Did you get as far as this in McGinn's paper?
"Should we say that the mind-body problem is onlyrelatively closed or is the closure absolute? This depends on what we allow as a possible concept-forming mind, which is not an easy question. If we allow for minds that form their concepts of the brain and consciousness in ways that are quite independent of perception and introspection, then there may be room for the idea that there are possible minds for which the mind-body problem is soluble, and easily so. But if we suppose that all concept formation is tied to perception and introspection, however loosely, then no mind will be capable of understanding how it relates to its own body—the insolubility will be absolute. I think we can just about make sense of the former kind of mind, by exploiting our own faculty of a priori reasoning. Our mathematical concepts (say) do not seem tied either to perception or to introspection, so there does seem to be a mode of concept formation that operates without the constraints I identified earlier. The suggestion might then be that a mind that formed all of its concepts in this way—including its concepts of the brain and consciousness—would be free of the biases that prevent us from coming up with the right theory of how the two connect. Such a mind would have to be able to think of the brain and consciousness in ways that utterly prescind from the perceptual and the introspective—in somewhat the way we now (it seems) think about numbers. This mind would conceive of the psychophysical link in totally apriori terms. Perhaps this is how we should think of God's mind, and God's understanding of the mind-body relation. At any rate, something pretty radical is going to be needed if we are to devise a mind that can escape the kinds of closure that make the problem insoluble for us—if I am right in my diagnosis of our difficulty. If the problem is only relatively insoluble, then the type of mind that can solve it is going to be very different from ours and the kinds of mind we can readily make sense of(there may, of course, be cognitive closure here too). It certainly seems tome to be at least an open question whether the problem is absolutely insoluble; I would not be surprised if it were."
I'm not sure he's right about how we think of math...see Lakoff and Nunez...but if so or if there are otherwise minds such as he describes, how does this answer to
@Soupie's "self reference" and
@Michael Allen 's broader skepticism?