ThursdayNov 21, 2024
Quotes: 53419 Authors: 9969
Value is coextensive with reality.
The major advances in civilization are processes which all but wreck the societies in which they occur.
True courage is not the brutal force of vulgar heroes, but the firm resolve of virtue and reason.
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.
Wisdom alone is true ambition's aim. Wisdom the source of virtue, and of fame, Obtained with labor, for mankind employed, And then, when most you share it, best enjoyed.
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 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.
On the ostensible exactitude of certain branches of human knowledge, including mathematics. The exactness is a fake.
Education with inert ideas is not only useless; it is above all things harmful.
It is as true to say that God is permanent and the World fluent, as that the World is permanent and God is fluent. It is as true to say that God is one and the World many, as that the World is one and God many. It is as true to say that, in comparison with the World, God is actual eminently, as that, in comparison with God, the World is actual eminently. It is as true to say that the World is immanent in God, as that God is immanent in the World. It is as true to say that God transcends the World, as that the World transcends God. It is as true to say that God creates the World, as that the World creates God.
Our minds are finite, and yet even in these circumstances of finitude we are surrounded by possibilities that are infinite, and the purpose of life is to grasp as much as we can out of that infinitude.
War can protect; it cannot create.
The race that does not value trained intelligence is doomed.
Religion increasingly is tending to degenerate into a decent formula wherewith to embellish a comfortable life.
Civilization advances by extending the number of important operations that we can perform without thinking about them.
The study of mathematics is apt to commence in disappointment.... We are told that by its aid the stars are weighed and the billions of molecules in a drop of water are counted. Yet, like the ghost of Hamlet's father, this greatest science eludes the efforts of our mental weapons to grasp it.
Symbolism is no mere idle fancy or corrupt degeneration: it is inherent in the very texture of human life.
In the study of ideas, it is necessary to remember that insistence on hard-headed clarity issues from sentimental feeling, as it were a mist, cloaking the perplexities of fact. Insistence on clarity at all costs is based on sheer superstition as to the mode in which human intelligence functions. Our reasonings grasp at straws for premises and float on gossamers for deductions.
The progress of Science consists in observing interconnections and in showing with a patient ingenuity that the events of this ever-shifting world are but examples of a few general relations, called laws. To see what is general in what is particular, and what is permanent in what is transitory, is the aim of scientific thought.
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.
It is the business of the future to be dangerous.
Fundamental progress has to do with the reinterpretation of basic ideas.
Through and through the world is infested with quantity: To talk sense is to talk quantities. It is no use saying the nation is large.... How large? It is no use saying the radium is scarce.... How scarce? You cannot evade quantity. You may fly to poetry and music, and quantity and number will face you in your rhythms and your octaves.
Let us grant that the pursuit of mathematics is a divine madness of the human spirit, a refuge from the goading urgency of contingent happenings.
The science of pure mathematics ... may claim to be the most original creation of the human spirit.
[In many circumstances,] the most important thing about a proposition is not that it be true, but that it be interesting.
The 'silly question' is the first intimation of some totally new development.
Seek simplicity, and distrust it.
Disputing the commonsense notion that all events require the prior existence of some underlying matter or substance. There is no antecedent static cabinet.
It is a profoundly erroneous truism, repeated by all copy books and by eminent people when they are making speeches, that we should cultivate the habit of thinking of what we are doing. The precise opposite is the case. Civilization advances by extending the number of important operations which we can perform without thinking about them.
Every really new idea looks crazy at first.
'Necessity is the mother of invention' is a silly proverb. 'Necessity is the mother of futile dodges' is much nearer the truth.
There is no nature at an instant.
What is morality in any given time or place? It is what the majority then and there happen to like and immorality is what they dislike.
It is a safe rule to apply that, when a mathematical or philosophical author writes with a misty profundity, he is talking nonsense.
The merely well-informed man is the most useless bore on God's earth.
Mathematics as a science, commenced when first someone, probably a Greek, proved propositions about 'any' things or about 'some' things, without specifications of definite particular things.
So far as the mere imparting of information is concerned, no university has had any justification for existence since the popularization of printing in the fifteenth century.
'One and one make two' assumes that the changes in the shift of circumstance are unimportant. But it is impossible for us to analyze this notion of unimportant change.
It is more important that a proposition be interesting than that it be true. This statement is almost a tautology. For the energy of operation of a proposition in an occasion of experience is its interest and is its importance. But of course a true proposition is more apt to be interesting than a false one.
Life is an offensive, directed against the repetitious mechanism of the Universe.
There is a technique, a knack, for thinking, just as there is for doing other things. You are not wholly at the mercy of your thoughts, any more than they are you. They are a machine you can learn to operate.
There is a tradition of opposition between adherents of induction and of deduction. In my view it would be just as sensible for the two ends of a worm to quarrel.
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.
No Roman ever died in contemplation over a geometrical diagram. A reference to the death of Archimedes.
We think in generalities, but we live in details.
A general definition of civilization: a civilized society is exhibiting the fine qualities of truth, beauty, adventure, art, peace.
I regret that it has been necessary for me in this lecture to administer a large dose of four-dimensional geometry. I do not apologize, because I am really not responsible for the fact that nature in its most fundamental aspect is four-dimensional. Things are what they are.
On the ostensible exactitude of certain branches of human knowledge, including mathematics: The exactness is a fake.
Everything of importance has been said before by somebody who did not discover it.
The essence of Christianity is the appeal to the life of Christ as a revelation of the nature of God and of God's agency in the world. The record is fragmentary, inconsistent, and uncertain.... But there can be no doubt as to what elements in the record have evoked a response from all that is best in human nature. The Mother, the Child, and the bare manger: the lowly man, homeless and self-forgetful, with his message of peace, love, and sympathy: the suffering, the agony, the tender words as life ebbed, the final despair: and the whole with the authority of supreme victory.
If a dog jumps up into your lap, it is because he is fond of you; but if a cat does the same thing, it is because your lap is warmer.
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.
Now in creative thought common sense is a bad master. Its sole criterion for judgement is that the new ideas shall look like the old ones. In other words it can only work by suppressing originality.
Periods of tranquility are seldom prolific of creative achievement. Mankind has to be stirred up.
In ancient times cats were worshipped as gods, they have never forgotten this.
Apart from blunt truth, our lives sink decadently amid the perfume of hints and suggestions.
Familiar things happen, and mankind does not bother about them. It requires a very unusual mind to undertake the analysis of the obvious.
It requires a very unusual mind to undertake the analysis of the obvious.
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.
Algebra is the intellectual instrument which has been created for rendering clear the quantitative aspects of the world.
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.
Religion is the last refuge of human savagery.
The art of progress is to preserve order amid change And to preserve change amid order.
The total absence of humor from the Bible is one of the most singular things in all literature.
Wisdom alone is true ambition's aim Wisdom the source of virtue, and of fame, Obtained with labor, for mankind employed, And then, when most you share it, best enjoyed.
One main factor in the upward trend of animal life has been the power of wandering.
It is the essence of life that it exists for its own sake.
The history of Western philosophy is, after all, no more than a series of footnotes to Plato's philosophy.
Civilization advances by extending the number of important operations which we can perform without thinking of them.
Ideas won't keep; something must be done about them.
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