Wikipedia: Paradox

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*Simpson's paradox: data sets support opposite hypothesis when taken together than when taken separately.

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*[Zeno's paradoxes]?: when you reach the turtle's spot, it has already advanced a bit, so you can never catch it.

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.
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.