` :It's not an argument.  The diagonal argument doesn't have programs ``T`` and ``H`` running on the same machine, we have (more-or-less) ``H`` emulating ``T``.  If there isn't a ``universal`` program (a program on the machine which can emulate, step-by-step, any program on the machine), then the precise diagonal argument doesn't apply.  Most people in the field consider such a machine ``uninteresting``.  —    `