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 believe that this Nation should commit itself to achieving the goal, before this decade is out, of landing a man on the moon and returning him safely to earth.”
more quiz questions >>
Home > Category Index for Science Quotations > Category Index D > Category: Deductive

Deductive Quotes (13 quotes)

Fiction is, indeed, an indispensable supplement to logic, or even a part of it; whether we are working inductively or deductively, both ways hang closely together with fiction: and axioms, though they seek to be primary verities, are more akin to fiction. If we had realized the nature of axioms, the doctrine of Einstein, which sweeps away axioms so familiar to us that they seem obvious truths, and substitutes others which seem absurd because they are unfamiliar, might not have been so bewildering.
In The Dance of Life (1923), 86.
Science quotes on:  |  Absurd (60)  |  Akin (5)  |  Axiom (65)  |  Bewildering (5)  |  Both (496)  |  Doctrine (81)  |  Einstein (101)  |  Albert Einstein (624)  |  Familiar (47)  |  Fiction (23)  |  Hang (46)  |  Indeed (323)  |  Indispensable (31)  |  Inductive (20)  |  Logic (311)  |  More (2558)  |  Nature (2017)  |  Obvious (128)  |  Other (2233)  |  Primary (82)  |  Realize (157)  |  Seek (218)  |  Substitute (47)  |  Supplement (7)  |  Sweep (22)  |  Together (392)  |  Truth (1109)  |  Unfamiliar (17)  |  Verity (5)  |  Way (1214)

I like to look at mathematics almost more as an art than as a science; for the activity of the mathematician, constantly creating as he is, guided though not controlled by the external world of the senses, bears a resemblance, not fanciful I believe but real, to the activity of an artist, of a painter let us say. Rigorous deductive reasoning on the part of the mathematician may be likened here to technical skill in drawing on the part of the painter. Just as no one can become a good painter without a certain amount of skill, so no one can become a mathematician without the power to reason accurately up to a certain point. Yet these qualities, fundamental though they are, do not make a painter or mathematician worthy of the name, nor indeed are they the most important factors in the case. Other qualities of a far more subtle sort, chief among which in both cases is imagination, go to the making of a good artist or good mathematician.
From 'Fundamental Conceptions and Methods in Mathematics', Bulletin American Mathematical Society (1904), 9, 133. As cited in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 182.
Science quotes on:  |  Activity (218)  |  Amount (153)  |  Art (680)  |  Artist (97)  |  Bear (162)  |  Become (821)  |  Both (496)  |  Certain (557)  |  Chief (99)  |  Control (182)  |  Create (245)  |  Do (1905)  |  Drawing (56)  |  External (62)  |  Factor (47)  |  Fundamental (264)  |  Good (906)  |  Guide (107)  |  Imagination (349)  |  Important (229)  |  Indeed (323)  |  Look (584)  |  Making (300)  |  Mathematician (407)  |  Mathematics (1395)  |  Mathematics As A Fine Art (23)  |  More (2558)  |  Most (1728)  |  Name (359)  |  Other (2233)  |  Painter (30)  |  Point (584)  |  Power (771)  |  Reason (766)  |  Reasoning (212)  |  Resemblance (39)  |  Rigorous (50)  |  Say (989)  |  Sense (785)  |  Skill (116)  |  Subtle (37)  |  Technical (53)  |  World (1850)  |  Worth (172)

It would appear that Deductive and Demonstrative Sciences are all, without exception, Inductive Sciences: that their evidence is that of experience, but that they are also, in virtue of the peculiar character of one indispensable portion of the general formulae according to which their inductions are made, Hypothetical Sciences. Their conclusions are true only upon certain suppositions, which are, or ought to be, approximations to the truth, but are seldom, if ever, exactly true; and to this hypothetical character is to be ascribed the peculiar certainty, which is supposed to be inherent in demonstration.
In System of Logic, Bk. 2, chap. 6, 1.
Science quotes on:  |  Accord (36)  |  According (236)  |  Appear (122)  |  Approximation (32)  |  Ascribe (18)  |  Certain (557)  |  Certainty (180)  |  Character (259)  |  Conclusion (266)  |  Demonstration (120)  |  Demonstrative (14)  |  Evidence (267)  |  Exactly (14)  |  Exception (74)  |  Experience (494)  |  Formula (102)  |  General (521)  |  Hypothetical (6)  |  Indispensable (31)  |  Induction (81)  |  Inductive (20)  |  Inherent (43)  |  Nature Of Mathematics (80)  |  Peculiar (115)  |  Portion (86)  |  Seldom (68)  |  Suppose (158)  |  Supposition (50)  |  True (239)  |  Truth (1109)  |  Virtue (117)

Let us now declare the means whereby our understanding can rise to knowledge without fear of error. There are two such means: intuition and deduction. By intuition I mean not the varying testimony of the senses, nor the deductive judgment of imagination naturally extravagant, but the conception of an attentive mind so distinct and so clear that no doubt remains to it with regard to that which it comprehends; or, what amounts to the same thing, the self-evidencing conception of a sound and attentive mind, a conception which springs from the light of reason alone, and is more certain, because more simple, than deduction itself. …
It may perhaps be asked why to intuition we add this other mode of knowing, by deduction, that is to say, the process which, from something of which we have certain knowledge, draws consequences which necessarily follow therefrom. But we are obliged to admit this second step; for there are a great many things which, without being evident of themselves, nevertheless bear the marks of certainty if only they are deduced from true and incontestable principles by a continuous and uninterrupted movement of thought, with distinct intuition of each thing; just as we know that the last link of a long chain holds to the first, although we can not take in with one glance of the eye the intermediate links, provided that, after having run over them in succession, we can recall them all, each as being joined to its fellows, from the first up to the last. Thus we distinguish intuition from deduction, inasmuch as in the latter case there is conceived a certain progress or succession, while it is not so in the former; … whence it follows that primary propositions, derived immediately from principles, may be said to be known, according to the way we view them, now by intuition, now by deduction; although the principles themselves can be known only by intuition, the remote consequences only by deduction.
In Rules for the Direction of the Mind, Philosophy of Descartes. [Torrey] (1892), 64-65.
Science quotes on:  |  Accord (36)  |  According (236)  |  Add (42)  |  Admit (49)  |  Alone (324)  |  Amount (153)  |  Ask (420)  |  Attentive (15)  |  Bear (162)  |  Being (1276)  |  Case (102)  |  Certain (557)  |  Certainty (180)  |  Chain (51)  |  Clear (111)  |  Comprehend (44)  |  Conceive (100)  |  Conception (160)  |  Consequence (220)  |  Continuous (83)  |  Declare (48)  |  Deduce (27)  |  Deduction (90)  |  Derive (70)  |  Distinct (98)  |  Distinguish (168)  |  Doubt (314)  |  Draw (140)  |  Error (339)  |  Evident (92)  |  Extravagant (10)  |  Eye (440)  |  Fear (212)  |  Fellow (88)  |  First (1302)  |  Follow (389)  |  Former (138)  |  Glance (36)  |  Great (1610)  |  Hold (96)  |  Imagination (349)  |  Immediately (115)  |  Inasmuch (5)  |  Incontestable (3)  |  Intermediate (38)  |  Intuition (82)  |  Join (32)  |  Judgment (140)  |  Know (1538)  |  Knowing (137)  |  Knowledge (1647)  |  Known (453)  |  Last (425)  |  Latter (21)  |  Let (64)  |  Light (635)  |  Link (48)  |  Long (778)  |  Mark (47)  |  Mean (810)  |  Means (587)  |  Mind (1377)  |  Mode (43)  |  More (2558)  |  Movement (162)  |  Naturally (11)  |  Nature Of Mathematics (80)  |  Necessarily (137)  |  Nevertheless (90)  |  Obliged (6)  |  Other (2233)  |  Primary (82)  |  Principle (530)  |  Process (439)  |  Progress (492)  |  Proposition (126)  |  Provide (79)  |  Reason (766)  |  Recall (11)  |  Regard (312)  |  Remain (355)  |  Remote (86)  |  Rise (169)  |  Run (158)  |  Same (166)  |  Say (989)  |  Second (66)  |  Self (268)  |  Sense (785)  |  Simple (426)  |  Something (718)  |  Sound (187)  |  Spring (140)  |  Step (234)  |  Succession (80)  |  Testimony (21)  |  Themselves (433)  |  Therefrom (2)  |  Thing (1914)  |  Thought (995)  |  True (239)  |  Two (936)  |  Understand (648)  |  Understanding (527)  |  Uninterrupted (7)  |  Vary (27)  |  View (496)  |  Way (1214)  |  Whereby (2)  |  Why (491)

Mathematical reasoning is deductive in the sense that it is based upon definitions which, as far as the validity of the reasoning is concerned (apart from any existential import), needs only the test of self-consistency. Thus no external verification of definitions is required in mathematics, as long as it is considered merely as mathematics.
In Universal Algebra (1898), Preface, vi.
Science quotes on:  |  Base (120)  |  Concern (239)  |  Consider (428)  |  Consistency (31)  |  Definition (238)  |  Existential (3)  |  External (62)  |  Far (158)  |  Import (5)  |  Long (778)  |  Mathematics (1395)  |  Merely (315)  |  Nature Of Mathematics (80)  |  Need (320)  |  Reason (766)  |  Reasoning (212)  |  Require (229)  |  Required (108)  |  Self (268)  |  Sense (785)  |  Test (221)  |  Validity (50)  |  Verification (32)

Mathematics in its widest signification is the development of all types of formal, necessary, deductive reasoning.
In Universal Algebra (1898), Preface, vi.
Science quotes on:  |  Definitions and Objects of Mathematics (33)  |  Development (441)  |  Formal (37)  |  Mathematics (1395)  |  Necessary (370)  |  Reason (766)  |  Reasoning (212)  |  Signification (2)  |  Type (171)  |  Wide (97)

Pure mathematics is a collection of hypothetical, deductive theories, each consisting of a definite system of primitive, undefined, concepts or symbols and primitive, unproved, but self-consistent assumptions (commonly called axioms) together with their logically deducible consequences following by rigidly deductive processes without appeal to intuition.
In 'Non-Euclidian Geometry of the Fourth Dimension', collected in Henry Parker Manning (ed.), The Fourth Dimension Simply Explained (1910), 58.
Science quotes on:  |  Appeal (46)  |  Assumption (96)  |  Axiom (65)  |  Call (781)  |  Collection (68)  |  Commonly (9)  |  Concept (242)  |  Consequence (220)  |  Consist (223)  |  Consistent (50)  |  Definite (114)  |  Definitions and Objects of Mathematics (33)  |  Follow (389)  |  Hypothetical (6)  |  Intuition (82)  |  Logic (311)  |  Mathematics (1395)  |  Primitive (79)  |  Process (439)  |  Pure (299)  |  Pure Mathematics (72)  |  Rigidly (4)  |  Self (268)  |  Self-Consistent (2)  |  Symbol (100)  |  System (545)  |  Theory (1015)  |  Together (392)  |  Undefined (3)  |  Unproved (2)

The distinctive Western character begins with the Greeks, who invented the habit of deductive reasoning and the science of geometry.
In 'Western Civilization', collected in In Praise of Idleness and Other Essays (1935), 161.
Science quotes on:  |  Begin (275)  |  Character (259)  |  Distinctive (25)  |  Geometry (271)  |  Greek (109)  |  Habit (174)  |  Invent (57)  |  Logic (311)  |  Reasoning (212)  |  Western (45)

The mathematician starts with a few propositions, the proof of which is so obvious that they are called self-evident, and the rest of his work consists of subtle deductions from them. The teaching of languages, at any rate as ordinarily practised, is of the same general nature authority and tradition furnish the data, and the mental operations are deductive.
In 'Scientific Education: Notes of an After-Dinner Speech' (Delivered to Liverpool Philomathic Society, Apr 1869), published in Macmillan’s Magazine (Jun 1869), 20, No. 116, 177. Collected in Lay Sermons, Addresses, and Reviews (1871), Chap 4, 66.
Science quotes on:  |  Authority (99)  |  Call (781)  |  Consist (223)  |  Data (162)  |  Deduction (90)  |  Evident (92)  |  Furnish (97)  |  General (521)  |  Language (308)  |  Mathematician (407)  |  Mental (179)  |  Nature (2017)  |  Obvious (128)  |  Operation (221)  |  Operations (107)  |  Practise (7)  |  Proof (304)  |  Proposition (126)  |  Rest (287)  |  Self (268)  |  Self-Evident (22)  |  Start (237)  |  Subtle (37)  |  Teach (299)  |  Teaching (190)  |  Tradition (76)  |  Work (1402)

The observed phenomena of meteorology and the well-established laws of physics are the two extremes of the science of meteorology between which we trace the connection of cause and effect; in so far as we can do this successfully meteorology becomes an exact deductive science.
In 'The Meteorological Work of the U.S. Signal Service, 1870 to 1891', U.S. Department of Agriculture, Weather Bureau, Bulletin No. 11, Report of the International Meteorological Congress, Chicago, Ill., August 21-24, 1893 (1894), 242.
Science quotes on:  |  Become (821)  |  Cause And Effect (21)  |  Connection (171)  |  Exact (75)  |  Extreme (78)  |  Law (913)  |  Meteorology (36)  |  Observe (179)  |  Phenomenon (334)  |  Physics (564)  |  Successful (134)  |  Trace (109)  |  Well-Established (6)

The science of optics, like every other physical science, has two different directions of progress, which have been called the ascending and the descending scale, the inductive and the deductive method, the way of analysis and of synthesis. In every physical science, we must ascend from facts to laws, by the way of induction and analysis; and we must descend from laws to consequences, by the deductive and synthetic way. We must gather and group appearances, until the scientific imagination discerns their hidden law, and unity arises from variety; and then from unity must reduce variety, and force the discovered law to utter its revelations of the future.
In On a General Method of Expressing the Paths of Light, & of the Planets, by the Coefficients of a Characteristic Function (1833), 7-8. [The spelling as “groupe” in the original text, has her been corrected to “group” to avoid an intrusive “sic”.]
Science quotes on:  |  Analysis (244)  |  Appearance (145)  |  Arise (162)  |  Ascend (30)  |  Ascent (7)  |  Call (781)  |  Consequence (220)  |  Descend (49)  |  Different (595)  |  Direction (185)  |  Discern (35)  |  Discover (571)  |  Fact (1257)  |  Facts (553)  |  Force (497)  |  Future (467)  |  Gather (76)  |  Group (83)  |  Hide (70)  |  Imagination (349)  |  Induction (81)  |  Inductive (20)  |  Law (913)  |  Method (531)  |  Must (1525)  |  Optics (24)  |  Other (2233)  |  Physical (518)  |  Physical Science (104)  |  Progress (492)  |  Reduce (100)  |  Revelation (51)  |  Scale (122)  |  Scientific (955)  |  Synthesis (58)  |  Synthetic (27)  |  Two (936)  |  Unity (81)  |  Utter (8)  |  Variety (138)  |  Way (1214)

The ultimate aim of those who are devoted to science is to penetrate beyond the phenomena observed on the surface to the ultimate causes, and to reduce the whole … to a simple deductive system of mechanics, in which the phenomena observed shall be shown to flow naturally from the few simple laws that underlie the structure of the universe.
In article, 'Meteorolgy', Encyclopaedia Britannica, (11th ed., 1911), Vol. 18, 281
Science quotes on:  |  Aim (175)  |  Cause (561)  |  Flow (89)  |  Mechanics (137)  |  Natural Law (46)  |  Observe (179)  |  Penetrate (68)  |  Phenomenon (334)  |  Reduce (100)  |  Show (353)  |  Simple (426)  |  Structure (365)  |  Surface (223)  |  System (545)  |  Ultimate (152)  |  Underlie (19)  |  Universe (900)  |  Whole (756)

The value of mathematical instruction as a preparation for those more difficult investigations, consists in the applicability not of its doctrines but of its methods. Mathematics will ever remain the past perfect type of the deductive method in general; and the applications of mathematics to the simpler branches of physics furnish the only school in which philosophers can effectually learn the most difficult and important of their art, the employment of the laws of simpler phenomena for explaining and predicting those of the more complex. These grounds are quite sufficient for deeming mathematical training an indispensable basis of real scientific education, and regarding with Plato, one who is … as wanting in one of the most essential qualifications for the successful cultivation of the higher branches of philosophy
In System of Logic, Bk. 3, chap. 24, sect. 9.
Science quotes on:  |  Applicability (7)  |  Application (257)  |  Art (680)  |  Basis (180)  |  Branch (155)  |  Complex (202)  |  Consist (223)  |  Cultivation (36)  |  Deem (7)  |  Difficult (263)  |  Doctrine (81)  |  Education (423)  |  Effectually (2)  |  Employment (34)  |  Essential (210)  |  Explain (334)  |  Furnish (97)  |  General (521)  |  Ground (222)  |  High (370)  |  Important (229)  |  Indispensable (31)  |  Instruction (101)  |  Investigation (250)  |  Law (913)  |  Learn (672)  |  Mathematics (1395)  |  Method (531)  |  More (2558)  |  Most (1728)  |  Past (355)  |  Perfect (223)  |  Phenomenon (334)  |  Philosopher (269)  |  Philosophy (409)  |  Physic (515)  |  Physics (564)  |  Plato (80)  |  Predict (86)  |  Preparation (60)  |  Qualification (15)  |  Real (159)  |  Regard (312)  |  Remain (355)  |  School (227)  |  Scientific (955)  |  Simple (426)  |  Successful (134)  |  Sufficient (133)  |  Training (92)  |  Type (171)  |  Value (393)  |  Value Of Mathematics (60)  |  Want (504)  |  Will (2350)


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.