TODAY IN SCIENCE HISTORY ®  •  TODAYINSCI ®
Celebrating 24 Years on the Web
Find science on or your birthday

Today in Science History - Quickie Quiz
Who said: “I have no satisfaction in formulas unless I feel their arithmetical magnitude.”
more quiz questions >>
Home > Category Index for Science Quotations > Category Index G > Category: Generalize

Generalize Quotes (19 quotes)
Generalise Quotes

Man muss immer generalisieren
One must always generalize.
Quoted, without citation, in Arnold Dresden, An Invitation to Mathematics (1936), 231. Dresden states this is a “principle usually attributed to Jacobi”.
Science quotes on:  |  Man (2252)  |  Must (1525)

Another characteristic of mathematical thought is that it can have no success where it cannot generalize.
In Eberhard Zeidler, Applied Functional Analysis: main principles and their applications (1995), 282.
Science quotes on:  |  Characteristic (154)  |  Mathematics (1395)  |  Success (327)  |  Thinking (425)  |  Thought (995)

Before you generalize, formalize, and axiomatize there must be mathematical substance.
In Eberhard Zeidler, Applied Functional Analysis: main principles and their applications (1995), 282.
Science quotes on:  |  Axiom (65)  |  Mathematics (1395)  |  Must (1525)  |  Substance (253)

But it is just this characteristic of simplicity in the laws of nature hitherto discovered which it would be fallacious to generalize, for it is obvious that simplicity has been a part cause of their discovery, and can, therefore, give no ground for the supposition that other undiscovered laws are equally simple.
From Herbert Spencer lecture delivered at Oxford (1914) 'On Scientific Method in Philosophy', collected in Mysticism and Logic and Other Essays (1919), 102.
Science quotes on:  |  Cause (561)  |  Characteristic (154)  |  Discover (571)  |  Discovery (837)  |  Equally (129)  |  Fallacious (13)  |  Ground (222)  |  Law (913)  |  Nature (2017)  |  Obvious (128)  |  Other (2233)  |  Simple (426)  |  Simplicity (175)  |  Supposition (50)  |  Undiscovered (15)

Every science begins by accumulating observations, and presently generalizes these empirically; but only when it reaches the stage at which its empirical generalizations are included in a rational generalization does it become developed science.
In The Data of Ethics (1879), 61.
Science quotes on:  |  Accumulate (30)  |  Become (821)  |  Begin (275)  |  Develop (278)  |  Developed (11)  |  Empirical (58)  |  Generalization (61)  |  Observation (593)  |  Rational (95)  |  Stage (152)

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:  |  Act (278)  |  Agree (31)  |  Analytic (11)  |  Certain (557)  |  Coincide (6)  |  Comparison (108)  |  Discover (571)  |  Erroneous (31)  |  General (521)  |  Individual (420)  |  Induction (81)  |  Infer (12)  |  Instance (33)  |  Law (913)  |  Number (710)  |  Object (438)  |  Observation (593)  |  Perform (123)  |  Process (439)  |  Pure (299)  |  Purely (111)  |  Quality (139)  |  Respect (212)  |  Synthetic (27)  |  View (496)

How can a modern anthropologist embark upon a generalization with any hope of arriving at a satisfactory conclusion? By thinking of the organizational ideas that are present in any society as a mathematical pattern.
In Rethinking Anthropology (1961), 2.
Science quotes on:  |  Anthropologist (8)  |  Arrive (40)  |  Conclusion (266)  |  Embark (7)  |  Generalization (61)  |  Hope (321)  |  Idea (881)  |  Mathematics (1395)  |  Modern (402)  |  Organization (120)  |  Pattern (116)  |  Present (630)  |  Satisfactory (19)  |  Society (350)  |  Think (1122)  |  Thinking (425)

In a word, to get the law from experiment, it is necessary to generalize; this is a necessity imposed upon the most circumspect observer.
From La Valeur de la Science (1908), 142, as translated by George Bruce Halsted in The Value of Science (1907), 77. From the original French, “En un mot, pour tirer la loi de l’expérience, il faut généraliser; c’est une nécessité qui s’impose à l’observateur le plus circonspect.” An alternate translation is given “approximately” as “In one word, to draw the rule from experience, one must generalize; this is a necessity that imposes itself on the most circumspect observer,” in Anton Bovier, Statistical Mechanics of Disordered Systems (2006), 186, footnote.
Science quotes on:  |  Draw (140)  |  Experience (494)  |  Most (1728)  |  Must (1525)  |  Necessity (197)  |  Observation (593)  |  Plus (43)  |  Rule (307)  |  Word (650)

Induction is the process of generalizing from our known and limited experience, and framing wider rules for the future than we have been able to test fully. At its simplest, then, an induction is a habit or an adaptation—the habit of expecting tomorrow’s weather to be like today’s, the adaptation to the unwritten conventions of community life.
Science quotes on:  |  Adaptation (59)  |  Community (111)  |  Experience (494)  |  Future (467)  |  Habit (174)  |  Induction (81)  |  Know (1538)  |  Known (453)  |  Life (1870)  |  Limit (294)  |  Limited (102)  |  Logic (311)  |  Process (439)  |  Rule (307)  |  Test (221)  |  Today (321)  |  Tomorrow (63)  |  Weather (49)

It is not Cayley’s way to analyze concepts into their ultimate elements. … But he is master of the empirical utilization of the material: in the way he combines it to form a single abstract concept which he generalizes and then subjects to computative tests, in the way the newly acquired data are made to yield at a single stroke the general comprehensive idea to the subsequent numerical verification of which years of labor are devoted. Cayley is thus the natural philosopher among mathematicians.
In Mathematische Annalen, Bd. 46 (1895), 479. As quoted and cited in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 146.
Science quotes on:  |  Abstract (141)  |  Acquired (77)  |  Analyze (12)  |  Arthur Cayley (17)  |  Combine (58)  |  Comprehensive (29)  |  Compute (19)  |  Concept (242)  |  Data (162)  |  Devote (45)  |  Devoted (59)  |  Element (322)  |  Empirical (58)  |  Form (976)  |  General (521)  |  Idea (881)  |  Labor (200)  |  Master (182)  |  Material (366)  |  Mathematician (407)  |  Mathematicians and Anecdotes (141)  |  Natural (810)  |  Natural Philosopher (4)  |  Numerical (39)  |  Philosopher (269)  |  Single (365)  |  Stroke (19)  |  Subject (543)  |  Subsequent (34)  |  Test (221)  |  Ultimate (152)  |  Utilization (16)  |  Verification (32)  |  Way (1214)  |  Year (963)  |  Yield (86)

Man is made for science; he reasons from effects to causes, and from causes to effects; but he does not always reason without error. In reasoning, therefore, from appearances which are particular, care must be taken how we generalize; we should be cautious not to attribute to nature, laws which may perhaps be only of our own invention.
'Theory of the Earth', Transactions of the Royal Society of Edinburgh, 1788, 1, 273.
Science quotes on:  |  Appearance (145)  |  Attribute (65)  |  Care (203)  |  Cause (561)  |  Effect (414)  |  Error (339)  |  Invention (400)  |  Law (913)  |  Man (2252)  |  Must (1525)  |  Nature (2017)  |  Reason (766)  |  Reasoning (212)

Mathematics is a science of Observation, dealing with reals, precisely as all other sciences deal with reals. It would be easy to show that its Method is the same: that, like other sciences, having observed or discovered properties, which it classifies, generalises, co-ordinates and subordinates, it proceeds to extend discoveries by means of Hypothesis, Induction, Experiment and Deduction.
In Problems of Life and Mind: The Method of Science and its Application (1874), 423-424. [The reals are the relations of magnitude.]
Science quotes on:  |  Classify (8)  |  Coordinate (5)  |  Deal (192)  |  Deduction (90)  |  Discover (571)  |  Easy (213)  |  Experiment (736)  |  Extend (129)  |  Hypothesis (314)  |  Induction (81)  |  Mathematics (1395)  |  Mean (810)  |  Means (587)  |  Method (531)  |  Observation (593)  |  Observed (149)  |  Other (2233)  |  Precisely (93)  |  Proceed (134)  |  Property (177)  |  Real (159)  |  Show (353)  |  Subordinate (11)

No generalizing beyond the data, no theory. No theory, no insight. And if no insight, why do research.
'Developing Theory About the Development of Theory,' in Ken G. Smith and Michael A. Hitt, Great Minds in Management: the Theory of Process Development (2005), 361.
Science quotes on:  |  Beyond (316)  |  Data (162)  |  Do (1905)  |  Insight (107)  |  Research (753)  |  Theory (1015)  |  Why (491)

One-story intellects, two-story intellects, three-story intellects with skylights. All fact-collectors, who have no aim beyond their facts, are one-story men. Two-story men compare, reason, generalize, using the labors of the fact-collectors as well as their own. Three-story men idealize, imagine, predict; their best illumination comes from above, through the skylight. There are minds with large ground-floors, that can store an infinite amount of knowledge; some librarians, for instance, who know enough of books to help other people, without being able to make much other use of their knowledge, have intellects of this class. Your great working lawyer has two spacious stories; his mind is clear, because his mental floors are large, and he has room to arrange his thoughts so that lie can get at them,—facts below, principles above, and all in ordered series; poets are often narrow below, incapable of clear statement, and with small power of consecutive reasoning, but full of light, if sometimes rather bare of furniture, in the attics.
The Poet at the Breakfast Table (1883), 50.
Science quotes on:  |  Aim (175)  |  Amount (153)  |  Arrange (33)  |  Bare (33)  |  Being (1276)  |  Best (467)  |  Beyond (316)  |  Book (413)  |  Class (168)  |  Collector (8)  |  Compare (76)  |  Comparison (108)  |  Enough (341)  |  Fact (1257)  |  Facts (553)  |  Furniture (8)  |  Generalization (61)  |  Great (1610)  |  Ground (222)  |  Idealization (3)  |  Illumination (15)  |  Imagine (176)  |  Incapable (41)  |  Infinite (243)  |  Intellect (251)  |  Know (1538)  |  Knowledge (1647)  |  Labor (200)  |  Large (398)  |  Lawyer (27)  |  Librarian (2)  |  Lie (370)  |  Light (635)  |  Mental (179)  |  Mind (1377)  |  Narrow (85)  |  Order (638)  |  Other (2233)  |  People (1031)  |  Poet (97)  |  Power (771)  |  Predict (86)  |  Prediction (89)  |  Principle (530)  |  Reason (766)  |  Reasoning (212)  |  Series (153)  |  Small (489)  |  Statement (148)  |  Store (49)  |  Story (122)  |  Thought (995)  |  Through (846)  |  Two (936)  |  Use (771)

Random search for data on ... off-chance is hardly scientific. A questionnaire on 'Intellectual Immoralities' was circulated by a well-known institution. 'Intellectual Immorality No. 4' read: 'Generalizing beyond one's data'. [Wilder Dwight] Bancroft asked whether it would not be more correct to word question no. 4 'Not generalizing beyond one's data.'
From Dream to Discovery: On Being a Scientist (1964), 279. In Henry Mintzberg, essay, 'Developing Theory About the Development of Theory,' in Ken G. Smith and Michael A. Hitt, Great Minds in Management: the Theory of Process Development (2005), 361.
Science quotes on:  |  Ask (420)  |  Wilder Dwight Bancroft (6)  |  Beyond (316)  |  Chance (244)  |  Data (162)  |  Immorality (7)  |  Institution (73)  |  Intellect (251)  |  Intellectual (258)  |  Known (453)  |  More (2558)  |  Question (649)  |  Questionnaire (3)  |  Random (42)  |  Read (308)  |  Scientific (955)  |  Search (175)  |  Word (650)

The book [Future of an Illusion] testifies to the fact that the genius of experimental science is not necessarily joined with the genius of logic or generalizing power.
…...
Science quotes on:  |  Book (413)  |  Experimental (193)  |  Fact (1257)  |  Future (467)  |  Genius (301)  |  Illusion (68)  |  Join (32)  |  Logic (311)  |  Necessarily (137)  |  Power (771)  |  Testify (7)

There are, at present, fundamental problems in theoretical physics … the solution of which … will presumably require a more drastic revision of our fundmental concepts than any that have gone before. Quite likely, these changes will be so great that it will be beyond the power of human intelligence to get the necessary new ideas by direct attempts to formulate the experimental data in mathematical terms. The theoretical worker in the future will, therefore, have to proceed in a more direct way. The most powerful method of advance that can be suggested at present is to employ all the resources of pure mathematics in attempts to perfect and generalize the mathematical formalism that forms the existing basis of theoretical physics, and after each success in this direction, to try to interpret the new mathematical features in terms of physical entities.
At age 28.
Proceedings of the Royal Society (1931), A133, 60. In A. Pais, 'Playing With Equations, the Dirac Way'. Behram N. Kursunoglu (Ed.) and Eugene Paul Wigner (Ed.), Paul Adrien Maurice Dirac: Reminiscences about a Great Physicist (1990), 109.
Science quotes on:  |  Advance (298)  |  Age (509)  |  Attempt (266)  |  Basis (180)  |  Beyond (316)  |  Change (639)  |  Concept (242)  |  Data (162)  |  Direct (228)  |  Direction (185)  |  Employ (115)  |  Experimental (193)  |  Form (976)  |  Formalism (7)  |  Fundamental (264)  |  Future (467)  |  Great (1610)  |  Human (1512)  |  Idea (881)  |  Intelligence (218)  |  Mathematics (1395)  |  Method (531)  |  More (2558)  |  Most (1728)  |  Necessary (370)  |  New (1273)  |  Perfect (223)  |  Physic (515)  |  Physical (518)  |  Physics (564)  |  Power (771)  |  Powerful (145)  |  Present (630)  |  Problem (731)  |  Proceed (134)  |  Pure (299)  |  Pure Mathematics (72)  |  Require (229)  |  Revision (7)  |  Solution (282)  |  Success (327)  |  Term (357)  |  Terms (184)  |  Theoretical Physics (26)  |  Try (296)  |  Way (1214)  |  Will (2350)

Thinking is merely the comparing of ideas, discerning relations of likeness and of difference between ideas, and drawing inferences. It is seizing general truths on the basis of clearly apprehended particulars. It is but generalizing and particularizing. Who will deny that a child can deal profitably with sequences of ideas like: How many marbles are 2 marbles and 3 marbles? 2 pencils and 3 pencils? 2 balls and 3 balls? 2 children and 3 children? 2 inches and 3 inches? 2 feet and 3 feet? 2 and 3? Who has not seen the countenance of some little learner light up at the end of such a series of questions with the exclamation, “Why it’s always that way. Isn’t it?” This is the glow of pleasure that the generalizing step always affords him who takes the step himself. This is the genuine life-giving joy which comes from feeling that one can successfully take this step. The reality of such a discovery is as great, and the lasting effect upon the mind of him that makes it is as sure as was that by which the great Newton hit upon the generalization of the law of gravitation. It is through these thrills of discovery that love to learn and intellectual pleasure are begotten and fostered. Good arithmetic teaching abounds in such opportunities.
In Arithmetic in Public Education (1909), 13. As quoted and cited in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 68.
Science quotes on:  |  Abound (17)  |  Afford (19)  |  Apprehend (5)  |  Arithmetic (144)  |  Ball (64)  |  Basis (180)  |  Child (333)  |  Children (201)  |  Clearly (45)  |  Compare (76)  |  Countenance (9)  |  Deal (192)  |  Deny (71)  |  Difference (355)  |  Discern (35)  |  Discerning (16)  |  Discovery (837)  |  Drawing (56)  |  Effect (414)  |  End (603)  |  Exclamation (3)  |  Feel (371)  |  Feeling (259)  |  Foster (12)  |  General (521)  |  Generalization (61)  |  Genuine (54)  |  Glow (15)  |  Good (906)  |  Gravitation (72)  |  Great (1610)  |  Himself (461)  |  Hit (20)  |  Idea (881)  |  Inference (45)  |  Intellectual (258)  |  Joy (117)  |  Law (913)  |  Law Of Gravitation (23)  |  Learn (672)  |  Learner (10)  |  Life (1870)  |  Life-Giving (2)  |  Light (635)  |  Likeness (18)  |  Little (717)  |  Love (328)  |  Marble (21)  |  Merely (315)  |  Mind (1377)  |  Sir Isaac Newton (363)  |  Opportunity (95)  |  Particular (80)  |  Pencil (20)  |  Pleasure (191)  |  Question (649)  |  Reality (274)  |  Relation (166)  |  Sequence (68)  |  Series (153)  |  Step (234)  |  Successful (134)  |  Teach (299)  |  Teaching (190)  |  Think (1122)  |  Thinking (425)  |  Thrill (26)  |  Through (846)  |  Truth (1109)  |  Value Of Mathematics (60)  |  Way (1214)  |  Why (491)  |  Will (2350)

To generalize is to be an idiot. To particularize is the alone distinction of merit. General knowledges are those knowledges that idiots possess.
Annotations to Sir Joshua Reynolds, 'Discourse II', Discourses (c.1808), as given in Geoffrey Keynes, Complete Writings (1957).
Science quotes on:  |  Alone (324)  |  Distinction (72)  |  General (521)  |  Idiot (22)  |  Knowledge (1647)  |  Merit (51)  |  Possess (157)


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 |
Thank you for sharing.
- 100 -
Sophie Germain
Gertrude Elion
Ernest Rutherford
James Chadwick
Marcel Proust
William Harvey
Johann Goethe
John Keynes
Carl Gauss
Paul Feyerabend
- 90 -
Antoine Lavoisier
Lise Meitner
Charles Babbage
Ibn Khaldun
Euclid
Ralph Emerson
Robert Bunsen
Frederick Banting
Andre Ampere
Winston Churchill
- 80 -
John Locke
Bronislaw Malinowski
Bible
Thomas Huxley
Alessandro Volta
Erwin Schrodinger
Wilhelm Roentgen
Louis Pasteur
Bertrand Russell
Jean Lamarck
- 70 -
Samuel Morse
John Wheeler
Nicolaus Copernicus
Robert Fulton
Pierre Laplace
Humphry Davy
Thomas Edison
Lord Kelvin
Theodore Roosevelt
Carolus Linnaeus
- 60 -
Francis Galton
Linus Pauling
Immanuel Kant
Martin Fischer
Robert Boyle
Karl Popper
Paul Dirac
Avicenna
James Watson
William Shakespeare
- 50 -
Stephen Hawking
Niels Bohr
Nikola Tesla
Rachel Carson
Max Planck
Henry Adams
Richard Dawkins
Werner Heisenberg
Alfred Wegener
John Dalton
- 40 -
Pierre Fermat
Edward Wilson
Johannes Kepler
Gustave Eiffel
Giordano Bruno
JJ Thomson
Thomas Kuhn
Leonardo DaVinci
Archimedes
David Hume
- 30 -
Andreas Vesalius
Rudolf Virchow
Richard Feynman
James Hutton
Alexander Fleming
Emile Durkheim
Benjamin Franklin
Robert Oppenheimer
Robert Hooke
Charles Kettering
- 20 -
Carl Sagan
James Maxwell
Marie Curie
Rene Descartes
Francis Crick
Hippocrates
Michael Faraday
Srinivasa Ramanujan
Francis Bacon
Galileo Galilei
- 10 -
Aristotle
John Watson
Rosalind Franklin
Michio Kaku
Isaac Asimov
Charles Darwin
Sigmund Freud
Albert Einstein
Florence Nightingale
Isaac Newton


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