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A paradox is a statement or concept that contains conflicting ideas. In logic, a paradox is a statement that contradicts itself; for example, the statement I never tell the truth is a paradox because if the statement is true (T), it must be false (F) and if it is false (F), it must be true (T).
Definition of paradoxical. 1a : of the nature of a paradox the paradoxical theory that global warming will lead to the next Ice Ageb : inclined to paradoxes. 2 : not being the normal or usual kind a paradoxical pulse paradoxical drug reactions.