Oh okay, I guess that entire paragraph is just a complicated way of rephrasing their claim, which is that there is at least one TM for which no TM can possibly

Oh okay, I guess that entire paragraph is just a complicated way of rephrasing their claim, which is that there is at least one TM for which no TM can possibly answer the halting problem, but for which humans can. So then, the claim is that it's at least conceivable that humans can do this, because you can remove a finite or even infinite number of elements from an infinite set and still be left with an infinite set. I still don't understand how this is a remotely useful insight or in any way an indication that humans may have super-Turing abilities.