George Novack
An Introduction to the Logic Of Marxism: LECTURE I
These lectures deal with the ideas of materialist dialectics, the logic of Marxism.
Has it struck you how exceptional a project this is? Here are members and sympathisers of a revolutionary political party under government persecution in the midst of World War II, the biggest war in world history. These industrial workers, these professional revolutionists, have come together, not to discuss matters and decide upon measures requiring immediate action, but for the purpose of studying a science which seems to be as remote as higher mathematics from everyday political struggle.
What a contrast to the malicious caricature of the Marxist movement deliberately drawn by capitalist hands! The possessing classes depict revolutionary socialists as demented individuals who delude themselves and others by fantastic visions of a workers’ world. The capitalist rulers are like children who can’t picture a world in which they don’t exist and in which they aren’t the central figures.
They claim to be guided by logic and by reason. Yet it takes only one look at the world today to determine who is irrational and who is sane: the capitalists or their revolutionary opponents. The present monarchs of society have run amok and are behaving like maniacs. They have plunged the world into mass murder for the second time in a quarter of a century; put the torch to civilisation; and threaten to destroy along with themselves the rest of humanity. And the spokesmen for these unbalanced people presume to call us “crazy” and our struggle for socialism evidence of “unrealism.”
No, the shoe is on the other foot. In fighting against the mad chaos of capitalism for a socialist system free from class exploitation and oppression, wars, crises, imperialist enslavement and barbarism, we Marxists are the most reasonable individuals alive. That is why, unlike all other social and political groupings, we take the science of logic so very seriously. Our logic is the indispensable instrument for prosecuting the struggle against capitalism and for socialism.
The logic of the materialist dialectic is, to be sure, quite different from the prevailing logic of the bourgeois world. Our method, like our ideas, is, as we propose to prove, more scientific, far more practical, and also far more “logical” than any other logic. We maintain with greater comprehension and comprehensiveness the fundamental principle of science that there exists an inner logic of relations throughout all reality and that the laws of this logic can be known and transmitted to others. The social world around us is only superficially senseless. There is method even in the madness of the capitalist class. Our task is to find out what the most general laws of that inner logic of nature, society, and the human mind are. While the bourgeoisie are losing their heads, we shall try to improve and to clarify ours.
We have excellent precedents for this kind of enterprise. During the early months of the First World War, Lenin, in exile at Berne, Switzerland, resumed his study of Hegel’s logic simultaneously with developing his Bolshevik program of struggle against imperialist war. The impress of this theoretical work can be discerned in all his subsequent thinking, writing, and acting. Lenin prepared himself and his party for the coming revolutionary events by mastering dialectics. In the first months of the Second World War, while conducting the fight against the petty-bourgeois opposition in the Socialist Workers Party, Trotsky stressed time and again the crucial importance of the method of materialist dialectics in revolutionary socialist politics. His book, In Defence of Marxism, revolves around this theoretical axis.
Here, as in all our activities, we are guided by the leaders of scientific socialism who taught the dialectical truth that there is nothing so practical in proletarian politics as the right method of thought. That method can be only the method of materialist dialectics we are going to study.
Logic is a science. Every science studies a particular kind of motion in its connections with other modes of material motion and seeks to discover the general laws and specific modes of that movement. Logic is the science of the thought process. Logicians investigate the activities of the thought process which goes on in human heads and formulate the laws, forms and interrelations of those mental processes.
Two main types of logic have arisen out of the two main stages in the development of the science of logic: formal logic and dialectics. These are the most highly developed forms of mental motion. They have as their function the conscious understanding of all forms of motion, including their own.
Although we are primarily interested in materialist dialectics, we shall not proceed at once to consider the dialectical method of reasoning. We shall approach dialectics indirectly by first examining the fundamental ideas of another kind of reasoning: the method of formal logic. As a method of thought, formal logic is the polar opposite of materialist dialectics.
Why, then, do we begin our study of the dialectical method by studying its opposite in logical science?
There are excellent reasons for such a procedure. First of all, dialectics has grown out of formal logic in the course of historical development. Formal logic was the first great system of the scientific knowledge of the thought processes. It was the consummation of the philosophical work of the ancient Greeks, the crowning glory of Greek thought. The early Greek thinkers made many important discoveries about the nature of the thought process and its products. The synthesiser of Greek thought, Aristotle, collected, classified, criticised and systematised these positive results of thinking about thought and thereby created formal logic. Euclid did the same for elementary geometry; Archimedes for elementary mechanics; Ptolemy of Alexandria later for astronomy and geography; Galen for anatomy.
Aristotle’s logic held sovereign sway in the realm of thought for over two thousand years. It had no rival until it was challenged, overthrown and superseded by dialectics, the second great system of logical science. Dialectics was likewise the outcome of a revolutionary scientific movement covering centuries of intellectual labor. It came as the consummation of the brainwork of the outstanding philosophers of the bourgeois-democratic revolution in Western Europe from the sixteenth to the nineteenth centuries. Hegel, the titan of the revolutionary German bourgeois school of idealist philosophy, was the mastermind who transformed the science of logic by being the first, as Marx pointed out, to “expound the general forms of movement (of the dialectic) in a comprehensive and fully conscious way.”
Marx and Engels were Hegel’s disciples in the field of logic. They in turn effected a revolution in the Hegelian revolution of logical science by purging his dialectics of its mystical elements and placing his idealist dialectics on a consistent materialist foundation.
If, therefore, we approach materialist dialectics by way of formal logic, we shall be retracing the steps of the actual historical progress of the science of logic which developed through formal logic to dialectics.
It would be wrong to assume from this brief sketch of the history of logic either that the Greeks knew nothing whatsoever about dialectics or that Hegel and Marx utterly rejected the ideas of formal logic. As Engels remarked: “The ancient Greek philosophers were all natural-born dialecticians and Aristotle, the most encyclopedic intellect among them, had even already analysed the most essential forms of dialectical thought.” Nevertheless dialectics remained an embryonic element in Greek thinking. The Greek philosophers did not and could not succeed in developing their scattered acute insights into systematic scientific shape. They bequeathed to posterity in finished form Aristotle’s formal logic. At the same time, their dialectical observations, their criticisms of formal thinking, and their paradoxes first posed the problems and exposed the limitations of formal logic which the science of logic wrestled with in the succeeding centuries and which the Hegelian and then the Marxist dialectics eventually solved.
These modern dialecticians did not look upon formal logic as worthless. Quite the contrary. They pointed out that formal logic was not only a historically necessary method of thought but also quite indispensable even now for correct thinking. But in itself formal logic was clearly deficient. Its valid elements became a constituent part of dialectics. The relations between formal logic and dialectics were reversed. Whereas among the classical Greek philosophers the formal side of logic became predominant and the dialectical aspects receded in importance, in the modern school dialectics occupies the front rank and the purely formal side of logic becomes subordinated to it.
Since these two opposing types of thought have so many points in common and formal logic enters as structural material into the framework of dialectical logic, it will be worth while to occupy ourselves first with formal logic. In studying formal logic we are already on the way to dialectics. By grasping the shortcomings, or rather the limits, of formal logic, we shall in fact already be over the threshold separating formal logic from dialectics. Hegel expressed this same thought in his Logic as follows: “It is immanent in the limit to be a contradiction which sends something beyond itself.”
Finally, from this procedure we can derive an important lesson in dialectical thinking. Hegel somewhere remarks that something is not truly known until it is known through its opposite. You cannot, for example, really understand the nature of a wage worker until you know what his socioeconomic opposite, the capitalist, is. You cannot know what Trotskyism is until you have plumbed to the depths the essence of its political antithesis, Stalinism. So you cannot grasp the innermost nature of dialectics without first obtaining a thorough understanding of its historical predecessor and theoretical antithesis, formal logic.
There are three fundamental laws of formal logic. First and most important is the law of identity. This law can be stated in various ways such as: A thing is always equal to or identical with itself. In algebraic terms: A equals A.
The particular formulation of this law is not so important as the idea involved. The essential thought contained in the law of identity is this. To say that a thing is always equal to itself is equivalent to asserting that under all conditions it remains one and the same. A given thing exists absolutely at any given moment. As physicists used to state: “Matter cannot be created or destroyed,” i.e., matter always remains matter.
This unconditional assertion of the absolute identity of a thing with itself excludes difference from the essence of things and of thought. If a thing is always and under all conditions equal to or identical with itself, it can never be unequal to or different from itself. This conclusion follows logically and inevitably from the law of identity. If A always equals A, it can never equal non-A.
This conclusion is made explicit in the second law of formal logic: the law of contradiction. The law of contradiction states: A is not non-A. This is no more than the negative formulation of the positive assertion expressed in the first law of formal logic. If A is A, it follows, according to formal thinking, that A cannot be non-A. Thus the second law of formal logic, the law of contradiction, forms the essential supplement to the first law.
Some examples: a man cannot be inhuman; a democracy cannot be undemocratic; a wageworker cannot be a non-wageworker.
The law of contradiction signifies the exclusion of difference from the essence of things and of thought about things. If A is necessarily always identical with itself, it cannot be different from itself. Difference and identity are, according to these two rules of logic, completely different, utterly disconnected, mutually exclusive characteristics of both things and thoughts.
This mutually exclusive quality of things is expressly taken note of in the third law of formal logic. This is the law of the excluded middle. According to this law, everything is and must be either one of two mutually exclusive things. If A equals A, it cannot equal non-A. A cannot be part of two opposing classes at one and the same time. Wherever two opposing statements or state of affairs confront each other, both cannot be true or false. A is either B or it is not B. The correctness of one judgment invariably implies the incorrectness of its contrary and vice versa.
This third law is a combination of the first two and flows logically from them.
These three laws comprise the basis of formal logic. All formal reasoning proceeds in accordance with these propositions. For some two thousand years they were the unquestioned axioms of Aristotle’s system of thought, just as the law of the exchange of equivalent values forms the foundation of commodity-producing societies.
Let me cite an interesting example of this kind of thinking from Aristotle’s writings. In his Posterior Analytics (Book I; ch. 33), Aristotle says that a man cannot simultaneously apprehend first, that man is essentially animal, i.e., cannot be other than animal — and second, that man is not essentially animal, that is, may assume that he is other than animal. That is to say, a man is essentially a man and can never be or be thought of as not being a man.
This must certainly be so according to the dictates of the laws of formal logic. Yet we all know that it is contrary to fact. The theory of natural evolution teaches that man is essentially animal and cannot be other than animal. Logically speaking, man is an animal. But we know also from the theory of social evolution, which is a continuation and development of purely animal evolution, that man is more than and is other than an animal. That is to say, he is not essentially an animal but man, which is a species of being quite different from all other animals. We are, and we know that we are, two different and mutually exclusive things at one and the same time, Aristotle and the laws of formal logic to the contrary notwithstanding.
You can see from this example how speedily and spontaneously the dialectical character of things and thoughts emerges from a critical consideration of formal thinking. Despite good intentions to restrict my view to formal logic, you will observe that I was compelled to step beyond the limits of that logic the moment I wanted to get at the truth of things. Now let us return to the province of formal logic.
I stated before that modern dialecticians do not deny all truth to the laws of formal logic. Such an attitude would be contrary to the spirit of dialectics which sees some element of truth in all assertions. At the same time dialectics enables us to detect the limitations and errors in formalised thinking about things.
The laws of formal logic contain important and undeniable elements of truth. They are reasonable generalisations, not purely arbitrary ideas which have been concocted out of nowhere and out of nothing. They were not imposed upon the thought process and upon the real world by Aristotle and his followers and then slavishly imitated for thousands of years thereafter. Billions of people who never heard of Aristotle or thought about logic have thought and still think in obedience to the laws he first formulated. In like fashion all bodies fall more or less in accordance with Newton’s laws of motion although, except for human bodies, they are incapable of comprehending his theories. Why do people think and things act in the objective world in line with the theoretical generalisations of Aristotle and Newton? Because the essential nature of reality constrains them to think or act that way. Aristotle’s laws of thought have as much material content and as much of a basis in the objective world as Newton’s laws of mechanical motion. “. . . our methods of thought, both formal logic and the dialectic, are not arbitrary constructions of our reason but rather expressions of the actual interrelationships in nature itself.” ( Trotsky, In Defence of Marxism, p. 84. )
What characteristics of material reality are reflected and conceptually reproduced in these formal laws of thought?
The law of identity formulates the material fact that definite things, and traits of things, persist and maintain recognisable similarity amidst all their phenomenal changes. Wherever essential continuity exists in reality, the law of identity is applicable.
We could neither act nor think correctly without consciously or unconsciously obeying this law. If we couldn’t recognise ourselves as the same person from moment to moment and from day to day — and there are people who cannot, who through amnesia or some other mental disturbance have lost their consciousness of self-identity — we would be lost. But the law of identity is no less valid for the rest of the universe than for human consciousness. It applies every day and everywhere to social life. If we couldn’t recognise the same piece of metal through all its various operations, we couldn’t get very far with production. If a farmer couldn’t follow the corn he sows from the seed to the ear and then on to the meal, agriculture would be impossible.
The infant takes a great step forward in understanding the nature of the world when he grasps for the first time the fact that the mother who feeds him remains the same person throughout various acts of feeding. The recognition of this truth is nothing but a particular instance of the recognition of the law of identity.
If we couldn’t tell what a workers’ state was through all its changes, we could easily go astray in the complicated circumstances of the contemporary class struggle. In fact, the petty-bourgeois oppositionists went wrong in regard to the Russian question, not only because they opposed dialectics, but especially because they couldn’t correctly apply the law of identity in the process of the development of the Soviet Union. They couldn’t see that, despite all the changes in the USSR produced by its degeneration under the Stalinist political regime, the Soviet Union retained the socio-economic foundations of the workers’ state created by the Russian workers and peasants through the October revolution.
Correct classification, arising from the comparison of likenesses with unlikenesses, is the necessary basis and the first stage in all scientific investigations. Classification, the inclusion of things in the same classes and the exclusion of other things and their grouping in different classes, would be impossible without the law of identity. Darwin’s theory of organic evolution originated in and depends upon the recognition of the essential identity of all the diverse creatures on this earth. Newton’s laws of mechanical motion brought under a single head all the movements of masses, from the falling stone to the whirling planets in the solar system. All science as well as all intelligent behaviour rests in part upon this law of identity.
The law of identity directs us to recognise likenesses amidst diversity, permanence amidst changes, to single out the basic similarities between separated and apparently different instances and entities, to uncover the real bonds of unity between them, to trace the connections between different and consecutive phases of the same phenomena. That is why the discovery and amplification of this law was so epoch-making in the history of scientific thought and why we continue to honour Aristotle for grasping its extraordinary significance. That is also why mankind continues to act and to think in accordance with this basic law of formal logic.
“ What is so remarkable in this law of identity?” you may ask. It says nothing more than the obvious fact that “a thing is a thing,” or” this is this.”
Nevertheless this law is not so self-evident nor so trivial as it may appear at first glance. It is extremely important that the momentous law be properly appraised and the historical significance of its discovery be understood.
It was a great advance in the knowledge of the universe when mankind discovered that clouds, steam, rain, ice were all water or that the heavens and the earth — hitherto conceived as different and opposing substances — were really one and the same. Biology was revolutionised with the discovery that all grades of living beings between unicellular organisms and mankind consisted of the selfsame substance. Physical science was revolutionised by the demonstration that all forms of material motion were convertible into one another and therefore essentially identical.
Isn’t it an enormous step forward in social and political understanding when a worker discovers on the one hand that a wageworker is a wageworker, and on the other hand that a capitalist is a capitalist? And that workers everywhere have common class interests that transcend all craft, national and racial boundaries? Thus a recognition of the truth contained in the law of identity is a necessary condition for becoming a revolutionary socialist.
It is one thing, however, to obey a law and to use it and quite a different thing to understand and to formulate it in a scientific manner. Everybody eats according to definite physiological laws, but they do not know what the laws of digestion are and how they operate. It is the same with the laws of logic. Everybody thinks, but not everyone knows what kind of laws regulate his thinking activity. It was one of Aristotle’s outstanding merits that he made explicit and expressed in logical terms this law of identity which runs through our thought processes.
The law of contradiction formulates the material fact that co-existing things and kinds of things, or consecutive states of the same thing, differ from and exclude each other. Obviously I am not the same kind of human being as you; I am quite different. Nor am I the same person I was yesterday; I am different. The Soviet Union is not the same as other states, nor is it the same as it was twenty years ago. It is different.
The formal law of contradiction, or the discerning of difference, is as necessary for correct classification as the law of identity. Indeed, without the existence of differences there would be no need for classification, just as without identity there would be no possibility of classification.
The law of the excluded middle expresses the fact that things oppose and mutually exclude each other in reality. I must be either myself or somebody else; today I must either be the same or be different from what I was yesterday. The Soviet Union must either be the same or be different from other states; it cannot be both at the same time. I must be either a man or an animal; I can’t be both simultaneously and in the same sense.
Thus the laws of formal logic express representative features of the real world. They have a material content and an objective basis. They are at one and the same time laws of thought, of society, and of nature. This threefold root gives them a universal character.
The three laws we have concentrated upon do not constitute the whole of formal logic. They simply form its foundations. Upon this basis and out of it there has arisen a complex structure of logical science which examines in detail the elements and mechanisms of the forms of thought. But we shall not enter into a discussion of the various categories, forms of propositions, judgments, syllogisms, etc., which make up the content of this body of formal logic. These can be found in any textbook of elementary logic and are not germane to our present purpose. We are principally concerned with understanding the essential ideas of formal logic, not their detailed developments.
In bourgeois intellectual circles common sense is held in high esteem as a method of thought and as a guide to action. Only science stands above it in the hierarchy of value. It is in the name of common sense and science, for example, that Max Eastman calls upon Marxists to discard “metaphysical” and “mystical” dialectics. Unfortunately, the bourgeois and petty-bourgeois ideologists rarely inform us what the logical content of common sense consists of and what relations exist between common sense and their” science.”
We shall here have to do that job for them, for in fact the anti-dialecticians not only don’t know what dialectics is. They don’t even know what formal logic really is. This is not surprising. Do the capitalists know what capitalism is, what its laws are, how these laws necessarily operate? If they did, they would not be taken unawares by its crises and its wars, nor be so confident of the permanence of their cherished system. Surely the Stalinists don’t know what Stalinism really is and what it necessarily leads to. If they did, they would no longer be Stalinists but would be on their way to becoming something else.
Insofar as common sense has systematic, logical characteristics, they are moulded upon the laws of formal logic. Common sense may be defined as an unsystematised or semiconscious version of the science of formal logic. The ideas and methods of formal logic have been in use now for so many centuries and have become so interwoven into our processes of thought and into the fabric of our civilisation that to most people they seem the exclusive, normal, natural mode of thought. The conceptions and the mechanisms of formal logic, like the syllogism, are tools of thought as familiar and universal as knives and other tools.
You know that the bourgeoisie believes that capitalist society is eternal because, they say, it conforms to unchangeable human nature. Socialism, they say, is impossible or inconceivable because human beings will always divide into opposing classes, the rich and the poor, the strong and the weak, the rulers and ruled, the propertied and unpropertied, and these classes will always fight to the death for the good things of life. A form of social organisation in which there are no classes, in which planning reigns instead of anarchy, in which the weak are protected against the strong, in which solidarity rules instead of savage struggle, appears the height of absurdity to them. They dismiss such socialist ideas as Utopian fantasies, idle wishes.
Yet we know that socialism is not a dream but a historical necessity, the inevitable next stage in social evolution. We know that capitalism is not eternal but a special historical form of material production which has been preceded by less developed forms of social production and is destined to be superseded by the superior form of socialist production.
Now let us consider the science of thought from the same standpoint as we consider the science of society. Bourgeois and petty-bourgeois thinkers believe that formal thinking is the ultimate form of logic, fixed and final. They dismiss as ridiculous the claim that materialist dialectics is a higher form of thought.
Do you remember that when someone first questioned the permanence of capitalism or urged the necessity of socialism, you were inclined to doubt these new revolutionary ideas? Why? Because your minds were still enslaved by the ruling ideas of our epoch which, as Marx declared, are the ideas of the ruling class. The ruling ideas of the ruling class in logical science today are the ideas of formal logic lowered to the level of common sense. All the opponents and critics of dialectics stand upon the ground of formal logic, whether or not they are fully aware of their position or will honestly admit it.
Indeed, the ideas of formal logic constitute the most tenacious of all theoretical prejudices in our society. Even after individuals have cast off their faith in capitalism and have become revolutionary socialists, they cannot entirely rid their minds of the habits of formal thinking which they absorbed in bourgeois life and which they continue to receive from their environment. The keenest of dialecticians can relapse at times into formalism, if they are not extremely careful and conscious in their thinking.
Just as Marxism denies the eternal reality of capitalism, so does it deny eternal validity to the forms of thought most characteristic of such class societies as capitalism. Human thought has changed and developed along with human society and to the same degree. The laws of thought are no more eternal than the laws of society. Just as capitalism is only one link in the chain of historical forms of social organisation of production, so formal logic is simply one link in the chain of historical forms of intellectual production. Just as the forces of socialism are fighting to replace the obsolete capitalist form of social production with a more developed system, so the advocates of materialist dialectics, the logic of scientific socialism, are struggling against the outworn formal logic. The theoretical struggle and the practical political struggle are integral parts of one and the same revolutionary process.
Before the rise of modern astronomy, people believed that the sun and other planets revolved around the earth. They uncritically trusted in the “common sense” evidence presented by their eyes. Aristotle taught that the earth was fixed and the perfect and invariable heavenly spheres revolved about it. This year marks the 400th anniversary of the publication of Copernicus’ book, On the Revolutions of the Heavenly Bodies, which revolutionised the prevailing notion of a static universe with the earth at its center.
A century later Galileo demonstrated that the Copernican theory of the revolution of the earth and other planets about the sun was true. The learned professors of Galileo’s day ridiculed his ideas and turned their backs upon them. Galileo complained: “As I wished to show the satellites of Jupiter to the Professors in Florence, they would see neither them nor the telescope.” The professors invoked the traditional authority of Aristotle and finally the power of the Index and the Inquisition against Galileo to force him to recant his views. These servants of official authority sought to silence the arguments, ban the books, terrorise and even kill their scientific opponents because their ideas were revolutionary, threatened the ideas of the ruling order, and thereby the power of the ruling class.
It is the same with dialectics, particularly materialist dialectics. The ideas and method of dialectics are even more revolutionary in the science of logic than were Copernicus’ ideas in astronomy. One turned the heavens upside down. The other, harnessed to the only progressive class in modern society, will help turn capitalist society upside down. That is why its ideas are so strongly opposed by all the adherents of formal logic and apostles of common sense. Today, under capitalism, dialectics is not common but “uncommon” sense. It is understood and consciously employed only by the socialist vanguard of humanity. Tomorrow, with the socialist revolution, dialectics will become “common sense” while formal logic will take its proper and subordinate place as an aid to thought, instead of acting, as it does now, to dominate thought, to mislead thought and to obstruct its advance.