Celebrating 20 Years on the Web
TODAY IN SCIENCE HISTORY ®
Find science on or your birthday

Today in Science History - Quickie Quiz
Who said: “The path towards sustainable energy sources will be long and sometimes difficult. But America cannot resist this transition, we must lead it... That is how we will preserve our planet, commanded to our care by God. That’s what will lend meaning to the creed our fathers once declared.”
more quiz questions >>
Home > Category Index for Science Quotations > Category Index M > Category: Meanings

Meanings Quotes (5 quotes)

It is admitted by all that a finished or even a competent reasoner is not the work of nature alone; the experience of every day makes it evident that education develops faculties which would otherwise never have manifested their existence. It is, therefore, as necessary to learn to reason before we can expect to be able to reason, as it is to learn to swim or fence, in order to attain either of those arts. Now, something must be reasoned upon, it matters not much what it is, provided it can be reasoned upon with certainty. The properties of mind or matter, or the study of languages, mathematics, or natural history, may be chosen for this purpose. Now of all these, it is desirable to choose the one which admits of the reasoning being verified, that is, in which we can find out by other means, such as measurement and ocular demonstration of all sorts, whether the results are true or not. When the guiding property of the loadstone was first ascertained, and it was necessary to learn how to use this new discovery, and to find out how far it might be relied on, it would have been thought advisable to make many passages between ports that were well known before attempting a voyage of discovery. So it is with our reasoning faculties: it is desirable that their powers should be exerted upon objects of such a nature, that we can tell by other means whether the results which we obtain are true or false, and this before it is safe to trust entirely to reason. Now the mathematics are peculiarly well adapted for this purpose, on the following grounds:
1. Every term is distinctly explained, and has but one meaning, and it is rarely that two words are employed to mean the same thing.
2. The first principles are self-evident, and, though derived from observation, do not require more of it than has been made by children in general.
3. The demonstration is strictly logical, taking nothing for granted except self-evident first principles, resting nothing upon probability, and entirely independent of authority and opinion.
4. When the conclusion is obtained by reasoning, its truth or falsehood can be ascertained, in geometry by actual measurement, in algebra by common arithmetical calculation. This gives confidence, and is absolutely necessary, if, as was said before, reason is not to be the instructor, but the pupil.
5. There are no words whose meanings are so much alike that the ideas which they stand for may be confounded. Between the meaning of terms there is no distinction, except a total distinction, and all adjectives and adverbs expressing difference of degrees are avoided.
In On the Study and Difficulties of Mathematics (1898), chap. 1.
Science quotes on:  |  Absolutely (39)  |  Actual (117)  |  Adapt (66)  |  Adjective (2)  |  Admit (45)  |  Adverb (2)  |  Algebra (113)  |  Alike (60)  |  All (4108)  |  Alone (311)  |  Arithmetical (11)  |  Art (657)  |  Ascertain (38)  |  Attain (125)  |  Attempt (251)  |  Authority (95)  |  Avoid (116)  |  Being (1278)  |  Calculation (127)  |  Certainty (174)  |  Child (307)  |  Children (200)  |  Choose (112)  |  Chosen (48)  |  Common (436)  |  Competent (20)  |  Conclusion (254)  |  Confidence (69)  |  Confound (21)  |  Degree (276)  |  Demonstration (113)  |  Derive (65)  |  Desirable (33)  |  Develop (268)  |  Difference (337)  |  Discovery (780)  |  Distinction (72)  |  Distinctly (5)  |  Do (1908)  |  Education (378)  |  Employ (113)  |  Entirely (34)  |  Evident (91)  |  Exert (39)  |  Existence (456)  |  Expect (200)  |  Experience (467)  |  Explain (322)  |  Express (186)  |  Faculty (72)  |  False (100)  |  Falsehood (28)  |  Far (154)  |  Fence (11)  |  Find (998)  |  Find Out (21)  |  Finish (59)  |  First (1283)  |  Follow (378)  |  General (511)  |  Geometry (255)  |  Give (202)  |  Grant (73)  |  Ground (217)  |  Guide (97)  |  History (673)  |  Idea (843)  |  Independent (67)  |  Instructor (5)  |  Know (1518)  |  Known (454)  |  Language (293)  |  Learn (629)  |  Lodestone (7)  |  Logical (55)  |  Manifest (21)  |  Mathematics (1328)  |  Matter (798)  |  Mean (809)  |  Meaning (233)  |  Means (579)  |  Measurement (174)  |  Mind (1338)  |  More (2559)  |  Must (1526)  |  Natural (796)  |  Natural History (70)  |  Nature (1926)  |  Necessary (363)  |  Never (1087)  |  New (1216)  |  Nothing (966)  |  Object (422)  |  Observation (555)  |  Obtain (163)  |  Ocular (3)  |  Opinion (281)  |  Order (632)  |  Other (2236)  |  Passage (50)  |  Peculiarly (4)  |  Port (2)  |  Power (746)  |  Principle (507)  |  Probability (130)  |  Property (168)  |  Provide (69)  |  Pupil (61)  |  Purpose (317)  |  Rarely (21)  |  Reason (744)  |  Reasoning (207)  |  Rely (11)  |  Require (219)  |  Rest (280)  |  Result (677)  |  Safe (54)  |  Same (157)  |  Say (984)  |  Self (267)  |  Self-Evident (21)  |  Something (719)  |  Sort (49)  |  Stand (274)  |  Strictly (13)  |  Study (653)  |  Swim (30)  |  Tell (340)  |  Term (349)  |  Terms (184)  |  Thing (1915)  |  Thought (953)  |  Total (94)  |  True (212)  |  Trust (66)  |  Truth (1057)  |  Two (937)  |  Use (766)  |  Value Of Mathematics (60)  |  Verify (23)  |  Voyage (11)  |  Word (619)  |  Work (1351)

The anxious precision of modern mathematics is necessary for accuracy, … it is necessary for research. It makes for clearness of thought and for fertility in trying new combinations of ideas. When the initial statements are vague and slipshod, at every subsequent stage of thought, common sense has to step in to limit applications and to explain meanings. Now in creative thought common sense is a bad master. Its sole criterion for judgment is that the new ideas shall look like the old ones, in other words it can only act by suppressing originality.
In Introduction to Mathematics (1911), 157.
Science quotes on:  |  Accuracy (78)  |  Act (272)  |  Anxious (3)  |  Application (242)  |  Bad (180)  |  Clearness (11)  |  Combination (144)  |  Common (436)  |  Common Sense (130)  |  Creative (137)  |  Criterion (27)  |  Explain (322)  |  Fertility (19)  |  Idea (843)  |  In Other Words (9)  |  Initial (17)  |  Judgment (132)  |  Limit (280)  |  Look (582)  |  Master (178)  |  Mathematics (1328)  |  Meaning (233)  |  Modern (385)  |  Modern Mathematics (50)  |  Necessary (363)  |  New (1216)  |  New Ideas (16)  |  Old (481)  |  Originality (19)  |  Other (2236)  |  Precision (68)  |  Research (664)  |  Sense (770)  |  Sole (49)  |  Stage (143)  |  Statement (142)  |  Step (231)  |  Study And Research In Mathematics (61)  |  Subsequent (33)  |  Suppress (6)  |  Thought (953)  |  Try (283)  |  Trying (144)  |  Vague (47)  |  Word (619)

The belief that mathematics, because it is abstract, because it is static and cold and gray, is detached from life, is a mistaken belief. Mathematics, even in its purest and most abstract estate, is not detached from life. It is just the ideal handling of the problems of life, as sculpture may idealize a human figure or as poetry or painting may idealize a figure or a scene. Mathematics is precisely the ideal handling of the problems of life, and the central ideas of the science, the great concepts about which its stately doctrines have been built up, are precisely the chief ideas with which life must always deal and which, as it tumbles and rolls about them through time and space, give it its interests and problems, and its order and rationality. That such is the case a few indications will suffice to show. The mathematical concepts of constant and variable are represented familiarly in life by the notions of fixedness and change. The concept of equation or that of an equational system, imposing restriction upon variability, is matched in life by the concept of natural and spiritual law, giving order to what were else chaotic change and providing partial freedom in lieu of none at all. What is known in mathematics under the name of limit is everywhere present in life in the guise of some ideal, some excellence high-dwelling among the rocks, an “ever flying perfect” as Emerson calls it, unto which we may approximate nearer and nearer, but which we can never quite attain, save in aspiration. The supreme concept of functionality finds its correlate in life in the all-pervasive sense of interdependence and mutual determination among the elements of the world. What is known in mathematics as transformation—that is, lawful transfer of attention, serving to match in orderly fashion the things of one system with those of another—is conceived in life as a process of transmutation by which, in the flux of the world, the content of the present has come out of the past and in its turn, in ceasing to be, gives birth to its successor, as the boy is father to the man and as things, in general, become what they are not. The mathematical concept of invariance and that of infinitude, especially the imposing doctrines that explain their meanings and bear their names—What are they but mathematicizations of that which has ever been the chief of life’s hopes and dreams, of that which has ever been the object of its deepest passion and of its dominant enterprise, I mean the finding of the worth that abides, the finding of permanence in the midst of change, and the discovery of a presence, in what has seemed to be a finite world, of being that is infinite? It is needless further to multiply examples of a correlation that is so abounding and complete as indeed to suggest a doubt whether it be juster to view mathematics as the abstract idealization of life than to regard life as the concrete realization of mathematics.
In 'The Humanization of Teaching of Mathematics', Science, New Series, 35, 645-46.
Science quotes on:  |   (2863)  |  Abide (12)  |  Abound (17)  |  Abstract (124)  |  All (4108)  |  Approximate (25)  |  Aspiration (32)  |  Attain (125)  |  Attention (190)  |  Bear (159)  |  Become (815)  |  Being (1278)  |  Belief (578)  |  Birth (147)  |  Boy (94)  |  Build (204)  |  Call (769)  |  Case (99)  |  Cease (79)  |  Central (80)  |  Change (593)  |  Chaotic (2)  |  Chief (97)  |  Cold (112)  |  Complete (204)  |  Conceive (98)  |  Concept (221)  |  Concrete (51)  |  Constant (144)  |  Content (69)  |  Correlate (6)  |  Correlation (18)  |  Deal (188)  |  Deep (233)  |  Detach (5)  |  Determination (78)  |  Discovery (780)  |  Doctrine (75)  |  Dominant (26)  |  Doubt (304)  |  Dream (208)  |  Element (310)  |  Ralph Waldo Emerson (150)  |  Enterprise (54)  |  Equation (132)  |  Especially (31)  |  Estate (5)  |  Everywhere (94)  |  Example (94)  |  Excellence (39)  |  Explain (322)  |  Far (154)  |  Fashion (30)  |  Father (110)  |  Figure (160)  |  Find (998)  |  Finite (59)  |  Fixed (17)  |  Flux (21)  |  Fly (146)  |  Flying (72)  |  Freedom (129)  |  Functionality (2)  |  General (511)  |  Give (202)  |  Gray (8)  |  Great (1574)  |  Guise (5)  |  Handle (28)  |  High (362)  |  Hope (299)  |  Human (1468)  |  Idea (843)  |  Ideal (99)  |  Idealization (3)  |  Impose (22)  |  Indeed (324)  |  Indication (33)  |  Infinite (231)  |  Infinitude (3)  |  Interdependence (4)  |  Interest (386)  |  Invariance (4)  |  Know (1518)  |  Known (454)  |  Law (894)  |  Lawful (7)  |  Life (1795)  |  Limit (280)  |  Man (2251)  |  Match (29)  |  Mathematics (1328)  |  Mean (809)  |  Meaning (233)  |  Midst (7)  |  Mistake (169)  |  Most (1731)  |  Multiply (37)  |  Must (1526)  |  Mutual (52)  |  Name (333)  |  Natural (796)  |  Nature Of Mathematics (80)  |  Nearer (45)  |  Needless (4)  |  Never (1087)  |  Notion (113)  |  Object (422)  |  Order (632)  |  Orderly (38)  |  Painting (44)  |  Partial (10)  |  Passion (114)  |  Past (337)  |  Perfect (216)  |  Permanence (24)  |  Pervasive (5)  |  Poetry (143)  |  Precisely (92)  |  Presence (63)  |  Present (619)  |  Problem (676)  |  Process (423)  |  Provide (69)  |  Pure (291)  |  Rationality (24)  |  Realization (43)  |  Regard (305)  |  Represent (155)  |  Restriction (11)  |  Rock (161)  |  Roll (40)  |  Save (118)  |  Scene (36)  |  Science (3879)  |  Sculpture (12)  |  Seem (145)  |  Sense (770)  |  Serve (59)  |  Serving (15)  |  Show (346)  |  Space (500)  |  Spiritual (91)  |  Stately (12)  |  Static (8)  |  Successor (14)  |  Suffice (7)  |  Suggest (34)  |  Supreme (71)  |  System (537)  |  Thing (1915)  |  Through (849)  |  Time (1877)  |  Time And Space (39)  |  Transfer (20)  |  Transformation (69)  |  Transmutation (22)  |  Tumble (2)  |  Turn (447)  |  Unto (8)  |  Variability (5)  |  Variable (34)  |  View (488)  |  Will (2355)  |  World (1774)  |  Worth (169)

We should therefore, with grace and optimism, embrace NOMA’s tough-minded demand: Acknowledge the personal character of these human struggles about morals and meanings, and stop looking for definite answers in nature’s construction. But many people cannot bear to surrender nature as a ‘transitional object’–a baby’s warm blanket for our adult comfort. But when we do (for we must) , nature can finally emerge in her true form: not as a distorted mirror of our needs, but as our most fascinating comp anion. Only then can we unite the patches built by our separate magisteria into a beautiful and coherent quilt called wisdom.
…...
Science quotes on:  |   (2863)  |  Acknowledge (33)  |  Adult (19)  |  Anion (4)  |  Answer (366)  |  Baby (28)  |  Bear (159)  |  Beautiful (258)  |  Blanket (10)  |  Build (204)  |  Call (769)  |  Character (243)  |  Coherent (13)  |  Comfort (59)  |  Construction (112)  |  Definite (110)  |  Demand (123)  |  Distort (22)  |  Do (1908)  |  Embrace (46)  |  Emerge (22)  |  Fascinating (37)  |  Finally (26)  |  Form (959)  |  Grace (31)  |  Human (1468)  |  Looking (189)  |  Meaning (233)  |  Mind (1338)  |  Mirror (41)  |  Moral (195)  |  Most (1731)  |  Must (1526)  |  Nature (1926)  |  Need (290)  |  Object (422)  |  Optimism (14)  |  Patch (8)  |  People (1005)  |  Personal (67)  |  Separate (143)  |  Stop (80)  |  Struggle (105)  |  Surrender (20)  |  Tough (19)  |  Transitional (2)  |  True (212)  |  Unite (42)  |  Warm (69)  |  Wisdom (221)

Words change their meanings, just as organism s evolve. We would impose an enormous burden on our economy if we insisted on payment in cattle every time we identified a bonus as a pecuniary advantage (from the Latin pecus, or cattle, a verbal fossil from a former commercial reality).
…...
Science quotes on:  |   (2863)  |  Advantage (134)  |  Bonus (2)  |  Burden (27)  |  Cattle (18)  |  Change (593)  |  Commercial (26)  |  Economy (55)  |  Enormous (41)  |  Evolution (590)  |  Former (137)  |  Fossil (136)  |  Identify (13)  |  Impose (22)  |  Insist (20)  |  Latin (38)  |  Meaning (233)  |  Organism (220)  |  Payment (6)  |  Pecuniary (2)  |  Reality (261)  |  Time (1877)  |  Verbal (10)  |  Word (619)


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
Quotations by:Albert EinsteinIsaac NewtonLord KelvinCharles DarwinSrinivasa RamanujanCarl SaganFlorence NightingaleThomas EdisonAristotleMarie CurieBenjamin FranklinWinston ChurchillGalileo GalileiSigmund FreudRobert BunsenLouis PasteurTheodore RooseveltAbraham LincolnRonald ReaganLeonardo DaVinciMichio KakuKarl PopperJohann GoetheRobert OppenheimerCharles Kettering  ... (more people)

Quotations about:Atomic  BombBiologyChemistryDeforestationEngineeringAnatomyAstronomyBacteriaBiochemistryBotanyConservationDinosaurEnvironmentFractalGeneticsGeologyHistory of ScienceInventionJupiterKnowledgeLoveMathematicsMeasurementMedicineNatural ResourceOrganic ChemistryPhysicsPhysicianQuantum TheoryResearchScience and ArtTeacherTechnologyUniverseVolcanoVirusWind PowerWomen ScientistsX-RaysYouthZoology  ... (more topics)
Sitewide search within all Today In Science History pages:
Visit our Science and Scientist Quotations index for more Science Quotes from archaeologists, biologists, chemists, geologists, inventors and inventions, mathematicians, physicists, pioneers in medicine, science events and technology.

Names index: | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z |

Categories index: | 1 | 2 | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z |
- 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


by Ian Ellis
who invites your feedback
Thank you for sharing.
Today in Science History
Sign up for Newsletter
with quiz, quotes and more.