How exactly does someone observe the "unobservable"? How could one come to confidently believe in a realm built up out of "unempirical" content?
If anyone can satisfactorily answer these questions, chances are they have done science, and discovered that the unempirical content everyone was talking about was scientifically describable after all, unique from other science only in its being particularly difficult to apprehend.
Until we get there, this unempirical component of consciousness being posited shares common heritage with the Luminiferous aether, the life-force, hollow earth theory, mythic gods of natural forces and any number of premature theories which hover in the closing gaps of indeterminacy before a science comes along to explain them.