The point about zero is that we do not need to use it in the operations of daily life. No one goes out to buy zero fish. It is in a way the most civilised of all the cardinals, and its use is only forced on us by the needs of cultivated modes of thought.
But you can catch yourself entertaining habitually certain ideas and setting others aside; and that, I think, is where our personal destinies are largely decided.
It is natural to think that an abstract science cannot be of much importance in affairs of human life, because it has omitted from its consideration everything of real interest.
A culture is in its finest flower before it begins to analyze itself.
You may not divide the seamless coat of learning.
The many become one and are increased by one.
The main importance of Francis Bacon's influence does not lie in any peculiar theory of inductive reasoning which he happened to express, but in the revolt against second-hand information of which he was a leader.
Our habitual experience is a complex of failure and success in the enterprise of interpretation. If we desire a record of uninterpreted experience, we must ask a stone to record its autobiography.
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 will not go so far as to say that to construct a history of thought without profound study of the mathematical ideas of successive epochs is like omitting Hamlet from the play which is named after him. That would be claiming too much. But it is certainly analogous to cutting out the part of Ophelia. This simile is singularly exact. For Ophelia is quite essential to the play, she is very charming . . . and a little mad.
The point of mathematics is that in it we have always got rid of the particular instance, and even of any particular sorts of entities. So that for example, no mathematical truths apply merely to fish, or merely to stones, or merely to colours. So long as you are dealing with pure mathematics, you are in the realm of complete and absolute abstraction. . . . Mathematics is thought moving in the sphere of complete abstraction from any particular instance of what it is talking about.
The English never abolish anything. They put it in cold storage.
Shakespeare wrote better poetry for not knowing too much; Milton, I think, knew too much finally for the good of his poetry.
Nature, even in the act of satisfying anticipation, often provides a surprise.
In every age of well-marked transition, there is the pattern of habitual dumb practice and emotion which is passing and there is oncoming a new complex of habit.
A man really writes for an audience of about ten persons. Of course if others like it, that is clear gain. But if those ten are satisfied, he is content.
Youth is life as yet unblemished by much tragedy, but hardly by TV.
We think in generalities, but we live in detail. To make the past live, we must perceive it in detail in addition to thinking of it in generalities.
Vigorous societies harbor a certain extravagance of objectives, so that men wander beyond the safe provision of personal gratifications.
From the moment of birth we are immersed in action, and can only fitfully guide it by taking thought.
The task of a university is the creation of the future, so far as rational thought and civilized modes of appreciation can affect the issue.
That knowledge which adds greatness to character is knowledge so handled as to transform every phase of immediate experience.
To be an abstraction does not mean that an entity is nothing. It merely means that its existence is only a factor of a more concrete element of nature.
In this modern world, the celibacy of the medieval learned class has been replaced by a celibacy of the intellect which is divorced from the concrete contemplation of the complete facts.
The Universe is vast. Nothing is more curious than the self-satisfied dogmatism with which mankind at each period of its history cherishes the delusion of the finality of existing modes of knowledge. Skeptics and believers are alike. At this moment scientists and skeptics are the leading dogmatists. Advance in detail is admitted; fundamental novelty is barred. This dogmatic common sense is the death of philosophic adventure.
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