfest paradox concerns the kinematics of a rotating disk. ... In quantum mechanics, the EPR paradox is a thought experiment which demonstrates that the result of a measurement performed on one part of a quantum system can have an instantaneous effect on the result of a measurement performed on another part, regardless of the distance separating the two parts. ... For a less technical and generally accessible introduction to the topic, see Introduction to quantum mechanics. ... A graphical representation of the Arecibo message - Humanitys first attempt to use radio waves to communicate its existence to alien civilizations The Fermi paradox is the apparent contradiction between high estimates of the probability of the existence of extraterrestrial civilizations and the lack of evidence for or contact with... The introduction to this article provides insufficient context for those unfamiliar with the subject matter. ... An ideal gas or perfect gas is a hypothetical gas consisting of identical particles of zero volume, with no intermolecular forces. ... For other uses, see: information entropy (in information theory) and entropy (disambiguation). ... In physics and chemistry, an extensive quantity (also referred to as an extensive variable) is a physical quantity whose value is proportional to the size of the system it describes. ... The Greisen-Zatsepin-Kuzmin limit (GZK limit) is a theoretical upper limit on the energy of cosmic rays from distant sources. ... Cosmic rays can loosely be defined as energetic particles originating outside of the Earth. ... The Greisen-Zatsepin-Kuzmin limit (GZK limit) is a theoretical upper limit on the energy of cosmic rays from distant sources. ... For a less technical and generally accessible introduction to the topic, see Introduction to special relativity. ... This is a trivia section. ... The ladder paradox or (barn-pole paradox) is a thought experiment in special relativity. ... Loschmidts paradox states that if there is a motion of a system that leads to a steady decrease of H (increase of entropy) with time, then there is certainly another allowed state of motion of the system, found by time reversal, in which H must increase. ... For a list of set rules, see Laws of science. ... T-symmetry is the symmetry of physical laws under a time-reversal transformation— The universe is not symmetric under time reversal, although in restricted contexts one may find this symmetry. ... The Mpemba effect is the observation that, in some specific, fairly common circumstances, hotter water freezes faster than colder water. ... Olbers paradox, described by the German astronomer Heinrich Wilhelm Olbers in 1826 and earlier by Johannes Kepler in 1610 and Halley and Cheseaux in the 18th century, is the paradoxical observation that the night sky is dark, when in a static infinite universe the night sky ought to be bright. ... An ontological paradox is a paradox of time travel that questions the existence and creation of information and objects that travel in time. ... Schrödingers Cat: If the nucleus in the bottom left decays, the geiger counter on its right will sense it and trigger the release of the gas. ... In relativistic physics, Supplees paradox (also submarine paradox) arises when considering the buoyancy forces exerted on a relativistic object (such as a bullet) moving through a dense fluid such as water in a gravitational field. ... In physics, buoyancy is the upward force on an object produced by the surrounding fluid (i. ... Albert Einsteins theory of relativity is a set of two theories in physics: special relativity and general relativity. ... This article is about firearms projectiles. ... In physics, the twin paradox refers to a thought experiment in Special Relativity, in which a person who makes a journey into space in a high-speed rocket will return home to find they have aged less than an identical twin who stayed on Earth. ...

Philosophical

• Epicurean paradox: The existence of evil seems to be incompatible with the existence of an omnipotent and caring God.
• Newcomb's paradox: A paradoxical game between two players, one of whom can predict the actions of the other.
• Grandfather paradox: You travel back in time and kill your grandfather before he meets your grandmother 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: It is impossible to have both a commitment to "Minimal Liberty", and 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."
• 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 to lift?
• Irresistible force paradox: Can an irresistible force move an immovable object?
• 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. A classic example occurs in the film Somewhere in Time, in which a pocket watch is given to a young man by an older woman, only for the younger man to travel back in time, then give it to that same woman's younger self, who then goes on to give it to him. At no point is it ever revealed where the watch came from.
• 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..."
• Future Paradox: If the future hasn't happened, it does not exist. The future cannot come, because the day in the future becomes the present.

... This article or section may contain original research or unverified claims. ... 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. ... While people dream, they usually do not realize they are dreaming (in non-lucid dreams). ... The liberal paradox is a logical paradox advanced by Amartya Sen, building on the work of Kenneth Arrow and his general possibility theorem, which showed that within a system of menu-independent social choice, it is impossible to have both a commitment to Minimal Liberty, which was defined as the... Pareto efficiency, or Pareto optimality, is a central concept in game theory with broad applications in economics, engineering and the social sciences. ... The mere addition paradox is a problem in ethics, due to Derek Parfit, and first appearing in his book, Reasons and Persons. ... G. E. Moore remarked once in a lecture on the absurdity involved in saying something like Its raining outside but I dont believe that it is. ... Nihilism is a doctrine stating that no objects have an intrinsic characteristic of truth. ... Listen to this article ( info/dl) This audio file was created from an article revision dated 2007-09-04, and may not reflect subsequent edits to the article. ... Omnipotence (literally, all power) is the power to do absolutely anything. ... This is a trivia section. ... The paradox of hedonism, also called the pleasure paradox, is the idea in the study of ethics which points out on that pleasure and happiness are strange phenomena that do not obey normal principles. ... A predestination paradox, also called either a causal loop, or a causality loop and (less frequently) either a closed loop or closed time loop, is a paradox of time travel that is often used as a convention in science fiction. ... An ontological paradox is a paradox of time travel that questions the existence and creation of information and objects that travel in time. ... This article is about the 1980 film. ... “Arrow paradox” redirects here. ...

Economic

See also: Category:Economics paradoxes

• Abilene paradox: A group of people often has to decide against each member's own personal interests or views.
• Allais paradox: A change in a possible outcome which is shared by different alternatives affects people's choices among those alternatives, in contradiction with expected utility theory.
• Bertrand paradox: Two players reaching a state of Nash equilibrium both find themselves with no profits.
• Diamond-water paradox (or paradox of value) Neither water nor diamonds are rare, but water is cheaper than diamonds, though humans need water to survive, not diamonds.
• Edgeworth paradox: With capacity constraints, there may not be an equilibrium.
• Ellsberg paradox: People exhibit ambiguity aversion (as distinct from risk aversion), in contradiction with expected utility theory.
• Gibson's paradox: Why were interest rates and prices correlated?
• Giffen paradox: Increasing the price of bread makes poor people eat more of it.
• Jevons paradox: Increases in efficiency lead to even larger increases in demand.
• Leontief paradox: Some countries export labor-intensive commodities and import capital-intensive commodities, in contradiction with Heckscher-Ohlin theory.
• Paradox of thrift: If everyone saves more money during times of recession, then aggregate demand will fall and will in turn lower total savings in the population.
• Parrondo's paradox: It is possible to play two losing games alternately to eventually win.
• Productivity paradox, Solow computer paradox Worker productivity may go down, despite technological improvements...
• St. Petersburg paradox: People will only offer a modest fee for a reward of infinite value.

The Abilene paradox is a paradox in which the limits of a particular situation force a group of people to act in a way that is directly the opposite of their actual preferences. ... The Allais paradox, more neutrally described as the Allais problem, is a choice problem designed by Maurice Allais to show an inconsistency of actual observed choices with the predictions of expected utility theory. ... The expected utility hypothesis is the hypothesis in economics that the utility of an agent facing uncertainty is calculated by considering utility in each possible state and constructing a weighted average. ... In economics, the Bertrand paradox–so named for its creator, Joseph Bertrand–describes a situation in which two players (frims) reaching a state of Nash equilibrium in economic competition find themselves with no profits. ... In game theory, the Nash equilibrium (named after John Forbes Nash, who proposed it) is a kind of solution concept of a game involving two or more players, where no player has anything to gain by changing only his or her own strategy unilaterally. ... The paradox of value (also known as the diamond-water paradox) is the apparent contradiction, or paradox, that although water is on the whole more useful, in terms of survival, than diamonds, diamonds command a higher price in the market. ... In economics, the Edgeworth paradox describes a situation in which two players cannot reach a state of equilibrium with pure strategies, i. ... The Ellsberg paradox is a paradox in decision theory and experimental economics in which peoples choices violate the expected utility hypothesis. ... Ambiguity aversion (also known as uncertainty aversion) describes an attitude of preference for known risks over unknown risks. ... Risk aversion is a concept in economics and finance theory explaining the behaviour of consumers and investors under uncertainty. ... The expected utility hypothesis is the hypothesis in economics that the utility of an agent facing uncertainty is calculated by considering utility in each possible state and constructing a weighted average. ... Gibsons Paradox was the observation that, during the gold standard era, the rate of interest and the general level of prices were observed to be correlated. ... A Giffen good is a product for which a rise in price of this product makes people buy even more of the product. ... In economics, the Jevons Paradox is an observation made by William Stanley Jevons who stated that as technological improvements increase the efficiency with which a resource is used, total consumption of that resource may increase, rather than decrease. ... Leontiefs paradox in economics was the result of Professor Wassily W. Leontiefs attempt to test the Heckscher-Ohlin theory. ... The Heckscher-Ohlin model (H-O model) is a General equilibrium mathematical model of the macroeconomy in international trade, developed by Eli Heckscher and Bertil Ohlin at the Stockholm School of Economics. ... The paradox of thrift is a paradox of economics propounded by John Maynard Keynes. ... Parrondos paradox is a paradox in game theory and is often described as: A losing strategy that wins. ... The so-called productivity paradox is the observation made in Computer Supported Cooperative Work and other business process analysis that, as new information technology is introduced, worker productivity tends to go down, not up. ... The Solow computer paradox is that the productivity of the work force has not risen as information technology has extended through western industry. ... In probability theory and decision theory the St. ... Infinity is a word carrying a number of different meanings in mathematics, philosophy, theology and everyday life. ... To meet Wikipedias quality standards, this article or section may require cleanup. ...

See also

• Bracketing paradox
• Buttered cat paradox, a humorous example of a paradox from contradicting folk tales
• Ethics
• Impossible object
• Proof that 0.999... equals 1
• Logical fallacy
• Puzzle