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.

Woman is the most moral element in all humanity.

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

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.

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.

nd now that man's history has been for the first time systematically considered as a whole, and has been found to be, like all other phenomena, subject to invariable laws, the preparatory labours of modern Science are ended.

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