A science which hesitates to forget its founders is lost.

Aristotle discovered all the half-truths which were necessary to the creation of science.

Every philosophy is tinged with the colouring of some secret imaginative background, which never emerges explicitly into its train of reasoning.

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 toward a victory.

In the conditions of modern life the rule is absolute, the race which does not value trained intelligence is doomed. Not all your heroism, not all your social charm, not all your wit, not all your victories on land or at sea, can move back the finger of fate. To-day we maintain ourselves. To-morrow science will have moved forward yet one more step, and there will be no appeal from the judgment which will then be pronounced on the uneducated.

Inventive genius requires pleasurable mental activity as a condition for its vigorous exercise. 'Necessity is the mother of invention' is a silly proverb. 'Necessity is the mother of futile dodges' is much closer to the truth. The basis of growth of modern invention is science, and science is almost wholly the outgrowth of pleasurable intellectual curiosity.

It does not matter what men say in words, so long as their activities are controlled by settled instincts. The words may ultimately destroy the instincts. But until this has occurred, words do not count.

It is impossible not to feel stirred at the thought of the emotions of man at certain historic moments of adventure and discovery—Columbus when he first saw the Western shore, Pizarro when he stared at the Pacific Ocean, Franklin when the electric spark came from the string of his kite, Galileo when he first turned his telescope to the heavens. Such moments are also granted to students in the abstract regions of thought, and high among them must be placed the morning when Descartes lay in bed and invented the method of co-ordinate geometry.

It is rigid dogma that destroys truth; and, please notice, my emphasis is not on the dogma, but on the rigidity. When men say of any question, 'This is all there is to be known or said of the subject; investigation ends here,' that is death. It may be that the mischief comes not from the thinker but for the use made of his thinking by late-comers. Aristotle, for example, gave us out scientific technique ... yet his logical propositions, his instruction in sound reasoning which was bequeathed to Europe, are valid only within the limited framework of formal logic, and, as used in Europe, they stultified the minds of whole generations of mediaeval Schoolmen. Aristotle invented science, but destroyed philosophy.

It is the business of the future to be dangerous; and it is among the merits of science that it equips the future for its duties.

It requires a very unusual mind to undertake the analysis of the obvious.

No man of science wants merely to know. He acquires knowledge to appease his passion for discovery. He does not discover in order to know, he knows in order to discover.

Order is not sufficient. What is required, is something much more complex. It is order entering upon novelty; so that the massiveness of order does not degenerate into mere repetition; and so that the novelty is always reflected upon a background of system.

Our minds are finite, and yet even in these circumstances of finitude we are surrounded by possibilities that are infinite, and the purpose of human life is to grasp as much as we can out of the infinitude.

Religion will not regain its old power until it can face change in the same spirit as does science.

The true method of discovery is like the flight of an aeroplane. It starts from the ground of particular observation; it makes a flight in the thin air of imaginative generalization; and it again lands for renewed observation rendered acute by rational interpretation.

The way in which the persecution of Galileo has been remembered is a tribute to the quiet commencement of the most intimate change in outlook which the human race had yet encountered. Since a babe was born in a manger, it may be doubted whether so great a thing has happened with so little stir

Whenever a text-book is written of real educational worth, you may be quite certain that some reviewer will say that it will be difficult to teach from it. Of course it will be difficult to teach from it. It it were easy, the book ought to be burned.

Without deductive logic science would be entirely useless. It is merely a barren game to ascend from the particular to the general, unless afterwards we can reverse the process and descend from the general to the particular, ascending and descending like angels on Jacob's ladder.