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.

Induction for deduction, with a view to construction.

Every attempt to employ mathematical methods in the study of chemical questions must be considered profoundly irrational and contrary to the spirit of chemistry.... if mathematical analysis should ever hold a prominent place in chemistry -- an aberration which is happily almost impossible -- it would occasion a rapid and widespread degeneration of that science.

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

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

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

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.