George Novack
An Introduction to the Logic Of Marxism: LECTURE III
In the first two lectures we learned what the basic laws of formal logic are; how and why they came into existence; what relations they have with dialectics; and the limits of their usefulness. We now want to make a comprehensive survey of the limitations of formal logic in order to clear the ground for an exposition of the evolution and the principal laws of dialectics in the succeeding lectures.
We can single out five basic errors, or elements of fiction, inherent in the laws of formal logic.
First and foremost is the fact that these laws exclude movement, change, development from themselves and thereby from the rest of reality. They do not explicitly deny the real existence or the rational significance of motion. But they are compelled to do so indirectly by the necessary implication of their own internal logic.
If, as the law of identity states, everything is always equal to itself, then, as the law of contradiction asserts, nothing can ever be unequal to itself. But inequality is a manifestation of difference — and difference indicates the operation and presence of change. Where all difference is logically excluded, there can be no real motion or change, and therefore no reason for anything to become other than it originally is. What is forever identical, and nothing more, can never undergo alteration and must by definition be immutable.
If formal logic wants to remain true to itself, to abide by its own laws, it can never admit the real existence or rationality of motion. There is no place for change in the universe pictured or presumed by formal logic. There is no self-movement, no springs of motion within any of its laws or between them. There is no logical impulsion for these laws to pass over and into the world beyond themselves. There is no dynamism within this external world which keeps forcing things out of their present conditions and drives them onward into new formations. Motion can neither be drawn out of nor introduced into this static realm of rigid forms, where everything is frozen into its proper place and drawn up in perfectly ordered ranks side by side, like the traditional Prussian regiment.
Why does this formalism shy away from and turn its back upon so central a feature of reality as motion? Because motion has such a self-contradictory character. As Engels remarks: “. . . even simple mechanical change of place can only come about through a body at one and the same moment of time being both in one place and in another place, being in one and the same place and also not in it.” (AntiDuhring, p. 137.) Everything in motion is continually bringing forth this contradiction of being in two different places at the same time, and also overcoming this contradiction by proceeding from one place to the next.
More developed and complex forms of movement, such as the growth of trees and plants, the evolution of species, the development of society in history and the evolution of philosophical ideas, present even greater difficulties for formal logic. Here the successive stages in the process of development negate one another, with the result that the unified process is a series of contradictions. In the growth of a plant, for example, the bud is negated by the blossom, the blossom by the fruit.
Whenever they are confronted with such real contradictions, the formal logicians are hopelessly baffled. What do they do? Children, upon encountering some strange, horrifying phenomenon they do not understand and cannot cope with, close their eyes, clasp their hands to their faces, and hope thereby to get rid of the bogie. Formal logicians reacted — and still react — in the same infantile way to the presence of contradiction. Since they do not comprehend its real nature and do not know what to do with this terrible thing that upsets the foundations of their logical world, they proceed to decree the expulsion of contradiction from their logic and their world of ideas.
Whenever reactionary authorities are threatened by subversive forces, they seek to suppress, imprison, or exile them from their regime. The formalists treat contradiction that way. They thunder like Sir Anthony Absolute to his son in Sheridan’s comedy, “The Rivals.” Sir Anthony laid down the following conditions to his son if the latter did not agree “without any condition” to his views: “. . . don’t enter the same hemisphere with me! don’t dare to breathe the same air or use the same light with me; but get an atmosphere and a sun of your own!”
The so-called law of contradiction in formal logic does not, as it claims, express the true nature of contradiction. It is an edict excommunicating it from logic and ordering it to “get an atmosphere and a sun of its own!”
This law asserts that A is never non-A. This is not an expression of real contradiction, which would read: A is not-A or A is both itself and its other. It is the opposite of contradiction, identity. The Gilbert-Sullivan song goes: “Things are seldom what they seem, skim milk masquerades as cream.” In this instance, in the so-called law of contradiction, identity masquerades as difference. This law is an imposter which pretends to be contradiction, but is nothing but identity in a negative form.
Formal logic cannot tolerate actual contradiction within its own system. It suppresses, nullifies, banishes it — or so it thinks. For a ukase decreeing the expulsion of contradiction from their world of ideas still does not eradicate the existence of contradiction in the real world. In their effort to free themselves of contradiction, the formalists fasten absolute contradictions upon objective reality. In the world represented by formal logic everything stands in absolute opposition to everything else. A is A; B is B; C is C. Logically they have nothing in common. Contradiction is king!
Contradiction eliminated from the system of formal logic thus becomes elevated to supremacy in the real world. Contradiction is dead, long live contradiction. The formalists avoid contradiction within their system only at the cost of restoring it to supremacy outside their system.
Real contradiction must include both identity and difference within itself. This formalism cannot do. In all the laws of formal logic there is actually nothing but identity in various versions or disguises. There is not an ounce of real difference in them or between them.
That is why the laws of fixed categories of formal logic are incapable of explaining the essence of motion. Motion is so utterly, explicitly, even rudely contradictory. It contains within itself two diametrically different moments, elements, phases, at one and the same time. A moving thing is both here and there simultaneously. Otherwise it is not in motion but at rest. A is not simply equal to A but likewise to non-A. Rest is arrested motion; motion a continuous interruption of rest.
Formal logic cannot acknowledge or analyse this real contradictory nature of motion without violating its own self, without overthrowing its own laws and passing over and into something other than itself. This is tantamount to expecting and demanding that formalism be or become explicitly dialectical. This is precisely what happened to logic in the course of its evolution. But formal logic, in itself and by itself, cannot take this revolutionary jump out of its own skin. All consistent formal thinkers remain riveted to the original basis of the omnipotence and universality of identity, and continue to deny — quite logically according to their logic but quite illogically according to reality — the real objective existence of self-difference, or contradiction.
The category of abstract identity contained and repeated in the laws of formal logic is the direct conceptual expression and logical equivalent of immobility in objective existence. That is why formal logic is essentially the logic of lifelessness, of rigid relations, of fixed things, of eternal repetition and repose. “So long as we consider things as static and lifeless, each one by itself, alongside of and after each other, it is true that we do not run up against any contradictions in them. We find certain qualities which are partly common to, partly diverse from, and even contradictory to each other, but which in this case [i.e., in the system of formal logic] are distributed among different objects and therefore contain no contradiction.” (AntiDuhring, p. 137.)
Observe what happens in the other case when things begin to move, not only in relation to each other but in relation to themselves, not only externally but also internally. They begin to lose their identity and tend to transform themselves into something else. The Hudson River rises, flows on, and merges with the Atlantic Ocean; the German mark withers into a worthless scrap of paper; even perfectly machined cone bearings wear out and eventually become scrap metal. The utmost these things can do is to postpone the date of their loss of identity; they cannot escape it in the end. These results of the internal and external movement of real things are manifestly contradictory — but they are no less obviously true, that is, in correspondence with reality.
Nothing is permanent. Reality is never resting, ever changeable, always in flux. This unquestionable universal process forms the material foundation of the theory which, in Engels’ words, teaches that”. . . the whole of nature, from the smallest element to the greatest, from grains of sand to suns, from protista [unicellular organisms] to men, has its existence in eternal coming into being and passing away, in ceaseless flux, in unresting motion and change....” (Dialectics of Nature, p. 13.) No generalisation of modern science is more securely based upon experimentally demonstrated facts than this theory of universal development, which was the outstanding achievement of human thought in the nineteenth century.
The laws of formal logic, which outlaw contradiction, stand in stark contradiction to this theory and reality of universal development. The law of abstract identity asserts that nothing changes; the dialectic states that everything is constantly changing. Which of these two opposing propositions is true, which false? Which should we hold onto and which discard? That is the question materialist dialecticians, who base their logic upon processes in nature, address to the diehard formalists. That is the question scientific thought itself posed to formal logic not merely in the last century but long before. That is the question formal logic dreads to hear or to consider, for it exposes the emptiness of its claims and sounds the death knell of its two thousand-year rule over the realm of thought.
Formal logic is false and defective because it erects impassable barriers between one thing and another, between successive phases in the development of the same thing, and in the reflections of objective reality in our minds. To all questions it answers with either a flat yes or unqualified no. Between truth and falsehood there is no intermediary, no transitional stages or connecting links.
Hegel says on this point in the preface to his Phenomenology of Mind (p. 68): “The more the ordinary mind takes the opposition between true and false to be fixed, the more is it accustomed to expect either agreement or contradiction with a given philosophical system, and only to see reason for the one or the other in any explanatory statement concerning such a system. It does not conceive the diversity of philosophical systems as the progressive evolution of truth; rather, it sees only contradiction in that variety.
“The bud disappears when the blossom breaks through, and we might say that the former is negated by the latter; in the same way when the fruit comes, the blossom may be explained to be a false form of the plant’s existence, for the fruit appears as its true nature in place of the blossom. These stages are not merely differentiated; they supplant one another as being incompatible with one another. But the ceaseless activity of their own inherent nature makes them at the same time moments of an organic unity, where they not merely do not contradict one another, but where one is as necessary as the other; and this equal necessity of all moments constitutes alone and thereby the life of the whole. But contradiction as between philosophical systems is not wont to be conceived in this way; on the other hand, the mind perceiving the contradiction does not commonly know how to relieve it or keep it free from its one-sidedness, and to recognise in what seems conflicting and inherently antagonistic the presence of mutually necessary moments.”
If we take the laws of formal logic at face value, we have to assume that any and every single thing, or every single state of any thing, is absolutely independent of any or every other thing or state. A world is presupposed in which everything exists in perfect solitude, apart from every other thing.
The philosophical position that draws this logic to its ultimate conclusion is the philosophy of subjective idealism, which arises out of the assumption that nothing really exists save one’s self. This is known as solipsism, from the Latin solus ipse (I alone).
It does not take much reflection to see how absurd and untenable such a position is. Whatever his theory, every sane person proceeds in practice upon the basis that nothing exists by itself. Moreover, if we think a bit, we see that every single thing, no matter how isolated and independent it may seem to be, really needs every other thing
in order to exist and to become itself. If we couldn’t relate one thing to another, and these in turn with the rest of reality, we would be in a hopeless fix.
Moreover, any one thing is always passing over into and transforming itself into some other thing. To do this, it must necessarily break down and efface the boundaries which formerly separated it from that other thing. So far as we know, there are no immovable and insurmountable partitions between things.
“The fundamental proposition of Marxian dialectics is that all boundaries in nature and society are conventional and mobile, that there is not a single phenomenon which cannot under certain conditions be transformed into its opposite,” remarked Lenin. ( Collected Works, vol. 19, p. 203.)
On the broad historical scale, Trotsky noted: “Consciousness grew out of the unconscious, psychology out of physiology, the organic world out of the inorganic, the solar system out of nebulae.” (In Defence of Marxism, p. 51.)
This breaking down of boundaries, this passage of one thing into another, this mutual dependence of one thing upon another has not merely occurred over extended stretches of historical development; it goes on all the time in us and around us. Thoughts keep shuttling back and forth between the unconscious and conscious mind. When we act upon the basis of an idea, this idea loses its predominantly mental character and becomes a materially active force in the world at large through ourselves. Marx pointed out that a system of ideas, like socialism, becomes a material power when it takes possession of the minds of the working masses and they go ahead to realise these ideas in social action.
Everything has definite lines of demarcation which set it off from all other things. Otherwise it would not be a distinct entity with a unique identity. We have to discover these boundaries in practice and take them into account in our thinking.
But these boundaries do not remain unaltered under all
conditions; nor are they the same at all times. They fluctuate according to changing circumstances. This relative, mobile, fluid character of boundaries is ignored and denied by the laws of formal logic. These laws assert that everything has definite limits — but they overlook the far more important fact that these limits themselves have limitations.
We have already noted that formal logic draws the sharpest dividing line between identity and difference. They are placed in absolute opposition to each other, staring into each other’s face like complete strangers. Insofar as they are admitted to have relations with each other, these are purely external and accidental and do not affect their simple undivided inner being.
The formalists consider it a logical contradiction, a monstrosity, to say as the dialecticians do that identity is (or becomes) difference and difference identity. ‘They insist: identity is identity; difference is difference; they cannot be the same as each other. Let us compare these assertions with the facts of experience, which is the test of the truth of all laws and ideas.
In Dialectics of Nature Engels states: “The plant, the animal, every cell is at every moment of its life identical with itself and yet becoming distinct from itself, by absorption and excretion of substances, by respiration, by cell formation and death of cells, by the process of circulation taking place, in short by a sum of incessant molecular changes which make up life and the sum total of whose results are evident to our eyes in the phases of life — embryonic life, youth, sexual maturity, process of reproduction, old age, death. This is apart, moreover, from the evolution of species. The further physiology develops, the more important for it become these incessant, infinitely small changes, and hence the more important for it also the consideration of difference within identity, and the old abstract standpoint of formal identity, that an organic being is to be treated as something simply identical with itself, as something constant, becomes out of date.
“Nevertheless, the mode of thought based thereon, together with its categories, persists. But even in inorganic nature identity as such is non-existent in reality. Every body is continually exposed to mechanical, physical, and chemical influences, which are always changing it and modifying its identity.”
The insuperable barriers erected by formal logic between these two interpenetrating traits of reality are continually being washed away in the process of development. What is different becomes identical. We were all in different parts of New York before we came together tonight in this hall. What is identical becomes different. After this lecture is over, we shall disperse to different places again. This transformation of difference into identity and identity into difference takes place not only in simple spatial relations but in all relations. The bud becomes the flower, the flower becomes the fruit — yet all these different phases of growth belong to the same plant.
Thus, despite the laws of formal logic, real material identity does not exclude difference from itself but contains it as an essential part of itself. Real difference likewise does not exclude identity but includes it as an essential element within itself. These two features of reality can be separated from each other by making distinctions in thought. But that does not mean, as formal logic implies, that they can be disjoined in reality.
The fourth defect in the laws of formal logic is that they present themselves as absolute, final, unconditional laws. Exception to them is impossible. They rule the world of thought in totalitarian fashion, exacting unquestionable obedience from all things, claiming unlimited authority for their sovereign sway. A always equals A — and woe unto those who do not acknowledge this dogma or dare assert otherwise.
Unfortunately for the formalists, nothing in the universe corresponds to such specifications. Everything real originates and presents itself to us under specific historical and material conditions, in indissoluble connection with other things, and at all times in definite and measurable proportions. Human society, for example, came into existence at a definite, materially determined turning point in the evolution of man from the higher animals; it is inseparable from the rest of organic and inorganic nature; it has developed by degrees and has far from attained its full quantitative and qualitative growth. Each stage of this social development has its own laws growing out of and corresponding to its special characteristics.
Absolute laws can no longer find any foothold in the physical world. At various stages in the development of the physical sciences, chemical elements, molecules, atoms, electrons were considered by metaphysical-minded thinkers to be unchanging substances. Beyond and behind these mankind could not go. With the further advance of the natural sciences, each one of these eternal absolutes has been in turn overthrown. Each of these constituent parts of material formations has been experimentally demonstrated to be conditioned, limited and relative. All their pretensions to be absolute, unlimited and unchanging have been proven false.
At the close of the nineteenth century, while scientists were harping on the immutability of this or that element, the social scientists of the United States were insisting that bourgeois democracy was the crowning form of government for civilised mankind. Historical experience since 1917, which has witnessed bourgeois democracy undermined and overthrown from two opposite directions by fascism and Bolshevism, has proven how historically limited, how inadequate and conditional, this particular form of capitalist government really is.
If everything comes into existence under definite material and historical limitations, develops, diversifies itself, alters and then disappears, how can any absolute law be applied to anything in the same way, to the same degree, at all times and under all conditions? Yet this is precisely the claim put forward by the laws of formal logic and the demand they make upon reality. And in their search for laws that hold at all times and under all conditions, scientists fell into this blind alley of formal logic.
In the last analysis God is the only being that can completely meet the standards of formal logic. God is supposedly absolute, boundless, perfect, independent of everything except himself. But God, too, has a slight imperfection. Outside of the imaginations of devoutly religious people, he doesn’t exist.
Finally, the laws of formal logic, which are supposed to provide a rational explanation for everything, have this serious flaw. Formal logic cannot account for itself. According to the theory of Marxism, everything comes into being as the result of material causes, develops through successive phases, and finally perishes.
What about formal logic and its laws? Where, when, why did they originate; how have they developed; are they eternal? The formal logicians imply, where they do not dare assert outright, that their logic did not have earthly roots but is the product of divine revelation; that its laws are invariant laws of reason; that their logic is the only possible system of logic, and therefore eternal.
If you challenge the formal logicians and ask: By what right do you elevate the laws of logic above history, exempt them from the universal rule that nothing is invariable? they can answer only in the same way that absolute monarchs did. We do so by divine right.
We see how much truth there is in the identification of dialectics with religion made by professors like James Burnham and Sidney Hook. In reality, formal logic goes hand in hand with religion and dogmatism. Eternal laws
of logic stand in the same position as eternal principles of morality, of which Trotsky remarked: “Heaven remains the only fortified position for military operations against dialectic materialism.” (Their Morals and Ours, p. 16. )
As a matter of fact, formal logic appeared in human society at a definite stage of its development and at a definite point in man’s conquest over the operations of nature; it has developed along with the growth of society and its productive forces, and has been incorporated into and supplanted by the more developed logic of dialectics. This places logic on a par with everything else — but it required a revolution in human thought to put it in its proper place.
One of the superior features of materialist dialectics over formal logic consists in the fact that, unlike formal logic, dialectics can not only account for the existence of formal logic but can also tell why it supersedes formal logic. Dialectics can explain itself to itself and to others. That is why it is incomparably more logical than formal thinking.
* * *
Observe how our criticism of formal logic has progressed. We started out by affirming the truth in the laws of formal logic. Then we went on to point out the limits of that truth and the tendency of these laws to generate error once they were pushed beyond definite boundaries. That led us to deny the unconditional truth of what we had previously affirmed.
The laws of formalism were seen to have two sides, one true, the other false. They were shown to be complex and contradictory, capable of development and change by reason of opposing tendencies constantly at work within them. We analysed the two opposing poles of their contradictory character, unfolded their interrelations, and indicated how and why they become transformed into each other.
That is the dialectical method of thinking about thought. As a result we have arrived at the frontier of dialectics by a genuinely dialectical route. That is also the way humanity arrived at dialectics as a formulated system of thought. Men found out the limitations of formal logic in practice and then overcame these limitations in theory by creating a higher form of logic. Dialectics proves its truth by applying its own method of thought to explain itself and its origins.
Dialectics came into existence as the result of a colossal social revolution pervading all departments of life. In politics the representatives of the aroused masses, unconsciously guided by a dialectical understanding of events, knocked at the doors of the unlimited monarchies and thundered: Times have changed; we demand equality. In the spirit of formalism, the defenders of absolutism replied: You are wrong, you are subversive; things do not change or cannot change that much. The king is always and everywhere king; A equals A; sovereignty cannot equal the people, who are non-A. Such formal reasoning did not halt the march of progress, the triumph of the popular bourgeois-democratic revolutions, the dethronement and destruction of the monarchies. Revolutionary dialectics, and not formal logic, prevailed in political practice.
In the sphere of knowledge, formalism was plunged into the same revolutionary crisis as absolutism in politics. The new forces of knowledge arising out of the development of the natural and social sciences came into collision with the forms of logic which had reigned for over two thousand years, sought self-expression, demanded their rights. How that revolution in logic came about and what it led to will be the topic of our next lecture.