The word "duty" is used in philosophy as a synonym for moral obligation, As so sued it requires us to understand wrong and right uses of the phrase "categorical imperatives." Immanuel Kant's use of that phrase is an instance of extreme rationalism in moral philosophy. (See Casuistry.) A truly categorical imperative is one that is self-evident. It is derived from the understanding of prescriptive truth.
All the main propositions of moral philosophy are prescriptive rather than descriptive. They are statements of what ought or ought not to be sought and done. In short, they are statements of our moral obligations or duties.
The one categorical imperative is that we ought to seek everything that is really good for us, and nothing else. Seeking goods that are merely apparent goods is permissible, but not obligatory.
The categorical imperative, or first principle of moral philosophy, is self-evident. It is impossible to think that we ought not to seek what is really good for us, or that we ought to seek what is really bad for us. The words "really good " and "really bad complicate the words "ought" and "ought not."
If a moral philosophy is formulated entirely in terms of ends and means, it is utilitarian or pragmatic. It is an ethics without duties or moral obligation. The word "deontological" is philosophical jargon for an ethics or moral philosophy the principles of which are imperatives that prescribe duties.
The moral philosophy of Immanuel Kant is wholly deontological. It rejects what Kant calls "the serpentine windings of utilitarianism." J. S. Mill's Utilitarianism contains the opposite error: it is purely pragmatic, and has great difficulty with the notion of duty or moral obligation.