noun

• (obsolete) A statement which is difficult to believe, or which goes against general belief.
  "Ay, truly; for the power of beauty will sooner / transform honesty from what it is to a bawd than the / force of honesty can translate beauty into his / likeness: this was sometime a paradox, but now the / time gives it proof."
• (uncountable) The use of counterintuitive or contradictory statements (paradoxes) in speech or writing.
  "The need for paradox is no doubt rooted deep in the very nature of the use we make of language."
• (uncountable, philosophy) A state in which one is logically compelled to contradict oneself.
  "Thus, like modern disputants, they aimed either to confute the respondent or to land him in paradox."
• (countable, 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.
  "Defiance-based paradox is employed so that the family will actively oppose and deliberately sabotage the prescription."