Our rate of progress is such that an individual human being, of ordinary length of life, will be called on to face novel situations which find no parallel in his past. The fixed person, for the fixed duties, who, in older societies was such a godsend, in the future will be a public danger.
By relieving the brain of all unnecessary work, a good notation sets it free to concentrate on more advanced problems, and in effect increases the mental power of the race.
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 whole of mathematics consists in the organization of a series of aids to the imagination in the process of reasoning.
The only use of a knowledge of the past is to equip us for the present. The present contains all that there is. It is holy ground; for it is the past, and it is the future.
The term many presupposes the term one , and the term one presupposes the term many.
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.
Civilizations can only be understood by those who are civilized.
The defense of morals is the battle-cry which best rallies stupidity against change.
Identification of rhythm as the casual counterpart of life; wherever there is some life, only perceptible to us when the analogies are sufficiently close.
The theme of Cosmology, which is the basis of all religions, is the story of the dynamic effort of the World passing into everlasting unity, and of the static majesty of God's vision, accomplishing its purpose of completion by absorption of the World's multiplicity of effort.
I always feel that I have two duties to perform with a parting guest: one, to see that he doesn't forget anything that is his; the other, to see that he doesn't take anything that is mine.
The vigor of civilized societies is preserved by the widespread sense that high aims are worth-while.
Algebra reverses the relative importance of the factors in ordinary language.
All practical teachers know that education is a patient process of mastery of details, minute by minute, hour by hour, day by day.
A philosopher of imposing stature doesn't think in a vacuum. Even his most abstract ideas are, to some extent, conditioned by what is or is not known in the time when he lives.
It must be admitted that there is a degree of instability which is inconsistent with civilization. But, on the whole, the great ages have been unstable ages.
The aim of science is to seek the simplest explanation of complex facts... Seek simplicity and distrust it.
Algebra reverses the relative importance of the factors in ordinary language. It is essentially a written language, and it endeavors to exemplify in its written structures the patterns which it is its purpose to convey. The pattern of the marks on paper is a particular instance of the pattern to be conveyed to thought. The algebraic method is our best approach to the expression of necessity, by reason of its reduction of accident to the ghostlike character of the real variable.
Disputing the commonsense notion that all events require the prior existence of some underlying matter or substance. There is no antecedent static cabinet.
Apart from blunt truth, our lives sink decadently amid the perfume of hints and suggestions.
In modern times the belief that the ultimate explanation of all things was to be found in Newtonian mechanics was an adumbration of the truth that all science, as it grows towards perfection, becomes mathematical in its ideas.
The ideas of Freud were popularized by people who only imperfectly understood them, who were incapable of the great effort required to grasp them in their relationship to larger truths, and who therefore assigned to them a prominence out of all proportion to their true importance.
But in the prevalent discussion of classes, there are illegitimate transitions to the notions of a 'nexus' and of a 'proposition'. The appeal to a class to perform the services of a proper entity is exactly analogous to an appeal to an imaginary terrier to kill a real rat. Process and Reality
The great achievements of the past were the adventures of the past. Only the adventurous can understand the greatness of the past.
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