Comte's work has two aims: first, to provide a philosophical foundation for sociology (or "social physics"), and second, to provide an organizational scheme for all of "positive" knowledge (mathematics, astronomy, physics, chemistry, and biology).

Essential to this work was Comte's development of "the law of three stages," which describes what he thought was a kind of intellectual progression common to all human thought. These stages are the theological, the metaphysical, and the positive. The theological stage, in Comte's view the starting point of human thought, assigns creation to supernatural agents: the world was created by God (or gods). The metaphysical stage is a transitory stage, in which the role of God is replaced by abstract ideas (examples include the Reformation, the Renaissance, and the Enlightenment). This "negative state" is finally replaced by the final, "positive" stage, in which the question of first causes is replaced by understanding fundamental laws that govern these principles.

Comte organized the sciences in the order in which they developed, and from abstract to particular. Mathematics begins the hierarchy as the most abstract and fundamental science, followed by astronomy, physics, chemistry, biology, and, finally, sociology. Comte regarded sociology as the "final" science, in which the laws that govern human interactions are discovered, replacing the certainty of the theological stage with the relativism of humanity. Sociology therefore is the "result" of all the other sciences, the one science that is truly universal, and which, by virtue of its place at the apex of human knowledge, recapitulates the whole of human thought.