> if we make him write it down (as a computer program)
He did. Diagonalization is an algorithm. It's a non-halting algorithm (because it operates on infinite input and produces infinite output) but it is nonetheless a perfectly well defined algorithm that can be implemented by a Turing Machine.
> we can always (eventually) find a program which will trick it
He did. Diagonalization is an algorithm. It's a non-halting algorithm (because it operates on infinite input and produces infinite output) but it is nonetheless a perfectly well defined algorithm that can be implemented by a Turing Machine.
> we can always (eventually) find a program which will trick it
No, you can't.