Positivism is Auguste Comte's program for finishing the Enlightenment: if the natural sciences have escaped theology and metaphysics by confining themselves to observable regularities, then the study of society can do the same, and the resulting knowledge can be used to govern.
Comte's law of three stages holds that every branch of knowledge passes from theological explanation, through metaphysical abstraction, to the positive stage of ascertained relations between phenomena. Sociology — his word — is the last science to make the passage, and the most important, because it alone can supply the principles on which industrial society might be reorganized after the collapse of the old religious order. His late proposal of a Religion of Humanity, with a calendar of secular saints and a priesthood of sociologists, was ridiculed even by admirers, but it is the honest expression of the ambition: positive knowledge was to do the work that faith had done.
Durkheim made the method serious. Treating social facts as things — external to the individual, exercising constraint, and explicable only by other social facts rather than by psychology — he turned the program into a research discipline, and Suicide (1897) demonstrated that even the most private act shows regularities that belong to the group rather than the person.
The political inheritance is double-edged and runs everywhere. Technocratic government, evidence-based policy and the authority of the expert all descend from the claim that society yields to scientific study; so does the standing objection, pressed by Weber, the Frankfurt School and Hayek alike, that treating a society as an object of administration mistakes what kind of thing it is.