It shows a complete lack of comprehension of the nature of the dialectic to regard it as Herr Duehring does, as an instrument of mere proof, just as one can after a limited fashion employ formal logic or elementary mathematics. Formal logic is itself more than anything else a method for the discovery of new results, for advancing from the known to the unknown, and so, but in a much more distinguished sense, is the dialectic, which, since it transcends the narrow limits of formal logic, attains a more comprehensive philosophical position. It is the same with mathematics. Elementary mathematics, the mathematics of constant quantities, proceeds within the limits of formal logic, at least as a rule: the mathematics of variable quantities which is peculiarly concerned with calculations running to the infinite, is substantially nothing but the application of the dialectic in mathematics. Mere proof becomes secondary before the manifold application of the method to new fields of investigation. But nearly all the proofs of higher mathematics from the first of the differential calculus, are, strictly speaking, false from the standpoint of elementary mathematics. This cannot be otherwise, if one, as is here the case, wishes to establish results won in the realm of dialectics by means of formal logic. For a crass metaphysician like Herr Duehring to want to prove anything by means of the dialectic would be the same wasted labor as Leibnitz and his pupils went through when they tried to establish the thesis of calculation to infinity by means of the mathematics of their time. The differential gave them the same spasms as the negation of the negation gives Herr Duehring and it played a role in it as we shall see. They admitted it at last, at least as many as did not die first, not because they were convinced but because it always worked out right. Herr Duehring, is, as he says, just in his forties, and if he attains old age, as we hope he will, he may also experience the same.