Mathematics may be compared to a mill of exquisite workmanship, which grinds you stuff of any degree of fineness; but, nevertheless, what you get out depends upon what you put in; and as the grandest mill in the world will not extract wheat-flour from peascods, so pages of formulae will not get a definite result out of loose data.

The whole analogy of natural operations furnishes so complete and crushing an argument against the intervention of any but what are termed secondary causes, in the production of all the phenomena of the universe; that, in view of the intimate relations between Man and the rest of the living world; and between the forces exerted by the latter and all other forces, I can see no excuse for doubting that all are co-ordinated terms of Nature's great progression, from the formless to the formed from the inorganic to the organic from blind force to conscious intellect and will.

Perhaps the most valuable result of all education is the ability to make yourself do the thing you have to do, when it ought to be done, whether you like it or not. It is the first lesson that ought to be learned and however early a man's training begins, it is probably the last lesson that he learns thoroughly.

There is nothing of permanent value (putting aside a few human affections) nothing that satisfies quiet reflection--except the sense of having worked according to one's capacity and light to make things clear and get rid of cant and shams of all sorts.

I am too much of a sceptic to deny the possibility of anything...

Men can intoxicate themselves with ideas as effectually as with alcohol or with bang and produce, be dint of serious thinking, mental conditions hardly distinguishable from monomania.

It is the first duty of a hypothesis to be intelligible.