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: Vague

Vague Quotes (47 quotes)

Il est impossible de contempler le spectacle de l’univers étoilé sans se demander comment il s’est formé: nous devions peut-être attendre pour chercher une solution que nous ayons patiemment rassemblé les éléments …mais si nous étions si raisonnables, si nous étions curieux sans impatience, il est probable que nous n’avions jamais créé la Science et que nous nous serions toujours contentés de vivre notre petite vie. Notre esprit a donc reclamé impérieusement cette solution bien avant qu’elle fut mûre, et alors qu’il ne possédait que de vagues lueurs, lui permettant de la deviner plutôt que de l’attendre.
It is impossible to contemplate the spectacle of the starry universe without wondering how it was formed: perhaps we ought to wait, and not look for a solution until have patiently assembled the elements … but if we were so reasonable, if we were curious without impatience, it is probable we would never have created Science and we would always have been content with a trivial existence. Thus the mind has imperiously laid claim to this solution long before it was ripe, even while perceived in only faint glimmers—allowing us to guess a solution rather than wait for it.
From Leçons sur les Hypothèses Consmogoniques (1913) as cited in D. Ter Haar and A.G.W. Cameron, 'Historical Review of Theories of the Origin of the Solar System', collected in Robert Jastrow and A. G. W. Cameron (eds.), Origin of the Solar System: Proceedings of a Conference Held at the Goddard Institute for Space Studies, New York, January 23-24, 1962, (1963), 3. 'Cosmogonical Hypotheses' (1913), collected in Harlow Shapley, Source Book in Astronomy, 1900-1950 (1960), 347.
Science quotes on:  |   (2863)  |  Assemble (13)  |  Claim (146)  |  Contemplation (73)  |  Content (69)  |  Created (6)  |  Curious (91)  |  Element (310)  |  Existence (456)  |  Faint (9)  |  Form (959)  |  Formation (96)  |  Glimmer (5)  |  Guess (61)  |  Impatience (13)  |  Impossibility (61)  |  Impossible (251)  |  Long (790)  |  Look (582)  |  Mind (1338)  |  Never (1087)  |  Origin Of The Universe (16)  |  Patience (56)  |  Perceived (4)  |  Reasonable (27)  |  Ripe (5)  |  Science (3879)  |  Solution (267)  |  Spectacle (33)  |  Star (427)  |  Trivial (57)  |  Universe (857)  |  Wait (58)  |  Wonder (236)

A little science is something that they must have. I should like my nephews to know what air is, and water; why we breathe, and why wood burns; the nutritive elements essential to plant life, and the constituents of the soil. And it is no vague and imperfect knowledge from hearsay I would have them gain of these fundamental truths, on which depend agriculture and the industrial arts and our health itself; I would have them know these things thoroughly from their own observation and experience. Books here are insufficient, and can serve merely as aids to scientific experiment.
Science quotes on:  |  Agriculture (68)  |  Aid (97)  |  Air (347)  |  Art (657)  |  Book (392)  |  Breathe (45)  |  Burn (87)  |  Constituent (45)  |  Depend (228)  |  Element (310)  |  Essential (199)  |  Experience (467)  |  Experiment (695)  |  Fundamental (250)  |  Gain (145)  |  Health (193)  |  Hearsay (5)  |  Imperfect (45)  |  Industrial (13)  |  Insufficient (9)  |  Know (1518)  |  Knowledge (1529)  |  Life (1795)  |  Little (707)  |  Merely (316)  |  Must (1526)  |  Nephew (2)  |  Observation (555)  |  Plant (294)  |  Science (3879)  |  Scientific (941)  |  Serve (59)  |  Soil (86)  |  Something (719)  |  Thing (1915)  |  Thoroughly (67)  |  Truth (1057)  |  Water (481)  |  Why (491)  |  Wood (92)

A number of years ago, when I was a freshly-appointed instructor, I met, for the first time, a certain eminent historian of science. At the time I could only regard him with tolerant condescension.
I was sorry of the man who, it seemed to me, was forced to hover about the edges of science. He was compelled to shiver endlessly in the outskirts, getting only feeble warmth from the distant sun of science- in-progress; while I, just beginning my research, was bathed in the heady liquid heat up at the very center of the glow.
In a lifetime of being wrong at many a point, I was never more wrong. It was I, not he, who was wandering in the periphery. It was he, not I, who lived in the blaze.
I had fallen victim to the fallacy of the “growing edge;” the belief that only the very frontier of scientific advance counted; that everything that had been left behind by that advance was faded and dead.
But is that true? Because a tree in spring buds and comes greenly into leaf, are those leaves therefore the tree? If the newborn twigs and their leaves were all that existed, they would form a vague halo of green suspended in mid-air, but surely that is not the tree. The leaves, by themselves, are no more than trivial fluttering decoration. It is the trunk and limbs that give the tree its grandeur and the leaves themselves their meaning.
There is not a discovery in science, however revolutionary, however sparkling with insight, that does not arise out of what went before. “If I have seen further than other men,” said Isaac Newton, “it is because I have stood on the shoulders of giants.”
Adding A Dimension: Seventeen Essays on the History of Science (1964), Introduction.
Science quotes on:  |  Advance (280)  |  Air (347)  |  All (4108)  |  Arise (158)  |  Beginning (305)  |  Behind (137)  |  Being (1278)  |  Belief (578)  |  Certain (550)  |  Condescension (3)  |  Count (105)  |  Discovery (780)  |  Edge (47)  |  Everything (476)  |  Exist (443)  |  Fad (10)  |  Fallacy (30)  |  First (1283)  |  Form (959)  |  Frontier (38)  |  Giant (67)  |  Grandeur (31)  |  Green (63)  |  Growing (98)  |  Halo (7)  |  Heat (174)  |  Historian (54)  |  History Of Science (63)  |  Hover (8)  |  Insight (102)  |  Leaf (66)  |  Liquid (50)  |  Man (2251)  |  Meaning (233)  |  Mid-Air (3)  |  More (2559)  |  Never (1087)  |  Newborn (5)  |  Sir Isaac Newton (333)  |  Number (699)  |  Other (2236)  |  Point (580)  |  Progress (465)  |  Regard (305)  |  Research (664)  |  Revolutionary (31)  |  Science (3879)  |  Scientific (941)  |  Shoulder (33)  |  Sorry (30)  |  Sparkling (7)  |  Spring (133)  |  Sun (385)  |  Surely (101)  |  Themselves (433)  |  Time (1877)  |  Tree (246)  |  Trivial (57)  |  Trunk (21)  |  Twig (14)  |  Victim (35)  |  Warmth (21)  |  Wrong (234)  |  Year (933)

Another advantage of a mathematical statement is that it is so definite that it might be definitely wrong; and if it is found to be wrong, there is a plenteous choice of amendments ready in the mathematicians’ stock of formulae. Some verbal statements have not this merit; they are so vague that they could hardly be wrong, and are correspondingly useless.
From 'Mathematics of War and Foreign Politics', in James R. Newman, The World of Mathematics (1956), Vol. 2, 1248.
Science quotes on:  |  Advantage (134)  |  Amendment (2)  |  Choice (110)  |  Corresponding (3)  |  Definite (110)  |  Find (998)  |  Formula (98)  |  Hardly (19)  |  Mathematician (387)  |  Mathematics (1328)  |  Merit (50)  |  Ready (39)  |  Statement (142)  |  Stock (7)  |  Useless (33)  |  Verbal (10)  |  Wrong (234)

As for a future life, every man must judge for himself between conflicting vague probabilities.
In The Life and Letters of Charles Darwin edited by Sir Francis Darwin (1887).
Science quotes on:  |  Conflicting (13)  |  Future (429)  |  Himself (461)  |  Judge (108)  |  Life (1795)  |  Man (2251)  |  Must (1526)

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.
Science quotes on:  |  Adapt (66)  |  All (4108)  |  Both (493)  |  Change (593)  |  Chemist (156)  |  Chemistry (353)  |  Conduct (69)  |  Consequence (203)  |  Definition (221)  |  Distinguish (160)  |  Element (310)  |  Enter (141)  |  Explain (322)  |  Explanation (234)  |  Fact (1210)  |  Fire (189)  |  Form (959)  |  Free (232)  |  Hypothesis (296)  |  Instant (45)  |  More (2559)  |  Observation (555)  |  Phlogiston (9)  |  Principle (507)  |  Reasoning (207)  |  Rigorous (48)  |  Systematic (57)  |  Through (849)  |  Time (1877)  |  Transparency (7)  |  Vessel (63)  |  Wish (212)

Do you remember what Darwin says about music? He claims that the power of producing and appreciating it existed among the human race long before the power of speech was arrived at. Perhaps that is why we are so subtly influenced by it. There are vague memories in our souls of those misty centuries when the world was in its childhood.
Spoken by character, Sherlock Holmes, in A Study in Scarlet (1887), Chap. 5. Collected in Works of Arthur Conan Doyle (1902), Vol. 11, 68-69.
Science quotes on:  |  Appreciate (63)  |  Century (310)  |  Childhood (38)  |  Claim (146)  |  Charles Darwin (303)  |  Do (1908)  |  Exist (443)  |  Human (1468)  |  Human Race (100)  |  Influence (222)  |  Long (790)  |  Memory (134)  |  Misty (6)  |  Music (129)  |  Power (746)  |  Produce (104)  |  Race (268)  |  Remember (179)  |  Say (984)  |  Soul (226)  |  Speech (61)  |  Subtle (35)  |  Why (491)  |  World (1774)

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 (25)  |  Accept (191)  |  Actual (117)  |  All (4108)  |  Begin (260)  |  Detail (146)  |  Difficulty (196)  |  Down (456)  |  Evolution (590)  |  Faith (203)  |  Never (1087)  |  Precise (68)  |  Precision (68)  |  Proof (287)  |  Relativity (88)  |  Theory (970)  |  Two (937)  |  Vagueness (15)

Far better an approximate answer to the right question, which is often vague, than an exact answer to the wrong question, which can always be made precise.
In 'The Future of Data Analysis', Annals of Mathematical Statistics (1962), 33, No. 1, 13-14.
Science quotes on:  |  Answer (366)  |  Approximate (25)  |  Better (486)  |  Exact (68)  |  Precise (68)  |  Question (621)  |  Right (452)  |  Wrong (234)

Finally, I aim at giving denominations to things, as agreeable to truth as possible. I am not ignorant that words, like money, possess an ideal value, and that great danger of confusion may be apprehended from a change of names; in the mean time it cannot be denied that chemistry, like the other sciences, was formerly filled with improper names. In different branches of knowledge, we see those matters long since reformed: why then should chemistry, which examines the real nature of things, still adopt vague names, which suggest false ideas, and favour strongly of ignorance and imposition? Besides, there is little doubt but that many corrections may be made without any inconvenience.
Physical and Chemical Essays (1784), Vol. I, xxxvii.
Science quotes on:  |  Agreeable (18)  |  Aim (165)  |  Change (593)  |  Chemistry (353)  |  Confusion (57)  |  Correction (40)  |  Danger (115)  |  Denomination (6)  |  Different (577)  |  Doubt (304)  |  Error (321)  |  Examine (78)  |  Great (1574)  |  Idea (843)  |  Ideal (99)  |  Ignorance (240)  |  Ignorant (90)  |  Knowledge (1529)  |  Little (707)  |  Long (790)  |  Matter (798)  |  Mean (809)  |  Money (170)  |  Name (333)  |  Nature (1926)  |  Nature Of Things (29)  |  Other (2236)  |  Possess (156)  |  Possible (552)  |  Reform (22)  |  Reformed (4)  |  Science (3879)  |  See (1081)  |  Still (613)  |  Thing (1915)  |  Time (1877)  |  Truth (1057)  |  Value (365)  |  Why (491)  |  Word (619)

Gel’fand amazed me by talking of mathematics as though it were poetry. He once said about a long paper bristling with formulas that it contained the vague beginnings of an idea which could only hint at and which he had never managed to bring out more clearly. I had always thought of mathematics as being much more straightforward: a formula is a formula, and an algebra is an algebra, but Gel’fand found hedgehogs lurking in the rows of his spectral sequences!
In '1991 Ruth Lyttle Satter Prize', Notices of the American Mathematical Society (Mar 1991), 38, No. 3, 186. This is from her acceptance of the 1991 Ruth Lyttle Satter Prize.
Science quotes on:  |  Algebra (113)  |  Amazed (4)  |  Beginning (305)  |  Beginnings (5)  |  Being (1278)  |  Bring Out (4)  |  Bristle (3)  |  Clearly (41)  |  Contain (68)  |  Find (998)  |  Formula (98)  |  Hedgehog (4)  |  Hint (21)  |  Idea (843)  |  Long (790)  |  Lurk (5)  |  Lurking (7)  |  Manage (23)  |  Mathematics (1328)  |  More (2559)  |  Never (1087)  |  Paper (182)  |  Poetry (143)  |  Row (9)  |  Sequence (68)  |  Straightforward (10)  |  Talk (100)  |  Talking (76)  |  Thought (953)

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:  |   (2863)  |  Advance (280)  |  Advancement (62)  |  Answer (366)  |  Cataclysm (2)  |  Catastrophe (31)  |  Change (593)  |  Choose (112)  |  Comprehension (66)  |  Confusion (57)  |  Disadvantage (10)  |  Earth (996)  |  Explanation (234)  |  Extraordinary (79)  |  General (511)  |  Geologist (75)  |  Idea (843)  |  Imagination (328)  |  Imagine (164)  |  Impart (23)  |  Inquiry (78)  |  Obscurity (27)  |  Physical (508)  |  Recourse (12)  |  Revolution (129)  |  Science (3879)  |  State (491)  |  Stop (80)  |  Sundry (4)  |  Supposition (50)  |  Surface (209)  |  Term (349)  |  Thing (1915)  |  Time (1877)  |  Usually (176)  |  Vagueness (15)  |  Violence (34)

Germs of a theory, though in their present condition they are vague and formless … may be said to resemble stones in the quarry, rough and unhewn, but which may some time become corner-stones, columns, and entablatures in the future edifice.
In Report on the Geology of the High Plateaus of Utah (1880), 114.
Science quotes on:  |  Become (815)  |  Column (15)  |  Condition (356)  |  Corner (57)  |  Cornerstone (6)  |  Edifice (26)  |  Formless (4)  |  Future (429)  |  Germ (53)  |  Hypothesis (296)  |  Present (619)  |  Quarry (13)  |  Resemble (63)  |  Rough (6)  |  Stone (162)  |  Theory (970)  |  Time (1877)

Governments and parliaments must find that astronomy is one of the sciences which cost most dear: the least instrument costs hundreds of thousands of dollars, the least observatory costs millions; each eclipse carries with it supplementary appropriations. And all that for stars which are so far away, which are complete strangers to our electoral contests, and in all probability will never take any part in them. It must be that our politicians have retained a remnant of idealism, a vague instinct for what is grand; truly, I think they have been calumniated; they should be encouraged and shown that this instinct does not deceive them, that they are not dupes of that idealism.
In Henri Poincaré and George Bruce Halsted (trans.), The Value of Science: Essential Writings of Henri Poincare (1907), 84.
Science quotes on:  |  All (4108)  |  Appropriation (5)  |  Astronomy (229)  |  Complete (204)  |  Cost (86)  |  Deceive (26)  |  Dollar (22)  |  Dupe (5)  |  Eclipse (23)  |  Election (7)  |  Encourage (40)  |  Far (154)  |  Find (998)  |  Government (110)  |  Grand (27)  |  Hundred (229)  |  Idealism (4)  |  Instinct (88)  |  Instrument (144)  |  Millions (17)  |  Most (1731)  |  Must (1526)  |  Never (1087)  |  Observatory (15)  |  Parliament (7)  |  Politician (38)  |  Probability (130)  |  Remnant (7)  |  Retain (56)  |  Science (3879)  |  Show (346)  |  Star (427)  |  Stars (304)  |  Stranger (15)  |  Supplementary (4)  |  Think (1086)  |  Thousand (331)  |  Truly (116)  |  Will (2355)

Humanism is only another name for spiritual laziness, or a vague half-creed adopted by men of science and logicians whose heads are too occupied with the world of mathematics and physics to worry about religious categories.
In The Outsider (1956), 279.
Science quotes on:  |  Adopt (19)  |  Creed (27)  |  Laziness (8)  |  Logician (17)  |  Mathematics (1328)  |  Men Of Science (143)  |  Name (333)  |  Occupied (45)  |  Physic (517)  |  Physics (533)  |  Religion (361)  |  Religious (126)  |  Science (3879)  |  Science And Religion (307)  |  Spiritual (91)  |  World (1774)  |  Worry (33)

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 (578)  |  Common (436)  |  General (511)  |  Generality (45)  |  History (673)  |  Loss (110)  |  Natural (796)  |  Natural History (70)  |  Treatment (130)  |  Vagueness (15)

I have always liked horticulturists, people who make their living from orchards and gardens, whose hands are familiar with the feel of the bark, whose eyes are trained to distinguish the different varieties, who have a form memory. Their brains are not forever dealing with vague abstractions; they are satisfied with the romance which the seasons bring with them, and have the patience and fortitude to gamble their lives and fortunes in an industry which requires infinite patience, which raise hopes each spring and too often dashes them to pieces in fall. They are always conscious of sun and wind and rain; must always be alert lest they lose the chance of ploughing at the right moment, pruning at the right time, circumventing the attacks of insects and fungus diseases by quick decision and prompt action. They are manufacturers of a high order, whose business requires not only intelligence of a practical character, but necessitates an instinct for industry which is different from that required by the city dweller always within sight of other people and the sound of their voices. The successful horticulturist spends much time alone among his trees, away from the constant chatter of human beings.
Science quotes on:  |  Abstraction (47)  |  Action (327)  |  Alert (13)  |  Alone (311)  |  Attack (84)  |  Bark (18)  |  Being (1278)  |  Brain (270)  |  Business (149)  |  Chance (239)  |  Character (243)  |  City (78)  |  Constant (144)  |  Decision (91)  |  Different (577)  |  Disease (328)  |  Distinguish (160)  |  Eye (419)  |  Fall (230)  |  Feel (367)  |  Forever (103)  |  Form (959)  |  Fortune (49)  |  Fungus (5)  |  Garden (60)  |  High (362)  |  Hope (299)  |  Horticulture (9)  |  Human (1468)  |  Human Being (175)  |  Human Beings (117)  |  Industry (137)  |  Infinite (231)  |  Insect (77)  |  Instinct (88)  |  Intelligence (211)  |  Live (628)  |  Living (491)  |  Lose (159)  |  Memory (134)  |  Moment (253)  |  Must (1526)  |  Order (632)  |  Other (2236)  |  Patience (56)  |  People (1005)  |  Practical (200)  |  Prompt (14)  |  Pruning (7)  |  Rain (62)  |  Require (219)  |  Required (108)  |  Right (452)  |  Romance (15)  |  Season (47)  |  Sight (132)  |  Sound (183)  |  Spend (95)  |  Spring (133)  |  Successful (123)  |  Sun (385)  |  Time (1877)  |  Train (114)  |  Tree (246)  |  Wind (128)

I never said a word against eminent men of science. What I complain of is a vague popular philosophy which supposes itself to be scientific when it is really nothing but a sort of new religion and an uncommonly nasty one. When people talked about the fall of man, they knew they were talking about a mystery, a thing they didn’t understand. Now they talk about the survival of the fittest: they think they do understand it, whereas they have not merely no notion, they have an elaborately false notion of what the words mean.
In The Club of Queer Trades (1903, 1905), 241.
Science quotes on:  |  Against (332)  |  Complaint (11)  |  Do (1908)  |  Elaborate (28)  |  Eminence (23)  |  Fall (230)  |  False (100)  |  Man (2251)  |  Mean (809)  |  Men Of Science (143)  |  Merely (316)  |  Mystery (177)  |  Nasty (7)  |  Never (1087)  |  New (1216)  |  Nothing (966)  |  Notion (113)  |  People (1005)  |  Philosophy (380)  |  Popular (29)  |  Religion (361)  |  Science (3879)  |  Scientific (941)  |  Suppose (156)  |  Supposition (50)  |  Survival (94)  |  Survival Of The Fittest (40)  |  Talk (100)  |  Talking (76)  |  Thing (1915)  |  Think (1086)  |  Thinking (414)  |  Uncommon (14)  |  Understand (606)  |  Understanding (513)  |  Word (619)

I would like to be rather more special, and I would like to be understood in an honest way rather than in a vague way.
In The Character of Physical Law (1965, 2001), 13.
Science quotes on:  |  Honest (50)  |  More (2559)  |  Special (184)  |  Understood (156)  |  Way (1217)

If an explanation is so vague in its inherent nature, or so unskillfully molded in its formulation, that specific deductions subject to empirical verification or refutation can not be based upon it, then it can never serve as a working hypothesis. A hypothesis with which one can not work is not a working hypothesis.
'Role of Analysis in Scientific Investigation', Bulletin of the Geological Society of America (1933), 44, 479.
Science quotes on:  |  Deduction (82)  |  Empirical (54)  |  Empiricism (21)  |  Explanation (234)  |  Formulation (36)  |  Hypothesis (296)  |  Inherent (42)  |  Mold (33)  |  Nature (1926)  |  Never (1087)  |  Specific (95)  |  Subject (521)  |  Verification (31)  |  Work (1351)

In every case the awakening touch has been the mathematical spirit, the attempt to count, to measure, or to calculate. What to the poet or the seer may appear to be the very death of all his poetry and all his visions—the cold touch of the calculating mind,—this has proved to be the spell by which knowledge has been born, by which new sciences have been created, and hundreds of definite problems put before the minds and into the hands of diligent students. It is the geometrical figure, the dry algebraical formula, which transforms the vague reasoning of the philosopher into a tangible and manageable conception; which represents, though it does not fully describe, which corresponds to, though it does not explain, the things and processes of nature: this clothes the fruitful, but otherwise indefinite, ideas in such a form that the strict logical methods of thought can be applied, that the human mind can in its inner chamber evolve a train of reasoning the result of which corresponds to the phenomena of the outer world.
In A History of European Thought in the Nineteenth Century (1896), Vol. 1, 314.
Science quotes on:  |  Algebra (113)  |  All (4108)  |  Appear (118)  |  Applied (177)  |  Apply (160)  |  Attempt (251)  |  Awaken (15)  |  Awakening (11)  |  Born (33)  |  Calculate (54)  |  Chamber (7)  |  Cold (112)  |  Conception (154)  |  Correspond (9)  |  Count (105)  |  Create (235)  |  Death (388)  |  Definite (110)  |  Describe (128)  |  Diligent (19)  |  Dry (57)  |  Estimates of Mathematics (30)  |  Evolution (590)  |  Explain (322)  |  Figure (160)  |  Form (959)  |  Formula (98)  |  Fruitful (58)  |  Geometry (255)  |  Human (1468)  |  Human Mind (128)  |  Hundred (229)  |  Idea (843)  |  Indefinite (20)  |  Inner (71)  |  Knowledge (1529)  |  Logical (55)  |  Mathematics (1328)  |  Measure (232)  |  Method (505)  |  Methods (204)  |  Mind (1338)  |  Nature (1926)  |  New (1216)  |  Otherwise (24)  |  Phenomenon (318)  |  Philosopher (258)  |  Poet (83)  |  Poetry (143)  |  Problem (676)  |  Process (423)  |  Prove (250)  |  Reasoning (207)  |  Represent (155)  |  Result (677)  |  Science (3879)  |  Seer (4)  |  Spell (9)  |  Spirit (265)  |  Strict (17)  |  Student (300)  |  Tangible (15)  |  Thing (1915)  |  Thought (953)  |  Touch (141)  |  Train (114)  |  Transform (73)  |  Vision (123)  |  World (1774)

In reality the origin of the notion of derivatives is in the vague feeling of the mobility of things, and of the greater or less speed with which phenomena take place; this is well expressed by the terms fluent and fluxion, which were used by Newton and which we may believe were borrowed from the ancient mathematician Heraclitus.
From address to the section of Algebra and Analysis, International Congress of Arts and Sciences, St. Louis (22 Sep 1904), 'On the Development of Mathematical Analysis and its Relation to Certain Other Sciences,' as translated by M.W. Haskell in Bulletin of the American Mathematical Society (May 1905), 11, 407.
Science quotes on:  |  Ancient (189)  |  Borrow (30)  |  Derivative (6)  |  Express (186)  |  Feeling (250)  |  Fluent (2)  |  Fluxion (7)  |  Greater (288)  |  Heraclitus (15)  |  Mathematician (387)  |  Mobility (11)  |  Sir Isaac Newton (333)  |  Nomenclature (146)  |  Notion (113)  |  Origin (239)  |  Phenomenon (318)  |  Reality (261)  |  Speed (65)  |  Term (349)  |  Terms (184)  |  Thing (1915)

In scientific study, or, as I prefer to phrase it, in creative scholarship, the truth is the single end sought; all yields to that. The truth is supreme, not only in the vague mystical sense in which that expression has come to be a platitude, but in a special, definite, concrete sense. Facts and the immediate and necessary inductions from facts displace all pre-conceptions, all deductions from general principles, all favourite theories. Previous mental constructions are bowled over as childish play-structures by facts as they come rolling into the mind. The dearest doctrines, the most fascinating hypotheses, the most cherished creations of the reason and of the imagination perish from a mind thoroughly inspired with the scientific spirit in the presence of incompatible facts. Previous intellectual affections are crushed without hesitation and without remorse. Facts are placed before reasonings and before ideals, even though the reasonings and the ideals be more beautiful, be seemingly more lofty, be seemingly better, be seemingly truer. The seemingly absurd and the seemingly impossible are sometimes true. The scientific disposition is to accept facts upon evidence, however absurd they may appear to our pre-conceptions.
The Ethical Functions of Scientific Study: An Address Delivered at the Annual Commencement of the University of Michigan, 28 June 1888, 7-8.
Science quotes on:  |  Absurd (59)  |  Accept (191)  |  Affection (43)  |  All (4108)  |  Beautiful (258)  |  Better (486)  |  Cherish (22)  |  Childish (20)  |  Conception (154)  |  Concrete (51)  |  Construction (112)  |  Creation (327)  |  Creative (137)  |  Crush (18)  |  Deduction (82)  |  Definite (110)  |  Displace (8)  |  Disposition (42)  |  End (590)  |  Evidence (248)  |  Expression (175)  |  Fact (1210)  |  Facts (553)  |  Fascinating (37)  |  General (511)  |  Hesitation (19)  |  Hypothesis (296)  |  Ideal (99)  |  Imagination (328)  |  Immediate (95)  |  Impossible (251)  |  Induction (77)  |  Intellectual (255)  |  Mental (177)  |  Mind (1338)  |  More (2559)  |  Most (1731)  |  Necessary (363)  |  Perish (50)  |  Phrase (61)  |  Presence (63)  |  Principle (507)  |  Reason (744)  |  Reasoning (207)  |  Remorse (9)  |  Scholarship (20)  |  Scientific (941)  |  Scientific Method (175)  |  Seemingly (28)  |  Sense (770)  |  Single (353)  |  Special (184)  |  Spirit (265)  |  Structure (344)  |  Study (653)  |  Supreme (71)  |  Theory (970)  |  Thoroughly (67)  |  Truth (1057)  |  Yield (81)

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 (110)  |  Choose (112)  |  Electrical (57)  |  Electricity (159)  |  Essential (199)  |  Example (94)  |  Expression (175)  |  Extreme (75)  |  Furnish (96)  |  General (511)  |  Generality (45)  |  Good (889)  |  Hide (69)  |  Hiding (12)  |  History (673)  |  Hover (8)  |  Implication (23)  |  More (2559)  |  Necessarily (135)  |  Nomenclature (146)  |  Phenomenon (318)  |  Physical (508)  |  Point (580)  |  Proof (287)  |  Prove (250)  |  Term (349)  |  Terms (184)  |  Theory (970)  |  Two (937)  |  Use (766)  |  Vagueness (15)  |  Word (619)

In the year 1902 (while I was attempting to explain to an elementary class in chemistry some of the ideas involved in the periodic law) becoming interested in the new theory of the electron, and combining this idea with those which are implied in the periodic classification, I formed an idea of the inner structure of the atom which, although it contained certain crudities, I have ever since regarded as representing essentially the arrangement of electrons in the atom ... In accordance with the idea of Mendeleef, that hydrogen is the first member of a full period, I erroneously assumed helium to have a shell of eight electrons. Regarding the disposition in the positive charge which balanced the electrons in the neutral atom, my ideas were very vague; I believed I inclined at that time toward the idea that the positive charge was also made up of discrete particles, the localization of which determined the localization of the electrons.
Valence and the Structure of Atoms and Molecules (1923), 29-30.
Science quotes on:  |  Arrangement (91)  |  Atom (355)  |  Atomic Structure (3)  |  Becoming (96)  |  Certain (550)  |  Charge (59)  |  Chemistry (353)  |  Class (164)  |  Classification (97)  |  Discrete (11)  |  Disposition (42)  |  Electron (93)  |  Elementary (96)  |  Explain (322)  |  First (1283)  |  Form (959)  |  Helium (11)  |  Hydrogen (75)  |  Idea (843)  |  Inclined (41)  |  Inner (71)  |  Interest (386)  |  Involved (90)  |  Law (894)  |  Localization (3)  |  Neutral (13)  |  New (1216)  |  Particle (194)  |  Period (198)  |  Periodic Law (6)  |  Positive (94)  |  Regard (305)  |  Shell (63)  |  Structure (344)  |  Theory (970)  |  Time (1877)  |  Year (933)

It would indeed be a great delusion, if we stated that those sports of Nature [we find] enclosed in rocks are there by chance or by some vague creative power. Ah, that would be superficial indeed! In reality, those shells, which once were alive in water and are now dead and decomposed, were made thus by time not Nature; and what we now find as very hard, figured stone, was once soft mud and which received the impression of the shape of a shell, as I have frequently demonstrated.
La vana speculazione disingannata del senso (1670), trans. Ezio Vaccari, 83-4.
Science quotes on:  |  Alive (90)  |  Chance (239)  |  Creation (327)  |  Creative (137)  |  Dead (59)  |  Decomposition (18)  |  Delusion (25)  |  Demonstration (113)  |  Figure (160)  |  Find (998)  |  Great (1574)  |  Hard (243)  |  Impression (114)  |  Indeed (324)  |  Life (1795)  |  Mud (26)  |  Nature (1926)  |  Power (746)  |  Reality (261)  |  Rock (161)  |  Shape (72)  |  Shell (63)  |  Soft (29)  |  Sport (22)  |  Stone (162)  |  Superficial (12)  |  Time (1877)  |  Water (481)

Mathematical proofs are essentially of three different types: pre-formal; formal; post-formal. Roughly the first and third prove something about that sometimes clear and empirical, sometimes vague and ‘quasi-empirical’ stuff, which is the real though rather evasive subject of mathematics.
In Mathematics, Science and Epistemology (1980), Vol. 2, 69.
Science quotes on:  |  Clear (100)  |  Different (577)  |  Empirical (54)  |  Essential (199)  |  First (1283)  |  Formal (33)  |  Mathematics (1328)  |  Proof (287)  |  Prove (250)  |  Real (149)  |  Something (719)  |  Subject (521)  |  Type (167)

May we not suspect that the vague but very real fears of children, which are quite independent of experience, are the inherited effects of real dangers and abject superstitions during ancient savage times?
Mind, 1877
Science quotes on:  |  Ancient (189)  |  Children (200)  |  Danger (115)  |  Effect (393)  |  Emotion (100)  |  Experience (467)  |  Fear (197)  |  Inherit (33)  |  Inherited (21)  |  Superstition (66)  |  Time (1877)

No problem can be solved until it is reduced to some simple form. The changing of a vague difficulty into a specific, concrete form is a very essential element in thinking.
Seen, for example, in The Grain and Feed Review (1931), 21, 34.
Science quotes on:  |  Changing (7)  |  Concrete (51)  |  Difficulty (196)  |  Element (310)  |  Essential (199)  |  Form (959)  |  Problem (676)  |  Reduction (51)  |  Simple (406)  |  Solution (267)  |  Specific (95)  |  Thinking (414)

Ohm (a distinguished mathematician, be it noted) brought into order a host of puzzling facts connecting electromotive force and electric current in conductors, which all previous electricians had only succeeded in loosely binding together qualitatively under some rather vague statements. Even as late as 20 years ago, “quantity” and “tension” were much used by men who did not fully appreciate Ohm's law. (Is it not rather remarkable that some of Germany's best men of genius should have been, perhaps, unfairly treated? Ohm; Mayer; Reis; even von Helmholtz has mentioned the difficulty he had in getting recognised. But perhaps it is the same all the world over.)
Science quotes on:  |   (2863)  |  All (4108)  |  Appreciate (63)  |  Best (459)  |  Conductor (16)  |  Current (118)  |  Difficulty (196)  |  Distinguish (160)  |  Distinguished (83)  |  Electric (76)  |  Electrician (6)  |  Electricity (159)  |  Fact (1210)  |  Facts (553)  |  Force (487)  |  Genius (284)  |  Germany (13)  |  Hermann von Helmholtz (28)  |  Late (118)  |  Law (894)  |  Mathematician (387)  |  Robert Mayer (9)  |  Men Of Science (143)  |  Mention (82)  |  Ohm (5)  |  Georg Simon Ohm (3)  |  Order (632)  |  Puzzle (44)  |  Puzzling (8)  |  Quantity (132)  |  Recognition (88)  |  Johann Philipp Reis (2)  |  Statement (142)  |  Succeed (109)  |  Tension (24)  |  Together (387)  |  Treatment (130)  |  Unfair (8)  |  World (1774)  |  Year (933)

Our popular lecturers on physics present us with chains of deductions so highly polished that it is a luxury to let them slip from end to end through our fingers. But they leave nothing behind but a vague memory of the sensation they afforded.
Said by the fictional character Lydia in Cashel Byron’s Profession (1886, 1906), 88.
Science quotes on:  |  Behind (137)  |  Chain (50)  |  Deduction (82)  |  End (590)  |  Finger (44)  |  Highly (16)  |  Leave (130)  |  Lecturer (12)  |  Luxury (21)  |  Memory (134)  |  Nothing (966)  |  Physic (517)  |  Physics (533)  |  Polish (15)  |  Popular (29)  |  Present (619)  |  Sensation (57)  |  Slip (5)  |  Through (849)

Quantity is that which is operated with according to fixed mutually consistent laws. Both operator and operand must derive their meaning from the laws of operation. In the case of ordinary algebra these are the three laws already indicated [the commutative, associative, and distributive laws], in the algebra of quaternions the same save the law of commutation for multiplication and division, and so on. It may be questioned whether this definition is sufficient, and it may be objected that it is vague; but the reader will do well to reflect that any definition must include the linear algebras of Peirce, the algebra of logic, and others that may be easily imagined, although they have not yet been developed. This general definition of quantity enables us to see how operators may be treated as quantities, and thus to understand the rationale of the so called symbolical methods.
In 'Mathematics', Encyclopedia Britannica (9th ed.).
Science quotes on:  |  Accord (36)  |  According (237)  |  Algebra (113)  |  Already (222)  |  Both (493)  |  Call (769)  |  Consistent (48)  |  Definition (221)  |  Definitions and Objects of Mathematics (33)  |  Derive (65)  |  Develop (268)  |  Distributive (2)  |  Division (65)  |  Do (1908)  |  Enable (119)  |  Fix (25)  |  General (511)  |  Include (90)  |  Law (894)  |  Linear (13)  |  Logic (287)  |  Meaning (233)  |  Method (505)  |  Methods (204)  |  Multiplication (43)  |  Must (1526)  |  Mutually (7)  |  Object (422)  |  Operate (17)  |  Operation (213)  |  Operator (3)  |  Ordinary (160)  |  Other (2236)  |  Charles Sanders Peirce (22)  |  Quantity (132)  |  Quaternion (9)  |  Question (621)  |  Rationale (7)  |  Reader (40)  |  Reflect (32)  |  Save (118)  |  See (1081)  |  Sufficient (128)  |  Understand (606)  |  Will (2355)

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:  |  All (4108)  |  Biography (240)  |  Concentration (29)  |  Danger (115)  |  Dangerous (105)  |  Else (4)  |  Engineer (121)  |  Enthusiasm (52)  |  Everything (476)  |  Example (94)  |  Excitement (50)  |  Expression (175)  |  Full (66)  |  Genuine (52)  |  Happen (274)  |  Happened (88)  |  Hearty (3)  |  Himself (461)  |  Honorable (14)  |  Honour (56)  |  Indemnification (2)  |  Inhuman (3)  |  Little (707)  |  Logic (287)  |  Man (2251)  |  Sir Hiram Maxim (4)  |  Men Of Science (143)  |  Obvious (126)  |  Old (481)  |  Philosophy (380)  |  Physical (508)  |  Physical Science (101)  |  Poetry (143)  |  Real (149)  |  Required (108)  |  Requirement (63)  |  Romance (15)  |  Romantic (13)  |  Romanticism (5)  |  Science (3879)  |  Simplicity (167)  |  Superhuman (5)  |  Train (114)  |  Training (80)  |  Typical (13)  |  Vagueness (15)

Tactics used by many practitioners of pseudoscience: make a large number of vaguely scientific arguments in the hope of making the desired conclusion seem inevitable. It is essential to recognize that a disconnected assemblage of weak arguments does not create a single, strong scientific argument.
Co-author with Matt Ford, Chris Lee and Jonathan Gitlin, in 'Diluting the Scientific Method: Ars Looks at Homeopathy' (11 Sep 2007) on arstechnica.com web site.
Science quotes on:  |  Argument (138)  |  Assemblage (17)  |  Conclusion (254)  |  Create (235)  |  Desired (6)  |  Disconnect (3)  |  Essential (199)  |  Hope (299)  |  Inevitable (49)  |  Large (394)  |  Making (300)  |  Number (699)  |  Practitioner (20)  |  Pseudoscience (16)  |  Recognize (125)  |  Scientific (941)  |  Single (353)  |  Strong (174)  |  Tactic (7)  |  Weak (71)

That sometimes clear … and sometimes vague stuff … which is … mathematics.
In Mathematics, Science and Epistemology (1980), Vol. 2, 69. This quote condensed from a longer quote which begins, “Mathematical proofs are…”, on the Imre Lakatos Quotes page of this website.
Science quotes on:  |  Clear (100)  |  Mathematics (1328)  |  Sometimes (45)  |  Stuff (21)

The arithmetization of mathematics … which began with Weierstrass … had for its object the separation of purely mathematical concepts, such as number and correspondence and aggregate, from intuitional ideas, which mathematics had acquired from long association with geometry and mechanics. These latter, in the opinion of the formalists, are so firmly entrenched in mathematical thought that in spite of the most careful circumspection in the choice of words, the meaning concealed behind these words, may influence our reasoning. For the trouble with human words is that they possess content, whereas the purpose of mathematics is to construct pure thought. But how can we avoid the use of human language? The … symbol. Only by using a symbolic language not yet usurped by those vague ideas of space, time, continuity which have their origin in intuition and tend to obscure pure reason—only thus may we hope to build mathematics on the solid foundation of logic.
In Tobias Dantzig and Joseph Mazur (ed.), Number: The Language of Science (1930, ed. by Joseph Mazur 2007), 99.
Science quotes on:  |  Acquire (39)  |  Acquired (78)  |  Aggregate (23)  |  Association (46)  |  Avoid (116)  |  Begin (260)  |  Behind (137)  |  Build (204)  |  Careful (24)  |  Choice (110)  |  Circumspection (5)  |  Conceal (18)  |  Concealed (25)  |  Concept (221)  |  Construct (124)  |  Content (69)  |  Continuity (38)  |  Correspondence (23)  |  Entrench (2)  |  Firmly (6)  |  Foundation (171)  |  Geometry (255)  |  Hope (299)  |  Human (1468)  |  Idea (843)  |  Influence (222)  |  Intuition (75)  |  Language (293)  |  Latter (21)  |  Logic (287)  |  Long (790)  |  Mathematics (1328)  |  Mean (809)  |  Meaning (233)  |  Mechanic (119)  |  Mechanics (131)  |  Most (1731)  |  Number (699)  |  Object (422)  |  Obscure (62)  |  Opinion (281)  |  Origin (239)  |  Possess (156)  |  Pure (291)  |  Purely (109)  |  Purpose (317)  |  Reason (744)  |  Reasoning (207)  |  Separation (57)  |  Solid (116)  |  Space (500)  |  Spite (55)  |  Symbol (93)  |  Tend (124)  |  Thought (953)  |  Time (1877)  |  Trouble (107)  |  Use (766)  |  Karl Weierstrass (9)  |  Word (619)

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)  |  Meanings (5)  |  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)  |  Word (619)

The deep study of nature is the most fruitful source of mathematical discoveries. By offering to research a definite end, this study has the advantage of excluding vague questions and useless calculations; besides it is a sure means of forming analysis itself and of discovering the elements which it most concerns us to know, and which natural science ought always to conserve.
Théorie Analytique de la Chaleur, Discours Préliminaire. Translation as in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath's Quotation-book (1914), 89.
Science quotes on:  |  Advantage (134)  |  Analysis (233)  |  Calculation (127)  |  Concern (228)  |  Deep (233)  |  Definite (110)  |  Discovery (780)  |  Element (310)  |  End (590)  |  Forming (42)  |  Fruitful (58)  |  Know (1518)  |  Mathematics (1328)  |  Mean (809)  |  Means (579)  |  Most (1731)  |  Natural (796)  |  Natural Science (128)  |  Nature (1926)  |  Question (621)  |  Research (664)  |  Science (3879)  |  Study (653)

The difficulties connected with my criterion of demarcation (D) are important, but must not be exaggerated. It is vague, since it is a methodological rule, and since the demarcation between science and nonscience is vague. But it is more than sharp enough to make a distinction between many physical theories on the one hand, and metaphysical theories, such as psychoanalysis, or Marxism (in its present form), on the other. This is, of course, one of my main theses; and nobody who has not understood it can be said to have understood my theory.
The situation with Marxism is, incidentally, very different from that with psychoanalysis. Marxism was once a scientific theory: it predicted that capitalism would lead to increasing misery and, through a more or less mild revolution, to socialism; it predicted that this would happen first in the technically highest developed countries; and it predicted that the technical evolution of the 'means of production' would lead to social, political, and ideological developments, rather than the other way round.
But the (so-called) socialist revolution came first in one of the technically backward countries. And instead of the means of production producing a new ideology, it was Lenin's and Stalin's ideology that Russia must push forward with its industrialization ('Socialism is dictatorship of the proletariat plus electrification') which promoted the new development of the means of production.
Thus one might say that Marxism was once a science, but one which was refuted by some of the facts which happened to clash with its predictions (I have here mentioned just a few of these facts).
However, Marxism is no longer a science; for it broke the methodological rule that we must accept falsification, and it immunized itself against the most blatant refutations of its predictions. Ever since then, it can be described only as nonscience—as a metaphysical dream, if you like, married to a cruel reality.
Psychoanalysis is a very different case. It is an interesting psychological metaphysics (and no doubt there is some truth in it, as there is so often in metaphysical ideas), but it never was a science. There may be lots of people who are Freudian or Adlerian cases: Freud himself was clearly a Freudian case, and Adler an Adlerian case. But what prevents their theories from being scientific in the sense here described is, very simply, that they do not exclude any physically possible human behaviour. Whatever anybody may do is, in principle, explicable in Freudian or Adlerian terms. (Adler's break with Freud was more Adlerian than Freudian, but Freud never looked on it as a refutation of his theory.)
The point is very clear. Neither Freud nor Adler excludes any particular person's acting in any particular way, whatever the outward circumstances. Whether a man sacrificed his life to rescue a drowning, child (a case of sublimation) or whether he murdered the child by drowning him (a case of repression) could not possibly be predicted or excluded by Freud's theory; the theory was compatible with everything that could happen—even without any special immunization treatment.
Thus while Marxism became non-scientific by its adoption of an immunizing strategy, psychoanalysis was immune to start with, and remained so. In contrast, most physical theories are pretty free of immunizing tactics and highly falsifiable to start with. As a rule, they exclude an infinity of conceivable possibilities.
'The Problem of Demarcation' (1974). Collected in David Miller (ed.) Popper Selections (1985), 127-128.
Science quotes on:  |   (2863)  |  Accept (191)  |  Alfred Adler (3)  |  Against (332)  |  Anybody (42)  |  Behaviour (41)  |  Being (1278)  |  Blatant (3)  |  Break (99)  |  Call (769)  |  Capitalism (10)  |  Child (307)  |  Circumstance (136)  |  Circumstances (108)  |  Conceivable (28)  |  Connect (125)  |  Contrast (44)  |  Course (409)  |  Criterion (27)  |  Cruel (25)  |  Develop (268)  |  Development (422)  |  Different (577)  |  Distinction (72)  |  Do (1908)  |  Doubt (304)  |  Dream (208)  |  Enough (340)  |  Everything (476)  |  Evolution (590)  |  Fact (1210)  |  Facts (553)  |  Falsification (10)  |  First (1283)  |  Form (959)  |  Forward (102)  |  Free (232)  |  Sigmund Freud (69)  |  Happen (274)  |  Happened (88)  |  Himself (461)  |  Human (1468)  |  Idea (843)  |  Ideology (14)  |  Immunization (2)  |  Infinity (90)  |  Interesting (153)  |  Lead (384)  |  Life (1795)  |  Look (582)  |  Lot (151)  |  Man (2251)  |  Marxism (3)  |  Mean (809)  |  Means (579)  |  Mention (82)  |  Metaphysical (38)  |  Metaphysics (50)  |  Methodology (12)  |  Mild (7)  |  Misery (30)  |  More (2559)  |  More Or Less (68)  |  Most (1731)  |  Must (1526)  |  Never (1087)  |  New (1216)  |  Nobody (104)  |  Non-Science (2)  |  Non-Scientific (7)  |  Other (2236)  |  People (1005)  |  Person (363)  |  Physical (508)  |  Plus (43)  |  Point (580)  |  Political (121)  |  Possible (552)  |  Possibly (111)  |  Predict (79)  |  Prediction (82)  |  Present (619)  |  Prevent (94)  |  Principle (507)  |  Production (183)  |  Psychoanalysis (37)  |  Psychological (42)  |  Push (62)  |  Reality (261)  |  Refutation (12)  |  Remain (349)  |  Rescue (13)  |  Revolution (129)  |  Rule (294)  |  Say (984)  |  Science (3879)  |  Scientific (941)  |  Scientific Theory (24)  |  Sense (770)  |  Situation (113)  |  So-Called (71)  |  Social (252)  |  Special (184)  |  Start (221)  |  Strategy (13)  |  Term (349)  |  Terms (184)  |  Theory (970)  |  Through (849)  |  Treatment (130)  |  Truth (1057)  |  Understood (156)  |  Way (1217)  |  Whatever (234)

The employment of mathematical symbols is perfectly natural when the relations between magnitudes are under discussion; and even if they are not rigorously necessary, it would hardly be reasonable to reject them, because they are not equally familiar to all readers and because they have sometimes been wrongly used, if they are able to facilitate the exposition of problems, to render it more concise, to open the way to more extended developments, and to avoid the digressions of vague argumentation.
From Recherches sur les Principes Mathématiques de la Théorie des Richesses (1838), as translated by Nathaniel T. Bacon in 'Preface', Researches Into Mathematical Principles of the Theory of Wealth (1897), 3-4. From the original French, “L’emploi des signes mathématiques est chose naturelle toutes les fois qu'il s'agit de discuter des relations entre des grandeurs ; et lors même qu’ils ne seraient pas rigoureusement nécessaires, s’ils peuvent faciliter l’exposition, la rendre plus concise, mettre sur la voie de développements plus étendus, prévenir les écarts d’une vague argumentation, il serait peu philosophique de les rebuter, parce qu'ils ne sont pas également familiers à tous les lecteurs et qu'on s'en est quelquefois servi à faux.”
Science quotes on:  |  All (4108)  |  Avoid (116)  |  Concise (8)  |  Development (422)  |  Digression (3)  |  Discussion (72)  |  Employment (32)  |  Equally (130)  |  Exposition (15)  |  Extend (128)  |  Facilitate (5)  |  Familiar (43)  |  Magnitude (83)  |  Mathematics (1328)  |  Mathematics As A Language (20)  |  More (2559)  |  Natural (796)  |  Necessary (363)  |  Open (274)  |  Problem (676)  |  Reader (40)  |  Reasonable (27)  |  Reject (63)  |  Relation (157)  |  Render (93)  |  Rigorous (48)  |  Symbol (93)  |  Way (1217)  |  Wrong (234)

The observer is not he who merely sees the thing which is before his eyes, but he who sees what parts the thing is composed of. To do this well is a rare talent. One person, from inattention, or attending only in the wrong place, overlooks half of what he sees; another sets down much more than he sees, confounding it with what he imagines, or with what he infers; another takes note of the kind of all the circumstances, but being inexpert in estimating their degree, leaves the quantity of each vague and uncertain; another sees indeed the whole, but makes such an awkward division of it into parts, throwing into one mass things which require to be separated, and separating others which might more conveniently be considered as one, that the result is much the same, sometimes even worse than if no analysis had been attempted at all.
In A System of Logic Ratiocinative and Inductive (1858), 216.
Science quotes on:  |  All (4108)  |  Analysis (233)  |  Attempt (251)  |  Attend (65)  |  Awkward (11)  |  Being (1278)  |  Circumstance (136)  |  Circumstances (108)  |  Composed (3)  |  Confound (21)  |  Confounding (8)  |  Consider (416)  |  Convenience (50)  |  Degree (276)  |  Division (65)  |  Do (1908)  |  Down (456)  |  Estimate (57)  |  Eye (419)  |  Half (56)  |  Imagine (164)  |  Inattention (5)  |  Indeed (324)  |  Inexpert (2)  |  Infer (12)  |  Kind (557)  |  Mass (157)  |  Merely (316)  |  More (2559)  |  Note (34)  |  Observation (555)  |  Observer (43)  |  Other (2236)  |  Overlook (31)  |  Part (222)  |  Person (363)  |  Place (177)  |  Quantity (132)  |  Rare (89)  |  Require (219)  |  Result (677)  |  See (1081)  |  Separate (143)  |  Set (394)  |  Set Down (2)  |  Talent (94)  |  Thing (1915)  |  Throwing (17)  |  Uncertain (44)  |  Whole (738)  |  Worse (24)  |  Wrong (234)

The sciences are like a beautiful river, of which the course is easy to follow, when it has acquired a certain regularity; but if one wants to go back to the source, one will find it nowhere, because it is everywhere; it is spread so much [as to be] over all the surface of the earth; it is the same if one wants to go back to the origin of the sciences, one will find only obscurity, vague ideas, vicious circles; and one loses oneself in the primitive ideas.
In Essai sur les machines en général (1783), conclusion, as translated in Ivor Grattan-Guinness, Convolutions in French Mathematics, 1800-1840 (1990), Vol. 1, 32.
Science quotes on:  |  Acquired (78)  |  All (4108)  |  Back (390)  |  Beautiful (258)  |  Certain (550)  |  Circle (110)  |  Course (409)  |  Earth (996)  |  Easy (204)  |  Everywhere (94)  |  Find (998)  |  Follow (378)  |  Idea (843)  |  Lose (159)  |  Nowhere (28)  |  Obscurity (27)  |  Oneself (33)  |  Origin (239)  |  Primitive (75)  |  Regularity (40)  |  River (119)  |  Science (3879)  |  Source (93)  |  Spread (83)  |  Surface (209)  |  Surface Of The Earth (36)  |  Vicious Circle (2)  |  Want (497)  |  Will (2355)

Think of how many religions attempt to validate themselves with prophecy. Think of how many people rely on these prophecies, however vague, however unfulfilled, to support or prop up their beliefs. Yet has there ever been a religion with the prophetic accuracy and reliability of science? ... No other human institution comes close.
The Demon-Haunted World: Science as a Candle in the Dark (1997), 30.
Science quotes on:  |  Accuracy (78)  |  Attempt (251)  |  Belief (578)  |  Human (1468)  |  Institution (69)  |  Other (2236)  |  People (1005)  |  Prophecy (13)  |  Reliability (17)  |  Religion (361)  |  Science (3879)  |  Support (147)  |  Themselves (433)  |  Think (1086)

To see the clear, logical ideas gradually being disentangled from vagueness and confusion is vastly more instructive than simply starting with the logical ideas.
In 'Projective Geometery', Prelude to Mathematics (1955), 145.
Science quotes on:  |  Being (1278)  |  Clear (100)  |  Confusion (57)  |  Disentangle (4)  |  Gradual (27)  |  Gradually (102)  |  Idea (843)  |  Instruction (91)  |  Logic (287)  |  More (2559)  |  See (1081)  |  Simply (53)  |  Start (221)  |  Vagueness (15)  |  Vast (177)

Vagueness is very much more important in the theory of knowledge than you would judge it to be from the writings of most people. Everything is vague to a degree you do not realize till you have tried to make it precise, and everything precise is so remote from everything that we normally think, that you cannot for a moment suppose that is what we really mean when we say what we think.
In The Philosophy of Logical Atomism (1918, 1919), 2.
Science quotes on:  |  Degree (276)  |  Do (1908)  |  Everything (476)  |  Important (209)  |  Judge (108)  |  Knowledge (1529)  |  Mean (809)  |  Moment (253)  |  More (2559)  |  Most (1731)  |  Normal (28)  |  People (1005)  |  Precise (68)  |  Realize (147)  |  Remote (83)  |  Say (984)  |  Suppose (156)  |  Theory (970)  |  Think (1086)  |  Vagueness (15)  |  Writing (189)

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:  |  Become (815)  |  Call (769)  |  Clear (100)  |  Critical (66)  |  Data (156)  |  Degree (276)  |  Distinction (72)  |  Doubt (304)  |  Doubtful (29)  |  Hard (243)  |  Influence (222)  |  Matter (798)  |  Mean (809)  |  Mind (1338)  |  More (2559)  |  More Or Less (68)  |  Must (1526)  |  Operation (213)  |  Process (423)  |  Reflection (90)  |  Resistance (40)  |  Seriousness (10)  |  Situation (113)  |  Soft (29)  |  Solvent (6)  |  Vagueness (15)

We can see our forests vanishing, our water-powers going to waste, our soil being carried by floods into the sea; and the end of our coal and our iron is in sight. But our larger wastes of human effort, which go on every day through such of our acts as are blundering, ill-directed, or inefficient, … are less visible, less tangible, and are but vaguely appreciated.
In The Principles of Scientific Management (1911), 5.
Science quotes on:  |  Act (272)  |  Appreciate (63)  |  Being (1278)  |  Blunder (21)  |  Carry (127)  |  Coal (57)  |  Direct (225)  |  Efficiency (44)  |  Effort (227)  |  End (590)  |  Flood (50)  |  Forest (150)  |  Human (1468)  |  Inefficient (3)  |  Iron (96)  |  Power (746)  |  Productivity (21)  |  Sea (308)  |  See (1081)  |  Sight (132)  |  Soil (86)  |  Tangible (15)  |  Through (849)  |  Vanish (18)  |  Vanishing (11)  |  Visible (84)  |  Waste (101)  |  Water (481)  |  Water Power (6)


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.