A paradox is a statement that seems to lead to a logical self-contradiction. The identification of a paradox based on seemingly simple and reasonable concepts has often lead to siginificant advances in science, philosophy and mathematics.
- Banach-Tarski paradox: cut a ball into 5 pieces, reassemble the pieces to get two balls.
- Epimenides paradox: a Cretan says "all Cretans are liars".
- Liar paradox: this statement is false.
- Olbers' paradox: the sky should be bright because there's a star in every direction
- Russell's paradox: the barber who shaves all people who don't shave themselves.
- Simpson's paradox: data sets support opposite hypothesis when taken together than when taken separately.
- Voting paradox: non-transitive collective preferences.
- Zeno's paradoxes: when you reach the turtle's spot, it has already advanced a bit, so you can never catch it.