29

p Nikolai Semyonov,
Member of the Presidium, USSR Academy of Sciences

p Marx enriched science by his discovery and elaboration of materialist dialectics. Since it is a method of cognition, a method of reasoning, materialist dialectics is equally applicable to the development of all sciences, whether social or natural. Dialectical materialism is fundamental to any conscious attempt to change society, its industry and culture.

p Engels was instrumental in developing and applying the Marxist dialectical method to the problems of natural science.

p Lenin made an original contribution to Marxist theory by relating it to the new conditions of social life, that is to say, by putting Marx’s concepts into practice.

p Lenin’s behest that we should establish and consolidate an alliance between philosophy and natural science, an alliance equally necessary for both sciences, calls for a clear conception of how they can and must enrich each other.

p Further reflection upon this question inevitably suggests the conclusion that the Marxist dialectical method of reasoning is philosophy’s most valuable achievement, an achievement it can and must share with natural science. It is from this standpoint that philosophy appears above all as Logic with a capital L, as a theory of knowledge that corresponds with the present level of development of the 20th century natural and socio-historical sciences and their current needs.

p Lenin regarded this as the main principle of dialectical materialism. Agreeing with Engels, he stated this concept most emphatically in the following words: “Dialectical materialism ’does not need any philosophy standing above 30 the other sciences’. From previous philosophy there remains ’the science of thought and its laws—formal logic and dialectics’. Dialectics, as understood by Marx, and also in conformity with Hegel, includes what is now called the theory of knowledge, or epistemology."  [30•1 

p Obviously, only such a conception of philosophy can justify the notion of an alliance, of voluntary and fruitful co-operation between philosophy and natural science for the purpose of understanding and transforming the world. Indeed, all the unfavourable tendencies which have variously overshadowed the relations between philosophers and natural scientists may well have been due to the abandonment of Lenin’s conception of philosophy, of what philosophy’s subject-matter and, consequently, its role in developing a scientific world outlook should be.

p Philosophy can play an active role in developing a scientific world outlook only if it is treated like all the other sciences, that is, as a distinct science with its own clearly defined subject-matter, to be studied in the same thorough and specific way as the subject-matter of any other science.

p It is quite clear that, contrary to the assertions of some philosophers, philosophy’s subject-matter cannot be the “universe”, because the universe is cognised by the entire system of natural and social sciences. Such an approach virtually deprives philosophy of its subject-matter.

p The conception of philosophy as a distinct science concerned with the “universe” was understandable and justifiable at a time when the natural and social sciences were in their infancy, and had not yet produced, or even tried to produce, any definite view of the world and of man himself. Under those conditions, philosophy was forced to find means to compensate for the inadequate development of the specific sciences, and to construct a special, “philosophical” world outlook which stood side by side with specific scientific knowledge and even above it. That time, however, is long since past.

p During the second half of the 19th century the natural and social sciences matured to a point where they could, with their own resources, produce an integral, coherent concept of the universe and man’s role therein.

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p Some philosophers occasionally voice the apprehension that if Marxist-Leninist philosophy is identified with Logic and with the theory of knowledge it may lose its significance as a world outlook and come to play a lesser role, and that a break may even result between philosophy and natural science.

p No such consequences need be feared if we take a truly Leninist view of Logic. On the contrary, our sciences, our entire culture are being developed through reasoning based on human practice, and the science of reasoning, therefore, retains its universal significance and primary role in the development of a scientific understanding of the world.

p The categories of materialist dialectics are meaningful; they reflect the objective world with all its contradictions and interrelations. They are not stagnant concepts, but continue to develop and acquire greater meaning. That is why the application of the system of dialectical categories, dialectics as a method of cognition, to various spheres of science stimulates and develops thinking in these sciences and thus leads to the practical transformation of objective reality.

p The proletariat’s revolutionary class struggle became meaningful and purposeful only after Karl Marx laid the foundation of scientific communism by applying the method of dialectical materialism to the economic sciences and thus initiating the scientifically grounded ideology of the revolutionary movement.

p The concept of the “universe” as the subject of philosophy has impelled some philosophers to invent universal abstract schemes and to produce a slightly renovated natural philosophy. This, as Engels pointed out in his day, is an absolutely useless and in certain circumstances even harmful occupation, because it occasionally leads to attempts to impose upon natural science not only a preconceived pattern of development but even conclusions.

p I have no wish to accuse Soviet philosophers, most of whom adopted sound views. Some of them, however, and some others who were not philosophers, rejected, and rather strongly as a matter of fact, the principle of relativity, cybernetics, and the concept of resonance in chemistry. There were also attempts to provide philosophical substantiation for the erroneous general biological theory 32 propounded by Lysenko, Prezent and others, who wished to dictate to science.

p I think this was due to a misunderstanding on their part not only of natural science, but of the very essence of Marxist-Leninist dialectics.

p Scientists can finally shake off their superficial positivist interpretation of the results of their own work and the rubbish of nature philosophy and its influence only by accepting dialectics in the Leninist sense of modern materialist logic and the theory of knowledge.

p Some natural scientists reason as follows. Our task is to observe and describe empirical facts and to establish their interrelationships, formulating these in the language of mathematics. The important thing is to construct a formally non-contradictory system of equations; how that system is interpreted in respect of a world outlook is entirely immaterial and can well be left to the philosophers, who love “pseudo-problems”. Such positivist attitudes are sometimes the result of philosophical naivete, sometimes of lack of faith in the power of dialectical thinking and man’s ability to understand the external world.

p But natural science itself has to pay a high price for this attitude. Already at the dawn of the 20th century, the positivist orientation of Mach and Ostwald had begun to interfere with the promising trend in science towards studying the basic causes of phenomena, their intrinsic essence, and their common basis, which is connected primarily with the structure and properties of the atom. It will be recalled that in the 19th century Boltzmann’s great discovery of the nature of entropy and its connection with probability evoked a sharply unfavourable reaction from positivist thinkers.

p Logic with a capital L (which is, as I have said, Lenin’s definition of logic, dialectics and the theory of knowledge as a unity) takes account of the legitimate rights of formal logic. But dialectics, like logic and the theory of knowledge, brings out the true role of formal logic in the development of scientific cognition. The role of formal logic in the advance of cognition is most clearly revealed in mathematics, especially when applied to the processing of data supplied by the other sciences. That is why the relation between logic and mathematics has attracted the attention of both mathematicians and philosophers specialising in logic.

33

p It is rather widely accepted that mathematics is in general identical with formal logic: both mathematics and logic are regarded as a purely formal apparatus of reasoning, as a “language of science" (its “vocabulary” and “syntax”). This view was given its most consistent expression in Bertrand Russell’s dictum that logic is the youth of mathematics, and mathematics the maturity of logic. This would be an incorrect view of mathematics, taken as a whole, as a distinct science in its development. But of this more below.

p However, in the application of the available mathematical apparatus to the processing of data supplied by other sciences mathematics is indeed a formal-logical apparatus. The apparatus of mathematical logic—precisely because of its purely formal character—has served as the theoretical basis for the creation of modern computing techniques. In principle, all the automated and strictly formalised operations of the human brain without exception can be transferred to a machine, thereby relieving man of a mass of work which requires time rather than intelligence and creative ability. Thus, despite (and, to some extent, thanks to) the circumscribed character of formal logic, its application has had tremendous consequences, which are already engulfing the social sphere as well.

p But it is already safe to say that machines will prove powerless in every case involving contradictions which cannot be resolved by purely formal means.

p For all the importance of formal logic, it is, however, by no means the main part of Logic with a capital L. Here is the opinion of a group of French mathematicians: “The mode of reasoning which consists in building a chain of syllogisms, is only a transforming mechanism which can be applied regardless of premises. ... In other words, it is only the external form ... a language, you might say, which is proper to mathematics and no more. To regulate the vocabulary of this language, to make its syntax more precise, is to do a very useful thing.. .. But—and we insist—this is only one side and the least interesting one at that."  [33•1 

p The limited role of formal logic in the development of the sciences springs from its “indifference” both to initial 34 premises and to the composition of the “concepts” subjected to demonstrative exposition (that is, to the “content” side of the matter in general, to the “extralinguistic factors”), and this allows it to be used for the most diverse purposes, some unscientific and essentially retrograde. Let us recall, for instance, that the scholastic interpretation of Aristotle’s logic has served theologists as a formal apparatus of reasoning and has been used by them for their unscientific purposes (especially in the Middle Ages). One need give no other examples than the scholastics’ struggle against the concepts of Giordano Bruno and Galileo.

p These premises, and the concepts of the natural and social sciences which reflect them, arise through the interpretation of experiments, the experience of real human activity, and the practice of transforming nature. In certain cases this becomes quite obvious even in mathematics.

Euclid’s famous Elements, which laid the foundations of geometry, rest on premises (axioms or postulates) which are clearly non-formal. Euclid’s axioms are based on reality, that is to say, on the practice of surveying, architecture, road-building, shipbuilding, military science and other similar branches of material culture in antiquity. In other cases it is not so easy to trace the roots of theoretical premises and concepts in mathematics, and it is therefore no accident that the neo-positivists appeal to modern mathematics in their effort to prove that our knowledge has in general nothing in common with objective reality and is purely a mental contrivance. It would be highly important for Marxist philosophers, working in close contact with mathematicians, to elaborate this important epistemological and ideological problem.

p The natural sciences study the properties of matter and set themselves the immediate task of helping man to understand the material world. In the past, this entailed improving the active, purposeful, and clearly reproducible contact between man’s thinking and the objects of the surrounding world. Only such contact could lead to formation of the basic postulates and concepts in theoretical mechanics, physics and chemistry, and determine the advance of natural 35 science as a whole. By the close of the Renaissance conscious, purposeful contact between thinking and the surrounding world, expressed in the shape of experiment, had developed into the definitive instrument of scientific cognition.

p Experiment differs essentially from the contemplation and observation of nature to which the thinkers of ancient Greece mostly confined themselves. Experiment must be purposeful, if it is to wrest from nature the answer to a question formulated according to strict theoretical principles. (The result, admittedly, is sometimes quite unexpected, and instead of an answer, nature sets the scientist another problem.) This means that experiment can play a revolutionaiy role only where it is closely linked with the development of theoretical thinking. It was this close contact between the development of theoretical thinking and the development of scientific experiment that marked the birth of the natural sciences in the modern meaning of the word. Experimentally verified premises were systematically put into the basis of scientific knowledge. And the subsequent development of science assumed the form of a dramatic dialogue between the existing system of concepts and the data yielded by new experiments.

p Theory usually develops in such a manner that a new experiment (or more precisely, the old one, now interpreted) causes, or, rather, brings out and reveals the contradictory situation inherent in the existing system of concepts. This necessitates creative thinking of a kind that formal logic no longer provides, namely, dialectical thinking.

p Experiments are usually staged to clarify some particular aspects of theory within the framework of the existing concepts. Such inquiries are very useful for the verification and expansion of theory, and for establishing the conditions for its application in practice. However, they do not go beyond the framework of existing concepts; nor do they lead to revolutionary advances in science. Substantial advances in science follow discoveries that come into conflict with existing systems of concepts. The resolution of such contradictions leads to the emergence of new scientific concepts, which are sometimes epoch-making and revolutionise science as a whole. But much more often experiments are of limited significance, ensuring a substantial advance only with reference to some particular scientific question. Nevertheless, 36 taken together, all these discoveries, major or minor, do in the main determine the revolutionary advance of scientific knowledge.

p The Marxist-Leninist theory of knowledge objectively reflects the process of creative scientific endeavour even when that endeavour is spontaneous. When this theory is applied consciously by the scientist, natural science tends to develop at a more rapid rate. This relationship between the scientist’s work and the theory of knowledge is much more clearly expressed in the brilliant, though rare works of epoch-making significance.

p At the moment, however, I should like to go into this matter with reference to some of the very common “minor” discoveries, confining myself, of course, to those that entail the emergence of a new, albeit specific concept. I intend to cite a concrete example from the history of those “minor” discoveries, and to follow closely the train of thought that leads from the contradiction brought out in the experiment to the emergence of a new concept. As a rule, scientists, in their treatises, never deal with this preliminary process of reasoning. Purely because of this (and not because I attach any special importance to the experiment), I have chosen as an example one of our early studies, namely, the discovery, between 1925 and 1928, of what is known as limiting phenomena in chemical kinetics and the establishment of the concept of branched chain reactions. This discovery was made by myself and my closest pupils, then very young (among them are the present Academicians Y. Khariton and V. Kondratyev and Corresponding Members of the USSR Academy of Sciences A. Kovalsky and A. Shalnikov).

p We were to study the phenomenon of chemiluminescence that occurs during the oxidation of phosphorus vapour by oxygen. To detect optimal light emission, the experiments were carried out under low oxygen pressures. Quite unexpectedly we discovered that with the reduction of the initial pressure of the gas mixture down to a certain pressure PI (we called this pressure the lower limit), the mixture completely failed to react and, therefore, to emit any light. In that state it could be kept for days without any signs of a reaction. When the pressure was slightly above this limit, the reaction was very rapid, with intensive emission of light. 37 The rapid reaction at pressure above the limit came to a complete halt as soon as the pressure of the reactive mixture fell to a certain residual level, slightly below the lower limit.

p We observed the same phenomena with various other mixtures of oxygen and various combustible gases. The value of the lower limit proved to be dependent on a number of other parameters besides pressure, such as temperature, the radius of the vessel, dilution of the combustible mixture with the inert gas argon, and the number of active admixtures slowing down the reaction. Each of these parameters, when varied smoothly under constant pressure and constant other parameters, has its own limiting value, separating the region of the very rapid reaction from that of chemical inertness.

p A phenomenon outwardly similar to our discovery was already known. This is the spontaneous explosion of combustible gases when the temperature rises above a certain critical point. We found it necessary to make a special study of this phenomenon. It turned out that the mixture reacted mildly at a slow, but entirely measurable speed, which increased with a rise in temperature. When the temperature reached a certain critical value an explosion followed. It was found that at a constant temperature there is a critical pressure and even a critical vessel size. In other words, everything looked very much like the discovery I have described.

p Our group then began to study the causes of this phenomenon and so arrived at the theory of thermal explosion. It showed that this type of explosion had nothing in common with the limiting phenomena we had observed in the phosphorus oxidation type of reaction. An attempt to dismiss our phenomenon as a thermal avalanche failed (although the thermal explosion theory paved the way for the general theory of combustion and explosion).

p Consequently, in our work on phosphorus oxidation we had discovered some absolutely new and unusual phenomena in chemical kinetics which could be called “all- or-nothing" phenomena, with a marked boundary between them. These phenomena were in basic contradiction to all the fundamental propositions of chemical kinetics of the time, which held above all that the rates of all chemical 38 reactions varied smoothly with temperature and pressure, in accordance with certain universal regularities.

p Our first report, published in early 1926, was sharply criticised by the eminent German Professor Bodenstein, then the doyen of chemical kinetics. He wrote that our results were impossible theoretically and contained gross methodological errors experimentally.

p We had to go back to our experiment and eliminate all the methodological errors pointed out by Bodenstein. In 1927, we published another and longer article which confirmed and enlarged on the 1925 experiments. Bodenstein thereupon withdrew all his objections, first in a private letter, and then in a public statement. The new facts could be considered well established. The contradiction between them and the existing concepts in chemical kinetics stood out with ample clarity.

p Since we had no idea how to resolve this contradiction, we turned to experiment once again to establish with the utmost precision the empirical regularities of limiting phenomena, mathematically expressed. We discovered that all these regularities fitted into the rather simple formula ®S =1, where 8 is the value characteristic of each type of reaction, and O is any given, fairly simple combination of the parameters mentioned above (pressure, temperature, vessel radius, etc.). At first, this provided no explanation of the phenomenon in question.

p In our case, the molecules of oxygen and phosphorus below the given pressure limit were inert in respect of each other. This could naturally be attributed to the high energy of activation and the low temperature of the experiment. But this implied that such a reaction ought not to occur even above the limit. Consequently, the rapid reaction above the limit, which we had actually observed, had an entirely different mechanism. At this point, we recalled Bodenstein’s remarkable discovery, made between 1913 and 1916 in his study of the photochemical reaction producing HC1 from the gaseous H₂ and C1₂. He had demonstrated that for each quantum of light absorbed by a C1₂ molecule there was produced up to one million HCl molecules (known as the quantum yield), instead of a pair of molecules, as Einstein’s formula had suggested and as had frequently been confirmed in experiments with other photochemical reactions. 39 Bodenstein had called this remarkable phenomenon a “chain reaction”. After three years of search and failure, Nernst and Bodenstein produced a correct reaction mechanism, which was a brilliant description of all the experimentally discovered kinetic regularities. It introduced into chemical kinetics for the first time the concept of particles with a high reactivity—free atoms and radicals—which are produced when one of the bonds of a molecule is ruptured.

p Mechanism of H₂ -t- C1₂ Reaction C1₂ + quantum of ligM Cl + Cl}g-eneration of chain chain propagation chain termination H, ———- HCl + H HCt + Cl HCl -t- H H +C1₂ Cl + H₂ etc. Ct+CI———— C1₂ Cl + active admixture H₂ + C1₂ = 2 HCl

p From the kinetic regularities developed by Bodenstein, it is easy to determine the length of the chain v, i.e., the value proportional to the rate of the reaction, which is made up of the number of elementary reactions in the chain from its generation to its termination. Both experimentally and theoretically, this value varies smoothly with the variations of all the parameters, and that is why it was of no direct assistance to us in explaining our limiting phenomena, which were characterised by a sharp difference in reaction rates. Nevertheless, we were haunted by the idea or rather, a vague feeling, that the phosphorus oxidation reaction was somehow connected with the concept of Bodenstein’s chain reaction.

p In our experiments, we were amazed by the fact that the limiting pressure depended on such parameters as the vessel diameter or the pressure of the inert gas admixture, which, seemingly, should have nothing to do with the elementary 40 steps of reactions. According to our experiments, the limiting pressure PI was inversely proportional to the square of the vessel diameter. Here one could make the purely mental experiment of enlarging the vessel ad infinitum. In that case the limiting pressure would tend towards zero. In other words, the limiting pressure would disappear, and the rapid reaction would occur under negligible pressures. This meant that the development of the reaction was hindered by the walls of the vessel. It then occurred to us that the vessel diameter might exert a similar effect on Bodenstein’s chain reaction as well. If Bodenstein’s chains could be terminated as a result of the capture of atoms and radicals by active admixtures, there was the probability—greater or lesser— that they would be captured by the vessel’s walls, through chemosorption. This type of termination of Bodenstein’s chains should naturally appear under reduced pressures, when termination in the gas phase was less intensive. This called for an experiment to study the dependence of the rate of the photochemical reaction of hydrogen and chlorine on vessel diameter and pressure. In 1928, these experiments fully bore out our hypothesis. The termination of chains on walls later turned out to be common for all chain reactions.

p Towards the end of 1927 we adopted our hypothesis as a basis, without waiting for the results of these experiments. Under this assumption it was not hard to find a mathematical expression for Bodenstein’s length of chain. It was at this point that we unexpectedly realised that the combination of parameters ® in our empirical expression for limiting phenomena was identical with the expression v, provided the chains were terminated on the vessel walls. A connection between our discovery and Bodenstein’s chain reactions became increasingly probable. Our empirical equation v8 = l could thus be rewritten as v8=l. This, as I have said, did not, of course, directly lead us to the solution of the main question. For the length of chain in the Bodenstein-type reaction varied quite smoothly with the diameter, whereas we had a critical diameter di (Pi remaining constant) below which the reaction did not occur at all, while developing very rapidly above it.

p Psychologically, the benefits, however, were very great. The contradiction had become even more precise and acute. If earlier we had had to discover the reason why the 41 reaction could reveal limiting phenomena, we were now faced with the question: why was it possible for a chain reaction, capable of termination at the vessel wall, to show limiting phenomena? The sum of our reasoning and experimenting suggested a one-way path at the end of which, and nowhere else, lay the answer.

p At this point, we had a flash of inspiration, seemingly intuitive, though in the light of what had gone before we cannot call it a revelation, for it had been prepared by everything I have described above. When a scientist writes about his discovery he is usually hesitant about revealing the personal aspects of the quest which led to the emergence of a new basic concept. He usually begins with that concept. Hence the myth about intuition, in which he himself may later come to believe.

p The really important thing in epistemology, however, is the description of the scientist’s preparatory mental work, for that is based on a study of the whole history of thought, beginning with the ancient Greeks. But the Greeks were much less inhibited about describing their process of reasoning than our modern scientists are. Perhaps we should change this; at least, I shall now try to do so. What interests me particularly is the meaning of the vague concept of intuition in the light of dialectics.

p I wish I could recall what I was thinking just before that flash of inspiration. I may have been thinking that the properties of the free atoms and radicals in Bodenstein’s chains were analogous to the actions of bacteria, which, so to speak, swallow up the original molecules, turning them into the products of the reaction. Suddenly it occurred to me that bacteria were able not only to eat but also to multiply. Just a minute, I said to myself. What if the free atoms and radicals were also capable of multiplying? There it was: there was the answer!

p This culminating point set me arguing with myself. Why, I asked myself, should they be capable of multiplying at all? That would call for the appearance of more than one radical in the given elementary act of development of Bodenstein’s chain. There should be at least one more or, rather, two more, because in the final count the whole thing comes to dissociation of a molecule into two free radicals. But dissociation requires sufficient energy. Where does that 42 come from? Well, coincident with the elementary reaction there could be a release of a large amount of energy which some time later, a very short time later, it is true, is diffused into heat. But before that happens it could be used, like a quantum of light, to dissociate a molecule of the initial substance, thereby causing a branching of the chain. But how, precisely? That, I decided, could wait. I was sure that the answer to the contradiction lay in the possibility of the chain’s branching.

p I do not recall exactly how it was; it may have actually been by analogy with bacteria. In Newton’s case we are told it was a falling apple. In other cases it was something else. That is not so important. If a gun is loaded and you play about with it long enough, something will cause it to go off. What mattered was the long train of thought that came before, which clearly brought out and sharpened the contradictions, and not what actually triggered that flash of inspiration.

p Now that we had our answer, the task was to formulate our hypothesis properly. Let us assume, then, that each link of Bodenstein’s chain may produce with probability 8 a branching, giving a secondary Bodenstein chain. In that case, over the whole length of the Bodenstein chain, consisting of v links, there will appear v8 new chains. This will apply not only to the primary but also to the secondary chains generated in the branching. The expression v8 =1 which determines the limit, means that each Bodenstein chain with a length v, when terminated, produces an average of one branching which starts a secondary chain, etc. Every termination of the chain is compensated by one branching, making the chain as a whole infinite, so to speak.

p Let us assume that we inject into each cubic centimetre of gas one primary free radical to start such an infinite chain. Taking T to designate the time of the radical’s entry into each elementary reaction, we find that we have    reactions a second. In t seconds we shall have X=—= molecules of the initial substances reacting. Owing to the great reactivity of atoms and radicals, Y is usually small.

Let us take, for example, T = 10- 5 sec. Assuming further that the pressure P₄ = 1/100 atm., i.e., 3-10 17 initial molecules in a cubic centimetre, let us calculate the time it will take to bring the reaction X=—; t=10 sec P= 1/lOOatm-3-10 17 rnolecules/cm 3 3 niln years etc.

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p Let us now assume the initial gas pressure to be above the limiting pressure. In that case, more than one branching will arise on each section of Bodenstein’s chain. More chains will originate than are destroyed. As a result, one primary free radical admitted into the gas will produce a chain avalanche, in accordance with the Ae?1 law, where the reproduction coefficient cp is proportional to the difference 8v—1 and inversely proportional to the length of Bodenstein’s chain v and time t.

Even with a minor change in the initial pressure of the mixture, say, by 1 per cent, above the limit and respectively with v3—1 = 0.01, the avalanche wiil develop so rapidly, that 30 per cent of the substance will react in roughly 4 minutes (see Fig. 3).

p t₃o% 4min

p Fig. 3

p up to

p 30% - = 10 14 sec fa 3 million years (see Fig. 2).

p 10 17 = 10 3 t; hence,

p 130%

p Naturally enough, below the limit, when v3<l, and the number of terminations is in excess of the number of branchings, the admission of one radical cannot result in a 44 reaction at all and the incipient chain will quickly be extinguished.

However, in most cases, the reaction above the limit proceeds even faster. After all, the majority of rapid branching chain reactions proceed quite differently from the long Bodenstein chains with rare branchings. The branchings take place virtually on every link of the chain; the chains turn out to be almost continuously branched (see Fig. 4).

p etc.

p Fig. 4

p In fact, the concept of Bodenstein’s chain disappears altogether. The amazing thrhg is that this concept, which was such a great help in solving the contradiction we had discovered, turned out in the end to be irrelevant.

p In the continuously branching chain reaction the propagation of the chain is automatically connected with its branching. Each free atom or radical is capable either of disappearing (termination of chain) or propagating the chain, as it enters the reaction. This being so, it is simple to find the conditions for the limits and the rate of the chain avalanche development, both above and below the limit, where pressure varies by + 1 per cent.

p We find that here again there arises at the limit something like a single infinite chain (see Fig. 5), so that the time t_300/o continues to be 3 million years. The reaction above the limit will develop in accordance with the avalanche law ecft, but here cp will be higher than for chains with rare branchings.

, t_30%^3 mln years

p etc.

p Fig. 5

45

p If in this case we increase the initial pressure by 1 per cent above the limit PI, the admission of one primary free atom or radical into one cubic centimetre of gas will produce a reaction which takes not 4 minutes, as we have seen above, but roughly 3 seconds, instead of millions of years at the limit.

p We have examined an ideal case, where the spontaneous origination of free atoms in a reactive gas does not take place at all, or takes place very rarely, and where the reaction is started by admitting at least one free radical from outside.

If r[o such primary free radicals appear in each cubic centimetre in a second, it is easy to produce an expression for the rate of the branched chain reaction, and the quantity of molecules X which have reacted in time t, as has been done above. The results are shown in the following table.

i!₀=1free radical/sec, cm 3 r(₀=100 free radical/sec, cm 3 P = _Pl t₃₀^1year t_30?t ^ 2 weeKs P = 1.01P₁ t₃₀₅,^4sec t   *^ SPf* P=0.99P, tso%   3 °i°0° years t_m^ 300 years

p Consequently, our hypothesis furnishes a good explanation why some chemical reactions are based on the “all- or-nothing" principle.

p It would be wrong to assume that once the hypothesis was clearly formulated our work was over. On the contrary, that was when it really began. And it is still going on, in a measure. Step by step the theory has been given increasing precision and clarity, becoming a quantitative theory that has predictive power.

p So it was that we succeeded in establishing the occurrence of two types of avalanche-like chemical processes which, in certain conditions, lead to explosion: the thermal explosion, which arises as a result of the build-up of the thermal avalanche, which I have dealt with here in brief, and the chain explosion, which results from the avalanche-like 46 reproduction of active chemical particles and free atoms and radicals, whose concentration in the development of the chain avalanche attains, theoretically and experimentally, tremendous values comparable with the concentrations of primary molecules. It later turned out that only these two types of explosion occur in nature. Even in atomic physics, blasts can be only of the chain type (atomic explosion) or of the thermal type (thermonuclear explosion).

p I should like to add another remark in connection with my analysis of this discovery. Experiments have shown that the general regularities governing branched chain reactions, notably the “all-or-nothing” limit itself, and the development of chains in time depend very little on the actual mechanism of these reactions. The important fact is that they branch out and that chains terminate. Quantitatively, these regularities also depend on certain constants which can be determined, to their first approximation, from experiments according to the optimal values.

This applies not only to chemical branched chain reactions but also to physical reactions, which include nuclear fission chain reactions and also, iji essence, the reactions of multiplication of light quanta in lasers and masers. In the former, the active particles of the chain are the excited compound-nuclei, which arise in the capture of neutrons by the atomic nuclei of active substances, and the neutrons emitted, numbering three for every act of fission of the compoundnucleus. The termination of the chain takes place through the emergence of neutrons beyond the limits of the active body (similar to the termination of the chain on the wall) or the capture of neutrons by certain admixtures. In density, dimensions, admixtures of active substances, dilution with U-238, etc., limiting phenomena are identical with those which are observed in chemistry. The formation of vast quantities of neutrons in the course of the reaction, the exponential growth of the rate of reaction in time during an atomic blast are similar to the corresponding phenomena in chemical branched chain reactions. The “all-or-nothing” principle is here manifested in an especially clear-cut form, and in essence provides the sole basis on which one can build atomic bombs and piles without fear of explosion, and set off an explosion through the insignificant alteration of one of the parameters. The formal relations in our 47 insignificant-scale chemical phenomena remain true even for these powerful reactions. From the analysis of this discovery it can be seen that it is not so much the confirmation of existing concepts that is of especial importance to scientific cognition as the emergence of concepts contradicting the former. These contradictions are the main stimulus in the development of science. It is a gift of fortune for a scientist to come up against a contradiction, major or minor, and he should seize upon it. Yet, it is so easy to overlook it, to brush it off, especially when a deadline looms for the publication of an article or the presentation ol a thesis.

p Let us now pass from “minor” to “major” contradictions, which reveal much more strikingly the principal logical components of scientific discoveries at the time of decisive scientific revolutions. When it comes to changes in the basic scientific concepts supporting the whole edifice of a theoretical system, not only the concepts themselves change but also the logic of thinking itself, the very understanding of what is “logical” and what is “illogical”. Here is what Max Born says about it: “The situation here (in quantum mechanics—N.S.) is so confused that the only option is this: either to rest content with the feeble adaptation of concepts to the system of formulas ... or to modify the rules of thinking, of logic itself."  [47•1 

p At such moments, the theoretical physicist begins to work as a pure logician, as a transformer of Logic. He has to work in the sphere of such contradictory concepts as continuity and discontinuity, interconnection and establishment, time and space, probability and necessity; for the specific purposes of natural science he must modify, develop and review the primary logical categories. This is a subtle business and in the absence of sufficient erudition and philosophical training it is very easy to repeat former mistakes. Engels used to say that materialism changes its form with every great new discovery in science. This is where a developed and properly mastered logic of historico-philosophical thinking ceases to be luxury, a mere pleasant supplement 48 to a training in natural science, and becomes a matter of primary and most acute necessity. One such revolutionary logician was Einstein when he worked out his theory of relativity (revising the concept of time as a logical concept). Another leading revolutionary in logic was Niels Bohr, who, to all intents and purposes, was the founder of the modern quantum theory. His quantum theory of the atom emerged as a result of a bold resolution of the contradiction between Rutherford’s planetary model of the atom, introduced virtually straight from the experiment, and classical electrodynamics.

p Bohr’s principle of complementarity went even further in revolutionising the logic of physical cognition, for it tacitly introduced into the very structure of physical theory the idea of contradiction; at the same time, Bohr’s conception of the fundamental epistemological importance of the “instrument-object” relationship to some extent corresponded to Marx’s conception of the active epistemological role of the instrument in the cognition of things.

p The dualism of wave and corpuscular concepts, discovered by Planck and Einstein in fespect of light, was taken by de Broglie to be a universal contradiction of microobjects and applied to a description of the motion of electrons (which was shortly confirmed experimentally). De Broglie’s conception was one of the sources that gave rise to quantum mechanics.

p Our last example is Dirac’s anticipation of the positron. Attempts to unite quantum mechanics and Einstein’s relativistic mechanics had run into the difficulty of having to recognise the existence (because there were expressions containing a square root) of particles carrying a plus and a minus sign, i.e., positive and negative energy. But particles with negative energy seemed to be an absurdity, pure nonsense. It was, therefore, necessary to invent a principle which would rule out their existence in nature and which at the same time would admit the possibility of their existence. The contradiction was formulated with the utmost logical incision. Using Pauli’s exclusion principle, Dirac introduced his “holes in a vacuum" concept (a vacuum filled with a vast number of what were virtually electrons in a state of negative energy). This somewhat obscure concept, literally invented on the basis of a most strictly formulated 49 antinomy, was then concentrated into the rational concept of a fully material particle, “the electron with a positive charge”, i.e., the positron. But the initial vague and even logically contradictory concept was in fact the nutrient medium, so to speak, which produced not only the concept of the positron but modern relativistic quantum mechanics as a whole in its new and even more striking but, I regret to say, not so stringently formulated antinomies.

p The example of Dirac’s discovery is a very characteristic one and provides a summing up, as it were, of the creative process of theoretical thinking. From this example, or, rather, this food for thought, one can obtain the clearest possible picture of some of the primary concepts of dialectical logic.

p As for the significance of these concepts, let us see whether it is possible to define the actual process of scientific endeavour (say, in the aspects dealt with above) as a process subject to the laws of Logic with a capital L. Every scientist knows that theoretical work is anything but a smooth movement forward and only forward. It may appear to be so from afar, just as the Earth, for example, appears to be an ideal geometric sphere when viewed from outer space, but certainly not to a mountaineer climbing Mount Everest.

p The harder a scientist tries to recall “how it all actually happened”, the stronger is his impression that it is in general quite impossible to discover any “rational” principle or logic in the development of scientific knowledge and that this development is governed by nothing more than the whims of unrestrained will with its “mad notions”. Thus Louis de Broglie writes in his Paths of Science: “Human science, essentially rational in its principles and in its methods, cannot achieve its most remarkable conquests except by executing sudden and perilous leaps of the mind, involving the play of faculties called imagination, intuition and perception, released from the hard constraints of rigorous reasoning. Let us perhaps say that the scientist carries out the rational analysis and goes over link by link of the chain of his deductions; he is bound by this chain up to a point where he suddenly escapes from it, and the liberty of his imagination, once recaptured, enables him to look out onto new horizons."  [49•1 

50

p This, one might say, makes it clear that formal mathematical logic, while being an effective and invaluable instrument for the solution of tasks of a definite type, proves to be powerless when it comes to explaining the actual process of scientific work leading to the production of new concepts.

p If we assume that scientific thinking is “logical” and “rational” only insofar as it proceeds in strict accord with the axioms, postulates and theorems of formal mathematical logic, the scientific thinking that actually takes place inevitably seems to be irrational, so that science itself appears to be a madhouse where only superficial order is maintained by the logician-attendants but by no means by the inmates, whose sole aim is to disrupt it.

p If this were so, the whole theory of scientific knowledge would prove to be a purely outward and absolutely inexplicable fusion of two different and irreconcilable sciences— formal mathematical logic and the purely psychological description of intuition.

p It would appear that there ought to be trends in science that would provide an exact and specific description of certain universal laws governing the process of scientific reasoning. From the viewpoint of dialectics it is clear that these so-called “mad notions" are essential, logical processes of reasoning.

p In fact, whenever the result of a new experiment (or a more thorough analysis of a previous experiment) leads to a basic contradiction within the system of existing concepts, that very contradiction constitutes a determination of the conditions engendering a hypothesis; that is to say, the contradiction prescribes a vector of reasoning in the formation of the hypothesis.

p In short, in any given case we may expect to find the following “mechanism”. At first the contradiction within the old theory appears to be rather generalised and vague. Clearly, the new experimental fact, if and insofar as it is understood, contradicts the old theory and the old concepts in general; but it is far from clear where the apex of the contradiction is located and exactly what old key principle has to be modified. Gradually, as a result of further experiments and of the refinement of the old concepts themselves (no such refinement had been needed before), the contradiction is sharpened and narrowed down until it becomes 51 apparent exactly which old concept must be modified first. The contradiction acquires the acuteness of an antinomy formulated with the utmost stringency. But this is also a formulation, although only implied, of a negative definition, as it were, of the new concept. It then remains to understand the positive content of the new concept, to define it not only as a clearly formulated question, but also as an answer, as a new concept. The new concept is usually a qualitative and basic reformulation of the old initial concept, though it is simultaneously the embryonic form of a new theoretical system. Such is the origin of a hypothesis.

p At this point the following new logical cycle begins. Parallel with the verification and confirmation of the hypothesis in the course of countless experimental variations and mathematical concretisation (let us assume that our hypothesis is correct) there follows an examination and enrichment, as it were, of the initial concept alone, and its articulation into a series of interrelated, more specific auxiliary concepts, with the result that the hypothesis develops into a detailed, experimentally verified theory.

p From the concrete material I have introduced into this article it will be seen that this logical picture is a legitimate idealisation of the specific process of creative reasoning.

p The initial contradiction which destroys the old theory is thereby resolved (“removed”) within the new, more profound and specific theoretical understanding which includes the old theory as a particular limiting case. Intuition, thus understood, emerges as nothing else but the form in which a perfectly rational process of reasoning takes effect. The contradiction, therefore, destroys not the theory in general, but only the old, limited theory, or, to be more precise, the illusion that the old theory was a final, complete and concrete (“absolutely true”) reflection of objective reality. The contradiction brings out the nodal points within the system of the old theory, in which its growth points are concentrated and in which its ability to “grow through contradiction" becomes apparent. Moreover, it is the strictest and most formally perfect movement of thought that arrives at those growth points in which the basic (dialectical) contradiction begins to show, a contradiction which confronts intuition with the task of constructing a hypothesis, that is, reaching 52 a point beyond which any purely formal movement becomes impossible.

We have tried, by analysing the process of scientific discovery, to show how dialectical logic works and how it helps the scientist understand and refine the actual process of creative scientific thinking.

p The birth of dialectical logic is connected with the names of Kant and Hegel. Kant had already demonstrated that the appearance of a contradiction within a scientific concept was not the result of some regrettable error of reasoning, logical carelessness or imprecision, but a very natural state of the human mind at which the mind arrives because it has observed most painstakingly all the postulates and demands of strict formal logic, or definiteness of concepts. Developing this point of view, Hegel began to examine the logical contradiction as an internal motive force of development, as the “motor” of man’s cultural development, in the spiritual and theoretical sphere above all.

p Marx purged Hegel’s dialectics of its idealistic bias and gave it a materialistic interpretation, thereby laying the foundation of materialist dialectics.

p For obvious reasons arising out of his life and struggle, Marx did not have time to refute Hegel’s dialectics by an equally systematic exposition of dialectics on the new, materialist basis. Lenin wrote: “If Marx did not leave behind him a ‘Logic’ (with a capital letter), he did leave the logic of Capital, and this ought to be utilised to the full in this question. In Capital, Marx applied to a single science logic, dialectics and the theory of knowledge of materialism [three words are not needed: it is one and the same thing] which has taken everything valuable in Hegel and developed it further."  [52•1  In Capital, Marx did, indeed, demonstrate to the scientific world, using very concrete material, the tremendous methodological power which materialistic dialectics carries within itself.

p It was materialist dialectics that enabled Marx to arrive at a scientific resolution of the fatal contradictions which 53 were inherent in the classic labour theory of value, and, notably, one of the central paradoxes of that theory: the contradiction between the concept (and law) of value and the concept of profit (surplus value and all its derivative forms).

p A strictly scientific formulation of this contradiction suggested a scientific way of solving it, made it possible to formulate a hypothesis, discover its confirmation within the system of economic relations and thereby turn the hypothesis into a strictly demonstrated theory, the theory of surplus value. That was the basis on which a theoretical conception was achieved, which embraced not only the whole of the economy of capitalism but also all the remote consequences of its contradictory evolution, including its inevitable collapse.

p We find that, on the whole, Marx’s theoretical thinking ran on the same lines that we observe in the development of natural science, with the one difference that Marx reasoned quite consciously, whereas in natural science the dialectical movement of thought is still mainly spontaneous. Hence the fact that natural scientists very often have an inadequate conception of the true logic of their own reasoning. Not having mastered the system of concepts of dialectical logic, they consider their own actions in terms of inadequate concepts, and this hampers, at the critical points in the development of natural science, their quest for a way out of the blind-alley of contradictions.

p Marx pointed out that already in capitalist society science becomes an immediate productive force. At the same time Engels noted that under capitalism the development of the productive forces is a menace to society.

p In 1918, Lenin stressed that by unleashing the First World War with powerful modern scientific and technical achievements being used for the purpose of destroying millions of human lives, monopoly capital had created a situation which could “undermine the very foundations of human society".  [53•1 

The last few decades have seen qualitative changes in science which vastly increase both its creative and its destructive potential. In former times, science, by analysing production processes and facilitating their improvement,

54 served production directly. Today, it has another and much more important function. As a result of the experimental and theoretical probing of the mysteries of matter and penetration into the original causes of macroscopic phenomena, modern science has begun to produce basically different, unprecedented means of production and new technologies which surpass man’s boldest flights of fancy. Over the last few decades, there has been a steady growth in the pace of development and application of science, offering real prospects of providing for the well-being of the world’s population in a relatively short time-span. On the other hand, this development of science, this scientific and technological revolution gives rise to basically new types of weapons of unprecedented destructive force.

p If science is to serve the interests of mankind, society and the state must make the welfare of all the working people their main aim and do their utmost to attain it. But the capitalist system is fundamentally incapable of setting, let alone achieving such an aim, because it is an aim that clashes with the very basis and essence of the capitalist relations of production.

p Capitalism and chauvinism hold the menace of another world war, which with the existence of modern weapons would, as Lenin warned, be disastrous for mankind.

p The transition from capitalism to socialism on a worldwide scale must resolve the profound contradiction between the vast productive forces, including modern science with its two different uses, and the relations of production under monopoly capitalism, which breeds the aforesaid potentially catastrophic phenomena.

Capitalism and chauvinism are currently in contradiction not only with the productive forces; they are actually inimical to human existence itself. Sooner or later, the nations of the world will come to see the objective necessity for the transition to socialism and communism. The ideals of scientific communism, substantiated and developed in the brilliant works of Marx, Engels and Lenin, have already won the hearts and minds of a great part of humanity. Eventually, they will be shared by all.