On the ostensible exactitude of certain branches of human knowledge, including mathematics. The exactness is a fake.
The whole of mathematics consists in the organization of a series of aids to the imagination in the process of reasoning.
Imagination is not to be divorced from the facts. It is a way of illuminating the facts.
The many become one and are increased by one.
Algebra is the intellectual instrument which has been created for rendering clear the quantitative aspects of the world.
Style, in its finest sense, is the last acquirement of the educated mind; it is also the most useful. It pervades the whole being.
To come very near to a true theory, and to grasp its precise application, are two different things, as the history of science teaches us. Everything of importance has been said before by someone who did not discover it.
The foundations of the world are to be found, not in the cognitive experience of conscious thought, but in the aesthetic experience of everyday life.
A race preserves its vigor so long as it harbors a real contrast between what has been and what may be; and so long as it is nerved by the vigor to adventure beyond the safeties of the past. Without adventure civilization is in full decay.
We must not expect simple answers to far-reaching questions. However far our gaze penetrates, there are always heights beyond which block our vision.
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 great achievements of the past were the adventures of the past. Only the adventurous can understand the greatness of the past.
Every epoch has its character determined by the way its population reacts to the material events which they encounter.
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.
Aristotle discovered all the half-truths which were necessary to the creation of science.
A science which hesitates to forget its founders is lost.
Speech is human nature itself, with none of the artificiality of written language.
The only use of knowledge of the past is to equip us for the present.
A clash of doctrine is not a disaster, it is an opportunity.
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.