If a dog jumps in your lap, it is because he is fond of you; but if a cat does the same thing, it is because your lap is warmer. - Alfred North Whitehead

Nothing is more impressive than the fact that as mathematics withdrew increasingly into the upper regions of ever greater extremes of abstract thought, it returned back to earth with a corresponding growth of importance for the analysis of concrete fact. ...The paradox is now fully established that the utmost abstractions are the true weapons with which to control our thought of concrete fact.

In formal logic, a contradiction is the signal of a defeat; but in the evolution of real knowledge it marks the first step in progress towards a victory.

Philosophy, in one of its functions, is the critic of cosmologies. It is its function to harmonise, refashion, and justify divergent intuitions as to the nature of things. It has to insist on the scrutiny of the ultimate ideas, and on the retention of the whole of the evidence in shaping our cosmological scheme. Its business is to render explicit, and — so far as may be — efficient, a process which otherwise is unconsciously performed without rational tests.