Now arises the question, how are all these imperatives possible? This question does not seek to know how we can conceive the accomplishment of the action which the imperative ordains, but merely how we can conceive the obligation of the will which the imperative expresses. No special explanation is needed to show how an imperative of skill is possible. Whoever wills the end, wills also (so far as reason decides his conduct) the means in his power which are indispensably necessary thereto. This proposition is, as regards the volition, analytical; for, in willing an object as my effect, there is already thought the causality of myself as an acting cause, that is to say, the use of the means; and the imperative educes from the conception of volition of an end the conception of actions necessary to this end. Synthetical propositions must no doubt be employed in defining the means to a proposed end; but they do not concern the principle, the act of the will, but the object and its realization. E.g., that in order to bisect a line on an unerring principle I must draw from its extremities two intersecting arcs; this no doubt is taught by mathematics only in synthetical propositions; but if I know that it is only by this process that the intended operation can be performed, then to say that, if I fully will the operation, I also will the action required for it, is an analytical proposition; for it is one and the same thing to conceive something as an effect which I can produce in a certain way, and to conceive myself as acting in this way.