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Who said: “God does not care about our mathematical difficulties. He integrates empirically.”
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Home > Category Index for Science Quotations > Category Index C > Category: Confidence

Confidence Quotes (69 quotes)

L'imagination au contraire qui tend à nous porter continuellement au-delà du vrai, l'amour-propre et la confiance en nous-mêmes, qu'il sait si bien nous inspirer, nous sollicitent à tirer des conséquences qui ne dérivent pas immédiatement des faits.
Imagination, on the contrary, which is ever wandering beyond the bounds of truth, joined to self-love and that self-confidence we are so apt to indulge, prompt us to draw conclusions which are not immediately derived from facts.
From the original French in Traité élémentaire de chimie (1789, 1793), discours préliminaire, ix; and from edition translated into English by Robert Kerr, as Elements of Chemistry (1790), Preface, xvii.
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A general course in mathematics should be required of all officers for its practical value, but no less for its educational value in training the mind to logical forms of thought, in developing the sense of absolute truthfulness, together with a confidence in the accomplishment of definite results by definite means.
In 'Mathematics at West Point and Annapolis', United States Bureau of Education, Bulletin 1912, No. 2, 11.
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A key concept is that security is an enabler, not a disabler. … Security … enables you to keep your job, security enables you to move into new markets, security enables you to have confidence in what you’re doing.
As quoted in magazine article, an interview by John McCormick, 'Computer Security as a Business Enabler', Baseline (7 Jul 2007).
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A man can do his best only by confidently seeking (and perpetually missing) an unattainable perfection.
In Forbes (1946), 57, 46.
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Sigmund Freud quote: A man who has been the indisputable favorite of his mother keeps for life the feeling of a
A man who has been the indisputable favorite of his mother keeps for life the feeling of a conqueror, that confidence of success that often induces real success.
Quoted in Ernest Jones, The Life and Work of Sigmund Freud (1957), Vol. 1, 5.
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Are we prepared to admit, that our confidence in the regularity of nature is merely a corollary from Bernoulli’s theorem?
In 'On the Foundations of the Theory of Probabilities', read 14 Feb 1842, printed in Transactions of the Cambridge Philosophical Society (1849), 8, 1. Collected in William Walton (ed.), The Mathematical and Other Writings of Robert Leslie Ellis (1863), 1. Note: Jacques Bernouill’s theorem is also known as the Law of Averages.
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As to how far in advance of the first flight the man should know he’s going. I’m not in agreement with the argument that says word should be delayed until the last possible moment to save the pilot from developing a bad case of the jitters. If we don’t have the confidence to keep from getting clutched at that time, we have no business going at all. If I’m the guy going, I’ll be glad to get the dope as soon as possible. As for keeping this a big secret from us and having us all suited up and then saying to one man “you go” and stuffing him in and putting the lid on that thing and away he goes, well, we’re all big boys now.
As he wrote in an article for Life (14 Sep 1959), 38. In fact, he was the first to fly in Earth orbit on 20 Feb 1962, though Alan Shepard was picked for the earlier first suborbital flight.
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As to what Simplicius said last, that to contend whether the parts of the Sun, Moon, or other celestial body, separated from their whole, should naturally return to it, is a vanity, for that the case is impossible, it being clear by the demonstrations of Aristotle that the celestial bodies are impassible, impenetrable, unpartable, etc., I answer that none of the conditions whereby Aristotle distinguishes the celestial bodies from the elementary has any foundation other than what he deduces from the diversity of their natural motions; so that, if it is denied that the circular motion is peculiar to celestial bodies, and affirmed instead that it is agreeable to all naturally moveable bodies, one is led by necessary confidence to say either that the attributes of generated or ungenerated, alterable or unalterable, partable or unpartable, etc., equally and commonly apply to all bodies, as well to the celestial as to the elementary, or that Aristotle has badly and erroneously deduced those from the circular motion which he has assigned to celestial bodies.
Dialogue on the Great World Systems (1632). Revised and Annotated by Giorgio De Santillana (1953), 45.
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As, no matter what cunning system of checks we devise, we must in the end trust some one whom we do not check, but to whom we give unreserved confidence, so there is a point at which the understanding and mental processes must be taken as understood without further question or definition in words. And I should say that this point should be fixed pretty early in the discussion.
Samuel Butler, Henry Festing Jones (ed.), The Note-Books of Samuel Butler (1917), 220-221.
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Better to withdraw confidence than measure it.
From the original French, “Mieux vaut retirer sa confiance que la mesurer”, in Actes de l'Académie Nationale des Sciences, Belles-Lettres et Arts de Bordeaux (1872), 479. English as in Franz Liszt, The Letters of Franz Liszt to Olga Von Meyendorff (1979), 82.
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Chemically induced hallucinations, delusions and raptures may be frightening or wonderfully gratifying; in either case they are in the nature of confidence tricks played on one’s own nervous system.
In 'Return Trip to Nirvana', Sunday Telegraph (12 Mar 1961), as collected in Kaleidoscope: Essays from Drinkers of Infinity, and The Heel of Achilles and Later Pieces and Stories (1981), 80 (source cited on p.72, footnote).
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Darwin's characteristic perspicacity is nowhere better illustrated than in his prophecy of the reaction of the world of science. He admitted at once that it would be impossible to convince those older men '...whose minds are stocked with a multitude of facts, all viewed ... from a point of view directly opposite to mine ... A few naturalists endowed with much flexibility of mind and who have already begun to doubt the immutability of species, may be influenced by this volume; but I look with confidence to the young and rising naturalists, who will be able to view both sides with equal impartiality.
'The Reaction of American scientists to Darwinism', American Historical Review 1932), 38, 687. Quoted in David L. Hull, Science as Process (), 379.
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DOCTOR. Always preceded by “The good”. Among men, in familiar conversation, “Oh! balls, doctor!” Is a wizard when he enjoys your confidence, a jack-ass when you're no longer on terms. All are materialists: “you can't probe for faith with a scalpel.”
The Dictionary of Accepted Ideas (1881), trans. Jaques Barzun (1968), 30.
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Every great anthropologic and paleontologic discovery fits into its proper place, enabling us gradually to fill out, one after another, the great branching lines of human ascent and to connect with the branches definite phases of industry and art. This gives us a double means of interpretation, archaeological and anatomical. While many branches and links in the chain remain to be discovered, we are now in a position to predict with great confidence not only what the various branches will be like but where they are most like to be found.
In Henry Fairfield Osborn, 'Osborn States the Case For Evolution', New York Times (12 Jul 1925), XX1
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For the truth of the conclusions of physical science, observation is the supreme Court of Appeal. It does not follow that every item which we confidently accept as physical knowledge has actually been certified by the Court; our confidence is that it would be certified by the Court if it were submitted. But it does follow that every item of physical knowledge is of a form which might be submitted to the Court. It must be such that we can specify (although it may be impracticable to carry out) an observational procedure which would decide whether it is true or not. Clearly a statement cannot be tested by observation unless it is an assertion about the results of observation. Every item of physical knowledge must therefore be an assertion of what has been or would be the result of carrying out a specified observational procedure.
In ’Scientific Epistemology', The Philosophy of Physical Science (1938, 2012), 9.
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From the freedom to explore comes the joy of learning. From knowledge acquired by personal initiative arises the desire for more knowledge. And from mastery of the novel and beautiful world awaiting every child comes self-confidence.
In The Creation: An Appeal to Save Life on Earth (2010), 147.
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He is the best Physician in whom the Patient has the greatest Confidence.
The Reflector: Representing Human Affairs As They Are (1750). In Allan Ingram, Patterns of Madness in the Eighteenth Century (1998), 69.
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His mother’s favorite, he [Freud] possessed the self-confidence that told him he would achieve something worth while in life, and the ambition to do so, though for long the direction this would take remained uncertain.
In The Life and Work of Sigmund Freud: The Formative Years and the Great Discoveries, 1856-1900 (1957), 15.
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I believe that only scientists can understand the universe. It is not so much that I have confidence in scientists being right, but that I have so much in nonscientists being wrong.
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I feel more confident and more satisfied when I reflect that I have two professions and not one. Medicine is my lawful wife and literature is my mistress. When I get tired of one I spend the night with the other. Though it's disorderly it's not so dull, and besides, neither really loses anything, through my infidelity.
In letter to A.S. Suvorin (11 Sep 1888).
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I have found no better expression than ‘religious’ for confidence in the rational nature of reality, insofar as it is accessible to human reason. Whenever this feeling is absent, science degenerates into uninspired empiricism.
…...
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I learned this, at least, by my experiment: that if one advances confidently in the direction of his dreams, and endeavors to live the life which he has imagined, he will meet with a success unexpected in common hours.
In Walden: or, Life in the Woods (1854, 1893), 496.
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I undertake my scientific research with the confident assumption that the earth follows the laws of nature which God established at creation. … My studies are performed with the confidence that God will not capriciously confound scientific results by “slipping in” a miracle.
Quoted in Lenny Flank, Deception by Design: The Intelligent Design Movement in America (2007), 81. Also seen as cited from Arthur Newell Strahler, Science and Earth History: the Evolution/Creation Controversy (1987), 40-41.
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I watched his countenance closely, to see if he was not deranged ... and I was assured by other senators after he left the room that they had no confidence in it.
Reminiscence by Oliver Hampton Smith, Senator for Indiana, upon meeting Morse at the demonstration of his telegraph to the U.S. Congress in 1842.
Early Indiana Trials and Sketches (1858), 413
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I've always felt that maybe one of the reasons that I did well as a student and made such good grades was because I lacked ... self-confidence, and I never felt that I was prepared to take an examination, and I had to study a little bit extra. So that sort of lack of confidence helped me, I think, to make a good record when I was a student.
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Ideologues of all persuasions think they know how the economy will respond to the Administration’s strange mixture of Lafferism and monetarism. Indeed, their self-confidence is so vast, and their ability to rationalize so crafty, that one cannot imagine a scenario for the next few years, that they would regard as falsifying their dogma. The failure of any prediction can always be blamed on quirky political decisions or unforeseen historical events.
In 'Mathematical Games: The Laffer Curve', Scientific American (Dec 1981), 245, No. 6, 30. Collected in The Night Is Large: Collected Essays, 1938-1995 (1997), 135.
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Ignorance more frequently begets confidence than does knowledge: it is those who know little, and not those who know much, who so positively assert that this or that problem will never be solved by science.
The Descent of Man (1871), Vol. 1, 3.
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In 1891, during the Presidency of William Henry Harrison [Benjamin Harrison], electric lights were first installed in the White House, the residence of the leaders of our country. At that time, commercial electricity was not economically feasible, but President Harrison wanted to affirm his confidence in the technological capability of our country.
Speech, at dedication of solar panels on the White House roof, 'Solar Energy Remarks Announcing Administration Proposals' (20 Jun 1979).
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In 1925 [state legislators] prohibited by law the teaching of evolution in Tennessee. … Anti-evolutionists feared that a scientific idea would undermine religious belief. In the present…, pro-evolutionists fear that a religious idea will undermine scientific belief. The former had insufficient confidence in religion; the latter, insufficient confidence in science.
In Building a Bridge to the 18th Century: How the Past Can Improve Our Future (1999), 167.
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In the beginning there was an explosion. Not an explosion like those familiar on earth, starting from a definite center and spreading out to engulf more and more of the circumambient air, but an explosion which occurred simultaneously everywhere, filling all space from the beginning, with every particle of matter rushing apart from every other particle. ‘All space’ in this context may mean either all of an infinite universe, or all of a finite universe which curves back on itself like the surface of a sphere. Neither possibility is easy to comprehend, but this will not get in our way; it matters hardly at all in the early universe whether space is finite or infinite. At about one-hundredth of a second, the earliest time about which we can speak with any confidence, the temperature of the universe was about a hundred thousand million (1011) degrees Centigrade. This is much hotter than in the center of even the hottest star, so hot, in fact, that none of the components of ordinary matter, molecules, or atoms, or even the nuclei of atoms, could have held together. Instead, the matter rushing apart in this explosion consisted of various types of the so-called elementary particles, which are the subject of modern high­energy nuclear physics.
The First Three Minutes: A Modern View of the Origin of the Universe (1977), 5.
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In the fight which we have to wage incessantly against ignorance and quackery among the masses and follies of all sorts among the classes, diagnosis, not drugging, is our chief weapon of offence. Lack of systematic personal training in the methods of the recognition of disease leads to the misapplication of remedies, to long courses of treatment when treatment is useless, and so directly to that lack of confidence in our methods which is apt to place us in the eyes of the public on a level with empirics and quacks.
Address to the Canadian Medical Association, Montreal (17 Sep 1902), 'Chauvinism in Medicine', published in The Montreal Medical Journal (1902), 31, 267. Collected in Aequanimitas, with Other Addresses to Medical Students, Nurses and Practitioners of Medicine (1904), 299.
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In the light of knowledge attained, the happy achievement seems almost a matter of course, and any intelligent student can grasp it without too much trouble. But the years of anxious searching in the dark, with their intense longing, their alternations of confidence and exhaustion, and the final emergence into the light—only those who have experienced it can understand that.
Quoted in Banesh Hoffmann and Helen Dukas, Albert Einstein: Creator and Rebel (1972), 124.
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In the modern world, science and society often interact in a perverse way. We live in a technological society, and technology causes political problems. The politicians and the public expect science to provide answers to the problems. Scientific experts are paid and encouraged to provide answers. The public does not have much use for a scientist who says, “Sorry, but we don’t know.” The public prefers to listen to scientists who give confident answers to questions and make confident predictions of what will happen as a result of human activities. So it happens that the experts who talk publicly about politically contentious questions tend to speak more clearly than they think. They make confident predictions about the future, and end up believing their own predictions. Their predictions become dogmas which they do not question. The public is led to believe that the fashionable scientific dogmas are true, and it may sometimes happen that they are wrong. That is why heretics who question the dogmas are needed.
Frederick S. Pardee Distinguished Lecture (Oct 2005), Boston University. Collected in 'Heretical Thoughts About Science and Society', A Many-Colored Glass: Reflections on the Place of Life in the Universe (2007), 43-44.
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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 also a good rule not to put overmuch confidence in the observational results that are put forward until they are confirmed by theory.
New Pathways in Science (1935), 211.
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It is baffling, I must say, that in our modern world we have such blind trust in science and technology that we all accept what science tells us about everything—until, that is, it comes to climate science. All of a sudden, and with a barrage of sheer intimidation, we are told by powerful groups of deniers that the scientists are wrong and we must abandon all our faith in so much overwhelming scientific evidence. So thank goodness for our young entrepreneurs here this evening, who have the far-sightedness and confidence in what they know is happening to ignore the headless chicken brigade and do something practical to help.
Speech, awards ceremony for green entrepreneurs, Buckingham Palace (30 Jan 2014). As quoted in Benn Quinn, 'Climate Change Sceptics are ‘Headless Chickens’, Says Prince Charles', The Guardian (31 Jan 2014).
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It is the surgeon’s duty to tranquillize the temper, to beget cheerfulness, and to impart confidence of recovery.
The Lectures of Sir Astley Cooper (1824), 30.
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It may be said “In research, if you know what you are doing, then you shouldn't be doing it.” In a sense, if the answer turns out to be exactly what you expected, then you have learned nothing new, although you may have had your confidence increased somewhat.
In Numerical Methods for Scientists and Engineers (1973), 704.
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It must be conceded that a theory has an important advantage if its basic concepts and fundamental hypotheses are 'close to experience,' and greater confidence in such a theory is certainly justified. There is less danger of going completely astray, particularly since it takes so much less time and effort to disprove such theories by experience. Yet more and more, as the depth of our knowledge increases, we must give up this advantage in our quest for logical simplicity in the foundations of physical theory...
'On the Generalized Theory of Gravitation', Scientific American (Apr 1950), 13. In David H. Levy (Ed.), The Scientific American Book of the Cosmos (2000), 19.
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Life is not easy for any of us, but what of that? We must have perseverance and above all confidence in ourselves. We must believe that we are gifted in something, and that this thing, at whatever cost, must be attained.
Letter to brother (1894). In Eve Curie, Madame Curie: a Biography by Eve Curie (1937, 2007), 158.
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Logic is only the art of going wrong with confidence.
This is a slightly reworded version of part of a quote by Joseph Wood Krutch (see the quote beginning “Metaphysics…”, on the Joseph Wood Krutch Quotes page of this website.) This note by Webmaster is included here to help readers identify that it is incorrectly cited when found attributed to Morris Kline, John Ralston Saul or W.H. Auden. In fact, the quote is simply attributed to Anonymous by Kline in his Mathematics: The Loss of Certainty (1980), 197; and as an “old conundrum” in Saul's On Equilibrium: The Six Qualities of the New Humanism (2004), 124.
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Many times every day I think of taking off in that missile. I’ve tried a thousand times to visualize that moment, to anticipate how I’ll feel if I’m first, which I very much want to be. But whether I go first or go later. I approach it now with some awe, and I’m sure I’ll approach it with even more awe on my day. In spite of the fact that I will he very busy getting set and keeping tabs on all the instruments, there’s no question that I’ll need—and will have—all my confidence.
As he wrote in an article for Life (14 Sep 1959), 38.
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Mathematics … above all other subjects, makes the student lust after knowledge, fills him, as it were, with a longing to fathom the cause of things and to employ his own powers independently; it collects his mental forces and concentrates them on a single point and thus awakens the spirit of individual inquiry, self-confidence and the joy of doing; it fascinates because of the view-points which it offers and creates certainty and assurance, owing to the universal validity of its methods. Thus, both what he receives and what he himself contributes toward the proper conception and solution of a problem, combine to mature the student and to make him skillful, to lead him away from the surface of things and to exercise him in the perception of their essence. A student thus prepared thirsts after knowledge and is ready for the university and its sciences. Thus it appears, that higher mathematics is the best guide to philosophy and to the philosophic conception of the world (considered as a self-contained whole) and of one’s own being.
In Die Mathematik die Fackelträgerin einer neuen Zeit (1889), 40. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 49.
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Mathematics … engages, it fructifies, it quickens, compels attention, is as circumspect as inventive, induces courage and self-confidence as well as modesty and submission to truth. It yields the essence and kernel of all things, is brief in form and overflows with its wealth of content. It discloses the depth and breadth of the law and spiritual element behind the surface of phenomena; it impels from point to point and carries within itself the incentive toward progress; it stimulates the artistic perception, good taste in judgment and execution, as well as the scientific comprehension of things.
In Die Mathematik die Fackelträgerin einer neuen Zeit (1889), 40. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 49.
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Metaphysics may be, after all, only the art of being sure of something that is not so and logic only the art of going wrong with confidence.
In The Modern Temper (1929), 228. The second part of this quote is often seen as a sentence by itself, and a number of authors cite it incorrectly. For those invalid attributions, see quote beginning “Logic is only the art…” on the Joseph Wood Krutch Quotes page of this website.
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Often the confidence of the patient in his physician does more for the cure of his disease than the physician with all his remedies.
Reasserting the statement by Avicenna.
In James Joseph Walsh, Old-Time Makers of Medicine (1911), 270.
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Optimism is the faith that leads to achievement. Nothing can be done without hope or confidence.
…...
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Psychoanalytic theory is the most stupendous intellectual confidence trick of the twentieth century and a terminal product as well—something akin to a dinosaur or zeppelin in the history of ideas, a vast structure of radically unsound design and with no posterity.
'Victims of Psychiatry', The New York Review of Books (23 Jan 1975), 21. Cited in David E. Stannard, Shrinking History: On Freud and the Failure of Psychohistory (1980), 150.
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Scientific progress is the discovery of a more and more comprehensive simplicity... The previous successes give us confidence in the future of science: we become more and more conscious of the fact that the universe is cognizable.
In O. Godart and M. Heller (eds.), Cosmology of Lemaitre (1985), 162.
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Scientists are the easiest to fool. ... They think in straight, predictable, directable, and therefore misdirectable, lines. The only world they know is the one where everything has a logical explanation and things are what they appear to be. Children and conjurors—they terrify me. Scientists are no problem; against them I feel quite confident.
Code of the Lifemaker (1983, 2000),Chapter 1.
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That the enthusiasm which characterizes youth should lift its parricide hands against freedom and science would be such a monstrous phenomenon as I cannot place among possible things in this age and country.
[Expressing confidence in the next generation to preserve the freedom of the human mind, and of the press, which grew out of America's Declaration of Independence.]
Letter to a student, William Green Mumford (18 Jun 1799), In Merrill D. Peterson, Thomas Jefferson and the New Nation (1970), 616.
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The crown and glory of life is Character. It is the noblest possession of a man, constituting a rank in itself, and an estate in the general goodwill; dignifying every station, and exalting every position in society. It exercises a greater power than wealth, and secures all the honour without the jealousies of fame. It carries with it an influence which always tells; for it is the result of proved honour, rectitude, and consistency—qualities which, perhaps more than any other, command the general confidence and respect of mankind.
In Self-help: With Illustrations of Character and Conduct (1859, 1861), 396.
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The fact is that up to now the free society has not been good for the intellectual. It has neither accorded him a superior status to sustain his confidence nor made it easy for him to acquire an unquestioned sense of social usefulness. For he derives his sense of usefulness mainly from directing, instructing, and planning-from minding other people’s business-and is bound to feel superfluous and neglected where people believe themselves competent to manage individual and communal affairs, and are impatient of supervision and regulation. A free society is as much a threat to the intellectual’s sense of worth as an automated economy is to the workingman’s sense of worth. Any social order that can function with a minimum of leadership will be anathema to the intellectual.
In 'Concerning Individual Freedom', The Ordeal of Change (1963), 141.
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The final results [of work on the theory of relativity] appear almost simple; any intelligent undergraduate can understand them without much trouble. But the years of searching in the dark for a truth that one feels, but cannot express; the intense effort and the alternations of confidence and misgiving, until one breaks through to clarity and understanding, are only known to him who has himself experienced them.
Concluding remark of George Gibson lecture at the University of Glasgow, 'The Origins of the General Theory of Relativity', (20 Jun 1933). Published by Glasgow University as The Origins of the General Theory of Relativity: Being the First Lecture on the George A. Gibson Foundation in the University of Glasgow, Delivered on June 20th, 1933 (1933), 11. Also quoted in 'No Hitching Posts' The Atlantic (1936), 157, 251.
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The inherent unpredictability of future scientific developments—the fact that no secure inference can be drawn from one state of science to another—has important implications for the issue of the limits of science. It means that present-day science cannot speak for future science: it is in principle impossible to make any secure inferences from the substance of science at one time about its substance at a significantly different time. The prospect of future scientific revolutions can never be precluded. We cannot say with unblinking confidence what sorts of resources and conceptions the science of the future will or will not use. Given that it is effectively impossible to predict the details of what future science will accomplish, it is no less impossible to predict in detail what future science will not accomplish. We can never confidently put this or that range of issues outside “the limits of science”, because we cannot discern the shape and substance of future science with sufficient clarity to be able to say with any assurance what it can and cannot do. Any attempt to set “limits” to science—any advance specification of what science can and cannot do by way of handling problems and solving questions—is destined to come to grief.
The Limits of Science (1984), 102-3.
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The most ordinary things are to philosophy a source of insoluble puzzles. In order to explain our perceptions it constructs the concept of matter and then finds matter quite useless either for itself having or for causing perceptions in a mind. With infinite ingenuity it constructs a concept of space or time and then finds it absolutely impossible that there be objects in this space or that processes occur during this time ... The source of this kind of logic lies in excessive confidence in the so-called laws of thought.
'On Statistical Mechanics' (1904), in Theoretical Physics and Philosophical Problems (1974), 164-5.
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The only solid piece of scientific truth about which I feel totally confident is that we are profoundly ignorant about nature. Indeed, I regard this as the major discovery of the past hundred years of biology. It is, in its way, an illuminating piece of news. … It is this sudden confrontation with the depth and scope of ignorance that represents the most significant contribution of twentieth-century science to the human intellect.
Essay, 'The Hazards of Science', collected in The Medusa and the Snail: More Notes of a Biology Watcher (1979), 73.
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The professor may choose familiar topics as a starting point. The students collect material, work problems, observe regularities, frame hypotheses, discover and prove theorems for themselves. … the student knows what he is doing and where he is going; he is secure in his mastery of the subject, strengthened in confidence of himself. He has had the experience of discovering mathematics. He no longer thinks of mathematics as static dogma learned by rote. He sees mathematics as something growing and developing, mathematical concepts as something continually revised and enriched in the light of new knowledge. The course may have covered a very limited region, but it should leave the student ready to explore further on his own.
In A Concrete Approach to Abstract Algebra (1959), 1-2.
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The speculative propositions of mathematics do not relate to facts; … all that we are convinced of by any demonstration in the science, is of a necessary connection subsisting between certain suppositions and certain conclusions. When we find these suppositions actually take place in a particular instance, the demonstration forces us to apply the conclusion. Thus, if I could form a triangle, the three sides of which were accurately mathematical lines, I might affirm of this individual figure, that its three angles are equal to two right angles; but, as the imperfection of my senses puts it out of my power to be, in any case, certain of the exact correspondence of the diagram which I delineate, with the definitions given in the elements of geometry, I never can apply with confidence to a particular figure, a mathematical theorem. On the other hand, it appears from the daily testimony of our senses that the speculative truths of geometry may be applied to material objects with a degree of accuracy sufficient for the purposes of life; and from such applications of them, advantages of the most important kind have been gained to society.
In Elements of the Philosophy of the Human Mind (1827), Vol. 3, Chap. 1, Sec. 3, 180.
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We academic scientists move within a certain sphere, we can go on being useless up to a point, in the confidence that sooner or later some use will be found for our studies. The mathematician, of course, prides himself on being totally useless, but usually turns out to be the most useful of the lot. He finds the solution but he is not interested in what the problem is: sooner or later, someone will find the problem to which his solution is the answer.
'Concluding Remarks', Proceedings of the Royal Society of London, Series A, A Discussion of New Materials, 1964, 282, 152-3.
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We may indeed live yet to see, or at least we may feel some confidence that those who come after us will see, such bodies as oxygen and hydrogen in the liquid, perhaps even in the solid state, and the question of their metallic or non-metallic nature thereby finally settled.
In Thomas Andrews, Peter Guthrie Tait (ed.) and Alexander Crum Brown (ed.) The Scientific Papers of the Late Thomas Andrews (1889), lx.
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We reverence ancient Greece as the cradle of western science. Here for the first time the world witnessed the miracle of a logical system which proceeded from step to step with such precision that every single one of its propositions was absolutely indubitable—I refer to Euclid’s geometry. This admirable triumph of reasoning gave the human intellect the necessary confidence in itself for its subsequent achievements. If Euclid failed to kindle your youthful enthusiasm, then you were not born to be a scientific thinker.
From 'On the Method of Theoretical Physics', in Essays in Science (1934, 2004), 13.
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When I was growing up, I always knew I’d be in the top of my class in math, and that gave me a lot of self-confidence. [But now that students can see beyond their own school, they see that] there are always going to be a million people better than you at times, or someone will always be far better than you. I feel there’s an existential angst among young people. I didn’t have that. They see enormous mountains, where I only saw one little hill to climb.
From address at a conference on Google campus, co-hosted with Common Sense Media and the Joan Ganz Cooney Center at Sesame Workshop 'Breakthrough Learning in the Digital Age'. As quoted in Technology blog report by Dan Fost, 'Google co-founder Sergey Brin wants more computers in schools', Los Angeles Times (28 Oct 2009). On latimesblogs.latimes.com website. As quoted, without citation, in Can Akdeniz, Fast MBA (2014), 280.
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Whoever limits his exertions to the gratification of others, whether by personal exhibition, as in the case of the actor and of the mimic, or by those kinds of literary composition which are calculated for no end but to please or to entertain, renders himself, in some measure, dependent on their caprices and humours. The diversity among men, in their judgments concerning the objects of taste, is incomparably greater than in their speculative conclusions; and accordingly, a mathematician will publish to the world a geometrical demonstration, or a philosopher, a process of abstract reasoning, with a confidence very different from what a poet would feel, in communicating one of his productions even to a friend.
In Elements of the Philosophy of the Human Mind (1827), Vol. 3, Chap. 1, Sec. 3, 202.
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You can find that sort of regularity in Stock Exchange quotations.
[Expressing his lack of confidence in reported regularities in the periodic classification of elements.]
As quoted in Stanley I. Levy, 'Brauner Memorial Lecture', Journal of the Chemical Society (1935), Pt. 2, 1878. It has also been quoted as “One might just as well seek regularities in the figures of stock exchange bulletins” in L. Vlasov and D. Trifonov, trans. from Russian by David Sobolev, 107 Stories About Chemistry (1970).
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Young men, have confidence in those powerful and safe methods, of which we do not yet know all the secrets. And, whatever your career may be, do not let yourselves become tainted by a deprecating and barren skepticism … Live … until the time comes when you have the immense happiness of thinking that you have contributed in some way to the progress and to the good of humanity.
Acceptance speech (27 Dec 1892) when awarded a 70th birthday commemorative medal by the Academy of Sciences in the great theatre of the Sorbonne, as translated in René Vallery-Radot and Mrs R.L. Devonshire (trans.), The Life of Pasteur (1902), Vol. 2, 297-298. Pasteur addressed an audience that included “deep masses of students” and “boys from the lycées.”
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[In mathematics] we behold the conscious logical activity of the human mind in its purest and most perfect form. Here we learn to realize the laborious nature of the process, the great care with which it must proceed, the accuracy which is necessary to determine the exact extent of the general propositions arrived at, the difficulty of forming and comprehending abstract concepts; but here we learn also to place confidence in the certainty, scope and fruitfulness of such intellectual activity.
In Ueber das Verhältnis der Naturwissenschaften zur Gesammtheit der Wissenschaft, Vorträge und Reden (1896), Bd. 1, 176. Also seen translated as “In mathematics we see the conscious logical activity of our mind in its purest and most perfect form; here is made manifest to us all the labor and the great care with which it progresses, the precision which is necessary to determine exactly the source of the established general theorems, and the difficulty with which we form and comprehend abstract conceptions; but we also learn here to have confidence in the certainty, breadth, and fruitfulness of such intellectual labor”, in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 20. From the original German, “Hier sehen wir die bewusste logische Thätigkeit unseres Geistes in ihrer reinsten und vollendetsten Form; wir können hier die ganze Mühe derselben kennen lernen, die grosse Vorsicht, mit der sie vorschreiten muss, die Genauigkeit, welche nöthig ist, um den Umfang der gewonnenen allgemeinen Sätze genau zu bestimmen, die Schwierigkeit, abstracte Begriffe zu bilden und zu verstehen; aber ebenso auch Vertrauen fassen lernen in die Sicherheit, Tragweite und Fruchtbarkeit solcher Gedankenarbeit.”
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[Magic] enables man to carry out with confidence his important tasks, to maintain his poise and his mental integrity in fits of anger, in the throes of hate, of unrequited love, of despair and anxiety. The function of magic is to ritualize man's optimism, to enhance his faith in the victory of hope over fear. Magic expresses the greater value for man of confidence over doubt, of steadfastness over vacillation, of optimism over pessimism.
Magic, Science and Religion (1925), 90.
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[My] numberless observations... made on the Strata... [have] made me confident of their uniformity throughout this Country & [have] led me to conclude that the same regularity... will be found to extend to every part of the Globe for Nature has done nothing by piecemeal. [T]here is no inconsistency in her productions. [T]he Horse never becomes an Ass nor the Crab an Apple by any intermixture or artificial combination whatever[. N]or will the Oak ever degenerate into an Ash or an Ash into an Elm. [H]owever varied by Soil or Climate the species will still be distinct on this ground. [T]hen I argue that what is found here may be found elsewhere[.] When proper allowances are made for such irregularities as often occur and the proper situation and natural agreement is well understood I am satisfied there will be no more difficulty in ascertaining the true quality of the Strata and the place of its possition [sic] than there is now in finding the true Class and Character of Plants by the Linean [sic] System.
Natural Order of the Strata in England and Wales Accurately Delineated and Described, unpublished manuscript, Department of Geology, University of Oxford, 1801, f. 7v.
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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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- 80 -
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- 70 -
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- 60 -
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- 50 -
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- 40 -
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- 30 -
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- 20 -
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