As a human this explanation is emotionally satisfying. It appeals to my sense of human exceptionalism. However how many true but unprovable theorems do we know about? Has anyone ever bothered to compile a list of true but unprovable under the axioms xyz? I would think it is exceedingly hard to manage such research as every axiom set xyz would require companion axioms abc to be provable, and such theorems (at least the non-trivial interesting ones) are possibly hard to reach.
This intuition for unprovableness may just be a mechanism for escaping local minima that gets lucky often enough.
This intuition for unprovableness may just be a mechanism for escaping local minima that gets lucky often enough.