Actually, this comment makes sense and is used in logic to derive true but non-provable propositions withing the current axiom system assuming it is sound. The

Actually, this comment makes sense and is used in logic to derive true but non-provable propositions withing the current axiom system assuming it is sound. The problem is that you dont know if the checker that you use to detect if a program halts will itself halt on your given input or continue forever. But given a sound checker with some assumption, one can find non-halting programs which wont be detected by the checker using the diagonalization trick.