which may perhaps conduct us to the real, conception. " The Universe or world is the reality of mathe-
matical ideas, or, in simpler language, of mathematics.
"Philosophy is the recognition of mathematical ideas as constituting the world, or the repetition of the origin of the world in consciousness.
"Spirit is the motion of mathematical ideas ; Nature their manifestation.
"The philosophy of Spirit is the representation of the movements of ideas in consciousness.
"The philosophy of Nature (is) that of the phenomena or manifestations of ideas in consciousness.
"The whole of philosophy depends upon the demonstration of the parallelism that exists between the activities of Nature and of Spirit.
"Science is a series of necessarily interdependent and consecutive propositions, which rest upon a certain fundamental proposition.
"The mathematical is certain ; and by virtue of this character it stands also alone. Mathematics is the only true science. . . . The fundamental propositions of mathematics must, therefore, be fundamental propositions for all other sciences also.
"Mathematics is, however, a science of mere
