Gottlob Frege Quotes

• Every good mathematician is at least half a philosopher, and every good philosopher is at least half a mathematician.

  Gottlob Frege

  Philosophy, Science, Analysis

  Attributed in "Mathematics as grammar: 'Grammar' in Wittgenstein's philosophy of mathematics during the Middle Period" by A. A. B. Aspeitia, Indiana University, (p. 25), 2000.

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• 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

  Science, Judging, Judgement

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• '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

  Science, Men, Mind

  "The thought: A logical inquiry" by Gottlob Frege in "Readings in the Philosophy of Language" edited by Peter Ludlow, (p. 27), 1997.

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• The thought: A logical inquiry

  Gottlob Frege

  Inquiry, Logical

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• ...one can hardly deny that mankind has a common store of thoughts which is transmitted from one generation to another.

  Gottlob Frege

  Knowledge, Mind, Generations

  Gottlob Frege (1952). “Translations from the Philosophical Writings of Gottlob Frege”

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• Having visual impressions is, of course, necessary for seeing things, but it is not sufficient. What must be added is not anything sensible. And it is precisely this that unlocks the outer world for us; for without this non-sensible something, each of us would remain locked up in his inner world.

  Gottlob Frege

  World, Impression, Locked Up

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• 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

  Roots, Tree, Technique

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• 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.

  Gottlob Frege

  Math, Giving, Foundation

  Note in the appendix of "Grundlagen der Arithmetik" (Vol. 2), after Frege had received a letter of Bertrand Russell in which Russell had explained his discovery of, what is now known as, Russell's paradox, 1903.

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• 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

  Growing Up, Tree, Heaven

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• 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

  Mean, Science, Decision

  Gottlob Frege (1952). “Translations from the Philosophical Writings of Gottlob Frege”

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• It is possible, of course, to operate with figures mechanically, just as it is possible to speak like a parrot: but that hardly deserves the names of thought. It only becomes possible at all after the mathematical notation has, as a result of genuine thought, been so developed that it does the thinking for us, so to speak.

  Gottlob Frege

  Knowledge, Thinking, Names

  Gottlob Frege, J. L. Austin (1980). “The Foundations of Arithmetic: A Logico-Mathematical Enquiry Into the Concept of Number”, p.4, Northwestern University Press

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• Your discovery of the contradiction caused me the greatest surprise and, I would almost say, consternation, since it has shaken the basis on which I intended to build my arithmetic.

  Gottlob Frege

  Loss, Discovery, Serious

  "From Frege to Godel: A Source Book in Mathematical Logic, 1879-1931". Book edited by J. van Heijenoort, "Letter to Bertrand Russel" (1902), 1967.

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• Arithmetic has began to totter.

  Gottlob Frege

  Arithmetic

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• What are numbers? What is the nature of arithmetical truth?

  Gottlob Frege

  Numbers

  18 Copy quote

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