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Definition Quotes (86 quotes)

Energie is the operation, efflux or activity of any being: as the light of the Sunne is the energie of the Sunne, and every phantasm of the soul is the energie of the soul.
[The first recorded definition of the term energy in English]
In Platonica: A Platonicall Song of the Soul (1642). In this book of poems, More uses the word energie many times, and in the opening section, 'To the Reader'. The definition quoted appears at the end of the book in 'The interpretation of the more unusual names or words that occurre in the foregoing Poems.'
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[Defining Life] The constant uniformity of phenomena under diversity of external influences.
Biologie (1802). As cited in translated form in George Henry Lewes, Physiology of Common Life (1875), Vol. 2, 356.
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A totally blind process can by definition lead to anything; it can even lead to vision itself.
In Jacques Monod and Austryn Wainhouse (trans.), Chance and Necessity: An Essay on the Natural Philosophy of Modern Biology (1972), 98.
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A definition is the enclosing a wilderness of idea within a wall of words.
Samuel Butler, Henry Festing Jones (ed.), The Note-Books of Samuel Butler (1917), 221.
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A discovery must be, by definition, at variance with existing knowledge. During my lifetime, I made two. Both were rejected offhand by the popes of the field. Had I predicted these discoveries in my applications, and had those authorities been my judges, it is evident what their decisions would have been.
In 'Dionysians and Apollonians', Science (2 Jun 1972), 176, 966. Reprinted in Mary Ritchie Key, The Relationship of Verbal and Nonverbal Communication (1980), 318.
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A poet is, after all, a sort of scientist, but engaged in a qualitative science in which nothing is measurable. He lives with data that cannot be numbered, and his experiments can be done only once. The information in a poem is, by definition, not reproducible. ... He becomes an equivalent of scientist, in the act of examining and sorting the things popping in [to his head], finding the marks of remote similarity, points of distant relationship, tiny irregularities that indicate that this one is really the same as that one over there only more important. Gauging the fit, he can meticulously place pieces of the universe together, in geometric configurations that are as beautiful and balanced as crystals.
In The Medusa and the Snail: More Notes of a Biology Watcher (1974, 1995), 107.
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According to Gandhi, the seven sins are wealth without works, pleasure without conscience, knowledge without character, commerce without morality, science without humanity, worship without sacrifice, and politics without principle. Well, Hubert Humphrey may have sinned in the eyes of God, as we all do, but according to those definitions of Gandhi’s, it was Hubert Humphrey without sin.
Eulogy at funeral of Vice President Hubert Humphrey, St. Paul, Minnesota (16 Jan 1978). In Public Papers of the Presidents of the United States: Jimmy Carter (1978), Vol. 1, 82.
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And, to prevent mistakes, I must advertize you, that I now mean by elements, as those chymists that speak plainest do by their principles, certain primitive or simple, or perfectly unmingled bodies; which not being made of any other bodies, or of one another, are the ingredients of which all those called perfectly mixt bodies are immediately compounded, and into which they are ultimately resolved: now whether there be any such body to be constantly met with in all, and each, of those that are said to be elemented bodies, is the thing I now question.
The Sceptical Chemist (1661), 187.
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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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Chance ... must be something more than the name we give to our ignorance.
In Science and Method (1908) translated by Francis Maitland (1914, 2007), 66.
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Chemists have made of phlogiston a vague principle which is not at all rigorously defined, and which, in consequence, adapts itself to all explanations in which it is wished it shall enter; sometimes it is free fire, sometimes it is fire combined with the earthy element; sometimes it passes through the pores of vessels, sometimes they are impenetrable to it; it explains both the causticity and non-causticity, transparency and opacity, colours and absence of colours. It is a veritable Proteus which changes its form every instant. It is time to conduct chemistry to a more rigorous mode of reasoning ... to distinguish fact and observation from what is systematic and hypothetical.
'Réflexions sur le phlogistique', Mémoires de l'Académie des Sciences, 1783, 505-38. Reprinted in Oeuvres de Lavoisier (1864), Vol. 2, 640, trans. M. P. Crosland.
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Definitions are a kind of scratching and generally leave a sore place more sore than it was before.
Samuel Butler, Henry Festing Jones (ed.), The Note-Books of Samuel Butler (1917), 221.
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Descriptive geometry has two objects: the first is to establish methods to represent on drawing paper which has only two dimensions,—namely, length and width,—all solids of nature which have three dimensions,—length, width, and depth,—provided, however, that these solids are capable of rigorous definition.
The second object is to furnish means to recognize accordingly an exact description of the forms of solids and to derive thereby all truths which result from their forms and their respective positions.
From On the Purpose of Descriptive Geometry as translated by Arnold Emch in David Eugene Smith, A Source Book in Mathematics (1929), 426.
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Disease may be defined as “A change produced in living things in consequence of which they are no longer in harmony with their environment.”
In Disease and its Causes (1913), 9.
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Engineering is the art or science of making practical.
The Existential Pleasures of Engineering (1976), x.
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Engineering is the professional and systematic application of science to the efficient utilization of natural resources to produce wealth.
T. J. Hoover and John Charles Lounsbury (J.C.L.) Fish, The Engineering Profession (1941), 10.
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Experiments on ornamental plants undertaken in previous years had proven that, as a rule, hybrids do not represent the form exactly intermediate between the parental strains. Although the intermediate form of some of the more striking traits, such as those relating to shape and size of leaves, pubescence of individual parts, and so forth, is indeed nearly always seen, in other cases one of the two parental traits is so preponderant that it is difficult or quite impossible, to detect the other in the hybrid. The same is true for Pisum hybrids. Each of the seven hybrid traits either resembles so closely one of the two parental traits that the other escapes detection, or is so similar to it that no certain distinction can be made. This is of great importance to the definition and classification of the forms in which the offspring of hybrids appear. In the following discussion those traits that pass into hybrid association entirely or almost entirely unchanged, thus themselves representing the traits of the hybrid, are termed dominating and those that become latent in the association, recessive. The word 'recessive' was chosen because the traits so designated recede or disappear entirely in the hybrids, but reappear unchanged in their progeny, as will be demonstrated later.
'Experiments on Plant Hybrids' (1865). In Curt Stern and Eva R. Sherwood (eds.), The Origin of Genetics: A Mendel Source Book (1966), 9.
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Extinction has only separated groups: it has by no means made them; for if every form which has ever lived on this earth were suddenly to reappear, though it would be quite impossible to give definitions by which each group could be distinguished from other groups, as all would blend together by steps as fine as those between the finest existing varieties, nevertheless a natural classification, or at least a natural arrangement, would be possible.
From On the Origin of Species by Means of Natural Selection; or, The Preservation of Favoured Races in the Struggle for Life (1860), 431.
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For to define true madness,
What is't but to be nothing else but mad?
Hamlet (1601), II, ii.
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Gyroscope, n.: A wheel or disk mounted to spin rapidly about an axis and also free to rotate about one or both of two axes perpendicular to each other and the axis of spin so that a rotation of one of the two mutually perpendicular axes results from application of torque to the other when the wheel is spinning and so that the entire apparatus offers considerable opposition depending on the angular momentum to any torque that would change the direction of the axis of spin.
Webster's New Collegiate Dictionary (8th Ed., 1973), 513. (Webmaster comments: A definition which is perfectly easy to understand. Right?)
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I have no patience with attempts to identify science with measurement, which is but one of its tools, or with any definition of the scientist which would exclude a Darwin, a Pasteur or a Kekulé. The scientist is a practical man and his are practical aims. He does not seek the ultimate but the proximate. He does not speak of the last analysis but rather of the next approximation. His are not those beautiful structures so delicately designed that a single flaw may cause the collapse of the whole. The scientist builds slowly and with a gross but solid kind of masonry. If dissatisfied with any of his work, even if it be near the very foundations, he can replace that part without damage to the remainder. On the whole, he is satisfied with his work, for while science may never be wholly right it certainly is never wholly wrong; and it seems to be improving from decade to decade.
The Anatomy of Science (1926), 6-7.
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I use the word 'attraction' here in a general sense for any endeavor whatever of bodies to approach one another, whether that endeavor occurs as a result of the action of the bodies either drawn toward one other or acting on one another by means of spirits emitted or whether it arises from the action of aether or of air or of any medium whatsoever-whether corporeal or incorporeal-in any way impelling toward one another the bodies floating therein. I use the word 'impulse' in the same general sense, considering in this treatise not the species of forces and their physical qualities but their quantities and mathematical proportions, as I have explained in the definitions.
The Principia: Mathematical Principles of Natural Philosophy (1687), 3rd edition (1726), trans. I. B. Cohen and Anne Whitman (1999), Book I, Section II, Scholium, 588.
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If any layman were to ask a number of archaeologists to give, on the spur of the moment, a definition of archaeology, I suspect that such a person might find the answers rather confusing. He would, perhaps, sympathize with Socrates who, when he hoped to learn from the poets and artisans something about the arts they practised, was forced to go away with the conviction that, though they might themselves be able to accomplish something, they certainly could give no clear account to others of what they were trying to do.
Opening statement in lecture at Columbia University (8 Jan 1908), 'Archaeology'. Published by the Columbia University Press (1908).
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If E is considered to be a continuously divisible quantity, this distribution is possible in infinitely many ways. We consider, however—this is the most essential point of the whole calculation—E to be composed of a well-defined number of equal parts and use thereto the constant of nature h = 6.55 ×10-27 erg sec. This constant multiplied by the common frequency ? of the resonators gives us the energy element E in erg, and dividing E by E we get the number P of energy elements which must be divided over the N resonators.
[Planck's constant, as introduced in 1900; subsequently written e = h? .]
'On the theory of the energy distribution law of the normal spectrum', in D. ter Haar and Stephen G. Brush, trans., Planck's Original Papers in Quantum Physics (1972), 40.
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If it is possible to have a linear unit that depends on no other quantity, it would seem natural to prefer it. Moreover, a mensural unit taken from the earth itself offers another advantage, that of being perfectly analogous to all the real measurements that in ordinary usage are also made upon the earth, such as the distance between two places or the area of some tract, for example. It is far more natural in practice to refer geographical distances to a quadrant of a great circle than to the length of a pendulum.
'Histoire'. Histoire et Memoires de l'Academie Royale des Science de Paris (1788/1791), 9-10. In Charles Coulston Gillispie, Pierre-Simon Laplace, 1749-1827: A Life in Exact Science (2nd Ed., 2000), 151. by Charles Coulston Gillispie, Robert Fox
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If there is something very slightly wrong in our definition of the theories, then the full mathematical rigor may convert these errors into ridiculous conclusions.
Feynman Lectures on Gravitation, edited by Brian Hatfield (2002), 21.
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If you ask ... the man in the street ... the human significance of mathematics, the answer of the world will be, that mathematics has given mankind a metrical and computatory art essential to the effective conduct of daily life, that mathematics admits of countless applications in engineering and the natural sciences, and finally that mathematics is a most excellent instrumentality for giving mental discipline... [A mathematician will add] that mathematics is the exact science, the science of exact thought or of rigorous thinking.
Address (28 Mar 1912), Michigan School Masters' Club, Ann Arbor, 'The Humanization of the Teaching of Mathematics. Printed in Science (26 Apr 1912). Collected in The Human Worth of Rigorous Thinking: Essays and Addresses (1916), 65-66.
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In despair, I offer your readers their choice of the following definitions of entropy. My authorities are such books and journals as I have by me at the moment.
(a) Entropy is that portion of the intrinsic energy of a system which cannot be converted into work by even a perfect heat engine.—Clausius.
(b) Entropy is that portion of the intrinsic energy which can be converted into work by a perfect engine.—Maxwell, following Tait.
(c) Entropy is that portion of the intrinsic energy which is not converted into work by our imperfect engines.—Swinburne.
(d) Entropy (in a volume of gas) is that which remains constant when heat neither enters nor leaves the gas.—W. Robinson.
(e) Entropy may be called the ‘thermal weight’, temperature being called the ‘thermal height.’—Ibid.
(f) Entropy is one of the factors of heat, temperature being the other.—Engineering.
I set up these bald statement as so many Aunt Sallys, for any one to shy at.
[Lamenting a list of confused interpretations of the meaning of entropy, being hotly debated in journals at the time.]
In The Electrician (9 Jan 1903).
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In Geometry, (which is the only Science that it hath pleased God hitherto to bestow on mankind,) men begin at settling the significations of their words; which settling of significations, they call Definitions; and place them in the beginning of their reckoning.
Leviathan (1651), ed. C. B. Macpherson (1968), Part 1, Chapter 4, 105.
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In the twenties the late Dr. Glenn Frank, an eminent social scientist, developed a new statement of the scientific code, which has been referred to as the “Five Fingers of the Scientific Method.” It may be outlined as follows: find the facts; filter the facts; focus the facts; face the facts; follow the facts. The facts or truths are found by experimentation; the motivation is material. The facts are filtered by research into the literature; the motivation is material. The facts are focused by the publication of results; again the motivation is material. Thus the first three-fifths of the scientific method have a material motivation. It is about time scientists acknowledge that there is more to the scientific convention than the material aspect. Returning to the fourth and fifth fingers of Dr. Frank's conception of the scientific method, the facts should be faced by the proper interpretation of them for society. In other words, a scientist must assume social responsibility for his discoveries, which means that he must have a moral motivation. Finally, in the fifth definition of the scientific method, the facts are to be followed by their proper application to everyday life in society, which means moral motivation through responsibility to society.
From 'Scientists and Society', American Scientist (Jul 1954), 42, No. 3, 495.
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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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It hath been an old remark, that Geometry is an excellent Logic. And it must be owned that when the definitions are clear; when the postulata cannot be refused, nor the axioms denied; when from the distinct contemplation and comparison of figures, their properties are derived, by a perpetual well-connected chain of consequences, the objects being still kept in view, and the attention ever fixed upon them; there is acquired a habit of reasoning, close and exact and methodical; which habit strengthens and sharpens the mind, and being transferred to other subjects is of general use in the inquiry after truth.
'The Analyst', in The Works of George Berkeley (1898), Vol. 3, 10.
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It is impossible to devise an experiment without a preconceived idea; devising an experiment, we said, is putting a question; we never conceive a question without an idea which invites an answer. I consider it, therefore, an absolute principle that experiments must always be devised in view of a preconceived idea, no matter if the idea be not very clear nor very well defined.
An Introduction to the Study of Experimental Medicine (1865, translation 1927, 1957), 23.
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It is natural for man to relate the units of distance by which he travels to the dimensions of the globe that he inhabits. Thus, in moving about the earth, he may know by the simple denomination of distance its proportion to the whole circuit of the earth. This has the further advantage of making nautical and celestial measurements correspond. The navigator often needs to determine, one from the other, the distance he has traversed from the celestial arc lying between the zeniths at his point of departure and at his destination. It is important, therefore, that one of these magnitudes should be the expression of the other, with no difference except in the units. But to that end, the fundamental linear unit must be an aliquot part of the terrestrial meridian. ... Thus, the choice of the metre was reduced to that of the unity of angles.
Lecture at the École Normale to the Year III (Apr 1795), Oeuvres Completes de Laplace (1878-1912), Vol. 14, 141. In Charles Coulston Gillispie, Dictionary of Scientific Biography (1978), Vol. 15, 335.
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It is notoriously difficult to define the word living.
Opening sentence in Of Molecules and Men (1966, 2004), 3.
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It is really laughable to see what different ideas are prominent in various naturalists' minds, when they speak of 'species'; in some, resemblance is everything and descent of little weight—in some, resemblance seems to go for nothing, and Creation the reigning idea—in some, descent is the key,—in some, sterility an unfailing test, with others it is not worth a farthing. It all comes, I believe, from trying to define the undefinable.
Letter to J. D. Hooker (24 Dec 1856). In Francis Darwin, The Life and Letters of Charles Darwin (1888), 446.
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It is usual to say that the two sources of experience are Observation and Experiment. When we merely note and record the phenomena which occur around us in the ordinary course of nature we are said to observe. When we change the course of nature by the intervention of our will and muscular powers, and thus produce unusual combinations and conditions of phenomena, we are said to experiment. [Sir John] Herschel has justly remarked that we might properly call these two modes of experience passive and active observation. In both cases we must certainly employ our senses to observe, and an experiment differs from a mere observation in the fact that we more or less influence the character of the events which we observe. Experiment is thus observation plus alteration of conditions.
Principles of Science: A Treatise on Logic and Scientific Method (1874, 2nd ed., 1913), 400.
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It would be well if engineering were less generally thought of, and even defined, as the art of constructing. In a certain important sense it is rather the art of not constructing; or, to define it rudely but not inaptly, it is the art of doing that well with one dollar, which any bungler can do with two after a fashion.
From The Economic Theory of the Location of Railways (1887, 1914), 1.
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Language is the principal tool with which we communicate; but when words are used carelessly or mistakenly, what was intended to advance mutual understanding may in fact hinder it; our instrument becomes our burden
Irving M. Copi and Carl Cohen (probably? in their Introduction to Logic), In K. Srinagesh, The Principles of Experimental Research (2006), 15.
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Life is the twofold internal movement of composition and decomposition at once general and continuous.
In The American Journal of the Medical Sciences (1858), 152.
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Logic issues in tautologies, mathematics in identities, philosophy in definitions; all trivial, but all part of the vital work of clarifying and organising our thought.
'Last Papers: Philosophy' (1929), in The Foundations of Mathematics and Other Logical Essays (1931), 264.
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Man is but a perambulating tool-box and workshop or office, fashioned for itself by a piece of very clever slime, as the result of long experience. ... Hence we speak of man's body as his “trunk.”
Samuel Butler, Henry Festing Jones (ed.), The Note-Books of Samuel Butler (1917), 18.
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Many errors, of a truth, consist merely in the application of the wrong names of things. For if a man says that the lines which are drawn from the centre of the circle to the circumference are not equal, he understands by the circle, at all events for the time, something else than mathematicians understand by it.
In 'Prop. 47: The human mind possesses an adequate knowledge of the eternal and infinite essence of God', Ethic, translated by William Hale White (1883), 93-94. Collected in The English and Foreign Philosophical Library, Vol. 21.
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Mathematics is the science which draws necessary conclusions.
Headline to opening paragraph, Linear Associative Algebra, read at National Academy of Sciences, Washington, D.C. (1870).
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Matter, though divisible in an extreme degree, is nevertheless not infinitely divisible. That is, there must be some point beyond which we cannot go in the division of matter. ... I have chosen the word “atom” to signify these ultimate particles.
Dalton's Manuscript Notes, Royal Institution Lecture 18 (30 Jan 1810). In Ida Freund, The Study of Chemical Composition: An Account of its Method and Historical Development (1910), 288.
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Medicine has been defined to be the art or science of amusing a sick man with frivolous speculations about his disorder, and of tampering ingeniously, till nature either kills or cures him.
Anonymous
In Tryon Edwards (ed.), A Dictionary of Thoughts (1908), 339.
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My Design in this Book is not to explain the Properties of Light by Hypotheses, but to propose and prove them by Reason and Experiments: In order to which, I shall premise the following Definitions and Axioms.
Opticks (1704), Book 1, Part 1, Introduction, 1.
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One cannot explain words without making incursions into the sciences themselves, as is evident from dictionaries; and, conversely, one cannot present a science without at the same time defining its terms.
'Of the Division of the Sciences' (1765), Book 4, Chap. 21, in New Essays on Human Understanding, trans. and ed. Peter Remnal (1981), 522.
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Physio-philosophy has to show how, and in accordance indeed with what laws, the Material took its origin; and, therefore, how something derived its existence from nothing. It has to portray the first periods of the world's development from nothing; how the elements and heavenly bodies originated; in what method by self-evolution into higher and manifold forms, they separated into minerals, became finally organic, and in Man attained self-consciousness.
In Lorenz Oken, trans. by Alfred Tulk, Elements of Physiophilosophy (1847), 1.
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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 has a simple faith, which transcends utility. Nearly all men of science, all men of learning for that matter, and men of simple ways too, have it in some form and in some degree. It is the faith that it is the privilege of man to learn to understand, and that this is his mission. If we abandon that mission under stress we shall abandon it forever, for stress will not cease. Knowledge for the sake of understanding, not merely to prevail, that is the essence of our being. None can define its limits, or set its ultimate boundaries.
Science is Not Enough (1967), 191.
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Scientific method is often defined as if it were a set procedure, to be learned, like a recipe, as if anyone could like a recipe, as if anyone could become a scientist simply by learning the method. This is as absurd ... [so I shall not] discuss scientific method, but rather the methods of scientists. We proceed by common sense and ingenuity. There are no rules, only the principles of integrity and objectivity, with a complete rejection of all authority except that of fact.
In Science in the Making (1957), 8.
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Scientific Terminology [is] the Scylla's cave which men of science are preparing for themselves to be able to pounce out upon us from it, and into which we cannot penetrate.
Samuel Butler, Henry Festing Jones (ed.), The Note-Books of Samuel Butler (1917), 218.
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Statistician: A man who believes figures don't lie but admits that, under analysis some of them won't stand up either.
Evan Esar
The Dictionary of Humorous Quotations (1949). In Robert Harris Shutler, Mathematics 436 - Finely Explained (2004), 3.
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Statistics: The only science that enables different experts using the same figures to draw different conclusions.
Evan Esar
The Dictionary of Humorous Quotations (1949). In Robert Harris Shutler, Mathematics 436 - Finely Explained (2004), 3.
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Superstition may be defined as constructive religion which has grown incongruous with intelligence.
In 'Science and Man', Fragments of Science (1879), Vol. 2, 370.
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Suppose we loosely define a religion as any discipline whose foundations rest on an element of faith, irrespective of any element of reason which may be present. Quantum mechanics for example would be a religion under this definition. But mathematics would hold the unique position of being the only branch of theology possessing a rigorous demonstration of the fact that it should be so classified.
Concluding remark in 'Consistency and Completeness—A Résumé', The American Mathematical Monthly (May 1956), 63, No.5, 305.
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That there is no such thing as the scientific method, one might easily discover by asking several scientists to define it. One would find, I am sure, that no two of them would exactly agree. Indeed, no two scientists work and think in just the same ways.
In Science in the Making (1957), 8-9.
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The cause, then, philosophically speaking, is the sum total of the conditions, positive and negative, taken together; the whole of the contingencies of every description, which being realized, the consequent invariably follows.
A System of Logic, Ratiocinative and Inductive (1858), 200.
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The definition of a good mathematical problem is the mathematics it generates rather than the problem itself.
From interview for PBS website on the NOVA program, 'The Proof'.
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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 Hypochondriake disease..[is] a drie and hote distemperature of Mesenterium, the liver and spleene.
Earliest citation in the etymology of the word hypochondriac given in the Oxford English Dictionary.
Discours de la conservation de la veue; des maladies mélancholiques, des catarrhes, et de la vieillese (1594). In Richard Surphlet (trans.) A Discourse of the Preservation of the Sight: of Melancholike Diseases; of Rheumes, and of Old Age (1599), 125.
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The institutional goal of science is the extension of certified knowledge. The technical methods employed toward this end provide the relevant definition of knowledge: empirically confirmed and logically consistent predictions. The institutional imperatives (mores) derive from the goal and the methods. The entire structure of technical and moral norms implements the final objective. The technical norm of empirical evidence, adequate, valid and reliable, is a prerequisite for sustained true prediction; the technical norm of logical consistency, a prerequisite for systematic and valid prediction. The mores of science possess a methodologic rationale but they are binding, not only because they are procedurally efficient, but because they are believed right and good. They are moral as well as technical prescriptions. Four sets of institutional imperatives–universalism, communism, disinterestedness, organized scepticism–comprise the ethos of modern science.
Social Theory and Social Structure (1957), 552-3.
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The life work of the engineer consists in the systematic application of natural forces and the systematic development of natural resources in the service of man.
Paper presented (15 Nov 1905) to the Association of American Agricultural Colleges and Experiment Stations, Washington, D.C., Proceedings of the 19th Annual Convention of the Association of American Agricultural Colleges and Experiment Stations (1906), Vol. 19-24, 90. Initials only given in this paper for H.W. Tyler (of Massachussetts); Webmaster tentatively matched with Harry Walter Tyler of M.I.T.
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The most satisfactory definition of man from the scientific point of view is probably Man the Tool-maker.
'The Earliest Tool-makers', Antiquity (1956), II 7, 4.
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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 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 subject-matter of Archaeology is threefold—the Oral, the Written and the Monumental.
In Lecture to the Oxford meeting of the Archaeological Institute (18 Jun 1850), printed in 'On the Study of Achaeology', Archaeological Journal (1851), 8, 2.
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The whole value of science consists in the power which it confers upon us of applying to one object the knowledge acquired from like objects; and it is only so far, therefore, as we can discover and register resemblances that we can turn our observations to account.
Principles of Science: A Treatise on Logic and Scientific Method (1874, 2nd ed., 1913), 1.
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The word “mathematics” is a Greek word and, by origin, it means “something that has been learned or understood,” or perhaps “acquired knowledge,” or perhaps even, somewhat against grammar, “acquirable knowledge,” that is, “learnable knowledge,” that is, “knowledge acquirable by learning.”
'Why Mathematics Grows', Journal of the History of Ideas (Jan-Mar 1965), 26, No. 1, 4. In Salomon Bochner and Robert Clifford Gunning (ed.) Collected Papers of Salomon Bochner (1992), Vol. 4, 192.
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There is no rigorous definition of rigor.

In Mathematics: The Loss of Certainty (1982), 315.
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There is one class of mind that loves to lean on rules and definitions, and another that discards them as far as possible. A faddist will generally ask for a definition of faddism, and one who is not a faddist will be impatient of being asked to give one.
Samuel Butler, Henry Festing Jones (ed.), The Note-Books of Samuel Butler (1917), 221.
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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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These microscopic organisms form an entire world composed of species, families and varieties whose history, which has barely begun to be written, is already fertile in prospects and findings of the highest importance. The names of these organisms are very numerous and will have to be defined and in part discarded. The word microbe which has the advantage of being shorter and carrying a more general meaning, and of having been approved by my illustrious friend, M. Littré, the most competent linguist in France, is one we will adopt.
In paper read to the Académie de Medecine (Mar 1878). In Charles-Emile Sedillot, 'Influence de M. Pasteur sur les progres de la chirurgie' [Influence of Pasteur on the progress of surgery].
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This method is, to define as the number of a class the class of all classes similar to the given class. Membership of this class of classes (considered as a predicate) is a common property of all the similar classes and of no others; moreover every class of the set of similar classes has to the set of a relation which it has to nothing else, and which every class has to its own set. Thus the conditions are completely fulfilled by this class of classes, and it has the merit of being determinate when a class is given, and of being different for two classes which are not similar. This, then, is an irreproachable definition of the number of a class in purely logical terms.
The Principles of Mathematics (1903), 115.
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Truth in science can be defined as the working hypothesis best suited to open the way to the next better one.
In On Aggression (1966, 2002), 279.
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Using any reasonable definition of a scientist, we can say that 80 to 90 percent of all the scientists that have ever lived are alive now. Alternatively, any young scientist, starting now and looking back at the end of his career upon a normal life span, will find that 80 to 90 percent of all scientific work achieved by the end of the period will have taken place before his very eyes, and that only 10 to 20 percent will antedate his experience.
Little Science, Big Science (1963), 1-2.
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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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Were I asked to define it, I should reply that archæology is that science which enables us to register and classify our knowledge of the sum of man’s achievement in those arts and handicrafts whereby he has, in time past, signalized his passage from barbarism to civilization.
In Pharaohs, Fellahs and Explorers (1891), 24.
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What is a good definition? For the philosopher or the scientist, it is a definition which applies to all the objects to be defined, and applies only to them; it is that which satisfies the rules of logic. But in education it is not that; it is one that can be understood by the pupils.
Science and Method (1914, 2003), 117.
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Whatever universe a professor believes in must at any rate be a universe that lends itself to lengthy discourse. A universe definable in two sentences is something for which the professorial intellect has no use. No faith in anything of that cheap kind!
First of eight lectures on ‘Pragmatism: A New Name For an Old Way of Thinking’ given at the Lowell Institute, Boston and the Departments of Philosophy and Psychology, Columbia University. In The Popular Science Monthly (Mar 1907), 193.
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Wherever man has left the stamp of mind on brute-matter; whether we designate his work as structure, texture, or mixture, mechanical or chymical; whether the result be a house, a ship, a garment, a piece of glass, or a metallic implement, these memorials of economy and invention will always be worthy of the attention of the Archaeologist.
In Lecture to the Oxford meeting of the Archaeological Institute (18 Jun 1850), printed in 'On the Study of Achaeology', Archaeological Journal (1851), 8, No. 29, 25.
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[Scientists] define these [terms] in tight phrases which convey a meaning only to those who already understand it.
In Science is a Sacred Cow (1950), 31.
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[Zoophytes (Protists, or simple life forms) are] the primitive types from which all the organisms of the higher classes had arisen by gradual development.
Entry for Gottfried Reinhold Treviranus in Encyclopedia Britannica (1911), Vol. 27, 255-256.
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“Bitzer,” said Thomas Gradgrind. “Your definition of a horse.”
“Quadruped. Graminivorous. Forty teeth; namely, twenty-four grinders, four eye-teeth, and twelve incisive. Sheds coat in the Spring; in marshy countries, sheds hoofs, too. Hoofs hard, but requiring to be shod with iron. Age known by marks in mouth.” Thus (and much more) Bitzer.
“Now girl number twenty,” said Mr. Gradgrind. “You know what a horse is.”
Spoken by fictional character Thomas Gringrind in his schoolroom with pupil Bitzer, Hard Times, published in Household Words (1 Apr 1854), Vol. 36, 3.
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“When I use a word,” Humpty Dumpty said, in rather a scornful tone, “it means just what I choose it to mean—neither more nor less.”
“The question is,” said Alice, “whether you can make words mean so many different things.”
“The question is,” said Humpty Dumpty, “which is to be master—that's all.”
Through the Looking Glass and What Alice Found There (1871, 1897), 124.


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