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Who said: “The path towards sustainable energy sources will be long and sometimes difficult. But America cannot resist this transition, we must lead it... That is how we will preserve our planet, commanded to our care by God. That’s what will lend meaning to the creed our fathers once declared.”
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Home > Category Index for Science Quotations > Category Index T > Category: True

True Quotes (208 quotes)

Ac kynde wit cometh
Of alle kynnes syghtes,
Of briddes and of beestes,
Of tastes of truthe and of deceites.

Mother-Wit comes from all kinds of experiences,
Of birds and beasts and of tests both true and false.
In William Langland and B. Thomas Wright (ed.) The Vision and Creed of Piers Ploughman (1842), 235. Modern translation by Terrence Tiller in Piers Plowman (1981, 1999), 123.
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He who doth with the greatest exactness imaginable, weigh every individual thing that shall or hath hapned to his Patient, and may be known from the Observations of his own, or of others, and who afterwards compareth all these with one another, and puts them in an opposite view to such Things as happen in a healthy State; and lastly, from all this with the nicest and severest bridle upon his reasoning faculty riseth to the knowledge of the very first Cause of the Disease, and of the Remedies fit to remove them; He, and only He deserveth the Name of a true Physician.
Aphorism No. 13 in Boerhaave’s Aphorisms: Concerning The Knowledge and Cure of Diseases (1715), 3.
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La verdadera, la aterradora, la inexorable senilidad comienza en la fase de temblor y balbuceo, es decir, cuando el cerebro está salpicado de placas seniles y entendimiento y carácter retroceden al estado infantil. A semejanza del edificio cuarteado por el terremoto, la citada agitación anuncia ruina inminente.
Like an earthquake, true senility announces itself by trembling and stammering.
In Charlas de Café: pensamientos, anécdotas y confidencias (1920, 1967), 95. (Café Chats: Thoughts, Anecdotes and Confidences). As translated in Peter McDonald (ed.) Oxford Dictionary of Medical Quotations (2004), 83. A more complete translation attempted by Webmaster with Google Translate is: “True, the terrifying, the inexorable senility begins at the stage of tremor and slurred speech, i.e. when the brain is dotted with senile plaques, and understanding and character regress to the infantile state. Like the building cracked by the earthquake, said agitation announces impending doom.”
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Se non è vero, è ben trovato.
If not true, it is very ingenious.
In Anthony Lejeune (ed.), The Concise Dictionary of Foreign Quotations (2001), 235.
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A great department of thought must have its own inner life, however transcendent may be the importance of its relations to the outside. No department of science, least of all one requiring so high a degree of mental concentration as Mathematics, can be developed entirely, or even mainly, with a view to applications outside its own range. The increased complexity and specialisation of all branches of knowledge makes it true in the present, however it may have been in former times, that important advances in such a department as Mathematics can be expected only from men who are interested in the subject for its own sake, and who, whilst keeping an open mind for suggestions from outside, allow their thought to range freely in those lines of advance which are indicated by the present state of their subject, untrammelled by any preoccupation as to applications to other departments of science. Even with a view to applications, if Mathematics is to be adequately equipped for the purpose of coping with the intricate problems which will be presented to it in the future by Physics, Chemistry and other branches of physical science, many of these problems probably of a character which we cannot at present forecast, it is essential that Mathematics should be allowed to develop freely on its own lines.
In Presidential Address British Association for the Advancement of Science, Sheffield, Section A, Nature (1 Sep 1910), 84, 286.
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A magician of old waved a wand that he might banish disease, a physician to-day peers through a microscope to detect the bacillus of that disease and plan its defeat. The belief in miracles was premature, that is all; it was based on dreams now coming true.
From chapter 'Jottings from a Note-book', in Canadian Stories (1918), 176.
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A man reserves his true and deepest love not for the species of woman in whose company he finds himself electrified and enkindled, but for that one in whose company he may feel tenderly drowsy.
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A mathematician of the first rank, Laplace quickly revealed himself as only a mediocre administrator; from his first work we saw that we had been deceived. Laplace saw no question from its true point of view; he sought subtleties everywhere; had only doubtful ideas, and finally carried the spirit of the infinitely small into administration.
As quoted in E.T. Bell, Men of Mathematics (1937, 1965), 182. Without citation, except, “As it is often quoted as … Napoleon’s famous estimate of Laplace, of which he is reported to have delivered himself while he was a prisoner at St. Helena.” Laplace had a six-week tenure in the Ministry of the Interior.
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A solid heavier than a fluid will, if placed in it, descend to the bottom of the fluid, and the solid will, when placed in the fluid, be lighter than its true weight by the weight of the fluid displaced.
In Thomas L. Heath (ed.), 'On Floating Bodies', The Works of Archimedes (1897), Vol. 1, Proposition 7, 258.
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A theory is a supposition which we hope to be true, a hypothesis is a supposition which we expect to be useful; fictions belong to the realm of art; if made to intrude elsewhere, they become either make-believes or mistakes.
As quoted by William Ramsay, in 'Radium and Its Products', Harper’s Magazine (Dec 1904), 52. The first part, about suppositions, appears in a paper read by G. Johnson Stoney to the American Philosophical Society, Philadelphia (3 Apr 1903), printed in 'On the Dependence of What Apparently Takes Place in Nature Upon What Actually Occurs in the Universe of Real Existences', Proceedings of the American Philosophical Society Held at Philadelphia for Promoting Useful Knowledge (Apr-May 1903) 42, No. 173, 107. If you know a primary source for the part on fictions and mistakes, please contact Webmaster.
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A very sincere and serious freshman student came to my office with a question that had clearly been troubling him deeply. He said to me, ‘I am a devout Christian and have never had any reason to doubt evolution, an idea that seems both exciting and well documented. But my roommate, a proselytizing evangelical, has been insisting with enormous vigor that I cannot be both a real Christian and an evolutionist. So tell me, can a person believe both in God and in evolution?’ Again, I gulped hard, did my intellectual duty, a nd reassured him that evolution was both true and entirely compatible with Christian belief –a position that I hold sincerely, but still an odd situation for a Jewish agnostic.
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All our dreams can come true, if we have the courage to pursue them.
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All people dream, but not equally. Those who dream by night in the dusty recesses of their mind, wake in the morning to find that it was vanity. But the dreamers of the day are dangerous people, for they dream their dreams with open eyes, and make them come true.
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All science has God as its author and giver. Much is heard of the conflict between science and religion, and of the contrast between sacred and secular. There may be aspects of truth to which religion is the gate, as indeed there are aspects of truth to which particular sciences are the gate. But if there be a Creator, and if truth be one of his attributes, then everything that is true can claim his authorship, and every search for truth can claim his authority.
In Margaret Duggan (ed.), Through the Year with Michael Ramsey: Devotional Readings for Every Day (1975).
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All the real true knowledge we have of Nature is intirely experimental, insomuch that, how strange soever the assertion seems, we may lay this down as the first fundamental unerring rule in physics, That it is not within the compass of human understanding to assign a purely speculative reason for any one phaenomenon in nature.
In The Procedure, Extent, and Limits of Human Understanding (1728, 1729), 205-206.
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All true science must aim at objective truth, and that means that the human observer must never allow himself to get emotionally mixed up with his subject-matter. His concern is to understand the universe, not to improve it. Detachment is obligatory.
From transcript of BBC radio Reith Lecture (12 Nov 1967), 'A Runaway World', on the bbc.co.uk website.
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Although to penetrate into the intimate mysteries of nature and thence to learn the true causes of phenomena is not allowed to us, nevertheless it can happen that a certain fictive hypothesis may suffice for explaining many phenomena.
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An informed appraisal of life absolutely require(s) a full understanding of life’s arena–the universe. … By deepening our understanding of the true nature of physical reality, we profoundly reconfigure our sense of ourselves and our experience of the universe.
In The Fabric of the Cosmos: Space, Time, and the Texture of Reality (2007), 5.
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Anatomy is the great ocean of intelligence upon which the true physician must sail. Bacteriology is but one little harbor.
In 'Advancement of Surgery', Journal of the American Medical Association (25 Feb 1893), 20, No. 8, 199.
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Are you aware that humanity is just a blip? Not even a blip. Just a fraction of a fraction of what the universe has been and will become? Talk about perspective. I figure I can’t feel so entirely stupid about saying what I said because, first of all, it’s true. And second of all, there will be no remnant of me or my stupidity. No fossil or geographical shift that can document, really, even the most important historical human beings, let alone my paltry admissions.
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As a nation, we are too young to have true mythic heroes, and we must press real human beings into service. Honest Abe Lincoln the legend is quite a different character from Abraham Lincoln the man. And so should they be. And so should both be treasured, as long as they are distinguished. In a complex and confusing world, the perfect clarity of sports provides a focus for legitimate, utterly unambiguous support or disdain. The Dodgers are evil, the Yankees good. They really are, and have been for as long as anyone in my family can remember.
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Be a good animal, true to your animal instinct.
In The White Peacock (1911), 224.
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By and large it is uniformly true in mathematics that there is a time lapse between a mathematical discovery and the moment when it is useful; and that this lapse of time can be anything from 30 to 100 years, in some cases even more.
From Address (1954) to Princeton Alumni, 'The Role of Mathematics in the Sciences and in Society', published in A.H. Taub (ed.), John von Neumann: Collected Works (1963), Vol. 6, 489. As quoted and cited in Rosemary Schmalz,Out of the Mouths of Mathematicians: A Quotation Book for Philomaths (1993), 123.
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Collective unity is not the result of the brotherly love of the faithful for each other. The loyalty of the true believer is to the whole—the church, party, nation—and not to his fellow true believer. True loyalty between individuals is possible only in a loose and relatively free society.
In The True Believer (1951), 122
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Confined to its true domain, mathematical reasoning is admirably adapted to perform the universal office of sound logic: to induce in order to deduce, in order to construct. … It contents itself to furnish, in the most favorable domain, a model of clearness, of precision, and consistency, the close contemplation of which is alone able to prepare the mind to render other conceptions also as perfect as their nature permits. Its general reaction, more negative than positive, must consist, above all, in inspiring us everywhere with an invincible aversion for vagueness, inconsistency, and obscurity, which may always be really avoided in any reasoning whatsoever, if we make sufficient effort.
In Synthèse Subjective (1856), 98. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 202-203. From the original French, “Bornée à son vrai domaine, la raison mathématique y peut admirablement remplir l’office universel de la saine logique: induire pour déduire, afin de construire. … Elle se contente de former, dans le domaine le plus favorable, un type de clarté, de précision, et de consistance, dont la contemplation familière peut seule disposer l’esprit à rendre les autres conceptions aussi parfaites que le comporte leur nature. Sa réaction générale, plus négative que positive, doit surtout consister à nous inspirer partout une invincible répugnance pour le vague, l’incohérence, et l’obscurité, que nous pouvons réellement éviter envers des pensées quelconques, si nous y faisons assez d’efforts.”
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Dare to live the life you have dreamed for yourself. Go forward and make your dreams come true.
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Dreams are the reality you are afraid to live, reality is the fact that your dreams will probably never come true. You can find the word me in dream, that is because it is up to you to make them come true.
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Duration is not a test of true or false.
In 'Double-Sunrise', Gift From the Sea (1955), 76.
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Each worldview was a cultural product, but evolution is true and separate creation is not ... Worldviews are social constructions, and they channel the search for facts. But facts are found and knowledge progresses, however fitfully. Fact and theory are intertwined, and all great scientists understand the interaction.
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Everywhere in nature we seek some certainty, but all this is nothing more than an arrangement of the dark feeling of our own. All the mathematical laws that we find in Nature are always suspicious to me, despite their beauty. They give me no pleasure. They are merely expedients. Everything is not true at close range.
From the original German, in Physikalische und Mathematische Schriften (1806), Vol. 4, 145, “Wir suchen in der Natur überall eine gewisse Bestimmtheit, aber das Alles ist weiter nichts, als Anordnung des dunkeln Gefühls unserer eigenen. Alle mathematischen Gesetze, die wir in der Natur finden, sind mir trotz ihrer Schönheit immer verdächtig. Sie Freuen mich nicht. Sie sind bloss Hülfsmittel. In der Nähe ist Alles nicht wahr.” English version by Webmaster using Google translate.
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Facts are meaningless. You could use facts to prove anything that's even remotely true! Facts, shmacts.
Spoken by character Homer Simpson in TV episode written by David X. Cohen, 'Lisa the Skeptic', of the animated comedy, The Simpsons (23 Nov 1997). Quoted in Kee Malesky, All Facts Considered: The Essential Library of Inessential Knowledge (2010), 201.
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Failure is, in a sense, the highway to success, inasmuch as every discovery of what is false leads us to seek earnestly after what is true.
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False interpretation of the Bible has often clashed with science, as false science has with true interpretation; but true science is the natural ally of religion, for both are from God.
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First, as concerns the success of teaching mathematics. No instruction in the high schools is as difficult as that of mathematics, since the large majority of students are at first decidedly disinclined to be harnessed into the rigid framework of logical conclusions. The interest of young people is won much more easily, if sense-objects are made the starting point and the transition to abstract formulation is brought about gradually. For this reason it is psychologically quite correct to follow this course.
Not less to be recommended is this course if we inquire into the essential purpose of mathematical instruction. Formerly it was too exclusively held that this purpose is to sharpen the understanding. Surely another important end is to implant in the student the conviction that correct thinking based on true premises secures mastery over the outer world. To accomplish this the outer world must receive its share of attention from the very beginning.
Doubtless this is true but there is a danger which needs pointing out. It is as in the case of language teaching where the modern tendency is to secure in addition to grammar also an understanding of the authors. The danger lies in grammar being completely set aside leaving the subject without its indispensable solid basis. Just so in Teaching of Mathematics it is possible to accumulate interesting applications to such an extent as to stunt the essential logical development. This should in no wise be permitted, for thus the kernel of the whole matter is lost. Therefore: We do want throughout a quickening of mathematical instruction by the introduction of applications, but we do not want that the pendulum, which in former decades may have inclined too much toward the abstract side, should now swing to the other extreme; we would rather pursue the proper middle course.
In Ueber den Mathematischen Unterricht an den hoheren Schulen; Jahresbericht der Deutschen Mathematiker Vereinigung, Bd. 11, 131.
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First... a new theory is attacked as absurd; then it is admitted to be true, but obvious and insignificant; finally it is seen to be so important that its adversaries claim that they themselves discovered it.
'Pragmatism's Conception of Truth', in Pragmatism: A New Name for some Old Ways of Thinking, Popular Lectures on Philosophy (1907), 198.
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Freudian psychoanalytical theory is a mythology that answers pretty well to Levi-Strauss's descriptions. It brings some kind of order into incoherence; it, too, hangs together, makes sense, leaves no loose ends, and is never (but never) at a loss for explanation. In a state of bewilderment it may therefore bring comfort and relief … give its subject a new and deeper understanding of his own condition and of the nature of his relationship to his fellow men. A mythical structure will be built up around him which makes sense and is believable-in, regardless of whether or not it is true.
From 'Science and Literature', The Hope of Progress: A Scientist Looks at Problems in Philosophy, Literature and Science (1973), 29.
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From this fountain (the free will of God) it is those laws, which we call the laws of nature, have flowed, in which there appear many traces of the most wise contrivance, but not the least shadow of necessity. These therefore we must not seek from uncertain conjectures, but learn them from observations and experimental. He who is presumptuous enough to think that he can find the true principles of physics and the laws of natural things by the force alone of his own mind, and the internal light of his reason, must either suppose the world exists by necessity, and by the same necessity follows the law proposed; or if the order of Nature was established by the will of God, the [man] himself, a miserable reptile, can tell what was fittest to be done.
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Gentlemen, that is surely true, it is absolutely paradoxical; we cannot understand it, and we don’t know what it means. But we have proved it, and therefore we know it is the truth.
In a lecture, after establishing the relation eπ/2 = ii in a lecture, “which evidently had a strong hold on his imagination. He dropped his chalk and rubber, put his hands in his pockets, and after contemplating the formula a few minutes turned to his class and said [this quote] very slowly and impressively.” As quoted in W. E. Byerly (writing as a Professor Emeritus at Harvard University, but a former student of Peirce), 'Benjamin Peirce: II. Reminiscences', The American Mathematical Monthly (Jan 1925), 32, No. 1, 6.
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Geometrical axioms are neither synthetic a priori conclusions nor experimental facts. They are conventions: our choice, amongst all possible conventions, is guided by experimental facts; but it remains free, and is only limited by the necessity of avoiding all contradiction. ... In other words, axioms of geometry are only definitions in disguise.
That being so what ought one to think of this question: Is the Euclidean Geometry true?
The question is nonsense. One might as well ask whether the metric system is true and the old measures false; whether Cartesian co-ordinates are true and polar co-ordinates false.
In George Edward Martin, The Foundations of Geometry and the Non-Euclidean Plane (1982), 110.
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Great thinkers build their edifices with subtle consistency. We do our intellectual forebears an enormous disservice when we dismember their visions and scan their systems in order to extract a few disembodied ‘gems’–thoughts or claims still accepted as true. These disarticulated pieces then become the entire legacy of our ancestors, and we lose the beauty and coherence of older systems that might enlighten us by their unfamiliarity–and their consequent challenge in our fallible (and complacent) modern world.
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He adhered, with a severity most unusual in Indians resident in England, to the religious observances of his caste; but his religion was a matter of observance and not of intellectual conviction, and I remember well his telling me (much to my surprise) that all religions seemed to him more or less equally true.
In obituary notice by G.H. Hardy in the Proceedings of the London Mathematical Society (2) (1921), 19, xl—lviii. Reprinted in G.H. Hardy, P.V. Seshu Aiyar and B.M. Wilson (eds.) Collected Papers of Srinivasa Ramanujan (1927), xxxi.
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He is not a true man of science who does not bring some sympathy to his studies, and expect to learn something by behavior as well as by application. It is childish to rest in the discovery of mere coincidences, or of partial and extraneous laws.
In A Week on the Concord and Merrimack Rivers (1862), 381.
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However, all scientific statements and laws have one characteristic in common: they are “true or false” (adequate or inadequate). Roughly speaking, our reaction to them is “yes” or “no.” The scientific way of thinking has a further characteristic. The concepts which it uses to build up its coherent systems are not expressing emotions. For the scientist, there is only “being,” but no wishing, no valuing, no good, no evil; no goal. As long as we remain within the realm of science proper, we can never meet with a sentence of the type: “Thou shalt not lie.” There is something like a Puritan's restraint in the scientist who seeks truth: he keeps away from everything voluntaristic or emotional.
Essays in Physics (1950), 68.
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I am born into an environment–I know not whence I came nor whither I go nor who I am. This is my situation as yours, every single one of you. The fact that everyone always was in this same situation, and always will be, tells me nothing. Our burning question as to the whence and whither–all we can ourselves observe about it is the present environment. That is why we are eager to find out about it as much as we can. That is science, learning, knowledge; it is the true source of every spiritual endeavour of man. We try to find out as much as we can about the spatial and temporal surroundings of the place in which we find ourselves put by birth.
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I am one of those philosophers who have held that that “the Common Sense view of the world” is in certain fundamental features, wholly true.
In 'A Defence of Common Sense', J.H. Muirhead (ed.), Contemporary British Philosophy (1925). Reprinted in Philosophical Papers of George Edward Moore (1959), 44.
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I believe the best test of a model is how well can the modeller answer the questions, ‘What do you know now that you did not know before?’ and ‘How can you find out if it is true?’
In Francis Crick, The Astonishing Hypothesis: the Scientific Search for the Soul (1995), 177.
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I concluded that I might take as a general rule the principle that all things which we very clearly and obviously conceive are true: only observing, however, that there is some difficulty in rightly determining the objects which we distinctly conceive.
In Discours de la Méthode (1637), as translated by J. Veitch, A Discourse on Method (1912), 27.
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I do not claim that intelligence, however defined, has no genetic basis–I regard it as trivially true, uninteresting, and unimportant that it does. The expression of any trait represents a complex interaction of heredity and environment ... a specific claim purporting to demonstrate a mean genetic deficiency in the intelligence of American blacks rests upon no new facts whatever and can cite no valid data in its support. It is just as likely that blacks have a genetic advantage over whites. And, either way, it doesn’t matter a damn. An individual can’t be judged by his group mean.
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I do not maintain that the chief value of the study of arithmetic consists in the lessons of morality that arise from this study. I claim only that, to be impressed from day to day, that there is something that is right as an answer to the questions with which one is able to grapple, and that there is a wrong answer—that there are ways in which the right answer can be established as right, that these ways automatically reject error and slovenliness, and that the learner is able himself to manipulate these ways and to arrive at the establishment of the true as opposed to the untrue, this relentless hewing to the line and stopping at the line, must color distinctly the thought life of the pupil with more than a tinge of morality. … To be neighborly with truth, to feel one’s self somewhat facile in ways of recognizing and establishing what is right, what is correct, to find the wrong persistently and unfailingly rejected as of no value, to feel that one can apply these ways for himself, that one can think and work independently, have a real, a positive, and a purifying effect upon moral character. They are the quiet, steady undertones of the work that always appeal to the learner for the sanction of his best judgment, and these are the really significant matters in school work. It is not the noise and bluster, not even the dramatics or the polemics from the teacher’s desk, that abide longest and leave the deepest and stablest imprint upon character. It is these still, small voices that speak unmistakably for the right and against the wrong and the erroneous that really form human character. When the school subjects are arranged on the basis of the degree to which they contribute to the moral upbuilding of human character good arithmetic will be well up the list.
In Arithmetic in Public Education (1909), 18. As quoted and cited in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 69.
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I have long since come to see that no one deserves either praise or blame for the ideas that come to him, but only for the actions resulting therefrom. Ideas and beliefs are certainly not voluntary acts. They come to us—we hardly know how or whence, and once they have got possession of us we can not reject or change them at will. It is for the common good that the promulgation of ideas should be free—uninfluenced by either praise or blame, reward or punishment. But the actions which result from our ideas may properly be so treated, because it is only by patient thought and work, that new ideas, if good and true, become adopted and utilized; while, if untrue or if not adequately presented to the world, they are rejected or forgotten.
In 'The Origin of the Theory of Natural Selection', Popular Science Monthly (1909), 74, 400.
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If it is true as Whewell says, that the essence of the triumphs of Science and its progress consists in that it enables us to consider evident and necessary, views which our ancestors held to be unintelligible and were unable to comprehend, then the extension of the number concept to include the irrational, and we will at once add, the imaginary, is the greatest forward step which pure mathematics has ever taken.
In Theorie der Complexen Zahlensysteme (1867), 60. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 281. From the original German, “Wenn es wahr ist, dass, wie Whewell meint, das Wesen der Triumphe der Wissenschaft und ihres Fortschrittes darin besteht, dass wir veranlasst werden, Ansichten, welche unsere Vorfahren für unbegreiflich hielten und unfähig waren zu begreifen, für evident und nothwendig zu halten, so war die Erweiterung des Zahlenbegriffes auf das Irrationale, und wollen wir sogleich hinzufügen, das Imaginäre, der grösste Fortschritt, den die reine Mathematik jemals gemacht hat.”
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If they don’t depend on true evidence, scientists are no better than gossips.
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In 1847 I gave an address at Newton, Mass., before a Teachers’ Institute conducted by Horace Mann. My subject was grasshoppers. I passed around a large jar of these insects, and made every teacher take one and hold it while I was speaking. If any one dropped the insect, I stopped till he picked it up. This was at that time a great innovation, and excited much laughter and derision. There can be no true progress in the teaching of natural science until such methods become general.
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In mathematics there are no true controversies. (1811)
This quote is usually seen without any specific source citation. The sense of it is given, not in quotation marks, as “In 1811 Gauss stated that there are no true controversies in mathematics,” in G. Waldo Dunnington, Jeremy Gray and Fritz-Egbert Dohse, Carl Friedrich Gauss: Titan of Science (2003), 418. If you know the primary source, please contact Webmaster.
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In nature hybrid species are usually sterile, but in science the reverse is often true. Hybrid subjects are often astonishingly fertile, whereas if a scientific discipline remains too pure it usually wilts.
In What Mad Pursuit: A Personal View of Scientific Discovery (1988), 150.
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In science the primary duty of ideas is to be useful and interesting even more than to be “true.”
Lecture delivered to Anthropological Society of University College, London (25 Jan 1929). Published in 'The Functions of the Human Skull', Nature (6 Apr 1929), 123, No. 3101, 533-537. Collected in The Collected Papers of Wilfred Trotter, FRS (1941), 73.
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In the case of elements, as in that of individuals, the determination of character is often attended with very great difficulty, a true estimate being only slowly arrived at, and when at last such an estimate is found, it can only be very partially expressed in words.
In The Encyclopaedia Britannica: Ninth Edition (1877), Vol. 5, 714.
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In the following pages I offer nothing more than simple facts, plain arguments, and common sense; and have no other preliminaries to settle with the reader, than that he will divest himself of prejudice and repossession, and suffer his reason and feelings to determine for themselves; and that he will put on, or rather that he will not put off, the true character of man, and generously enlarge his view beyond the present day.
In Common Sense: Addressed to the Inhabitants of America (1792), 15.
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In the history of science and throughout the whole course of its progress we see certain epochs following one another more or less rapidly. Some important view is expressed, it may be original or only revived; sooner or later it receives recognition; fellow-Workers spring up; the outcome of it finds its way into the schools; it is taught and handed down; and we observe, unhappily, that it does not in the least matter whether the view be true or false. In either case its course is the same; in either case it comes in the end to he a mere phrase, a lifeless word stamped on the memory.
In The Maxims and Reflections of Goethe (1906), 184.
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Indeed, if one understands by algebra the application of arithmetic operations to composite magnitudes of all kinds, whether they be rational or irrational number or space magnitudes, then the learned Brahmins of Hindostan are the true inventors of algebra.
In Geschichte der Mathematik im Altertum und im Mittelalter (1874), 195. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 284. From the original German, “Ja, wenn man unter Algebra die Anwendung arithmetischer Operationen auf zusammengesetzte Grössen aller Art, mögen sie rationale oder irrationale Zahl- oder Raumgrössen sein, versteht, so sind die gelehrten Brahmanen Hindustans die wahren Erfinder der Algebra.”
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Induction, then, is that operation of the mind by which we infer that what we know to be true in a particular case or cases, will be true in all cases which resemble the former in certain assignable respects. In other words, induction is the process by which we conclude that what is true of certain individuals of a class is true of the whole class, or that what is true at certain times will be true in similar circumstances at all times.
In A System of Logic, Ratiocinative and Inductive: Being a Connected View of the Principles of Evidence, and the Methods of Scientific Investigation (1843), Vol. 1, 352.
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Instead of adjusting students to docile membership in whatever group they happen to be placed, we should equip them to cope with their environment, not be adjusted to it, to be willing to stand alone, if necessary, for what is right and true.
In speech, 'Education for Creativity in the Sciences', Conference at New York University, Washington Square. As quoted by Gene Currivan in 'I.Q. Tests Called Harmful to Pupil', New York Times (16 Jun 1963), 66.
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Is evolution a theory, a system or a hypothesis? It is much more: it is a general condition to which all theories, all hypotheses, all systems must bow and which they must satisfy henceforth if they are to be thinkable and true. Evolution is a light illuminating all facts, a curve that all lines must follow. ... The consciousness of each of us is evolution looking at itself and reflecting upon itself....Man is not the center of the universe as once we thought in our simplicity, but something much more wonderful—the arrow pointing the way to the final unification of the world in terms of life. Man alone constitutes the last-born, the freshest, the most complicated, the most subtle of all the successive layers of life. ... The universe has always been in motion and at this moment continues to be in motion. But will it still be in motion tomorrow? ... What makes the world in which we live specifically modern is our discovery in it and around it of evolution. ... Thus in all probability, between our modern earth and the ultimate earth, there stretches an immense period, characterized not by a slowing-down but a speeding up and by the definitive florescence of the forces of evolution along the line of the human shoot.
In The Phenomenon of Man (1975), pp 218, 220, 223, 227, 228, 277.
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Is there a due regard to be had, … for the golden tongue of wisdom, that relisheth all not by imagination but true judgement.
In 'To the Reader', The Optick Glass of Humors (1607), 10.
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It is a test of true theories not only to account for but to predict phenomena.
Aphorism 12, 'Aphorisms Concerning Science', The Philosophy of the Inductive Sciences (1840), Vol. 1, xxxvi.
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It is admitted by all that a finished or even a competent reasoner is not the work of nature alone; the experience of every day makes it evident that education develops faculties which would otherwise never have manifested their existence. It is, therefore, as necessary to learn to reason before we can expect to be able to reason, as it is to learn to swim or fence, in order to attain either of those arts. Now, something must be reasoned upon, it matters not much what it is, provided it can be reasoned upon with certainty. The properties of mind or matter, or the study of languages, mathematics, or natural history, may be chosen for this purpose. Now of all these, it is desirable to choose the one which admits of the reasoning being verified, that is, in which we can find out by other means, such as measurement and ocular demonstration of all sorts, whether the results are true or not. When the guiding property of the loadstone was first ascertained, and it was necessary to learn how to use this new discovery, and to find out how far it might be relied on, it would have been thought advisable to make many passages between ports that were well known before attempting a voyage of discovery. So it is with our reasoning faculties: it is desirable that their powers should be exerted upon objects of such a nature, that we can tell by other means whether the results which we obtain are true or false, and this before it is safe to trust entirely to reason. Now the mathematics are peculiarly well adapted for this purpose, on the following grounds:
1. Every term is distinctly explained, and has but one meaning, and it is rarely that two words are employed to mean the same thing.
2. The first principles are self-evident, and, though derived from observation, do not require more of it than has been made by children in general.
3. The demonstration is strictly logical, taking nothing for granted except self-evident first principles, resting nothing upon probability, and entirely independent of authority and opinion.
4. When the conclusion is obtained by reasoning, its truth or falsehood can be ascertained, in geometry by actual measurement, in algebra by common arithmetical calculation. This gives confidence, and is absolutely necessary, if, as was said before, reason is not to be the instructor, but the pupil.
5. There are no words whose meanings are so much alike that the ideas which they stand for may be confounded. Between the meaning of terms there is no distinction, except a total distinction, and all adjectives and adverbs expressing difference of degrees are avoided.
In On the Study and Difficulties of Mathematics (1898), chap. 1.
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It is as true now, as it was in the days when Werner first drew his far-reaching inferences before his charmed listeners, that on the characteristic phenomena and varying distribution of the grand mineral masses of the rock-formations, almost all that concerns the relative habitability of a land depends.
In 'The Relations of Geology', Scottish Geographical Magazine (Aug 1902), 19, No. 8, 409.
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It is certainly true that all physical phenomena are subject to strictly mathematical conditions, and mathematical processes are unassailable in themselves. The trouble arises from the data employed. Most phenomena are so highly complex that one can never be quite sure that he is dealing with all the factors until the experiment proves it. So that experiment is rather the criterion of mathematical conclusions and must lead the way.
In Matter, Ether, Motion (1894), 89.
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It is most true that a natural and secret hatred and aversion towards society, in any man, hath somewhat of the savage beast.
…...
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It is now necessary to indicate more definitely the reason why mathematics not only carries conviction in itself, but also transmits conviction to the objects to which it is applied. The reason is found, first of all, in the perfect precision with which the elementary mathematical concepts are determined; in this respect each science must look to its own salvation .... But this is not all. As soon as human thought attempts long chains of conclusions, or difficult matters generally, there arises not only the danger of error but also the suspicion of error, because since all details cannot be surveyed with clearness at the same instant one must in the end be satisfied with a belief that nothing has been overlooked from the beginning. Every one knows how much this is the case even in arithmetic, the most elementary use of mathematics. No one would imagine that the higher parts of mathematics fare better in this respect; on the contrary, in more complicated conclusions the uncertainty and suspicion of hidden errors increases in rapid progression. How does mathematics manage to rid itself of this inconvenience which attaches to it in the highest degree? By making proofs more rigorous? By giving new rules according to which the old rules shall be applied? Not in the least. A very great uncertainty continues to attach to the result of each single computation. But there are checks. In the realm of mathematics each point may be reached by a hundred different ways; and if each of a hundred ways leads to the same point, one may be sure that the right point has been reached. A calculation without a check is as good as none. Just so it is with every isolated proof in any speculative science whatever; the proof may be ever so ingenious, and ever so perfectly true and correct, it will still fail to convince permanently. He will therefore be much deceived, who, in metaphysics, or in psychology which depends on metaphysics, hopes to see his greatest care in the precise determination of the concepts and in the logical conclusions rewarded by conviction, much less by success in transmitting conviction to others. Not only must the conclusions support each other, without coercion or suspicion of subreption, but in all matters originating in experience, or judging concerning experience, the results of speculation must be verified by experience, not only superficially, but in countless special cases.
In Werke [Kehrbach] (1890), Bd. 5, 105. As quoted, cited and translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 19.
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It is therefore easy to see why the churches have always fought science and persecuted its devotees. On the other hand, I maintain that the cosmic religious feeling is the strongest and noblest motive for scientific research. Only those who realize the immense efforts and, above all, the devotion without which pioneer work in theoretical science cannot be achieved are able to grasp the strength of the emotion out of which alone such work, remote as it is from the immediate realities of life, can issue. What a deep conviction of the rationality of the universe and what a yearning to understand, were it but a feeble reflection of the mind revealed in this world, Kepler and Newton must have had to enable them to spend years of solitary labor in disentangling the principles of celestial mechanics! Those whose acquaintance with scientific research is derived chiefly from its practical results easily develop a completely false notion of the mentality of the men who, surrounded by a skeptical world, have shown the way to kindred spirits scattered wide through the world and through the centuries. Only one who has devoted his life to similar ends can have a vivid realization of what has inspired these men and given them the strength to remain true to their purpose in spite of countless failures. It is cosmic religious feeling that gives a man such strength. A contemporary has said, not unjustly, that in this materialistic age of ours the serious scientific workers are the only profoundly religious people.
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It is this mythical, or rather this symbolic, content of the religious traditions which is likely to come into conflict with science. This occurs whenever this religious stock of ideas contains dogmatically fixed statements on subjects which be long in the domain of science. Thus, it is of vital importance for the preservation of true religion that such conflicts be avoided when they arise from subjects which, in fact, are not really essential for the pursuance of the religious aims.
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It is true that M. Fourier believed that the main aim of mathematics was public utility and the explanation of natural phenomena; but a philosopher of his ability ought to have known that the sole aim of science is the honour of the human intellect, and that on this ground a problem in numbers is as important as a problem on the system of the world.
In Letter to Legendre, as quoted in an Address by Emile Picard to the Congress of Science and Art, St. Louis (22 Sep 1904), translated in 'Development of Mathematical Analysis', The Mathematical Gazette (Jul 1905), 3, No. 52, 200. A different translation begins, “It is true that Fourier had the opinion…” on the Karl Jacobi Quotes web page on this site.
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It is true that when pride releases energies and serves as a spur to achievement, it can lead to a reconciliation with the self and the attainment of genuine self-esteem.
In The Passionate State of Mind (1955), 23.
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It may be true, that as Francis Thompson noted, ‘Thou canst not stir a flower without troubling a star’, but in computing the motion of stars and planets, the effects of flowers do not loom large. It is the disregarding of the effect of flowers on stars that allows progress in astronomy. Appropriate abstraction is critical to progress in science.
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It may be true, that men, who are mere mathematicians, have certain specific shortcomings, but that is not the fault of mathematics, for it is equally true of every other exclusive occupation. So there are mere philologists, mere jurists, mere soldiers, mere merchants, etc. To such idle talk it might further be added: that whenever a certain exclusive occupation is coupled with specific shortcomings, it is likewise almost certainly divorced from certain other shortcomings.
In Gauss-Schumacher Briefwechsel, Bd. 4, (1862), 387.
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It would appear that Deductive and Demonstrative Sciences are all, without exception, Inductive Sciences: that their evidence is that of experience, but that they are also, in virtue of the peculiar character of one indispensable portion of the general formulae according to which their inductions are made, Hypothetical Sciences. Their conclusions are true only upon certain suppositions, which are, or ought to be, approximations to the truth, but are seldom, if ever, exactly true; and to this hypothetical character is to be ascribed the peculiar certainty, which is supposed to be inherent in demonstration.
In System of Logic, Bk. 2, chap. 6, 1.
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It would be very discouraging if somewhere down the line you could ask a computer if the Riemann hypothesis is correct and it said, “Yes, it is true, but you won’t be able to understand the proof.”
As quoted in John Horgan, 'The Death of Proof', Scientific American (Oct 1993), 269, No. 4, 103.
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It would seem at first sight as if the rapid expansion of the region of mathematics must be a source of danger to its future progress. Not only does the area widen but the subjects of study increase rapidly in number, and the work of the mathematician tends to become more and more specialized. It is, of course, merely a brilliant exaggeration to say that no mathematician is able to understand the work of any other mathematician, but it is certainly true that it is daily becoming more and more difficult for a mathematician to keep himself acquainted, even in a general way, with the progress of any of the branches of mathematics except those which form the field of his own labours. I believe, however, that the increasing extent of the territory of mathematics will always be counteracted by increased facilities in the means of communication. Additional knowledge opens to us new principles and methods which may conduct us with the greatest ease to results which previously were most difficult of access; and improvements in notation may exercise the most powerful effects both in the simplification and accessibility of a subject. It rests with the worker in mathematics not only to explore new truths, but to devise the language by which they may be discovered and expressed; and the genius of a great mathematician displays itself no less in the notation he invents for deciphering his subject than in the results attained. … I have great faith in the power of well-chosen notation to simplify complicated theories and to bring remote ones near and I think it is safe to predict that the increased knowledge of principles and the resulting improvements in the symbolic language of mathematics will always enable us to grapple satisfactorily with the difficulties arising from the mere extent of the subject.
In Presidential Address British Association for the Advancement of Science, Section A., (1890), Nature, 42, 466.
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It [mathematics] is in the inner world of pure thought, where all entia dwell, where is every type of order and manner of correlation and variety of relationship, it is in this infinite ensemble of eternal verities whence, if there be one cosmos or many of them, each derives its character and mode of being,—it is there that the spirit of mathesis has its home and its life.
Is it a restricted home, a narrow life, static and cold and grey with logic, without artistic interest, devoid of emotion and mood and sentiment? That world, it is true, is not a world of solar light, not clad in the colours that liven and glorify the things of sense, but it is an illuminated world, and over it all and everywhere throughout are hues and tints transcending sense, painted there by radiant pencils of psychic light, the light in which it lies. It is a silent world, and, nevertheless, in respect to the highest principle of art—the interpenetration of content and form, the perfect fusion of mode and meaning—it even surpasses music. In a sense, it is a static world, but so, too, are the worlds of the sculptor and the architect. The figures, however, which reason constructs and the mathematic vision beholds, transcend the temple and the statue, alike in simplicity and in intricacy, in delicacy and in grace, in symmetry and in poise. Not only are this home and this life thus rich in aesthetic interests, really controlled and sustained by motives of a sublimed and supersensuous art, but the religious aspiration, too, finds there, especially in the beautiful doctrine of invariants, the most perfect symbols of what it seeks—the changeless in the midst of change, abiding things hi a world of flux, configurations that remain the same despite the swirl and stress of countless hosts of curious transformations.
In 'The Universe and Beyond', Hibbert Journal (1904-1906), 3, 314.
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It’s always been true that whatever pleases teaches more efficiently.
In 'Classroom Without Walls', Explorations (May 1957), No. 7. Collected in Edmund Carpenter and Marshall McLuhan (eds.), Explorations in Communication, an Anthology (1960), 3.
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Know the true value of time; snatch, seize, and enjoy every moment of it. No idleness, no delay, no procrastination; never put off till tomorrow what you can do today.
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Laws and institutions are constantly tending to gravitate. Like clocks, they must be occasionally cleansed, and wound up, and set to true time.
In Life Thoughts (1860), 80.
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Let us now declare the means whereby our understanding can rise to knowledge without fear of error. There are two such means: intuition and deduction. By intuition I mean not the varying testimony of the senses, nor the deductive judgment of imagination naturally extravagant, but the conception of an attentive mind so distinct and so clear that no doubt remains to it with regard to that which it comprehends; or, what amounts to the same thing, the self-evidencing conception of a sound and attentive mind, a conception which springs from the light of reason alone, and is more certain, because more simple, than deduction itself. …
It may perhaps be asked why to intuition we add this other mode of knowing, by deduction, that is to say, the process which, from something of which we have certain knowledge, draws consequences which necessarily follow therefrom. But we are obliged to admit this second step; for there are a great many things which, without being evident of themselves, nevertheless bear the marks of certainty if only they are deduced from true and incontestable principles by a continuous and uninterrupted movement of thought, with distinct intuition of each thing; just as we know that the last link of a long chain holds to the first, although we can not take in with one glance of the eye the intermediate links, provided that, after having run over them in succession, we can recall them all, each as being joined to its fellows, from the first up to the last. Thus we distinguish intuition from deduction, inasmuch as in the latter case there is conceived a certain progress or succession, while it is not so in the former; … whence it follows that primary propositions, derived immediately from principles, may be said to be known, according to the way we view them, now by intuition, now by deduction; although the principles themselves can be known only by intuition, the remote consequences only by deduction.
In Rules for the Direction of the Mind, Philosophy of Descartes. [Torrey] (1892), 64-65.
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Little could Plato have imagined, when, indulging his instinctive love of the true and beautiful for their own sakes, he entered upon these refined speculations and revelled in a world of his own creation, that he was writing the grammar of the language in which it would be demonstrated in after ages that the pages of the universe are written.
From Lecture (4 Dec 1854) delivered to the Gresham Committee and the members of the Common Council of the City of London, 'A Probationary Lecture on Geometry', collected in Collected Mathematical Papers of James Joseph Sylvester (1908), Vol. 2, 7.
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Logic is not concerned with human behavior in the same sense that physiology, psychology, and social sciences are concerned with it. These sciences formulate laws or universal statements which have as their subject matter human activities as processes in time. Logic, on the contrary, is concerned with relations between factual sentences (or thoughts). If logic ever discusses the truth of factual sentences it does so only conditionally, somewhat as follows: if such-and-such a sentence is true, then such-and-such another sentence is true. Logic itself does not decide whether the first sentence is true, but surrenders that question to one or the other of the empirical sciences.
Logic (1937). In The Language of Wisdom and Folly: Background Readings in Semantics (1967), 44.
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Mankind cannot survive without technology. But unless technology becomes a true servant of man, the survival of mankind is in jeopardy. And if technology is to be the servant, then the engineer’s paramount loyalty must be to society.
In 'Preface', Conference on Engineering Ethics, May 18-19, 1975, Baltimore, Md. (1975), 1.
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Mathematics accomplishes really nothing outside of the realm of magnitude; marvellous, however, is the skill with which it masters magnitude wherever it finds it. We recall at once the network of lines which it has spun about heavens and earth; the system of lines to which azimuth and altitude, declination and right ascension, longitude and latitude are referred; those abscissas and ordinates, tangents and normals, circles of curvature and evolutes; those trigonometric and logarithmic functions which have been prepared in advance and await application. A look at this apparatus is sufficient to show that mathematicians are not magicians, but that everything is accomplished by natural means; one is rather impressed by the multitude of skilful machines, numerous witnesses of a manifold and intensely active industry, admirably fitted for the acquisition of true and lasting treasures.
In Werke [Kehrbach] (1890), Bd. 5, 101. As quoted, cited and translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 13.
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Mathematics may be defined as the the subject in which we never know what we are talking about, not whether what we are saying is true.
In 'Recent Work on the Principles of Mathematics', International Monthly (1901), 4, 84. This sentence is part of a longer quote that begins, “Pure mathematics consists entirely…”, on the Bertrand Russell Quotes page of this website.
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Mathematics … certainly would never have come into existence if mankind had known from the beginning that in all nature there is no perfectly straight line, no true circle, no standard of measurement.
From 'Of the First and Last Things', All Too Human: A Book For Free Spirits (1878, 1908), Part 1, section 11, 31.
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Men despise religion; they hate it, and they fear it is true.
In Pensées (1670), Section 16, No. 26. From Blaise Pascal and W.F. Trotter (trans.), 'Thoughts', collected in Charles W. Eliot (ed.), The Harvard Classics (1910), Vol. 48, 68. From the French, “Les hommes ont mépris pour la religion; ils en ont haine, et peur qu’elle soit vraie,” in Pensées de Blaise Pascal (1847), 203.
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Most scientists think wars and national boundaries are a menace to the true creative spirit by which science must live, they hate war and they are terrified of atomic war—because they know its possibilities.
As quoted in Michael Amrine, 'I’m A Frightened Man', Collier’s (1946), 117, 51.
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Mssr. Fermat—what have you done?
Your simple conjecture has everyone
Churning out proofs,
Which are nothing but goofs!
Could it be that your statement’s an erudite spoof?
A marginal hoax
That you’ve played on us folks?
But then you’re really not known for your practical jokes.
Or is it then true
That you knew what to do
When n was an integer greater than two?
Oh then why can’t we find
That same proof…are we blind?
You must be reproved, for I’m losing my mind.
In 'Fermat's Last Theorem', Mathematics Magazine (Apr 1986), 59, No. 2, 76.
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My father’s collection of fossils was practically unnamed, but the appearance of Phillips’ book [Geology of the Yorkshire Coast], in which most of our specimens were figured, enabled us to remedy this defect. Every evening was devoted by us to accomplishing the work. This was my first introduction to true scientific study. ... Phillips’ accurate volume initiated an entirely new order of things. Many a time did I mourn over the publication of this book, and the consequences immediately resulting from it. Instead of indulging in the games and idleness to which most lads are prone, my evenings throughout a long winter were devoted to the detested labour of naming these miserable stones. Such is the short-sightedness of boyhood. Pursuing this uncongenial work gave me in my thirteenth year a thorough practical familiarity with the palaeontological treasures of Eastern Yorkshire. This early acquisition happily moulded the entire course of my future life.
In Reminiscences of a Yorkshire naturalist (1896), 12.
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My visceral perception of brotherhood harmonizes with our best modern biological knowledge ... Many people think (or fear) that equality of human races represents a hope of liberal sentimentality probably squashed by the hard realities of history. They are wrong. This essay can be summarized in a single phrase, a motto if you will: Human equality is a contingent fact of history. Equality is not true by definition; it is neither an ethical principle (though equal treatment may be) nor a statement about norms of social action. It just worked out that way. A hundred different and plausible scenarios for human history would have yielded other results (and moral dilemmas of enormous magnitude). They didn’t happen.
…...
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My work has always tried to unite the true with the beautiful and when I had to choose one or the other, I usually chose the beautiful.
In Obituary by Freeman J. Dyson, 'Prof. Hermann Weyl, For. Mem. R.S.', Nature (10 Mar 1956), 177, 458. Dyson notes that this was told to him personally, by Weyl who was “half joking”.
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Natural forces within us are the true healers of disease.
…...
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No gun is perfectly true. So the marksman, that he may hit the bull's-eye, points elsewhere.
From chapter 'Jottings from a Note-Book', in Canadian Stories (1918), 169.
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No physician, in so far as he is a physician, considers his own good in what he prescribes, but the good of his patient; for the true physician is also a ruler having the human body as a subject, and is not a mere money-maker.
Plato
In Plato and B. Jowett (trans.), The Dialogues of Plato (1875), Vol. 3, 211.
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Not every one of our desires can be immediately gratified. We’ve got to learn to wait patiently for our dreams to come true, especially on the path we’ve chosen. But while we wait, we need to prepare symbolically a place for our hopes and dreams.
…...
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Nothing is less applicable to life than mathematical reasoning. A proposition in mathematics is decidedly false or true. Everywhere else the true is mingled with the false.
Quoted, without citation, in David Eugene Smith, The Teaching of Elementary Mathematics (1904), 170.
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Notwithstanding all that has been discovered since Newton’s time, his saying that we are little children picking up pretty pebbles on the beach while the whole ocean lies before us unexplored remains substantially as true as ever, and will do so though we shovel up the pebbles by steam shovels and carry them off in carloads.
From 'Lessons from the History of Science: The Scientific Attitude' (c.1896), in Collected Papers (1931), Vol. 1, 47.
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Once a mathematical result is proven to the satisfaction of the discipline, it doesn’t need to be re-evaluated in the light of new evidence or refuted, unless it contains a mistake. If it was true for Archimedes, then it is true today.
In 'The Unplanned Impact of Mathematics', Nature (14 Jul 2011), 475, No. 7355, 166.
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Once you have mastered time, you will understand how true it is that most people overestimate what they can accomplish in a year-and underestimate what they can achieve in a decade!
…...
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One geometry cannot be more true than another; it can only be more convenient. Geometry is not true, it is advantageous.
…...
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One of the big misapprehensions about mathematics that we perpetrate in our classrooms is that the teacher always seems to know the answer to any problem that is discussed. This gives students the idea that there is a book somewhere with all the right answers to all of the interesting questions, and that teachers know those answers. And if one could get hold of the book, one would have everything settled. That’s so unlike the true nature of mathematics.
As quoted in L.A. Steen and D.J. Albers (eds.), Teaching Teachers, Teaching Students (1981), 89.
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One of the most curious and interesting reptiles which I met with in Borneo was a large tree-frog, which was brought me by one of the Chinese workmen. He assured me that he had seen it come down in a slanting direction from a high tree, as if it flew. On examining it, I found the toes very long and fully webbed to their very extremity, so that when expanded they offered a surface much larger than the body. The forelegs were also bordered by a membrane, and the body was capable of considerable inflation. The back and limbs were of a very deep shining green colour, the undersurface and the inner toes yellow, while the webs were black, rayed with yellow. The body was about four inches long, while the webs of each hind foot, when fully expanded, covered a surface of four square inches, and the webs of all the feet together about twelve square inches. As the extremities of the toes have dilated discs for adhesion, showing the creature to be a true tree frog, it is difficult to imagine that this immense membrane of the toes can be for the purpose of swimming only, and the account of the Chinaman, that it flew down from the tree, becomes more credible. This is, I believe, the first instance known of a “flying frog,” and it is very interesting to Darwinians as showing that the variability of the toes which have been already modified for purposes of swimming and adhesive climbing, have been taken advantage of to enable an allied species to pass through the air like the flying lizard. It would appear to be a new species of the genus Rhacophorus, which consists of several frogs of a much smaller size than this, and having the webs of the toes less developed.
Malay Archipelago
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Only one who devotes himself to a cause with his whole strength and soul can be a true master. For this reason mastery demands all of a person.
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Only reason can convince us of those three fundamental truths without a recognition of which there can be no effective liberty: that what we believe is not necessarily true; that what we like is not necessarily good; and that all questions are open.
In Civilization: An Essay (1928), 125.
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Our children will attain to a far more fundamental insight into language, if we, when teaching them, connect the words more with the actual perception of the thing and the object. … Our language would then again become a true language of life, that is, born of life and producing life.
In Friedrich Fröbel and Josephine Jarvis (trans.), The Education of Man (1885), 145.
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Our reasonings are grounded upon two great principles, that of contradiction, in virtue of which we judge false that which involves a contradiction, and true that which is opposed or contradictory to the false.
The Monadology and Other Philosophical Writings (1714), trans. Robert Latta (1898) 235.
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People are like stained glass windows: they sparkle and shine when the sun is out, but when the darkness sets in their true beauty is revealed only if there is a light within.
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Philosophers say, that Man is a Microcosm, or little World, resembling in Miniature every Part of the Great: And, in my Opinion, the Body Natural may be compared to the Body Politic: and if this be so, how can the Epicureans Opinion be true, that the Universe was formed by a fortuitous Concourse of Atoms; which I will no more believe, than that the accidental Jumbling of the Letters of the Alphabet, could fall by Chance into a most ingenious and learned Treatise of Philosophy. Risum teneatis Amici, Hor.
In 'A Tritical Essay Upon the Faculties of the Mind' (6 Aug 1707), collected in various volumes and editions, for example, The Works of J.S, D.D, D.S.P.D.: Volume 1: Miscellanies in Prose (1739), 173. An earlier, undated, fourth volume of Miscellanies gives the 6 Aug 1707 date the essay was written. The final Latin phrase can be translated as, “Can you help laughing, friends?” attributed to Horace. In Jonathan Swift and Temple Scott (ed.), The Prose Works of Jonathan Swift: A Tale of a Tub: the Battle of the Books, and Other Early Works (1897, reprint 1907), Vol. 1, 291, the editor footnotes that “this essay is a parody on the pseudo-philosophical essays of the time, in which all sense was lost in the maze of inconsequential quotations.” Indeed, the rest of the essay is, by design, a jumble of disjointed thoughts and makes next to no sense.
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Proper Experiments have always Truth to defend them; also Reasoning join’d with Mathematical Evidence, and founded upon Experiment, will hold equally true; but should it be true, without those Supports it must be altogether useless.
In Academical Lectures on the Theory of Physic (1751), Vol. 1. As quoted in Thomas Steele Hall, A Source Book in Animal Biology (1951), 485.
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Psychology appeared to be a jungle of confusing, conflicting, and arbitrary concepts. These pre-scientific theories doubtless contained insights which still surpass in refinement those depended upon by psychiatrists or psychologists today. But who knows, among the many brilliant ideas offered, which are the true ones? Some will claim that the statements of one theorist are correct, but others will favour the views of another. Then there is no objective way of sorting out the truth except through scientific research.
From The Scientific Analysis of Personality (1965), 14.
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Pure mathematics … reveals itself as nothing but symbolic or formal logic. It is concerned with implications, not applications. On the other hand, natural science, which is empirical and ultimately dependent upon observation and experiment, and therefore incapable of absolute exactness, cannot become strictly mathematical. The certainty of geometry is thus merely the certainty with which conclusions follow from non-contradictory premises. As to whether these conclusions are true of the material world or not, pure mathematics is indifferent.
In 'Non-Euclidian Geometry of the Fourth Dimension', collected in Henry Parker Manning (ed.), The Fourth Dimension Simply Explained (1910), 58.
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Returning now to the Malay Archipelago, we find that all the wide expanse of sea which divides Java, Sumatra, and Borneo from each other, and from Malacca and Siam, is so shallow that ships can anchor in any part of it, since it rarely exceeds forty fathoms in depth; and if we go as far as the line of a hundred fathoms, we shall include the Philippine Islands and Bali, east of Java. If, therefore, these islands have been separated from each other and the continent by subsidence of the intervening tracts of land, we should conclude that the separation has been comparatively recent, since the depth to which the land has subsided is so small. It is also to be remarked that the great chain of active volcanoes in Sumatra and Java furnishes us with a sufficient cause for such subsidence, since the enormous masses of matter they have thrown out would take away the foundations of the surrounding district; and this may be the true explanation of the often-noticed fact that volcanoes and volcanic chains are always near the sea. The subsidence they produce around them will, in time, make a sea, if one does not already exist.
Malay Archipelago
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Saturated with that speculative spirit then pervading the Greek mind, he [Pythagoras] endeavoured to discover some principle of homogeneity in the universe. Before him, the philosophers of the Ionic school had sought it in the matter of things; Pythagoras looked for it in the structure of things. He observed the various numerical relations or analogies between numbers and the phenomena of the universe. Being convinced that it was in numbers and their relations that he was to find the foundation to true philosophy, he proceeded to trace the origin of all things to numbers. Thus he observed that musical strings of equal lengths stretched by weights having the proportion of 1/2, 2/3, 3/4, produced intervals which were an octave, a fifth and a fourth. Harmony, therefore, depends on musical proportion; it is nothing but a mysterious numerical relation. Where harmony is, there are numbers. Hence the order and beauty of the universe have their origin in numbers. There are seven intervals in the musical scale, and also seven planets crossing the heavens. The same numerical relations which underlie the former must underlie the latter. But where number is, there is harmony. Hence his spiritual ear discerned in the planetary motions a wonderful “Harmony of spheres.”
In History of Mathematics (1893), 67.
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Science, in the immediate, produces knowledge and, indirectly, means of action. It leads to methodical action if definite goals are set up in advance. For the function of setting up goals and passing statements of value transcends its domain. While it is true that science, to the extent of its grasp of causative connections, may reach important conclusions as to the compatibility and incompatibility of goals and evaluations, the independent and fundamental definitions regarding goals and values remain beyond science’s reach.
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Scientists often have a naive faith that if only they could discover enough facts about a problem, these facts would somehow arrange themselves in a compelling and true solution.
In Mankind Evolving: The Evolution of the Human Species, 128. As cited in Ted Woods & Alan Grant, Reason in Revolt - Dialectical Philosophy and Modern Science (2003), Vol. 2, 183.
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Scientists [still] refuse to consider man as an object of scientific scrutiny except through his body. The time has come to realise that an interpretation of the universe—even a positivist one—remains unsatisfying unless it covers the interior as well as the exterior of things; mind as well as matter. The true physics is that which will, one day, achieve the inclusion of man in his wholeness in a coherent picture of the world.
In Teilhard de Chardin and Bernard Wall (trans.), The Phenomenon of Man (1959, 2008), 36. Originally published in French as Le Phénomene Humain (1955).
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Since the world is what it is, it is clear that valid reasoning from sound principles cannot lead to error; but a principle may be so nearly true as to deserve theoretical respect, and yet may lead to practical consequences which we feel to be absurd. There is therefore a justification for common sense in philosophy, but only as showing that our theoretical principles cannot be quite correct so long as their consequences are condemned by an appeal to common sense which we feel to be irresistible.
In A History of Western Philosophy, (1945, 1996), 553.
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Such startling announcements as these should be deprecated as being unworthy of science and mischievous to its true progress.
(1880), commenting on the manner in which Edison announced a successful light bulb. In Charles William Siemens and ‎Edward Fisher Bamber (ed.), The Scientific Works of C. William Siemens: A Collection of Addresses, lectures, etc. (1889), Vol. 3, 221.
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Suppose then I want to give myself a little training in the art of reasoning; suppose I want to get out of the region of conjecture and probability, free myself from the difficult task of weighing evidence, and putting instances together to arrive at general propositions, and simply desire to know how to deal with my general propositions when I get them, and how to deduce right inferences from them; it is clear that I shall obtain this sort of discipline best in those departments of thought in which the first principles are unquestionably true. For in all our thinking, if we come to erroneous conclusions, we come to them either by accepting false premises to start with—in which case our reasoning, however good, will not save us from error; or by reasoning badly, in which case the data we start from may be perfectly sound, and yet our conclusions may be false. But in the mathematical or pure sciences,—geometry, arithmetic, algebra, trigonometry, the calculus of variations or of curves,— we know at least that there is not, and cannot be, error in our first principles, and we may therefore fasten our whole attention upon the processes. As mere exercises in logic, therefore, these sciences, based as they all are on primary truths relating to space and number, have always been supposed to furnish the most exact discipline. When Plato wrote over the portal of his school. “Let no one ignorant of geometry enter here,” he did not mean that questions relating to lines and surfaces would be discussed by his disciples. On the contrary, the topics to which he directed their attention were some of the deepest problems,— social, political, moral,—on which the mind could exercise itself. Plato and his followers tried to think out together conclusions respecting the being, the duty, and the destiny of man, and the relation in which he stood to the gods and to the unseen world. What had geometry to do with these things? Simply this: That a man whose mind has not undergone a rigorous training in systematic thinking, and in the art of drawing legitimate inferences from premises, was unfitted to enter on the discussion of these high topics; and that the sort of logical discipline which he needed was most likely to be obtained from geometry—the only mathematical science which in Plato’s time had been formulated and reduced to a system. And we in this country [England] have long acted on the same principle. Our future lawyers, clergy, and statesmen are expected at the University to learn a good deal about curves, and angles, and numbers and proportions; not because these subjects have the smallest relation to the needs of their lives, but because in the very act of learning them they are likely to acquire that habit of steadfast and accurate thinking, which is indispensable to success in all the pursuits of life.
In Lectures on Teaching (1906), 891-92.
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The advantage which science gained by Gauss’ long-lingering method of publication is this: What he put into print is as true and important today as when first published; his publications are statutes, superior to other human statutes in this, that nowhere and never has a single error been detected in them. This justifies and makes intelligible the pride with which Gauss said in the evening of his life of the first larger work of his youth: “The Disquisitiones arithmeticae belong to history.”
In Allgemeine Deutsche Biographie (1878, 8, 435. As cited and translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 158.
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The aim of poetry is to give a high and voluptuous plausibility to what is palpably not true. I offer the Twenty-third Psalm as an example: ‘The Lord is my shepherd: I shall not want.’ It is immensely esteemed by the inmates of almshouses, and by gentlemen waiting to be hanged. I have to limit my own reading of it, avoiding soft and yielding moods, for I too, in my way, am a gentleman waiting to be hanged, as you are.
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The art of discovering the causes of phenomena, or true hypothesis, is like the art of deciphering, in which an ingenious conjecture greatly shortens the road.
In Gottfried Leibniz and Alfred Fideon Langley (trans.), 'Leibniz’s Critique of Locke', New Essays Concerning Human Understanding (1896), Book 4, Chap. 12, 526.
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The attitude of the intellectual community toward America is shaped not by the creative few but by the many who for one reason or another cannot transmute their dissatisfaction into a creative impulse, and cannot acquire a sense of uniqueness and of growth by developing and expressing their capacities and talents. There is nothing in contemporary America that can cure or alleviate their chronic frustration. They want power, lordship, and opportunities for imposing action. Even if we should banish poverty from the land, lift up the Negro to true equality, withdraw from Vietnam, and give half of the national income as foreign aid, they will still see America as an air-conditioned nightmare unfit for them to live in.
In 'Some Thoughts on the Present', The Temper of Our Time (1967), 107.
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The child asks, “What is the moon, and why does it shine?” “What is this water and where does it run?” “What is this wind?” “What makes the waves of the sea?” “Where does this animal live, and what is the use of this plant?” And if not snubbed and stunted by being told not to ask foolish questions, there is no limit to the intellectual craving of a young child; nor any bounds to the slow, but solid, accretion of knowledge and development of the thinking faculty in this way. To all such questions, answers which are necessarily incomplete, though true as far as they go, may be given by any teacher whose ideas represent real knowledge and not mere book learning; and a panoramic view of Nature, accompanied by a strong infusion of the scientific habit of mind, may thus be placed within the reach of every child of nine or ten.
In 'Scientific Education', Lay Sermons, Addresses, and Reviews (1870), 71. https://books.google.com/books?id=13cJAAAAIAAJ Thomas Henry Huxley - 1870
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The Commissioner of Patents may be likened to a wine merchant. He has in his office the wine of human progress of every kind and quality—wine, one may say, produced from the fermentation of the facts of the world through the yeast of human effort. Sometimes the yeast is “wild” and sometimes the “must” is poor, and while it all lies there shining with its due measure of the sparkle of divine effort, it is but occasionally that one finds a wine whose bouquet is the result of a pure culture on the true fruit of knowledge. But it is this true, pure wine of discovery that is alone of lasting significance.
In Some Chemical Problems of Today (1911), 108.
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The critical mathematician has abandoned the search for truth. He no longer flatters himself that his propositions are or can be known to him or to any other human being to be true; and he contents himself with aiming at the correct, or the consistent. The distinction is not annulled nor even blurred by the reflection that consistency contains immanently a kind of truth. He is not absolutely certain, but he believes profoundly that it is possible to find various sets of a few propositions each such that the propositions of each set are compatible, that the propositions of each such set imply other propositions, and that the latter can be deduced from the former with certainty. That is to say, he believes that there are systems of coherent or consistent propositions, and he regards it his business to discover such systems. Any such system is a branch of mathematics.
In George Edward Martin, The Foundations of Geometry and the Non-Euclidean Plane (1982), 94. Also in Science (1912), New Series, 35, 107.
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The fact that something is far-fetched is no reason why it should not be true; it cannot be as far-fetched as the fact that something exists.
In The Decline and Fall of Science (1976), 1.
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The facts of nature are what they are, but we can only view them through the spectacles of our mind. Our mind works largely by metaphor and comparison, not always (or often) by relentless logic. When we are caught in conceptual traps, the best exit is often a change in metaphor–not because the new guideline will be truer to nature (for neither the old nor the new metaphor lies ‘out there’ in the woods), but because we need a shift to more fruitful perspectives, and metaphor is often the best agent of conceptual transition.
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The familiar idea of a god who is omniscient: someone who knows everything … does not immediately ring alarm bells in our brains; it is plausible that such a being could exist. Yet, when it is probed more closely one can show that omniscience of this sort creates a logical paradox and must, by the standards of human reason, therefore be judged impossible or be qualified in some way. To see this consider this test statement:
This statement is not known to be true by anyone.
Now consider the plight of our hypothetical Omniscient Being (“Big O”). Suppose first that this statement is true and Big O does not know it. Then Big O would not be omniscient. So, instead, suppose our statement is false. This means that someone must know the statement to be true; hence it must be true. So regardless of whether we assume at the outset that this statement is true or false, we are forced to conclude that it must be true! And therefore, since the statement is true, nobody (including Big O) can know that it is true. This shows that there must always be true statements that no being can know to be true. Hence there cannot be an Omniscient Being who knows all truths. Nor, by the same argument, could we or our future successors, ever attain such a state of omniscience. All that can be known is all that can be known, not all that is true.
In Impossibility: The Limits of Science and the Science of Limits (1999), 11.
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The finest emotion of which we are capable is the mystic emotion. Herein lies the germ of all art and all true science.
Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 16
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The great mathematicians have acted on the principle “Divinez avant de demontrer”, and it is certainly true that almost all important discoveries are made in this fashion.
In 'The Present Problems in Geometry', Bulletin American Mathematical Society, 11, 285. [The French phrase has the sense of “Guess before proving”. —Webmaster]
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The greatest enemy, however, to true arithmetic work is found in so-called practical or illustrative problems, which are freely given to our pupils, of a degree of difficulty and complexity altogether unsuited to their age and mental development. … I am, myself, no bad mathematician, and all the reasoning powers with which nature endowed me have long been as fully developed as they are ever likely to be; but I have, not infrequently, been puzzled, and at times foiled, by the subtle logical difficulty running through one of these problems, given to my own children. The head-master of one of our Boston high schools confessed to me that he had sometimes been unable to unravel one of these tangled skeins, in trying to help his own daughter through her evening’s work. During this summer, Dr. Fairbairn, the distinguished head of one of the colleges of Oxford, England, told me that not only had he himself encountered a similar difficulty, in the case of his own children, but that, on one occasion, having as his guest one of the first mathematicians of England, the two together had been completely puzzled by one of these arithmetical conundrums.
Address before the Grammar-School Section of the Massachusetts Teachers’ Association (25 Nov 1887), 'The Teaching of Arithmetic in the Boston Schools', printed The Academy (Jan 1888). Collected in Francis Amasa Walker, Discussions in Education (1899), 253.
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The honor you have given us goes not to us as a crew, but to ... all Americans, who believed, who persevered with us. What Apollo has begun we hope will spread out in many directions, not just in space, but underneath the seas, and in the cities to tell us unforgettably what we will and must do. There are footprints on the moon. Those footprints belong to each and every one of you, to all mankind. They are there because of the blood, sweat, and tears of millions of people. Those footprints are the symbol of true human spirit.
From his acceptance speech (13 Aug 1969) for the Medal of Freedom presented to him as one of the three astronauts on the first manned moon landing mission. In Leon Wagener, One Giant Leap: Neil Armstrong's Stellar American Journey (2004), 226.
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The Internet’s been so great, and it’s so nice to have fans do nice, elaborate websites, but I think the downside is some of the things... for real fans to go on and see that 90 percent of the information isn’t true or to see pictures that aren’t really me, or for them to be able to sell these things, that’s one of the downsides, I think.
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The job of theorists, especially in biology, is to suggest new experiments. A good theory makes not only predictions, but surprising predictions that then turn out to be true. (If its predictions appear obvious to experimentalists, why would they need a theory?)
In What Mad Pursuit: A Personal View of Scientific Discovery (1988), 142.
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The man of true genius never lives before his time, he never undertakes impossibilities, and always embarks on his enterprise at the suitable place and period. Though he may catch a glimpse of the coming light as it gilds the mountain top long before it reaches the eyes of his contemporaries, and he may hazard a prediction as to the future, he acts with the present.
Closing Address (19 Mar 1858) at the Exhibition of the Metropolitan Mechanics' Institute, of Washington. Published as a pamphlet by the M.M. Institute (1853). Collected in Smithsonian Miscellaneous Collections, Vol. 30.
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The modern, and to my mind true, theory is that mathematics is the abstract form of the natural sciences; and that it is valuable as a training of the reasoning powers not because it is abstract, but because it is a representation of actual things.
From 'Introduction', Mathematical Teaching and its Modern Methods (1886), 9-10.
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The more wittily a good thought is defined the less it is true.
As quoted in Franz Liszt, The Letters of Franz Liszt to Olga Von Meyendorff (1979), 82.
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The most beautiful emotion we can experience is the mystical. It is the power of all true art and science. He to whom this emotion is a stranger, who can no longer wonder and stand rapt in awe, is as good as dead. To know that what is impenetrable to us really exists, manifesting itself as the highest wisdom and the most radiant beauty, which our dull faculties can comprehend only in their most primitive forms — this knowledge, this feeling, is at the center of true religiousness. In this sense, and in this sense only, I belong to the rank of devoutly religious men.
As quoted in Philip Frank, Einstein: His Life and Times (1947), chap. 12, sec. 5 - “Einstein’s Attitude Toward Religion.”
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The most beautiful thing to experience is the mysterious. It is the true source of life, art and science.
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The oldest empires,—what we called venerable antiquity, now that we have true measures of duration, show like creations of yesterday. … The old six thousand years of chronology become a kitchen clock,—no more a measure of time than an hour-glass or an egg-glass,—since the duration of geologic periods has come into view.
In 'Progress of Culture', an address read to the Phi Beta Kappa Society at Cambridge, 18 July 1867. Collected in Works of Ralph Waldo Emerson (1883), 475.
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The only true voyage of discovery, the only fountain of Eternal Youth, would be not to visit strange lands but to possess other eyes, to behold the universe through the eyes of another, of a hundred others, to behold the hundred universes that each of them beholds, that each of them is.
From La Prisonnière (1923), a volume in the series of novels À la Recherche du Temps Perdu (Remembrance of Things Past). Translated by C.K. Moncrief as The Captive (1929, 1949), 70-71. This text is often seen paraphrased as “The real voyage of discovery consists not in seeing new sights, but in looking with new eyes.” [Note that the context refers to the “eyes” of artists (including composers), and their ability to transport the viewer or listener with “a pair of wings, … which would enable us to traverse infinite space” to see new vistas through their art.]
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The origin of a science is usually to be sought for not in any systematic treatise, but in the investigation and solution of some particular problem. This is especially the case in the ordinary history of the great improvements in any department of mathematical science. Some problem, mathematical or physical, is proposed, which is found to be insoluble by known methods. This condition of insolubility may arise from one of two causes: Either there exists no machinery powerful enough to effect the required reduction, or the workmen are not sufficiently expert to employ their tools in the performance of an entirely new piece of work. The problem proposed is, however, finally solved, and in its solution some new principle, or new application of old principles, is necessarily introduced. If a principle is brought to light it is soon found that in its application it is not necessarily limited to the particular question which occasioned its discovery, and it is then stated in an abstract form and applied to problems of gradually increasing generality.
Other principles, similar in their nature, are added, and the original principle itself receives such modifications and extensions as are from time to time deemed necessary. The same is true of new applications of old principles; the application is first thought to be merely confined to a particular problem, but it is soon recognized that this problem is but one, and generally a very simple one, out of a large class, to which the same process of investigation and solution are applicable. The result in both of these cases is the same. A time comes when these several problems, solutions, and principles are grouped together and found to produce an entirely new and consistent method; a nomenclature and uniform system of notation is adopted, and the principles of the new method become entitled to rank as a distinct science.
In A Treatise on Projections (1880), Introduction, xi. Published as United States Coast and Geodetic Survey, Treasury Department Document, No. 61.
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The peculiar character of mathematical truth is, that it is necessarily and inevitably true; and one of the most important lessons which we learn from our mathematical studies is a knowledge that there are such truths, and a familiarity with their form and character.
This lesson is not only lost, but read backward, if the student is taught that there is no such difference, and that mathematical truths themselves are learned by experience.
In Thoughts on the Study of Mathematics. Principles of English University Education (1838).
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The progress of science requires more than new data; it needs novel frameworks and contexts. And where do these fundamentally new views of the world arise? They are not simply discovered by pure observation; they require new modes of thought. And where can we find them, if old modes do not even include the right metaphors? The nature of true genius must lie in the elusive capacity to construct these new modes from apparent darkness. The basic chanciness and unpredictability of science must also reside in the inherent difficulty of such a task.
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The true beauty of nature is her amplitude; she exists neither for nor because of us, and possesses a staying power that all our nuclear arsenals cannot threaten (much as we can easily destroy our puny selves).
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The true laboratory is the mind, where behind illusions we uncover the laws of truth.
Quoted in India Today (Apr 2008), 33, No 16, as cited on webpage of Dhirubhai Ambani Institute of Information and Communication Technology.
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The true man of science will know nature better by his finer organization; he will smell, taste, see, hear, feel, better than other men. His will be a deeper and finer experience.
In 'Natural history of Massachusetts', The Dial: A Magazine for Literature, Philosophy, and Religion (Jul 1842), 3, No. 1, 40.
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The true mathematician is always a good deal of an artist, an architect, yes, of a poet. Beyond the real world, though perceptibly connected with it, mathematicians have intellectually created an ideal world, which they attempt to develop into the most perfect of all worlds, and which is being explored in every direction. None has the faintest conception of this world, except he who knows it.
In Jahresbericht der Deutschen Mathematiker Vereinigung, 32, 381. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 184.
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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.
Gifford lectures delivered in the University of Edinburgh during the session 1927-28. Process and Reality: An Essay in Cosmology (1929, 1979), 5.
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The true purpose of education is to teach a man to carry himself triumphant to the sunset.
In Philip Dorf, Liberty Hyde Bailey: An Informal Biography: a Pioneer Educator in Horticulture (1956), 227.
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The true value of a human being is determined primarily by the measure and the sense in which he has attained to liberation from the self.
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The true way to render age vigorous is to prolong the youth of the mind.
In Mortimer Collins and Frances Cotton Collins, The Village Comedy (1878), Vol. 1, 56.
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The true wealth of a nation consists not in the stored-up gold but in the intellectual and physical strength of its people.
Quoted in India Today (Apr 2008), 33, No 16, as cited on webpage of Dhirubhai Ambani Institute of Information and Communication Technology.
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The truth may be puzzling. It may take some work to grapple with. It may be counterintuitive. It may contradict deeply held prejudices. It may not be consonant with what we desperately want to be true. But our preferences do not determine what's true. We have a method, and that method helps us to reach not absolute truth, only asymptotic approaches to the truth—never there, just closer and closer, always finding vast new oceans of undiscovered possibilities. Cleverly designed experiments are the key.
In 'Wonder and Skepticism', Skeptical Enquirer (Jan-Feb 1995), 19, No. 1.
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The weeping philosopher too often impairs his eyesight by his woe, and becomes unable from his tears to see the remedies for the evils which he deplores. Thus it will often be found that the man of no tears is the truest philanthropist, as he is the best physician who wears a cheerful face, even in the worst of cases.
From Memoirs of Extraordinary Popular Delusions (1841), Vol. 1, 323.
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The work of science does not consist of creation but of the discovery of true thoughts.
From the first chapter of an unfinished book, The Thought: A Logical Inquiry (1918), collected in Arthur Sullivan (ed.), Logicism and the Philosophy of Language: Selections from Frege and Russell (2003), 215.
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The “conflict” between the fundamental realities of Religion and the established facts of Science, is seen to be unreal as soon as Religion and Science each recognises the true borders of its dominion.
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There are pessimists who hold that such a state of affairs is necessarily inherent in human nature; it is those who propound such views that are the enemies of true religion, for they imply thereby that religious teachings are utopian ideals and unsuited to afford guidance in human affairs. The study of the social patterns in certain so-called primitive cultures, however, seems to have made it sufficiently evident that such a defeatist view is wholly unwarranted.
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There are two kinds of physician - those who work for love, and those who work for their own profit. They are both known by their works; the true and just physician is known by his love and by his unfailing love for his neighbor. The unjust physicians are known for their transgressions against the commandment; for they reap, although they have not sown, and they are like ravening wolves; they reap because they want to reap, in order to increase their profit, and they are heedless of the commandment of love.
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There is much that is true which does not admit of being calculated; just as there are a great many things that cannot be brought to the test of a decisive experiment.
In The Maxims and Reflections of Goethe (1906), 191.
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This is the most beautiful place on Earth. There are many such places. Every man, every woman, carries in heart and mind the image of the ideal place, the right place, the one true home, known or unknown, actual or visionary.
Opening sentences in 'The First morning', Desert Solitaire (1968,1988), 1.
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Through the reading of popular scientific books I soon reached the conviction that much in the stories of the Bible could not be true. The consequence was a positively fanatic orgy of freethinking coupled with the impression that youth is intentionally being deceived by the state through lies; it was a crushing impression. Mistrust of every kind of author ity grew out of this experience, a skeptical attitude toward the convictions that were alive in any specific social environment–an attitude that has never again left me, even though, later on, it has been tempered by a better insight into the causal connections.
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Thus, remarkably, we do not know the true number of species on earth even to the nearest order of magnitude. My own guess, based on the described fauna and flora and many discussions with entomologists and other specialists, is that the absolute number falls somewhere between five and thirty million.
Conservation for the 21st Century
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Time is the only true purgatory.
Samuel Butler, Henry Festing Jones (ed.), The Note-Books of Samuel Butler (1917), 219.
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To fully understand the mathematical genius of Sophus Lie, one must not turn to books recently published by him in collaboration with Dr. Engel, but to his earlier memoirs, written during the first years of his scientific career. There Lie shows himself the true geometer that he is, while in his later publications, finding that he was but imperfectly understood by the mathematicians accustomed to the analytic point of view, he adopted a very general analytic form of treatment that is not always easy to follow.
In Lectures on Mathematics (1911), 9.
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To know that we know what we know, and to know that we do not know what we do not know, that is true knowledge.
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To write the true natural history of the world, we should need to be able to follow it from within. It would thus appear no longer as an interlocking succession of structural types replacing one another, but as an ascension of inner sap spreading out in a forest of consolidated instincts. Right at its base, the living world is constituted by conscious clothes in flesh and bone.
In Teilhard de Chardin and Bernard Wall (trans.), The Phenomenon of Man (1959, 2008), 151. Originally published in French as Le Phénomene Humain (1955).
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True artists are the antennae of nature.
In On Love & Psychological Exercises: With Some Aphorisms & Other Essays (1998), 59.
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True conservation provides for wise use by the general public. The American people do not want our resources preserved for the exclusive use of the wealthy. These land and water resources belong to the people, and people of all income levels should have easy access to them.
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True majorities, in a TV-dominated and anti-intellectual age, may need sound bites and flashing lights–and I am not against supplying such lures if they draw children into even a transient concern with science. But every classroom has one [Oliver] Sacks, one [Eric] Korn, or one [Jonathan] Miller, usually a lonely child with a passionate curiosity about nature, and a zeal that overcomes pressures for conformity. Do not the one in fifty deserve their institutions as well–magic places, like cabinet museums, that can spark the rare flames of genius?
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True optimization is the revolutionary contribution of modern research to decision processes.
In Eberhard Zeidler, Applied Functional Analysis: main principles and their applications (1995), 1.
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True physics was founded the day when Galileo, rejecting fruitless speculations, conceived the idea … of defining the general form to give to experiments, by assigning for their immediate purpose the measure of all that can be measurable in natural phenomena.
From the original French, “La vraie physique a été fondée le jour où Galilée, rejetant des spéculations depuis si longtemps stériles, a conçu l’idée … de préciser la forme générale à donner aux expériences, en leur assignant pour objet immédiat la mesure de tout ce qui peut être mesurable dans les phénomènes naturels,” in De l’origine et des limites de la correspondance entre l’algèbre et la géométrie (1847), 375. English version by Webmaster using Google translate. This may be the basis of Thomas-Henri Martin describing Galileo’s experimental method , often translated as Measure what is measurable, and make measurable what is not so, from the original French in Galilée: Les droits de la science et la méthode des sciences physiques (1868), 289. Note that in both cases, the words were narrative by the authors, not quoting actual words by Galileo. What the authors wrote was in their own words, and should not be attributed to Galileo with quotation marks.
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True rigor is productive, being distinguished in this from another rigor which is purely formal and tiresome, casting a shadow over the problems it touches.
From address to the section of Algebra and Analysis, International Congress of Arts and Sciences, St. Louis (22 Sep 1904), 'On the Development of Mathematical Analysis and its Relation to Certain Other Sciences,' as translated by M.W. Haskell in Bulletin of the American Mathematical Society (May 1905), 11, 417.
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True science investigates and brings to human perception such truths and such knowledge as the people of a given time and society consider most important. Art transmits these truths from the region of perception to the region of emotion.
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True science is distinctively the study of useless things. For the useful things will get studied without the aid of scientific men. To employ these rare minds on such work is like running a steam engine by burning diamonds.
From 'Lessons from the History of Science: The Scientific Attitude' (c.1896), in Collected Papers (1931), Vol. 1, 32.
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True science teaches us to doubt and, in ignorance, to refrain.
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True science thrives best in glass houses where everyone can look in. When the windows are blacked out, as in war, the weeds take over; when secrecy muffles criticism, charlatans and cranks flourish.
In Is Science Necessary?: Essays on Science and Scientists (1989), xvi.
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True science, which is the knowledge of facts, and true philosophy, which is the knowledge of principles, are always allied to true religion, which is the harmony of the soul with both facts and principles.
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True wisdom consists not in seeing what is immediately before our eyes, but in foreseeing what is to come.
Terence
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True wisdom is to know what is best worth knowing, and to do what is best worth doing.
In Hialmer Day Gould, New Practical Spelling (1905), 16.
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We all know, from what we experience with and within ourselves, that our conscious acts spring from our desires and our fears. Intuition tells us that that is true also of our fellows and of the higher animals. We all try to escape pain and death, while we seek what is pleasant. We are all ruled in what we do by impulses; and these impulses are so organized that our actions in general serve for our self preservation and that of the race. Hunger, love, pain, fear are some of those inner forces which rule the individual’s instinct for self preservation. At the same time, as social beings, we are moved in the relations with our fellow beings by such feelings as sympathy, pride, hate, need for power, pity, and so on. All these primary impulses, not easily described in words, are the springs of man’s actions. All such action would cease if those powerful elemental forces were to cease stirring within us. Though our conduct seems so very different from that of the higher animals, the primary instincts are much alike in them and in us. The most evident difference springs from the important part which is played in man by a relatively strong power of imagination and by the capacity to think, aided as it is by language and other symbolical devices. Thought is the organizing factor in man, intersected between the causal primary instincts and the resulting actions. In that way imagination and intelligence enter into our existence in the part of servants of the primary instincts. But their intervention makes our acts to serve ever less merely the immediate claims of our instincts.
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We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances.
From Isaac Newton, Rules of Reasoning in Philosophy, Rule 1, as translated by Andrew Motte in The Mathematical Principles of Natural Philosophy (1803), Vol. 2, 160.
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We grow great by dreams. All big men are dreamers. They see things in the soft haze of a spring day or in the red fire of a long winter’s evening. Some of us let these great dreams die, but others nourish and protect them; nurse them through bad days till they bring them to the sunshine and light which comes always to those who sincerely hope that their dreams will come true.
Quoted, for example, in The American Exporter (1930), Vol. 106, 158. Webmaster has found this quote in numerous texts, but as yet has not identified the original. (Can you help?)
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We live in a world where unfortunately the distinction between true and false appears to become increasingly blurred by manipulation of facts, by exploitation of uncritical minds, and by the pollution of the language.
As attributed in prepared statement by David I. Haberman to Tiselius (1970 Nobel Prize Ceremony) in United States Congress, Senate Committee on Foreign Relations, Subcommittee on Multinational Corporations, Multinational Corporations and United States Foreign Policy (1974), 41.
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We should therefore, with grace and optimism, embrace NOMA’s tough-minded demand: Acknowledge the personal character of these human struggles about morals and meanings, and stop looking for definite answers in nature’s construction. But many people cannot bear to surrender nature as a ‘transitional object’–a baby’s warm blanket for our adult comfort. But when we do (for we must) , nature can finally emerge in her true form: not as a distorted mirror of our needs, but as our most fascinating comp anion. Only then can we unite the patches built by our separate magisteria into a beautiful and coherent quilt called wisdom.
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What a true saying it is that he who wants to deceive mankind must before all things make absurdity plausible.
In The Maxims and Reflections of Goethe (1906), 200.
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What I tell you three times is true.
The Hunting of the Snark: An Agony, in Eight Fits (1876), 3.
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What is the true end and aim of science but the discovery of the ultimate power—a seeking after God through the study his ways?
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What is the use of straining after an amiable view of things, when a cynical view is most likely to be the true one?
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When a true genius appears in the world you may know him by this sign: that all the dunces are in confederacy against him.
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When it is not in our power to determine what is true, we ought to act according to what is most probable.
In Discours de la Méthode: Troisième partie, collected in Oeuvres Philosophiques de Descartes (1835), 23. As quoted and translated in Joseph William Mellor, Higher Mathematics for Students of Chemistry and Physics (1901), 416. From the original French, “Lorsqu’il n’est pas eu notre pouvoir de discerner les plus vraies opinions, nous devons suivre les plus probables.”
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When the first “thermonuclear device” was approaching the test stage and someone asked Teller, “Will it work?” he had to admit that he didn’t know. “But you didn’t know that five years ago,” the questioner pointed out. “True,” Teller answered, “but now we don’t know on much better grounds.”
As given by in Robert Coughlan, 'Dr. Edward Teller’s Magnificent Obsession', Life (6 Sep 1954), 70.
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When the mathematician says that such and such a proposition is true of one thing, it may be interesting, and it is surely safe. But when he tries to extend his proposition to everything, though it is much more interesting, it is also much more dangerous. In the transition from one to all, from the specific to the general, mathematics has made its greatest progress, and suffered its most serious setbacks, of which the logical paradoxes constitute the most important part. For, if mathematics is to advance securely and confidently, it must first set its affairs in order at home.
With co-author James R. Newman, in Mathematics and the Imagination (1940), 219.
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Whenever … a controversy arises in mathematics, the issue is not whether a thing is true or not, but whether the proof might not be conducted more simply in some other way, or whether the proposition demonstrated is sufficiently important for the advancement of the science as to deserve especial enunciation and emphasis, or finally, whether the proposition is not a special case of some other and more general truth which is as easily discovered.
In Mathematical Essays and Recreations (1898), 88.
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Without this language [mathematics] most of the intimate analogies of things would have remained forever unknown to us; and we should forever have been ignorant of the internal harmony of the world, which is the only true objective reality. …
This harmony … is the sole objective reality, the only truth we can attain; and when I add that the universal harmony of the world is the source of all beauty, it will be understood what price we should attach to the slow and difficult progress which little by little enables us to know it better.
From La Valeur de la Science, as translated by George Bruce Halsted, in 'The Value of Science', Popular Science Monthly (Sep 1906), 69 195-196.
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You can prepare yourself for work. The paintings of the great masters, the compositions of great musicians, the sermons of great preachers, the policies of great statesmen, and the campaigns of great generals, do not spring full bloom from barren rock. … If you are a true student you will be more dissatisfied with yourself when you graduate than you are now.
From Cameron Prize Lecture (1928), delivered before the University of Edinburgh. As quoted in J.B. Collip 'Frederick Grant Banting, Discoverer of Insulin', The Scientific Monthly (May 1941), 52, No. 5, 473-474.
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Your theory is crazy...but it’s not crazy enough to be true.
…...
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[With] our critical faculties in decline, unable to distinguish between what feels good and what’s true, we slide, almost without noticing, back into superstition. … We have also arranged things so that almost no one understands science and technology. We might get away with it for a while, but eventually this combustible mixture of ignorance and power is going to blow up in our faces.
In 'With Science on Our Side', Washington Post (9 Jan 1994).
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~~[Dubious]~~ A plagiarist steals from one person. A true artist steals from everybody.
Seen feral on the web, but never with source citation. Webmaster has not yet found any primary source, and regards the quote as spurious. Compare the believed authentic quote, “When there's anything to steal, I steal,” See the Pablo Picasso Quotes page on this site.
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…so slow is moral progress. True, we have the bicycle, the motor-car, the dirigible airship and other marvellous means of breaking our bones; but our morality is not one rung the higher for it all. One would even say that, the farther we proceed in our conquest of matter, the more our morality recedes. The most advanced of our inventions consists in bringing men down with grapeshot and explosives with the swiftness of the reaper mowing the corn.
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“Divide et impera” is as true in algebra as in statecraft; but no less true and even more fertile is the maxim “auge et impera”.The more to do or to prove, the easier the doing or the proof.
In 'Proof of the Fundamental Theorem of Invariants', Philosophic Magazine (1878), 186. In Collected Mathematical Papers, 3, 126. [The Latin phrases, “Divide/auge et impera” translate as “Divide/increase and rule”.
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“Mother like son” is a saying so true, the world will judge largely of mother by you.
In Silk Parachute.
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Carl Sagan Thumbnail In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
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- 90 -
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- 70 -
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- 50 -
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- 40 -
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