A paradox is an apparently true statement or group of statements
that seems to lead to a contradiction or to a situation that defies
intuition. Typically, either the statements in question do not
really imply the contradiction, the puzzling result is not really a
contradiction, or the premises themselves are not all really true
(or, cannot all be true together). The recognition of ambiguities,
equivocations, and unstated assumptions underlying known paradoxes
has led to significant advances in science, philosophy and
mathematics.
The word paradox is often used interchangeably and wrongly with
contradiction; but where a contradiction by definition cannot be
true, many paradoxes do allow for resolution, though many remain
unresolved or only contentiously resolved

self-flowing flask fills itself in this diagram, but perpetual
motion machines cannot exist.