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Home > Category Index for Science Quotations > Category Index D > Category: Deduction

Deduction Quotes (44 quotes)

The supreme task of the physicist is to arrive at those universal elementary laws from which the cosmos can be built up by pure deduction. There is no logical path to these laws; only intuition, resting on sympathetic understanding of experience, can reach them. In this methodological uncertainty, one might suppose that there were any number of possible systems of theoretical physics all equally well justified; and this opinion is no doubt correct, theoretically. But the development of physics has shown that at any given moment, out of all conceivable constructions, a single one has always proved itself decidedly superior to all the rest.
Address (1918) for Max Planck's 60th birthday, at Physical Society, Berlin, 'Principles of Research' in Essays in Science (1934), 4.
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All science is full of statements where you put your best face on your ignorance, where you say: … we know awfully little about this, but more or less irrespective of the stuff we don’t know about, we can make certain useful deductions.
From Assumption and Myth in Physical Theory (1967), 11.
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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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Deduction, which takes us from the general proposition to facts again—teaches us, if I may so say, to anticipate from the ticket what is inside the bundle.
'On the Educational Value of the Natural History Sciences' (1854). In Collected Essays (1893), Vol. 3, 52.
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Either one or the other [analysis or synthesis] may be direct or indirect. The direct procedure is when the point of departure is known-direct synthesis in the elements of geometry. By combining at random simple truths with each other, more complicated ones are deduced from them. This is the method of discovery, the special method of inventions, contrary to popular opinion.
Ampère gives this example drawn from geometry to illustrate his meaning for “direct synthesis” when deductions following from more simple, already-known theorems leads to a new discovery. In James R. Hofmann, André-Marie Ampère (1996), 159. Cites Académie des Sciences Ampère Archives, box 261.
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Forces of nature act in a mysterious manner. We can but solve the mystery by deducing the unknown result from the known results of similar events.
In The Words of Gandhi (2001), 87.
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Half a century ago Oswald (1910) distinguished classicists and romanticists among the scientific investigators: the former being inclined to design schemes and to use consistently the deductions from working hypotheses; the latter being more fit for intuitive discoveries of functional relations between phenomena and therefore more able to open up new fields of study. Examples of both character types are Werner and Hutton. Werner was a real classicist. At the end of the eighteenth century he postulated the theory of “neptunism,” according to which all rocks including granites, were deposited in primeval seas. It was an artificial scheme, but, as a classification system, it worked quite satisfactorily at the time. Hutton, his contemporary and opponent, was more a romanticist. His concept of “plutonism” supposed continually recurrent circuits of matter, which like gigantic paddle wheels raise material from various depths of the earth and carry it off again. This is a very flexible system which opens the mind to accept the possible occurrence in the course of time of a great variety of interrelated plutonic and tectonic processes.
In 'The Scientific Character of Geology', The Journal of Geology (Jul 1961), 69, No. 4, 456-7.
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I must begin with a good body of facts and not from a principle (in which I always suspect some fallacy) and then as much deduction as you please.
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I presume that few who have paid any attention to the history of the Mathematical Analysis, will doubt that it has been developed in a certain order, or that that order has been, to a great extent, necessary—being determined, either by steps of logical deduction, or by the successive introduction of new ideas and conceptions, when the time for their evolution had arrived. And these are the causes that operate in perfect harmony. Each new scientific conception gives occasion to new applications of deductive reasoning; but those applications may be only possible through the methods and the processes which belong to an earlier stage.
Explaining his choice for the exposition in historical order of the topics in A Treatise on Differential Equations (1859), Preface, v-vi.
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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 an idea presents itself to us, we must not reject it simply because it does not agree with the logical deductions of a reigning theory.
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In experimenting on the arc, my aim was not so much to add to the large number of isolated facts that had already been discovered, as to form some idea of the bearing of these upon one another, and thus to arrive at a clear conception of what takes place in each part of the arc and carbons at every moment. The attempt to correlate all the known phenomena, and to bind them together into one consistent whole, led to the deduction of new facts, which, when duly tested by experiment, became parts of the growing body, and, themselves, opened up fresh questions, to be answered in their turn by experiment.
In The Electric Arc (1902), Preface, iii. Ayrton described the growth of her published work on the electric arc, from a series of articles in The Electrician in 1895-6, to the full book, which “has attained to its present proportions almost with the growth of an organic body.”
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In the beginning (if there was such a thing), God created Newton’s laws of motion together with the necessary masses and forces. This is all; everything beyond this follows from the development of appropriate mathematical methods by means of deduction.
Autobiographical Notes (1946), 19. In Albert Einstein, Alice Calaprice, Freeman Dyson , The Ultimate Quotable Einstein (2011), 397.
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Induction for deduction, with a view to construction.
Attributed in John Arthur Thomson, quote at heading of chapter 'Scientific Method', Introduction to Science (1911), 57, but without further citation. Webmaster has found no primary source for confirmation. Please contact if you can help.
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Insight is not the same as scientific deduction, but even at that it may be more reliable than statistics.
In Science is a Sacred Cow (1950), 123.
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It is often held that scientific hypotheses are constructed, and are to be constructed, only after a detailed weighing of all possible evidence bearing on the matter, and that then and only then may one consider, and still only tentatively, any hypotheses. This traditional view however, is largely incorrect, for not only is it absurdly impossible of application, but it is contradicted by the history of the development of any scientific theory. What happens in practice is that by intuitive insight, or other inexplicable inspiration, the theorist decides that certain features seem to him more important than others and capable of explanation by certain hypotheses. Then basing his study on these hypotheses the attempt is made to deduce their consequences. The successful pioneer of theoretical science is he whose intuitions yield hypotheses on which satisfactory theories can be built, and conversely for the unsuccessful (as judged from a purely scientific standpoint). Co-author with British astronomer, Raymond Arthur Lyttleton (1911-95).
'The Internal Constitution of the Stars', Occasional Notes of the Royal Astronomical Society 1948, 12, 90.
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It must be admitted that science has its castes. The man whose chief apparatus is the differential equation looks down upon one who uses a galvanometer, and he in turn upon those who putter about with sticky and smelly things in test tubes. But all of these, and most biologists too, join together in their contempt for the pariah who, not through a glass darkly, but with keen unaided vision, observes the massing of a thundercloud on the horizon, the petal as it unfolds, or the swarming of a hive of bees. And yet sometimes I think that our laboratories are but little earthworks which men build about themselves, and whose puny tops too often conceal from view the Olympian heights; that we who work in these laboratories are but skilled artisans compared with the man who is able to observe, and to draw accurate deductions from the world about him.
The Anatomy of Science (1926), 170- 1.
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Mathematics is not a deductive science—that's a cliché. When you try to prove a theorem, you don't just list the hypotheses, and then start to reason. What you do is trial and error, experiment and guesswork.
I Want to be a Mathematician: an Automathography in Three Parts (1985), 321.
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Mathematics, including not merely Arithmetic, Algebra, Geometry, and the higher Calculus, but also the applied Mathematics of Natural Philosophy, has a marked and peculiar method or character; it is by preeminence deductive or demonstrative, and exhibits in a nearly perfect form all the machinery belonging to this mode of obtaining truth. Laying down a very small number of first principles, either self-evident or requiring very little effort to prove them, it evolves a vast number of deductive truths and applications, by a procedure in the highest degree mathematical and systematic.
In Education as a Science (1879), 148.
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Now having (I know not by what accident) engaged my thoughts upon the Bills of Mortality, and so far succeeded therein, as to have reduced several great confused Volumes into a few perspicuous Tables, and abridged such Observations as naturally flowed from them, into a few succinct Paragraphs, without any long Series of multiloquious Deductions, I have presumed to sacrifice these my small, but first publish'd, Labours unto your Lordship, as unto whose benign acceptance of some other of my Papers even the birth of these is due; hoping (if I may without vanity say it) they may be of as much use to persons in your Lordships place, as they are of none to me, which is no more than fairest Diamonds are to the Journeymen Jeweller that works them, or the poor Labourer that first digg'd them from Earth.
[An early account demonstrating the value of statistical analysis of public health data. Graunt lived in London at the time of the plague epidemics.]
From Graunt's 'Epistle Dedicatory', for Natural and Political Observations Mentioned in a Following Index and Made upon Bills of Mortality (1662). Reproduced in Cornelius Walford, The Insurance Cyclopaedia (1871), Vol. 1, 286. (This text used abbreviations for “Mort.” and “vols.”) The italicized words are given as from other sources. Note: bills of mortality are abstracts from parish registers showing the numbers that have died in each week, month or year.
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Organs, faculties, powers, capacities, or whatever else we call them; grow by use and diminish from disuse, it is inferred that they will continue to do so. And if this inference is unquestionable, then is the one above deduced from it—that humanity must in the end become completely adapted to its conditions—unquestionable also. Progress, therefore, is not an accident, but a necessity.
Social Statics: Or, The Conditions Essential to Human Happiness Specified, and the First of them Developed (1851), 65.
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Pure mathematics consists entirely of such asseverations as that, if such and such is a proposition is true of anything, then such and such another propositions is true of that thing. It is essential not to discuss whether the first proposition is really true, and not to mention what the anything is of which it is supposed to be true. … If our hypothesis is about anything and not about some one or more particular things, then our deductions constititute mathematics. Thus mathematics may be defined as the the subject in which we never know what we are talking about, not whether what we are saying is true.
'Recent Work on the Principles of Mathematics', International Monthly (1901), 4, 84. In Robert Édouard Moritz, Memorabilia Mathematica (1914), 7.
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Science is a game—but a game with reality, a game with sharpened knives … If a man cuts a picture carefully into 1000 pieces, you solve the puzzle when you reassemble the pieces into a picture; in the success or failure, both your intelligences compete. In the presentation of a scientific problem, the other player is the good Lord. He has not only set the problem but also has devised the rules of the game—but they are not completely known, half of them are left for you to discover or to deduce. The experiment is the tempered blade which you wield with success against the spirits of darkness—or which defeats you shamefully. The uncertainty is how many of the rules God himself has permanently ordained, and how many apparently are caused by your own mental inertia, while the solution generally becomes possible only through freedom from its limitations.
Quoted in Walter Moore, Schrödinger: Life and Thought (1989), 348.
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Science, in its ultimate ideal, consists of a set of propositions arranged in a hierarchy, the lowest level of the hierarchy being concerned with particular facts, and the highest with some general law, governing everything in the universe. The various levels in the hierarchy have a two-fold logical connection, travelling one up, one down; the upward connection proceeds by induction, the downward by deduction.
In The Scientific Outlook (1931, 2009), 38.
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Sir Arthur Eddington deduces religion from the fact that atoms do not obey the laws of mathematics. Sir James Jeans deduces it from the fact that they do.
In The Scientific Outlook (1931, 2009), 77.
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The business of their weekly Meetings shall be, To order, take account, consider, and discourse of Philosophical Experiments, and Observations: to read, hear, and discourse upon Letters, Reports, and other Papers containing Philosophical matters, as also to view, and discourse upon the productions and rarities of Nature, and Art: and to consider what to deduce from them, or how they may be improv'd for use, or discovery.
'An Abstract of the Statutes of the Royal Society', in Thomas Sprat, History of the Royal Society (1667), 145.
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The experimental investigation by which Ampere established the law of the mechanical action between electric currents is one of the most brilliant achievements in science. The whole theory and experiment, seems as if it had leaped, full grown and full armed, from the brain of the 'Newton of Electricity'. It is perfect in form, and unassailable in accuracy, and it is summed up in a formula from which all the phenomena may be deduced, and which must always remain the cardinal formula of electro-dynamics.
A Treatise on Electricity and Magnetism (1873), Vol. 2, 162.
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The faith of scientists in the power and truth of mathematics is so implicit that their work has gradually become less and less observation, and more and more calculation. The promiscuous collection and tabulation of data have given way to a process of assigning possible meanings, merely supposed real entities, to mathematical terms, working out the logical results, and then staging certain crucial experiments to check the hypothesis against the actual empirical results. But the facts which are accepted by virtue of these tests are not actually observed at all. With the advance of mathematical technique in physics, the tangible results of experiment have become less and less spectacular; on the other hand, their significance has grown in inverse proportion. The men in the laboratory have departed so far from the old forms of experimentation—typified by Galileo's weights and Franklin's kite—that they cannot be said to observe the actual objects of their curiosity at all; instead, they are watching index needles, revolving drums, and sensitive plates. No psychology of 'association' of sense-experiences can relate these data to the objects they signify, for in most cases the objects have never been experienced. Observation has become almost entirely indirect; and readings take the place of genuine witness.
Philosophy in a New Key; A Study in Inverse the Symbolism of Reason, Rite, and Art (1942), 19-20.
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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 grand aim of all science is to cover the greatest number of empirical facts by logical deduction from the smallest possible number of hypotheses or axioms.
As quoted in Lincoln Barnett, The Universe and Dr. Einstein (1950), 110.
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The intensity and quantity of polemical literature on scientific problems frequently varies inversely as the number of direct observations on which the discussions are based: the number and variety of theories concerning a subject thus often form a coefficient of our ignorance. Beyond the superficial observations, direct and indirect, made by geologists, not extending below about one two-hundredth of the Earth's radius, we have to trust to the deductions of mathematicians for our ideas regarding the interior of the Earth; and they have provided us successively with every permutation and combination possible of the three physical states of matter—solid, liquid, and gaseous.
'Address delivered by the President of Section [Geology] at Sydney (Friday, Aug 21), Report of the Eighty-Fourth Meeting of the British Association for the Advancement of Science: Australia 1914, 1915, 345.
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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 fundamental difference between compounds of low molecular weight and macromolecular compounds resides in the fact that the latter may exhibit properties that cannot be deduced from a close examination of the low molecular weight materials. Not very different structures can be obtained from a few building blocks; but if 10,000 or 100,000 blocks are at hand, the most varied structures become possible, such as houses or halls, whose special structure cannot be predicted from the constructions that are possible with only a few building blocks... Thus, a chromosome can be viewed as a material whose macromolecules possess a well defined arrangement, like a living room in which each piece of furniture has its place and not, as in a warehouse, where the pieces of furniture are placed together in a heap without design.
Quoted, without citation, in Ralph E. Oesper (ed.), The Human Side of Scientists (1975), 175.
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The scientist, if he is to be more than a plodding gatherer of bits of information, needs to exercise an active imagination. The scientists of the past whom we now recognize as great are those who were gifted with transcendental imaginative powers, and the part played by the imaginative faculty of his daily life is as least as important for the scientist as it is for the worker in any other field—much more important than for most. A good scientist thinks logically and accurately when conditions call for logical and accurate thinking—but so does any other good worker when he has a sufficient number of well-founded facts to serve as the basis for the accurate, logical induction of generalizations and the subsequent deduction of consequences.
‘Imagination in Science’, Tomorrow (Dec 1943), 38-9. Quoted In Barbara Marinacci (ed.), Linus Pauling In His Own Words: Selected Writings, Speeches, and Interviews (1995), 82.
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There can be no ultimate statements science: there can be no statements in science which can not be tested, and therefore none which cannot in principle be refuted, by falsifying some of the conclusions which can be deduced from them.
The Logic of Scientific Discovery (1959), 47.
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There is synthesis when, in combining therein judgments that are made known to us from simpler relations, one deduces judgments from them relative to more complicated relations.
There is analysis when from a complicated truth one deduces more simple truths.
In James R. Hofmann, André-Marie Ampère (1996), 158. Cites Académie des Sciences Ampère Archives, lecture notes, box 261.
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There is a tradition of opposition between adherents of induction and of deduction. In my view it would be just as sensible for the two ends of a worm to quarrel.
From address to the Mathematical and Physical Science Section of the British Association, Newcastle-on-Tyne (1916). In The Chemical News and Journal of Physical Science (22 Sep 1916), 142.114, No. 2965,
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There is nothing distinctively scientific about the hypothetico-deductive process. It is not even distinctively intellectual. It is merely a scientific context for a much more general stratagem that underlies almost all regulative processes or processes of continuous control, namely feedback, the control of performance by the consequences of the act performed. In the hypothetico-deductive scheme the inferences we draw from a hypothesis are, in a sense, its logical output. If they are true, the hypothesis need not be altered, but correction is obligatory if they are false. The continuous feedback from inference to hypothesis is implicit in Whewell’s account of scientific method; he would not have dissented from the view that scientific behaviour can be classified as appropriately under cybernetics as under logic.
Induction and Intuition in Scientific Thought (1969), 54-5.
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To be acceptable as scientific knowledge a truth must be a deduction from other truths.
Unverified. Webmaster has not yet pinpointed the source in these words. In Astounding Science Fiction (1945), 35, No. 5, it appears as an epigraph, and cites 'Nichomachean Ethics'. This may only be a summary of a theme of Archimedes. Please contact Webmaster if you have a specific reference to the primary source.
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Unless the structure of the nucleus has a surprise in store for us, the conclusion seems plain—there is nothing in the whole system if laws of physics that cannot be deduced unambiguously from epistemological considerations. An intelligence, unacquainted with our universe, but acquainted with the system of thought by which the human mind interprets to itself the contents of its sensory experience, and should be able to attain all the knowledge of physics that we have attained by experiment.
In Clive William Kilmister, Eddington's Search for a Fundamental Theory (1994), 202.
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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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We shall therefore say that a program has common sense if it automatically deduces for itself a sufficient wide class of immediate consequences of anything it is told and what it already knows. ... Our ultimate objective is to make programs that learn from their experience as effectively as humans do.
'Programs with Common Sense', (probably the first paper on AI), delivered to the Teddington Conference on the Mechanization of Thought Processes (Dec 1958). Printed in National Physical Laboratory, Mechanisation of Thought Processes: Proceedings of a Symposium Held at the National Physical Laboratory on 24th, 25th, 26th and 27th November 1958 (1959), 78. Also Summary in John McCarthy and Vladimir Lifschitz (ed.), Formalizing Common Sense: Papers by John McCarthy (1990), 9-10.
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When the pioneer in science sets forth the groping feelers of his thought, he must have a vivid, intuitive imagination, for new ideas are not generated by deduction, but by an artistically creative imagination.
In Scientific Autobiography and Other Papers (1968), 109.
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“I should have more faith,” he said; “I ought to know by this time that when a fact appears opposed to a long train of deductions it invariably proves to be capable of bearing some other interpretation.”
Spoken by character, Sherlock Holmes, in A Study in Scarlet (1887), in Works of Arthur Conan Doyle (1902), Vol. 11, 106.
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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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