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Home > Dictionary of Science Quotations > Scientist Names Index F > Gottlob Frege Quotes

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Gottlob Frege
(8 Nov 1848 - 26 Jul 1925)

German mathematician and logician.


Science Quotes by Gottlob Frege (10 quotes)

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A scientific writer can scarcely encounter anything more undesirable than, after completing a work, to have one of the foundations shaken. I became aware of this situation through a letter from Mr. Bertrand Russell as the printing of this volume neared completion.
— Gottlob Frege
In Epilog, Grundgestze der Arithmetic (1903), Vol. 2, 253. Russell wrote in 1901, just as Frege was about to publish Volume 2 of his last major work. English translation by Webmaster using Google translate and online dictionaries, from the original German: “Einem wissenschaftlichen Schriftsteller kann kaum etwas Unerwόnschteres begegnen, als dass ihm nach Vollendung einer Arbeit eine der Grundlagen seines Baues erschόttert wird. In diese Lage wurde ich durch einen Brief des Herrn Bertrand Russell versetzt, als der Druck dieses Bandes sich seinem Ende nδherte.” The translation in John E. Hopcroft, 'Turing Machines', Scientific American (May 1984), 250, No. 5, 95, gives: “A scientist can hardly meet with anything more undesirable than to have the foundations give way just as the work is finished. I was put in this position by a letter from Mr. Bertrand Russell when the work was nearly through the press.”
Science quotes on:  |  Completion (22)  |  Encounter (22)  |  Finish (59)  |  Foundation (173)  |  Letter (109)  |  More (2559)  |  Printing (23)  |  Bertrand Russell (184)  |  Scarcely (74)  |  Scientific (940)  |  Shaken (2)  |  Situation (113)  |  Through (849)  |  Undesirable (3)  |  Work (1351)  |  Writer (86)

Every good mathematician is at least half a philosopher, and every good philosopher at least half a mathematician.
— Gottlob Frege
Quoted, without citation, in 'Gottlob Frege', The New Encyclopedia Britannica (1992), Vol. 4, 968. If you know a primary source, please contact Webmaster.
Science quotes on:  |  Good (889)  |  Half (56)  |  Least (75)  |  Mathematician (389)  |  Philosopher (259)

I compare arithmetic with a tree that unfolds upwards in a multitude of techniques and theorems while the root drives into the depths.
— Gottlob Frege
Grundgesetze der Arithmetik (1893), xiii, trans. Ivor Grattan-Guinness.
Science quotes on:  |  Arithmetic (139)  |  Compare (70)  |  Depth (94)  |  Multitude (47)  |  Root (120)  |  Technique (80)  |  Theorem (112)  |  Tree (246)  |  Upward (43)

It really is worth the trouble to invent a new symbol if we can thus remove not a few logical difficulties and ensure the rigour of the proofs. But many mathematicians seem to have so little feeling for logical purity and accuracy that they will use a word to mean three or four different things, sooner than make the frightful decision to invent a new word.
— Gottlob Frege
Grundgesetz der Arithmetik(1893), Vol. 2, Section 60, In P. Greach and M. Black (eds., Translations from the Philosophical Writings of Gottlob Frege (1952), 144.
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Not everything is an idea. Otherwise psychology would contain all the sciences within it or at least it would be the highest judge over all the sciences. Otherwise psychology would rule over logic and mathematics. But nothing would be a greater misunderstanding of mathematics than its subordination to psychology.
— Gottlob Frege
In Elmer Daniel Klemke, Essays on Frege (1968), 531.
Science quotes on:  |  All (4107)  |  Everything (476)  |  Greater (288)  |  Idea (845)  |  Judge (108)  |  Logic (287)  |  Mathematics (1333)  |  Misunderstanding (12)  |  Nothing (969)  |  Psychology (154)  |  Rule (295)  |  Science (3880)  |  Subordination (5)

Strictly speaking, it is really scandalous that science has not yet clarified the nature of number. It might be excusable that there is still no generally accepted definition of number, if at least there were general agreement on the matter itself. However, science has not even decided on whether number is an assemblage of things, or a figure drawn on the blackboard by the hand of man; whether it is something psychical, about whose generation psychology must give information, or whether it is a logical structure; whether it is created and can vanish, or whether it is eternal. It is not known whether the propositions of arithmetic deal with those structures composed of calcium carbonate [chalk] or with non-physical entities. There is as little agreement in this matter as there is regarding the meaning of the word “equal” and the equality sign. Therefore, science does not know the thought content which is attached to its propositions; it does not know what it deals with; it is completely in the dark regarding their proper nature. Isn’t this scandalous?
— Gottlob Frege
From opening paragraph of 'Vorwort', άber die Zahlen des Herrn H. Schubert (1899), iii. ('Foreword', On the Numbers of Mr. H. Schubert). Translated by Theodore J. Benac in Friedrich Waismann, Introduction to Mathematical Thinking: The Formation of Concepts in Modern Mathematics (1959, 2003), 107. Webmaster added “[chalk]”.
Science quotes on:  |  Accept (192)  |  Agreement (53)  |  Arithmetic (139)  |  Assemblage (17)  |  Attach (56)  |  Attached (36)  |  Blackboard (11)  |  Calcium (7)  |  Calcium Carbonate (2)  |  Chalk (8)  |  Clarify (3)  |  Completely (135)  |  Compose (17)  |  Content (70)  |  Create (235)  |  Dark (140)  |  Deal (188)  |  Decide (44)  |  Definition (224)  |  Draw (137)  |  Entity (35)  |  Equal (84)  |  Equality (31)  |  Eternal (111)  |  Figure (160)  |  General (511)  |  Generation (242)  |  Information (166)  |  Know (1519)  |  Known (454)  |  Little (708)  |  Logic (287)  |  Man (2249)  |  Matter (801)  |  Meaning (235)  |  Must (1526)  |  Nature (1928)  |  Number (701)  |  Physical (508)  |  Proper (145)  |  Proposition (123)  |  Psychology (154)  |  Scandal (5)  |  Science (3880)  |  Sign (58)  |  Something (719)  |  Speaking (119)  |  Still (613)  |  Structure (346)  |  Thing (1915)  |  Thought (954)  |  Vanish (19)  |  Word (622)

The aim of scientific work is truth. While we internally recognise something as true, we judge, and while we utter judgements, we assert.
— Gottlob Frege
In Manuscripts 2 (after 1879). As cited and translated by Ivor Grattan-Guinness in The Search for Mathematical Roots, 1870-1940 (2011), 177.
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The work of science does not consist of creation but of the discovery of true thoughts.
— Gottlob Frege
From the first chapter of an unfinished book, The Thought: A Logical Inquiry (1918), collected in Arthur Sullivan (ed.), Logicism and the Philosophy of Language: Selections from Frege and Russell (2003), 215.
Science quotes on:  |  Consist (223)  |  Creation (329)  |  Discovery (785)  |  Science (3880)  |  Thought (954)  |  True (214)  |  Work (1351)

There is more danger of numerical sequences continued indefinitely than of trees growing up to heaven. Each will some time reach its greatest height.
— Gottlob Frege
Grundgesetz der Arithmetik(1893), Vol. 2, Section 60, In P. Greach and M. Black (eds., Translations from the Philosophical Writings of Gottlob Frege (1952), 204.
Science quotes on:  |  Danger (116)  |  Greatest (329)  |  Growing (98)  |  Heaven (258)  |  More (2559)  |  Number (701)  |  Numerical (39)  |  Reach (281)  |  Sequence (68)  |  Series (149)  |  Time (1877)  |  Tree (246)  |  Will (2354)

“Facts, facts, facts,” cries the scientist if he wants to emphasize the necessity of a firm foundation for science. What is a fact? A fact is a thought that is true. But the scientist will surely not recognize something which depends on men's varying states of mind to be the firm foundation of science.
— Gottlob Frege
From the first chapter of an unfinished book, The Thought: A Logical Inquiry (1918), collected in Arthur Sullivan (ed.), Logicism and the Philosophy of Language: Selections from Frege and Russell (2003), 215.
Science quotes on:  |  Depend (228)  |  Emphasize (23)  |  Fact (1212)  |  Facts (553)  |  Firm (47)  |  Foundation (173)  |  Mind (1339)  |  Necessity (191)  |  Recognize (125)  |  Science (3880)  |  Scientist (825)  |  Something (719)  |  State (491)  |  Surely (101)  |  Thought (954)  |  Truth (1062)  |  Want (497)  |  Will (2354)



Quotes by others about Gottlob Frege (1)

Since the examination of consistency is a task that cannot be avoided, it appears necessary to axiomatize logic itself and to prove that number theory and set theory are only parts of logic. This method was prepared long ago (not least by Frege’s profound investigations); it has been most successfully explained by the acute mathematician and logician Russell. One could regard the completion of this magnificent Russellian enterprise of the axiomatization of logic as the crowning achievement of the work of axiomatization as a whole.
Address (11 Sep 1917), 'Axiomatisches Denken' delivered before the Swiss Mathematical Society in Zόrich. Translated by Ewald as 'Axiomatic Thought', (1918), in William Bragg Ewald, From Kant to Hilbert (1996), Vol. 2, 1113.
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See also:
  • 8 Nov - short biography, births, deaths and events on date of Frege's birth.
  • Gottlob Frege - context of quote “I compare arithmetic with a tree” - Medium image (500 x 250 px)
  • Gottlob Frege - context of quote “I compare arithmetic with a tree” - Large image (800 x 400 px)
  • Gottlob Frege - context of quote “The aim of scientific work is truth” - Medium image (500 x 250 px)
  • Gottlob Frege - context of quote “The aim of scientific work is truth” - Large image (800 x 400 px)
  • The Frege Reader, by Gottlob Frege and Michael Beaney (ed.). - book suggestion.
  • Booklist for Gottlob Frege.

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