Celebrating 19 Years on the Web
TODAY IN SCIENCE HISTORY ®
Find science on or your birthday

Today in Science History - Quickie Quiz
Who said: “As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.”
more quiz questions >>
Home > Category Index for Science Quotations > Category Index V > Category: Vagueness

Vagueness Quotes (11 quotes)

Bernard Bolzano dispelled the clouds that throughout all the foregone centuries had enveloped the notion of Infinitude in darkness, completely sheared the great term of its vagueness without shearing it of its strength, and thus rendered it forever available for the purposes of logical discourse.
In Lectures on Science, Philosophy and Art (1908), 42.
Science quotes on:  |  Available (25)  |  Century (131)  |  Cloud (69)  |  Completely (32)  |  Darkness (43)  |  Discourse (18)  |  Dispel (5)  |  Envelop (5)  |  Forego (4)  |  Forever (60)  |  Great (534)  |  Infinitude (3)  |  Logical (55)  |  Mathematicians and Anecdotes (141)  |  Notion (59)  |  Purpose (194)  |  Render (33)  |  Shear (2)  |  Strength (81)  |  Term (122)

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.”
Science quotes on:  |  Adapt (28)  |  Alone (106)  |  Aversion (8)  |  Avoid (55)  |  Clearness (11)  |  Close (67)  |  Conception (92)  |  Confine (26)  |  Consist (46)  |  Consistent (18)  |  Construct (41)  |  Contemplation (52)  |  Content (69)  |  Deduce (25)  |  Domain (42)  |  Effort (144)  |  Favorable (12)  |  Furnish (42)  |  General (160)  |  Inconsistent (9)  |  Induce (14)  |  Inspire (51)  |  Invincible (6)  |  Logic (260)  |  Mathematics (1205)  |  Mathematics And Logic (10)  |  Mind (760)  |  Model (81)  |  Nature (1223)  |  Negative (34)  |  Obscurity (27)  |  Perfect (89)  |  Perform (38)  |  Permit (31)  |  Positive (44)  |  Precision (52)  |  Prepare (35)  |  Reaction (62)  |  Reasoning (100)  |  Render (33)  |  Sufficient (42)  |  True (208)  |  Universal (105)

Evolution ... is really two theories, the vague theory and the precise theory. The vague theory has been abundantly proved.... The precise theory has never been proved at all. However, like relativity, it is accepted on faith.... On getting down to actual details, difficulties begin.
In Science is a Sacred Cow (1950), 101 & 103.
Science quotes on:  |  Abundance (21)  |  Accept (65)  |  Detail (87)  |  Difficulty (146)  |  Evolution (535)  |  Precision (52)  |  Proof (245)  |  Relativity (56)  |  Theory (696)

Geologists have usually had recourse for the explanation of these changes to the supposition of sundry violent and extraordinary catastrophes, cataclysms, or general revolutions having occurred in the physical state of the earth's surface.
As the idea imparted by the term Cataclysm, Catastrophe, or Revolution, is extremely vague, and may comprehend any thing you choose to imagine, it answers for the time very well as an explanation; that is, it stops further inquiry. But it also has had the disadvantage of effectually stopping the advance of science, by involving it in obscurity and confusion.
Considerations on Volcanoes (1825), iv.
Science quotes on:  |  Advancement (40)  |  Answer (249)  |  Catastrophe (21)  |  Change (364)  |  Comprehension (57)  |  Confusion (42)  |  Disadvantage (9)  |  Earth (638)  |  Explanation (177)  |  Geologist (47)  |  Imagination (275)  |  Impart (7)  |  Inquiry (45)  |  Obscurity (27)  |  Recourse (12)  |  Revolution (69)  |  Science (2067)  |  State (137)  |  Stop (76)  |  Sundry (4)  |  Supposition (37)  |  Surface (101)  |  Term (122)  |  Violence (23)

I believe that natural history has lost much by the vague general treatment that is so common.
From 'Note to the Reader', introducing Wild Animals I Have Known (1898), 9. The author explains this is his motivation for writing true stories about individual animals as real characters.
Science quotes on:  |  Belief (504)  |  Common (122)  |  Generality (34)  |  Loss (73)  |  Natural History (50)  |  Treatment (100)

I do not intend to go deeply into the question how far mathematical studies, as the representatives of conscious logical reasoning, should take a more important place in school education. But it is, in reality, one of the questions of the day. In proportion as the range of science extends, its system and organization must be improved, and it must inevitably come about that individual students will find themselves compelled to go through a stricter course of training than grammar is in a position to supply. What strikes me in my own experience with students who pass from our classical schools to scientific and medical studies, is first, a certain laxity in the application of strictly universal laws. The grammatical rules, in which they have been exercised, are for the most part followed by long lists of exceptions; accordingly they are not in the habit of relying implicitly on the certainty of a legitimate deduction from a strictly universal law. Secondly, I find them for the most part too much inclined to trust to authority, even in cases where they might form an independent judgment. In fact, in philological studies, inasmuch as it is seldom possible to take in the whole of the premises at a glance, and inasmuch as the decision of disputed questions often depends on an aesthetic feeling for beauty of expression, or for the genius of the language, attainable only by long training, it must often happen that the student is referred to authorities even by the best teachers. Both faults are traceable to certain indolence and vagueness of thought, the sad effects of which are not confined to subsequent scientific studies. But certainly the best remedy for both is to be found in mathematics, where there is absolute certainty in the reasoning, and no authority is recognized but that of one’s own intelligence.
In 'On the Relation of Natural Science to Science in general', Popular Lectures on Scientific Subjects, translated by E. Atkinson (1900), 25-26.
Science quotes on:  |  Absolute (98)  |  Accordingly (5)  |  Aesthetic (35)  |  Application (170)  |  Attainable (3)  |  Authority (66)  |  Beauty (248)  |  Best (173)  |  Both (81)  |  Case (99)  |  Certain (126)  |  Certainly (31)  |  Certainty (131)  |  Classical (16)  |  Compel (22)  |  Confine (26)  |  Conscious (45)  |  Course (84)  |  Decision (72)  |  Deduction (69)  |  Deeply (17)  |  Depend (90)  |  Dispute (22)  |  Education (347)  |  Effect (166)  |  Exception (40)  |  Exercise (69)  |  Experience (342)  |  Expression (110)  |  Extend (44)  |  Fact (733)  |  Far (154)  |  Fault (33)  |  Feel (167)  |  Find (408)  |  First (314)  |  Follow (124)  |  Form (314)  |  Genius (249)  |  Glance (20)  |  Grammar (14)  |  Grammatical (2)  |  Habit (112)  |  Happen (82)  |  Important (205)  |  Improve (56)  |  Inasmuch (5)  |  Inclined (12)  |  Independent (67)  |  Individual (221)  |  Indolence (7)  |  Inevitably (6)  |  Intelligence (168)  |  Intend (16)  |  Judgment (101)  |  Language (228)  |  Legitimate (14)  |  List (10)  |  Logical (55)  |  Long (174)  |  Mathematics (1205)  |  Medical (24)  |  Often (106)  |  Organization (84)  |  Part (222)  |  Pass (93)  |  Philological (3)  |  Place (175)  |  Position (76)  |  Possible (158)  |  Premise (27)  |  Proportion (72)  |  Question (404)  |  Range (57)  |  Reality (190)  |  Reason (471)  |  Recognize (69)  |  Refer (14)  |  Rely (11)  |  Remedy (54)  |  Representative (14)  |  Rule (177)  |  Sadness (34)  |  School (119)  |  Science (2067)  |  Scientific (236)  |  Seldom (30)  |  Strict (17)  |  Strictly (13)  |  Strike (40)  |  Student (203)  |  Study (476)  |  Subsequent (19)  |  Supply (47)  |  System (191)  |  Teacher (120)  |  Thought (546)  |  Traceable (2)  |  Training (66)  |  Trust (49)  |  Universal Law (3)  |  Value Of Mathematics (60)  |  Whole (192)

In studying the fate of our forest king, we have thus far considered the action of purely natural causes only; but, unfortunately, man is in the woods, and waste and pure destruction are making rapid headway. If the importance of the forests were even vaguely understood, even from an economic standpoint, their preservation would call forth the most watchful attention of government
John Muir
In The Mountains of California (1894), 198.
Science quotes on:  |  Action (185)  |  Attention (121)  |  Call (128)  |  Cause (285)  |  Consideration (85)  |  Destruction (85)  |  Economy (54)  |  Fate (46)  |  Forest (107)  |  Government (93)  |  Headway (2)  |  Importance (218)  |  King (35)  |  Man (373)  |  Natural (173)  |  Preservation (33)  |  Rapid (32)  |  Standpoint (10)  |  Understanding (325)  |  Unfortunately (18)  |  Waste (65)  |  Watch (65)  |  Wood (49)

In the expressions we adopt to prescribe physical phenomena we necessarily hover between two extremes. We either have to choose a word which implies more than we can prove, or we have to use vague and general terms which hide the essential point, instead of bringing it out. The history of electrical theories furnishes a good example.
Opening Address to the Annual Meeting of the British Association by Prof. Arthur Schuster, in Nature (4 Aug 1892), 46, 325.
Science quotes on:  |  Choice (79)  |  Electricity (136)  |  Essential (117)  |  Example (94)  |  Expression (110)  |  Extreme (56)  |  Furnish (42)  |  Generality (34)  |  Good (345)  |  Hiding (6)  |  History (369)  |  Hover (5)  |  Implication (22)  |  Nomenclature (138)  |  Phenomenon (278)  |  Point (123)  |  Proof (245)  |  Term (122)  |  Theory (696)  |  Word (302)

Sir Hiram Maxim is a genuine and typical example of the man of science, romantic, excitable, full of real but somewhat obvious poetry, a little hazy in logic and philosophy, but full of hearty enthusiasm and an honorable simplicity. He is, as he expresses it, “an old and trained engineer,” and is like all of the old and trained engineers I have happened to come across, a man who indemnifies himself for the superhuman or inhuman concentration required for physical science by a vague and dangerous romanticism about everything else.
In G.K. Chesterton, 'The Maxims of Maxim', Daily News (25 Feb 1905). Collected in G. K. Chesterton and Dale Ahlquist (ed.), In Defense of Sanity: The Best Essays of G.K. Chesterton (2011), 87.
Science quotes on:  |  Biography (232)  |  Concentration (19)  |  Danger (78)  |  Else (4)  |  Engineer (97)  |  Enthusiasm (43)  |  Everything (181)  |  Example (94)  |  Excitement (40)  |  Expression (110)  |  Full (63)  |  Genuine (26)  |  Hearty (3)  |  Honour (25)  |  Indemnification (2)  |  Inhuman (3)  |  Logic (260)  |  Sir Hiram Maxim (4)  |  Men Of Science (130)  |  Obvious (83)  |  Old (147)  |  Philosophy (259)  |  Physical Science (66)  |  Poetry (124)  |  Real (149)  |  Requirement (47)  |  Romance (9)  |  Romanticism (5)  |  Simplicity (147)  |  Superhuman (4)  |  Training (66)  |  Typical (13)

We are … led to a somewhat vague distinction between what we may call “hard” data and “soft” data. This distinction is a matter of degree, and must not be pressed; but if not taken too seriously it may help to make the situation clear. I mean by “hard” data those which resist the solvent influence of critical reflection, and by “soft” data those which, under the operation of this process, become to our minds more or less doubtful.
Our Knowledge of the External World (1925), 75.
Science quotes on:  |  Clear (98)  |  Critical (41)  |  Data (120)  |  Distinction (46)  |  Doubt (160)  |  Hard (99)  |  Influence (140)  |  Mind (760)  |  Operation (121)  |  Process (267)  |  Reflection (60)  |  Resistance (26)  |  Seriousness (9)  |  Situation (52)  |  Soft (15)  |  Solvent (5)

You must not know too much, or be too precise or scientific about birds and trees and flowers and water-craft; a certain free margin, and even vagueless—perhaps ignorance, credulity—helps your enjoyment of these things.
Specimen Days in America (1887), 282.
Science quotes on:  |  Bird (120)  |  Credulity (11)  |  Enjoyment (29)  |  Flower (77)  |  Ignorance (213)  |  Knowledge (1306)  |  Margin (6)  |  Precision (52)  |  Scientific (236)  |  Tree (171)


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



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