Quotes by Mathematicians - Page 22

Grammar and ordinary language are bad guides to metaphysics. A great book might be written showing the influence of syntax on philosophy.
Bertrand Russell
I started studying law, but this I could stand just for one semester. I couldn't stand more. Then I studied languages and literature for two years. After two years I passed an examination with the result I have a teaching certificate for Latin and Hungarian for the lower classes of the gymnasium, for kids from 10 to 14. I never made use of this teaching certificate. And then I came to philosophy, physics, and mathematics. In fact, I came to mathematics indirectly. I was really more interested in physics and philosophy and thought about those. It is a little shortened but not quite wrong to say: I thought I am not good enough for physics and I am too good for philosophy. Mathematics is in between.
George Pólya
It is immoral to hold an opinion in order to curry another's favor; mercenary, servile, and against the dignity of human liberty to yield and submit; supremely stupid to believe as a matter of habit; irrational to decide according to the majority opinion, as if the number of sages exceeded the infinite number of fools.
Giordano Bruno
It is possible that mankind is on the threshold of a golden age; but, if so, it will be necessary first to slay the dragon that guards the door, and this dragon is religion.
Bertrand Russell
Man is but a reed, the most feeble thing in nature; but he is a thinking reed.
Blaise Pascal
Never let yourself be diverted, either by what you wish to believe, or what you think could have beneficent social effects if it were believed; but look only and solely at what are the facts.
Bertrand Russell
I have been accused of a habit of changing my opinions. I am not myself in any degree ashamed of having changed my opinions. What physicist who was already active in 1900 would dream of boasting that his opinions had not changed during the last half century? In science men change their opinions when new knowledge becomes available; but philosophy in the minds of many is assimilated rather to theology than to science. The kind of philosophy that I value and have endeavoured to pursue is scientific, in the sense that there is some definite knowledge to be obtained and that new discoveries can make the admission of former error inevitable to any candid mind. For what I have said, whether early or late, I do not claim the kind of truth which theologians claim for their creeds. I claim only, at best, that the opinion expressed was a sensible one to hold at the time when it was expressed. I should be much surprised if subsequent research did not show that it needed to be modified. I hope, therefore, that whoever uses this dictionary will not suppose the remarks which it quotes to be intended as pontifical pronouncements, but only as the best I could do at the time towards the promotion of clear and accurate thinking. Clarity, above all, has been my aim.
Bertrand Russell
The man who has no tincture of philosophy goes through life imprisoned in the prejudices derived from common sense, from the habitual beliefs of his age or his nation, and from convictions which have grown up in his mind without the cooperation or consent of his deliberate reason.
Bertrand Russell
The world is a good judge of things, for it is in natural ignorance, which is man's true state. The sciences have two extremes which meet. The first is the pure natural ignorance in which all men find themselves at birth. The other extreme is that reached by great intellects, who, having run through all that men can know, find they know nothing, and come back again to that same ignorance from which they set out; but this is a learned ignorance which is conscious of itself. Those between the two, who have departed from natural ignorance and not been able to reach the other, have some smattering of this vain knowledge and pretend to be wise. These trouble the world and are bad judges of everything. The people and the wise constitute the world; these despise it, and are despised. They judge badly of everything, and the world judges rightly of them.
Blaise Pascal
How, in such an alien and inhuman world, can so powerless a creature as man preserve his aspirations untarnished? A strange mystery it is that nature, omnipotent but blind, in the revolutions of her secular hurryings through the abysses of space, has brought forth at last a child, subject still to her power, but gifted with sight, with knowledge of good and evil, with the capacity of judging all the works of his unthinking mother. In spite of death, the mark and seal of the parental control, man is yet free, during his brief years, to examine, to criticize, to know, and in imagination to create. To him alone, in the world with which he is aquainted, this freedom belongs; and in this lies his superiority to the resistless forces that control his outward life.
Bertrand Russell
Do you mean that you think you can find out the answer to it?" said the March Hare."Exactly so," said Alice."Then you should say what you mean," the March Hare went on."I do," Alice hastily replied; "at least--at least I mean what I say--that's the same thing, you know.""You might just as well say," added the Dormouse, which seemed to be talking in its sleep, "that 'I breathewhen I sleep' is the same thing as 'I sleep when I breathe!
Lewis Carroll
Upon this first, and in one sense this sole, rule of reason, that in order to learn you must desire to learn, and in so desiring not be satisfied with what you already incline to think, there follows one corollary which itself deserves to be inscribed upon every wall of the city of philosophy: Do not block the way of inquiry.
Charles Sanders Peirce
What does it matter where my body happens to be?' he said. 'My mind goes on working all the same.
Lewis Carroll
Whoever wishes to become a philosopher must learn not to be frightened by absurdities.
Bertrand Russell
The search for something permanent is one of the deepest of the instincts leading men to philosophy.
Bertrand Russell
There lies before us, if we choose, continual progress in happiness, knowledge and wisdom. Shall we instead choose death, because we cannot forget our quarrels? I appeal as a human being to human beings; remember your humanity, and forget the rest.
Bertrand Russell
Philosophy, from the earliest times, has made greater claims, and achieved fewer results, than any other branch of learning.
Bertrand Russell
If the ordinary wage-earner worked four hours a day, there would be enough for everybody and no unemployment -- assuming a certain very moderate amount of sensible organization. This idea shocks the well-to-do, because they are convinced that the poor would not know how to use so much leisure. In America men often work long hours even when they are well off; such men, naturally, are indignant at the idea of leisure for wage-earners, except as the grim punishment of unemployment; in fact, they dislike leisure even for their sons.
Bertrand Russell
The aim of science is to seek the simplest explanations of complex facts. We are apt to fall into the error of thinking that the facts are simple because simplicity is the goal of our quest. The guiding motto in the life of every natural philosopher should be, 'Seek simplicity and distrust it.
Alfred North Whitehead
If you ask me to tell you anything about the nature of what lies beyond the phaneron… my answer is “How should I know?”… I am not dismayed by ultimate mysteries… I can no more grasp what is behind such questions as my cat can understand what is behind the clatter I make while I type this paragraph.
Martin Gardner
Each religion makes scores of purportedly factual assertions about everything from the creation of the universe to the afterlife. But on what grounds can believers presume to know that these assertions are true? The reasons they give are various, but the ultimate justification for most religious people’s beliefs is a simple one: we believe what we believe because our holy scriptures say so. But how, then, do we know that our holy scriptures are factually accurate? Because the scriptures themselves say so. Theologians specialize in weaving elaborate webs of verbiage to avoid saying anything quite so bluntly, but this gem of circular reasoning really is the epistemological bottom line on which all 'faith' is grounded. In the words of Pope John Paul II: 'By the authority of his absolute transcendence, God who makes himself known is also the source of the credibility of what he reveals.' It goes without saying that this begs the question of whether the texts at issue really were authored or inspired by God, and on what grounds one knows this. 'Faith' is not in fact a rejection of reason, but simply a lazy acceptance of bad reasons. 'Faith' is the pseudo-justification that some people trot out when they want to make claims without the necessary evidence.But of course we never apply these lax standards of evidence to the claims made in the other fellow’s holy scriptures: when it comes to religions other than one’s own, religious people are as rational as everyone else. Only our own religion, whatever it may be, seems to merit some special dispensation from the general standards of evidence.And here, it seems to me, is the crux of the conflict between religion and science. Not the religious rejection of specific scientific theories (be it heliocentrism in the 17th century or evolutionary biology today); over time most religions do find some way to make peace with well-established science. Rather, the scientific worldview and the religious worldview come into conflict over a far more fundamental question: namely, what constitutes evidence.Science relies on publicly reproducible sense experience (that is, experiments and observations) combined with rational reflection on those empirical observations. Religious people acknowledge the validity of that method, but then claim to be in the possession of additional methods for obtaining reliable knowledge of factual matters — methods that go beyond the mere assessment of empirical evidence — such as intuition, revelation, or the reliance on sacred texts. But the trouble is this: What good reason do we have to believe that such methods work, in the sense of steering us systematically (even if not invariably) towards true beliefs rather than towards false ones? At least in the domains where we have been able to test these methods — astronomy, geology and history, for instance — they have not proven terribly reliable. Why should we expect them to work any better when we apply them to problems that are even more difficult, such as the fundamental nature of the universe?Last but not least, these non-empirical methods suffer from an insuperable logical problem: What should we do when different people’s intuitions or revelations conflict? How can we know which of the many purportedly sacred texts — whose assertions frequently contradict one another — are in fact sacred?
Alan Sokal
It is the man of science, eager to have his every opinion regenerated, his every idea rationalized, by drinking at the fountain of fact, and devoting all the energies of his life to the cult of truth, not as he understands it, but as he does not yet understand it, that ought properly to be called a philosopher.
Charles Sanders Peirce
When you come to look into this argument from design, it is a most astonishing thing that people can believe that this world, with all the things that are in it, with all its defects, should be the best that omnipotence and omniscience have been able to produce in millions of years. I really cannot believe it. Do you think that, if you were granted omnipotence and omniscience and millions of years in which to perfect your world, you could produce nothing better than the Ku Klux Klan or the Fascists? Moreover, if you accept the ordinary laws of science, you have to suppose that human life and life in general on this planet will die out in due course: it is a stage in the decay of the solar system; at a certain stage of decay you get the sort of conditions of temperature and so forth which are suitable to protoplasm, and there is life for a short time in the life of the whole solar system. You see in the moon the sort of thing to which the earth is tending -- something dead, cold, and lifeless.
Bertrand Russell
Philosophy, though unable to tell us with certainty what is the true answer to the doubts which it raises, is able to suggest many possiblities which enlarge our thoughts and free them from the tyranny of custom. Thus, while diminishing our feeling of certainty as to what things are, it greatly increases our knowledge as to what the may be; it removes the somewhat arrogant dogmatism of those who have never travelled into the region of liberating doubt, and it keeps alive our sense of wonder by showing familar things in an unfamilar aspect
Bertrand Russell
When I see the blind and wretched state of men, when I survey the whole universe in its deadness, and man left to himself with no light, as though lost in this corner of the universe without knowing who put him there, what he has to do, or what will become of him when he dies, incapable of knowing anything, I am moved to terror, like a man transported in his sleep to some terrifying desert island, who wakes up quite lost, with no means of escape. Then I marvel that so wretched a state does not drive people to despair.
Blaise Pascal
Philosophy begins in wonder. And at the end when philosophic thought has done its best the wonder remains.
Alfred North Whitehead
Let whoever can do so deceive me, he will never bring it about that I am nothing, so long as I continue to think I am something.
René Descartes
Anything you're good at contributes to happiness.
Bertrand Russell
Almost everything that distinguishes the modern world from earlier centuries is attibutable to science, which achieved its most spectacular triumphs in the seventeenth century.
Bertrand Russell
Is there any knowledge in the world which is so certain that no reasonable man could doubt it?
Bertrand Russell
To ridicule philosophy is really to philosophize.
Blaise Pascal
I desire to live in peace and to continue the life I have begun under the motto 'to live well you must live unseen
René Descartes
Except our own thoughts, there is nothing absolutely in our power.
René Descartes
My desire and wish is that the things I start with should be so obvious that you wonder why I spend my time stating them. This is what I aim at because the point of philosophy is to start with something so simple as not to seem worth stating, and to end with something so paradoxical that no one will believe it.
Bertrand Russell
To make light of philosophy is to be a true philosopher.
Blaise Pascal
As a philosopher, if I were speaking to a purely philosophic audience I should say that I ought to describe myself as an Agnostic, because I do not think that there is a conclusive argument by which one can prove that there is not a God. On the other hand, if I am to convey the right impression to the ordinary man in the street I think that I ought to say that I am an Atheist, because, when I say that I cannot prove that there is not a God, I ought to add equally that I cannot prove that there are not the Homeric gods.
Bertrand Russell
Nature is pleased with simplicity. And nature is no dummy
Isaac Newton
I suppose therefore that all things I see are illusions; I believe that nothing has ever existed of everything my lying memory tells me. I think I have no senses. I believe that body, shape, extension, motion, location are functions. What is there then that can be taken as true? Perhaps only this one thing, that nothing at all is certain.
René Descartes
To teach how to live without certainty, and yet without being paralyzed by hesitation, is perhaps the chief thing that philosophy, in our age, can still do for those who study it.
Bertrand Russell
I would never die for my beliefs because I might be wrong.
Bertrand Russell
Do not fear to be eccentric in opinion, for every opinion now accepted was once eccentric.
Bertrand Russell
Take care of the sense and the sounds will take care of themselves.
Lewis Carroll
Lastly, she pictured to herself how this same little sister of hers would, in the after-time, be herself a grown woman; and how she would keep, through all her riper years, the simple and loving heart of her childhood: and how she would gather about her other little children, and make their eyes bright and eager with many a strange tale, perhaps even with the dream of Wonderland of long ago: and how she would feel with all their simple sorrows, and find a pleasure in all their simple joys, remembering her own child-life, and the happy summer days.
Lewis Carroll
Common sense is the most widely shared commodity in the world, for every man is convinced that he is well supplied with it.
René Descartes
Now, here, you see, it takes all the running you can do, to keep in the same place. If you want to get somewhere else, you must run at least twice as fast as that!
Lewis Carroll
I made this [letter] very long, because I did not have the leisure to make it shorter.
Blaise Pascal
Speak in French when you can’t think of the English for a thing--turn your toes out when you walk---And remember who you are!
Lewis Carroll
I have only made this letter longer because I have not had the time to make it shorter.", 1657)
Blaise Pascal
Take some more tea," the March Hare said to Alice, very earnestly."I've had nothing yet," Alice replied in an offended tone, "so I can't take more." than nothing." opinion," said Alice.
Lewis Carroll
If you drink much from a bottle marked 'poison' it is certain to disagree with you sooner or later.
Lewis Carroll
Alice laughed. 'There's no use trying,' she said. 'One can't believe impossible things.'I daresay you haven't had much practice,' said the Queen. 'When I was your age, I always did it for half-an-hour a day. Why, sometimes I've believed as many as six impossible things before breakfast. There goes the shawl again!
Lewis Carroll
Curiouser and curiouser.
Lewis Carroll
Why it's simply impassible!Alice: Why, don't you mean impossible? Nothing's impossible!
Lewis Carroll
have i gone mad?im afraid so, but let me tell you something, the best people usualy are.
Lewis Carroll
Begin at the beginning," the King said, very gravely, "and go on till you come to the end: then stop.
Lewis Carroll
There are two motives for reading a book; one, that you enjoy it; the other, that you can boast about it.
Bertrand Russell
Remember your humanity, and forget the rest.
Bertrand Russell
We can only see a short distance ahead, but we can see plenty there that needs to be done.
Alan Turing
Dead yesterdays and unborn tomorrows, why fret about it, if today be sweet.
Omar Khayyám
Three passions, simple but overwhelmingly strong, have governed my life: the longing for love, the search for knowledge, and unbearable pity for the suffering of mankind. These passions, like great winds, have blown me hither and thither, in a wayward course, over a great ocean of anguish, reaching to the very verge of despair. I have sought love, first, because it brings ecstasy - ecstasy so great that I would often have sacrificed all the rest of life for a few hours of this joy. I have sought it, next, because it relieves loneliness--that terrible loneliness in which one shivering consciousness looks over the rim of the world into the cold unfathomable lifeless abyss. I have sought it finally, because in the union of love I have seen, in a mystic miniature, the prefiguring vision of the heaven that saints and poets have imagined. This is what I sought, and though it might seem too good for human life, this is what--at last--I have found.With equal passion I have sought knowledge. I have wished to understand the hearts of men. I have wished to know why the stars shine. And I have tried to apprehend the Pythagorean power by which number holds sway above the flux. A little of this, but not much, I have achieved. Love and knowledge, so far as they were possible, led upward toward the heavens. But always pity brought me back to earth. Echoes of cries of pain reverberate in my heart. Children in famine, victims tortured by oppressors, helpless old people a burden to their sons, and the whole world of loneliness, poverty, and pain make a mockery of what human life should be. I long to alleviate this evil, but I cannot, and I too suffer. This has been my life. I have found it worth living, and would gladly live it again if the chance were offered me.
Bertrand Russell