Paradox 

A paradox is a statement that seems to lead to a logical self-contradiction, or to a situation that contradicts common intuition. The identification of a paradox based on seemingly simple and reasonable concepts has often led to significant advances in science, philosophy and mathematics.

See also:

• Abilene paradox: People take actions in contradiction to what they really want to do, and therefore defeat the very purposes of what they were trying to accomplish.
• Arrow's paradox: You can't have all the attributes of an ideal voting system at once
• Banach-Tarski paradox: Cut a ball into 5 pieces, re-assemble the pieces to get two balls, both of equal size to the first.
• Barber paradox: The barber who shaves all men who don't shave themselves, and no-one else.
• Berry paradox: What is "The first number not nameable in under ten words"?
• Birthday paradox: What is the chance that two people in a room have the same birthday?
• Braess' paradox[?]: sometimes adding extra capacity to a network can reduce overall performance
• Burali-Forti paradox: If the ordinal numbers formed a set, it would be an ordinal number which is smaller than itself.
• Control paradox Man can never be free of control, for to be free of control is to be controlled by oneself.
• Curry's paradox: "If I'm not mistaken, Gödel exists."
• Epimenides paradox: A Cretan says "All Cretans are liars".
• Einstein-Podolsky-Rosen paradox: Can far away events influence each other in quantum mechanics?
• Fermi paradox: If there are many other sentient species in the Universe, then where are they? Shouldn't their presence be obvious?
• Grandfather paradox: You travel back in time and kill your grandfather before he meets your grandmother, resulting in you never being conceived.
• 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
• Hilbert's paradox of the Grand Hotel: If a hotel with infinitely many rooms is full, it can still take in more guests.
• Horse paradox: All horses are the same color.
• Jevons paradox[?]: Energy rebound effect
• Liar paradox: "This sentence is false."
• Moore's Paradox: "It's raining but I don't believe that it is."
• Newcomb's paradox: How do you play a game against an omniscient opponent?
• Olbers' paradox: If the universe is infinite, the sky should be entirely bright because there's a star in every direction.
• Omnipotence paradox: Can an omnipotent being create a rock too heavy to lift? Can an irresistible force move an unmovable object?
• Predestination paradox: A man travels back in time and impregnates his great-great-grandmother. The result is a line of offspring and descendants, including the man's parent(s) and the man himself. Therefore, unless he makes the time-travel trip at all, he will never exist.
• Quine's Liar Paradox[?]: "Yields a falsehood when appended to its own quotation."
• Raven paradox: Observing a red apple increases the likelihood of all ravens being black.
• Richard paradox: A complete list of definitions of real numbers doesn't exist.
• Russell's paradox: Is there a set of all those sets that do not contain themselves?
• Simpson's paradox: Data sets support opposite hypothesis when taken together than when taken separately.
• Sorites paradox: At what point does a heap stop being a heap as I take away grains of sand?
• Twin paradox: When the travelling twin returns, he's younger and older than his brother who stayed put.
• Unexpected hanging paradox: The day of the hanging will be a surprise, so it can't happen at all.
• Voting paradox (Condorcet paradox): Non-transitive collective preferences.
• Weyl's paradox: Is the word "heterodox", meaning "not applicable to itself," a heterodox word?
• Zeno's paradoxes: When you reach the turtle's spot, it has already advanced a bit, so you can never catch it.

See also: Impossible objects

External links:

• Google Directory category: Paradoxes (http://directory.google.com/Top/Society/Philosophy/Philosophy_of_Logic/Paradoxes/)