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 … - Gottlob Frege

Ein Philosoph, der keine Beziehung zur Geometrie hat, ist nur ein halber Philosoph, und ein Mathematiker, der keine philosophische Ader hat, ist nur ein halber Mathematiker.

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.

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.