This Day in Philosophy — 5 September: Comte and Boltzmann, the founder and the casualty of the faith in science

Two deaths, forty-nine years apart, on the same date. Between them lies the whole arc of the nineteenth century's faith in science: its confident announcement, and the cost paid by one of the men who did the actual work.

Auguste Comte died in Paris on 5 September 1857. Ludwig Boltzmann hanged himself at Duino, near Trieste, on 5 September 1906.

Comte: the law of three stages#

Comte gave the age its self-description. In the Course of Positive Philosophy, delivered as lectures from 1830, he set out what he called the law of three stages: human thought passes through a theological stage, then a metaphysical one, and arrives at the positive.

The distinction turns on the kind of question asked.

In the theological stage we explain events by the will of persons — gods, spirits. In the metaphysical stage the persons are replaced by abstractions: essences, natures, forces, "the vital principle". In the positive stage we abandon the search for ultimate causes altogether and confine ourselves to the laws connecting observable phenomena.

The crucial move is that last renunciation. Positive science does not ask why bodies fall; it establishes how they fall, and with what regularity. The question "why" is not answered but retired.

Sociology#

From that scheme follows the project for which Comte is best remembered. If every domain of phenomena passes through the three stages, one domain has not yet arrived: human society itself.

Comte proposed a science of society on the model of the physical sciences, and gave it a name that stuck — sociology. He arranged the sciences in a hierarchy from mathematics up through astronomy, physics, chemistry and biology, with sociology at the summit as the most complex and the last to mature.

The strange second half#

What is usually left out of the textbook account is what Comte did next.

In his later years he designed a Religion of Humanity: a positivist cult with a calendar of secular saints, temples, sacraments and a priesthood, with Humanity itself as the object of worship. He named himself its high priest.

John Stuart Mill, who had championed Comte's early work, was appalled. Thomas Huxley's verdict became famous: Comtism was "Catholicism minus Christianity".

The episode is not merely biographical curiosity. It exposes a tension inside positivism itself. If science retires the question of ultimate ends, something has to occupy the space that question leaves. Comte, unusually, admitted the vacancy and tried to fill it deliberately.

Boltzmann: the man who defended atoms#

Half a century later, a physicist was destroyed by the other side of the same problem.

Ludwig Boltzmann built statistical mechanics. His central achievement was to explain the second law of thermodynamics — the increase of entropy — in terms of probability: a system moves toward the macroscopic state that can be realised by the greatest number of microscopic arrangements. The formula S = k log W is cut into his gravestone in Vienna.

The explanation depends on atoms being real.

And that was precisely what a powerful group of his contemporaries denied. Ernst Mach and Wilhelm Ostwald held that science should confine itself to what is observable. Nobody had seen an atom. Atoms were, at best, a useful calculating device — a fiction that helped the equations work.

The position was rigorous positivism, and it was applied against Boltzmann with force. He spent years in a public argument he found exhausting, convinced that his life's work was being dismissed as metaphysics.

He suffered from what would now be recognised as severe depression, and he killed himself while on holiday with his family in 1906.

Within a few years the argument was settled against Mach. Einstein's 1905 paper on Brownian motion and Jean Perrin's experiments established the reality of atoms beyond reasonable doubt. Ostwald conceded. Boltzmann did not live to see it.

The two halves of one question#

Comte and Boltzmann stand on opposite sides of the same problem, and that is what makes the coincidence of the date worth pausing on.

Comte asked science to stop at observable regularities. Boltzmann's physics required him to postulate entities nobody could observe — and it turned out to be right.

The question is still live, and the site has covered its current form. It is the argument between scientific realism and its critics: does a successful theory describe an unobservable reality, or is it merely empirically adequate? Bas van Fraassen's constructive empiricism, honoured with the 2026 Rolf Schock Prize, is the most careful modern descendant of Mach's caution — with the crucial difference that van Fraassen grants that theories about unobservables are meaningful, and only suspends belief in them.

Boltzmann's case is the standard cautionary tale told against strict empiricism. It is worth adding the other half: the same caution, applied elsewhere, has protected science from a great deal of nonsense. Neither side of this argument has a clean record.

Also on this date#

Tommaso Campanella was born at Stilo in Calabria on 5 September 1568. A Dominican friar, he spent twenty-seven years in Neapolitan prisons after a failed revolt, and wrote The City of the Sun there — a utopia governed by a priest-philosopher, with knowledge painted on the city's concentric walls so that citizens learn simply by walking through it. He also wrote the Apologia in defence of Galileo, from a cell.

Sarvepalli Radhakrishnan was born on 5 September 1888. He held the Spalding Chair of Eastern Religions and Ethics at Oxford, wrote the two-volume Indian Philosophy that introduced a generation of English readers to the Vedantic tradition, and served as the second President of India. His birthday is observed in India as Teachers' Day — at his own suggestion, when admirers proposed celebrating it as his birthday.

---

Each day in this column we take up an event from the history of philosophy that falls on today's date.