what you need to understand about the halting problem is that at is core it is an epistemological problem. An other expresion of it are Gödel's incompleteness theorems. Imagine a blank sheet of paper the area of the paper is what is knowable now start building logic as a data structure. We start with the first nodes which are the axioms now everything derived conects to other nodes etc as it expands as mold its going to cover some of the paper but wont be able to cover all. So the danger here is that computers are living on that fractal dimension and will never be able to see outside of it but us human beings have as kurt said intuition. The fact that we can find this paradoxes in logic means that our brains operate on a higher dimension and that computers will allways have blind spots.