“To understand a science it is necessary to know its history.”

Each department of knowledge passes through three stages. The theoretic stage; the theological stage and the metaphysical or abstract stage.

In mathematics we find the primitive source of rationality; and to mathematics must the biologists resort for means to carry out their researches.

The sacred formula of positivism: love as a principle, the order as a foundation, and progress as a goal.

Monotheism occupies so large a space in the view of modern minds, that it is scarcely possible to form a just estimate of the preceding phases of the theological philosophy.

All good intellects have repeated, since Bacon’s time, that there can be no real knowledge but which is based on observed facts.

Religion is an illusion of childhood, outgrown under proper education.

If we do not allow free thinking in chemistry or biology, why should we allow it in morals or politics?

Mathematical Analysis is… the true rational basis of the whole system of our positive knowledge.

Nothing is destroyed until it is replaced.

The dead govern the living.

Woman is the most moral element in all humanity.

The word right should be excluded from political language, as the word cause from the language of philosophy.

Men are not allowed to think freely about chemistry and biology: why should they be allowed to think freely about political philosophy?

The universe displays no proof of an all-directing mind.

Humanity is always made up of more dead than living.

Positivism is a theory of knowledge according to which the only kind of sound knowledge available to human kind is that if science grounded in observation.