Paradox

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.

See also:

• 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.