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

Today in Science History - Quickie Quiz
Who said: “A people without children would face a hopeless future; a country without trees is almost as helpless.”
more quiz questions >>
Home > Category Index for Science Quotations > Category Index D > Category: Demonstrative

Demonstrative Quotes (14 quotes)

A demonstrative and convincing proof that an acid does consist of pointed parts is, that not only all acid salts do Crystallize into edges, but all Dissolutions of different things, caused by acid liquors, do assume this figure in their Crystallization; these Crystalls consist of points differing both in length and bigness from one another, and this diversity must be attributed to the keener or blunter edges of the different sorts of acids
A Course of Chymistry (1675), trans. W. Harris (1686), 24.
Science quotes on:  |  Acid (83)  |  All (4108)  |  Both (493)  |  Consist (223)  |  Crystal (68)  |  Crystallize (12)  |  Different (577)  |  Dissolution (11)  |  Diversity (73)  |  Do (1908)  |  Edge (47)  |  Figure (160)  |  Must (1526)  |  Point (580)  |  Proof (287)  |  Salt (46)  |  Thing (1915)

But Medicine is a demonstrative Science, and all its processes should be proved by established principles, and be based on positive inductions. That the proceedings of Medicine are not of this character, in to be attributed to the manner of its cultivation, and not to the nature of the Science itself.
Samuel Jackson, Principles of Medicine (1832). Quoted in Alva Curtis, A Fair Examination and Criticism of All the Medical Systems in Vogue (1855), 1.
Science quotes on:  |  All (4108)  |  Character (243)  |  Cultivation (35)  |  Induction (77)  |  Medicine (378)  |  Nature (1926)  |  Positive (94)  |  Principle (507)  |  Proceeding (39)  |  Science (3879)

But notwithstanding these Arguments are so convictive and demonstrative, its marvellous to see how some Popish Authors (Jesuites especially) strain their wits to defend their Pagan Master Aristotle his Principles. Bullialdus speaks of a Florentine Physitian, that all the Friends he had could ever perswade him once to view the Heavens through a Telescope, and he gave that reason for his refusal, because he was afraid that then his Eyes would make him stagger concerning the truth of Aristotle’s Principles, which he was resolved he would not call into question. It were well, if these Men had as great veneration for the Scripture as they have, for Aristotles (if indeed they be his) absurd Books de cζlo Sed de his satis.
(Indicating a belief that the Roman Catholic church impeded the development of modern science.)
Kometographia, Or a Discourse Concerning Comets (Boston 1684). Quoted in Michael Garibaldi Hall, The Last American Puritan: The Life of Increase Mather, 1639-1723 (1988), 167.
Science quotes on:  |   (2863)  |  Absurd (59)  |  All (4108)  |  Argument (138)  |  Aristotle (163)  |  Author (167)  |  Belief (578)  |  Book (392)  |  Call (769)  |  Catholic (15)  |  Church (56)  |  Development (422)  |  Eye (419)  |  Friend (168)  |  Great (1574)  |  Heaven (258)  |  Heavens (125)  |  Indeed (324)  |  Marvellous (25)  |  Master (178)  |  Modern (385)  |  Modern Science (52)  |  Principle (507)  |  Question (621)  |  Reason (744)  |  Refusal (22)  |  Religion (361)  |  Roman (36)  |  Science (3879)  |  See (1081)  |  Speak (232)  |  Telescope (98)  |  Through (849)  |  Truth (1057)  |  View (488)  |  Wit (59)

I would beg the wise and learned fathers (of the church) to consider with all diligence the difference which exists between matters of mere opinion and matters of demonstration. ... [I]t is not in the power of professors of the demonstrative sciences to alter their opinions at will, so as to be now of one way of thinking and now of another. ... [D]emonstrated conclusions about things in nature of the heavens, do not admit of being altered with the same ease as opinions to what is permissible or not, under a contract, mortgage, or bill of exchange.
Letter to Cristina di Lorena, Grand Duchess of Tuscany (the mother of his patron Cosmo), 1615. Quoted in Sedley Taylor, 'Galileo and Papal Infallibility' (Dec 1873), in Macmillan's Magazine: November 1873 to April 1874 (1874) Vol 29, 94.
Science quotes on:  |  All (4108)  |  Alter (62)  |  Altered (32)  |  Being (1278)  |  Church (56)  |  Conclusion (254)  |  Consider (416)  |  Contract (11)  |  Demonstration (113)  |  Difference (337)  |  Diligence (20)  |  Do (1908)  |  Exchange (37)  |  Exist (443)  |  Father (110)  |  Heaven (258)  |  Heavens (125)  |  Learn (629)  |  Learned (235)  |  Matter (798)  |  Mortgage (2)  |  Nature (1926)  |  Opinion (281)  |  Permissible (8)  |  Power (746)  |  Professor (128)  |  Religion (361)  |  Science (3879)  |  Thing (1915)  |  Thinking (414)  |  Way (1217)  |  Will (2355)  |  Wise (131)

If any human being earnestly desire to push on to new discoveries instead of just retaining and using the old; to win victories over Nature as a worker rather than over hostile critics as a disputant; to attain, in fact, clear and demonstrative knowlegde instead of attractive and probable theory; we invite him as a true son of Science to join our ranks.
Novum Organum (1620), 34, Preface.
Science quotes on:  |  Attain (125)  |  Attractive (23)  |  Being (1278)  |  Desire (204)  |  Discovery (780)  |  Fact (1210)  |  Human (1468)  |  Human Being (175)  |  Men Of Science (143)  |  Nature (1926)  |  New (1216)  |  Old (481)  |  Push (62)  |  Rank (67)  |  Science (3879)  |  Theory (970)  |  Win (52)

In the mathematical investigations I have usually employed such methods as present themselves naturally to a physicist. The pure mathematician will complain, and (it must be confessed) sometimes with justice, of deficient rigour. But to this question there are two sides. For, however important it may be to maintain a uniformly high standard in pure mathematics, the physicist may occasionally do well to rest content with arguments which are fairly satisfactory and conclusive from his point of view. To his mind, exercised in a different order of ideas, the more severe procedure of the pure mathematician may appear not more but less demonstrative. And further, in many cases of difficulty to insist upon the highest standard would mean the exclusion of the subject altogether in view of the space that would be required.
In Preface to second edition, The Theory of Sound (1894), Vol. 1, vii.
Science quotes on:  |  Appear (118)  |  Argument (138)  |  Complain (8)  |  Conclusive (11)  |  Confess (42)  |  Deficient (3)  |  Demonstrate (76)  |  Different (577)  |  Difficulty (196)  |  Do (1908)  |  Employ (113)  |  Exclusion (16)  |  High (362)  |  Idea (843)  |  Insist (20)  |  Investigation (230)  |  Justice (39)  |  Maintain (105)  |  Mathematics (1328)  |  Mean (809)  |  Method (505)  |  Methods (204)  |  Mind (1338)  |  More (2559)  |  Must (1526)  |  Order (632)  |  Physicist (259)  |  Point (580)  |  Point Of View (80)  |  Present (619)  |  Procedure (41)  |  Pure (291)  |  Pure Mathematics (67)  |  Question (621)  |  Required (108)  |  Rest (280)  |  Rigour (21)  |  Satisfactory (17)  |  Severe (16)  |  Side (233)  |  Space (500)  |  Standard (57)  |  Subject (521)  |  Themselves (433)  |  Two (937)  |  Usually (176)  |  View (488)  |  Will (2355)

In this manner the whole substance of our geometry is reduced to the definitions and axioms which we employ in our elementary reasonings; and in like manner we reduce the demonstrative truths of any other science to the definitions and axioms which we there employ.
In The Philosophy of the Inductive Sciences: Founded Upon Their History (1840), Vol. 1, 67.
Science quotes on:  |  Axiom (63)  |  Definition (221)  |  Demonstrate (76)  |  Elementary (96)  |  Employ (113)  |  Geometry (255)  |  Other (2236)  |  Reasoning (207)  |  Reduce (94)  |  Science (3879)  |  Substance (248)  |  Truth (1057)  |  Whole (738)

It is evidently equally foolish to accept probable reasoning from a mathematician and to demand from a rhetorician demonstrative proofs.
Aristotle
Nicomachean Ethics, 1094b, 25-7. In Jonathan Barnes (ed.), The Complete Works of Aristotle (1984), Vol. 2, 1730.
Science quotes on:  |  Accept (191)  |  Demand (123)  |  Equally (130)  |  Evidently (26)  |  Foolish (40)  |  Logic (287)  |  Mathematician (387)  |  Proof (287)  |  Reasoning (207)

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 (237)  |  All (4108)  |  Appear (118)  |  Approximation (31)  |  Ascribe (17)  |  Certain (550)  |  Certainty (174)  |  Character (243)  |  Conclusion (254)  |  Deductive (11)  |  Demonstration (113)  |  Evidence (248)  |  Exactly (13)  |  Exception (73)  |  Experience (467)  |  Formula (98)  |  General (511)  |  Hypothetical (5)  |  Indispensable (28)  |  Induction (77)  |  Inductive (20)  |  Inherent (42)  |  Nature Of Mathematics (80)  |  Peculiar (113)  |  Portion (84)  |  Science (3879)  |  Seldom (65)  |  Suppose (156)  |  Supposition (50)  |  True (212)  |  Truth (1057)  |  Virtue (109)

Mathematics, including not merely Arithmetic, Algebra, Geometry, and the higher Calculus, but also the applied Mathematics of Natural Philosophy, has a marked and peculiar method or character; it is by preeminence deductive or demonstrative, and exhibits in a nearly perfect form all the machinery belonging to this mode of obtaining truth. Laying down a very small number of first principles, either self-evident or requiring very little effort to prove them, it evolves a vast number of deductive truths and applications, by a procedure in the highest degree mathematical and systematic.
In Education as a Science (1879), 148.
Science quotes on:  |  Algebra (113)  |  All (4108)  |  Application (242)  |  Applied (177)  |  Applied Mathematics (15)  |  Arithmetic (136)  |  Belonging (37)  |  Calculus (65)  |  Character (243)  |  Deduction (82)  |  Degree (276)  |  Demonstration (113)  |  Down (456)  |  Effort (227)  |  Evident (91)  |  First (1283)  |  Form (959)  |  Geometry (255)  |  Little (707)  |  Machinery (56)  |  Marked (55)  |  Mathematics (1328)  |  Merely (316)  |  Method (505)  |  Natural (796)  |  Natural Philosophy (52)  |  Nearly (137)  |  Number (699)  |  Peculiar (113)  |  Perfect (216)  |  Philosophy (380)  |  Preeminence (3)  |  Principle (507)  |  Procedure (41)  |  Prove (250)  |  Self (267)  |  Self-Evident (21)  |  Small (477)  |  Systematic (57)  |  Truth (1057)  |  Vast (177)

Mechanical Notation ... I look upon it as one of the most important additions I have made to human knowledge. It has placed the construction of machinery in the rank of a demonstrative science. The day will arrive when no school of mechanical drawing will be thought complete without teaching it.
Passages From the Life of a Philosopher (1864), 452.
Science quotes on:  |  Addition (66)  |  Complete (204)  |  Computer (127)  |  Construction (112)  |  Drawing (56)  |  Human (1468)  |  Knowledge (1529)  |  Look (582)  |  Machinery (56)  |  Mechanical (140)  |  Most (1731)  |  Notation (27)  |  Rank (67)  |  School (219)  |  Science (3879)  |  Teaching (188)  |  Thought (953)  |  Will (2355)

The mathematician pays not the least regard either to testimony or conjecture, but deduces everything by demonstrative reasoning, from his definitions and axioms. Indeed, whatever is built upon conjecture, is improperly called science; for conjecture may beget opinion, but cannot produce knowledge.
In Essays on the Intellectual Powers of Man, Essay 1, chap. 3.
Science quotes on:  |  Axiom (63)  |  Beget (4)  |  Build (204)  |  Call (769)  |  Conjecture (49)  |  Deduce (25)  |  Definition (221)  |  Everything (476)  |  Indeed (324)  |  Knowledge (1529)  |  Least (75)  |  Mathematician (387)  |  Nature Of Mathematics (80)  |  Opinion (281)  |  Pay (43)  |  Produce (104)  |  Reason (744)  |  Reasoning (207)  |  Regard (305)  |  Science (3879)  |  Testimony (21)  |  Whatever (234)

What science can there be more noble, more excellent, more useful for men, more admirably high and demonstrative, than this of the mathematics?
In 'On the Usefulness of Mathematics', Works (1840), Vol. 2, 69.
Science quotes on:  |  Admirable (19)  |  Estimates of Mathematics (30)  |  Excellent (28)  |  High (362)  |  Mathematics (1328)  |  More (2559)  |  Noble (90)  |  Science (3879)  |  Useful (250)

[The] second fundamental rule of historical science may be thus simply expressed:—we should not wish to explain every thing. Historical tradition must never be abandoned in the philosophy of history—otherwise we lose all firm ground and footing. But historical tradition, ever so accurately conceived and carefully sifted, doth not always, especially in the early and primitive ages, bring with it a full and demonstrative certainty.
In Friedrich von Schlegel and James Burton Robertson (trans.), The Philosophy of History (1835), 12.
Science quotes on:  |  Abandon (68)  |  Age (499)  |  All (4108)  |  Carefully (65)  |  Certainty (174)  |  Early (185)  |  Everything (476)  |  Explain (322)  |  Explanation (234)  |  Express (186)  |  Firm (47)  |  Footing (2)  |  Fundamental (250)  |  Ground (217)  |  Historical (70)  |  History (673)  |  History Of Science (63)  |  Lose (159)  |  Must (1526)  |  Never (1087)  |  Philosophy (380)  |  Primitive (75)  |  Rule (294)  |  Science (3879)  |  Thing (1915)  |  Tradition (69)  |  Wish (212)


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 Einstein • Isaac Newton • Lord Kelvin • Charles Darwin • Srinivasa Ramanujan • Carl Sagan • Florence Nightingale • Thomas Edison • Aristotle • Marie Curie • Benjamin Franklin • Winston Churchill • Galileo Galilei • Sigmund Freud • Robert Bunsen • Louis Pasteur • Theodore Roosevelt • Abraham Lincoln • Ronald Reagan • Leonardo DaVinci • Michio Kaku • Karl Popper • Johann Goethe • Robert Oppenheimer • Charles Kettering  ... (more people)

Quotations about: • Atomic  Bomb • Biology • Chemistry • Deforestation • Engineering • Anatomy • Astronomy • Bacteria • Biochemistry • Botany • Conservation • Dinosaur • Environment • Fractal • Genetics • Geology • History of Science • Invention • Jupiter • Knowledge • Love • Mathematics • Measurement • Medicine • Natural Resource • Organic Chemistry • Physics • Physician • Quantum Theory • Research • Science and Art • Teacher • Technology • Universe • Volcano • Virus • Wind Power • Women Scientists • X-Rays • Youth • Zoology  ... (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.