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

To reorganize society without God or King, by the systematic culture of Humanity.

The law is this: that each of our leading conceptions-each branch of our knowledge-passes successively through three different theoretical conditions: the Theological, or fictitious: the Metaphysical, or abstract; and the Scientific, or positive.

All good intellects have repeated, since Bacon's time, that there can be no real knowledge but that which is based on observed facts. This is incontestable, in our present advanced stage; but, if we look back to the primitive stage of human knowledge, we shall see that it must have been otherwise then. If it is true that every theory must be based upon observed facts; it is equally true that facts can not be observed without the guidance of some theory. Without such guidance, our facts would be desultory and fruitless; we could not retain them: for the most part we could not even perceive them.

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

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.

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.