Paradoxical, a.
1. Of the nature of a paradox.
2. Inclined to paradoxes, or to tenets or notions contrary to received opinions. Southey. -- Par`a*dox"ic*al*ly, adv. -- Par`a*dox"ic*al*ness, n.
Shades of meaning
Fernald has no entry of its own for paradoxical; he lists it under absurd.
Where he writes about it:
A paradoxical statement appears at first thought contradictory or absurd, while it may be really true. — from absurd