Gottlob Frege: Arithmetic

Gottlob Frege was mathematician, logician, philosopher. Explore interesting quotes on arithmetic.
Gottlob Frege: 44 quotes14 likes

“If I compare arithmetic with a tree that unfolds upward into a multitude of techniques and theorems while its root drives into the depths, then it seems to me that the impetus of the root.”

Gottlob Frege

Gottlob Frege, Montgomery Furth (1964). The Basic Laws of Arithmetic: Exposition of the System. p. 10

“This ideography is a "formula language", that is, a lingua characterica, a language written with special symbols, "for pure thought", that is, free from rhetorical embellishments, "modeled upon that of arithmetic", that is, constructed from specific symbols that are manipulated according to definite rules.”

Gottlob Frege

paraphrasing Frege's Begriffsschrift, a formula language, modeled upon that of arithmetic, for pure thought (1879) in Jean Van Heijenoort ed., in From Frege to Gödel: A Source Book in Mathematical Logic, 1879-1931 (1967)

“I hope I may claim in the present work to have made it probable that the laws of arithmetic are analytic judgments and consequently a priori. Arithmetic thus becomes simply a development of logic, and every proposition of arithmetic a law of logic, albeit a derivative one. To apply arithmetic in the physical sciences is to bring logic to bear on observed facts; calculation becomes deduction.”

Gottlob Frege book The Foundations of Arithmetic

Gottlob Frege (1950 [1884]). The Foundations of Arithmetic. p. 99.

“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 arithmetic.”

Gottlob Frege

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

“I hope I may claim in the present work to have made it probable that the laws of arithmetic are analytic judgments and consequently a priori.”

Gottlob Frege book The Foundations of Arithmetic

Arithmetic thus becomes simply a development of logic, and every proposition of arithmetic a law of logic, albeit a derivative one. To apply arithmetic in the physical sciences is to bring logic to bear on observed facts; calculation becomes deduction.
Gottlob Frege (1950 [1884]). The Foundations of Arithmetic. p. 99.