Now all imperatives command either hypothetically or categorically.  The former represent the practical necessity of a possible action as means to something else that is willed (or at least which one might possibly will).  The categorical imperative would be that which represented an action as necessary of itself without reference to another end, i. e., as objectively necessary.

Since every practical law represents a possible action as good, and on this account, for a subject who is practically determinable by reason, necessary, all imperatives are formulae determining an action which is necessary according to the principle of a will good in some respects.  If now the action is good only as a means to something else, then the imperative is hypothetical; if it is conceived as good in itself and consequently as being necessarily the principle of a will which of itself conforms to reason, then it is categorical.

Thus the imperative declares what action possible by me would be good, and presents the practical rule in relation to a will which does not forthwith perform an action simply because it is good, whether because the subject does not always know that it is good, or because, even if it know this, yet its maxims might be opposed to the objective principles of practical reason.

Accordingly the hypothetical imperative only says that the action is good for some purpose, possible or actual.  In the first case it is a Problematical, in the second an Assertorial practical principle.  The categorical imperative which declares an action to be objectively necessary in itself without reference to any purpose, i. e., without any other end, is valid as an Apodictic (practical) principle.

Whatever is possible only by the power of some rational being may also be conceived as a possible purpose of some will; and therefore the principles of action as regards the means necessary to attain some possible purpose are in fact infinitely numerous.  All sciences have a practical part, consisting of problems expressing that some end is possible for us, and of imperatives directing how it may be attained.  These may, therefore, be called in general imperatives of Skill.  Here there is no question whether the end is rational and good, but only what one must do in order to attain it.  The precepts for the physician to make his patient thoroughly healthy, and for a poisoner to ensure certain death, are of equal value in this respect, that each serves to effect its purpose perfectly.  Since in early youth it cannot be known what ends are likely to occur to us in the course of life, parents seek to have their children taught a great many things, and provide for their skill in the use of means for all sorts of arbitrary ends, of none of which can they determine whether it may not perhaps hereafter be an object to their pupil, but which it is at all events possible that he might aim at; and this anxiety is so great that they commonly neglect to form and correct their judgment on the value of the things which may be chosen as ends.