"paradoxical fact" is correct and usable in written English.
You can use it when referring to an odd or contradictory truth. For example, "The paradoxical fact that we can't always have what we want is one of life's greatest lessons."
At 74, he is an American institution, the paradoxical fact of an anti-orthodox career.
The most important and paradoxical fact shaping the future of online learning is this: A brain is not a computer.
The other is the paradoxical fact that technology has made it easier to print letterpress than ever before.
They reveal an equally true, if paradoxical, fact about segregation: blacks and whites mixed constantly, as the needs of employment, work or even play demanded.
Medieval thinkers were aware of the paradoxical fact that line segments of varying lengths seemed to have the same number of points.
At the heart of all of this is the paradoxical fact that an article such as Lammy's will only serve to further alienate a proportion of the population who already doubted their ability to be accepted.
The world's political landscape reveals not only the paradoxical facts of profound interconnectedness and great inequality, but also a vivid panorama of fresh resistance and struggles -- against the despotism of Putin, but also against such elected and evidently successful stewards of national economies as Rousseff in Brazil and Erdogan in Turkey.
Although this observation at first seems paradoxical, in fact, it provides strong support for recent hypotheses that structural plasticity and conformational changes are involved in the arrestin rhodopsin binding interface and that the two proteins may be able to interact through multiple docking modes, with arrestin binding to both monomeric and dimeric rhodopsin.
Patrick Maher, in "Inductive Logic and the Ravens Paradox" (1999), argues that the conclusion of the Ravens paradox is in fact not paradoxical, and that its appearance as such is deceptive.
"Africa has been for a long time a chronically food insecure place, which is paradoxical because in fact it has a lot more productive capacity.
The situation is made more paradoxical by the fact that the Breuer building exists in a comfortable relationship to the five brownstones beside it (which would be demolished to make way for the Graves addition), even though those brownstones are more completely different from the Breuer building than anything Michael Graves has ever proposed.
