It is often said that experiments should be made without preconceived ideas. That is impossible. Not only would it make every experiment fruitless, but even if we wished to do so, it could not be done. Every man has his own conception of the world, and this he cannot so easily lay aside. We must, example, use language, and our language is necessarily steeped in preconceived ideas. Only they are unconscious preconceived ideas, which are a thousand times the most dangerous of all.

Pure logic could never lead us to anything but tautologies; it can create nothing new; not from it alone can any science issue.

The aim of science is not things themselves, as the dogmatists in their simplicity imagine, but the relation between things.

[T]he different branches of Arithmetic - Ambition [G]eometry is not true, it is advantageous.

It is the harmony of the diverse parts, their symmetry, their happy balance; in a word it is all that introduces order, all that gives unity, that permits us to see clearly and to comprehend at once both the ensemble and the details.

Later generations will regard Mengenlehre (set theory) as a disease from which one has recovered.

Intuition is more important to discovery than logic.