never be created by thought nor derived from it but only from the external world. Hereupon the entire matter undergoes a change. We see that principles are not the starting point of investigation but the conclusion of it, they are not to be applied to nature and history but are derived from them. Nature and Humanity are not steered by principles, but principles are, on the other hand, only correct so far as they correspond with nature and history. That is just the materialistic conception of the matter, and the opposite, that of Herr Duehring is the idealistic conception, it turns things upside down and constructs a real world out of the world of thought, arrangements, plans and categories existing from everlasting before the world, just like Hegelianism.
As a matter of fact, we prefer Hegel's "Encyclopedia," with all its fever phantoms, to the "final truths of the last instance" of Herr Duehring. In the first place, according to Herr Duehring we have the general scheme of the universe which by Hegel is called "logic." Then according to both of them we have the application of this scheme to nature by means of the logical categories, the philosophy of nature, and finally their application to Humanity, by what Hegel calls "the Philosophy of the Spirit." "The inner logical arrangement" of Duehring's scheme brings us therefore logically back to Hegel's "Encyclopedia" from which it is taken with a fidelity which would move that Wandering Jew of the Hegelian school, Professor Michelet of Berlin, to tears.
Such a result follows if one takes it for granted that "consciousness," "thought," is something which has existed from the beginning in contradistinction to nature. It would then be of the greatest importance to bring consciousness and Nature, thought and existence, into harmony, to harmonise the laws of thought and the laws of Nature. But one enquires further what are thought and consciousness and whence do they originate. It is consequently discovered that they are products of the brain of man, and that Humanity is itself a product of nature which has developed in and along with its environment; wherefore it becomes self-apparent that the products of the brain of man being themselves, in the last instance, natural products, do not contradict all the rest of Nature but correspond with it.
But Herr Duehring cannot allow so simple a treatment of the subject. He thinks not only in the name of Humanity which would be quite a large affair, but in the name of the conscious and thinking beings of the whole universe. Indeed, it would be "a degradation of the foundation concepts of knowledge and consciousness if one should wish to exclude or even to throw suspicion upon their sovereign value and undoubted claims to truth by means of the epithet 'human.'" In order that there may be no suspicion that upon some heavenly body or other twice two may make five, Herr Duehring does not venture to call thought a human attribute, and therefore he is obliged to separate it from the only true foundation on which it rests, as far as we are concerned, namely, from man and nature, and thereby falls, without any possibility of getting out, into an "ideology" which causes him to play baby to Hegel. It is self-evident that one cannot build materialistic doctrines on foundations so ideological. We shall see later that Herr Duehring is compelled to push nature to the front as a conscious agent and, therefore, as that, which people in plain English call God.
Indeed, our philosopher had other motives in shifting the foundation of reality from the material world to that of thought. The knowledge of this general scheme of the universe, of these formal principles of being is just the foundation of Herr Duehring's philosophy. If we derive the scheme of the universe not from our own brain, but merely by means of our own brain, from the material world, we need no philosophy, but simply knowledge of the world and what occurs in it, and the results of this knowledge likewise do not constitute a philosophy, but positive science. In such a case, however, Herr Duehring's entire book would have been love's labor lost.
Further, if no philosophy, as such, is longer required there is no longer the necessity of any philosophy of nature even. The view that all the phenomena of nature stand in systematic mutual relations compels science to prove this systematic interconnection in all respects, in single cases as well as in the entirety. But an appropriate creative, scientific representation of this mutual connection in such a way as to show the composition of an exact thought-picture of the system of the universe in which we live remains not only for us but for all time an impossibility. Should such a final conclusive system of the interconnection of the various activities of the universe, physical, as well as intellectual and historical, ever be brought to completion at any point of time in the history of the human race, human knowledge would forthwith come to an end and future historical progress would be cut off from the very moment in which society was directed in accordance with the system, which would be an absurdity, mere nonsense.
Man is therefore confronted by a contradiction, on the one hand he is obliged to study the interconnections of the world-system exhaustively, and, on the other hand, he is unable to fully accomplish the task either as regards himself or as regards the system of nature. This contradiction, however, does not consist solely in the nature of the two factors World and Man; it is the main lever also of universal intellectual progress and is solved every day and for ever in an endless progressive development of humanity, just as mathematical problems find their solution in an endless progression of a recurring decimal. As a matter of fact also every concept of the universe is subject to objective limitations owing to the conditions of historical knowledge, and subjectively in addition owing to the physical and mental make up of the author of the concept. But Herr Duehring exhibits a mode of thought which is confined in its application to a limited and subjective idea of the universe. We saw earlier that he was omnipresent, in all possible forms of the universe, now we see that he is omniscient. He has solved the final problems of science and has nailed up tight all future knowledge.
Herr Duehring considers that he can, as with the fundamental forms of existence, produce aprioristically by means of his own cogitations the whole of pure mathematics without making any use of the experience which is afforded us in the objective world. In pure mathematics the understanding is engaged "in its own free creations and imaginations"; the concepts of number and form are "self-sufficient objects proceeding from themselves" and so have "a value independent of individual experience and actual objective reality."
That pure mathematics has a significance independent of particular individual experience is quite true as are also the established facts of all the sciences and indeed of all facts. The magnetic poles, the formation of water from oxygen and hydrogen, the fact that Hegel is dead and that Herr Duehring is alive, are facts independent of my experience or that of any other single individual, and will be independent of that of Herr Duehring himself, as soon as he shall sleep the sleep of the just. But in pure mathematics the mind is not by any means engaged with its own creations and imaginings. The concepts of number and form have only come to us by the way of the real world. The ten fingers on which men count and thereby performed the first arithmetical calculations are anything but a free creation of the mind. To count not only requires objects capable of being counted but the ability, when these objects are regarded, of subtracting all qualities from them except number and this ability is the product of long historical development of actual experience. The concept form is, like that of number, derived exclusively from the external world and is not a purely mental product. To it things possessed of shape were necessary and these shapes men compared until the concept form was arrived at. Pure mathematics considers the shapes and quantities of things in the actual world, very real objects. The fact that these objects appear in a very abstract form only superficially conceals their origin in the world of external nature. In order to understand these forms and qualities in their purity it is necessary to separate them from their content and thus one gets the point, without dimensions, the line, without breadth and thickness, a and b, x and y, constants and variables, and we finally first arrive at independent creations of the imagination and intellect, imaginary magnitudes. Also the apparent derivation of mathematical magnitudes from each other does not prove their aprioristic origin, but only their rational interconnection. Before one attained the concept that the form of a cylinder was derived from the revolution of a rectangle round one of its sides, he must have examined a number of rectangles and cylinders even if of imperfect form. Like all sciences, mathematics has sprung from the necessities of men, from the measurement of land and the content of vessels, from the calculation of time and mechanics. But, as in every department of thought, at a certain stage of development, laws are abstracted from the actual phenomena,
