What he is dealing with are therefore principles, formal tenets derived from thought and not from the external world, which are to be applied to nature and the realm of man, and to which therefore nature and man have to conform. But whence does thought obtain these principles? From itself? No, for Herr D hring himself says: the realm of pure thought is limited to logical schemata and mathematical forms {42} (the latter, moreover, as we shall see, is wrong). Logical schemata can only relate to forms of thought; but what we are dealing with here is solely forms of being, of the external world, and these forms can never be created and derived by thought out of itself, but only from the external world. But with this the whole relationship is inverted: the principles are not the starting-point of the investigation, but its final result; they are not applied to nature and human history, but abstracted from them, it is not nature and the realm of man which conform to these principles, but the principles are only valid in so far as they are in conformity with nature and history. That is the only materialist conception of the matter, and Herr D hring's contrary conception is idealistic, makes things stand completely on their heads, and fashions the real world out of ideas, out of schemata, schemes or categories existing somewhere before the world, from eternity just like a Hegel. In fact, let us compare Hegel s Encyclopaedia  and all its delirious fantasies with Herr D hring s final and ultimate truths. With Herr D hring we have in the first place general world schematism, which Hegel calls Logic. Then with both of them we have the application of these schemata or logical categories to nature: the philosophy of nature; and finally their application to the realm of man, which Hegel calls the philosophy of mind. The inner logical sequence of the D hring succession therefore leads us quite naturally {D. Ph. 15} back to Hegel s Encyclopaedia, from which it has been taken with a loyalty which would move that wandering Jew of the Hegelian school, Professor Michelet of Berlin, to tears.  That is what comes of accepting consciousness , thought , quite naturalistically, as something given, something opposed from the outset to being, to nature. If that were so, it must seem extremely strange that consciousness and nature, thinking and being, the laws of thought and the laws of nature, should correspond so closely. But if the further question is raised what thought and consciousness really are and where they come from, it becomes apparent that they are products of the human brain and that man himself is a product of nature, which has developed in and along with its environment; hence it is self-evident that the products of the human brain, being in the last analysis also products of nature, do not contradict the rest of nature's interconnections but are in correspondence with them.  But Herr D hring cannot permit himself such a simple treatment of the subject. He thinks not only in the name of humanity in itself no small achievement but in the name of the conscious and reasoning beings on all celestial bodies. Indeed, it would be It goes without saying that no materialist doctrine can be founded on such an ideological basis. Later on we shall see that Herr D hring is forced more than once to endow nature surreptitiously with conscious activity, with what in plain language is called God. However, our philosopher of reality had also other motives for shifting the basis of all reality from the real world to the world of thought. The science of this general world schematism, of these formal principles of being, is precisely the foundation of Herr D hring's philosophy. If we deduce world schematism not from our minds, but only through our minds from the real world, if we deduce principles of being from what is, we need no philosophy for this purpose, but positive knowledge of the world and of what happens in it; and what this yields is also not philosophy, but positive science. In that case, however, Herr D hring's whole volume would be nothing but love's labour lost. Further: if no philosophy as such is any longer required, then also there is no more need of any system, not even of any natural system of philosophy. The perception that all the processes of nature are systematically connected drives science on to prove this systematic connection throughout, both in general and in particular. But an adequate, exhaustive scientific exposition of this interconnection, the formation of an exact mental image of the world system in which we live, is impossible for us, and will always remain impossible. If at any time in the development of mankind such a final, conclusive system of the interconnections within the world physical as well as mental and historical were brought about, this would mean that human knowledge had reached its limit, and, from the moment when society had been brought into accord with that system, further historical development would be cut short which would be an absurd idea, sheer nonsense. Mankind therefore finds itself faced with a contradiction: on the one hand, it has to gain an exhaustive knowledge of the world system in all its interrelations; and on the other hand, because of the nature both of men and of the world system, this task can never be completely fulfilled. But this contradiction lies not only in the nature of the two factors the world, and man it is also the main lever of all intellectual advance, and finds its solution continuously, day by day, in the endless progressive development of humanity, just as for example mathematical problems find their solution in an infinite series or continued fractions. Each mental image of the world system is and remains in actual fact limited, objectively by the historical conditions and subjectively by the physical and mental constitution of its originator. But Herr D hring explains in advance that his mode of reasoning is such that it excludes any tendency to a subjectively limited conception of the world. We saw above that he was omnipresent on all possible celestial bodies. We now see that he is also omniscient. He has solved the ultimate problems of science and thus nailed boards across the future of all science. As with the basic forms of being, so also with the whole of pure mathematics: Herr D hring thinks that he can produce it a priori that is, without making use of the experience offered us by the external world, can construct it in his head. But just as Herr D hring imagines that, out of the axioms of mathematics, Mathematical axioms are expressions of the scantiest thought-content, which mathematics is obliged to borrow from logic. They can be reduced to two: 1) The whole is greater than its part. This statement is pure tautology, as the quantitatively conceived idea part is from the outset definitely related to the idea whole , and in fact in such a way that part simply means that the quantitative whole consists of several quantitative parts . In stating this explicitly, the so-called axiom does not take us a step further. This tautology can even in a way be proved by saying: a whole is that which consists of several parts; a part is that of which several make a whole; hence the part is less than the whole in which the inanity of repetition brings out even more clearly the inanity of content. 2) If two quantities are equal to a third, they are equal to each other. This statement, as Hegel has already shown, is a conclusion, the correctness of which is vouched for by logic, and which is therefore proved, although outside of pure mathematics. The remaining axioms relating to equality and inequality are merely logical extensions of this conclusion. These meagre principles do not cut much ice, either in mathematics or anywhere else. In order to get any further, we are obliged to bring in real relations, relations and space forms which are taken from real bodies. The ideas of lines, planes, angles, polygons, cubes, spheres, etc., are all taken from reality, and it requires a pretty good portion of naive ideology to believe the mathematicians that the first line came into existence through the movement of a point in space, the first plane through the movement of a line, the first solid through the movement of a plane, and so on. Even language rebels against such a conception. A mathematical figure of three dimensions is called a solid body, corpus solidum, hence, in Latin, even a tangible object; it therefore has a name derived from sturdy reality and by no means from the free imagination of the mind. But why all this prolixity? After Herr D hring, on pages 42 and 43,  has enthusiastically sung the independence of pure mathematics from the world of experience, its apriority, its preoccupation with the mind s own free creations and imaginations, he says on page 63:
1877: Anti-Duhring