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

Consistency Quotes (31 quotes)

...the question undoubtedly is, or soon will be, not whether or no we shall employ notation in chemistry, but whether we shall use a bad and incongruous, or a consistent and regular notation.
'On the Employment of Notation in Chemistry', Journal of the Royal Institution (1838), 1, 438. Cited in Timothy L. Alborn, 'Negotiating Notation: Chemical Symbols and British Society, 1831-1835', Annals of Science (1989), 46, 437.
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[In refutation of evolution] There is not enough evidence, consistent evidence to make it as fact, and I say that because for theory to become a fact, it needs to consistently have the same results after it goes through a series of tests. The tests that they put—that they use to support evolution do not have consistent results. Now too many people are blindly accepting evolution as fact. But when you get down to the hard evidence, it’s merely a theory.
[In favor of the teaching of creationism alongside evolution in schools.]
From interview by Miles O'Brien on CNN (30 Mar 1996). Reported from transcript, via Nexis, in New York Magazine (15 Sep 2010).
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A foolish consistency is the hobgoblin of little minds, adored by little statesmen and philosophers and divines.
From 'Self-Reliance', collected in The Complete Works of Ralph Waldo Emerson (1903), 57.
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Any conception which is definitely and completely determined by means of a finite number of specifications, say by assigning a finite number of elements, is a mathematical conception. Mathematics has for its function to develop the consequences involved in the definition of a group of mathematical conceptions. Interdependence and mutual logical consistency among the members of the group are postulated, otherwise the group would either have to be treated as several distinct groups, or would lie beyond the sphere of mathematics.
In 'Mathematics', Encyclopedia Britannica (9th ed.).
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Confined to its true domain, mathematical reasoning is admirably adapted to perform the universal office of sound logic: to induce in order to deduce, in order to construct. … It contents itself to furnish, in the most favorable domain, a model of clearness, of precision, and consistency, the close contemplation of which is alone able to prepare the mind to render other conceptions also as perfect as their nature permits. Its general reaction, more negative than positive, must consist, above all, in inspiring us everywhere with an invincible aversion for vagueness, inconsistency, and obscurity, which may always be really avoided in any reasoning whatsoever, if we make sufficient effort.
In Synthèse Subjective (1856), 98. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 202-203. From the original French, “Bornée à son vrai domaine, la raison mathématique y peut admirablement remplir l’office universel de la saine logique: induire pour déduire, afin de construire. … Elle se contente de former, dans le domaine le plus favorable, un type de clarté, de précision, et de consistance, dont la contemplation familière peut seule disposer l’esprit à rendre les autres conceptions aussi parfaites que le comporte leur nature. Sa réaction générale, plus négative que positive, doit surtout consister à nous inspirer partout une invincible répugnance pour le vague, l’incohérence, et l’obscurité, que nous pouvons réellement éviter envers des pensées quelconques, si nous y faisons assez d’efforts.”
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Essentially only one thing in life interests us: our psychical constitution, the mechanism of which was and is wrapped in darkness. All human resources, art, religion, literature, philosophy and historical sciences, all of them join in bringing lights in this darkness. But man has still another powerful resource: natural science with its strictly objective methods. This science, as we all know, is making huge progress every day. The facts and considerations which I have placed before you at the end of my lecture are one out of numerous attempts to employ a consistent, purely scientific method of thinking in the study of the mechanism of the highest manifestations of life in the dog, the representative of the animal kingdom that is man's best friend.
'Physiology of Digestion', Nobel Lecture (12 Dec 1904). In Nobel Lectures: Physiology or Medicine 1901-1921 (1967), 134
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Every natural scientist who thinks with any degree of consistency at all will, I think, come to the view that all those capacities that we understand by the phrase psychic activities (Seelenthiitigkeiten) are but functions of the brain substance; or, to express myself a bit crudely here, that thoughts stand in the same relation to the brain as gall does to the liver or urine to the kidneys. To assume a soul that makes use of the brain as an instrument with which it can work as it pleases is pure nonsense; we would then be forced to assume a special soul for every function of the body as well.
Carl Vogt
In Physiologische Briefe für Gelbildete aIle Stünde (1845-1847), 3 parts, 206. as translated in Frederick Gregory, Scientific Materialism in Nineteenth Century Germany (1977), 64.
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Every writer must reconcile, as best he may, the conflicting claims of consistency and variety, of rigour in detail and elegance in the whole. The present author humbly confesses that, to him, geometry is nothing at all, if not a branch of art.
Concluding remark in preface to Treatise on Algebraic Plane Curves (1931), x.
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Great thinkers build their edifices with subtle consistency. We do our intellectual forebears an enormous disservice when we dismember their visions and scan their systems in order to extract a few disembodied ‘gems’–thoughts or claims still accepted as true. These disarticulated pieces then become the entire legacy of our ancestors, and we lose the beauty and coherence of older systems that might enlighten us by their unfamiliarity–and their consequent challenge in our fallible (and complacent) modern world.
…...
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Mathematical reasoning is deductive in the sense that it is based upon definitions which, as far as the validity of the reasoning is concerned (apart from any existential import), needs only the test of self-consistency. Thus no external verification of definitions is required in mathematics, as long as it is considered merely as mathematics.
In Universal Algebra (1898), Preface, vi.
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Mathematicians deal with possible worlds, with an infinite number of logically consistent systems. Observers explore the one particular world we inhabit. Between the two stands the theorist. He studies possible worlds but only those which are compatible with the information furnished by observers. In other words, theory attempts to segregate the minimum number of possible worlds which must include the actual world we inhabit. Then the observer, with new factual information, attempts to reduce the list further. And so it goes, observation and theory advancing together toward the common goal of science, knowledge of the structure and observation of the universe.
Lecture to Sigma Xi, 'The Problem of the Expanding Universe' (1941), printed in Sigma Xi Quarterly (1942), 30, 104-105. Reprinted in Smithsonian Institution Report of the Board of Regents (1943), 97, 123. As cited by Norriss S. Hetherington in 'Philosophical Values and Observation in Edwin Hubble's Choice of a Model of the Universe', Historical Studies in the Physical Sciences (1982), 13, No. 1, 63.
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Mathematics is the science of consistency; it is a picture of the universe; as Plato is said to have expressed the idea, “God eternally geometrizes.”
In 'The Poetry of Mathematics', The Mathematics Teacher (May 1926), 19, No. 5, 295.
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May every young scientist remember … and not fail to keep his eyes open for the possibility that an irritating failure of his apparatus to give consistent results may once or twice in a lifetime conceal an important discovery.
Commenting on the discovery of thoron gas because one of Rutherford’s students had found his measurements of the ionizing property of thorium were variable. His results even seemed to relate to whether the laboratory door was closed or open. After considering the problem, Rutherford realized a radioactive gas was emitted by thorium, which hovered close to the metal sample, adding to its radioactivity—unless it was dissipated by air drafts from an open door. (Thoron was later found to be argon.)
In Barbara Lovett Cline, Men Who Made a New Physics (1987), 21.
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Nothing is too wonderful to be true if it be consistent with the laws of nature.
Laboratory notebook (19 Mar 1850), while musing on the possible relation of gravity to electricy. In Michael Faraday and Bence Jones (ed.), The Life and Letters of Faraday (1870), 253
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People of the same trade seldom meet together, even for merriment and diversion, but the conversation ends in a conspiracy against the public, or in some contrivance to raise prices. It is impossible indeed to prevent such meetings, by any law which either could be executed, or would be consistent with liberty and justice.
An Enquiry into the Nature and Causes of the Wealth of Nations (1776). In R. H. Campbell and A. S. Skinner (eds.), An Enquiry Into the Nature and Causes of the Wealth of Nations (1976), Vol. 1, Book 1, Chapter 10, Part 2, 145.
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Pierre Curie, a brilliant scientist, happened to marry a still more brilliant one—Marie, the famous Madame Curie—and is the only great scientist in history who is consistently identified as the husband of someone else.
View from a Height (1963), 119.
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Since the examination of consistency is a task that cannot be avoided, it appears necessary to axiomatize logic itself and to prove that number theory and set theory are only parts of logic. This method was prepared long ago (not least by Frege’s profound investigations); it has been most successfully explained by the acute mathematician and logician Russell. One could regard the completion of this magnificent Russellian enterprise of the axiomatization of logic as the crowning achievement of the work of axiomatization as a whole.
Address (11 Sep 1917), 'Axiomatisches Denken' delivered before the Swiss Mathematical Society in Zürich. Translated by Ewald as 'Axiomatic Thought', (1918), in William Bragg Ewald, From Kant to Hilbert (1996), Vol. 2, 1113.
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The critical mathematician has abandoned the search for truth. He no longer flatters himself that his propositions are or can be known to him or to any other human being to be true; and he contents himself with aiming at the correct, or the consistent. The distinction is not annulled nor even blurred by the reflection that consistency contains immanently a kind of truth. He is not absolutely certain, but he believes profoundly that it is possible to find various sets of a few propositions each such that the propositions of each set are compatible, that the propositions of each such set imply other propositions, and that the latter can be deduced from the former with certainty. That is to say, he believes that there are systems of coherent or consistent propositions, and he regards it his business to discover such systems. Any such system is a branch of mathematics.
In George Edward Martin, The Foundations of Geometry and the Non-Euclidean Plane (1982), 94. Also in Science (1912), New Series, 35, 107.
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The crown and glory of life is Character. It is the noblest possession of a man, constituting a rank in itself, and an estate in the general goodwill; dignifying every station, and exalting every position in society. It exercises a greater power than wealth, and secures all the honour without the jealousies of fame. It carries with it an influence which always tells; for it is the result of proved honour, rectitude, and consistency—qualities which, perhaps more than any other, command the general confidence and respect of mankind.
In Self-help: With Illustrations of Character and Conduct (1859, 1861), 396.
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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 mathematical framework of quantum theory has passed countless successful tests and is now universally accepted as a consistent and accurate description of all atomic phenomena. The verbal interpretation, on the other hand – i.e., the metaphysics of quantum theory – is on far less solid ground. In fact, in more than forty years physicists have not been able to provide a clear metaphysical model.
In The Tao of Physics (1975), 132.
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The mathematical framework of quantum theory has passed countless successful tests and is now universally accepted as a consistent and accurate description of all atomic phenomena. The verbal interpretation, on the other hand, i.e. the metaphysics of quantum physics, is on far less solid ground. In fact, in more than forty years physicists have not been able to provide a clear metaphysical model.
In The Tao of Physics: An Exploration of the Parallels Between Modern Physics (1975), 132.
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The whole question of imagination in science is often misunderstood by people in other disciplines. ... They overlook the fact that whatever we are allowed to imagine in science must be consistent with everything else we know.
In The Feynman Lectures in Physics (1964), Vol. 2, Lecture 20, p.20-10. As quoted by James Gleick in Genius: The Life and Science of Richard Feynman (1992), 324.
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There are diverse views as to what makes a science, but three constituents will be judged essential by most, viz: (1) intellectual content, (2) organization into an understandable form, (3) reliance upon the test of experience as the ultimate standard of validity. By these tests, mathematics is not a science, since its ultimate standard of validity is an agreed-upon sort of logical consistency and provability.
In 'The Future of Data Analysis', Annals of Mathematical Statistics (1962), 33, No. 1, 5-6.
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There is more evidence to prove that saltiness [of the sea] is due to the admixture of some substance ... It is this stuff which makes salt water heavy (it weighs more than fresh water) and thick. The difference in consistency is such that ships with the same cargo very nearly sink in a river when they are quite fit to navigate in the sea. This circumstance has before now caused loss to shippers freighting their ships in a river. That the thicker consistency is due to an admixture of something is proved by the fact that if you make strong brine by the admixture of salt, eggs, even when they are full, float in it. It almost becomes like mud; such a quantity of earthy matter is there in the sea.
[Aristotle recognised the different density of fresh (river) or salty (sea) water. He describes an experiment using an egg (which sinks in fresh water) that floats in a strong brine solution.]
Aristotle
Meteorology (350 B.C.), Book II, translated by E. W. Webster. Internet Classics Archive, (classics.mit.edu).
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To every bushel of the powdered cement add one bushel of sand, mix them together and pass them through a sieve, then add a sufficient quantity of water to make it (by well mixing and working) about the consistency of a soft putty. It is then fit to use but should not be kept more than six or eight hours and should be thoroughly worked just before it is used.
Directions for Using White's Patent Hydraulic Cement.
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To the average mathematician who merely wants to know his work is securely based, the most appealing choice is to avoid difficulties by means of Hilbert's program. Here one regards mathematics as a formal game and one is only concerned with the question of consistency ... . The Realist position is probably the one which most mathematicians would prefer to take. It is not until he becomes aware of some of the difficulties in set theory that he would even begin to question it. If these difficulties particularly upset him, he will rush to the shelter of Formalism, while his normal position will be somewhere between the two, trying to enjoy the best of two worlds.
In Axiomatic Set Theory (1971), 9-15. In Thomas Tymoczko, New Directions in the Philosophy of Mathematics: an Anthology (), 11-12.
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To vary the compression of the muscle therefore, and so to swell and shrink it, there needs nothing but to change the consistency of the included ether… . Thus may therefore the soul, by determining this ethereal animal spirit or wind into this or that nerve, perhaps with as much ease as air is moved in open spaces, cause all the motions we see in animals.
From 'An Hypothesis explaining the Properties of Light, discoursed of in my several Papers', in Thomas Birch, The History of the Royal Society (1757), Vol. 3, 252. This was from Newton’s Second Paper on Color and Light, read at the Royal Society (9 Dec 1675).
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We have seen that the cytoplasm of nerve has a fluid consistency. Hence its molecules are free to move. According to the thermodynamic principle known as the Gibbs-Thompson rule, any substance in the interior of a liquid which will reduce the free energy of the surface of the liquid, will be concentrated in the surface. The composition of the surface is, therefore, determined by the composition of the fluid from which it is formed; and as the rule is one having universal application, it must hold also for the cytoplasm of nerve. We must think of the surface membrane, then, as a structure which is in equilibrium with the interior of the axon, or at least as one which deviates from equilibrium only because, for dynamic reasons, equilibrium cannot be attained.
With Joseph Erlanger (1874-1965), American physiologist.
Joseph Erlanger and Herbert S. Gasser (eds.), Electrical Signs of Nervous Activity (1937), 136.
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We have the satisfaction to find, that in nature there is wisdom, system and consistency. For having, in the natural history of this earth, seen a succession of worlds, we may from this conclude that, there is a system in nature; in like manner as, from seeing revolutions of the planets, it is concluded, that there is a system by which they are intended to continue those revolutions. But if the succession of worlds is established in the system of nature, it is vain to look for anything higher in the origin of the earth. The result, therefore, of our present enquiry is, that we find no vestige of a beginning,-no prospect of an end.
'Theory of the Earth', Transactions of the Royal Society of Edinburgh, 1788, 1, 304.
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When ultra-violet light acts on a mixture of water, carbon dioxide, and ammonia, a vast variety of organic substances are made, including sugars and apparently some of the materials from which proteins are built up…. But before the origin of life they must have accumulated till the primitive oceans reached the consistency of hot dilute soup…. The first living or half-living things were probably large molecules synthesized under the influence of the sun’s radiation, and only capable of reproduction in the particularly favorable medium in which they originated….
In 'The Origin of Life', The Inequality of Man: And Other Essays (1932, 1937), 152.
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Carl Sagan Thumbnail In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
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- 90 -
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