The fact that Greeks made great advances in mathematics before quantum mechanics became possible, and that sophisticated physiology required breakthroughs in physics and chemistry, demonstrates that there is a 'cunning of the insane'—a profound brilliance in Comte's hierarchical organization of the sciences.

The problem of positivistic moral and political theory is the Achilles heel of positivism; all great empiricists and positivists face the challenge of grounding ethics and morality in a purely naturalistic worldview without metaphysical or transcendent foundations.

Comte's thinking is long, ponderous, and not terribly accessible, and towards the end of his life he suffered a mental breakdown that makes his work appear pathological and self-parodying.

Despite his difficulties in reception, Comte's early work is profound and brilliant and has had an almost incalculably important influence on the philosophy of science, history of science, and development of social science in the modern West.

Although utopian socialism's solutions are generally unsatisfactory (and Comte's especially so), the questions it raises about new problems generated by industrialization remain valid and must be reformulated, as they are concomitant with the world we live in.

All technocratic tendencies in modern politics—decisions made by technical experts rather than democratic majorities—owe something to Comte; they represent a practical implementation of his vision of rule by scientific experts.

Unlike later Vienna Circle reductionists, Comte does not reduce all disciplines to physics; rather, he holds that each discipline must develop its own canons of reasoning and procedures for developing legitimate knowledge, though all study the same reality and have logical and ontological divisions corresponding to natural kinds.

Comte's two great political mottos are 'order' and 'progress'—order representing the static immobility of feudal Europe that he finds attractive, and progress representing necessary change, with his political theory attempting to enable progress without the convulsive disorder of religious wars or the French Revolution.

Many contemporary social scientists are indebted to Comte but do not realize it, and yet his work does not appear on many great books curricula despite being quite influential on modern social science.

Comte's polymathic intellect gave him expertise across all scientific disciplines of his time—he was an adept mathematician, well-versed in physics, biology, and chemistry—allowing him to synthesize and unify the sciences under one intellectual structure.

Comte's project is to synthesize and logically organize all the natural sciences developed since the age of Copernicus and Galileo, with the ontological presupposition that nature is all there is, so that once the natural sciences are unified and logically organized, all knowledge is organized.

The French Revolution was a major influence on Comte's thought; he disliked revolutionary convulsions and viewed the Revolution as an example of what must be avoided in future political progress, yet he wanted to allow for salutary changes without accompanying misery.

Comte's philosophy of history has resonances with Vico's stages (age of gods, age of heroes, age of men) and shares the idea that knowledge development follows necessary triadic patterns across all cultures.

Comte was always an intellectual outsider, never able to get a university post due to his naturalistic inclinations, reactionary political views, and personal psychological problems; instead he gave lectures from his apartment in an intellectual salon over 12 years, which were occasionally interrupted by psychotic breaks.

Comte's mental gifts and mental diseases grew apace, causing him to become increasingly the object of ridicule; within France he had almost no influence, but his influence was significant among scattered intellectuals in various countries and periphery areas outside metropolitan Western culture.

Comte's first major work, the six-volume Course on Positive Philosophy (formulated 1830-1842), reformulates his home lectures and covers all natural science, which he understands as all science and all knowledge, by collapsing psychology into behavioral sciences and all social science into a new discipline he calls sociology.

In Comte's three-stage theory, all elements of human knowledge—mathematics, astronomy, physics, chemistry, physiology (understood as subsumable to behavioristic psychology), and sociology—go through three necessary stages of development, with sociology as the final stage representing human self-consciousness.

The theological (or mythological) phase is the earliest phase of human knowledge, in which knowledge is bound up with myth, and anthropomorphic entities and intentionality are attributed to natural phenomena; examples include ancient astronomy fused with astrology and early physics couched in mythology.

Mathematical knowledge in the early theological stage was conceived as divinely ordained; when Pythagoras discovered the Pythagorean theorem, he sacrificed an ox to Apollo because mathematical knowledge was believed to come from the gods.

In the theological phase, magic thinking attributes intentionality and responsibility to objects; ancient Greeks could hold a statue responsible if it fell on someone, a holdover from magical thinking about the attribution of agency to inanimate objects.