How did John Stuart Mill’s positivism differ from Auguste Comte’s?

While both Auguste Comte and John Stuart Mill are regarded as central figures in the development of positivism, their philosophical approaches contained significant differences.

Auguste Comte’s positivism was defined by his "law of the three phases," which posited that human intellectual development progresses from theological and metaphysical stages to a final, mature "scientific" or "positive" stage. He sought to organize the sciences into a hierarchical pyramid, with sociology at the pinnacle, and he was deeply skeptical of introspection, viewing it as a distortion of mental states. Furthermore, Comte’s later work emphasized morality and social organization, eventually leading him to establish a secular religion centered on the worship of humanity.123

In contrast, John Stuart Mill maintained a more strictly empiricist theory of knowledge. While Comte excluded psychology from his system of sciences, Mill’s approach in his System of Logic was characterized by a thoroughgoing empiricism that even classified logic and mathematics as empirical sciences derived from massive experience, rather than as purely formal or a priori disciplines. Mill’s positivism lacked the rigid hierarchical system and the religious dimensions that Comte developed in his later years.142