The thought: A logical inquiry

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

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

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.

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

Arithmetic has began to totter.

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.