Like all historical ideas that result in great developments, those in the new mathematics, the new natural science, and the new philosophy live in very diverse noetic modes in the consciousness of the persons who function as the bearers of their development: sometimes they strive forward like instincts, without these persons having any ability to give an account of where they are going; sometimes they are the results of a more or less clear realization, as plainly and simply grasped goals, possibly crystallizing into ever more precise goals through repeated consideration.