I compare arithmetic with a tree that unfolds upwards in a multitude of techniques and theorems while the root drives into the depths.

Arithmetic has began to totter.

The aim of scientific work is truth. While we internally recognise something as true, we judge, and while we utter judgements, we assert.

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.

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.

I compare arithmetic with a tree that unfolds upwards in a multitude of techniques and theorems while the root drives into the depths.

'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.