ABC of Materialist Dialectics

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Trotsky's 'ABC of Materialist Dialectics' is a brilliant short explanation of Marxist philosophy. It was written as part of a defence of Marxism against a middle class revisionist tendency in the American Trotskyist movement in the late 1930s, which attempted to challenge its basic principles. As opposed to pragmatism and empiricism, Trotsky defended dialectical materialism as a richer, fuller, more comprehensive view of society and life in general. Reprinted in 1994 with a new introduction by Rob Sewell and a short addition summary of the basic points of dialectical materialism by John Pickard.

Trotsky's 'ABC of Materialist Dialectics' is a brilliant short explanation of Marxist philosophy. It was written as part of a defence of Marxism against a middle class revisionist tendency in the American Trotskyist movement in the late 1930s, which attempted to challenge its basic principles. As opposed to pragmatism and empiricism, Trotsky defended dialectical materialism as a richer, fuller, more comprehensive view of society and life in general. Reprinted in 1994 with a new introduction by Rob Sewell and a short addition summary of the basic points of dialectical materialism by John Pickard.


The dialectic is neither fiction nor mysticism, but a science of the forms of our thinking insofar as it is not limited to the daily problems of life but attempts to arrive at an understanding of more complicated and drawn-out processes. The dialectic and formal logic bear a relationship similar to that between higher and lower mathematics.

I will here attempt to sketch the substance of the problem in a very concise form. The Aristotelian logic of the simple syllogism starts from the proposition that 'A' is equal to 'A'. This postulate is accepted as an axiom for a multitude of practical human actions and elementary generalisations. But in reality 'A' is not equal to 'A'. This is easy to prove if we observe these two letters under a lens - they are quite different from each other. But, one can object, the question is not of the size or the form of the letters, since they are only symbols for equal quantities, for instance, a pound of sugar. The objection is beside the point; in reality a pound of sugar is never equal to a pound of sugar - a more delicate scale always discloses a difference. Again one can object: but a pound of sugar is equal to itself. Neither is this true - all bodies change uninterruptedly in size, weight, colour, etc. They are never equal to themselves. A sophist will respond that a pound of sugar is equal to itself 'at any given moment.'

Aside from the extremely dubious practical value of this 'axiom,' it does not withstand theoretical criticism either. How should we really conceive the word 'moment'? If it is an infinitesimal interval of time, then a pound of sugar is subjected during the course of that 'moment' to inevitable changes. Or is the 'moment a purely mathematical abstraction, that is, a zero of time? But everything exists in time; and existence itself is an uninterrupted process of transformation; time is consequently a fundamental element of existence. Thus the axiom 'A' is equal to 'A' signifies that a thing is equal to itself if it does not change, that is, if it does not exist.

At first glance it could seem that these 'subtleties' are useless. In reality they are of decisive significance. The axiom 'A' is equal to 'A appears on the one hand to be the point of departure for all our knowledge, on the other hand the point of departure for all the errors in our knowledge. To make use of the axiom 'A' is equal to 'A' with impunity is possible only within certain limits. When quantitative changes in 'A' are negligible for the task at hand then we can presume that 'A' is equal to 'A'. This is, for example, the manner in which a buyer and a seller consider a pound of sugar. We consider the temperature of the sun likewise. Until recently we considered the buying power of the dollar in the same way. But quantitative changes beyond certain limits become converted into qualitative. A pound of sugar subjected to the action of water or kerosene ceases to be a pound of sugar. A dollar in the embrace of a president ceases to be a dollar. To determine at the right moment the critical point where quantity changes into quality is one of the most important and difficult tasks in all the spheres of knowledge including sociology.

Every worker knows that it is impossible to make two completely equal objects. In the elaboration of bearing-brass into cone bearings, a certain deviation is allowed for the cones which should not, however, go beyond certain limits (this is called tolerance). By observing the norms of tolerance, the cores are considered being equal. ( 'A' is equal to 'A'.) When the tolerance is exceeded the quantity goes over into quality; in other words, the cone bearings become inferior or completely worthless.

Our scientific thinking is only a part of our general practice including techniques. For concepts there also exist 'tolerance' which is established not by formal logic issuing from the axiom 'A' is equal to 'A', but by dialectical logic issuing from the axiom that everything is always changing. 'Common sense' is characterised by the fact that it systematically exceeds dialectical 'tolerance.'

Vulgar thought operates with such concepts as capitalism, morals, freedom, workers' state, etc. as fixed abstractions, presuming that capitalism is equal to capitalism, morals is equal to morals, etc. Dialectical thinking analyses all things and phenomena in their continuous change, while determining in the material conditions of those changes that critical limit beyond which 'A' ceases to be 'A', a workers' state ceases to be a workers' state.

The fundamental flaw of vulgar thought lies in the fact that it wishes to content itself with motionless imprints of a reality which consists of eternal motion. Dialectical thinking gives to concepts, by means of closer approximations, corrections, concretisations, a richness of content and flexibility; I would say even a succulence which to a certain extent brings them close to living phenomena. Not capitalism in general, but a given capitalism at a given stage of development. Not a workers' state in general, but a given workers' state in a backward country in an imperialist encirclement, etc.

Dialectical thinking is related to vulgar thinking in the same way that a motion picture is related to a still photograph. The motion picture does not outlaw the still photograph but combines a series of them according to the laws of motion. Dialectics does not deny the syllogism, but teaches us to combine syllogisms in such a way as to bring our understanding closer to the eternally changing reality. Hegel in his Logic established a series of laws: change of quantity into quality, development through contradiction, conflict of content and form, interruption of continuity, change of possibility into inevitability, etc., which are just as important for theoretical thought as in the simple syllogism for more elementary tasks.

Hegel wrote before Darwin and before Marx. Thanks to the powerful impulse given to thought by the French Revolution, Hegel anticipated the general movement of science. But because it was only an anticipation, although by a genius, it received from Hegel an idealistic character. Hegel operated with ideological shadows as the ultimate reality. Marx demonstrated that the movement of these ideological shadows reflected nothing but the movement of material bodies.

We call our dialectic, materialist, since its roots are neither in heaven nor in the depths of our 'free will', but in objective reality, in nature. Consciousness grew out of the unconscious, psychology out of physiology, the organic world out of the inorganic, the solar system out of nebulae. On all the rungs of this ladder of development, the quantitative changes were transformed into qualitative. Our thought, including dialectical thought, is only one of the forms of the expression of changing matter. There is place within this system for neither God, nor Devil, nor immortal soul, nor eternal norms of laws and morals. The dialectic of thinking, having grown out of the dialectic of nature, possesses consequently a thoroughly materialist character.

Darwinism, which explained the evolution of species through quantitative transformations passing into qualitative, was the highest triumph of the dialectic in the whole field of organic matter. Another great triumph was the discovery of the table of atomic weights of chemical elements and further the transformation of one element into another.

With these transformations (species, elements, etc.) is closely linked the question of classification, equally important in the natural as in the social sciences. Linnaeus' system (18th century), utilising as its starting point the immutability of species, was limited to the description and classification of plants according to their external characteristics. The infantile period of botany is analogous to the infantile period of logic, since the forms of our thought develop like everything that lives. Only decisive repudiation of the idea of fixed species, only the study of the history of the evolution of plants and their anatomy, prepared the basis for a really scientific classification.

Marx, who in distinction from Darwin was a conscious dialectician, discovered a basis for the scientific classification of human societies in the development of their productive forces and the structure of the relations of ownership which constitute the anatomy of society. Marxism substituted for the vulgar descriptive classification of societies and states, which even up to now still flourishes in the universities, a materialistic dialectical classification. Only through using the method of Marx is it possible correctly to determine both the concept of a workers' state and the moment of its downfall.

All this, as we see, contains nothing 'metaphysical' or 'scholastic', as conceited ignorance affirms. Dialectical logic expresses the laws of motion in contemporary scientific thought. The struggle against materialist dialectics on the contrary expresses a distant past, conservatism of the petty bourgeoisie, the self-conceit of university routinists and ... a spark of hope for an after-life.

15th December, 1939.


Introduction to The ABC of Materialist Dialectics

by Rob Sewell

Over the past period, especially since the collapse of the Berlin Wall, there has been a systematic and vitriolic attack on the ideas of Marxism. From the citadels of higher learning to the pulpit, from free market institutes to the gutter press, a deafening torrent has rained down on the Marxist viewpoint. In order to confuse and disorient the class conscious worker, nothing is spared by the arch defenders of capitalism to discredit scientific socialism. But given that capitalism has meant the return of mass unemployment and the social ills of the inter-war period, a layer of workers and youth are searching for answers to their problems. Increasingly they are driven by the harsh realities of life under capitalism to look for a way out.

Marxism offers thinking workers and youth a clear understanding of society and their place within it. It offers them a new world outlook. It offers them a future. In the words of Lenin, "The Marxian doctrine is omnipotent because it is true. It is complete and harmonious, and provides men with an integral world conception which is irreconcilable with any form of superstition, reaction or defence of bourgeois oppression." (The Three Sources and Three Component Parts of Marxism). The theories of Marxism provide workers with a clear understanding - a thread which is capable of taking him through the confused labyrinth of events, of the turmoil of the class struggle and the complexities of capitalist society.

Marxism was not simply plucked ready-made from Marx's head. Its theories represented a great development of the teachings of the greatest representatives of philosophy, economic thought and socialism. In essence, it was the fusion of German philosophy, English classic economic theory, and the best of French socialism. This combination provided the basis for a revolution in understanding. It was the birth of a new world outlook, enriched and deepened by the historical experience of the working class. It transformed the various trends of utopian socialism into a scientific socialism rooted in society and the class struggle.

Trotsky's 'ABC of Materialist Dialectics' is a brilliant short explanation of Marxist philosophy. It was written as part of a defence of Marxism against a middle class revisionist tendency in the American Trotskyist movement in the late 1930s, which attempted to challenge its basic principles. (See Trotsky's In Defence of Marxism). As opposed to pragmatism and empiricism, Trotsky defended dialectical materialism as a richer, fuller, more comprehensive view of society and life in general.

He explained that the dialectic "is the logic of evolution. Just as a machine shop in a plant supplies instruments for all departments, so logic is indispensable for all spheres of human knowledge... I know of two systems of logic worthy of attention: the logic of Aristotle (formal logic) and the logic of Hegel (the dialectic)."

The ancient Greeks, more than 2,000 years ago, made an outstanding contribution to the development of human thought. They sought to understand the universe, society and man's place within it. As Engels explained, "The ancient Greek philosophers were all natural-born dialecticians and Aristotle, the most encyclopaedic intellect among them, had even already analysed the most essential forms of dialectical thought." They began to see things not as fixed and lifeless, but in their real development and movement. In Heraclitus's words: "Everything is and is not, for everything is in flux, is constantly changing, constantly coming into being and passing away." This graphic description is the basic core of dialectics. This corresponded to Engels view: "For dialectical philosophy nothing is final, absolute, sacred. It reveals the transitory character of everything and in everything: nothing can endure before it except the uninterrupted process of becoming and passing away, of endless ascendancy from the lower to the higher." (Anti-Duhring).

For the Greeks, however, dialectical thought was simply an anticipation. Their major contribution, especially Aristotle, was the development of formal logic, which has held sway for more than two thousand years. Its three basic laws are: law of identity (a thing is always equal to itself, or A equals A); law of contradiction (if a thing is always identical with itself, it cannot be different from itself, or if A equals A, it can never equal non-A); law of excluded middle (everything must be either one of two things; when two opposing statements confront one another, both cannot be true or false; the correctness of one implies the incorrectness of its contrary). These inseparable laws, which were deduced from argument, were the axioms of Aristotle's system of thought.

This conception of reasoning was a huge leap for human thought and understanding and is the basis for our day to day perceptions. On this everyday level, we assume things are static and motionless. And from is point of view, formal logic serves us well. Dialectical understanding, on the other hand, "is not limited to the daily problems of life but attempts to arrive at an understanding of more complicated and drawn-out processes." (Trotsky).

For everyday purposes and simple calculations, formal logic, or "common sense" is sufficient. It has its limits, however, and beyond these the application of "common sense" turns truth into its opposite. At bottom, it is incapable of appreciating change and attempts to rid itself of all contradictions (which are inherent in change). If we attempt to understand more than "everyday things", then formal (or vulgar) logic becomes completely inadequate. "The fundamental flaw of vulgar thought lies in the fact that it wishes to content itself with motionless imprints of a reality which consists of eternal motion." (Trotsky). For everyday purposes, it is possible to say whether a thing is alive or dead. But in reality it is not so simple. At what point is it dead? At what pointed did life begin? It is not a single "event", but a protracted process.

That is not to say that formal logic is useless. On the contrary, it was historically progressive and necessary. This method permitted enormous advances in science and knowledge. However, it reached its limits. Although subordinate to dialectical thought, it is, nevertheless, out of formal logic that dialectics emerged. "Dialectical thought," explained Trotsky, "is related to vulgar thinking in the same way that a motion picture is related to a still photograph. The motion picture does not outlaw the still photograph but combines a series of them according to the laws of motion." However, the truer, more complete approximation of reality is contained in the movie.

These laws of logic, of thought, although used by billions of people, are not necessarily recognised by them as such. For instance, everyone eats according to the definite laws of physiology, but not everyone knows these laws or how they operate. Likewise, in one of Moliere's plays there is a man who learns about prose for the first time. When they explain to him what it is, he exclaims: "Why, I've been speaking prose all my life!"

The limits, however, of formal logic can be clearly seen in relation to evolution. According to the law of identity, a man is essentially a man and nothing else. But we know this not to be the case. According to natural evolution man is an animal. Yet this must be extended to say man is more than an animal; man is a species that is different from all other animals. We are, in reality, two exclusively different things at one and the same time. This is a contradiction that vulgar logic is unable to grasp. Only dialectics can explain this phenomenon.

The contribution of Hegel(1770-1831), the outstanding German philosopher, under the impact of the Great French Revolution, was the development of a new higher system of logic known as dialectics. As already mentioned, the original dialectical thinkers were the ancient Greeks who attempted to understand the universe and man's place in it. But given the low level of science and technique, their outlook was more in the nature of inspired guesses, or anticipations of later developments. Hegel studied the great Greek thinkers and drew out and developed their dialectical method, combining it with later knowledge, and producing a comprehensive analysis of the laws of dialectics.

The fundamental weakness of Hegelian dialectics was that Hegel combined them with a mystical idealist view of life. It was the great contribution of Marx and Engels that purged the dialectical method from its mystical shell. Hegel's dialectic was on its head, believing that the material world was a reflection of a 'Universal Idea' or God. Marx explained, on the contrary, thoughts and ideas were simply the reflection of the material world. So Hegelian dialectics were fused with modern materialism to produce the higher understanding of dialectical materialism.

These laws of dialectical materialism were able to explain things in their development and motion. Whereas formal logic was essentially the logic of lifeless, rigid and static relationships, dialectics was precisely an understanding of real life-processes of motion, contradiction and change.

Everything, according to Engels, "has its existence in eternal coming into being and passing away, in ceaseless flux, in unresting motion and change..." (Dialectics of Nature, p130). Dialectics is the logic of evolution, movement, and change. Its starting point is reality itself. A series of general laws of dialectics, outlined by Hegel, centred around the law of quantity into quality (and of quality into quantity), the unity of opposites, and the negation of the negation, which operate throughout the material world. Each one is organically linked to the others.

These laws, however, are not all-embracing and eternal. As Trotsky explained: "Dialectical materialism is not of course an eternal and immutable philosophy. To think otherwise is to contradict the spirit of the dialectic. Further development of scientific thought will undoubtedly create a more profound doctrine into which dialectical materialism will enter merely as structural material."(In Defence of Marxism, p76). We have already noticed that dialectical thought had its basic origins 2,000 years ago, were systematically developed by Hegel, and then further deepened by Marx and Engels. At this time, modern materialist dialectics are the closest understanding and approximation to reality, fully appreciating all its internal contradictions.

"Dialectics gives expression to a law which is felt in all grades of consciousness and in general experience," stated Hegel. "Everything that surrounds us may be viewed as an instance of dialectic. We are aware that everything finite, instead of being inflexible, is rather changeable and transient; and this is exactly what we mean by the dialectic of the finite, by which the finite, as implicitly other than it is, is forced to surrender its own immediate or natural being, and turn suddenly into its opposite." (Encyclopaedia, p128)

Movement and change results from causes inherent in processes and things, from internal contradictions. These contradictory tendencies within phenomena represent, in reality, a unity of opposites. The opposites are bound together in a relation of mutual dependence, where each is a condition of existence of the other. In class society, for instance, the class antagonisms between the exploiters and exploited is a fundamental aspect. One cannot exist without the other. This contradiction is the driving force of change. However, these contradictions are not static, but in the process of working themselves out. The overthrow of class society will lead to the abolition of classes themselves. New contradictions will inevitably unfold, but will be of a fundamentally different character, on a new higher level. As Lenin remarked that "antagonism and contradiction are utterly different. Under socialism antagonism disappears, but contradiction remains." (Critical Notes on Bukharin's Economics of the Transition Period). The elements of antagonism and conflict between men disappear and give way to conscious and harmonious planning of society. Contradictions remain, but as they no longer take the form of class antagonisms they do not require the forcible domination of one set of material interests over another.

Change takes place not in a straight line, and continuous gradual smooth development, but in leaps and revolutions. All change has a quantitative element, but this reaches a certain point, when the gradual changes give rise to a qualitative leap forward. Something new is born, entirely different from before. To explain developments we need to study the facts. "The dialectic is not a magic master key for all questions," explained Trotsky. "It does not replace concrete scientific analysis. But it directs this analysis along the correct road, securing it against sterile wanderings in the desert of subjectivism and scholasticism." (In Defence of Marxism, p52).

Change is not simply a repetition of the past. The working out of contradictions does not mean that earlier stages of development are repeated exactly, but develop on a higher level. This is one of the most general laws of dialectics, the negation of the negation. An "extremely far reaching and important law" says Engels. Motion, change and development move through an uninterrupted series of negations. But the past is not totally obliterated, but overcome and preserved at the same time. Features of the past may reappear, but in a new and enriched form. As Marx explained, capitalism arose through the ruination of pre-capitalist individual producers (its negation). The abolition of capitalism (its negation) is carried through, individual property of producers is restored, but on a higher level. The producer, as a participant in socialised production, then enjoys, as his individual property, a share of the social product.

The task of Marxism is to lay bare the real contradictions and processes unfolding in society, economy and politics. To draw a clear distinction between the appearance and the essence of things. To uncover the truth. Only by doing this will the working class, and in particular its advanced layers, see clearly its historic task and mission.

Yet, as we explained before, there are obstacles in the path of the worker's struggle for theory and understanding far more intractable than the scribblings of priests and professors. A man or woman who is obliged to toil long hours in industry, who has not had the benefit of a decent education and consequently lacks the habit of reading, finds great difficulty in absorbing some of the more complex ideas, especially at the outset. Yet it was for workers that Marx and Engels wrote, and not for 'clever' students and middle class people. 'Every beginning is difficult' no matter what science we are talking about. Marxism is a science and therefore makes heavy demands upon the beginner. But every worker who is active in the trade unions or Labour Party knows that nothing is worthwhile if attained without a degree of struggle and sacrifice. It is the activists in the Labour Movement at whom the present pamphlet is aimed. To the active worker who is prepared to persevere. One promise can be made: once the initial effort is made to come to grips with unfamiliar and new ideas, the theories of Marxism will be found to be basically straight forward and simple. Moreover - and this should be emphasised - the worker who acquires by patient effort an understanding of Marxism will turn out to be a better theoretician than most students, just because he or she can grasp the ideas not merely in the abstract, but concretely, as applied to his or her own life and work.

In the final analysis, Marxist philosophy is a guide to action. "Philosophers have only interpreted the world in various ways; the point is, however, to change it." (Karl Marx, Theses on Feurbach).

Rob Sewell, 18 April, 1994.


DIALECTICAL MATERIALISM

by John Pickard

When we discuss the method of Marxism, we are dealing with the ideas which provide the basis for our activities in the labour movement, the arguments we raise in the discussions we take part in, and the articles we write.

It is generally accepted that Marxism took its form from three main roots. One of those roots was the development of Marx's analysis of French politics, particularly the bourgeois revolution in France in the 1790s, and the subsequent class struggles during the early 19th century. Another of the roots of Marxism is what is called 'English economics', ie., Marx's analysis of the capitalist system as it developed in England. The other root of Marxism, which was its starting point historically, is said to be 'German philosophy', and it is that aspect of it that I want to deal with here.

To begin with, we say that the basis of Marxism is materialism. That is to say, Marxism starts from the idea that matter is the essence of all reality, and that matter creates mind, and not vice versa.

In other words, thought and all the things that are said to derive from thought - artistic ideas, scientific ideas, ideas of law, politics, morality and so on - these things are in fact derived from the material world. The 'mind', ie., thought and thought processes, is a product of the brain; and the brain itself, and therefore ideas, arose at a certain stage in the development of living matter. It is a product of the material world.

Therefore, to understand the real nature of human consciousness and society, as Marx himself put it, it is a question "not of setting out from what men say, imagine, conceive... in order to arrive at men in the flesh; but setting out from real, active men, and on the basis of their real life-process demonstrating the development of the ideological reflexes and echoes of this life-process. The phantoms formed in the human brain are also, necessarily, images of their material life-process, which is empirically verifiable and bound to material premises. Morality, religion, metaphysics, all the rest of ideology and their corresponding forms of consciousness, thus no longer retain the semblance of independence. They have no history, no development; but men, developing their material production and their material intercourse, alter, along with their real existence, their thinking and the products of their thinking. Life is not determined by consciousness, but consciousness by life. In the first (non-materialist) method of approach the starting point is consciousness taken as the living individual; in the second (materialist) method, which conforms to real living individuals themselves, and consciousness is considered solely as their consciousness." (The German Ideology, Chapter one).

A materialist therefore seeks an explanation not only for ideas, but for material phenomena themselves, in terms of material causes and not in terms of supernatural intervention by gods and the like. And that is a very important aspect of Marxism, which clearly sets it aside from the methods of thinking and logic which have become established in capitalist society.

The development of scientific thought in the European countries in the 17th and 18th centuries displayed some really contradictory characteristics, which still remain typical of the approach of bourgeois theoreticians today. On the one hand there was a development towards a materialist method. Scientists looked for causes. They didn't just accept natural phenomena as god-ordained miracles, they sought some explanation for them. But at the same time these scientists did not yet possess a consistent or worked-out materialist understanding; and very often, behind the explanations for natural phenomena, they also saw, at the end of the chain, the hand of God at work.

Such an approach means accepting, or at least leaving open the possibility, that the material world we live in is ultimately shaped by forces from outside it, and that consciousness or ideas come first, in the sense that they can exist independently of the real world. This approach, which is the philosophical opposite of materialism, we call 'idealism'.

According to this approach, the development of mankind and of society - of art, science, etc. - is dictated not by material processes but by the development of ideas, by the perfection or degeneration of human thought. And it is no accident that this general approach, whether spoken or unspoken, pervades all the philosophies of capitalism.

Bourgeois philosophers and historians in general take the present system for granted. They accept that capitalism is some kind of finished, complete system which is incapable of being replaced by a new and higher system. And they try to present all past history as the efforts of lesser mortals to achieve the kind of 'perfect society' which they believe capitalism has achieved or can achieve.

So, when we look at the work of some of the greatest bourgeois scientists and thinkers in the past or even today, we can see how they have tended to jumble up materialist ideas and idealist ideas in their minds. For example Isaac Newton, who examined the laws of mechanics and the laws of motion of planets and planetary bodies, didn't believe that these processes were dictated by mind or thought. But what he did believe was that an original impetus was given to all matter, and that this initial push was provided by some sort of supernatural force, by God.

In the same way it is possible today for many biologists to accept the idea that species of plants and animals evolved from one type to another, and that mankind itself is a development from earlier species. And yet many of them cling to the notion that there is a qualitative difference between the human mind and the animal mind, consisting of the 'eternal soul' which leaves the human body after death. Even some of the most eminent scientists jumble up the materialist method with idealist ideas of this kind, which are really backward, scientifically speaking, and are more related to magic and superstition than to science.

Marxism therefore represents a systematic and fundamental break with idealism in all its forms, and the development in it place of a materialist understanding of what is taking place in reality. Materialism in this sense provides one of the basic starting points of Marxism. The other basic starting point is dialectics.

DIALECTICS

Dialectics is quite simply the logic of motion, or the logic of common sense to activists in the movement. We all know that things don't stand still, they change. But there is another form of logic which stands in contradiction to dialectics, which we call 'formal logic', which again is deeply embodied in capitalist society. It is perhaps necessary to begin by describing briefly what this method implies.

Formal logic is based on what is known as the 'law of identity', which says that 'A' equals 'A' - i.e. that things are what they are, and that they stand in definite relationships to each other. There are other derivative laws based on the law of identity; for example, if 'A' equals 'A', it follows that 'A' cannot equal 'B', nor 'C'.

On the face of it this method of thinking may again seem like common sense; and in fact it has been a very important tool, a very important device in the development of science and in the industrial revolution which created the present-day society. The development of mathematics and basic arithmetic, for example, was based on formal logic. You couldn't teach a child a table of multiplication or addition without using formal logic. One plus one equals two, and not three. And in the same way, the method of formal logic was also the basis for the development of mechanics, of chemistry, of biology, etc.

For example, in the 18th century the Scandinavian biologist Linnaeus developed a system of classification for all known plants and animals. Linnaeus divided all living things into classes, into orders, into families, in the order of primates, in the family of hominids, in the genus of homo, and represents the species homo sapiens.

The system of classification represented an enormous step forward in biology. It made possible, for the first time, a real systematic study of plants ad animals, to compare and contrast animal and plant species. But it was based on formal logic. It was based on saying that homo sapiens equals homo sapiens; that musca domestica (the common housefly) equals musca domestica; that an earthworm equals earthworm, and so on. It was, in other words, a fixed and rigid system. It wasn't possible, according to this system, for a species to equal to anything else, otherwise the system of classification would have completely collapsed.

The same applies in the field of chemistry, where Dalton's atomic theory meant a huge stride forward. Dalton's theory was based on the idea that matter is made up of atoms, and that each type of atom is completely separate and peculiar to itself - that its shape and weight is peculiar to that particular element and to none other.

After Dalton there was a more or less rigid classification of elements, again based on a rigid formal logic, whereby it was said that an atom of hydrogen was an atom of hydrogen, an atom of carbon was an atom of carbon, etc. And if any atom could have been something else, this whole system of classification, which has formed the basis of modern chemistry, would have collapsed.

Now it is important to see that there are limitations to the method of formal logic. It is a useful everyday method, and it gives us useful approximations for identifying things. For example, the Linnaean system of classification is still useful to biologists; but since the work of Charles Darwin in particular we can also see the weaknesses in that system.

Darwin pointed out, for instance, that in the Linnaean system some types of plants are given separate names, as separate species, but actually they are very similar to each other. And yet there are other plants with the same name, of the same species, which are said to be different varieties of the same plant, and yet they are very different from each other.

So even by the time of Charles Darwin it was possible to look at the Linnaean system of classification and say, 'well, there's something wrong somewhere'. And of course Darwin's own work provided a systematic basis for the theory of evolution, which for the first time said it is possible for one species to be transformed into another species.

And that left a big hole in the Linnaean system. Before Darwin it was thought that the number of species on the planet was exactly the same as the number of species created by God in the first six days of his labour - except, of course, for those destroyed by the Flood - and that those species had survived unchanged over the millennia. But Darwin produced the idea of species changing, and so inevitably the method of classification also had to be changed.

What applies in the field of biology applies also in the field of chemistry. Chemists became aware, by the late 19th century, that it was possible for one atomic element to become transformed into another. In other words, atoms aren't completely separated and peculiar to themselves. We know now that many atoms, many chemical elements, are unstable. For example, uranium and other radioactive atoms will split in the course of time and produce completely different atoms with completely different chemical properties and different atomic weights.

So we can see that the method of formal logic was beginning to break down with the development of science itself. But it is the method of dialectics which draws the conclusions of these factual discoveries, and points out there are no absolute or fixed categories, either in nature or in society.

Whereas the formal logician will say that 'A' equals 'A', the dialectician will say that 'A' does not necessarily equal 'A'. Or to take a practical example that Trotsky uses in his writings, one pound of sugar will not be precisely equal to another pound of sugar. It is a good enough approximation if you want to buy sugar in a shop, but if you look at it more carefully you will see that it's actually wrong.

So we need to have a form of understanding, a form of logic, that takes into account the fact that things, and life, and society, are in a state of constant motion and change. And that form of logic, of course, is dialectics.

But on the other hand it would be wrong to think that dialectics ascribes to the universe a process of even and gradual change. The laws of dialectics - and here is a word of warning: these concepts sound more intimidating than they really are - the laws of dialectics describe the manner in which the processes of change in reality take place.

QUANTITY INTO QUALITY

Let us take, to begin with, the law of the transformation of quantity into quality'. This law states that the processes of change - motion in the universe - are not gradual, they are not even. Periods of relatively gradual or slight change are interspersed with periods of enormously rapid change - change which cannot be measured in terms of quantity but only in terms of quality.

To use an example from natural science again, let us imagine the heating of water. You can actually measure ("quantify"), in terms of degrees of temperature, the change that takes place in the water as you add heat to it. From, let us say, 10 degrees centigrade (which is normal tap water) to about 98 degrees centigrade, the change will remain quantitative; i.e., the water will remain water, although it is getting warmer.

But then comes a point where the change in the water becomes qualitative, and the water turns into steam. You can no longer describe the change in the water as it is heated from 98 degrees to 102 degrees in purely quantitative terms. We have to say that a qualitative change (water into steam) has come about as a result of an accumulation of quantitative change (adding more and more heat).

And that is what Marx and Engels meant when they referred to the transformation of quantity into quality. The same can be seen in the development of species. There is always a great variety in every species. If we look around this room we can see the degree of variety in homo sapiens. That variety can be measured quantitatively, for example, in terms of height, weight, skin colour, length of nose, etc.

But if evolutionary changes progress to a certain point under the impact of environmental changes, then those quantitative changes can add up to a qualitative change. In other words, you would no longer characterise that change in animal or plant species merely in terms of quantitative details. The species will have become qualitatively different.

For example, we as a species are qualitatively different from chimpanzees or gorillas, and they in turn are qualitatively different from other species of mammals. And those qualitative differences, those evolutionary leaps, have come about as a result of quantitative changes in the past.

The idea of Marxism is that there will always be periods of gradual change interspersed with periods of sudden change. In pregnancy, there is a period of gradual development, and then a period of very sudden development at the end. The same applies to social development. Very often Marxists have used the analogy of pregnancy to describe the development of wars and revolutions. These represent qualitative leaps in social development; but they come about as a result of the accumulation of quantitative contradictions in society.

NEGATION OF THE NEGATION

A second law of dialectics is 'the law of the negation of the negation', and again it sounds more complicated than it really is. 'Negation' in this sense simply means the passing away of one thing, the death of one thing as it becomes transformed into another.

For example, the development of class society in the early history of humanity represented the negation of the previous classless society. And in future, with the development of communism, we will see another classless society, that would mean the negation of all present class society.

So the law of the negation of the negation simply states that as one system comes into existence, it forces another system to pass away. But that doesn't mean that the second system is permanent or unchangeable. That second system itself becomes negated as a result of the further developments and processes of change in society. As class society has been the negation of classless society, so communist society will be the negation of class society - the negation of the negation.

Another concept of dialectics is the law of the 'interpenetration of opposite'. This law quite simply states that processes of change take place because of contradictions - because of the conflicts between the different elements that are embodied in all natural and social processes.

Probably the best example of the interpenetration of opposites in natural science is the 'quantum theory'. This theory is based on the concept of energy having a dual character - that for some purposes, according to some experiments, energy exists in the form of waves, like electromagnetic energy. But for other purposes energy manifests itself as particles. In other words, it is quite accepted among scientists that matter and energy can actually exist in two different forms at one and the same time - on the one hand as a kind of intangible wave, on the other hand as a particle with a definite 'quantum' (amount) of energy embodied in it.

Therefore the basis of the quantum theory in modern physics is contradiction. But there are many other contradictions known to science. Electromagnetic energy, for example, is set in motion through the effect of positive and negative forces on each other. Magnetism depends on the existence of a north pole and a south pole. These things cannot exist separately. They exist and operate precisely because of the contradictory forces being embodied in one and the same system.

Similarly, every society today consists of different contradictory elements joined together in one system, which makes it impossible for any society, any country, to remain stable or unchanged. The dialectical method, in contrast to the method of formal logic, trains us to identify these contradictions, and thereby get to the bottom of the changes taking place.

Marxists are not embarrassed to say that there are contradictory elements within every social process. On the contrary, it is precisely by recognising and understanding the opposite interests embodied within the same process that we are able to work out the likely direction of change, and consequently to identify the aims and objectives which it is necessary and possible in that situation to strive for from the working class point of view.

At the same time, Marxism doesn't abandon formal logic altogether. But it is important to see, from the point of view of understanding social developments, that formal logic must take second position.

We all use formal logic for everyday purposes. It gives us the necessary approximations for communication and conducting our daily activities. We wouldn't be able to lead normal lives without paying lip service to formal logic, without using the approximation that one equals one.

But, on the other hand, we have to see the limitations of formal logic - the limitations that become evident in science when we study processes in more depth and detail, and also when we examine social and political processes more closely.

Dialectics is very rarely accepted by scientists. Some scientists are dialecticians, but the majority even today muddle up a materialist approach with all sorts of formal and idealistic ideas.

And if that's the case in natural science, it is much, much more the case as far as the social sciences are concerned. The reasons for this are fairly obvious. If you try to examine society and social processes from a scientific point of view, then you cannot avoid coming up against the contradictions of the capitalist system and the need for the socialist transformation of society.

But the universities, which are supposed to be centres of learning and study, are under capitalism far from being independent of the ruling class and the state. That is why natural science can still have a scientific method which leans towards dialectical materialism; but when it comes to the social sciences you will find in the colleges and universities some of the worst kinds of formalism and idealism possible.

That is not unrelated to the vested interests of the professors and academics who are highly paid. It is obvious and unavoidable that their privileged position in society will have some reflection, some effect on what they're supposed to teach. Their own views and prejudices will be contained in the 'knowledge' which they pass on to their students, and so on down to the level of the schools.

Bourgeois historians, in particular, are among the most shortsighted of all social scientists. How many times have we seen examples of bourgeois historians who imagine that history ended yesterday! Here in Britain they all seem to admit the horrors of British imperialism as far as the 17th, 18th and 19th centuries are concerned; that British imperialism engaged in slave traffic; that it was responsible for some of the most bloody subjugation of colonial peoples; that it was also responsible for some of the worst exploitation of British workers, including women and children, in the coal mines, the cotton mills, and so on.

They will accept all these iniquities - up until yesterday. But when it comes to today, of course, then British imperialism suddenly becomes democratic and progressive.

And that is completely one-sided, a completely lopsided view of history, which is diametrically opposed to the method of Marxism. The attitude of Marx and Engels was to view social processes from the same dialectical standpoint from which they viewed nature - from the standpoint of the processes that are actually taking place.

In our everyday discussions and debates in the labour movement, we will often come across people who are formalists. Even many on the left will look at things in a completely rigid and formal way, without understanding the direction in which things are moving.

The right wing in the labour movement, and also some on the left, believe that Marxist theory is a dogma, that 'theory' is like a 600 lb weight on the back of an activist, and the quicker you get rid of that weight, the more active and effective you can be.

But that is a complete misconception of the whole nature of Marxist theory. In point of fact Marxism is the opposite of a dogma. It is precisely a method for coming to grips with the processes of change that are taking place around us.

Nothing is fixed and nothing remains unchanged. It is the formalists who see society as a still photograph, who can get overawed by the situations they are faced with because they don't see how and why things will change. It is this kind of approach that can easily lead to a dogmatic acceptance of things as they are or as they have been, without understanding the inevitability of change.

Marxist theory is therefore an absolutely essential device for any activity within the labour movement. We need to be consciously attuned to the contradictory forces at work in the class struggle, in order to orient ourselves to the way in which events are developing.

Of course it isn't always easy to free ourselves from the prevailing framework of thinking in capitalist society and absorb the Marxist method. As Karl Marx said, there is no royal road to science. You have to treat the hard path sometimes in grappling with new political ideas.

But the discussion and study of Marxist theory is an absolutely essential part of the development of every activist. It is that theory alone that will provide comrades with a compass and a map amidst all the complexities of the struggle. It is all very well to be an activist. But without a conscious understanding of the processes you are involved in, you are no more effective than an explorer without a compass and a map.

And if you try to explore without scientific aids, you can be as energetic as you like but sooner or later you will fall into a ravine or a bog and disappear, as so many activists over the years have unfortunately done.

The idea of having a compass and a map is that you can take your bearings. You can judge where you are at any particular time, where you are going and where you will be. And that is the fundamental reason why we need to get to grips with Marxist theory. It provides us with an absolutely invaluable guide to action as far as our activities in the labour movement are concerned.

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