.
Preface Marx & Engels task to relate dialectics to nature
Introduction Historical overview and basic concepts
Chapter 1 Critique of Idealism
Chapter 4 Motion is the mode of existence of matter
Chapter 7 Eternal Truth
Chapter 9 Freedom is the insight into necessity
Chapter 10 Mathematics & Chemistry (example of quantity to quality)
Chapter 11 The historical process of negation
Whatever else I should have liked to alter relates in the main to two points. First, to the history of primitive society, the key to which was provided by Morgan only in 1877. But as I have since then had the opportunity, in my work: Der Ursprung der Familie, des Privateigenthums und des Stoats (Zurich, 1884) to work up the material which in the meantime had become available to me, a reference to this later work meets the case. The second point concerns the section dealing with theoretical natural science. There is much that is clumsy in my exposition and much of it could be expressed today in a clearer and more definite form. I have not allowed myself the right to improve this section, and for that very reason am under an obligation to criticise myself here instead.
Marx and I were pretty well the only people to rescue conscious
dialectics from German idealist philosophy and apply it in the materialist
conception of nature and history. But a knowledge of mathematics and natural
science is essential to a conception of nature which is dialectical and
at the same time materialist. Marx was well versed in mathematics, but
we could keep up with natural science only piecemeal, intermittently and
sporadically. For this reason, when I retired from business and transferred
my home to London, [15]
thus enabling myself to give the necessary time to it, I went through as
complete as possible a "moulting", as Liebig calls it, [16]
in mathematics and the natural sciences, and spent the best part of eight
years on it. I was right in the middle of this "moulting" process when
it happened that I had to occupy myself with Herr Dühring's so-called
natural philosophy. It was therefore only too natural that in dealing with
this subject I was sometimes unable to find the correct technical expression,
and in general moved with considerable clumsiness in the field of theoretical
natural science. On the other hand, my lack of assurance in this field,
which I had not yet overcome, made me cautious, and I cannot be charged
with real blunders in relation to the facts known at that time or with
incorrect presentation of recognised theories. In this connection there
was only one unrecognised genius of a mathematician a who complained in
a letter to Marx [17]
that I had made a wanton attack upon the honour of
.
It goes without saying that my recapitulation of mathematics and the natural sciences was undertaken in order to convince myself also in detail — of what in general I was not in doubt — that in nature, amid the welter of innumerable changes, the same dialectical laws of motion force their way through as those which in history govern the apparent fortuitousness of events; the same laws which similarly form the thread running through the history of the development of human thought and gradually rise to consciousness in thinking man; the laws which Hegel first developed in all-embracing but mystic form, and which we made it one of our aims to strip of this mystic form and to bring clearly before the mind in their complete simplicity and universality. It goes without saying that the old philosophy of nature — in spite of its real value and the many fruitful seeds it contained *1 — was unable to satisfy us. As is more fully brought out in this book, natural philosophy, particularly in the Hegelian form, erred because it did not concede to nature any development in time, any "succession", but only "co-existence". This was on the one hand grounded in the Hegelian system itself, which ascribed historical evolution only to the "spirit", but on the other hand was also due to the whole state of the natural sciences in that period. In this Hegel fell far behind Kant, whose nebular theory had already indicated the origin of the solar system,' and whose discovery of the retardation of the earth's rotation by the tides also had proclaimed the doom of that system. And finally, to me there could be no question of building the laws of dialectics into nature, but of discovering them in it and evolving them from it.
But to do this systematically and in each separate department, is a gigantic task. Not only is the domain to be mastered almost boundless; natural science in this entire domain is itself undergoing such a mighty process of being revolutionised that even people who can devote the whole of their spare time to it can hardly keep pace. Since Karl Marx's death, however, my time has been requisitioned for more urgent duties, and I have therefore been compelled to lay aside my work. For the present I must content myself with the indications given in this book, and must wait to find some later opportunity to put together and publish the results which I have arrived at, perhaps in conjunction with the extremely important mathematical manuscripts left by Marx. [18]
Yet the advance of theoretical natural science may possibly make my work to a great extent or even altogether superfluous. For the revolution which is being forced on theoretical natural science by the mere need to set in order the purely empirical discoveries great masses of which have been piled up, is of such a kind that it must bring the dialectical character of natural processes more and more to the consciousness even of those empiricists who are most opposed to it. The old rigid antagonisms, the sharp, impassable dividing lines are more and more disappearing. Since even the last "true" gases have been liquefied, and since it has been proved that a body can be brought into a condition in which the liquid and the gaseous forms are indistinguishable, the aggregate states have lost the last relics of their former absolute character. [19] With the thesis of the kinetic theory of gases, that in perfect gases at equal temperatures the squares of the speeds with which the individual gas molecules move are in inverse ratio to their molecular weights heat also takes its place directly among the forms of motion which can be immediately measured as such. Whereas only ten years ago the great basic law of motion, then recently discovered, was as yet conceived merely as a law of the conservation of energy, as the mere expression of the indestructibility and uncreatability of motion, that is, merely in its quantitative aspect, this narrow negative conception is being more and more supplanted by the positive idea of the transformation of energy, in which for the first time the qualitative content of the process comes into its own, and the last vestige of an extramundane creator is obliterated. That the quantity of motion (so-called energy) remains unaltered when it is transformed from kinetic energy (so-called mechanical force) into electricity, heat, potential energy, etc., and vice versa, no longer needs to be preached as something new; it serves as the already secured basis for the now much more pregnant investigation into the very process of transformation, the great basic process, knowledge of which comprises all knowledge of nature. And since biology has been pursued in the light of the theory of evolution, one rigid boundary line of classification after another has been swept away in the domain of organic nature. The almost unclassifiable intermediate links are growing daily more numerous, closer investigation throws organisms out of one class into another, and distinguishing characteristics which almost became articles of faith are losing their absolute validity; we now have mammals that lay eggs, and, if the report is confirmed, also birds that walk on all fours. Years ago Virchow was compelled, following on the discovery of the cell, to dissolve the unity of the individual animal being into a federation of cell-states — thus acting more progressively rather than scientifically and dialectically [20] — and now the conception of animal (therefore also human) individuality is becoming far more complex owing to the discovery of the white blood corpuscles which creep about amoeba-like within the bodies of the higher animals. It is however precisely the polar antagonisms put forward as irreconcilable and insoluble, the forcibly fixed lines of demarcation and class distinctions, which have given modern theoretical natural science its restricted, metaphysical character. The recognition that these antagonisms and distinctions, though to be found in nature, are only of relative validity, and that on the other hand their imagined rigidity and absolute validity have been introduced into nature only by our reflective minds — this recognition is the kernel of the dialectical conception of nature. It is possible to arrive at this recognition because the accumulating facts of natural science compel us to do so; but one arrives at it more easily if one approaches the dialectical character of these facts equipped with an understanding of the laws of dialectical thought. In any case natural science has now advanced so far that it can no longer escape dialectical generalisation. However it will make this process easier for itself if it does not lose sight of the fact that the results in which its experiences are summarised are concepts, that the art of working with concepts is not inborn and also is not given with ordinary everyday consciousness, but requires real thought, and that this thought similarly has a long empirical history, not more and not less than empirical natural science. Only by learning to assimilate the results of the development of philosophy during the past two and a half thousand years will it rid itself on the one hand of any natural philosophy standing apart from it, outside it and above it, and on the other hand also of its own limited method of thought, which is its inheritance from English empiricism.
London,
September 23, 1885
This mode of outlook is essentially that of all English and French and of the first German socialists, including Weitling. Socialism is the expression of absolute truth, reason and justice and has only to be discovered to conquer all the world by virtue of its own power. And as absolute truth is independent of time, space, and of the historical development of man,. it is a mere accident when and where it is discovered. With all this, absolute truth, reason, and justice are different with the founder of each different school. And as each one's special kind of absolute truth, reason, and justice is again conditioned by his subjective understanding, his conditions of existence, the measure of his knowledge and his intellectual training, there is no other ending possible in this conflict of absolute truths than that they shall be mutually exclusive one of the other. Hence, from this nothing could come but a kind of eclectic, average socialism, which, as a matter of fact, has up to the present time dominated the minds of most of the socialist workers in France and England. Hence, a mish-mash allowing of the most manifold shades of opinion; a mish-mash of less striking critical statements, economic theories pictures of future society by the founders of different sects, a mish-mash which is the more easily brewed the more the definite sharp edges of the individual constituents are rubbed down in the stream of debate, like rounded pebbles in a brook.
To make a science of socialism, it had first to be placed upon a real basis.
In the meantime, along with and after the French philosophy of the eighteenth century had arisen the new German philosophy, culminating in Hegel. Its greatest merit was the taking up again of dialectics as the highest form of reasoning. The old Greek philosophers were all born natural dialecticians, and Aristotle, the most encyclopaedic intellect of them, had already analysed the most essential forms of dialectic thought. The newer philosophy on the other hand, although in it also dialectics had brilliant exponents (e.g., Descartes and Spinoza), had, especially through English influence, become more and more rigidly fixed in the so-called metaphysical mode of reasoning, by which also the French of the eighteenth century were almost wholly dominated at all events in their special philosophical work. Outside philosophy in the restricted sense, the French nevertheless produced masterpieces of dialectic. We need only call to mind Diderot's Le neveu de Rameau [24] and Rousseau's Discours sur l'origine et les fondemens de l'inégalité parmi les hommes. We give here, in brief, the essential character of these two modes of thought. We shall have to return to them later in greater detail.
When we consider and reflect upon nature at large or the history of mankind or our own intellectual activity, at first we see the picture of an endless entanglement of relations and reactions in which nothing remains what, where and as it was, but everything moves, changes, comes into being and passes away. This primitive, naive but intrinsically correct conception of the world is that of ancient Greek philosophy, and was first clearly formulated by Heraclitus: everything is and is not, for everything is fluid, is constantly changing, constantly coming into being and passing away.
But this conception, correctly as it expresses the general character of the picture of appearances as a whole, does not suffice to explain the details of which this picture is made up, and so long as we do not understand these, we have not a clear idea of the whole picture. In order to understand these details we must detach them from their natural or historical connection and examine each one separately, its nature, special causes, effects, etc. This is, primarily, the task of natural science and historical research: branches of science which the Greeks of classical times on very good grounds, relegated to a subordinate position, because they had first of all to collect the material. The beginnings of the exact natural sciences were first worked out by the Greeks of the Alexandrian period, [25] and later on, in the Middle Ages, by the Arabs. Real natural science dates from the second half of the fifteenth century, and thence onward it has advanced with constantly increasing rapidity. The analysis of nature into its individual parts, the grouping of the different natural processes and objects in definite classes, the study of the internal anatomy of organic bodies in their manifold forms — these were the fundamental conditions of the gigantic strides in our knowledge of nature that have been made during the last four hundred years. But this method of work has also left us as legacy the habit of observing natural objects and processes in isolation, apart from their connection with the vast whole; of observing them in repose, not in motion; as constants, not as essentially variables, in their death, not in their life. And when this way of looking at things was transferred by Bacon and Locke from natural science to philosophy, it begot the narrow, metaphysical mode of thought peculiar to the preceding centuries.
To the metaphysician, things and their mental reflexes, ideas, are isolated, are to be considered one after the other and apart from each other, are objects of investigation fixed, rigid, given once for all. He thinks in absolutely irreconcilable antitheses. "His communication is 'yea, yea; nay, nay'; for whatsoever is more than these cometh of evil." [Matthew 5:37. — Ed.] For him a thing either exists or does not exist; a thing cannot at the same time be itself and something else. Positive and negative absolutely exclude one another, cause and effect stand in a rigid antithesis one to the other.
At first sight this mode of thinking seems to us very luminous, because it is that of so-called sound common sense. Only sound common sense, respectable fellow that he is, in the homely realm of his own four walls, has very wonderful adventures directly he ventures out into the wide world of research. And the metaphysical mode of thought, justifiable and even necessary as it is in a number of domains whose extent varies according to the nature of the particular object of investigation, sooner or later reaches a limit, beyond which it becomes one-sided, restricted, abstract, lost in insoluble contradictions. In the contemplation of individual things it forgets the connection between them; in the contemplation of their existence, it forgets the beginning and end of that existence; of their repose, it forgets their motion. It cannot see the wood for the trees.
For everyday purposes we know and can say, e.g., whether an animal is alive or not. But, upon closer inquiry, we find that this is, in many cases, a very complex question, as the jurists know very well. They have cudgelled their brains in vain to discover a rational limit beyond which the killing of the child in its mother's womb is murder. It is just as impossible to determine absolutely the moment of death, for physiology proves that death is not an instantaneous momentary phenomenon, but a very protracted process.
In like manner, every organic being is every moment the same and not the same, every moment it assimilates matter supplied from without, and gets rid of other matter; every moment some cells of its body die and others build themselves anew; in a longer or shorter time the matter of its body is completely renewed, and is replaced by other atoms of matter, so that every organic being is always itself, and yet something other than itself.
Further, we find upon closer investigation that the two poles of an antithesis positive and negative, e.g., are as inseparable as they are opposed and that despite all their opposition, they mutually interpenetrate. And we find, in like manner, that cause and effect are conceptions which only hold good in their application to individual cases; but as soon as we consider the individual cases in their general connection with the universe as a whole, they run into each other, and they become confounded when we contemplate that universal action and reaction in which causes and effects are eternally changing places, so that what is effect here and now will be cause there and then, and vice versa.
None of these processes and modes of thought enters into the framework of metaphysical reasoning. Dialectics, on the other hand, comprehends things and their representations, ideas, in their essential connection, concatenation, motion, origin, and ending. Such processes as those mentioned above are, therefore, so many corroborations of its own method of procedure.
Nature is the proof of dialectics, and it must be said for modern science that it has furnished this proof with very rich materials increasing daily, and thus has shown that, in the last resort, nature works dialectically and not metaphysically. But the naturalists who have learned to think dialectically are few and far between, and this conflict of the results of discovery with preconceived modes of thinking explains the endless confusion now reigning in theoretical natural science, the despair of teachers as well as learners, of authors and readers alike.
An exact representation of the universe, of its evolution, of the development of mankind, and of the reflection of this evolution in the minds of men, can therefore only be obtained by the methods of dialectics with its constant regard to the innumerable actions and reactions of life and death, of progressive or retrogressive changes. And in this spirit the new German philosophy has worked. Kant began his career by resolving the stable solar system of Newton and its eternal duration, after the famous initial impulse had once been given, into the result of a historic process, the formation of the sun and all the planets out of a rotating nebulous mass. From this he at the same time drew the conclusion that, given this origin of the solar system, its future death followed of necessity. His theory half a century later was established mathematically by Laplace, and half a century after that the spectroscope proved the existence in space of such incandescent masses of gas in various stages of condensation. [26]
This new German philosophy culminated in the Hegelian system. In this system — and herein is its great merit — for the first time the whole world, natural, historical, intellectual, is represented as a process, i.e., as in constant motion, change transformation, development; and the attempt is made to trace out the internal connection that makes a continuous whole of all this movement and development. From this point of view the history of mankind no longer appeared as a wild whirl of senseless deeds of violence, all equally condemnable at the judgment-seat of mature philosophic reason and which are best forgotten as quickly as possible, but as the process of evolution of man himself. It was now the task of the intellect to follow the gradual march of this process through all its devious ways, and to trace out the inner law running through all its apparently accidental phenomena.
That Hegel did not solve the problem is here immaterial. His epoch-making merit was that he propounded the problem. This problem is one that no single individual will ever be able to solve. Although Hegel was — with Saint-Simon — the most encyclopaedic mind of his time, yet he was limited, first, by the necessarily limited extent of his own knowledge and, second, by the limited extent and depth of the knowledge and conceptions of his age. To these limits a third must be added. Hegel was an idealist. To him the thoughts within his brain were not the more or less abstract pictures of actual things and processes, but, conversely, things and their evolution were only the realised pictures of the "Idea", existing somewhere from eternity before the world was. This way of thinking turned everything upside down, and completely reversed the actual connection of things in the world. Correctly and ingeniously as many individual groups of facts were grasped by Hegel, yet, for the reasons just given, there is much that is botched, artificial, laboured, in a word, wrong in point of detail. The Hegelian system, in itself, was a colossal miscarriage — but it was also the last of its kind. It was suffering, in fact, from an internal and incurable contradiction. Upon the one hand, its essential proposition was the conception that human history is a process of evolution, which, by its very nature, cannot find its intellectual final term in the discovery of any so-called absolute truth. But, on the other hand, it laid claim to being the very essence of this absolute truth. A system of natural and historical knowledge, embracing everything, and final for all time, is a contradiction to the fundamental laws of dialectic reasoning. This law, indeed, by no means excludes, but, on the contrary, includes the idea that the systematic knowledge of the external universe can make giant strides from age to age.
The perception of the fundamental contradiction in German idealism led necessarily back to materialism, but, nota bene, not to the simply metaphysical, exclusively mechanical materialism of the eighteenth century. In contrast to the naively revolutionary, simple rejection of all previous history, modern materialism sees in the latter the process of evolution of humanity, it being its task to discover the laws of motion thereof. With the French of the eighteenth century, and with Hegel, the conception obtained of nature as a whole, moving in narrow circles, and forever immutable, with its eternal celestial bodies, as Newton, and unalterable organic species, as Linnaeus, taught. Modern materialism embraces the more recent discoveries of natural science, according to which nature also has its history in time, the celestial bodies, like the organic species that, under favourable conditions, people them, being born and perishing. And even if nature, as a whole, must still be said to move in recurrent cycles, these cycles assume infinitely larger dimensions. In both cases modern materialism is essentially dialectic, and no longer needs any philosophy standing above the other sciences. As soon as each special science is bound to make clear its position in the great totality of things and of our knowledge of things, a special science dealing with this totality is superfluous. That which still survives, independently, of all earlier philosophy is the science of thought and its laws — formal logic and dialectics. Everything else is subsumed in the positive science of nature and history....
Whilst, however, the revolution in the conception of nature could only be made in proportion to the corresponding positive materials furnished by research, already much earlier certain historical facts had occurred which led to a decisive change in the conception of history. In 1831, the first working-class rising took place in Lyons; between 1838 and 1842, the first national working-class movement, that of the English Chartists, reached its height. The class struggle between proletariat and bourgeoisie came to the front in the history of the most advanced countries in Europe, in proportion to the development, upon the one hand, of modern industry [grosse Industrie], upon the other, of the newly-acquired political supremacy of the bourgeoisie. Facts more and more strenuously gave the lie to the teachings of bourgeois economy as to the identity of the interests of capital and labour, as to the universal harmony and universal prosperity that would be the consequence of unbridled competition. All these things could no longer be ignored, any more than the French and English socialism, which was their theoretical, though very imperfect, expression. But the old idealist conception of history, which was not yet dislodged knew nothing of class struggles based upon economic interests, knew nothing of economic interests; production and all economic relations appeared in it only as incidental, subordinate elements in the "history of civilisation".
So far Herr Dühring, and almost entirely word for word.
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 Dühring 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 Dühring'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 [30] and all its delirious fantasies with Herr Dühring's final and ultimate truths. With Herr Dühring 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 Dühring 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. [31]
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. [32]
But Herr Dühring 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
Matter, Herr Dühring says, is the bearer of all reality; accordingly, there can be no mechanical force apart from matter. Mechanical force is furthermore a state of matter {See D. Ph. 73}. In the original state, when nothing happened, matter and its state, mechanical force, were one. Afterwards, when something began to happen, this state must apparently have become different from matter. So we are to let ourselves be dismissed with these mystical phrases and with the assurance that the self-equal state was neither static nor dynamic, neither in equilibrium nor in motion. We still do not know where mechanical force was in that state, and how we are to get from absolute immobility to motion without an impulse from outside, that is, without God.
The materialists before Herr Dühring spoke of matter and motion. He reduces motion to mechanical force as its supposed basic form, and thereby makes it impossible for himself to understand the real connection between matter and motion, which moreover was also unclear to all former materialists. And yet it is simple enough. Motion is the mode of existence of matter. Never anywhere has there been matter without motion, nor can there be. Motion in cosmic space, mechanical motion of smaller masses on the various celestial bodies, the vibration of molecules as heat or as electrical or magnetic currents, chemical disintegration and combination, organic life — at each given moment each individual atom of matter in the world is in one or other of these forms of motion, or in several forms at once. All rest, all equilibrium, is only relative, only has meaning in relation to one or other definite form of motion. On the earth, for example, a body may be in mechanical equilibrium, may be mechanically at rest; but this in no way prevents it from participating in the motion of the earth and in that of the whole solar system, just as little as it prevents its most minute physical particles from carrying out the vibrations determined by its temperature, or its atoms from passing through a chemical process. Matter without motion is just as inconceivable as motion without matter. Motion is therefore as uncreatable and indestructible as matter itself; as the older philosophy (Descartes) expressed it, the quantity of motion existing in the world is always the same. Motion therefore cannot be created; it can only be transferred. When motion is transferred from one body to another, it may be regarded, in so far as it transfers itself, is active, as the cause of motion, in so far as the latter is transferred, is passive. We call this active motion force, and the passive, the manifestation of force. Hence it is as clear as daylight that a force is as great as its manifestation, because in fact the same motion takes place in both.
A motionless state of matter is therefore one of the most empty and nonsensical of ideas — a "delirious fantasy" of the purest water. In order to arrive at such an idea it is necessary to conceive the relative mechanical equilibrium, a state in which a body on the earth may be, as absolute rest, and then to extend this equilibrium over the whole universe. This is certainly made easier if universal motion is reduced to purely mechanical force. And the restriction of motion to purely mechanical force has the further advantage that a force can be conceived as at rest, as tied up, and therefore for the moment inoperative. For if, as is very often the case, the transfer of a motion is a somewhat complex process containing a number of intermediate links, it is possible to postpone the actual transmission to any moment desired by omitting the last link in the chain. This is the case, for instance, if a man loads a gun and postpones the moment when, by the pulling of the trigger, the discharge, the transfer of the motion set free by the combustion of the powder, takes place. It is therefore possible to imagine that during its motionless, self-equal state, matter was loaded with force, and this, if anything at all, seems to be what Herr Dühring understands by the unity of matter and mechanical force. This conception is nonsensical, because it transfers to the entire universe a state as absolute, which by its nature is relative and therefore can only affect a part of matter at any one time. Even if we overlook this point, the difficulty still remains: first, how did the world come to be loaded, since nowadays guns do not load themselves; and second, whose finger was it then that pulled the trigger? We may turn and twist as much as we like, but under Herr Dühring's guidance we always come back again to — the finger of God.
Up to now we have calmly put up with all these pompous phrases of Herr Dühring's about final and ultimate truths, the sovereignty of thought, absolute certainty of knowledge, and so forth, because it is only at the point which we have now reached that the matter can be settled. Up to this point it has been enough to enquire how far the separate assertions of the philosophy of reality had "sovereign validity" and "an unconditional claim to truth" {2}; now we come to the question whether any, and if so which, products of human knowledge ever can have sovereign validity and an unconditional claim to truth. When I say "of human knowledge" I do not use the phrase with the intention of insulting the inhabitants of other celestial bodies, whom I have not had the honour of knowing, but only for the reason that animals also have knowledge, though it is in no way sovereign. A dog acknowledges his master to be his God, though this master may be the biggest scoundrel on earth.
Is human thought sovereign? Before we can answer yes or no we must first enquire: what is human thought? Is it the thought of the individual man? No. But it exists only as the individual thought of many milliards [billions] of past, present and future men. If, then, I say that the total thought of all these human beings, including the future ones, which is embraced in my idea, is sovereign, able to know the world as it exists, if only mankind lasts long enough and in so far as no limits are imposed on its knowledge by its perceptive organs or the objects to be known, then I am saying something which is pretty banal and, in addition, pretty barren. For the most valuable result from it would be that it should make us extremely distrustful of our present knowledge, inasmuch as in all probability we are just about at the beginning of human history, and the generations which will put us right are likely to be far more numerous than those whose knowledge we — often enough with a considerable degree of contempt — have the opportunity to correct.
Herr Dühring himself proclaims it to be a necessity that consciousness, and therefore also thought and knowledge, can become manifest only in a series of individual beings. We can only ascribe sovereignty to the thought of each of these individuals in so far as we are not aware of any power which would be able to impose any idea forcibly on him, when he is of sound mind and wide awake. But as for the sovereign validity of the knowledge obtained by each individual thought, we all know that there can be no talk of such a thing, and that all previous experience shows that without exception such knowledge always contains much more that is-capable of being improved upon than that which cannot be improved upon, or is correct.
In other words, the sovereignty of thought is realised in a series of extremely unsovereignly-thinking human beings; the knowledge which has an unconditional claim to truth is realised in a series of relative errors; neither the one nor the other can be fully realised except through an unending duration of human existence.
Here once again we find the same contradiction as we found above, between the character of human thought, necessarily conceived as absolute, and its reality in individual human beings all of whom think only limitedly. This is a contradiction which can be resolved only in the course of infinite progress, in what is — at least practically for us — an endless succession of generations of mankind. In this sense human thought is just as much sovereign as not sovereign, and its capacity for knowledge just as much unlimited as limited. It is sovereign and unlimited in its disposition, its vocation, its possibilities and its historical ultimate goal; it is not sovereign and it is limited in its individual realisation and in reality at any particular moment.
It is just the same with eternal truths. If mankind ever reached the stage at which it should work only with eternal truths, with results of thought which possess sovereign validity and an unconditional claim to truth, it would then have reached the point where the infinity of the intellectual world both in its actuality and in its potentiality had been exhausted, and thus the famous miracle of the counted uncountable would have been performed.
But are there any truths which are so securely based that any doubt of them seems to us to be tantamount to insanity? That twice two makes four, that the three angles of a triangle are equal to two right angles, that Paris is in France, that a man who gets no food dies of hunger, and so forth? Are there then nevertheless eternal truths, final and ultimate truths {D. Ph. 2}?
Certainly there are. We can divide the whole realm of knowledge in the traditional way into three great departments. The first includes all sciences that deal with inanimate nature and are to a greater or lesser degree susceptible of mathematical treatment: mathematics, astronomy, mechanics, physics, chemistry. If it gives anyone any pleasure to use mighty words for very simple things, it can be asserted that certain results obtained by these sciences are eternal truths, final and ultimate truths; for which reason these sciences are known as the exact sciences. But very far from all their results have this validity. With the introduction of variable magnitudes and the extension of their variability to the infinitely small and infinitely large, mathematics, usually so strictly ethical, fell from grace; it ate of the tree of knowledge, which opened up to it a career of most colossal achievements, but at the same time a path of error. The virgin state of absolute validity and irrefutable proof of everything mathematical was gone for ever; the realm of controversy was inaugurated, and we have reached the point where most people differentiate and integrate not because they understand what they are doing but from pure faith, because up to now it has always come out right. Things are even worse with astronomy and mechanics, and in physics and chemistry we are swamped by hypotheses as if attacked by a swarm of bees. And it must of necessity be so. In physics we are dealing with the motion of molecules, in chemistry with the formation of molecules out of atoms, and if the interference of light waves is not a myth, we have absolutely no prospect of ever seeing these interesting objects with our own eyes. As time goes on, final and ultimate truths become remarkably rare in this field.
We are even worse off in geology which, by its nature, has to deal chiefly with processes which took place not only in our absence but in the absence of any human being whatever. The gleaning here of final and ultimate truths is therefore a very troublesome business, and the crop is extremely scanty.
The second department of science is the one which covers the investigation of living organisms. In this field there is such a multiplicity of interrelationships and causalities that not only does the solution of each question give rise to a host of other questions, but each separate problem can in most cases only be solved piecemeal, through a series of investigations which often require centuries; and besides, the need for a systematic presentation of interconnections makes it necessary again and again to surround the final and ultimate truths with a luxuriant growth of hypotheses. What a long series of intermediaries from Galen to Malpighi was necessary for correctly establishing such a simple matter as the circulation of the blood in mammals, how slight is our knowledge of the origin of blood corpuscles, and how numerous are the missing links even today, for example, to be able to bring the symptoms of a disease into some rational relationship with its cause! And often enough discoveries, such as that of the cell, are made which compel us to revise completely all formerly established final and ultimate truths in the realm of biology, and to put whole piles of them on the scrap-heap once and for all. Anyone who wants to establish really genuine and immutable truths here will therefore have to be content with such platitudes as: all men are mortal, all female mammals have lacteal glands, and the like; he will not even be able to assert that the higher animals digest with their stomachs and intestines and not with their heads, for the nervous activity, which is centralised in the head, is indispensable to digestion.
But eternal truths are in an even worse plight in the third, the historical, group of sciences, which study in their historical sequence and in their present resultant state the conditions of human life, social relationships, forms of law and government, with their ideal superstructure in the shape of philosophy, religion, art, etc. In organic nature we are at least dealing with a succession of processes which, so far as our immediate observation is concerned, recur with fair regularity within very wide limits. Organic species have on the whole remained unchanged since the time of Aristotle. In social history, however, the repetition of conditions is the exception and not the rule, once we pass beyond the primitive state of man, the so-called Stone Age; and when such repetitions occur, they never arise under exactly similar circumstances. Such, for example, is the existence of an original common ownership of the land among all civilised peoples, or the way it was dissolved. In the sphere of human history our knowledge is therefore even more backward than in the realm of biology. Furthermore, when by way of exception the inner connection between the social and political forms of existence in any epoch comes to be known, this as a rule occurs only when these forms have already by half outlived themselves and are nearing extinction. Therefore, knowledge is here essentially relative, inasmuch as it is limited to the investigation of interconnections and consequences of certain social and state forms which exist only in a particular epoch and among particular peoples and are by their very nature transitory. Anyone therefore who here sets out to hunt down final and ultimate truths, genuine, absolutely immutable truths, will bring home but little, apart from platitudes and commonplaces of the sorriest kind — for example, that, generally speaking, men cannot live except by labour; that up to the present they for the most part have been divided into rulers and ruled; that Napoleon died on May 5, 1821, and so on.
Now it is a remarkable thing that it is precisely in this sphere that we most frequently encounter truths which claim to be eternal, final and ultimate and all the rest of it. That twice two makes four, that birds have beaks, and similar statements, are proclaimed as eternal truths only by those who aim at deducing, from the existence of eternal truths in general, the conclusion that there are also eternal truths in the sphere of human history — eternal morality, eternal justice, and so on — which claim a validity and scope similar to those of the insights and applications of mathematics. And then we can confidently rely on this same friend of humanity taking the first opportunity to assure us that all previous fabricators of eternal truths have been to a greater or lesser extent asses and charlatans, that they all fell into error and made mistakes; but that their error and their fallibility are in accordance with nature's laws, and prove the existence of truth and accuracy precisely in his case; and that he, the prophet who has now arisen, has in his bag, all ready-made, final and ultimate truth, eternal morality and eternal justice. This has all happened so many hundreds and thousands of times that we can only feel astonished that there should still be people credulous enough to believe this, not of others, oh no! but of themselves. Nevertheless we have here before us at least one more such prophet, who also, quite in the accustomed way, flies into highly moral indignation when other people deny that any individual whatsoever is in a position to deliver the final and ultimate truth. Such a denial, or indeed mere doubt of it, is weakness, hopeless confusion, nothingness, mordant scepticism, worse than pure nihilism, utter chaos and other such pleasantries. As with all prophets, instead of critical and scientific examination and judgment one encounters moral condemnation out of hand.
We might have made mention above also of the sciences which investigate the laws of human thought, i.e., logic and dialectics. In these, however, eternal truths do not fare any better. Herr Dühring declares that dialectics proper is pure nonsense; and the many books which have been and are still being written on logic provide abundant proof that here, too, final and ultimate truths are much more sparsely sown than some people believe.
For that matter, there is absolutely no need to be alarmed at the fact that the stage of knowledge which we have now reached is as little final as all that have preceded it. It already embraces a vast mass of judgments and requires very great specialisation of study on the part of anyone who wants to become conversant with any particular science. But a man who applies the measure of genuine, immutable, final and ultimate truth to knowledge which, by its very nature, must either remain relative for many generations and be completed only step by step, or which, as in cosmogony, geology and the history of mankind, must always contain gaps and be incomplete because of the inadequacy of the historical material — such a man only proves thereby his own ignorance and perversity, even if the real thing behind it all is not, as in this case, the claim to personal infallibility. Truth and error, like all thought-concepts which move in polar opposites, have absolute validity only in an extremely limited field, as we have just seen, and as even Herr Dühring would realise if he had any acquaintance with the first elements of dialectics, which deal precisely with the inadequacy of all polar opposites. As soon as we apply the antithesis between truth and error outside of that narrow field which has been referred to above it becomes relative and therefore unserviceable for exact scientific modes of expression, and if we attempt to apply it as absolutely valid outside that field we really find ourselves altogether beaten: both poles of the antithesis become transformed into their opposites, truth becomes error and error truth. Let us take as an example the well-known Boyle's law. According to it, if the temperature remains constant, the volume of a gas varies inversely with the pressure to which it is subjected. Regnault found that this law does not hold good in certain cases. Had he been a philosopher of reality he would have had to say: Boyle's law is mutable, and is hence not a genuine truth, hence it is not a truth at all, hence it is an error. But had he done this he would have committed an error far greater than the one that was contained in Boyle's law; his grain of truth would have been lost sight of in a sand-hill of error; he would have distorted his originally correct conclusion into an error compared with which Boyle's law, along with the little particle of error that clings to it would have seemed like truth. But Regnault, being a man of science, did not indulge in such childishness, but continued his investigations and discovered that in general Boyle's law is only approximately true, and in particular loses its validity in the case of gases which can be liquefied by pressure, namely, as soon as the pressure approaches the point at which liquefaction begins. Boyle's law therefore was proved to be true only within definite limits. But is it absolutely and finally true within those limits? No physicist would assert that. He would maintain that it holds good within certain limits of pressure and temperature and for certain gases; and even within these more restricted limits he would not exclude the possibility of a still narrower limitation or altered formulation as the result of future investigations. *2 This is how things stand with final and ultimate truths in physics, for example. Really scientific works therefore, as a rule, avoid such dogmatically moral expressions as error and truth, while these expressions meet us everywhere in works such as the philosophy of reality, in which empty phrasemongering attempts to impose itself on us as the most sovereign result of sovereign thought.
But, a naive reader may ask, where has Herr Dühring expressly stated that the content of his philosophy of reality is final and even ultimate truth {D. Ph. 2}? Where? Well, for example, in the dithyramb on his system (page 13), a part of which we cited in Chapter II. Or when he says, in the passage quoted above: Moral truths, in so far as their ultimate bases are understood, claim the same validity as mathematical insights. And does not Herr Dühring assert that, working from his really critical standpoint {D. Ph. 404} and by means of those researches of his which go to the root of things {200}, he has forced his way through to these ultimate foundations, the basic schemata, and has thus bestowed final and ultimate validity on moral truths? Or, if Herr Dühring does not advance this claim either for himself or for his age, if he only meant to say that perhaps some day in the dark and nebulous future final and ultimate truths may be ascertained, if therefore he meant to say much the same, only in a more confused way, as is said by "mordant scepticism" and "hopeless confusion" {194} — then, in that case, what is all the noise about, what can we do for you, Herr Dühring? [Goethe, Faust, Act I, Scene III ("Faust's Study"). — Ed.]
"We base moral responsibility on freedom, which however means nothing more to us than susceptibility to conscious motives in accordance with our natural and acquired intelligence. All such motives operate with the inevitability of natural law, notwithstanding an awareness of possible contrary actions; but it is precisely on this unavoidable compulsion that we rely when we apply the moral levers" {218}.
This second definition of freedom, which quite unceremoniously gives a knock-out blow to the first one, is again nothing but an extreme vulgarisation of the Hegelian conception. Hegel was the first to state correctly the relation between freedom and necessity. To him, freedom is the insight into necessity.
"Necessity is blind only in so far as it is not understood."
Freedom does not consist in any dreamt-of independence from natural laws, but in the knowledge of these laws, and in the possibility this gives of systematically making them work towards definite ends. This holds good in relation both to the laws of external nature and to those which govern the bodily and mental existence of men themselves — two classes of laws which we can separate from each other at most only in thought but not in reality. Freedom of the will therefore means nothing but the capacity to make decisions with knowledge of the subject. Therefore the freer a man's judgment is in relation to a definite question, the greater is the necessity with which the content of this judgment will be determined; while the uncertainty, founded on ignorance, which seems to make an arbitrary choice among many different and conflicting possible decisions, shows precisely by this that it is not free, that it is controlled by the very object it should itself control. Freedom therefore consists in the control over ourselves and over external nature, a control founded on knowledge of natural necessity; it is therefore necessarily a product of historical development. The first men who separated themselves from the animal kingdom were in all essentials as unfree as the animals themselves, but each step forward in the field of culture was a step towards freedom. On the threshold of human history stands the discovery that mechanical motion can be transformed into heat: the production of fire by friction; at the close of the development so far gone through stands the discovery that heat can be transformed into mechanical motion: the steam-engine.
In spite of the gigantic liberating revolution in the social world which the steam-engine is carrying through, and which is not yet half completed, it is beyond all doubt that the generation of fire by friction has had an even greater effect on the liberation of mankind. For the generation of fire by friction gave man for the first time control over one of the forces of nature, and thereby separated him for ever from the animal kingdom. The steam-engine will never bring about such a mighty leap forward in human development, however important it may seem in our eyes as representing all those immense productive forces dependent on it — forces which alone make possible a state of society in which there are no longer class distinctions or anxiety over the means of subsistence for the individual, and in which for the first time there can be talk of real human freedom, of an existence in harmony with the laws of nature that have become known. But how young the whole of human history still is, and how ridiculous it would be to attempt to ascribe any absolute validity to our present views, is evident from the simple fact that all past history can be characterised as the history of the epoch from the practical discovery of the transformation of mechanical motion into heat up to that of the transformation of heat into mechanical motion.
True, Herr Dühring's treatment of history is different. In general, being a record of error, ignorance and barbarity, of violence and subjugation, history is a repulsive object to the philosophy of reality; but considered in detail it is divided into two great periods, namely (1) from the self-equal state of matter up to the French Revolution, (2) from the French Revolution up to Herr Dühring; the nineteenth century remains:
The thought-content of the two passages cited can be summed up in the statement that contradiction=absurdity, and therefore cannot occur in the real world. People who in other respects show a fair degree of common sense may regard this statement as having the same self-evident validity as the statement that a straight line cannot be a curve and a curve cannot be straight. But, regardless of all protests made by common sense, the differential calculus under certain circumstances nevertheless equates straight lines and curves, and thus obtains results which common sense, insisting on the absurdity of straight lines being identical with curves, can never attain. And in view of the important role which the so-called dialectics of contradiction has played in philosophy from the time of the ancient Greeks up to the present, even a stronger opponent than Herr Dühring should have felt obliged to attack it with other arguments besides one assertion and a good many abusive epithets.
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 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 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.
In connection with Herr Dühring'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 Dühring 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 Dühring 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 Dühring 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 Dühring, 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 Dühring 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 Dühring? He knew that:
"the eminently modern educative elements provided by the natural-scientific mode of thought are lacking precisely among those who, like Marx and his rival Lassalle, make half-science and a little philosophistics the meagre equipment with which to vamp up their learning" {D. K. G. 504} —
while with Herr Dühring
"the main achievements of exact knowledge in mechanics, physics and chemistry" {D. Ph. 517} and so forth serve as the basis —
we have seen how. However, in order to enable third persons, too, to reach a decision in the matter, we shall look a little more closely into the example cited in Marx's footnote.
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:
CnH2n+2 — the series of normal paraffins
CnH2n+2 — the series of primary alcohols
CnH2nO2 — the series of the monobasic fatty acids.
Let us take as an example the last of these series, and let us assume successively that n=l, n=2, n=3, etc. We then obtain the following results (omitting the isomers):
CH2O2 — formic acid: boiling point 100° melting point 1°
C2H4O2 — acetic acid: 118° melting point 17°
C3H6O2 — propionic acid: 140° " "
C8H8O2 — butyric acid: 162°
C5H10O2 — valerianic acid: 175°
and so on to C50H60O2, melissic acid, which melts only at 80° and has no boiling point at all, because it cannot evaporate without disintegrating.
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 Dühring is confused and befogged by it. And if Marx was the first to call attention to it, and if Herr Dühring 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 Dühringian philosophy of nature — to make it clear which of the two, Marx or Herr Dühring, 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:
"Two Mamelukes were undoubtedly more than a match for three Frenchmen; 100 Mamelukes were equal to 100 Frenchmen; 300 Frenchmen could generally beat 300 Mamelukes, and 1,000 Frenchmen invariably defeated 1,500 Mamelukes."
Just as with Marx a definite, though varying, minimum sum of exchange-values was necessary to make possible its transformation into capital, so with Napoleon a detachment of cavalry had to be of a definite minimum number in order to make it possible for the force of discipline, embodied in closed order and planned utilisation, to manifest itself and rise superior even to greater numbers of irregular cavalry, in spite of the latter being better mounted, more dexterous horsemen and fighters, and at least as brave as the former. But what does this prove as against Herr Dühring? Was not Napoleon miserably vanquished in his conflict with Europe? Did he not suffer defeat after defeat? And why? Solely in consequence of having introduced the confused, hazy Hegelian notion into cavalry tactics!
Up to this point we have proceeded from the assumption that Herr Dühring's persistent habit of misquoting is done at least in good faith, and arises either from his total incapacity to understand things or from a habit of quoting from memory — a habit which seems to be peculiar to historical depiction in the grand style, but is usually described as slovenly. But we seem to have reached the point at which, even with Herr Dühring, quantity is transformed into quality. For we must take into consideration in the first place that the passage in Marx is in itself perfectly clear and is moreover amplified in the same book by a further passage which leaves no room whatever for misunderstanding; secondly, that Herr Dühring had discovered the monstrosity of "property which is at once both individual and social" {505} neither in the critique of Capital, in the Ergäntungsblätter which was referred to above, nor even in the critique contained in the first edition of his Kritische Geschichte, but only in the second edition — that is, on the third reading of Capital; further, that in this second edition, which was rewritten in a socialist sense, it was deemed necessary by Herr Dühring to make Marx say the utmost possible nonsense about the future organisation of society, in order to enable him, in contrast, to bring forward all the more triumphantly — as he in fact does — "the economic commune as described by me in economic and juridical outline in my Cursus" {504} — when we take all this into consideration, we are almost forced to the conclusion that Herr Dühring has here deliberately made a "beneficent extension" of Marx's idea — beneficent for Herr Dühring.
But what role does the negation of the negation play in Marx? On page 791 and the following pages he sets out the final conclusions which he draws from the preceding fifty pages of economic and historical investigation into the so-called primitive accumulation of capital. [62] Before the capitalist era, petty industry existed, at least in England, on the basis o/ the private property of the labourer in his means of production. The so-called primitive accumulation of capital consisted there in the expropriation of these immediate producers, that is, in the dissolution of private property based on the labour of its owner. This became possible because the petty industry referred to above is compatible only with narrow and primitive bounds of production and society and at a certain stage brings forth the material agencies for its own annihilation. This annihilation, the transformation of the individual and scattered means of production into socially concentrated ones, forms the prehistory of capital. As soon as the labourers are turned into proletarians, their conditions of labour into capital, as soon as the capitalist mode of production stands on its own feet, the further socialisation of labour and further transformation of the land and other means of production, and therefore the further expropriation of private proprietors, takes a new form.
"That which is now to be expropriated is no longer the labourer working for himself, but the capitalist exploiting many labourers. This expropriation is accomplished by the action of the immanent laws of capitalistic production itself, by the concentration of capitals. One capitalist always kills many. Hand in hand with this concentration, or this expropriation of many capitalists by few, develop, on an ever extending scale, the co-operative form of the labour-process, the conscious technical application of science, the methodical collective cultivation of the soil, the transformation of the instruments of labour into instruments of labour only usable in common, the economising of all means of production by their use as the jointly owned means of production of combined, socialised labour. Along with the constantly diminishing number of the magnates of capital, who usurp and monopolise all advantages of this process of transformation, grows the mass of misery, oppression, slavery, degradation, exploitation; but with this too grows the revolt of the working class, a class always increasing in numbers, and disciplined, united, organised by the very mechanism of the process of capitalist production itself. Capital becomes a fetter upon the mode of production, which has sprung up and flourished along with, and under it. Concentration of the means of production and socialisation of labour at last reach a point where they become incompatible with their capitalist integument. This integument is burst asunder. The knell of capitalist private property sounds. The expropriators are expropriated."
And now I ask the reader: where are the dialectical frills and mazes and conceptual arabesques; where the mixed and misconceived ideas according to which everything is all one and the same thing in the end; where the dialectical miracles for his faithful followers; where the mysterious dialectical rubbish and the maze in accordance with the Hegelian Logos doctrine, without which Marx, according to Herr Dühring, is unable to put his exposition into shape? Marx merely shows from history, and here states in a summarised form, that just as formerly petty industry by its very development necessarily created the conditions of its own annihilation, i.e., of the expropriation of the small proprietors, so now the capitalist mode of production has likewise itself created the material conditions from which it must perish. The process is a historical one, and if it is at the same time a dialectical process, this is not Marx's fault, however annoying it may be to Herr Dühring.
It is only at this point, after Marx has completed his proof on the basis of historical and economic facts, that he proceeds:
"The capitalist mode of production and appropriation, hence the capitalist private property, is the first negation of individual private property founded on the labour of the proprietor. Capitalist production begets, with the inexorability of a process of nature, its own negation. It is the negation of the negation" — and so on (as quoted above).
Thus, by characterising the process as the negation of the negation, Marx does not intend to prove that the process was historically necessary. On the contrary: only after he has proved from history that in fact the process has partially already occurred, and partially must occur in the future, he in addition characterises it as a process which develops in accordance with a definite dialectical law. That is all. It is therefore once again a pure distortion of the facts by Herr Dühring when he declares that the negation of the negation has to serve here as the midwife to deliver the future from the womb of the past {D. K. G. 502-03}, or that Marx wants anyone to be convinced of the necessity of the common ownership of land and capital {503} (which is itself a Dühringian contradiction in corporeal form) on the basis of credence in the negation of the negation {479-80}.
Herr Dühring's total lack of understanding of the nature of dialectics is shown by the very fact that he regards it as a mere proof-producing instrument, as a limited mind might look upon formal logic or elementary mathematics. Even formal logic is primarily a method of arriving at new results, of advancing from the known to the unknown — and dialectics is the same, only much more eminently so; moreover, since it forces its way beyond the narrow horizon of formal logic, it contains the germ of a more comprehensive view of the world. The same correlation exists in mathematics. Elementary mathematics, the mathematics of constant quantities, moves within the confines of formal logic, at any rate on the whole; the mathematics of variables, whose most important part is the infinitesimal calculus, is in essence nothing other than the application of dialectics to mathematical relations. In it, the simple question of proof is definitely pushed into the background, as compared with the manifold application of the method to new spheres of research. But almost all the proofs of higher mathematics, from the first proofs of the differential calculus on, are from the standpoint of elementary mathematics strictly speaking, wrong. And this is necessarily so, when, as happens in this case, an attempt is made to prove by formal logic results obtained in the field of dialectics. To attempt to prove anything by means of dialectics alone to a crass metaphysician like Herr Dühring would be as much a waste of time as was the attempt made by Leibniz and his pupils to prove the principles of the infinitesimal calculus to the mathematicians of their time. The differential gave them the same cramps as Herr Dühring gets from the negation of the negation, in which, moreover, as we shall see, the differential also plays a certain role. Finally these gentlemen — or those of them who had not died in the interval — grudgingly gave way, not because they were convinced, but because it always came out right. Herr Dühring, as he himself tells us, is only in his forties, and if he attains old age, as we hope he may, perhaps his experience will be the same.
But what then is this fearful negation of the negation, which makes life so bitter for Herr Dühring and with him plays the same role of the unpardonable crime as the sin against the Holy Ghost does in Christianity? — A very simple process which is taking place everywhere and every day, which any child can understand as soon as it is stripped of the veil of mystery in which it was enveloped by the old idealist philosophy and in which it is to the advantage of helpless metaphysicians of Herr Dühring's calibre to keep it enveloped. Let us take a grain of barley. Billions of such grains of barley are milled, boiled and brewed and then consumed. But if such a grain of barley meets with conditions which are normal for it, if it falls on suitable soil, then under the influence of heat and moisture it undergoes a specific change, it germinates; the grain as such ceases to exist, it is negated, and in its place appears the plant which has arisen from it, the negation of the grain. But what is the normal life-process of this plant? It grows, flowers, is fertilised and finally once more produces grains of barley, and as soon as these have ripened the stalk dies, is in its turn negated. As a result of this negation of the negation we have once again the original grain of barley, but not as a single unit, but ten-, twenty- or thirtyfold. Species of grain change extremely slowly, and so the barley of today is almost the same as it-was a century ago. But if we take a plastic ornamental plant, for example a dahlia or an orchid, and treat the seed and the plant which grows from it according to the gardener's art, we get as a result of this negation of the negation not only more seeds, but also qualitatively improved seeds, which produce more beautiful flowers, and each repetition of this process, each fresh negation of the negation, enhances this process of perfection. — With most insects, this process follows the same lines as in the case of the grain of barley. Butterflies, for example, spring from the egg by a negation of the egg, pass through certain transformations until they reach sexual maturity, pair and are in turn negated, dying as soon as the pairing process has been completed and the female has laid its numerous eggs. We are not concerned at the moment with the fact that with other plants and animals the process does not take such a simple form, that before they die they produce seeds, eggs or offspring not once but many times; our purpose here is only to show that the negation of the negation really does take place in both kingdoms of the organic world. Furthermore, the whole of geology is a series of negated negations, a series of successive chatterings of old and deposits of new rock formations. First the original earth crust brought into existence by the cooling of the liquid mass was broken up by oceanic, meteorological and atmospherico-chemical action, and these fragmented masses were stratified on the ocean bed. Local upheavals of the ocean bed above the surface of the sea subject portions of these first strata once more to the action of rain, the changing temperature of the seasons and the oxygen and carbonic acid of the atmosphere. These same influences act on the molten masses of rock which issue from the interior of the earth, break through the strata and subsequently cool off. In this way, in the course of millions of centuries, ever new strata are formed and in turn are for the most part destroyed, ever anew serving as material for the formation of new strata. But the result of this process has been a very positive one: the creation of a soil composed of the most varied chemical elements and mechanically fragmented, which makes possible the most abundant and diversified vegetation.
It is the same in mathematics. Let us take any algebraic quantity whatever: for example, a. If this is negated, we get -a (minus a). If we negate that negation, by multiplying -a by -a, we get +a2, i.e., the original positive quantity, but at a higher degree, raised-to its second power. In this case also it makes no difference that we can obtain the same a2 by multiplying the positive a by itself, thus likewise getting a2. For the negated negation is so securely entrenched in a2 that the latter always has two square roots, namely, a and — a. And the fact that it is impossible to get rid of the negated negation, the negative root of the square, acquires very obvious significance as soon as we come to quadratic equations. — The negation of the negation is even more strikingly obvious in higher analysis, in those "summations of indefinitely small magnitudes" {D. Ph. 418} which Herr Dühring himself declares are the highest operations of mathematics, and in ordinary language are known as the differential and integral calculus. How are these forms of calculus used? In a given problem, for example, I have two variables, x and y, neither of which can vary without the other also varying in a ratio determined by the facts of the case. I differentiate x and y, i.e., I take x and y as so infinitely small that in comparison with any real quantity, however small, they disappear, that nothing is left of x and y but their reciprocal relation without any, so to speak, material basis, a quantitative ratio in which there is no quantity. Therefore, dy/dx, the ratio between the differentials of x and y, is dx equal to 0/0 but 0/0 taken as the expression of y/x. I only mention in passing that this ratio between two quantities which have disappeared, caught at the moment of their disappearance, is a contradiction; however, it cannot disturb us any more than it has disturbed the whole of mathematics for almost two hundred years. And now, what have I done but negate x and y, though not in such a way that I need not bother about them any more, not in the way that metaphysics negates, but in the way that corresponds with the facts of the case? In place of x and y, therefore, I have their negation, dx and dy, in the formulas or equations before me. I continue then to operate with these formulas, treating dx and dy as quantities which are real, though subject to certain exceptional laws, and at a certain point I negate the negation, i.e., I integrate the differential formula, and in place of dx and dy again get the real quantities x and y, and am then not where I was at the beginning, but by using this method I have solved the problem on which ordinary geometry and algebra might perhaps have broken their jaws in vain.
It is the same in history, as well. All civilised peoples begin with the common ownership of the land. With all peoples who have passed a certain primitive stage, this common ownership becomes in the course of the development of agriculture a fetter on production. It is abolished, negated, and after a longer or shorter series of intermediate stages is transformed into private property. But at a higher stage of agricultural development, brought about by private property in land itself, private property conversely becomes a fetter on production, as is the case today both with small and large landownership. The demand that it, too, should be negated, that it should once again be transformed into common property, necessarily arises. But this demand does not mean the restoration of the aboriginal common ownership, but the institution of a far higher and more developed form of possession in common which, far from being a hindrance to production, on the contrary for the first time will free production from all fetters and enable it to make full use of modern chemical discoveries and mechanical inventions.
Or let us take another example: The philosophy of antiquity was primitive, spontaneously evolved materialism. As such, it was incapable of clearing up the relation between mind and matter. But the need to get clarity on this question led to the doctrine of a soul separable from the body, then to the assertion of the immortality of this soul, and finally to monotheism. The old materialism was therefore negated by idealism. But in the course of the further development of philosophy, idealism, too, became untenable and was negated by modern materialism. This modern materialism, the negation of the negation, is not the mere re-establishment of the old, but adds to the permanent foundations of this old materialism the whole thought-content of two thousand years of development of philosophy and natural science, as well as of the history of these two thousand years. It is no longer a philosophy at all, but simply a world outlook which has to establish its validity and be applied not in a science of sciences standing apart, but in the real sciences. Philosophy is therefore "sublated" here, that is, "both overcome and preserved" {D. K. G. 503}; overcome as regards its form, and preserved as regards its real content. Thus, where Herr Dühring sees only "verbal jugglery", closer inspection reveals an actual content.
Finally: Even the Rousseau doctrine of equality — of which Dühring's is only a feeble and distorted echo — could not have seen the light but for the midwife's services rendered by the Hegelian negation of the negation {502-03} — though it was nearly twenty years before Hegel was born. [63] And far from being ashamed of this, the doctrine in its first presentation bears almost ostentatiously the imprint of its dialectical origin. In the state of nature and savagery men were equal; and as Rousseau regards even language as a perversion of the state of nature, he is fully justified in extending the equality of animals within the limits of a single species also to the animal-men recently classified by Haeckel hypothetically as Alali: speechless. But these equal animal-men had one quality which gave them an advantage over the other animals: perfectibility, the capacity to develop further; and this became the cause of inequality. So Rousseau regards the rise of inequality as progress. But this progress contained an antagonism: it was at the same time retrogression.
Already in Rousseau, therefore, we find not only a line of thought which corresponds exactly to the one developed in Marx's Capital, but also, in details, a whole series of the same dialectical turns of speech as Marx used: processes which in their nature are antagonistic, contain a contradiction; transformation of one extreme into its opposite; and finally, as the kernel of the whole thing, the negation of the negation. And though in 1754 Rousseau was not yet able to speak the Hegelian jargon {D. K. G. 491}, he was certainly, sixteen years before Hegel was born, deeply bitten with the Hegelian pestilence, dialectics of contradiction, Logos doctrine, theologies, and so forth. And when Herr Dühring, in his shallow version of Rousseau's theory of equality, begins to operate with his victorious two men, he is himself already on the inclined plane down which he must slide helplessly into the arms of the negation of the negation. The state of things in which the equality of the two men flourished, which was also described as an ideal one, is characterised on page 271 of his Philosophie as the "primitive state". This primitive state, however, according to page 279, was necessarily sublated by the "robber system" — the first negation. But now, thanks to the philosophy of reality, we have gone so far as to abolish the robber system and establish in its stead the economic commune {504} based on equality which has been discovered by Herr Dühring — negation of the negation, equality on a higher plane. What a delightful spectacle, and how beneficently it extends our range of vision: Herr Dühring's eminent self committing the capital crime of the negation of the negation!
And so, what is the negation of the negation? An extremely general — and for this reason extremely far-reaching and important — law of development of nature, history, and thought; a law which, as we have seen, holds good in the animal and plant kingdoms, in geology, in mathematics, in history and in philosophy — a law which even Herr Dühring, in spite of all his stubborn resistance, has unwittingly and in his own way to follow. It is obvious that I do not say anything concerning the particular process of development of, for example, a grain of barley from germination to the death of the fruit-bearing plant, if I say it is a negation of the negation. For, as the integral calculus is also a negation of the negation, if I said anything of the sort I should only be making the nonsensical statement that the life-process of a barley plant was integral calculus or for that matter that it was socialism. That, however, is precisely what the metaphysicians are constantly imputing to dialectics. When I say that all these processes are a negation of the negation, I bring them all together under this one law of motion, and for this very reason I leave out of account the specific peculiarities of each individual process. Dialectics, however, is nothing more than the science of the general laws of motion and development of nature, human society and thought.
But someone may object: the negation that has taken place in this case is not a real negation: I negate a grain of barley also when I grind it, an insect when I crush it underfoot, or the positive quantity a when I cancel it, and so on. Or I negate the sentence: the rose is a rose, when I say: the rose is not a rose; and what do I get if I then negate this negation and say: but after all the rose is a rose? — These objections are in fact the chief arguments put forward by the metaphysicians against dialectics, and they are wholly worthy of the narrow-mindedness of this mode of thought. Negation in dialectics does not mean simply saying no, or declaring that something does not exist, or destroying it in any way one likes. Long ago Spinoza said: Omnis determinatio est negatio — every limitation or determination is at the same time a negation. [64] And further: the kind of negation is here determined, firstly, by the general and, secondly, by the particular nature of the process. I must not only negate, but also sublate the negation. I must therefore so arrange the first negation that the second remains or becomes possible. How? This depends on the particular nature of each individual case. If I grind a grain of barley, or crush an insect, I have carried out the first part of the action, but have made the second part impossible. Every kind of thing therefore has a peculiar way of being negated in such manner that it gives rise to a development, and it is just the same with every kind of conception or idea. The infinitesimal calculus involves a form of negation which is different from that used in the formation of positive powers from negative roots. This has to be learnt, like everything else. The bare knowledge that the barley plant and the infinitesimal calculus are both governed by negation of negation does not enable me either to grow barley successfully or to differentiate and integrate; just as little as the bare knowledge of the laws of the determination of sound by the dimensions of the strings enables me to play the violin. — But it is clear that from a negation of the negation which consists in the childish pastime of alternately writing and cancelling a, or in alternately declaring that a rose is a rose and that it is not a rose, nothing eventuates but the silliness of the person who adopts such a tedious procedure. And yet the metaphysicians try to make us believe that this is the right way to carry out a negation of the negation, if we ever should want to do such a thing.
Once again, therefore, it is no one but Herr Dühring who is mystifying us when he asserts that the negation of the negation is a stupid analogy invented by Hegel, borrowed from the sphere of religion and based on the story of the fall of man and his redemption {D. K. G. 504}. Men thought dialectically long before they knew what dialectics was, just as they spoke prose long before the term prose existed. [An allusion to Molière's comedy Le Bourgeois gentilhomme, Act II, Scene 6 — Ed.] The law of negation of the negation, which is unconsciously operative in nature and history and, until it has been recognised, also in our heads, was only first clearly formulated by Hegel. And if Herr Dühring wants to operate with it himself on the quiet and it is only that he cannot stand the name, then let him find a better name. But if his aim is to banish the process itself from thought, we must ask him to be so good as first to banish it from nature and history and to invent a mathematical system in which -a x -a is not +a2 and in which differentiation and integration are prohibited under severe penalties.