The UN is not just a product of do-gooders. It is harshly real. The day will come when men will see the UN and what it means clearly. Everything will be all right — you know when? When people, just people, stop thinking of the United Nations as a weird Picasso abstraction, and see it as a drawing they made themselves.
The reliance on the abstract is thus not a result of an over-estimation but rather of an insight into the limited powers of our reason. It is the over-estimation of the powers of reason which leads to the revolt against the submission to abstract rules. Constructivist rationalism rejects the demand for this discipline of reason because it deceives itself that reason can directly master all the particulars; and it is thereby led to a preference for the concrete over the abstract, the particular over the general, because its adherents do not realize how much they thereby limit the span of true control by reason. The hubris of reason manifests itself in those who believe that they can dispense with abstraction and achieve a full mastery of the concrete and thus positively master the social process.
Denotation by means of sounds and markings is a remarkable abstraction. Three letters designate God for me; several lines a million things. How easy becomes the manipulation of the universe here, how evident the concentration of the intellectual world! Language is the dynamics of the spiritual realm. One word of command moves armies; the word Liberty entire nations.
I discovered the works of Euler and my perception of the nature of mathematics underwent a dramatic transformation. I was de-Bourbakized, stopped believing in sets, and was expelled from the Cantorianparadise. I still believe in abstraction, but now I know that one ends with abstraction, not starts with it. I learned that one has to adapt abstractions to reality and not the other way around. Mathematics stopped being a science of theories but reappeared to me as a science of numbers and shapes.