What is the X in X-mas?
1530s, "statement contrary to common belief or expectation," from Middle French paradoxe (14c.) and directly from Latin paradoxum "paradox, statement seemingly absurd yet really true," from Greek paradoxon, noun use of neuter of adjective paradoxos "contrary to expectation, incredible," from para- "contrary to" (see para- (1)) + doxa "opinion," from dokein "to appear, seem, think" (see decent). Meaning "statement that is seemingly self-contradictory yet not illogical or obviously untrue" is from 1560s.
paradox par·a·dox (pār'ə-dŏks')
That which is apparently, though not actually, inconsistent with or opposed to the known facts in any case.
A statement that seems contradictory or absurd but is actually valid or true. According to one proverbial paradox, we must sometimes be cruel in order to be kind. Another form of paradox is a statement that truly is contradictory and yet follows logically from other statements that do not seem open to objection. If someone says, “I am lying,” for example, and we assume that his statement is true, it must be false. The paradox is that the statement “I am lying” is false if it is true.