A normative science is one which studies what ought to be. How then does it differ from engineering, medicine, or any other practical science? If, however, logic, ethics, and esthetics, which are the families of normative science, are simply the arts of reasoning, of the conduct of life, and of fine art, they do not belong in the branch of theoretic science which we are alone considering, at all. There is no doubt that they are closely related to three corresponding arts, or practical sciences. But that which renders the word normative needful (and not purely ornamental) is precisely the rather singular fact that, though these sciences do study what ought to be, i.e., ideals, they are the very most purely theoretical of purely theoretical sciences.
It is pretty generally admitted that logic is a normative science, that is to say, it not only lays down rules which ought to be, but need not be followed; but it is the analysis of the conditions of attainment of something of which purpose is an essential ingredient. It is, therefore, closely related to an art; from which, however, it differs markedly in that its primary interest lies in understanding those conditions, and only secondarily in aiding the accomplishment of the purpose.
Philosophy has three grand divisions. [—] The second grand division is Normative Science, which investigates the universal and necessary laws of the relation of Phenomena to Ends, that is, perhaps, to Truth, Right, and Beauty.
Normative Science treats of the laws of the relation of phenomena to ends; that is, it treats of Phenomena in their Secondness.
There are sundry other widely spread misconceptions of the nature of Normative Science. One of these is that the chief, if not the only, problem of Normative Science is to say what is good and what bad, logically, ethically, and esthetically; or what degree of goodness a given description of phenomenon attains. Were this the case, normative science would be, in a certain sense, mathematical, since it would deal entirely with a question of quantity. But I am strongly inclined to think that this view will not sustain critical examination. Logic classifies arguments, and in doing so recognizes different kinds of truth. In ethics, too, qualities of good are admitted by the great majority of moralists. As for esthetics, in that field qualitative differences appear to be so prominent that, abstracted from them, it is impossible to say that there is any appearance which is not esthetically good.
Philosophy is divided into (a) Phenomenology; (b) Normative Science; (c) Metaphysics.
Phenomenology ascertains and studies the kinds of elements universally present in the phenomenon; meaning by the phenomenon, whatever is present at any time to the mind in any way. Normative science distinguishes what ought to be from what ought not to be, and makes many other divisions and arrangements subservient to its primary dualistic distinction. Metaphysics seeks to give an account of the universe of mind and matter. Normative science rests largely on phenomenology and on mathematics; metaphysics on phenomenology and on normative science.
Normative science considers the phenomenon only so far as it can be controlled, compares purpose with performance, and ascertains the general principles of the relation between them.
This quote has been taken from Kenneth Laine Ketner's 1983 reconstruction of Peirce's 'Autobiography'
Normative science is that science which considers any kind of excellence, and endeavors to formulate the conditions under which an object would possess that excellence, without undertaking to say whether given objects possess that excellence or not.
The normative sciences are wholly said to be esthetics, ethics, and logic; but Herbart and others put esthetics & ethics together, perhaps rightly. They are all largely & I may say principally occupied with a dual distinction, the distinction of the approved and the unapproved. Esthetics relates to the immediately contemplated; ethics to doings; logic to thought. [—] It is not very easy to seize the exact meaning of the phrase normative science. It means the science of the approvable and unapprovable, or better the blameable and the unblameable.
These sciences are distinguished from most others by involving the dual distinction. But it would be easy to exaggerate its prominence in them. This prominence is greatest in ethics, least in esthetics.
The Normative Sciences, Esthetics, Ethics, and Logic, […] are confined respectively to ascertaining how Feeling, Conduct, and Thought ought to be controlled supposing them to be subject in a measure, and only in a measure, to self-control, exercised by means of self-criticism, and the purposive formation of habit, as common sense tells us they are in a measure controllable.
A normative science may be defined as the theory of the facultative conditions under which a desirable result may be brought about. It necessarily has practical applications; but it is not necessarily studied mainly with reference to these, or with a view to the economies of the problem.