And if we do use implication to stand for this relation, we, of course, got the apparently paradoxical results that every false proposition implies every other proposition, both true and false, and that every true proposition implies every other true proposition: since it is quite clear that if is false then, whatever may be, it is not the case that is true and false, and quite clear also, that if and are both true, then also it is not the case that is true and false.