True, so long as we consider things as at rest and lifeless, each one by itself, alongside and after each other, we do not run up against any contradictions in them. We find certain qualities which are partly common to, partly different from, and even contradictory to each other, but which in the last-mentioned case are distributed among different objects and therefore contain no contradiction within. Inside the limits of this sphere of observation we can get along on the basis of the usual, metaphysical mode of thought. But the position is quite different as soon as we consider things in their motion, their change, their life, their reciprocal influence on one another. Then we immediately become involved in contradictions. Motion itself is a contradiction: even simple mechanical change of position can only come about through a body being at one and the same moment of time both in one place and in another place, being in one and the same place and also not in it. And the continuous origination and simultaneous solution of this contradiction is precisely what motion is. Here, therefore, we have a contradiction which is objectively present in things and processes themselves and can be met with in so to speak corporeal form . And what has Herr D hring to say about it? He asserts that If simple mechanical change of position contains a contradiction this is even more true of the higher forms of motion of matter, and especially of organic life and its development. We saw above that life consists precisely and primarily in this that a being is at each moment itself and yet something else. Life is therefore also a contradiction which is present in things and processes themselves, and which constantly originates and resolves itself; and as soon as the contradiction ceases, life, too, comes to an end, and death steps in. We likewise saw that also in the sphere of thought we could not escape contradictions, and that for example the contradiction between man's inherently unlimited capacity for knowledge and its actual presence only in men who are externally limited and possess limited cognition finds its solution in what is at least practically, for us an endless succession of generations, in infinite progress. We have already noted that one of the basic principles of higher mathematics is the contradiction that in certain circumstances straight lines and curves may be the same. It also gets up this other contradiction: that lines which intersect each other before our eyes nevertheless, only five or six centimetres from their point of intersection, can be shown to be parallel, that is, that they will never meet even if extended to infinity. And yet, working with these and with even far greater contradictions, it attains results which are not only correct but also quite unattainable for lower mathematics. But even lower mathematics teems with contradictions. It is for example a contradiction that a root of A should be a power of A, and yet A1/2 = . It is a contradiction that a negative quantity should be the square of anything, for every negative quantity multiplied by itself gives a positive square. The square root of minus one is therefore not only a contradiction, but even an absurd contradiction, a real absurdity. And yet is in many cases a necessary result of correct mathematical operations. Furthermore, where would mathematics lower or higher be, if it were prohibited from operation with ? In its operations with variable quantities mathematics itself enters the field of dialectics, and it is significant that it was a dialectical philosopher, Descartes, who introduced this advance. The relation between the mathematics of variable and the mathematics of constant quantities is in general the same as the relation of dialectical to metaphysical thought. But this does not prevent the great mass of mathematicians from recognising dialectics only in the sphere of mathematics, and a good many of them from continuing to work in the old, limited, metaphysical way with methods that were obtained dialectically. It would be possible to go more closely into Herr D hring s antagonism of forces and his antagonistic world schematism only if he had given us something more on this theme than the mere phrase. After accomplishing this feat this antagonism is not even once shown to us at work, either in his world schematism or in his natural philosophy the most convincing admission that Herr D hring can do absolutely nothing of a positive character with his basic form of all actions in the life of the world and its creatures . When someone has in fact lowered Hegel s Doctrine of Essence to the platitude of forces moving in opposite directions but not in contradictions, certainly the best thing he can do is to avoid any application of this commonplace. Marx's Capital furnishes Herr D hring with another occasion for venting his anti-dialectical spleen. At any rate, the most astonishing piece of information given by Herr D hring is the statement that from the Marxian standpoint it all amounts to one and the same thing in the end {496}, that therefore to Marx, for example, capitalists and wage-workers, feudal, capitalist and socialist modes of production are also one and the same thing no doubt in the end even Marx and Herr D hring are one and the same thing . Such utter nonsense can only be explained if we suppose that the mere mention of the word dialectics throws Herr D hring into such a state of mental irresponsibility that, as a result of a certain mixed and misconceived idea, what he says and does is one and the same thing in the end. We have here a sample of what Herr D hring calls And now let the reader admire the higher and nobler style, by virtue of which Herr D hring attributes to Marx the opposite of what he really said. Marx says: The fact that a sum of values can be transformed into capital only when it has reached a certain size, varying according to the circumstances, but in each case definite minimum size this fact is a proof of the correctness of the Hegelian law. Herr D hring makes him say: Because, according to the Hegelian law, quantity changes into quality, therefore an advance, when it reaches a certain size, becomes capital {D. K. G. 498}. That is to say, the very opposite. In connection with Herr D hring s examination of the Darwin case, we have already got to know his habit, in the interests of complete truth and because of his duty to the public which is free from the bonds of the guilds {507}, of quoting incorrectly. It becomes more and more evident that this habit is an inner necessity of the philosophy of reality, and it is certainly a very summary treatment {507}. Not to mention the fact that Herr D hring further makes Marx speak of any kind of advance whatsoever, whereas Marx only refers to an advance made in the form of raw materials, instruments of labour, and wages; and that in doing this Herr D hring succeeds in making Marx speak pure nonsense. And then he has the cheek to describe as comic the nonsense which he himself has fabricated. Just as he built up a Darwin of his own fantasy in order to try out his strength against him, so here he builds up a fantastic Marx. Historical depiction in the grand style {556}, indeed! We have already seen earlier, when discussing world schematism, that in connection with this Hegelian nodal line of measure relations in which quantitative change suddenly passes at certain points into qualitative transformation Herr D hring had a little accident: in a weak moment he himself recognised and made use of this line. We gave there one of the best-known examples that of the change of the aggregate states of water, which under normal atmospheric pressure changes at 0 C from the liquid into the solid state, and at 100 C from the liquid into the gaseous state, so that at both these turning-points the merely quantitative change of temperature brings about a qualitative change in the condition of the water. In proof of this law we might have cited hundreds of other similar facts from nature as well as from human society. Thus, for example, the whole of Part IV of Marx's Capital production of relative surplus-value deals, in the field of co-operation, division of labour and manufacture, machinery and modern industry, with innumerable cases in which quantitative change alters the quality, and also qualitative change alters the quantity, of the things under consideration; in which therefore, to use the expression so hated by Herr D hring, quantity is transformed into quality and vice versa. As for example the fact that the co-operation of a number of people, the fusion of many forces into one single force, creates, to use Marx's phrase, a new power , which is essentially different from the sum of its separate forces. Over and above this, in the passage which, in the interests of complete truth, Herr D hring perverted into its opposite, Marx had added a footnote: The molecular theory of modern chemistry first scientifically worked out by Laurent and Gerhardt rests on no other law. But what did that matter to Herr D hring? He knew that: What is referred to here is the homologous series of carbon compounds, of which a great many are already known and each of which has its own algebraic formula of composition. If, for example, as is done in chemistry, we denote an atom of carbon by C, an atom of hydrogen by H, an atom of oxygen by O, and the number of atoms of carbon contained in each compound by n, the molecular formulas for some of these series can be expressed as follows: Here therefore we have a whole series of qualitatively different bodies, formed by the simple quantitative addition of elements, and in fact always in the same proportion. This is most clearly evident in cases where the quantity of all the elements of the compound changes in the same proportion. Thus, in the normal paraffins CnH2n+2, the lowest is methane, CH4, a gas; the highest known, hexadecane, C16H34, is a solid body forming colourless crystals which melts at 21 and boils only at 278 . Each new member of both series comes into existence through the addition of CH2, one atom of carbon and two atoms of hydrogen, to the molecular formula of the preceding member, and this quantitative change in the molecular formula produces each time a qualitatively different body. These series, however, are only one particularly obvious example; throughout practically the whole of chemistry, even in the various nitrogen oxides and oxygen acids of phosphorus or sulphur, one can see how quantity changes into quality , and this allegedly confused, hazy Hegelian notion appears in so to speak corporeal form in things and processes and no one but Herr D hring is confused and befogged by it. And if Marx was the first to call attention to it, and if Herr D hring read the reference without even understanding it (otherwise he would certainly not have allowed this unparalleled outrage to pass unchallenged), this is enough even without looking back at the famous D hringian philosophy of nature to make it clear which of the two, Marx or Herr D hring, is lacking in the eminently modern educative elements provided by the natural-scientific mode of thought {D. K. G. 504} and in acquaintance with the main achievements of ... chemistry {D. Ph. 517}. In conclusion we shall call one more witness for the transformation of quantity into quality, namely Napoleon. He describes the combat between the French cavalry, who were bad riders but disciplined, and the Mamelukes, who were undoubtedly the best horsemen of their time for single combat, but lacked discipline, as follows:
1877: Anti-Duhring - XII. Quantity and Quality