France had got rid of a king, a republic and an empire inside twenty-five years, and had settled on nothing. Each new constitution was written against the last one. The old order — Catholic, hereditary, answerable to God — was intellectually finished, and the philosophy that had finished it, with its natural rights and its social contracts, could demolish but not build. The diagnosis that made Comte's name was that none of this was a political failure at all. Societies hold together on shared conviction, and Europe had none left; no arrangement of ministries would stick until people agreed again about what is true. Opinion had to be settled the way it had been settled in astronomy and chemistry — by evidence no faction could vote down.
He laid out the whole programme in May 1822, at twenty-four, in a pamphlet he would still be calling his fundamental work thirty years later. He had no qualification to write it: the École Polytechnique closed for reorganisation in 1816 and dismissed its students, he never asked to be readmitted when it reopened, and he never took a degree. What he had instead was employment as secretary to the reforming aristocrat Henri de Saint-Simon, from whom he took the idea that industrial society needed a new spiritual power, and from whom he parted bitterly in 1824.
The claim underneath everything he wrote is compact enough to carry away: human explanation passes through three stages, and the study of society is the last thing to reach the third. In the theological stage, events happen because a will wants them to. In the metaphysical, wills give way to abstractions — nature, essence, the rights of man — which explain no better. In the positive stage, the question why is dropped: what remains is to describe the constant relations between observable facts and use them to predict. The sciences had crossed over in order of difficulty — astronomy, then physics, chemistry, biology. Society was the most complex case, therefore the last, therefore still in the hands of theologians and lawyers. Comte proposed to end that, and in the Cours de philosophie positive, in 1839, he coined the word sociology, having abandoned "social physics" after the statistician Adolphe Quetelet took it for his own.
Executing the programme nearly destroyed him. He opened a public course in 1826 to an audience that included Fourier, Poinsot and Alexander von Humboldt, delivered three lectures, and collapsed; in the fourth week the doors were shut. He was hospitalised, and in 1827 he went into the Seine from the Pont des Arts and was pulled out. He restarted the course in 1829 and finished the six volumes in 1842. From 1838 he practised what he called cerebral hygiene, refusing to read other people's work so that the system would stay his own — a discipline and a wall at once. He was never made a professor. His examinership at the Polytechnique was not renewed in 1844, costing him half his income, and the last post went in 1852; he lived after that on subscriptions raised by admirers, first English ones including John Stuart Mill, later French.
Then, in 1844, he met Clotilde de Vaux, who died in April 1846, and everything turned. The second half of his life went into a Religion of Humanity, with a calendar of secular saints, sacraments modelled on the Catholic ones, and Comte as its high priest. Mill, who had done more than anyone to make him readable in English, denounced the result as a blueprint for despotism. Émile Littré, his closest French disciple, broke with him in 1852, over the religion and over Comte's welcome for Louis-Napoleon's coup.
He died in Paris in September 1857. The split those two men made — the rigorous early Comte against the late prophet — is still the argument scholars have about him, and the case for continuity is serious. What outlasted the system was the discipline, the word, and the assumption that claims about how societies work must answer to evidence. His churches dwindled but never quite closed: the chapel in Paris survives, positivist temples still stand in Porto Alegre, Curitiba and Rio de Janeiro, and Brazil put his motto of order and progress on its flag in 1889 and has not taken it off.