For scholars and laymen alike it is not philosophy but active experience in mathematics itself that can alone answer the question: What is mathematics?
It has generally been assumed that of two opposing systems of philosophy, e.g., realism and idealism, one only can be true and one must be false; and so philosophers have been hopelessly divided on the question, which is the true one.
A creative element is surely present in all great systems, and it does not seem possible that all sympathy or fundamental attitudes of will can be entirely eliminated from any human philosophy.
In thus pointing out certain respects in which philosophy resembles literature more than science, I do not mean, of course, to imply that it would be well for philosophy if it ceased to aim at scientific rigor.
