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Home > Category Index for Science Quotations > Category Index V > Category: Verification

Verification Quotes (31 quotes)

La théorie est l’hypothèse vérifiée, après qu’elle a été soumise au contrôle du raisonnement et de la critique expérimentale. La meilleure théorie est celle qui a été vérifiée par le plus grand nombre de faits. Mais une théorie, pour rester bonne, doit toujours se modifier avec les progrès de la science et demeurer constamment soumise à la vérification et à la critique des faits nouveaux qui apparaissent.
A theory is a verified hypothesis, after it has been submitted to the control of reason and experimental criticism. The soundest theory is one that has been verified by the greatest number of facts. But to remain valid, a theory must be continually altered to keep pace with the progress of science and must be constantly resubmitted to verification and criticism as new facts appear.
Original work in French, Introduction à l'Étude de la Médecine Expérimentale (1865), 385. English translation by Henry Copley Green in An Introduction to the Study of Experimental Medicine (1927, 1957), 220.
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All that we can hope from these inspirations, which are the fruits of unconscious work, is to obtain points of departure for such calculations. As for the calculations themselves, they must be made in the second period of conscious work which follows the inspiration, and in which the results of the inspiration are verified and the consequences deduced.
Science and Method (1914, 2003), 62.
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Any chemist reading this book can see, in some detail, how I have spent most of my mature life. They can become familiar with the quality of my mind and imagination. They can make judgements about my research abilities. They can tell how well I have documented my claims of experimental results. Any scientist can redo my experiments to see if they still work—and this has happened! I know of no other field in which contributions to world culture are so clearly on exhibit, so cumulative, and so subject to verification.
From Design to Discovery (1990), 119-20.
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Any one who has studied the history of science knows that almost every great step therein has been made by the “anticipation of Nature,” that is, by the invention of hypotheses, which, though verifiable, often had very little foundation to start with; and, not unfrequently, in spite of a long career of usefulness, turned out to be wholly erroneous in the long run.
In 'The Progress of Science 1837-1887' (1887), Collected Essays (1901), Vol. 1, 62.
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As every circumstance relating to so capital a discovery as this (the greatest, perhaps, that has been made in the whole compass of philosophy, since the time of Sir Isaac Newton) cannot but give pleasure to all my readers, I shall endeavour to gratify them with the communication of a few particulars which I have from the best authority. The Doctor [Benjamin Franklin], after having published his method of verifying his hypothesis concerning the sameness of electricity with the matter lightning, was waiting for the erection of a spire in Philadelphia to carry his views into execution; not imagining that a pointed rod, of a moderate height, could answer the purpose; when it occurred to him, that, by means of a common kite, he could have a readier and better access to the regions of thunder than by any spire whatever. Preparing, therefore, a large silk handkerchief, and two cross sticks, of a proper length, on which to extend it, he took the opportunity of the first approaching thunder storm to take a walk into a field, in which there was a shed convenient for his purpose. But dreading the ridicule which too commonly attends unsuccessful attempts in science, he communicated his intended experiment to no body but his son, who assisted him in raising the kite.
The kite being raised, a considerable time elapsed before there was any appearance of its being electrified. One very promising cloud passed over it without any effect; when, at length, just as he was beginning to despair of his contrivance, he observed some loose threads of the hempen string to stand erect, and to avoid one another, just as if they had been suspended on a common conductor. Struck with this promising appearance, he inmmediately presented his knuckle to the key, and (let the reader judge of the exquisite pleasure he must have felt at that moment) the discovery was complete. He perceived a very evident electric spark. Others succeeded, even before the string was wet, so as to put the matter past all dispute, and when the rain had wetted the string, he collected electric fire very copiously. This happened in June 1752, a month after the electricians in France had verified the same theory, but before he had heard of any thing that they had done.
The History and Present State of Electricity, with Original Experiments (1767, 3rd ed. 1775), Vol. 1, 216-7.
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Cosmology, for centuries consisting of speculation based on a minimum of observational evidence and a maximum of philosophical predilection, became in the twentieth century an observational science, its theories now subject to verification or refutation to a degree previously unimaginable.
Opening sentence in 'Philosophical Values and Observation in Edwin Hubble's Choice of a Model of the Universe', Historical Studies in the Physical Sciences (1982), 13, No. 1, 41.
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Great scientific discoveries have been made by men seeking to verify quite erroneous theories about the nature of things.
From 'Wordsworth in the Tropics', in Life and Letters and the London Mercury (1928), Vol. 1, 349.
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I was sitting writing at my textbook but the work did not progress; my thoughts were elsewhere. I turned my chair to the fire and dozed. Again the atoms were gambolling before my eyes. This time the smaller groups kept modestly in the background. My mental eye, rendered more acute by the repeated visions of the kind, could now distinguish larger structures of manifold confirmation: long rows, sometimes more closely fitted together all twining and twisting in snake like motion. But look! What was that? One of the snakes had seized hold of its own tail, and the form whirled mockingly before my eyes. As if by a flash of lightning I awoke; and this time also I spent the rest of the night in working out the rest of the hypothesis. Let us learn to dream, gentlemen, then perhaps we shall find the truth... But let us beware of publishing our dreams till they have been tested by waking understanding.
Kekule at Benzolfest in Berichte (1890), 23, 1302.
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If an explanation is so vague in its inherent nature, or so unskillfully molded in its formulation, that specific deductions subject to empirical verification or refutation can not be based upon it, then it can never serve as a working hypothesis. A hypothesis with which one can not work is not a working hypothesis.
'Role of Analysis in Scientific Investigation', Bulletin of the Geological Society of America (1933), 44, 479.
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If Darwin were alive today the insect world would delight and astound him with its impressive verification of his theories of the survival of the fittest. Under the stress of intensive chemical spraying the weaker members of the insect populations are being weeded out… . Only the strong and fit remain to defy our efforts to control them.
In Silent Spring (1952, 1962), 263.
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If you have to prove a theorem, do not rush. First of all, understand fully what the theorem says, try to see clearly what it means. Then check the theorem; it could be false. Examine the consequences, verify as many particular instances as are needed to convince yourself of the truth. When you have satisfied yourself that the theorem is true, you can start proving it.
In How to Solve It: A New Aspect of Mathematical Method (2004), 15.
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It is easy to obtain confirmations, or verifications, for nearly every theory—if we look for confirmations. Confirmations should count only if they are the result of risky predictions... A theory which is not refutable by any conceivable event is non-scientific. Irrefutability is not a virtue of a theory (as people often think) but a vice. Every genuine test of a theory is an attempt to falsify it, or refute it.
Conjectures and Refutations: The Growth of Scientific Knowledge (1963), 36.
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It is not Cayley’s way to analyze concepts into their ultimate elements. … But he is master of the empirical utilization of the material: in the way he combines it to form a single abstract concept which he generalizes and then subjects to computative tests, in the way the newly acquired data are made to yield at a single stroke the general comprehensive idea to the subsequent numerical verification of which years of labor are devoted. Cayley is thus the natural philosopher among mathematicians.
In Mathematische Annalen, Bd. 46 (1895), 479. As quoted and cited in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 146.
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Mathematical reasoning is deductive in the sense that it is based upon definitions which, as far as the validity of the reasoning is concerned (apart from any existential import), needs only the test of self-consistency. Thus no external verification of definitions is required in mathematics, as long as it is considered merely as mathematics.
In Universal Algebra (1898), Preface, vi.
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Progress is achieved by exchanging our theories for new ones which go further than the old, until we find one based on a larger number of facts. … Theories are only hypotheses, verified by more or less numerous facts. Those verified by the most facts are the best, but even then they are never final, never to be absolutely believed.
From An Introduction to the Study of Experimental Medicine (1865), as translated by Henry Copley Greene (1957), 165.
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Science deals with judgments on which it is possible to obtain universal agreement. These judgments do not concern individual facts and events, but the invariable association of facts and events known as the laws of science. Agreement is secured by observation and experiment—impartial courts of appeal to which all men must submit if they wish to survive. The laws are grouped and explained by theories of ever increasing generality. The theories at first are ex post facto—merely plausible interpretations of existing bodies of data. However, they frequently lead to predictions that can be tested by experiments and observations in new fields, and, if the interpretations are verified, the theories are accepted as working hypotheses until they prove untenable. The essential requirements are agreement on the subject matter and the verification of predictions. These features insure a body of positive knowledge that can be transmitted from person to person, and that accumulates from generation to generation.
From manuscript on English Science in the Renaissance (1937), Edwin Hubble collection, Box 2, Huntington Library, San Marino, California. As cited by Norriss S. Hetherington in 'Philosophical Values and Observation in Edwin Hubble's Choice of a Model of the Universe', Historical Studies in the Physical Sciences (1982), 13, No. 1, 41. (Hetherington comments parenthetically that the references to court, judgment and appeal may be attributable to his prior experiences as a Rhodes Scholar reading Roman law at Oxford, and to a year's practice as an attorney in Louisville, Kentucky.)
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Science is a system of statements based on direct experience, and controlled by experimental verification. Verification in science is not, however, of single statements but of the entire system or a sub-system of such statements.
The Unity of Science (1934), trans. Max Black, 42.
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The enthusiasm of Sylvester for his own work, which manifests itself here as always, indicates one of his characteristic qualities: a high degree of subjectivity in his productions and publications. Sylvester was so fully possessed by the matter which for the time being engaged his attention, that it appeared to him and was designated by him as the summit of all that is important, remarkable and full of future promise. It would excite his phantasy and power of imagination in even a greater measure than his power of reflection, so much so that he could never marshal the ability to master his subject-matter, much less to present it in an orderly manner.
Considering that he was also somewhat of a poet, it will be easier to overlook the poetic flights which pervade his writing, often bombastic, sometimes furnishing apt illustrations; more damaging is the complete lack of form and orderliness of his publications and their sketchlike character, … which must be accredited at least as much to lack of objectivity as to a superfluity of ideas. Again, the text is permeated with associated emotional expressions, bizarre utterances and paradoxes and is everywhere accompanied by notes, which constitute an essential part of Sylvester’s method of presentation, embodying relations, whether proximate or remote, which momentarily suggested themselves. These notes, full of inspiration and occasional flashes of genius, are the more stimulating owing to their incompleteness. But none of his works manifest a desire to penetrate the subject from all sides and to allow it to mature; each mere surmise, conceptions which arose during publication, immature thoughts and even errors were ushered into publicity at the moment of their inception, with utmost carelessness, and always with complete unfamiliarity of the literature of the subject. Nowhere is there the least trace of self-criticism. No one can be expected to read the treatises entire, for in the form in which they are available they fail to give a clear view of the matter under contemplation.
Sylvester’s was not a harmoniously gifted or well-balanced mind, but rather an instinctively active and creative mind, free from egotism. His reasoning moved in generalizations, was frequently influenced by analysis and at times was guided even by mystical numerical relations. His reasoning consists less frequently of pure intelligible conclusions than of inductions, or rather conjectures incited by individual observations and verifications. In this he was guided by an algebraic sense, developed through long occupation with processes of forms, and this led him luckily to general fundamental truths which in some instances remain veiled. His lack of system is here offset by the advantage of freedom from purely mechanical logical activity.
The exponents of his essential characteristics are an intuitive talent and a faculty of invention to which we owe a series of ideas of lasting value and bearing the germs of fruitful methods. To no one more fittingly than to Sylvester can be applied one of the mottos of the Philosophic Magazine:
“Admiratio generat quaestionem, quaestio investigationem investigatio inventionem.”
In Mathematische Annalen (1898), 50, 155-160. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 176-178.
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The entire annals of Observation probably do not elsewhere exhibit so extraordinary a verification of any theoretical conjecture adventured on by the human spirit!
[On the mathematical work by Urbain Le Verrier predicting the planet Neptune.]
In The Planet Neptune: An Exposition and History (1848), 90. The verification of the existence of the planet Neptune was made when Johan Galle found a star in an evening observation at the position predicted in the letter he received from Le Verrier earlier that same day.
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The experimental verification of a theory concerning any natural phenomenon generally rests on the result of an integration.
Epigraph in Higher Mathematics for Students of Chemistry and Physics: With Special Reference to Practical Work (1902), Chap 4, 150.
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The experimental verifications are not the basis of the theory, but its culmination.
As quoted in Philipp Frank, Modern Science and its Philosophy (1949), 16, which cites Théorie Physique; Son Objet—Son Structure (1906), 285. [Note: the experimentum crucis is a “crucial experiment” to be a conclusive test to decide between different hypotheses.]
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The improver of natural knowledge absolutely refuses to acknowledge authority as such. For him, scepticism is the highest of duties, blind faith the one unpardonable sin. The man of science has learned to believe in justification, not by faith, but by verification.
In Lecture (7 Jan 1866), a Lay Sermon delivered at St. Martin’s Hall, 'Advisableness of Improving Natural Knowledge', Lay Sermons, Addresses, and Reviews (1872), 18. Previously published in Fortnightly Review.
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The man of science has learned to believe in justification, not by faith, but by verification.
'On the Advisableness of Improving Natural knowledge' (1866). In Collected Essays (1893), Vol. 1, 41.
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The Mathematician deals with two properties of objects only, number and extension, and all the inductions he wants have been formed and finished ages ago. He is now occupied with nothing but deduction and verification.
In 'On the Educational Value of the Natural History Sciences', Lay Sermons, Addresses and Reviews (1872), 87.
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The prediction of nuclear winter is drawn not, of course, from any direct experience with the consequences of global nuclear war, but rather from an investigation of the governing physics. (The problem does not lend itself to full experimental verification—at least not more than once.)[co-author with American atmospheric chemist Richard P. Turco (1943- )]
A Path Where No Man Thought: Nuclear Winter and the End of the Arms Race (1990), 26.
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There is, however, no genius so gifted as not to need control and verification. ... [T]he brightest flashes in the world of thought are incomplete until they have been proved to have their counterparts in the world of fact. Thus the vocation of the true experimentalist may be defined as the continued exercise of spiritual insight, and its incessant correction and realisation. His experiments constitute a body, of which his purified intuitions are, as it were, the soul.
In 'Vitality', Scientific Use of the Imagination and Other Essays (1872), 43.
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We are told that “Mathematics is that study which knows nothing of observation, nothing of experiment, nothing of induction, nothing of causation.” I think no statement could have been made more opposite to the facts of the case; that mathematical analysis is constantly invoking the aid of new principles, new ideas, and new methods, not capable of being defined by any form of words, but springing direct from the inherent powers and activities of the human mind, and from continually renewed introspection of that inner world of thought of which the phenomena are as varied and require as close attention to discern as those of the outer physical world (to which the inner one in each individual man may, I think, be conceived to stand somewhat in the same relation of correspondence as a shadow to the object from which it is projected, or as the hollow palm of one hand to the closed fist which it grasps of the other), that it is unceasingly calling forth the faculties of observation and comparison, that one of its principal weapons is induction, that it has frequent recourse to experimental trial and verification, and that it affords a boundless scope for the exercise of the highest efforts of the imagination and invention.
In Presidential Address to British Association, Exeter British Association Report (1869), pp. 1-9, in Collected Mathematical Papers, Vol. 2, 654.
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We have seven or eight geological facts, related by Moses on the one part, and on the other, deduced solely from the most exact and best verified geological observations, and yet agreeing perfectly with each other, not only in substance, but in the order of their succession... That two accounts derived from sources totally distinct from and independent on each other should agree not only in the substance but in the order of succession of two events only, is already highly improbable, if these facts be not true, both substantially and as to the order of their succession. Let this improbability, as to the substance of the facts, be represented only by 1/10. Then the improbability of their agreement as to seven events is 1.7/10.7 that is, as one to ten million, and would be much higher if the order also had entered into the computation.
Geological Essays (1799), 52-3.
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With time, I attempt to develop hypotheses that are more risky. I agree with [Karl] Popper that scientists need to be interested in risky hypotheses because risky hypotheses advance science by producing interesting thoughts and potential falsifications of theories (of course, personally, we always strive for verification—we love our theories after all; but we should be ready to falsify them as well.
'Grand Theories and Mid-Range Theories&3039;, essay in Ken G. Smith (ed.) and Michael A. Hitt (ed), Great Minds in Management: the Theory of Process Development (2005), 89.
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[A scientist] naturally and inevitably … mulls over the data and guesses at a solution. [He proceeds to] testing of the guess by new data—predicting the consequences of the guess and then dispassionately inquiring whether or not the predictions are verified.
From manuscript on Francis Bacon as a scientist (1942), Edwin Hubble collection, Box 2, Huntington Library, San Marino, California. As cited by Norriss S. Hetherington in 'Philosophical Values and Observation in Edwin Hubble's Choice of a Model of the Universe', Historical Studies in the Physical Sciences (1982), 13, No. 1, 42.
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[The famous attack of Sir William Hamilton on the tendency of mathematical studies] affords the most express evidence of those fatal lacunae in the circle of his knowledge, which unfitted him for taking a comprehensive or even an accurate view of the processes of the human mind in the establishment of truth. If there is any pre-requisite which all must see to be indispensable in one who attempts to give laws to the human intellect, it is a thorough acquaintance with the modes by which human intellect has proceeded, in the case where, by universal acknowledgment, grounded on subsequent direct verification, it has succeeded in ascertaining the greatest number of important and recondite truths. This requisite Sir W. Hamilton had not, in any tolerable degree, fulfilled. Even of pure mathematics he apparently knew little but the rudiments. Of mathematics as applied to investigating the laws of physical nature; of the mode in which the properties of number, extension, and figure, are made instrumental to the ascertainment of truths other than arithmetical or geometrical—it is too much to say that he had even a superficial knowledge: there is not a line in his works which shows him to have had any knowledge at all.
In Examination of Sir William Hamilton's Philosophy (1878), 607.
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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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Max Planck
Henry Adams
Richard Dawkins
Werner Heisenberg
Alfred Wegener
John Dalton
- 40 -
Pierre Fermat
Edward Wilson
Johannes Kepler
Gustave Eiffel
Giordano Bruno
JJ Thomson
Thomas Kuhn
Leonardo DaVinci
Archimedes
David Hume
- 30 -
Andreas Vesalius
Rudolf Virchow
Richard Feynman
James Hutton
Alexander Fleming
Emile Durkheim
Benjamin Franklin
Robert Oppenheimer
Robert Hooke
Charles Kettering
- 20 -
Carl Sagan
James Maxwell
Marie Curie
Rene Descartes
Francis Crick
Hippocrates
Michael Faraday
Srinivasa Ramanujan
Francis Bacon
Galileo Galilei
- 10 -
Aristotle
John Watson
Rosalind Franklin
Michio Kaku
Isaac Asimov
Charles Darwin
Sigmund Freud
Albert Einstein
Florence Nightingale
Isaac Newton



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