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 Dühring to say about it?
He asserts that up to the present there is "no bridge" whatever "in rational mechanics from the strictly static to the dynamic" {D. Ph. 80}.
The reader can now at last see what is hidden behind this favourite phrase of Herr Dühring's -- it is nothing but this: the mind which thinks metaphysically is absolutely unable to pass from the idea of rest to the idea of motion, because the contradiction pointed out above blocks its path. To it, motion is simply incomprehensible because it is a contradiction.
And in asserting the incomprehensibility of motion, it admits against its will the existence of this contradiction, and thus admits the objective presence in things and processes themselves of a contradiction which is moreover an actual force.
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 A 1/2 = [--Missing Picture--]. 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 Dühring'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 Dühring 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 Dühring with another occasion for venting his anti-dialectical spleen.
