But to what purpose is all this prolixity? After Herr Duehring has enthusiastically proclaimed the independence of pure mathematics of the world of experience, their apriorism, their connection with free creation and imagination, he says "it will be readily seen that these mathematical elements (number, magnitude, time, space, geometric progression), are therefore ideal forms with relation to absolute magnitudes and therefore something quite empiric, no matter to what species they belong." But "mathematical general notions are, apart from experience, nevertheless capable of sufficient characterization," which latter proceeds, more or less, from each abstraction, but does not by any means prove that it is not deprived from the actual. In the scheme of the universe of our author pure mathematics originated in pure thought, in his philosophy of nature it is derived from the external world and then set apart from it. What are we then to believe? _The Scheme of the Universe._ "All-comprehending existence is sole. It is sufficient to itself and has nothing above or below it. To associate a second existence with it would be to make it just what it is not, a part of a constituent or all-embracing whole. When we conceive of our idea of soleness as a frame there is nothing which can enter into this, nothing which retains twofoldness can enter into this concept of unity. But nothing can alienate itself from this concept of unity. The essence of all thought consists in uniting the elements of consciousness in a unity. The indivisible concept of the universe has arisen by comprehending everything, and the universe, as the word signifies, is recognised as something in which everything is united into one unity." So far Herr Duehring is quoted. The mathematical method, "Everything must be decided on simple axiomatic foundation principles, just as if it were concerned with the simple principles of mathematics," this method is for the first time here applied.