A paradox is an apparently true statement or group of statements that leads to a contradiction or a situation which 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.
Common themes in paradoxes include direct and indirect self-reference, infinity, circular definitions, and confusion of levels of reasoning.
For more information about the topic Paradox, read the full article at Wikipedia.org, or see the following related articles:
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