See paradox in Webster's New World College Dictionary
noun
Archaic a statement contrary to common belief
a statement that seems contradictory, unbelievable, or absurd but that may be true in fact (Ex.: “Water, water, everywhere, nor any drop to drink”)
a statement that is self-contradictory and, hence, false
a person, situation, act, etc. that seems to have contradictory or inconsistent qualities
See paradox in American Heritage Dictionary 4
(părˈə-dŏksˌ)
noun
A seemingly contradictory statement that may nonetheless be true: the paradox that standing is more tiring than walking.
One exhibiting inexplicable or contradictory aspects: “The silence of midnight, to speak truly, though apparently a paradox, rung in my ears”(Mary Shelley).
An assertion that is essentially self-contradictory, though based on a valid deduction from acceptable premises.