Celebrating 18 Years on the Web
TODAY IN SCIENCE HISTORY ®
Find science on or your birthday

Today in Science History - Quickie Quiz
Who said: “Genius is two percent inspiration, ninety-eight percent perspiration.”
more quiz questions >>
Home > Category Index for Science Quotations > Category Index A > Category: Analytic

Analytic Quotes (10 quotes)

A principle of induction would be a statement with the help of which we could put inductive inferences into a logically acceptable form. In the eyes of the upholders of inductive logic, a principle of induction is of supreme importance for scientific method: “... this principle”, says Reichenbach, “determines the truth of scientific theories. To eliminate it from science would mean nothing less than to deprive science of the power to decide the truth or falsity of its theories. Without it, clearly, science would no longer have the right to distinguish its theories from the fanciful and arbitrary creations of the poet’s mind.” Now this principle of induction cannot be a purely logical truth like a tautology or an analytic statement. Indeed, if there were such a thing as a purely logical principle of induction, there would be no problem of induction; for in this case, all inductive inferences would have to be regarded as purely logical or tautological transformations, just like inferences in inductive logic. Thus the principle of induction must be a synthetic statement; that is, a statement whose negation is not self-contradictory but logically possible. So the question arises why such a principle should be accepted at all, and how we can justify its acceptance on rational grounds.
…...
Science quotes on:  |  Accept (65)  |  Acceptable (6)  |  Acceptance (45)  |  Arbitrary (20)  |  Arise (49)  |  Case (98)  |  Clearly (41)  |  Creation (239)  |  Decide (40)  |  Deprive (11)  |  Determine (72)  |  Distinguish (61)  |  Eliminate (21)  |  Eye (218)  |  Falsity (13)  |  Fanciful (6)  |  Form (308)  |  Ground (90)  |  Help (101)  |  Importance (216)  |  Induction (59)  |  Inductive (10)  |  Inference (31)  |  Justify (23)  |  Less (102)  |  Logic (247)  |  Logical (54)  |  Long (172)  |  Mean (101)  |  Mind (743)  |  Negation (2)  |  Nothing (385)  |  Poet (78)  |  Possible (155)  |  Power (358)  |  Principle (285)  |  Problem (490)  |  Purely (28)  |  Question (404)  |  Rational (56)  |  Regard (93)  |  Right (196)  |  Say (228)  |  Science (2043)  |  Scientific (232)  |  Scientific Method (166)  |  Scientific Theory (24)  |  Statement (72)  |  Supreme (37)  |  Synthetic (16)  |  Tautological (2)  |  Tautology (4)  |  Theory (690)  |  Transformation (54)  |  Truth (914)

Having discovered … by observation and comparison that certain objects agree in certain respects, we generalise the qualities in which they coincide,—that is, from a certain number of individual instances we infer a general law; we perform an act of Induction. This induction is erroneously viewed as analytic; it is purely a synthetic process.
In Lecture VI of his Biennial Course, by William Hamilton and Henry L. Mansel (ed.) and John Veitch (ed.), Metaphysics (1860), Vol. 1, 101.
Science quotes on:  |  Agree (25)  |  Coincide (5)  |  Comparison (61)  |  Discover (196)  |  Erroneous (4)  |  General (156)  |  Generalize (14)  |  Individual (215)  |  Induction (59)  |  Infer (12)  |  Instance (32)  |  Law (513)  |  Object (169)  |  Observation (445)  |  Process (261)  |  Pure (98)  |  Quality (93)  |  Synthetic (16)  |  View (171)

If a mathematician of the past, an Archimedes or even a Descartes, could view the field of geometry in its present condition, the first feature to impress him would be its lack of concreteness. There are whole classes of geometric theories which proceed not only without models and diagrams, but without the slightest (apparent) use of spatial intuition. In the main this is due, to the power of the analytic instruments of investigations as compared with the purely geometric.
In 'The Present Problems in Geometry', Bulletin American Mathematical Society (1906), 286.
Science quotes on:  |  Apparent (39)  |  Archimedes (53)  |  Class (83)  |  Compare (37)  |  Concreteness (4)  |  Condition (160)  |  René Descartes (81)  |  Diagram (13)  |  Due (20)  |  Feature (43)  |  Field (170)  |  First (313)  |  Geometric (5)  |  Geometry (215)  |  Impress (16)  |  Instrument (92)  |  Intuition (57)  |  Investigation (175)  |  Lack (77)  |  Main (27)  |  Mathematician (364)  |  Model (80)  |  Modern Mathematics (36)  |  Past (150)  |  Power (358)  |  Present (174)  |  Proceed (41)  |  Purely (28)  |  Slight (30)  |  Spatial (8)  |  Theory (690)  |  View (171)  |  Whole (189)

Mathematics in its pure form, as arithmetic, algebra, geometry, and the applications of the analytic method, as well as mathematics applied to matter and force, or statics and dynamics, furnishes the peculiar study that gives to us, whether as children or as men, the command of nature in this its quantitative aspect; mathematics furnishes the instrument, the tool of thought, which we wield in this realm.
In Psychologic Foundations of Education (1898), 325.
Science quotes on:  |  Algebra (92)  |  Application (166)  |  Apply (76)  |  Arithmetic (115)  |  Aspect (57)  |  Child (245)  |  Command (27)  |  Dynamics (9)  |  Force (249)  |  Form (308)  |  Furnish (40)  |  Geometry (215)  |  Give (200)  |  Instrument (92)  |  Mathematics (1149)  |  Matter (340)  |  Method (230)  |  Nature (1211)  |  Peculiar (43)  |  Pure (98)  |  Quantitative (18)  |  Realm (54)  |  Static (8)  |  Study (461)  |  Thought (536)  |  Tool (87)  |  Value Of Mathematics (55)  |  Wield (10)

The union of philosophical and mathematical productivity, which besides in Plato we find only in Pythagoras, Descartes and Leibnitz, has always yielded the choicest fruits to mathematics; To the first we owe scientific mathematics in general, Plato discovered the analytic method, by means of which mathematics was elevated above the view-point of the elements, Descartes created the analytical geometry, our own illustrious countryman discovered the infinitesimal calculus—and just these are the four greatest steps in the development of mathematics.
In Geschichte der Mathematik im Altertum und im Mittelalter (1874), 149-150. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 210. From the original German, “Die Verbindung philosophischer und mathematischer Productivität, wie wir sie ausser in Platon wohl nur noch in Pythagoras, Descartes, Leibnitz vorfinden, hat der Mathematik immer die schönsten Früchte gebracht: Ersterem verdanken wir die wissenschaftliche Mathematik überhaupt, Platon erfand die analytische Methode, durch welche sich die Mathematik über den Standpunct der Elemente erhob, Descartes schuf die analytische Geometrie, unser berühmter Landsmann den Infinitesimalcalcül—und eben daß sind die vier grössten Stufen in der Entwickelung der Mathematik.”
Science quotes on:  |  Analysis (159)  |  Calculus (48)  |  Countryman (4)  |  Create (150)  |  René Descartes (81)  |  Development (276)  |  Discover (196)  |  Element (162)  |  Elevate (11)  |  Find (405)  |  Fruit (70)  |  General (156)  |  Geometry (215)  |  Greatest (62)  |  Illustrious (5)  |  Infinitesimal (15)  |  Gottfried Wilhelm Leibniz (49)  |  Mathematics (1149)  |  Means (171)  |  Method (230)  |  Philosophy (257)  |  Plato (73)  |  Productivity (17)  |  Pythagoras (34)  |  Scientific (232)  |  Step (109)  |  Union (20)  |  Viewpoint (8)  |  Yield (35)

There is probably no other science which presents such different appearances to one who cultivates it and to one who does not, as mathematics. To this person it is ancient, venerable, and complete; a body of dry, irrefutable, unambiguous reasoning. To the mathematician, on the other hand, his science is yet in the purple bloom of vigorous youth, everywhere stretching out after the “attainable but unattained” and full of the excitement of nascent thoughts; its logic is beset with ambiguities, and its analytic processes, like Bunyan’s road, have a quagmire on one side and a deep ditch on the other and branch off into innumerable by-paths that end in a wilderness.
In 'The Theory of Transformation Groups', (A review of Erster Abschnitt, Theorie der Transformationsgruppen (1888)), Bulletin New York Mathematical Society (1893), 2 (First series), 61.
Science quotes on:  |  Ambiguity (14)  |  Ancient (103)  |  Appearance (85)  |  Attain (42)  |  Bloom (9)  |  Body (243)  |  Branch (102)  |  John Bunyan (5)  |  Complete (84)  |  Cultivate (19)  |  Different (178)  |  Dry (21)  |  Excitement (40)  |  Innumerable (23)  |  Irrefutable (4)  |  Logic (247)  |  Mathematician (364)  |  Mathematics (1149)  |  Nascent (2)  |  Nature Of Mathematics (77)  |  On The Other Hand (32)  |  Path (84)  |  Present (174)  |  Process (261)  |  Purple (3)  |  Reason (454)  |  Road (63)  |  Science (2043)  |  Stretch (18)  |  Thought (536)  |  Unambiguous (5)  |  Venerable (4)  |  Vigorous (20)  |  Wilderness (39)  |  Youth (75)

This [the fact that the pursuit of mathematics brings into harmonious action all the faculties of the human mind] accounts for the extraordinary longevity of all the greatest masters of the Analytic art, the Dii Majores of the mathematical Pantheon. Leibnitz lived to the age of 70; Euler to 76; Lagrange to 77; Laplace to 78; Gauss to 78; Plato, the supposed inventor of the conic sections, who made mathematics his study and delight, who called them the handles or aids to philosophy, the medicine of the soul, and is said never to have let a day go by without inventing some new theorems, lived to 82; Newton, the crown and glory of his race, to 85; Archimedes, the nearest akin, probably, to Newton in genius, was 75, and might have lived on to be 100, for aught we can guess to the contrary, when he was slain by the impatient and ill mannered sergeant, sent to bring him before the Roman general, in the full vigour of his faculties, and in the very act of working out a problem; Pythagoras, in whose school, I believe, the word mathematician (used, however, in a somewhat wider than its present sense) originated, the second founder of geometry, the inventor of the matchless theorem which goes by his name, the pre-cognizer of the undoubtedly mis-called Copernican theory, the discoverer of the regular solids and the musical canon who stands at the very apex of this pyramid of fame, (if we may credit the tradition) after spending 22 years studying in Egypt, and 12 in Babylon, opened school when 56 or 57 years old in Magna Græcia, married a young wife when past 60, and died, carrying on his work with energy unspent to the last, at the age of 99. The mathematician lives long and lives young; the wings of his soul do not early drop off, nor do its pores become clogged with the earthy particles blown from the dusty highways of vulgar life.
In Presidential Address to the British Association, Collected Mathematical Papers, Vol. 2 (1908), 658.
Science quotes on:  |  Account (67)  |  Act (115)  |  Action (184)  |  Age (174)  |  Aid (41)  |  Akin (5)  |  Apex (4)  |  Archimedes (53)  |  Art (284)  |  Aught (2)  |  Babylon (5)  |  Become (172)  |  Belief (503)  |  Blow (22)  |  Bring (90)  |  Call (127)  |  Called (9)  |  Canon (3)  |  Carry (59)  |  Clog (5)  |  Conic Section (7)  |  Contrary (34)  |  Copernican Theory (3)  |  Credit (20)  |  Crown (26)  |  Delight (64)  |  Die (81)  |  Discoverer (15)  |  Drop (39)  |  Dusty (8)  |  Early (61)  |  Earthy (2)  |  Egypt (22)  |  Energy (214)  |  Leonhard Euler (34)  |  Extraordinary (43)  |  Fact (725)  |  Faculty (65)  |  Fame (37)  |  Founder (15)  |  Full (63)  |  Carl Friedrich Gauss (73)  |  General (156)  |  Genius (243)  |  Geometry (215)  |  Glory (57)  |  Great (524)  |  Guess (48)  |  Handle (16)  |  Harmonious (9)  |  Highway (13)  |  Human Mind (80)  |  Impatient (3)  |  Invent (50)  |  Inventor (55)  |  Count Joseph-Louis de Lagrange (24)  |  Pierre-Simon Laplace (61)  |  Gottfried Wilhelm Leibniz (49)  |  Let (61)  |  Life (1124)  |  Live (269)  |  Long (172)  |  Longevity (6)  |  Manner (57)  |  Marry (8)  |  Master (93)  |  Mathematician (364)  |  Mathematics (1149)  |  Medicine (343)  |  Musical (7)  |  Name (165)  |  New (483)  |  Sir Isaac Newton (327)  |  Old (147)  |  Open (66)  |  Originate (21)  |  Pantheon (2)  |  Particle (99)  |  Past (150)  |  Philosophy (257)  |  Plato (73)  |  Pore (7)  |  Present (174)  |  Probably (47)  |  Problem (490)  |  Pursuit (76)  |  Pyramid (9)  |  Pythagoras (34)  |  Race (103)  |  Regular (13)  |  Roman (27)  |  Say (228)  |  School (117)  |  Second (59)  |  Send (22)  |  Sense (315)  |  Sergeant (2)  |  Solid (50)  |  Soul (163)  |  Spend (43)  |  Stand (107)  |  Study (461)  |  Suppose (49)  |  Theorem (88)  |  Tradition (49)  |  Undoubtedly (3)  |  Vigour (12)  |  Vulgar (15)  |  Wide (27)  |  Wife (23)  |  Wing (48)  |  Word (299)  |  Work (626)  |  Year (299)  |  Young (98)

To fully understand the mathematical genius of Sophus Lie, one must not turn to books recently published by him in collaboration with Dr. Engel, but to his earlier memoirs, written during the first years of his scientific career. There Lie shows himself the true geometer that he is, while in his later publications, finding that he was but imperfectly understood by the mathematicians accustomed to the analytic point of view, he adopted a very general analytic form of treatment that is not always easy to follow.
In Lectures on Mathematics (1911), 9.
Science quotes on:  |  Accustomed (16)  |  Adopt (18)  |  Book (257)  |  Career (57)  |  Collaboration (12)  |  Early (61)  |  Easy (98)  |  Ernst Engel (2)  |  Find (405)  |  First (313)  |  Follow (123)  |  Form (308)  |  Fully (21)  |  General (156)  |  Genius (243)  |  Geometer (22)  |  Imperfect (18)  |  Late (52)  |  Sophus Lie (5)  |  Mathematician (364)  |  Mathematicians and Anecdotes (123)  |  Mathematics (1149)  |  Memoir (11)  |  Point Of View (41)  |  Publication (90)  |  Publish (33)  |  Recently (3)  |  Scientific (232)  |  Show (90)  |  Treatment (100)  |  True (201)  |  Turn (118)  |  Understand (326)  |  Write (153)  |  Year (299)

While the method of the natural sciences is... analytic, the method of the social sciences is better described as compositive or synthetic. It is the so-called wholes, the groups of elements which are structurally connected, which we learn to single out from the totality of observed phenomena... Insofar as we analyze individual thought in the social sciences the purpose is not to explain that thought, but merely to distinguish the possible types of elements with which we shall have to reckon in the construction of different patterns of social relationships. It is a mistake... to believe that their aim is to explain conscious action ... The problems which they try to answer arise only insofar as the conscious action of many men produce undesigned results... If social phenomena showed no order except insofar as they were consciously designed, there would indeed be no room for theoretical sciences of society and there would be, as is often argued, only problems of psychology. It is only insofar as some sort of order arises as a result of individual action but without being designed by any individual that a problem is raised which demands a theoretical explanation... people dominated by the scientistic prejudice are often inclined to deny the existence of any such order... it can be shown briefly and without any technical apparatus how the independent actions of individuals will produce an order which is no part of their intentions... The way in which footpaths are formed in a wild broken country is such an instance. At first everyone will seek for himself what seems to him the best path. But the fact that such a path has been used once is likely to make it easier to traverse and therefore more likely to be used again; and thus gradually more and more clearly defined tracks arise and come to be used to the exclusion of other possible ways. Human movements through the region come to conform to a definite pattern which, although the result of deliberate decision of many people, has yet not be consciously designed by anyone.
…...
Science quotes on:  |  Action (184)  |  Aim (88)  |  Analyze (10)  |  Answer (249)  |  Anyone (35)  |  Apparatus (37)  |  Argue (23)  |  Arise (49)  |  Belief (503)  |  Best (172)  |  Better (190)  |  Break (54)  |  Briefly (5)  |  Clearly (41)  |  Conform (11)  |  Connect (30)  |  Conscious (43)  |  Consciously (6)  |  Construction (83)  |  Country (144)  |  Decision (72)  |  Define (49)  |  Definite (42)  |  Deliberate (12)  |  Demand (74)  |  Deny (41)  |  Describe (56)  |  Design (113)  |  Different (178)  |  Distinguish (61)  |  Dominate (19)  |  Easy (98)  |  Element (162)  |  Everyone (34)  |  Exclusion (13)  |  Existence (296)  |  Explain (105)  |  Explanation (177)  |  Fact (725)  |  First (313)  |  Form (308)  |  Gradually (21)  |  Group (72)  |  Human (548)  |  Inclined (12)  |  Independent (65)  |  Individual (215)  |  Instance (32)  |  Intention (28)  |  Learn (281)  |  Likely (33)  |  Merely (82)  |  Method (230)  |  Mistake (131)  |  Movement (82)  |  Natural Science (89)  |  Observe (75)  |  Often (106)  |  Order (239)  |  Part (220)  |  Path (84)  |  Pattern (79)  |  People (388)  |  Phenomenon (276)  |  Possible (155)  |  Prejudice (66)  |  Problem (490)  |  Produce (100)  |  Psychology (143)  |  Purpose (193)  |  Raise (34)  |  Reckon (14)  |  Region (35)  |  Relationship (71)  |  Result (376)  |  Room (38)  |  Seek (104)  |  Seem (143)  |  Show (90)  |  Single (119)  |  So-Called (21)  |  Social (108)  |  Social Science (31)  |  Society (227)  |  Sort (49)  |  Structurally (2)  |  Synthetic (16)  |  Technical (40)  |  Theoretical (21)  |  Theoretical Science (4)  |  Thought (536)  |  Totality (10)  |  Track (14)  |  Traverse (5)  |  Try (141)  |  Type (51)  |  Whole (189)  |  Wild (48)

[Concerning] the usual contempt with which an orthodox analytic group treats all outsiders and strangers ... I urge you to think of the young psychoanalysts as your colleagues, collaborators and partners and not as spies, traitors and wayward children. You can never develop a science that way, only an orthodox church.
Letter to a colleague (Nov 1960). In Colin Wilson, New Pathways in Psychology: Maslow and the Post-Freudian Revolution (1972, 2001), 154.
Science quotes on:  |  Child (245)  |  Church (34)  |  Colleague (23)  |  Contempt (14)  |  Development (276)  |  Orthodox (4)  |  Outsider (6)  |  Partner (5)  |  Psychoanalyst (4)  |  Science (2043)  |  Spy (4)  |  Stranger (15)  |  Traitor (3)  |  Treatment (100)  |  Wayward (3)


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.