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.

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.

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

The only real life is the collective life of the race; individual life has no existence except as an abstraction.

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 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.

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