ad. In a paradoxical manner; so as to create a paradox.
The Century Dictionary and Cyclopedia
In a paradoxical manner, or in a manner seemingly absurd or contradictory; in such a way or sense as to involve an apparent contradiction or absurdity.
WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
ad. in a paradoxical manner
Word Usage
"The proof of this, paradoxically, is that nobody can find any proof (or their assets) - such is the alchemic cleverness of our Mr. Big."