You and I are speaking about two very different things. The incompleteness theorems and the halting problem (which are deeply connected, by the way) are positiv

You and I are speaking about two very different things. The incompleteness theorems and the halting problem (which are deeply connected, by the way) are positive proofs. I am speaking of a negative proof. Imagine that I believe in Bigfoot. How shall I be dissuaded from my belief by evidence -- it would have to be negative proof. If I started out assuming Bigfoot wasn't real, that would be much, much easier. In the same way, people assume that logical incompleteness isn't real until there's positive evidence. They assume there's no halting problem until there's positive evidence. See the difference?