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Home > Category Index for Science Quotations > Category Index C > Category: Concept

Concept Quotes (38 quotes)

...the source of all great mathematics is the special case, the concrete example. It is frequent in mathematics that every instance of a concept of seemingly generality is, in essence, the same as a small and concrete special case.
I Want to be a Mathematician: an Automathography in Three Parts (1985), 324.
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A theory is the more impressive the greater the simplicity of its premises is, the more different kinds of things it relates, and the more extended is its area of applicability. Therefore the deep impression which classical thermodynamics made upon me. It is the only physical theory of universal content concerning which I am convinced that within the framework of the applicability of its basic concepts, it will never be overthrown.
Autobiographical Notes (1946), 33. Quoted in Gerald Holton and Yehuda Elkana, Albert Einstein: Historical and Cultural Perspectives (1997), 227.
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All human knowledge begins with intuitions, proceeds from thence to concepts, and ends with ideas.
Critique of Pure Reason (1781, 1787), B 730. As translated by Norman Kemp Smith in Immanuel Kant's Critique of Pure Reason (1929), 569.
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As an empiricist I continue to think of the conceptual scheme of science as a tool, ultimately, for predicting future experience in the light of past experience. Physical objects are conceptually imported into the situation as convenient intermediaries-not by definition in terms of experience, but simply as irreducible posits comparable, epistemologically, to the gods of Homer. For my part I do, qua lay physicist, believe in physical objects and not in Homer's gods; and I consider it a scientific error to believe otherwise. But in point of epistemological footing the physical objects and the gods differ only in degree and not in kind. Both sorts of entities enter our conception only as cultural posits. The myth of physical objects is epistemologically superior to most in that it has proved more efficacious than other myths as a device for working a manageable structure into the flux of experience.
From A Logical Point of View (1953), 44.
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Classes and concepts may, however, also be conceived as real objects, namely classes as 'pluralities of things' or as structures consisting of a plurality of things and concepts as the properties and relations of things existing independently of our definitions and constructions. It seems to me that the assumption of such objects is quite as legitimate as the assumption of physical bodies and there is quite as much reason to believe in their existence. They are in the same sense necessary to obtain a satisfactory system of mathematics as physical bodies are necessary for a satisfactory theory of our sense perceptions...
'Russell's Mathematical Logic', in P. A. Schilpp (ed.), The Philosophy of Bertrand Russell (1944), Vol. 1, 137.
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For strictly scientific or technological purposes all this is irrelevant. On a pragmatic view, as on a religious view, theory and concepts are held in faith. On the pragmatic view the only thing that matters is that the theory is efficacious, that it 'works' and that the necessary preliminaries and side issues do not cost too much in time and effort. Beyond that, theory and concepts go to constitute a language in which the scientistic matters at issue can be formulated and discussed.
'Slow Neutron Spectroscopy and the Grand Atlas of the Physical World', Nobel Lecture, 8 December 1994. In Nobel Lectures: Physics 1991-1995 (1997), 111.
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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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However, all scientific statements and laws have one characteristic in common: they are “true or false” (adequate or inadequate). Roughly speaking, our reaction to them is “yes” or “no.” The scientific way of thinking has a further characteristic. The concepts which it uses to build up its coherent systems are not expressing emotions. For the scientist, there is only “being,” but no wishing, no valuing, no good, no evil; no goal. As long as we remain within the realm of science proper, we can never meet with a sentence of the type: “Thou shalt not lie.” There is something like a Puritan's restraint in the scientist who seeks truth: he keeps away from everything voluntaristic or emotional.
Essays in Physics (1950), 68.
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I learnt to distrust all physical concepts as the basis for a theory. Instead one should put one's trust in a mathematical scheme, even if the scheme does not appear at first sight to be connected with physics. One should concentrate on getting interesting mathematics.
From a 1977 lecture. Quoted in Pesi Rustom Masani, Norbert Wiener, 1894-1964 (1990), 6.
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I once knew an otherwise excellent teacher who compelled his students to perform all their demonstrations with incorrect figures, on the theory that it was the logical connection of the concepts, not the figure, that was essential.
In Ernst Mach and Thomas Joseph McCormack, Space and Geometry (1906), 93.
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I suspect that the changes that have taken place during the last century in the average man's fundamental beliefs, in his philosophy, in his concept of religion. in his whole world outlook, are greater than the changes that occurred during the preceding four thousand years all put together. ... because of science and its applications to human life, for these have bloomed in my time as no one in history had had ever dreamed could be possible.
In The Autobiography of Robert A. Millikan (1951, 1980), xii.
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I'd like the [Cosmos] series to be so visually stimulating that somebody who isn't even interested in the concepts will just watch for the effects. And I'd like people who are prepared to do some thinking to be really stimulated.
Quoted by Dennis Meredith, in 'Carl Sagan's Cosmic Connection and Extraterrestrial Life-Wish', Science Digest (Jun 1979), 85, 38. Reproduced in Carl Sagan and Tom Head, Conversations With Sagan (2006), 55.
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In 1975, ... [speaking with Shiing Shen Chern], I told him I had finally learned ... the beauty of fiber-bundle theory and the profound Chern-Weil theorem. I said I found it amazing that gauge fields are exactly connections on fiber bundles, which the mathematicians developed without reference to the physical world. I added, “this is both thrilling and puzzling, since you mathematicians dreamed up these concepts out of nowhere.” He immediately protested: “No, no. These concepts were not dreamed up. They were natural and real.”
In 'Einstein's Impact on Theoretical Physics', collected in Jong-Ping Hsu, Leonard Hsu (eds.), JingShin Theoretical Physics Symposium in Honor of Professor Ta-You Wu (1998), 70. Reprinted from Physics Today (Jun 1980), 49. The article was adapted from a talk given at the Second Marcel Grossman meeting, held in Trieste, Italy (Jul 1979), in honor of the 100th anniversary of the birth of Albert Einstein.
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In general, we mean by any concept nothing more than a set of operations; the concept is synonymous with the corresponding set of operations.
The Logic of Modern Physics (1960), 5.

In physics we deal with states of affairs much simpler than those of psychology and yet we again and again learn that our task is not to investigate the essence of things—we do not at all know what this would mean&mash;but to develop those concepts that allow us to speak with each other about the events of nature in a fruitful manner.
Letter to H.P.E. Hansen (20 Jul 1935), Niels Bohr Archive. In Jan Faye, Henry J. Folse, Niels Bohr and Contemporary Philosophy (1994), 83.
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In the world of human thought generally, and in physical science particularly, the most important and fruitful concepts are those to which it is impossible to attach a well-defined meaning.
In M. Dresen, H. A. Kramers: Between Tradition and Revolution (1987), 539. In Magdolna Hargittai, In Our Own Image (2000), 3.
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Intelligence is an extremely subtle concept. It’s a kind of understanding that flourishes if it's combined with a good memory, but exists anyway even in the absence of good memory. It’s the ability to draw consequences from causes, to make correct inferences, to foresee what might be the result, to work out logical problems, to be reasonable, rational, to have the ability to understand the solution from perhaps insufficient information. You know when a person is intelligent, but you can be easily fooled if you are not yourself intelligent.
In Irv Broughton (ed.), The Writer's Mind: Interviews with American Authors (1990), Vol. 2, 57.
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It's important to always bear in mind that life occurs in historical time. Everyone in every culture lives in some sort of historical time, though it might not be perceived in the same way an outside observer sees it. It's an interesting question, “When is now?” “Now” can be drawn from some point like this hour, this day, this month, this lifetime, or this generation. “Now” can also have occurred centuries ago; things like unfair treaties, the Trail of Tears, and the Black Hawk War, for instance, remain part of the “Now” from which many Native Americans view their place in time today. Human beings respond today to people and events that actually occurred hundreds or even thousands of years ago. Ethnohistorians have played a major role in showing how now is a social concept of time, and that time is part of all social life. I can only hope that their work will further the understanding that the study of social life is a study of change over time.
From Robert S. Grumet, 'An Interview with Anthony F. C. Wallace', Ethnohistory (Winter 1998), 45, No. 1, 127.
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One of my guiding principles is don’t do anything that other people are doing. Always do something a little different if you can. The concept is that if you do it a little differently there is a greater potential for reward than if you the same thing that other people are doing. I think that this kind of goal for one’s work, having obviously the maximum risk, would have the maximum reward no matter what the field may be.
In transcript of a video history interview with Seymour Cray by David K. Allison at the National Museum of American History, Smithsonian Institution, (9 May 1995), 29.
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One should not understand this compulsion to construct concepts, species, forms, purposes, laws ('a world of identical cases') as if they enabled us to fix the real world; but as a compulsion to arrange a world for ourselves in which our existence is made possible:—we thereby create a world which is calculable, simplified, comprehensible, etc., for us.
The Will to Power (Notes written 1883-1888), book 3, no. 521. Trans. W. Kaufmann and R. J. Hollingdale and ed. W. Kaufmann (1968), 282.
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Pavlov’s data on the two fundamental antagonistic nervous processes—stimulation and inhibition—and his profound generalizations regarding them, in particular, that these processes are parts of a united whole, that they are in a state of constant conflict and constant transition of the one to the other, and his views on the dominant role they play in the formation of the higher nervous activity—all those belong to the most established natural—scientific validation of the Marxist dialectal method. They are in complete accord with the Leninist concepts on the role of the struggle between opposites in the evolution, the motion of matter.
In E. A. Asratyan, I. P. Pavlov: His Life and Work (1953), 153.
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Students using astrophysical textbooks remain essentially ignorant of even the existence of plasma concepts, despite the fact that some of them have been known for half a century. The conclusion is that astrophysics is too important to be left in the hands of astrophysicists who have gotten their main knowledge from these textbooks. Earthbound and space telescope data must be treated by scientists who are familiar with laboratory and magnetospheric physics and circuit theory, and of course with modern plasma theory.
[Lamenting the traditional neglect of plasma physics]
Quoted in Anthony L. Peratt, 'Dean of the Plasma Dissidents', Washington Times, supplement: The World and I (May 1988),197.
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The effect of a concept-driven revolution is to explain old things in new ways. The effect of a tool-driven revolution is to discover new things that have to be explained.
In Imagined Worlds (1997), 50-51.
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The first nonabsolute number is the number of people for whom the table is reserved. This will vary during the course of the first three telephone calls to the restaurant, and then bear no apparent relation to the number of people who actually turn up, or to the number of people who subsequently join them after the show/match/party/gig, or to the number of people who leave when they see who else has turned up.
The second nonabsolute number is the given time of arrival, which is now known to be one of the most bizarre of mathematical concepts, a recipriversexcluson, a number whose existence can only be defined as being anything other than itself. In other words, the given time of arrival is the one moment of time at which it is impossible that any member of the party will arrive. Recipriversexclusons now play a vital part in many branches of math, including statistics and accountancy and also form the basic equations used to engineer the Somebody Else's Problem field.
The third and most mysterious piece of nonabsoluteness of all lies in the relationship between the number of items on the check [bill], the cost of each item, the number of people at the table and what they are each prepared to pay for. (The number of people who have actually brought any money is only a subphenomenon of this field.)
Life, the Universe and Everything (1982, 1995), 47-48.
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The fundamental concept in social science is Power, in the same sense in which Energy is the fundamental concept in physics.
Power: A New Social Analysis (1938), 10.
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The idea that memory is linear is nonsense. What we have in our heads is a collection of frames. As to time itself—can it be linear when all these snatches of other presents exist at once in your mind? A very elusive and tricky concept, time."
Interview with Sarah Crown, in The Guardian (25 Jul 2009).
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The presentation of mathematics where you start with definitions, for example, is simply wrong. Definitions aren't the places where things start. Mathematics starts with ideas and general concepts, and then definitions are isolated from concepts. Definitions occur somewhere in the middle of a progression or the development of a mathematical concept. The same thing applies to theorems and other icons of mathematical progress. They occur in the middle of a progression of how we explore the unknown.
Interview for website of the Mathematical Association of America.
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The progress of science has always been the result of a close interplay between our concepts of the universe and our observations on nature. The former can only evolve out of the latter and yet the latter is also conditioned greatly by the former. Thus in our exploration of nature, the interplay between our concepts and our observations may sometimes lead to totally unexpected aspects among already familiar phenomena.
'Weak Interactions and Nonconservation of Parity', Nobel Lecture, 11 Dec 1957. In Nobel Lectures: Physics 1942-1962 (1964), 417.
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The results of mathematics are seldom directly applied; it is the definitions that are really useful. Once you learn the concept of a differential equation, you see differential equations all over, no matter what you do. This you cannot see unless you take a course in abstract differential equations. What applies is the cultural background you get from a course in differential equations, not the specific theorems. If you want to learn French, you have to live the life of France, not just memorize thousands of words. If you want to apply mathematics, you have to live the life of differential equations. When you live this life, you can then go back to molecular biology with a new set of eyes that will see things you could not otherwise see.
In 'A Mathematician's Gossip', Indiscrete Thoughts (2008), 213.
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The solutions put forth by imperialism are the quintessence of simplicity...When they speak of the problems of population and birth, they are in no way moved by concepts related to the interests of the family or of society...Just when science and technology are making incredible advances in all fields, they resort to technology to suppress revolutions and ask the help of science to prevent population growth. In short, the peoples are not to make revolutions, and women are not to give birth. This sums up the philosophy of imperialism.
From Fidel Castro (1968).
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The techniques have galloped ahead of the concepts. We have moved away from studying the complexity of the organism; from processes and organisation to composition.
[Commenting that growing use of new technologies and techniques, from molecular biology to genomics, has proved a mixed blessing.]
Quoted in Andrew Jack, "An Acute Talent for Innovation", Financial Times (1 Feb 2009).
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Thoughts without content are empty, intuitions without concepts are blind... The understanding can intuit nothing, the senses can think nothing. Only through their union can knowledge arise.
Critique of Pure Reason (1781), trans. Norman Kemp Smith (1929), 93.
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What distinguishes the language of science from language as we ordinarily understand the word? … What science strives for is an utmost acuteness and clarity of concepts as regards their mutual relation and their correspondence to sensory data.
In Out of My Later Years (1950, 1956), 112. Footnoted on page 277 as from 'The Common Language of Science', a broadcast recording for the Science Conference, London (28 Sep 1941) and published in Advancement of Science, 2, No. 5, 16.
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What the founders of modern science, among them Galileo, had to do, was not to criticize and to combat certain faulty theories, and to correct or to replace them by better ones. They had to do something quite different. They had to destroy one world and to replace it by another. They had to reshape the framework of our intellect itself, to restate and to reform its concepts, to evolve a new approach to Being, a new concept of knowledge, a new concept of science—and even to replace a pretty natural approach, that of common sense, by another which is not natural at all.
Galileo and Plato (1943), 405.
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Whenever a new scientific concept comes into prominence, it sends shock waves of surprise to the scholars contributing to that field.
In The Gene: A Critical History (1966), 77.
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Whereas the man of action binds his life to reason and its concepts so that he will not be swept away and lost, the scientific investigator builds his hut right next to the tower of science so that he will be able to work on it and to find shelter for himself beneath those bulwarks which presently exist.
On Truth and Lies in a Nonmoral Sense (1873). Collected in Keith Ansell-Pearson (ed.), and Duncan Large (ed.), The Nietzsche Reader (2006), 121.
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Without the discovery of uniformities there can be no concepts, no classifications, no formulations, no principles, no laws; and without these no science can exist.
Co-editor with American psychologist Henry Murray (1893-1988)
'Personality Formation: the Determinants'. In Clyde Kluckhohn and Henry A. Murray (eds.), Personality in Nature, Society, and Culture (1949), 37-8.
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[T]he laws of quantum mechanics itself cannot be formulated ... without recourse to the concept of consciousness.
From essay by Eugene Wigner, 'The Probability of the Existence of a Self-Reproducing Unit', contributed in M. Polanyi, The Logic of Personal Knowledge: Essays Presented to Michael Polanyi on his Seventieth Birthday, 11th March 1961 (1961), 232.
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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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- 100 -
Sophie Germain
Gertrude Elion
Ernest Rutherford
James Chadwick
Marcel Proust
William Harvey
Johann Goethe
John Keynes
Carl Gauss
Paul Feyerabend
- 90 -
Antoine Lavoisier
Lise Meitner
Charles Babbage
Ibn Khaldun
Euclid
Ralph Emerson
Robert Bunsen
Frederick Banting
Andre Ampere
Winston Churchill
- 80 -
John Locke
Bronislaw Malinowski
Bible
Thomas Huxley
Alessandro Volta
Erwin Schrodinger
Wilhelm Roentgen
Louis Pasteur
Bertrand Russell
Jean Lamarck
- 70 -
Samuel Morse
John Wheeler
Nicolaus Copernicus
Robert Fulton
Pierre Laplace
Humphry Davy
Thomas Edison
Lord Kelvin
Theodore Roosevelt
Carolus Linnaeus
- 60 -
Francis Galton
Linus Pauling
Immanuel Kant
Martin Fischer
Robert Boyle
Karl Popper
Paul Dirac
Avicenna
James Watson
William Shakespeare
- 50 -
Stephen Hawking
Niels Bohr
Nikola Tesla
Rachel Carson
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