What is a paradox?

What is a paradox? Here are some definitions.

Noun
  1. An apparently self-contradictory statement, which can only be true if it is false, and vice versa. transl. usage
  2. A counterintuitive conclusion or outcome. usage syn.
  3. A claim that two apparently contradictory ideas are true. transl.
  4. A thing involving contradictory yet interrelated elements that exist simultaneously and persist over time.
  5. A person or thing having contradictory properties. syn. transl.
  6. An unanswerable question or difficult puzzle, particularly one which leads to a deeper truth. usage syn.
  7. (obsolete) A statement which is difficult to believe, or which goes against general belief.
  8. (uncountable) The use of counterintuitive or contradictory statements (paradoxes) in speech or writing.
  9. (philosophy) A state in which one is logically compelled to contradict oneself.
  10. (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.
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