C'este donc par l'étude des mathématiques, et seulement par elle, que l'on peut se faire une idée juste et approfondie de ce que c'est qu'une science.

Language forms a kind of wealth, which all can make use of at once without causing any diminution of the store, and which thus admits a complete community of enjoyment; for all, freely participating in the general treasure, unconsciously aid in its preservation.

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

Everything is relative; and only that is absolute.

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

In the final, the positive, state, the mind has given over the vain search after absolute notions, the origin and destination of the universe, and the causes of phenomena, and applies itself to the study of their laws - that is, their invariable relations of succession and resemblance. Reasoning and observation, duly combined, are the means of this knowledge. What is now understood when we speak of an explanation of facts is simply the establishment of a connection between single phenomena and some general facts.

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