Paradox• a seemingly absurd or contradictory statement or proposition which when investigated may prove to be well founded or true.
“the uncertainty principle leads to all sorts of paradoxes, like the particles being in two places at once”
• synonyms: contradiction, contradiction in terms, self-contradiction, inconsistency, incongruity, anomaly, conflict;
• a statement or proposition which, despite sound (or apparently sound) reasoning from acceptable premises, leads to a conclusion that seems logically unacceptable or self-contradictory.
“the liar paradox”
• a person or thing that combines contradictory features or qualities.
“cathedrals face the paradox of having enormous wealth in treasures but huge annual expenses”
Mid 16th century (originally denoting a statement contrary to accepted opinion): via late Latin from Greek paradoxon ‘contrary (opinion)’, neuter adjective used as a noun, from para- ‘distinct from’ + doxa ‘opinion’.
(from Oxford Dictionary + Merriam-Webster Dictionary)