Gottlob Frege
“I compare arithmetic with a tree”

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Gottlob Frege quote I compare arithmetic with a tree

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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

Translated from Grundgesetze der Arithmetik (1893).

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This is a translation from the original text published in 1893 by the German mathematician, Gottlob Frege, Grundgesetze der Arithmetik. A good context for this quote is given by Michael H. McCarthy:

“Frege’s philosophic career began with his intensive study of the foundations of arithmetic. In the course of his research, he developed a complex of logical beliefs and analytic methods strongly divergent from those of his predecessors and contemporaries. He was driven to philosophical reflection because of his discontent with the theoretical foundations of arithmetic. The mathematicians of his day were more intent on developing techniques and proliferating theorems than with disclosing the underlying conceptual structure of their science.

‘If I compare arithmetic with a tree that unfolds upwards into a multitude of techniques and theorems while its roots drive into the depths, then it seems to me that the impetus of the root, at least in Germany, is rather weak.’

When Frege spoke of the roots of arithmetic he referred to its primitive axioms, elementary concepts, and rules of inference, the logical ground on which axiomization might proceed.”

Quoted from Michael H. McCarthy, The Crisis of Philosophy: Emerson in the Twenty-First Century (1990), 45-46. (source)

Gottlob Frege quote The aim of scientific work is truth

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See also:

Science Quotes by Gottlob Frege.
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” - 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.

Nature bears long with those who wrong her. She is patient under abuse. But when abuse has gone too far, when the time of reckoning finally comes, she is equally slow to be appeased and to turn away her wrath. (1882) -- Nathaniel Egleston, who was writing then about deforestation, but speaks equally well about the danger of climate change today.

Carl Sagan: 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) ...(more by Sagan)

Albert Einstein: I used to wonder how it comes about that the electron is negative. Negative-positive—these are perfectly symmetric in physics. There is no reason whatever to prefer one to the other. Then why is the electron negative? I thought about this for a long time and at last all I could think was “It won the fight!” ...(more by Einstein)

Richard Feynman: It is the facts that matter, not the proofs. Physics can progress without the proofs, but we can't go on without the facts ... if the facts are right, then the proofs are a matter of playing around with the algebra correctly. ...(more by Feynman)