paradox

American Heritage® Dictionary of the English Language, Fourth Edition

1. n. A seemingly contradictory statement that may nonetheless be true: the paradox that standing is more tiring than walking.
2. n. One exhibiting inexplicable or contradictory aspects: "The silence of midnight, to speak truly, though apparently a paradox, rung in my ears” ( Mary Shelley).
3. n. An assertion that is essentially self-contradictory, though based on a valid deduction from acceptable premises.
4. n. A statement contrary to received opinion.

Century Dictionary and Cyclopedia

1. n. A statement or proposition which at first view seems absurd, or at variance with common sense, or which actually or apparently contradicts some ascertained truth or received opinion, though on investigation or when explained it may appear to be well founded. As a rhetorical figure its use is well exemplified in the first quotation.
2. n. The platypus or water-mole, Ornithorhynchus paradoxus.

Wiktionary

1. n. A self-contradictory statement, which can only be true if it is false, and vice versa. transl. usage
2. n. A counterintuitive conclusion or outcome. usage syn.
3. n. A claim that two apparently contradictory ideas are true. transl.
4. n. A person or thing having contradictory properties. syn. transl.
5. n. An unanswerable question or difficult puzzle, particularly one which leads to a deeper truth. usage syn.
6. n. obsolete A statement which is difficult to believe, or which goes against general belief.
7. n. uncountable The use of counterintuitive or contradictory statements (paradoxes) in speech or writing.
8. n. uncountable, philosophy A state in which one is logically compelled to contradict oneself.
9. n. uncountable, psychotherapy The practice of giving instructions that are opposed to the therapist's actual intent, with the intention that the client will disobey or be unable to obey. syn.

GNU Webster's 1913

1. n. A tenet or proposition contrary to received opinion; an assertion or sentiment seemingly contradictory, or opposed to common sense; that which in appearance or terms is absurd, but yet may be true in fact.

WordNet 3.0

1. n. (logic) a statement that contradicts itself