Jean van Heijenoort writing as Jarvis Gerland

‘Science’—Burnham’s Style

Science—Burnham’s Style, Fourth International, June 1940, pp. 55–58, under the name‘Jarvis Gerland’.

Upon rejecting the position of the Fourth International on the class nature of the Soviet State, Burnham passed, whether he willed it or not, to a general offensive against the very foundations of Marxism. Such an offensive suffers from old age, but Burnham in his article ‘Science and Style’ proposes to ‘modernize’ it with the aid of ‘science.’

It is not with pleasure that one undertakes discussing this article. The repugnance which must be overcome in order to read it, is soon replaced by boredom—these platitudes, chewed over so many times, do not improve with age. The article contains nothing which has not been said again and again by all the hecklers of Marxism, professionals and amateurs. The most hackneyed arguments, the most worn out comparisons, all these rags which are scattered throughout the small town newspapers even, are assembled here and presented as the latest conquest of science by a mind emancipated from all superstition. It is true that he has not yet dared to present a few tatters in all their filth; we see only their fringes. Many arguments stop short and do not yet present all that is in reserve. With vulgarity and conceit is mixed a strong dose of hypocrisy. Burnham declares for instance, in his attack against Trotsky, ‘I have been scrupulously fair in presenting here your central argument.’ This ‘scrupulous fairness’ as we shall see presently, has the same value as that of his predecessors—it strongly resembles unscrupulous unfairness.

One of the first propositions which the document attributes to Trotsky is the following: ‘From dialectical materialism it follows that Marxian sociology, in particular the Marxian theory of the state, is true.’ The expression ‘it follows that’ is emphasized by Burnham himself who does not wish to leave the least doubt about his affirmation. In order to justify the attribution of such an assertion to his opponent, there is indeed in the page from which the above sentence is taken, the little word ‘thus.’ It is rather thin. As for the ‘proofs’ announced with such grandiloquence by Burnham ("Evidence, argument, proof: these only are my weapons.") his ‘scruples’ have permitted him to dispense with them.

In truth, such a proposition is foreign to the spirit and the letter of Marxism. Did Marx deduce ‘Capital’ from a few logical or metaphysical principles pegged at the head of the first chapter? Did he begin his work with nothing more than an abstract exposition of his dialectical and materialist ‘principles’? If this were so, why then did he spend his time in research among thousands of economic publications of the entire world in order to amass a formidable erudition? Burnham attributes to Trotsky, just as gratuitously, a second analogous affirmation: ‘From the Marxian theory of the state, it follows that Russia is a workers’ state.’ If this were true, why did the Left Opposition lose its time in analyzing the social, economic, and political conditions of the U.S.S.R. beginning with 1923? We have produced, it seems to me, a rather large number of documents and books on this subject. If our method were that which Burnham imputes—so ‘scrupulously’—we should have been content to state our conclusions in a few lines, if necessary in the form of a polished syllogism.

But there is more. Marxism has already refuted expressly this interpretation of its method. Burnham has the right, if he wishes, to view Engels as an outmoded reactionary preacher (this sweeping accusation is launched, by the way, without the slightest evidence), but perhaps he will recognize him as a faithful interpreter of Marx’s thought. Yet, Engels, answering the Burnham of his day, one shaped in a grander style, Eugene Dühring, had occasion to examine, more than seventy years ago, precisely the accusation which the Dühring of today presents as a product of the most recent science. Engels quotes[1] a long passage from the writings of the German professor, which in the profoundness of its science and the beauty of its style as well as in its scrupulous fairness rivals Burnham’s document. Dühring accused Marx of having deduced the necessity of the expropriation of the expropriators from a logical law, the negation of the negation. Engels had no trouble in refuting this absurdity; he simply quoted the passage where Marx analyzes this problem.

Why does Burnham serve us this ancient warmed-up hash? It is because he and Dühring have the same conception of logic, and both of them in an identical manner attribute this conception to Marxism. Their thought does not extend beyond a very formal idea of the dialectic, and it is this dialectic which they annihilate! We present them with a living being, they kill it and then cry out: ‘We told you so, it’s nothing but a corpse!’

They conceive of logic as consisting above all of some principles outside of and prior to knowledge. From these principles follows knowledge. This is what Burnham develops when, in his document, he speaks about the function of logic. To him it is reduced to a form from which thought cannot escape. Separated from the content of knowledge, logic can play nothing but a negative role. Form becomes a simple barrier; principles, the hand-rail. Burnham tells us that logic is rather useless. We agree with him insofar as such logic is concerned, that is, his, not ours.

Dialectic logic is not the banks between which flows the river of knowledge. It penetrates knowledge itself in all its various depths. It cannot live except in this current, it does not exist except in it. If you force logic out of the current it negates itself and withers into a few limiting, abstract, and sterile principles. Far from dominating knowledge from the outside, it recreates itself incessantly in it. ‘The form of thought merits being revived more than any other form,’ Hegel once remarked. The Philistines often reduce Hegel’s method to the monotonous application of a three part schema: thesis, antithesis, synthesis. In this caricature they reveal nothing but the conception which they themselves are incapable of passing beyond: For Hegel, every sphere of reality gives a specifically determined character to the contradiction and to the synthesis. Under an often mystical form, he expresses here a profound materialist conception. The dialectic is not reducible to a few isolated laws; this happens to be not one of the least difficulties in its systematization.

Far from molding itself into a form imposed from the outside or from expressing its limits in such a form, thought has its mode of development conditioned by its content. The conception of something outside of and prior to knowledge is precisely scholasticism in its most essential feature. Burnham cannot free himself from this conception and in quest of the most recent modernism it is to this dust-laden bin that he turns when he advocates replacing Hegel by Russell and the dialectic by symbolic logic.

Symbolic logic is the generic name for a collection of works which have developed largely since the end of the first third of the last century.

I shall indicate here only the general conclusions of this school without entering into a detailed technical analysis, although I have at hand dozens upon dozens of quotations from the German, Anglo-Saxon, and French mathematicians and logicians beginning from the middle of the last century. As for Burnham himself he does nothing in describing this tendency but pronounce some very flattering but purely subjective adjectives.

The artisans of this movement are for the most part mathematicians and semi-mathematicians. Its essential features are the use of symbols analogous to those of algebra in order to represent the content of thought—concepts, or relations—and the deductive inter-linking of these symbols according to a few formal rules in order to determine all the possible, that is, not-contradictory affirmations. This logical calculus does nothing but push to the extreme a deep-rooted tendency of mathematics since their origin: the deductive form according to the laws of formal logic and the continuous reduction of the number of axioms which serve as the point of departure. That is why, precisely because this constitutes nothing but an exacerbation of one of its tendencies, mathematics would run a great risk in confining itself entirely to this road: the risk of losing its life. All the great mathematicians, including those who are addicted to symbolic logic, agree on this point, and many of them recognize even in their own domain nothing beyond a very restricted value in symbolic logic. It seems, however, that it has definitely acquired the right of existence in this field, and so far as mathematics is concerned, it represents a conquest, only relative, it is true, of science.

If we enter the field of logic, the situation changes completely. Here the role of symbolic logic becomes completely retrogressive.

All the logicians of this school start from the three ‘fundamental laws’ of thought[2] ‘from which we can no more depart than we can jump over our own shadow’—the principles of identity, of contradiction, and of the excluded middle. The adepts of symbolic logic do not hazard a discussion upon these principles, or even making precise their content. Often they adopt them in silence, under cover of defining an algebraic symbol. If they discuss their entrance into the system, it is only in order to paste up the label ‘obvious’ (Russell and Whitehead in particular). How poor, hidebound and reactionary such a conception appears in comparison with that of a Hegel! This can be seen merely by reading (Burnham need not recoil in fright, it is not him I offer this advice) those pages where Hegel, at the beginning of the second book of his Great Logic (Science of Logic) examines the famous principles, demonstrating their limits and their contradictions. In these ten or fifteen pages there is more science—real science and not fruitless formalism—than in the entire three thick volumes of Principia Mathematica.

Once the three ‘fundamental laws’ of thought are admitted as governing the game, nothing remains but to determine, through operative rules which have an algebraic form, all the not-contradictory combinations which follow. The objective of logical calculus could thus be defined in its entire generality: to establish all the affirmations compatible with the three fundamental principles of thought. Science finds itself reduced to a vast formalism. Nothing remains after this except a secondary task: to see whether all the combinations determined as possible also exist in nature. But if all the possibilities do not exist, existence never fails to find a pigeon-hole in the immense texture of possibilities.

Insofar as thought furnishes reality with frames constructed outside and independent of it, symbolic logic appears as a vast scholasticism. This does not constitute an increase in the power of reason, but its abasement and its humiliation. Russell’s science of combinations in particular, has in view rendering human intellect absolutely useless in everything concerning logic and mathematics. Before Russell another logician of the same type, Stanley Jevons, constructed a kind of piano equipped with twenty-one keys which classified, selected and rejected the various combinations of terms and finally indicated the not-contradictory propositions. Is it necessary to add that this neo-scholasticism heads in the opposite direction from that of the development of human thought? Science does not force nature into a system of previously established compartments. Knowledge is activity and struggle; not passive contemplation, but a passionate discourse between man and nature. Thus, where man declares unity and continuity, nature answers with plurality and discontinuity; where he says plurality, it replies with unity. Knowledge does not advance except by this unceasing dialectic. Thought, insofar as it is penetration, invention, and extension, appears essentially as action, movement, and a going beyond itself, and is in no wise reducible to the degrading automatism of a system of tabulated labels and levers.

The adepts of logical algebra frequently flaunt a revolutionary air through hurling anathema upon Aristotle’s logic. But even here their progress is quite relative. Aristotle’s logic consisted of the classification of a certain number of the forms of thought, exactly as he catalogued some hundreds of birds according to external observations. As for symbolic logic, it starts from a few principles and deduces from them all the not-contradictory combinations. But this does not lead it much further. Thus the German mathematician, Hilbert, rediscovered after arduous calculation, the fifteen forms of the syllogism which Aristotle had already enumerated. Through its blind adoption of the three principles of departure, symbolic logic remains a part of formal logic, the most developed and the most systematic it is true, but dated 2,300 years after Aristotle!

An illustration is in order. Let us consider the propositions of Aristotelian logic as bricks with regular and well-defined forms. The syllogism is the simplest possible construction with three bricks: two bricks juxtaposed and a third lying on top of them. Every perfect example of reasoning is extended by the repetition of this elementary arrangement in exactly the same way a mason erects a wall. Aristotle’s logic is a catalog of the various mosaics which appear in the human mind. Symbolic logic takes upon itself a different task, that of deducing by reasoning all the arrangements possible to a given shape of brick. In this sense it goes beyond Aristotle’s logic. But it retains the brickwork with its three relations, that is, the three ‘fundamental laws’ of thought. The dialectic abandons brickwork and follows the movement of a living reality. It does not take as its point of departure a form imposed a priori but much more fundamental properties of matter such as resistance, elasticity, cohesion. In passing, it shows that the form and the dimensions of the bricks themselves are in the last analysis determined by their essential properties, exactly as Hegel demonstrated that the ‘three laws’ of formal logic represent a certain stage in the development of thought.

Formal logic is above all the logic of definition and classification. Its importance in many domains is not to be denied, particularly in the beginnings of science. Its laws are valid for the immutable and distinct entities. Yet, all modern science directs human knowledge in another direction: the development and inter-connection of things. The Hegelian dialectic gave to these fundamental things their logical expression. That is why the name of Hegel will be preserved in the annals of science, whereas that of many others will be forgotten. Symbolic logic indeed systematizes Aristotelian logic, yet it rests absolutely upon the same basis: immobility and the absolute disconnection of categories. It remains thus considerably in the rear of problems which the dialectic posed and to which it has brought the first solutions. Every progressive work in logic must start from the Hegelian logic in order to cleanse it of its mysticism and to develop it. Because of profound social causes, this task is deeply repugnant to contemporary science. Hegel’s logic was an offspring of the French revolution. Socialism will lift the dialectic to new heights.

We have examined the problem of symbolic logic as the only point in which Burnham’s document presents any novelty. On all the other questions Marxist literature is already sufficiently rich.

The criticism which Burnham makes of the dialectic is indeed not new: it is the first exercise to which one must habituate himself in order to enter upon the career of a renegade from Marxism.[3] Feeling where the shoe pinches, Burnham attempts to deny this frequently made affirmation. He tries to demonstrate that the acceptance or the rejection of the dialectic does not in any way affect the validity of the revolutionary teachings of Marxism. Thus he invokes in support of this thesis the fact that the Stalinists ‘also believe’ in the dialectic. Transposed to the field of philosophy, this is the identification of Stalinism with Bolshevism. It is not less superficial and reactionary here than under its political form. Stalinism has remained attached to the dialectic verbally as it has to many formulas of Bolshevism. But in reality it has substituted for it a mercenary sophistry fit only for the justification of all their crimes. When Burnham, as a good Philistine identifies one with the other, he devotes himself to the same reactionary task as Norman Thomas. The fact alone that the Bonapartistic bureaucracy covers its gross empiricism with phrases wrenched from a doctrine which is radically opposed to it should be a supplementary reason for considering it as a caste and not as a class which expresses its culture in a completed form.

If he follows an old route, Burnham nevertheless has an innovation in what he proposes to substitute for the dialectic. The critics of Marxism have generally grasped at Kant—it is the safest stock in the philosophic stock exchange. Some of them have recently sought refuge in pragmatism. Burnham, the most modern and the most ‘scientific’ of them all, discovers symbolic logic. The choice is not any the happier; it clearly reveals a well-known fact: formal logic retains a power over petty-bourgeois thought which all its vicissitudes have been unable to touch. Insofar as it constitutes a new illustration of this fact, Burnham’s document possesses a scientific value which its author did not foresee.

March 17, 1940


[1] Anti-Duhring, Part I, beginning of Chapter XIII. [2]A small unorthodox current during these last years has systematically developed the rejection of the principle of the excluded middle. We reserve for later examination this tendency which Burnham does not even mention. [3] See my article,‘The Algebra of Revolution.’ in the May issue of Fourth International.