 And, of course, (9) and (11) are contradictory. So if we assume PC and PD, then the existence of dilemmas generates an inconsistency of the old-fashioned logical sort. (Note: In standard deontic logic, the ‘\(\Box\)’ in PD typically designates logical necessity. Here I take it to indicate physical necessity so that the appropriate connection with premise (3) can be made. And I take it that logical necessity is stronger than physical necessity.)