 The Duty Argument employs the box and diamond in the standard fashion as operators for, respectively, conceptual necessity and possibility. The alpha is just a placeholder for actions, or kinds of actions. The locution “(overall) rational” or “(overall) irrational” presupposes that there are various kinds of rationality, including moral rationality, epistemic rationality, and prudential  rationality.[10]  The idea that there are various kinds of rationality, or put any way, that one can be under conflicting obligations at a particular time, recognizes that dilemmas are possible. One can be obligated to do various things even when it’s not possible to do all of them. Overall rationality is the all-things-considered perspective. It is what one ultimately should do, having taken into account the various obligations one is under at a particular time. Overall rationality, or all-things-considered rationality (ATC rationality), is, in W.D. Ross’s terms, one’s actual duty in the particular circumstances, even if one has other conflicting prima facie duties. The Duty Argument can be formulated without presupposing that there are various kinds of rationality, by replacing the principle that no one is ever irrational in doing her moral duty, with the principle that moral obligations take precedence whenever a dilemma of obligations occurs. In any case the Duty Argument assumes that if in doing something one is not ATC irrational, then it follows that one is ATC rational in doing it.