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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: Certainty

Certainty Quotes (174 quotes)


'Tis certain that our senses are extremely disproportioned for comprehending the whole compass and latitude of things.
In Mathematical Magic; or the Wonders That May Be Performed by Mechanical Geometry (1680), 116
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... I left Caen, where I was living, to go on a geologic excursion under the auspices of the School of Mines. The incidents of the travel made me forget my mathematical work. Having reached Coutances, we entered an omnibus to go to some place or other. At the moment when I put my foot on the step, the idea came to me, without anything in my former thoughts seeming to have paved the way for it, that the transformations I had used to define the Fuchsian functions were identical with those of non-Eudidean geometry. I did not verify the idea; I should not have had time, as upon taking my seat in the omnibus, I went on with a conversation already commenced, but I felt a perfect certainty. On my return to Caen, for convenience sake, I verified the result at my leisure.
Quoted in Sir Roger Penrose, The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics (1990), 541. Science and Method (1908) 51-52, 392.
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[Attributing the origin of life to spontaneous generation.] However improbable we regard this event, it will almost certainly happen at least once…. The time… is of the order of two billion years.… Given so much time, the “impossible” becomes possible, the possible probable, and the probable virtually certain. One only has to wait: time itself performs the miracles.
In 'The Origin of Life', Scientific American (Aug 1964), 191, 46. Note that the quoted time of 2 billion years is rejected as impossibly short by such authors as H. J. Morowitz, in Energy Flow in Biology (1968), 317.
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A common fallacy in much of the adverse criticism to which science is subjected today is that it claims certainty, infallibility and complete emotional objectivity. It would be more nearly true to say that it is based upon wonder, adventure and hope.
Quoted in E. J. Bowen's obituary of Hinshelwood, Chemistry in Britain (1967), Vol. 3, 536.
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A distinguished writer [Siméon Denis Poisson] has thus stated the fundamental definitions of the science:
“The probability of an event is the reason we have to believe that it has taken place, or that it will take place.”
“The measure of the probability of an event is the ratio of the number of cases favourable to that event, to the total number of cases favourable or contrary, and all equally possible” (equally like to happen).
From these definitions it follows that the word probability, in its mathematical acceptation, has reference to the state of our knowledge of the circumstances under which an event may happen or fail. With the degree of information which we possess concerning the circumstances of an event, the reason we have to think that it will occur, or, to use a single term, our expectation of it, will vary. Probability is expectation founded upon partial knowledge. A perfect acquaintance with all the circumstances affecting the occurrence of an event would change expectation into certainty, and leave neither room nor demand for a theory of probabilities.
An Investigation of the Laws of Thought (1854), 243-244. The Poisson quote is footnoted as from Recherches sur la Probabilité des Jugemens.
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A drop of old tuberculin, which is an extract of tubercle bacilli, is put on the skin and then a small superficial scarification is made by turning, with some pressure, a vaccination lancet on the surface of the skin. The next day only those individuals show an inflammatory reaction at the point of vaccination who have already been infected with tuberculosis, whereas the healthy individuals show no reaction at all. Every time we find a positive reaction, we can say with certainty that the child is tuberculous.
'The Relation of Tuberculosis to Infant Mortality', read at the third mid-year meeting of the American Academy of Medicine, New Haven, Conn, (4 Nov 1909). In Bulletin of the American Academy of Medicine (1910), 11, 75.
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A good ornithologist should be able to distinguish birds by their air as well as by their colors and shape; on the ground as well as on the wing, and in the bush as well as in the hand. For, though it must not be said that every species of birds has a manner peculiar to itself, yet there is somewhat, in most genera at least, that at first sight discriminates them and enables a judicious observer to pronounce upon them with some certainty.
Letter (7 Aug 1778) to Daines Barrington, collected in The Natural History of Selborne (1829), 274.
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A great advantage of X-ray analysis as a method of chemical structure analysis is its power to show some totally unexpected and surprising structure with, at the same time, complete certainty.
In 'X-ray Analysis of Complicated Molecules', Nobel Lecture (11 Dec 1964). In Nobel Lectures: Chemistry 1942-1962 (1964), 83.
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A great man, [who] was convinced that the truths of political and moral science are capable of the same certainty as those that form the system of physical science, even in those branches like astronomy that seem to approximate mathematical certainty.
He cherished this belief, for it led to the consoling hope that humanity would inevitably make progress toward a state of happiness and improved character even as it has already done in its knowledge of the truth.
Describing administrator and economist Anne-Robert-Jacques Turgot in Essai sur l’application de l’analyse à la probabilité des décisions rendues à la pluralité des voix (1785), i. Cited epigraph in Charles Coulston Gillispie, Science and Polity in France: The End of the Old Regime (2004), 3
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A great surgeon performs operations for stone by a single method; later he makes a statistical summary of deaths and recoveries, and he concludes from these statistics that the mortality law for this operation is two out of five. Well, I say that this ratio means literally nothing scientifically and gives us no certainty in performing the next operation; for we do not know whether the next case will be among the recoveries or the deaths. What really should be done, instead of gathering facts empirically, is to study them more accurately, each in its special determinism. We must study cases of death with great care and try to discover in them the cause of mortal accidents so as to master the cause and avoid the accidents.
From An Introduction to the Study of Experimental Medicine (1865), as translated by Henry Copley Greene (1957), 137-138. (Note that Bernard overlooks how the statistical method can be useful: a surgeon announcing a mortality rate of 40% invites comparison. A surgeon with worse outcomes should adopt this method. If a surgeon has a better results, that method should be adopted.)
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A habit of basing convictions upon evidence, and of giving to them only that degree or certainty which the evidence warrants, would, if it became general, cure most of the ills from which the world suffers.
In Bertrand Russell and Paul Edwards (ed.), 'Preface', Why I Am Not a Christian: And Other Essays on Religion and Related Subjects (1957), vi.
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After that, I thought about what a proposition generally needs in order to be true and certain because, since I had just found one that I knew was such, I thought I should also know what this certainty consists in. Having noticed that there is nothing at all in the proposition “I think, therefore I am” [cogito ergo sum] which convinces me that I speak the truth, apart from the fact that I see very clearly that one has to exist in order to think, I judged that I could adopt as a general rule that those things we conceive very clearly and distinctly are all true. The only outstanding difficulty is in recognizing which ones we conceive distinctly.
Discourse on Method in Discourse on Method and Related Writings (1637), trans. Desmond M. Clarke, Penguin edition (1999), Part 4, 25.
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All our knowledge merely helps us to die a more painful death than the animals that know nothing. A day will come when science will turn upon its error and no longer hesitate to shorten our woes. A day will come when it will dare and act with certainty; when life, grown wiser, will depart silently at its hour, knowing that it has reached its term.
Our Eternity, translated by Alexander Teixeira de Mattos (1913), 24.
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All that passes for knowledge can be arranged in a hierarchy of degrees of certainty, with arithmetic and the facts of perception at the top.
From 'Philosophy For Laymen', collected in Unpopular Essays (1950, 1996), 39.
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Although I was first drawn to math and science by the certainty they promised, today I find the unanswered questions and the unexpected connections at least as attractive.
In Warped Passages (2005), 65.
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And for mathematical sciences, he that doubts their certainty hath need of a dose of Hellebore.
The Vanity of Dogmatizing (1661), ch. xxi, 209.
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Any one whose disposition leads him to attach more weight to unexplained difficulties than to the explanation of facts will certainly reject my theory.
The Origin of Species (1859), 482.
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Are the atoms of the dextroacid (tartaric) grouped in the spirals of a right-hand helix or situated at the angles of an irregular tetrahedron, or arranged in such or such particular unsymmetrical fashion? We are unable to reply to these questions. But there can be no reason for doubting that the grouping of the atoms has an unsymmetrical arrangement with a non-superimposable image. It is not less certain that the atoms of the laevo-acid realize precisely an unsymmetrical arrangement of the inverse of the above.
Leçons de Chemie (1860), 25.
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As an adolescent I aspired to lasting fame, I craved factual certainty, and I thirsted for a meaningful vision of human life—so I became a scientist. This is like becoming an archbishop so you can meet girls.
In 'Seventy-five reasons to become a scientist', American Scientist (Sep/Oct 1988). 76, No. 5, 452.
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As arithmetic and algebra are sciences of great clearness, certainty, and extent, which are immediately conversant about signs, upon the skilful use whereof they entirely depend, so a little attention to them may possibly help us to judge of the progress of the mind in other sciences, which, though differing in nature, design, and object, may yet agree in the general methods of proof and inquiry.
In Alciphron: or the Minute Philosopher, Dialogue 7, collected in The Works of George Berkeley D.D. (1784), Vol. 1, 621.
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As soon … as it was observed that the stars retained their relative places, that the times of their rising and setting varied with the seasons, that sun, moon, and planets moved among them in a plane, … then a new order of things began.… Science had begun, and the first triumph of it was the power of foretelling the future; eclipses were perceived to recur in cycles of nineteen years, and philosophers were able to say when an eclipse was to be looked for. The periods of the planets were determined. Theories were invented to account for their eccentricities; and, false as those theories might be, the position of the planets could be calculated with moderate certainty by them.
Lecture delivered to the Royal Institution (5 Feb 1864), 'On the Science of History'. Collected in Notices of the Proceedings at the Meetings of the Members of the Royal Institution of Great Britain with Abstracts of the Discourses (1866), Vol. 4, 187.
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At this very minute, with almost absolute certainty, radio waves sent forth by other intelligent civilizations are falling on the earth. A telescope can be built that, pointed in the right place, and tuned to the right frequency, could discover these waves. Someday, from somewhere out among the stars, will come the answers to many of the oldest, most important, and most exciting questions mankind has asked.
In Intelligent Life in Space (1962), 111.
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Bigotry and science can have no communication with each other, for science begins where bigotry and absolute certainty end.
Ashley Montagu (ed.), Science and Creationism (1984), Introduction, 8-9.
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But just as much as it is easy to find the differential of a given quantity, so it is difficult to find the integral of a given differential. Moreover, sometimes we cannot say with certainty whether the integral of a given quantity can be found or not.
Webmaster has looked and found no citation, and no example, in books with this wording, earlier than in a list of quotes, without citation, in Baumslag Benjamin, Fundamentals Of Teaching Mathematics At University Level (2000), 214. The original would be in native French, so different translations are possible. Can you help?
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Can the cause be reached from knowledge of the effect with the same certainty as the effect can be shown to follow from its cause? Is it possible for one effect to have many causes? If one determinate cause cannot be reached from the effect, since there is no effect which has not some cause, it follows that an effect, when it has one cause, may have another, and so that there may be several causes of it.
As quoted in Alistair Cameron Crombie, Robert Grosseteste and the Origins of Experimental Science, 1100-1700 (1971), 81.
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CARTESIAN, adj. Relating to Descartes, a famous philosopher, author of the celebrated dictum, Cogito, ergo sum—whereby he was pleased to suppose he demonstrated the reality of human existence. The dictum might be improved, however, thus: Cogito ergo cogito sum—'I think that I think, therefore I think that I am;' as close an approach to certainty as any philosopher has yet made.
The Collected Works of Ambrose Bierce (1911), Vol. 7, The Devil's Dictionary,  46-47.
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Certainty is the most vivid condition of ignorance and the most necessay condition for knowledge.
Quotations: Superultramodern Science and Philosophy (2005), 2
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Certitude is not the test of certainty. We have been cocksure of many things that are not so.
In 'Natural Law', The Harvard Law Review, 32, (1918). In Oliver Wendell Holmes and Harold Joseph Laski, Collected Legal Papers (1920), 311.
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Clearly it is not reason that has failed. What has failed—as it has always failed—is the attempt to achieve certainty, to reach an absolute, to find the course of human events to a final end. ... It is not reason that has promised to eliminate risk in human undertakings; it is the emotional needs of men.
In The Quest For Identity (1958), 135.
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Criticism, though dignified from the earliest ages by the labours of men eminent for knowledge and sagacity, has not yet attained the certainty and stability of science.
In Samuel Austin Allibone, Prose Quotations from Socrates to Macaulay (1880), 151.
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Descartes, the father of modern philosophy … would never—so he assures us—have been led to construct his philosophy if he had had only one teacher, for then he would have believed what he had been told; but, finding that his professors disagreed with each other, he was forced to conclude that no existing doctrine was certain.
From 'Philosophy For Laymen', collected in Unpopular Essays (1950, 1996), 57.
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Every gambler stakes a certainty to gain an uncertainty, and yet he stakes a finite certainty against a finite uncertainty without acting unreasonably. … The uncertainty of gain is proportioned to the certainty of the stake, according to the proportion of chances of gain and loss, and if therefore there are as many chances on one side as on the other, the game is even.
In Blaise Pascal and C. Kegan Paul (trans.), 'Of The Need of Seeking Truth', The Thought of Blaise Pascal: Translated from the Text of M. Auguste Molinier (1905), 98.
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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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Experiment is the sole source of truth. It alone can teach us something new; it alone can give us certainty.
Science and Hypothesis (1902), trans. W. J. G. and preface by J. Larmor (1905), 140.
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Facts and theories are different things, not rungs in a hierarchy of increasing certainty. Facts are the world's data. Theories are structures of ideas that explain and interpret facts. Facts do not go away while scientists debate rival theories for explaining them. Einstein's theory of gravitation replaced Newton's, but apples did not suspend themselves in mid-air pending the outcome.
'Evolution as Fact and Theory', in Hen's Teeth and Horse's Toes (1983, 1994), Chap. 19.
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Facts are certainly the solid and true foundation of all sectors of nature study ... Reasoning must never find itself contradicting definite facts; but reasoning must allow us to distinguish, among facts that have been reported, those that we can fully believe, those that are questionable, and those that are false. It will not allow us to lend faith to those that are directly contrary to others whose certainty is known to us; it will not allow us to accept as true those that fly in the face of unquestionable principles.
Memoires pour Servir a l'Histoire des Insectes (1736), Vol. 2, xxxiv. Quoted in Jacques Roger, The Life Sciences in Eighteenth-Century French Thought, ed. Keith R. Benson and trans. Robert Ellrich (1997), 165.
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Far from becoming discouraged, the philosopher should applaud nature, even when she appears miserly of herself or overly mysterious, and should feel pleased that as he lifts one part of her veil, she allows him to glimpse an immense number of other objects, all worthy of investigation. For what we already know should allow us to judge of what we will be able to know; the human mind has no frontiers, it extends proportionately as the universe displays itself; man, then, can and must attempt all, and he needs only time in order to know all. By multiplying his observations, he could even see and foresee all phenomena, all of nature's occurrences, with as much truth and certainty as if he were deducing them directly from causes. And what more excusable or even more noble enthusiasm could there be than that of believing man capable of recognizing all the powers, and discovering through his investigations all the secrets, of nature!
'Des Mulets', Oeuvres Philosophiques, ed. Jean Piveteau (1954), 414. Quoted in Jacques Roger, The Life Sciences in Eighteenth-Century French Thought, ed. Keith R. Benson and trans. Robert Ellrich (1997), 458.
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Good applied science in medicine, as in physics, requires a high degree of certainty about the basic facts at hand, and especially about their meaning, and we have not yet reached this point for most of medicine.
The Medusa and the Snail (1979), 143.
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Gradually, at various points in our childhoods, we discover different forms of conviction. There’s the rock-hard certainty of personal experience (“I put my finger in the fire and it hurt,”), which is probably the earliest kind we learn. Then there’s the logically convincing, which we probably come to first through maths, in the context of Pythagoras’s theorem or something similar, and which, if we first encounter it at exactly the right moment, bursts on our minds like sunrise with the whole universe playing a great chord of C Major.
In short essay, 'Dawkins, Fairy Tales, and Evidence', 2.
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He who has heard the same thing told by twelve thousand ocular [eye]witnesses, has only twelve thousand probabilities, equal to one strong one, which is not equal to certainty.
In 'Truth', Philosophical Dictionary (1824), Vol. 6, 297.
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Here I shall present, without using Analysis [mathematics], the principles and general results of the Théorie, applying them to the most important questions of life, which are indeed, for the most part, only problems in probability. One may even say, strictly speaking, that almost all our knowledge is only probable; and in the small number of things that we are able to know with certainty, in the mathematical sciences themselves, the principal means of arriving at the truth—induction and analogy—are based on probabilities, so that the whole system of human knowledge is tied up with the theory set out in this essay.
Philosophical Essay on Probabilities (1814), 5th edition (1825), trans. Andrew I. Dale (1995), 1.
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Historians constantly rewrite history, reinterpreting (reorganizing) the records of the past. So, too, when the brain's coherent responses become part of a memory, they are organized anew as part of the structure of consciousness. What makes them memories is that they become part of that structure and thus form part of the sense of self; my sense of self derives from a certainty that my experiences refer back to me, the individual who is having them. Hence the sense of the past, of history, of memory, is in part the creation of the self.
The Strange, Familiar, and Forgotten: An Anatomy of Consciousness (1995), 87.
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I am certain of nothing but the holiness of the Heart’s affections and the truth of Imagination—What the imagination seizes as Beauty must be truth—whether it existed before or not.
Letter to Benjamin Bailey (22 Nov 1817). In H. E. Rollins (ed.), Letters of John Keats (1958), Vol. 1, 184.
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I am convinced that it is impossible to expound the methods of induction in a sound manner, without resting them upon the theory of probability. Perfect knowledge alone can give certainty, and in nature perfect knowledge would be infinite knowledge, which is clearly beyond our capacities. We have, therefore, to content ourselves with partial knowledge—knowledge mingled with ignorance, producing doubt.
The Principles of Science: A Treatise on Logic and Scientific Method, 2nd edition (1877), 197.
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I am not accustomed to saying anything with certainty after only one or two observations.
Epistola, Rationem, Modumque Propinandi Radicis Chynae Decocti (Letter on the China Root) in Charles Donald O'Malley (trans.), Andreas Vesalius of Brussels, 1514-1564 (1965), 201.
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I believe that we do not know anything for certain, but everything probably.
Letter to Pierre Perrault, 'Sur la préface de M. Perrault de son traité de l'Origine des fontaines' [1763], Oeuvres Complètes de Christiaan Huygens (1897), Vol. 7, 298. Quoted in Jacques Roger, The Life Sciences in Eighteenth-Century French Thought, ed. Keith R. Benson and trans. Robert Ellrich (1997), 163.
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I do not intend to go deeply into the question how far mathematical studies, as the representatives of conscious logical reasoning, should take a more important place in school education. But it is, in reality, one of the questions of the day. In proportion as the range of science extends, its system and organization must be improved, and it must inevitably come about that individual students will find themselves compelled to go through a stricter course of training than grammar is in a position to supply. What strikes me in my own experience with students who pass from our classical schools to scientific and medical studies, is first, a certain laxity in the application of strictly universal laws. The grammatical rules, in which they have been exercised, are for the most part followed by long lists of exceptions; accordingly they are not in the habit of relying implicitly on the certainty of a legitimate deduction from a strictly universal law. Secondly, I find them for the most part too much inclined to trust to authority, even in cases where they might form an independent judgment. In fact, in philological studies, inasmuch as it is seldom possible to take in the whole of the premises at a glance, and inasmuch as the decision of disputed questions often depends on an aesthetic feeling for beauty of expression, or for the genius of the language, attainable only by long training, it must often happen that the student is referred to authorities even by the best teachers. Both faults are traceable to certain indolence and vagueness of thought, the sad effects of which are not confined to subsequent scientific studies. But certainly the best remedy for both is to be found in mathematics, where there is absolute certainty in the reasoning, and no authority is recognized but that of one’s own intelligence.
In 'On the Relation of Natural Science to Science in general', Popular Lectures on Scientific Subjects, translated by E. Atkinson (1900), 25-26.
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I feel, sometimes, as the renaissance man must have felt in finding new riches at every point and in the certainty that unexplored areas of knowledge and experience await at every turn.
Address to the University Students (10 Dec 1956 ) in Göran Liljestrand (ed.), Les Prix Nobel en 1955 (1956).
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I have approximate answers and possible beliefs in different degrees of certainty about different things, but I am not absolutely sure of anything, and of many things I don’t know anything about but I don’t have to know an answer.
Interview, in BBC TV program, 'The Pleasure of Finding Things Out', Horizon (23 Nov 1981). As quoted in Caroline Baillie, Alice Pawley, Donna M. Riley, Engineering and Social Justice: In the University and Beyond (2012), 108.
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I have destroyed almost the whole race of frogs, which does not happen in that savage Batrachomyomachia of Homer. For in the anatomy of frogs, which, by favour of my very excellent colleague D. Carolo Fracassato, I had set on foot in order to become more certain about the membranous substance of the lungs, it happened to me to see such things that not undeservedly I can better make use of that [saying] of Homer for the present matter—
“I see with my eyes a work trusty and great.”
For in this (frog anatomy) owing to the simplicity of the structure, and the almost complete transparency of the vessels which admits the eye into the interior, things are more clearly shown so that they will bring the light to other more obscure matters.
De Pulmonibus (1661), trans. James Young, Proceedings of the Royal Society of Medicine (1929-30), 23, 7.
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I know with sure and certain knowledge that a man’s work is nothing but this slow trek to rediscover, through the detours of art, those two or three great and simple images in whose presence his heart first opened.
In Lyrical and Critical Essays (1967), 14.
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I never allow myself to become discouraged under any circumstances. … After we had conducted thousands of experiments on a certain project without solving the problem, … we had learned something. For we had learned for a certainty that the thing couldn’t be done that way, and that we would have to try some other way. We sometimes learn a lot from our failures if we have put into the effort the best thought and work we are capable of.
As quoted from an interview by B.C. Forbes in The American Magazine (Jan 1921), 89.
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I then began to study arithmetical questions without any great apparent result, and without suspecting that they could have the least connexion with my previous researches. Disgusted at my want of success, I went away to spend a few days at the seaside, and thought of entirely different things. One day, as I was walking on the cliff, the idea came to me, again with the same characteristics of conciseness, suddenness, and immediate certainty, that arithmetical transformations of indefinite ternary quadratic forms are identical with those of non-Euclidian geometry.
Science and Method (1908), trans. Francis Maitland (1914), 53-4.
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I think that we shall have to get accustomed to the idea that we must not look upon science as a 'body of knowledge,' but rather as a system of hypotheses; that is to say, as a system of guesses or anticipations which in principle cannot be justified, but with which we work as long as they stand up to tests, and of which we are never justified in saying that we know they are 'true' or 'more or less certain' or even 'probable.'
The Logic of Scientific Discovery (1959), 317.
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I venture to assert that the feelings one has when the beautiful symbolism of the infinitesimal calculus first gets a meaning, or when the delicate analysis of Fourier has been mastered, or while one follows Clerk Maxwell or Thomson into the strange world of electricity, now growing so rapidly in form and being, or can almost feel with Stokes the pulsations of light that gives nature to our eyes, or track with Clausius the courses of molecules we can measure, even if we know with certainty that we can never see them I venture to assert that these feelings are altogether comparable to those aroused in us by an exquisite poem or a lofty thought.
In paper (May 1891) read before Bath Branch of the Teachers’ Guild, published in The Practical Teacher (July 1891), reprinted as 'Geometry', in Frederic Spencer, Chapters on the Aims and Practice of Teaching (1897), 194.
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I wanted certainty in the kind of way in which people want religious faith. I thought that certainty is more likely to be found in mathematics than elsewhere. But I discovered that many mathematical demonstrations, which my teachers expected me to accept, were full of fallacies, and that, if certainty were indeed discoverable in mathematics, it would be in a new field of mathematics, with more solid foundations than those that had hitherto been thought secure. But as the work proceeded, I was continually reminded of the fable about the elephant and the tortoise. Having constructed an elephant upon which the mathematical world could rest, I found the elephant tottering, and proceeded to construct a tortoise to keep the elephant from falling. But the tortoise was no more secure than the elephant, and after some twenty years of very arduous toil, I came to the conclusion that there was nothing more that I could do in the way of making mathematical knowledge indubitable.
In 'Reflections on my Eightieth Birthday', Portraits from Memory (1956), 54.
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If it were possible for us to have so deep an insight into a man's character as shown both in inner and in outer actions, that every, even the least, incentive to these actions and all external occasions which affect them were so known to us that his future conduct could be predicted with as great a certainty as the occurrence of a solar or lunar eclipse, we could nevertheless still assert that the man is free.
Critique of Practical Reason (1788). In L. W. Beck (ed. & trans.), Critique of Practical Reason and Other Writings in Moral Philosophy (1949), 204-5.
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If we have not found heaven within, it is a certainty we will not find it without.
Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 250
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In a sense cosmology contains all subjects because it is the story of everything, including biology, psychology and human history. In that single sense it can be said to contain an explanation also of time's arrow. But this is not what is meant by those who advocate the cosmological explanation of irreversibility. They imply that in some way the time arrow of cosmology imposes its sense on the thermodynamic arrow. I wish to disagree with this view. The explanation assumes that the universe is expanding. While this is current orthodoxy, there is no certainty about it. The red-shifts might be due to quite different causes. For example, when light passes through the expanding clouds of gas it will be red-shifted. A large number of such clouds might one day be invoked to explain these red shifts. It seems an odd procedure to attempt to 'explain' everyday occurrences, such as the diffusion of milk into coffee, by means of theories of the universe which are themselves less firmly established than the phenomena to be explained. Most people believe in explaining one set of things in terms of others about which they are more certain, and the explanation of normal irreversible phenomena in terms of the cosmological expansion is not in this category.
'Thermodynamics, Cosmology) and the Physical Constants', in J. T. Fraser (ed.), The Study of Time III (1973), 117-8.
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In its efforts to learn as much as possible about nature, modern physics has found that certain things can never be “known” with certainty. Much of our knowledge must always remain uncertain. The most we can know is in terms of probabilities.
In The Feynman Lectures on Physics (1963), Vol. 1.
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In order to discover Truth in this manner by observation and reason, it is requisite we should fix on some principles whose certainty and effects are demonstrable to our senses, which may serve to explain the phenomena of natural bodies and account for the accidents that arise in them; such only are those which are purely material in the human body with mechanical and physical experiments … a physician may and ought to furnish himself with, and reason from, such things as are demonstrated to be true in anatomy, chemistry, and mechanics, with natural and experimental philosophy, provided he confines his reasoning within the bounds of truth and simple experiment.
As quoted in selection from the writings of Herman Boerhaave, collected in Oliver Joseph Thatcher (ed.), The Ideas that Have Influenced Civilization, in the Original Documents (1800), Vol. 6, 242.
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In our search after the Knowledge of Substances, our want of Ideas, that are suitable to such a way of proceeding, obliges us to a quite different method. We advance not here, as in the other (where our abstract Ideas are real as well as nominal Essences) by contemplating our Ideas, and considering their Relations and Correspondencies; that helps us very little, for the Reasons, and in another place we have at large set down. By which, I think it is evident, that Substances afford Matter of very little general Knowledge; and the bare Contemplation of their abstract Ideas, will carry us but a very little way in the search of Truth and Certainty. What then are we to do for the improvement of our Knowledge in Substantial beings? Here we are to take a quite contrary Course, the want of Ideas of their real essences sends us from our own Thoughts, to the Things themselves, as they exist.
An Essay Concerning Human Understanding (1690). Edited by Peter Nidditch (1975), Book 4, Chapter 12, Section 9, 644.
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In recent years several new particles have been discovered which are currently assumed to be “elementary,” that is, essentially structureless. The probability that all such particles should be really elementary becomes less and less as their number increases. It is by no means certain that nucleons, mesons, electrons, neutrinos are all elementary particles.
Opening statement, Enrico Fermi and C.N. Yang, 'Are Mesons Elementary Particles?', Physical Review (1949), 76, 1739. As cited in James Gleick, Genius: The Life and Science of Richard Feynman (1992), 283.
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It cannot, of course, be stated with absolute certainty that no elements can combine with argon; but it appears at least improbable that any compounds will be formed.
[This held true for a century, until in Aug 2000, the first argon compound was formed, argon fluorohydride, HArF, but stable only below 40 K (−233 °C).]
Gases of the Atmosphere (1896), 193. Referenced in William H. Brock, The Chemical Tree: A History of Chemistry (2000), 339 and 671.
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It has been pointed out already that no knowledge of probabilities, less in degree than certainty, helps us to know what conclusions are true, and that there is no direct relation between the truth of a proposition and its probability. Probability begins and ends with probability. That a scientific investigation pursued on account of its probability will generally lead to truth, rather than falsehood, is at the best only probable.
In A Treatise on Probability (1921), 322.
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It has come to pass, I know not how, that Mathematics and Logic, which ought to be but the handmaids of Physic, nevertheless presume on the strength of the certainty which they possess to exercise dominion over it.
From De Augmentis Scientiaurum as translated in Francis Guy Selby, The Advancement of Learning (1893), Vol. 2, 73.
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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 not surprising, in view of the polydynamic constitution of the genuinely mathematical mind, that many of the major heros of the science, men like Desargues and Pascal, Descartes and Leibnitz, Newton, Gauss and Bolzano, Helmholtz and Clifford, Riemann and Salmon and Plücker and Poincaré, have attained to high distinction in other fields not only of science but of philosophy and letters too. And when we reflect that the very greatest mathematical achievements have been due, not alone to the peering, microscopic, histologic vision of men like Weierstrass, illuminating the hidden recesses, the minute and intimate structure of logical reality, but to the larger vision also of men like Klein who survey the kingdoms of geometry and analysis for the endless variety of things that flourish there, as the eye of Darwin ranged over the flora and fauna of the world, or as a commercial monarch contemplates its industry, or as a statesman beholds an empire; when we reflect not only that the Calculus of Probability is a creation of mathematics but that the master mathematician is constantly required to exercise judgment—judgment, that is, in matters not admitting of certainty—balancing probabilities not yet reduced nor even reducible perhaps to calculation; when we reflect that he is called upon to exercise a function analogous to that of the comparative anatomist like Cuvier, comparing theories and doctrines of every degree of similarity and dissimilarity of structure; when, finally, we reflect that he seldom deals with a single idea at a tune, but is for the most part engaged in wielding organized hosts of them, as a general wields at once the division of an army or as a great civil administrator directs from his central office diverse and scattered but related groups of interests and operations; then, I say, the current opinion that devotion to mathematics unfits the devotee for practical affairs should be known for false on a priori grounds. And one should be thus prepared to find that as a fact Gaspard Monge, creator of descriptive geometry, author of the classic Applications de l’analyse à la géométrie; Lazare Carnot, author of the celebrated works, Géométrie de position, and Réflections sur la Métaphysique du Calcul infinitesimal; Fourier, immortal creator of the Théorie analytique de la chaleur; Arago, rightful inheritor of Monge’s chair of geometry; Poncelet, creator of pure projective geometry; one should not be surprised, I say, to find that these and other mathematicians in a land sagacious enough to invoke their aid, rendered, alike in peace and in war, eminent public service.
In Lectures on Science, Philosophy and Art (1908), 32-33.
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It is obvious that we know with certainty, that the Flütz [layered] and primitive mountains have been produced by a series of precipitations and depositions formed in succession; that they took place from water which covered the globe, existing always more or less generally, and containing the different substances which have been produced from them.
In New Theory of the Formation of Veins (1809), 110-1.
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IT IS SAID TO AWAIT CERTAINTY IS TO AWAIT ETERNITY.
Telegram to Basil O’Connor (8 Nov 1954). In J. S. Smith, Patenting the Sun: Polio and the Salk Vaccine (1990), 295.
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It is to them [fossils] alone that we owe the commencement of even a Theory of the Earth ... By them we are enabled to ascertain, with the utmost certainty, that our earth has not always been covered over by the same external crust, because we are thoroughly assured that the organized bodies to which these fossil remains belong must have lived upon the surface before they came to be buried, as they now are, at a great depth.
'Preliminary discourse', to Recherches sur les Ossemens Fossiles (1812), trans. R. Kerr Essay on the Theory of the Earth (1813), 54-55.
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It may well be doubted whether, in all the range of Science, there is any field so fascinating to the explorer—so rich in hidden treasures—so fruitful in delightful surprises—as that of Pure Mathematics. The charm lies chiefly, I think, in the absolute certainty of its results: for that is what, beyond all mental treasures, the human intellect craves for. Let us only be sure of something! More light, more light … “And if our fate be death, give light and let us die” This is the cry that, through all the ages, is going up from perplexed Humanity, and Science has little else to offer, that will really meet the demands of its votaries, than the conclusions of Pure Mathematics.
Opening of 'Introduction', A New Theory of Parallels (1890), xv. As a non-fiction work, the author’s name on the title page of this book was Charles Lutwidge Dodgson. Being better known for his works of fiction as Lewis Carroll, all quotes relating to this one person, published under either name, are gathered on this single web page under his pen name.
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It may well be doubted whether, in all the range of science, there is any field so fascinating to the explorer—so rich in hidden treasures—so fruitful in delightful surprises—as that of Pure Mathematics. The charm lies chiefly, I think, in the absolute certainty of its results; for that is what, beyond all mental treasures, the human intellect craves for. Let us only be sure of something! More light, more light!
Written without pseudonym as Charles L. Dodgson. Opening remarks in Introduction to A New Theory of Parallels (1888, 1890), xv.
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It was his [Leibnitz’s] love of method and order, and the conviction that such order and harmony existed in the real world, and that our success in understanding it depended upon the degree and order which we could attain in our own thoughts, that originally was probably nothing more than a habit which by degrees grew into a formal rule. This habit was acquired by early occupation with legal and mathematical questions. We have seen how the theory of combinations and arrangements of elements had a special interest for him. We also saw how mathematical calculations served him as a type and model of clear and orderly reasoning, and how he tried to introduce method and system into logical discussions, by reducing to a small number of terms the multitude of compound notions he had to deal with. This tendency increased in strength, and even in those early years he elaborated the idea of a general arithmetic, with a universal language of symbols, or a characteristic which would be applicable to all reasoning processes, and reduce philosophical investigations to that simplicity and certainty which the use of algebraic symbols had introduced into mathematics.
A mental attitude such as this is always highly favorable for mathematical as well as for philosophical investigations. Wherever progress depends upon precision and clearness of thought, and wherever such can be gained by reducing a variety of investigations to a general method, by bringing a multitude of notions under a common term or symbol, it proves inestimable. It necessarily imports the special qualities of number—viz., their continuity, infinity and infinite divisibility—like mathematical quantities—and destroys the notion that irreconcilable contrasts exist in nature, or gaps which cannot be bridged over. Thus, in his letter to Arnaud, Leibnitz expresses it as his opinion that geometry, or the philosophy of space, forms a step to the philosophy of motion—i.e., of corporeal things—and the philosophy of motion a step to the philosophy of mind.
In Leibnitz (1884), 44-45. [The first sentence is reworded to better introduce the quotation. —Webmaster]
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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 a mistake to suppose that a science consists entirely of strictly proved theses, and it would be unjust to require this. Only a disposition with a passion for authority will raise such a demand, someone with a craving to replace his religious catechism by another, though it is a scientific one. Science has only a few apodeictic propositions in its catechism: the rest are assertions promoted by it to some particular degree of probability. It is actually a sign of a scientific mode of thought to find satisfaction in these approximations to certainty and to be able to pursue constructive work further in spite of the absence of final confirmation.
In Introductory Lectures on Psycho-Analysis (1916-17).
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John Bahcall, an astronomer on the Institute of Advanced Study faculty since 1970 likes to tell the story of his first faculty dinner, when he found himself seated across from Kurt Gödel, … a man dedicated to logic and the clean certainties of mathematical abstraction. Bahcall introduced himself and mentioned that he was a physicist. Gödel replied, “I don’t believe in natural science.”
As stated in Adam Begley, 'The Lonely Genius Club', New York Magazine (30 Jan 1995), 63.
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Just as the spectroscope opened up a new astronomy by enabling the astronomer to determine some of the constituents of which distant stars are composed, so the seismograph, recording the unfelt motion of distant earthquakes, enables us to see into the earth and determine its nature with as great a certainty, up to a certain point, as if we could drive a tunnel through it and take samples of the matter passed through.
'The Constitution of the Interior of the Earth, as Revealed by Earthquakes', Quarterly Journal of the Geological Society (1906), 62, 456.
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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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LOGIC, n. The art of thinking and reasoning in strict accordance with the limitations and incapacities of the human misunderstanding. The basic of logic is the syllogism, consisting of a major and a minor premise and a conclusion—thus:
Major Premise: Sixty men can do a piece of work sixty times as quickly as one man.
Minor Premise: One man can dig a post-hole in sixty seconds; therefore—
Conclusion: Sixty men can dig a post-hole in one second.
This may be called the syllogism arithmetical, in which, by combining logic and mathematics, we obtain a double certainty and are twice blessed.
The Collected Works of Ambrose Bierce (1911), Vol. 7, The Devil's Dictionary,  196.
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Lord Kelvin was so satisfied with this triumph of science that he declared himself to be as certain of the existence of the ether as a man can be about anything.... “When you can measure what you are speaking about, and express it in numbers, you know something about it....” Thus did Lord Kelvin lay down the law. And though quite wrong, this time he has the support of official modern Science. It is NOT true that when you can measure what you are speaking about, you know something about it. The fact that you can measure something doesn't even prove that that something exists.... Take the ether, for example: didn't they measure the ratio of its elasticity to its density?
In Science is a Sacred Cow (1950), 69-70; 85.
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Mathematics gives the young man a clear idea of demonstration and habituates him to form long trains of thought and reasoning methodically connected and sustained by the final certainty of the result; and it has the further advantage, from a purely moral point of view, of inspiring an absolute and fanatical respect for truth. In addition to all this, mathematics, and chiefly algebra and infinitesimal calculus, excite to a high degree the conception of the signs and symbols—necessary instruments to extend the power and reach of the human mind by summarizing an aggregate of relations in a condensed form and in a kind of mechanical way. These auxiliaries are of special value in mathematics because they are there adequate to their definitions, a characteristic which they do not possess to the same degree in the physical and mathematical [natural?] sciences.
There are, in fact, a mass of mental and moral faculties that can be put in full play only by instruction in mathematics; and they would be made still more available if the teaching was directed so as to leave free play to the personal work of the student.
In 'Science as an Instrument of Education', Popular Science Monthly (1897), 253.
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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, from the earliest times to which the history of human reason can reach, has followed, among that wonderful people of the Greeks, the safe way of science. But it must not be supposed that it was as easy for mathematics as for logic, in which reason is concerned with itself alone, to find, or rather to make for itself that royal road. I believe, on the contrary, that there was a long period of tentative work (chiefly still among the Egyptians), and that the change is to be ascribed to a revolution, produced by the happy thought of a single man, whose experiments pointed unmistakably to the path that had to be followed, and opened and traced out for the most distant times the safe way of a science. The history of that intellectual revolution, which was far more important than the passage round the celebrated Cape of Good Hope, and the name of its fortunate author, have not been preserved to us. … A new light flashed on the first man who demonstrated the properties of the isosceles triangle (whether his name was Thales or any other name), for he found that he had not to investigate what he saw in the figure, or the mere concepts of that figure, and thus to learn its properties; but that he had to produce (by construction) what he had himself, according to concepts a priori, placed into that figure and represented in it, so that, in order to know anything with certainty a priori, he must not attribute to that figure anything beyond what necessarily follows from what he has himself placed into it, in accordance with the concept.
In Critique of Pure Reason, Preface to the Second Edition, (1900), 690.
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Men who do not know the truth of things try to reach certainty about them, so that, if they cannot satisfy their intellects by science, their wills at least may rest on conscience.
In The New Science (3rd ed., 1744), Book 1, Para. 137, as translated by Thomas Goddard Bergin and Max Harold Fisch, The New Science of Giambattista Vico (1948), 56.
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Modern Science has along with the theory that the Earth dated its beginning with the advent of man, swept utterly away this beautiful imagining. We can, indeed, find no beginning of the world. We trace back events and come to barriers which close our vistabarriers which, for all we know, may for ever close it. They stand like the gates of ivory and of horn; portals from which only dreams proceed; and Science cannot as yet say of this or that dream if it proceeds from the gate of horn or from that of ivory.
In short, of the Earth's origin we have no certain knowledge; nor can we assign any date to it. Possibly its formation was an event so gradual that the beginning was spread over immense periods. We can only trace the history back to certain events which may with considerable certainty be regarded as ushering in our geological era.
John Joly
Lecture at the Royal Dublin Society, 6 Feb 1914. Published in Science Progress, Vol. 9, 37. Republished in The Birth-Time of the World and Other Scientific Essays, (1915), 2.
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Moral certainty is intellectual immorality
Quotations: Superultramodern Science and Philosophy (2005), 2
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Moral certainty is never more than probability.
On Crimes and Punishments (1764), Chapter 14.
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My teacher, Hopkins, often commented on the craving for certainty that led so many physicists into mysticism or into the Church and similar organisations ... Faith seems to be an occupational hazard for physicists.
Penguin New Biology (1954), 16, 44
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Neither the Army nor the Navy is of any protection, or very slight protection, against aerial raids. We may therefore look forward with certainty to the time that is coming, and indeed is almost now at hand, when sea power and land power will be secondary to air power, and that nation which gains control of the air will practically control the world.
In 'Preparedness for Aerial Defense', Addresses Before the Eleventh Annual Convention of the Navy League of the United States, Washington, D.C., April 10-13, 1916 (1916), 76.
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No disorders have employed so many quacks, as those that have no cure; and no sciences have exercised so many quills, as those that have no certainty.
Lacon: Many Things in Few Words (1820-22, 1866), 314.
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No history of civilization can be tolerably complete which does not give considerable space to the explanation of scientific progress. If we had any doubts about this, it would suffice to ask ourselves what constitutes the essential difference between our and earlier civilizations. Throughout the course of history, in every period, and in almost every country, we find a small number of saints, of great artists, of men of science. The saints of to-day are not necessarily more saintly than those of a thousand years ago; our artists are not necessarily greater than those of early Greece; they are more likely to be inferior; and of course, our men of science are not necessarily more intelligent than those of old; yet one thing is certain, their knowledge is at once more extensive and more accurate. The acquisition and systematization of positive knowledge is the only human activity which is truly cumulative and progressive. Our civilization is essentially different from earlier ones, because our knowledge of the world and of ourselves is deeper, more precise, and more certain, because we have gradually learned to disentangle the forces of nature, and because we have contrived, by strict obedience to their laws, to capture them and to divert them to the gratification of our own needs.
Introduction to the History of Science (1927), Vol. 1, 3-4.
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Nor need you doubt that Pythagoras, a long time before he found the demonstration for the Hecatomb, had been certain that the square of the side subtending the right angle in a rectangular triangle was equal to the square of the other two sides; the certainty of the conclusion helped not a little in the search for a demonstration. But whatever was the method of Aristotle, and whether his arguing a priori preceded sense a posteriori, or the contrary, it is sufficient that the same Aristotle (as has often been said) put sensible experiences before all discourses. As to the arguments a priori, their force has already been examined.
Dialogue on the Great World Systems (1632). Revised and Annotated by Giorgio De Santillana (1953), 60.
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Objective evidence and certitude are doubtless very fine ideals to play with, but where on this moonlit and dream-visited planet are they found?
'The Will to Believe' (1896). In The Will to Believe and Other Essays in Popular Philosophy (1897), 14.
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Of the nucleosides from deoxyribonucleic acids, all that was known with any certainty [in the 1940s] was that they were 2-deoxy-­D-ribosides of the bases adenine, guanine, thymine and cytosine and it was assumed that they were structurally analogous to the ribonucleosides. The chemistry of the nucleotides—the phosphates of the nucleosides—was in a correspondingly primitive state. It may well be asked why the chemistry of these groups of compounds was not further advanced, particularly since we recognize today that they occupy a central place in the history of the living cell. True, their full significance was for a long time unrecognized and emerged only slowly as biochemical research got into its stride but I think a more important reason is to be found in the physical properties of compounds of the nucleotide group. As water-soluble polar compounds with no proper melting points they were extremely difficult to handle by the classic techniques of organic chemistry, and were accordingly very discouraging substances to early workers. It is surely no accident that the major advances in the field have coincided with the appearance of new experimental techniques such as paper and ion-exchange chromatography, paper electrophoresis, and countercurrent distribution, peculiarly appropriate to the compounds of this group.
In 'Synthesis in the Study of Nucleotides', Nobel Lecture, 11 December 1957. In Nobel Lectures: Chemistry 1942-1962 (1964), 524.
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On the whole, I cannot help saying that it appears to me not a little extraordinary, that a theory so new, and of such importance, overturning every thing that was thought to be the best established in chemistry, should rest on so very narrow and precarious a foundation, the experiments adduced in support of it being not only ambiguous or explicable on either hypothesis, but exceedingly few. I think I have recited them all, and that on which the greatest stress is laid, viz. That of the formation of water from the decomposition of the two kinds of air, has not been sufficiently repeated. Indeed it required so difficult and expensive an apparatus, and so many precautions in the use of it, that the frequent repetition of the experiment cannot be expected; and in these circumstances the practised experimenter cannot help suspecting the accuracy of the result and consequently the certainty of the conclusion.
Considerations on the Doctrine of Phlogiston (1796), 57-8.
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One must learn by doing the thing; though you think you know it, you have no certainty until you try.
Sophocles
In play, 'Trachiniae', collected in George Young (trans.), The Dramas of Sophocles: Rendered in English Verse: Dramatic and Lyric (1916), 191.
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Organisms ... are directed and limited by their past. They must remain imperfect in their form and function, and to that extent unpredictable since they are not optimal machines. We cannot know their future with certainty, if only because a myriad of quirky functional shifts lie within the capacity of any feature, however well adapted to a present role.
…...
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Owing to his lack of knowledge, the ordinary man cannot attempt to resolve conflicting theories of conflicting advice into a single organized structure. He is likely to assume the information available to him is on the order of what we might think of as a few pieces of an enormous jigsaw puzzle. If a given piece fails to fit, it is not because it is fraudulent; more likely the contradictions and inconsistencies within his information are due to his lack of understanding and to the fact that he possesses only a few pieces of the puzzle. Differing statements about the nature of things, differing medical philosophies, different diagnoses and treatments—all of these are to be collected eagerly and be made a part of the individual's collection of puzzle pieces. Ultimately, after many lifetimes, the pieces will fit together and the individual will attain clear and certain knowledge.
'Strategies of Resort to Curers in South India', contributed in Charles M. Leslie (ed.), Asian Medical Systems: A Comparative Study (1976), 185.
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Philosophy, though unable to tell us with certainty what is the true answer to the doubts which it raises, is able to suggest many possibilities which enlarge our thoughts and free them from the tyranny of custom.
In 'The Value of Philosophy', The Problems of Philosophy (1912), 157.
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Proof that a given condition always precedes or accompanies a phenomenon does not warrant concluding with certainty that a given condition is the immediate cause of that phenomenon. It must still be established that when this condition is removed, the phenomen will no longer appear.
From An Introduction to the Study of Experimental Medicine (1865), as translated by Henry Copley Greene (1957), 55.
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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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Science asks no questions about the ontological pedigree or a priori character of a theory, but is content to judge it by its performance; and it is thus that a knowledge of nature, having all the certainty which the senses are competent to inspire, has been attained—a knowledge which maintains a strict neutrality toward all philosophical systems and concerns itself not with the genesis or a priori grounds of ideas.
Originally published in North American Review (1865). 'The Philosophy of Herbert Spencer,' repr. In Philosophical Writings of Chauncey Wright (1963), p. 8.
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Science is a procedure for testing and rejecting hypotheses, not a compendium of certain knowledge. … Theories that cannot be tested in principle are not a part in science.
In The Flamingo's Smile: Reflections in Natural History (1985), 111.
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Science is a speculative enterprise. The validity of a new idea and the significance of a new experimental finding are to be measured by the consequences—consequences in terms of other ideas and other experiments. Thus conceived, science is not a quest for certainty; it is rather a quest which is successful only to the degree that it is continuous.
In Science and Common Sense (1951), 25-26.
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Science is certainty, is truth found out.
In The Evangel: in Verse (1874), 5.
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Science is not a system of certain, or -established, statements; nor is it a system which steadily advances towards a state of finality... And our guesses are guided by the unscientific, the metaphysical (though biologically explicable) faith in laws, in regularities which we can uncover—discover. Like Bacon, we might describe our own contemporary science—'the method of reasoning which men now ordinarily apply to nature'—as consisting of 'anticipations, rash and premature' and as 'prejudices'.
The Logic of Scientific Discovery (1959), 278.
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Science is the outcome of being prepared to live without certainty and therefore a mark of maturity. It embraces doubt and loose ends.
Quoted in interview by Tim Adams, 'This much I know: A.C. Grayling', The Observer (4 Jul 2009).
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Science is uncertain. Theories are subject to revision; observations are open to a variety of interpretations, and scientists quarrel amongst themselves. This is disillusioning for those untrained in the scientific method, who thus turn to the rigid certainty of the Bible instead. There is something comfortable about a view that allows for no deviation and that spares you the painful necessity of having to think.
The 'Threat' of Creationism. In Ashley Montagu (ed.), Science and Creationism (1984), 192.
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Science would have us believe that such accuracy, leading to certainty, is the only criterion of knowledge, would make the trial of Galileo the paradigm of the two points of view which aspire to truth, would suggest, that is, that the cardinals represent only superstition and repression, while Galileo represents freedom. But there is another criterion which is systematically neglected in this elevation of science. Man does not now—and will not ever—live by the bread of scientific method alone. He must deal with life and death, with love and cruelty and despair, and so must make conjectures of great importance which may or may not be true and which do not lend themselves to experimentation: It is better to give than to receive; Love thy neighbor as thyself; Better to risk slavery through non-violence than to defend freedom with murder. We must deal with such propositions, must decide whether they are true, whether to believe them, whether to act on them—and scientific method is no help for by their nature these matters lie forever beyond the realm of science.
In The End of the Modern Age (1973), 89.
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Science’s defenders have identified five hallmark moves of pseudoscientists. They argue that the scientific consensus emerges from a conspiracy to suppress dissenting views. They produce fake experts, who have views contrary to established knowledge but do not actually have a credible scientific track record. They cherry-pick the data and papers that challenge the dominant view as a means of discrediting an entire field. They deploy false analogies and other logical fallacies. And they set impossible expectations of research: when scientists produce one level of certainty, the pseudoscientists insist they achieve another.
In Commencement Address at the California Institute of Technology (10 Jun 2016). Published on the website of The New Yorker (10 Jun 2016).
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Scientists do not believe in fundamental and absolute certainties. For the scientist, certainty is never an end, but a search; not the ordering of certainty, but its exploration. For the scientist, certainty represents the highest degree of probability.
Ashley Montagu (ed.), Science and Creationism (1984), Introduction, 7-8.
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Several times every day I observed the portions of the polyp with a magnifying glass. On the 4th December, that is to say on the ninth day after having cut the polyp, I seemed in the morning to be able to perceive, on the edges of the anterior end of the second part (the part that had neither head nor arms), three little points arising from those edges. They immediately made me think of the horns that serve as the legs and arms of the polyp. Nevertheless I did not want to decide at once that these were actually arms that were beginning to grow. Throughout the next day I continually observed these points: this excited me extremely, and awaited with impatience the moment when I should know with certainty what they were. At last, on the following day, they were so big that there was no longer any room for doubt that they were actually arms growing at the anterior extremity of this second part. The next day two more arms started to grow out, and a few days later three more. The second part thus had eight of them, and they were all in a short time as long as those of the first part, that is to say as long as those the polyp possessed before it was cut. I then no longer found any difference between the second part and a polyp that had never been cut. I had remarked the same thing about the first part since the day after the operation. When I observed them with the magnifying glass with all the attention of which I was capable, each of the two appeared perceptibly to be a complete polyp, and they performed all the functions that were known to me: they extended, contracted, and walked.
Mémoires, pour servir à l'histoire d'un genre de polyps d'eau douce à bras en forme de cornes (1744), 7-16. Trans. John R. Baker, in Abraham Trembley of Geneva: Scientist and Philosopher 1710-1784 (1952), 32.
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Subatomic particles do not exist but rather show “tendencies to exist”, and atomic events do not occur with certainty at definite times and in definite ways, but rather show “tendencies to occur”.
In The Tao of Physics (1975), 133.
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Suppose it were perfectly certain that the life and fortune of every one of us would, one day or other, depend upon his winning or losing a game of chess. Don't you think that we should all consider it to be a primary duty to learn at least the names and the moves of the pieces; to have a notion of a gambit, and a keen eye for all the means of giving and getting out of check? Do you not think that we should look with a disapprobation amounting to scorn upon the father who allowed his son, or the state which allowed its members, to grow up without knowing a pawn from a knight?
Yet, it is a very plain and elementary truth that the life, the fortune, and the happiness of every one of us, and, more or less, of those who are connected with us, do depend upon our knowing something of the rules of a game infinitely more difficult and complicated than chess. It is a game which has been played for untold ages, every man and woman of us being one of the two players in a game of his or her own. The chess-board is the world, the pieces are the phenomena of the universe, the rules of the game are what we call the laws of nature. The player on the other side is hidden from us. We know that his play is always fair, just, and patient. But also we know, to our cost, that he never overlooks a mistake, or makes the smallest allowance for ignorance. To the man who plays well the highest stakes are paid with that sort of overflowing generosity with which the strong shows delight in strength. And one who plays ill is checkmated—without haste, but without remorse.
Address to the South London Working Men’s College. 'A Liberal Education; and Where to Find It', in David Masson, (ed.), Macmillan’s Magazine (Mar 1868), 17, 369. Also in 'A Liberal Education and Where to Find it' (1868). In Collected Essays (1893), Vol. 3, 82.
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The apodictic quality of mathematical thought, the certainty and correctness of its conclusions, are due, not to a special mode of ratiocination, but to the character of the concepts with which it deals. What is that distinctive characteristic? I answer: precision, sharpness, completeness,* of definition. But how comes your mathematician by such completeness? There is no mysterious trick involved; some ideas admit of such precision, others do not; and the mathematician is one who deals with those that do.
In 'The Universe and Beyond', Hibbert Journal (1904-1905), 3, 309. An editorial footnote indicates “precision, sharpness, completeness” — i.e., in terms of the absolutely clear and indefinable.
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The certainties of one age are the problems of the next.
Religion and the Rise of Capitalism (1926, 2008), 282.
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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 demand for certainty is one which is natural to man, but is nevertheless an intellectual vice. If you take your children for a picnic on a doubtful day, they will demand a dogmatic answer as to whether it will be fine or wet, and be disappointed in you when you cannot be sure.
From 'Philosophy For Laymen', collected in Unpopular Essays (1950, 1996), 38. This idea may be summarized as “What men want is not knowledge, but certainty” — a widely circulated aphorism attributed to Russell, but for which Webmaster has so far found no citation. (Perhaps it is a summary, never expressed in those exact words, but if you know the primary source, please contact Webmaster.)
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The determining cause of most wars in the past has been, and probably will be of all wars in the future, the uncertainty of the result; war is acknowledged to be a challenge to the Unknown, it is often spoken of as an appeal to the God of Battles. The province of science is to foretell; this is true of every department of science. And the time must come—how soon we do not know—when the real science of war, something quite different from the application of science to the means of war, will make it possible to foresee with certainty the issue of a projected war. That will mark the end of battles; for however strong the spirit of contention, no nation will spend its money in a fight in which it knows it must lose.
Times Literary Supplement (28 Nov 1902), 353-4.
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The doctrine called Philosophical Necessity is simply this: that, given the motives which are present to an individual’s mind, and given likewise the character and disposition of the individual, the manner in which he will act might be unerringly inferred: that if we knew the person thoroughly, and knew all the inducements which are acting upon him, we could foretell his conduct with as much certainty as we can predict any physical event.
A System of Logic, Ratiocinative and Inductive (1858), 522.
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The domain of mathematics is the sole domain of certainty. There and there alone prevail the standards by which every hypothesis respecting the external universe and all observation and all experiment must be finally judged. It is the realm to which all speculation and thought must repair for chastening and sanitation, the court of last resort, I say it reverently, for all intellection whatsoever, whether of demon, or man, or deity. It is there that mind as mind attains its highest estate.
In 'The Universe and Beyond', Hibbert Journal (1904-1906), 3, 314.
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The equations of dynamics completely express the laws of the historical method as applied to matter, but the application of these equations implies a perfect knowledge of all the data. But the smallest portion of matter which we can subject to experiment consists of millions of molecules, not one of which ever becomes individually sensible to us. We cannot, therefore, ascertain the actual motion of anyone of these molecules; so that we are obliged to abandon the strict historical method, and to adopt the statistical method of dealing with large groups of molecules … Thus molecular science teaches us that our experiments can never give us anything more than statistical information, and that no law derived from them can pretend to absolute precision. But when we pass from the contemplation of our experiments to that of the molecules themselves, we leave a world of chance and change, and enter a region where everything is certain and immutable.
'Molecules' (1873). In W. D. Niven (ed.), The Scientific Papers of James Clerk Maxwell (1890), Vol. 2, 374.
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The existence of a first cause of the universe is a necessity of thought ... Amid the mysteries which become more mysterious the more they are thought about, there will remain the one absolute certainty that we are over in the presence of an Infinite, Eternal Energy from which all things proceed.
As quoted in John Murdoch, India's Needs: Material, Political, Social, Moral, and Religious (1886), 126.
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The functional validity of a working hypothesis is not a priori certain, because often it is initially based on intuition. However, logical deductions from such a hypothesis provide expectations (so-called prognoses) as to the circumstances under which certain phenomena will appear in nature. Such a postulate or working hypothesis can then be substantiated by additional observations ... The author calls such expectations and additional observations the prognosis-diagnosis method of research. Prognosis in science may be termed the prediction of the future finding of corroborative evidence of certain features or phenomena (diagnostic facts). This method of scientific research builds up and extends the relations between the subject and the object by means of a circuit of inductions and deductions.
In 'The Scientific Character of Geology', The Journal of Geology (Jul 1961), 69, No. 4, 454-5.
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The fundamental biological variant is DNA. That is why Mendel's definition of the gene as the unvarying bearer of hereditary traits, its chemical identification by Avery (confirmed by Hershey), and the elucidation by Watson and Crick of the structural basis of its replicative invariance, are without any doubt the most important discoveries ever made in biology. To this must be added the theory of natural selection, whose certainty and full significance were established only by those later theories.
In Jacques Monod and Austryn Wainhouse (trans.), Chance and Necessity: An Essay on the Natural Philosophy of Modern Biology (1971), 104.
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The Greeks made Space the subject-matter of a science of supreme simplicity and certainty. Out of it grew, in the mind of classical antiquity, the idea of pure science. Geometry became one of the most powerful expressions of that sovereignty of the intellect that inspired the thought of those times. At a later epoch, when the intellectual despotism of the Church, which had been maintained through the Middle Ages, had crumbled, and a wave of scepticism threatened to sweep away all that had seemed most fixed, those who believed in Truth clung to Geometry as to a rock, and it was the highest ideal of every scientist to carry on his science “more geometrico.”
In Space,Time, Matter, translated by Henry Leopold Brose (1952), 1.
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The hypotheses which we accept ought to explain phenomena which we have observed. But they ought to do more than this; our hypotheses ought to foretell phenomena which have not yet been observed; ... because if the rule prevails, it includes all cases; and will determine them all, if we can only calculate its real consequences. Hence it will predict the results of new combinations, as well as explain the appearances which have occurred in old ones. And that it does this with certainty and correctness, is one mode in which the hypothesis is to be verified as right and useful.
Philosophy of the Inductive Sciences (1847), Vol. 2, 62-63.
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The knowledge of Natural-History, being Observation of Matters of Fact, is more certain than most others, and in my slender Opinion, less subject to Mistakes than Reasonings, Hypotheses, and Deductions are; ... These are things we are sure of, so far as our Senses are not fallible; and which, in probability, have been ever since the Creation, and will remain to the End of the World, in the same Condition we now find them.
A Voyage to the Islands Madera, Barbados, Nieves, S. Christophers and Jamaica: With the Natural History of the Herbs and Trees, Four-footed Beasts, Fishes, Birds, Insects, Reptiles, &c. of the Last of those Islands (1707), Vol. 1, 1.
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The most distinctive characteristic which differentiates mathematics from the various branches of empirical science, and which accounts for its fame as the queen of the sciences, is no doubt the peculiar certainty and necessity of its results.
First sentence of 'Geometry and Empirical Science', collected in Carl Hempel and James H. Fetzer (ed.), The Philosophy of Carl G. Hempel: Studies in Science, Explanation, and Rationality (2001), Chap. 2, 18. Also Carl Hempel, 'Geometry and Empirical Science', collected in J.R. Newman (ed.), The World of Mathematics (1956), Vol. 3, 1635.
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The motive for the study of mathematics is insight into the nature of the universe. Stars and strata, heat and electricity, the laws and processes of becoming and being, incorporate mathematical truths. If language imitates the voice of the Creator, revealing His heart, mathematics discloses His intellect, repeating the story of how things came into being. And Value of Mathematics, appealing as it does to our energy and to our honor, to our desire to know the truth and thereby to live as of right in the household of God, is that it establishes us in larger and larger certainties. As literature develops emotion, understanding, and sympathy, so mathematics develops observation, imagination, and reason.
In A Theory of Motives, Ideals and Values in Education (1907), 406.
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The mystery of life is certainly the most persistent problem ever placed before the thought of man. There is no doubt that from the time humanity began to think it has occupied itself with the problem of its origin and its future which undoubtedly is the problem of life. The inability of science to solve it is absolute. This would be truly frightening were it not for faith.
Address (10 Sep 1934) to the International Congress of Electro-Radio Biology, Venice. In Associated Press, 'Life a Closed Book, Declares Marconi', New York Times (11 Sep 1934), 15.
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The old scientific ideal of episteme — of absolutely certain, demonstrable knowledge — has proved to be an idol. The demand for scientific objectivity makes it inevitable that every scientific statement must remain tentative for ever. (1959)
The Logic of Scientific Discovery: Logik Der Forschung (1959, 2002), 280.
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The only certainty is that nothing is certain.
As quoted, without citation, in John Walker, A Fork in the Road: Answers to Daily Dilemmas from the Teachings of Jesus Christ (2005), 169.
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The orbits of certainties touch one another; but in the interstices there is room enough for error to go forth and prevail.
In The Maxims and Reflections of Goethe (1906), 187.
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The present state of the system of nature is evidently a consequence of what it was in the preceding moment, and if we conceive of an intelligence that at a given instant comprehends all the relations of the entities of this universe, it could state the respective position, motions, and general affects of all these entities at any time in the past or future. Physical astronomy, the branch of knowledge that does the greatest honor to the human mind, gives us an idea, albeit imperfect, of what such an intelligence would be. The simplicity of the law by which the celestial bodies move, and the relations of their masses and distances, permit analysis to follow their motions up to a certain point; and in order to determine the state of the system of these great bodies in past or future centuries, it suffices for the mathematician that their position and their velocity be given by observation for any moment in time. Man owes that advantage to the power of the instrument he employs, and to the small number of relations that it embraces in its calculations. But ignorance of the different causes involved in the production of events, as well as their complexity, taken together with the imperfection of analysis, prevents our reaching the same certainty about the vast majority of phenomena. Thus there are things that are uncertain for us, things more or less probable, and we seek to compensate for the impossibility of knowing them by determining their different degrees of likelihood. So it was that we owe to the weakness of the human mind one of the most delicate and ingenious of mathematical theories, the science of chance or probability.
'Recherches, 1º, sur l'Intégration des Équations Différentielles aux Différences Finies, et sur leur Usage dans la Théorie des Hasards' (1773, published 1776). In Oeuvres complètes de Laplace, 14 Vols. (1843-1912), Vol. 8, 144-5, trans. Charles Coulston Gillispie, Pierre-Simon Laplace 1749-1827: A Life in Exact Science (1997), 26.
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The Principle of Uncertainty is a bad name. In science or outside of it we are not uncertain; our knowledge is merely confined, within a certain tolerance. We should call it the Principle of Tolerance. And I propose that name in two senses: First, in the engineering sense, science has progressed, step by step, the most successful enterprise in the ascent of man, because it has understood that the exchange of information between man and nature, and man and man, can only take place with a certain tolerance. But second, I also use the word, passionately, about the real world. All knowledge, all information between human beings, can only be exchanged within a play of tolerance. And that is true whether the exchange is in science, or in literature, or in religion, or in politics, or in any form of thought that aspires to dogma. It’s a major tragedy of my lifetime and yours that scientists were refining, to the most exquisite precision, the Principle of Tolerance, and turning their backs on the fact that all around them, tolerance was crashing to the ground beyond repair. The Principle of Uncertainty or, in my phrase, the Principle of Tolerance, fixed once for all the realization that all knowledge is limited. It is an irony of history that at the very time when this was being worked out there should rise, under Hitler in Germany and other tyrants elsewhere, a counter-conception: a principle of monstrous certainty. When the future looks back on the 1930s it will think of them as a crucial confrontation of culture as I have been expounding it, the ascent of man, against the throwback to the despots’ belief that they have absolute certainty. It is said that science will dehumanize people and turn them into numbers. That is false: tragically false. Look for yourself. This is the concentration camp and crematorium at Auschwitz. This is where people were turned into numbers. Into this pond were flushed the ashes of four million people. And that was not done by gas. It was done by arrogance. It was done by dogma. It was done by ignorance. When people believe that they have absolute knowledge, with no test in reality this is how they behave. This is what men do when they aspire to the knowledge of gods. Science is a very human form of knowledge. We are always at the brink of the known; we always feel forward for what is to be hoped. Every judgment in science stands on the edge of error, and is personal. Science is a tribute to what we can know although we are fallible. In the end, the words were said by Oliver Cromwell: “I beseech you, in the bowels of Christ: Think it possible you may be mistaken.” We have to cure ourselves of the itch for absolute knowledge and power. We have to close the distance between the push-button order and the human act. We have to touch people. [Referring to Heisenberg’s Uncertainty Principle.]
'Knowledge or Certainty,' episode 11, The Ascent of Man (1972), BBC TV series.
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The propositions of mathematics have, therefore, the same unquestionable certainty which is typical of such propositions as “All bachelors are unmarried,” but they also share the complete lack of empirical content which is associated with that certainty: The propositions of mathematics are devoid of all factual content; they convey no information whatever on any empirical subject matter.
From 'On the Nature of Mathematical Truth', collected in Carl Hempel and James H. Fetzer (ed.), The Philosophy of Carl G. Hempel: Studies in Science, Explanation, and Rationality (2001), Chap. 1, 13. Also Carl Hempel, 'On the Nature of Mathematical Truth', collected in J.R. Newman (ed.), The World of Mathematics (1956), Vol. 3, 1631.
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The scientist believes in proof without certainty, the bigot in certainty without proof.
Ashley Montagu (ed.), Science and Creationism (1984), Introduction, 9. Commonly seem derivative quotes include: “Science has proof without any certainty. Creationists have certainty without any proof,” and “Religion gives us certainty without proof; science gives us proof without certainty.”
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The scientist has to take 95 per cent of his subject on trust. He has to because he can't possibly do all the experiments, therefore he has to take on trust the experiments all his colleagues and predecessors have done. Whereas a mathematician doesn't have to take anything on trust. Any theorem that's proved, he doesn't believe it, really, until he goes through the proof himself, and therefore he knows his whole subject from scratch. He's absolutely 100 per cent certain of it. And that gives him an extraordinary conviction of certainty, and an arrogance that scientists don't have.
Essay, 'Private Games', in Lewis Wolpert and Alison Richards, (eds.), A Passion for Science (1988), 61.
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Then I have more than an impression—it amounts to a certainty—that algebra is made repellent by the unwillingness or inability of teachers to explain why we suddenly start using a and b, what exponents mean apart from their handling, and how the paradoxical behavior of + and — came into being. There is no sense of history behind the teaching, so the feeling is given that the whole system dropped down readymade from the skies, to be used only by born jugglers. This is what paralyzes—with few exceptions—the infant, the adolescent, or the adult who is not a juggler himself.
In Teacher in America (1945), 82.
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There is no certainty where one can neither apply any of the mathematical sciences nor any of those which are based upon the mathematical sciences.
(G 96 v.) In Edward McCurdy (ed., trans.), Leonardo da Vinci’s Note-Books: Arranged and Rendered into English (1908), 54. Also translated elsewhere as, “No knowledge can be certain if it is not based upon mathematics or upon some other knowledge which is itself based upon the mathematical sciences.”
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There is no permanence in doubt; it incites the mind to closer inquiry and experiment, from which, if rightly managed, certainty proceeds, and in this alone can man find thorough satisfaction.
In James Wood, Dictionary of Quotations from Ancient and Modern, English and Foreign Sources (1893), 474:2.
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There is nothing more certain in nature than that it is impossible for any body to be utterly annihilated.
[Stating the conservation of matter.]
Sylva Sylvarum; or a Natural History in Ten Centuries (1627), Century 1, Experiment 100. Collected in The Works of Francis Bacon (1826), Vol 1, 285.
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This is the element that distinguishes applied science from basic. Surprise is what makes the difference. When you are organized to apply knowledge, set up targets, produce a usable product, you require a high degree of certainty from the outset. All the facts on which you base protocols must be reasonably hard facts with unambiguous meaning. The challenge is to plan the work and organize the workers so that it will come out precisely as predicted. For this, you need centralized authority, elaborately detailed time schedules, and some sort of reward system based on speed and perfection. But most of all you need the intelligible basic facts to begin with, and these must come from basic research. There is no other source. In basic research, everything is just the opposite. What you need at the outset is a high degree of uncertainty; otherwise it isn’t likely to be an important problem. You start with an incomplete roster of facts, characterized by their ambiguity; often the problem consists of discovering the connections between unrelated pieces of information. You must plan experiments on the basis of probability, even bare possibility, rather than certainty.
The Planning of Science, The Lives of a Cell: Notes of a Biology Watcher, (1974) .
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This, however, seems to be certain: the ichor, that is, the material I have mentioned that finally becomes red, exists before the heart begins to beat, but the heart exists and even beats before the blood reddens.
'On the Formation of the Chick in the Egg' (1673), in H. B. Adelmann (ed.), Marcello Malpighi and the Evolution of Embryology (1966), Vol. 2, 957.
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Those who have taken upon them to lay down the law of nature as a thing already searched out and understood, whether they have spoken in simple assurance or professional affectation, have therein done philosophy and the sciences great injury. For as they have been successful in inducing belief, so they have been effective in quenching and stopping inquiry; and have done more harm by spoiling and putting an end to other men's efforts than good by their own. Those on the other hand who have taken a contrary course, and asserted that absolutely nothing can be known — whether it were from hatred of the ancient sophists, or from uncertainty and fluctuation of mind, or even from a kind of fullness of learning, that they fell upon this opinion — have certainly advanced reasons for it that are not to be despised; but yet they have neither started from true principles nor rested in the just conclusion, zeal and affectation having carried them much too far...
Now my method, though hard to practice, is easy to explain; and it is this. I propose to establish progressive stages of certainty. The evidence of the sense, helped and guarded by a certain process of correction, I retain. But the mental operation which follows the act of sense I for the most part reject; and instead of it I open and lay out a new and certain path for the mind to proceed in, starting directly from the simple sensuous perception.
Novum Organum (1620)
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Thus the system of the world only oscillates around a mean state from which it never departs except by a very small quantity. By virtue of its constitution and the law of gravity, it enjoys a stability that can be destroyed only by foreign causes, and we are certain that their action is undetectable from the time of the most ancient observations until our own day. This stability in the system of the world, which assures its duration, is one of the most notable among all phenomena, in that it exhibits in the heavens the same intention to maintain order in the universe that nature has so admirably observed on earth for the sake of preserving individuals and perpetuating species.
'Sur l'Équation Séculaire de la Lune' (1786, published 1788). In Oeuvres complètes de Laplace, 14 Vols. (1843-1912), Vol. 11, 248-9, trans. Charles Coulston Gillispie, Pierre-Simon Laplace 1749-1827: A Life in Exact Science (1997), 145.
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To be uncertain is to be uncomfortable, but to be certain is to be ridiculous.
Chinese proverb.
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To show, therefore, that we are capable of knowing, i.e. being certain that there is a God, and how we may come by this certainty, I think we need go no further than ourselves, and that undoubted knowledge we have of our own existence... For man knows that he himself exists... If any one pretends to be so sceptical as to deny his own existence, (for really to doubt of it is manifestly impossible,) let him for me enjoy his beloved happiness of being nothing, until hunger or some other pain convince him of the contrary... He knows also that nothing cannot produce a being; therefore something must have existed from eternity... Next, it is evident, that what had its being and beginning from another, must also have all that which is in and belongs to its being from another too. All the powers it has must be owing to and received from the same source. This eternal source, then, of all being must also be the source and original of all power; and so this eternal Being must be also the most powerful... And most knowing. Again, a man finds in himself perception and knowledge. We have then got one step further; and we are certain now that there is not only some being, but some knowing, intelligent being in the world. There was a time, then, when there was no knowing being, and when knowledge began to be; or else there has been also a knowing being from eternity...And therefore God.
Essay Concerning Human Understanding (1690), book 4, ch. 10, sec 19.
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We can trace the development of a nervous system, and correlate with it the parallel phenomena of sensation and thought. We see with undoubting certainty that they go hand in hand. But we try to soar in a vacuum the moment we seek to comprehend the connexion between them … Man the object is separated by an impassable gulf from man the subject.
In 'Address Delivered Before The British Association Assembled at Belfast' (19 Aug 1874), in Fragments of Science for Unscientific People: A Series of Detached Essays, Lectures, and Reviews (1892), Vol. 2, 194-195.
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We may consequently regard it as certain that, neither by natural agencies of inanimate matter, nor by the operations arbitrarily effected by animated Creatures, can there be any change produced in the amount of mechanical energy in the Universe.
In Draft of 'On a Universal Tendency … ', PA 137, Kelvin Collection, Cambridge Univ Library. As cited in Crosbie Smith, The Science of Energy: A Cultural History of Energy Physics in Victorian Britain (1998), 139.
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We may not be able to get certainty, but we can get probability, and half a loaf is better than no bread.
Christian Reflections (1967), 111
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We pass with admiration along the great series of mathematicians, by whom the science of theoretical mechanics has been cultivated, from the time of Newton to our own. There is no group of men of science whose fame is higher or brighter. The great discoveries of Copernicus, Galileo, Newton, had fixed all eyes on those portions of human knowledge on which their successors employed their labors. The certainty belonging to this line of speculation seemed to elevate mathematicians above the students of other subjects; and the beauty of mathematical relations and the subtlety of intellect which may be shown in dealing with them, were fitted to win unbounded applause. The successors of Newton and the Bernoullis, as Euler, Clairaut, D’Alembert, Lagrange, Laplace, not to introduce living names, have been some of the most remarkable men of talent which the world has seen.
In History of the Inductive Sciences, Vol. 1, Bk. 4, chap. 6, sect. 6.
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We see it [the as-yet unseen, probable new planet, Neptune] as Columbus saw America from the coast of Spain. Its movements have been felt, trembling along the far-reaching line of our analysis with a certainty hardly inferior to that of ocular demonstration.
Address to the British Association, Southampton (10 Sep 1845). Quoted in Memoirs of the Royal Astronomical Society (1847), 16, 400.
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Well, evolution is a theory. It is also a fact. And facts and theories are different things, not rungs in a hierarchy of increasing certainty. Facts are the world’s data. Theories are structures of ideas that explain and interpret facts. Facts do not go away while scientists debate rival theories for explaining them. Einstein’s theory of gravitation replaced Newton’s, but apples did not suspend themselves in mid-air pending the outcome. And human beings evolved from apelike ancestors whether they did so by Darwin’s proposed mechanism or by some other, yet to be discovered … Evolutionists make no claim for perpetual truth, though creationists often do (and then attack us for a style of argument that they themselves favor).
'Evolution as Fact and Theory', in Hen’s Teeth and Horse’s Toes: Further Reflections in Natural History (1983), 254-255.
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What certainty can there be in a Philosophy which consists in as many Hypotheses as there are Phaenomena to be explained. To explain all nature is too difficult a task for any one man or even for any one age. 'Tis much better to do a little with certainty, & leave the rest for others that come after you, than to explain all things by conjecture without making sure of any thing.
Quoted in Richard S. Westfall, The Life of Isaac Newton (1994), 256.
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What is known for certain is dull.
'My Commonplace Book', in I Wish I'd Made You Angry Earlier (1998), 314.
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What men want is not knowledge, but certainty.
Uncertain attribution. Often seen, but Webmaster has not yet found this wording in a primary source, and remains uncertain that this is an actual Russell quote. It is included here to provide this caution. Contact Webmaster if you have more information.
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When you believe you have found an important scientific fact, and are feverishly curious to publish it, constrain yourself for days, weeks, years sometimes, fight yourself, try and ruin your own experiments, and only proclaim your discovery after having exhausted all contrary hypotheses. But when, after so many efforts you have at last arrived at a certainty, your joy is one of the greatest which can be felt by a human soul.
From Speech (14 Nov 1888) at the Inauguration of the Pasteur Institute, as translated in René Vallery-Radot and Mrs R.L. Devonshire (trans.), The Life of Pasteur (1915), 443.
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Whether moral and social phenomena are really exceptions to the general certainty and uniformity of the course of nature; and how far the methods, by which so many of the laws of the physical world have been numbered among truths irrevocably acquired and universally assented to, can be made instrumental to the gradual formation of a similar body of received doctrine in moral and political science.
A System of Logic, Ratiocinative and Inductive (1858), v.
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While no one can ascribe a single weather event to climate change with any degree of scientific certainty, higher maximum temperatures are one of the most predictable impacts of accelerated global warming, and the parallels—between global climate change and global terrorism—are becoming increasingly obvious.
In 'Global Warming is Now a Weapon of Mass Destruction', The Guardian (28 Jul 2003).
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While the dogmatist is harmful, the sceptic is useless …; one is certain of knowing, the other of not knowing. What philosophy should dissipate is certainty, whether of knowledge or of ignorance. Knowledge is not so precise a concept as is commonly thought. Instead of saying ‘I know this’, we ought to say ‘I more or less know something more or less like this’. … Knowledge in practical affairs has not the certainty or the precision of arithmetic.
From 'Philosophy For Laymen', collected in Unpopular Essays (1950, 1996), 38-39.
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Why had we come to the moon?
The thing presented itself to me as a perplexing problem. What is this spirit in man that urges him for ever to depart from happiness and security, to toil, to place himself in danger, to risk an even a reasonable certainty of death? It dawned upon me that there in the moon as a thing I ought always to have known, that man is not made to go about safe and comfortable and well fed and amused. ... against his interest, against his happiness, he is constantly being driven to do unreasonable things. Some force not himself impels him, and he must go.
The First Men in the Moon (1901)
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Winwood Reade … remarks that while a man is an insoluble puzzle, in the aggregate he becomes a mathematical certainty. You can, for example, never foretell what any one man will do, but you can say with precision what an average number will be up to. Individuals vary, but percentages remain constant. So says the statistician.
Character Sherlock Holmes recommends Winwood Reade’s book The Martyrdom of Man to Dr. Watson in The Sign of the Four (1890), 196. Earlier in the novel, Holmes calls Reade’s book “one of the most remarkable ever penned.” Reade is a real person and his book was published in 1872. The actual statement in it reads: “As a single atom man is an enigma: as a whole he is a mathematical problem.”
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[1157] The man who blames the supreme certainty of mathematics feeds on confusion, and can never silence the contradictions of sophistical sciences which lead to an eternal quackery.
W. An. III. 241 a. From the original Italian: “Chi biasima la soma certezza della matematica, si pasce di confusione mai porrà silentio alle contraditioni delle soffistiche sciētie, colle quali s’inpara vno eterno gridore.” English and Italian in Jean Paul Richter (trans.), 'Philosophical Maxims: Of Mechanics', The Literary Works of Leonardo da Vinci (1883), Vol. 1, Part 2, 289, Aphorism 1157. [Note: Da Vinci writes ē=en.] Also translated beginning, “Those who condemn…”. Also seen translated as “Whoever despises the high wisdom of mathematics nourishes himself on delusion and will never still the sophistic sciences whose only product is an eternal uproar,” in Nicholas J. Rose Mathematical Maxims and Minims (1988).
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[1158] There is no certainty in sciences where one of the mathematical sciences cannot be applied, or which are not in relation with these mathematics.
Notebook G (c.1515), sheet 95 back. In the original Italian: “Nessuna certezza delle sciētie è, dove no si può applicare vna delle sciētie matematiche e che non son vnight con esse matematiche.” English and Italian in Jean Paul Richter (trans.), 'Philosophical Maxims: Of Mechanics', The Literary Works of Leonardo da Vinci (1883), Vol. 1, Part 2, 289, Aphorism 1158. [Note: da Vinci wrote ē=en; v=u] The following, found on the web, without citation, seems to be a paraphrase: “No human investigation can be called real science if it cannot be demonstrated mathematically.”
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[An artist] will sooner and with more certainty, establish the character of skeletons, than the most learned anatomist, whose eye has not been accustomed to seize on every peculiarity.
Asserting his (incorrect) belief that the fossil teeth of the mastodon revealed it was a carnivorous animal.]
In An Historical Disquisition on the Mammoth, or, Great American Incognitum, an Extinct, Immense, Carnivorous Animal, whose Fossil Remains Have Been Found in North America (1903), 38-39, which was published for his London exhibit of a mastodon skeleton. As cited in Michele L. Aldrich article on Peale, in Charles Coulston Gillespie, Dictionary of Scientific Biography (1978), Vol. 15-16, 472.
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[Boswell]: Sir Alexander Dick tells me, that he remembers having a thousand people in a year to dine at his house: that is, reckoning each person as one, each time that he dined there.
[Johnson]: That, Sir, is about three a day.
[Boswell]: How your statement lessens the idea.
[Johnson]: That, Sir, is the good of counting. It brings every thing to a certainty, which before floated in the mind indefinitely.
Entry for Fri 18 Apr 1783. In George Birkbeck-Hill (ed.), Boswell's Life of Johnson (1934-50), Vol. 4, 204.
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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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[I]f in other sciences we should arrive at certainty without doubt and truth without error, it behooves us to place the foundations of knowledge in mathematics, in so far as disposed through it we are able to reach certainty in other sciences and truth by the exclusion of error. (c.1267)
Translation by Robert Burke, Opus Majus of Roger Bacon (1928), vol 1, 124. In Fred R. Shapiro, The Yale Book of Quotations (2006), 39.
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[Mathematics] is security. Certainty. Truth. Beauty. Insight. Structure. Architecture. I see mathematics, the part of human knowledge that I call mathematics, as one thing—one great, glorious thing. Whether it is differential topology, or functional analysis, or homological algebra, it is all one thing. … They are intimately interconnected, they are all facets of the same thing. That interconnection, that architecture, is secure truth and is beauty. That’s what mathematics is to me.
From interview with Donald J. Albers. In John H. Ewing and Frederick W. Gehring, Paul Halmos Celebrating 50 Years of Mathematics (1991), 13.
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[The unreactivity of the noble gas elements] belongs to the surest of experimental results.
Angewandte Chemie (1924), 37, 421. Trans. In Hilde Hein and George E. Hein, 'The Chemistry of Noble Gases- A Modern Case Study in Experimental Science', Journal of the History of Ideas (1966), 27, 420.
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[The] second fundamental rule of historical science may be thus simply expressed:—we should not wish to explain every thing. Historical tradition must never be abandoned in the philosophy of history—otherwise we lose all firm ground and footing. But historical tradition, ever so accurately conceived and carefully sifted, doth not always, especially in the early and primitive ages, bring with it a full and demonstrative certainty.
In Friedrich von Schlegel and James Burton Robertson (trans.), The Philosophy of History (1835), 12.
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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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- 40 -
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