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Definition of paradox : 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.

Synonyms:

puzzle, conundrum, mystery, riddle, ambiguity, error, enigma, problem, mistake

contradiction, silliness, absurdity, baloney, outlandishness, idiocy, inanity, eccentricity, ludicrousness, folly, meaninglessness, bizarreness, implausibility, craziness, anachronism, incongruity, impossibility, invalidity, irrationality, nonsense, inconsistency, farce, preposterousness, balderdash, foolishness, self-contradiction

Usage examples:

• " If you don't, you'll have to," replied Peckover with truth underlying paradox. - "A Poached Peerage", William Magnay.
• But if I may use a paradox, it is the important half, the primary half. - "Preaching and Paganism", Albert Parker Fitch.
• Here is a crying sin- an infernal paradox. - "The Call of the Canyon", Zane Grey.