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.
- 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