“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.”

“Error is the price we pay for progress.”

“The art of progress is to reserve order amid change, and to preserve change amid order.”

“Not ignorance, but ignorance of ignorance is the death of knowledge.”

“The truth is that science started its modern career by taking over ideas derived from the weakest side of the philosophies of Aristotle's successors. In some respects it was a happy choice. It enabled the knowledge of the seventeenth century to be formularised so far as physics and chemistry were concerned, with a completeness which has lasted to the present time. But the progress of biology and psychology has probably been checked by the uncritical assumption of half-truths. If science is not to degenerate into a medley of ad hoc hypothesis, it must become philosophical and must enter upon a thorough criticism of its own foundations.”

“For successful education there must always be a certain freshness in the knowledge dealt with. It must be either new in itself or invested with some novelty of application to the new world of new times. Knowledge does not keep any better than fish. You may be dealing with knowledge of the old species, with some old truth; but somehow it must come to the students, as it were, just drawn out of the sea and with the freshness of its immediate importance.”

“Every really new idea looks crazy at first.”