THE

LENIN

AND

PHYSICS S.

G.

DOCTRINE

ON

KNOWLEDGE

Suvorov

Lenin was not only the organizer and leader of the world's firstsocialist state, but also the great thinker and philosopher of our time. The combination in Lenin of a revolutionary and philosophertheorist is natural, this is because he was able to find the true path of transformation of a society and to determine the methods of constructing socialism which he, like Marx, understood profoundly and for which he developed the theory that lies as the basis of knowledge of mobile forces in nature and society, i.e., philosophy. In philosophy, Lenin was the direct pupil of Marx and Engels, i.e., he was a dialectic materialist. He not only succeeded Marx but he also developed and intensified, under new conditions of knowledge, the different aspects of Marxist philosophy. Below, we shall consider briefly the new knowledge that Lenin introduced into theory and which, in our opinion, is important to physicists. i. The fundamental complete philosophical work of Lenin, "Materialism and Empiriocriticsm ~ was written in 1908. Despite the fact that after the havoc of the revolution of 1905 many pointed practical and theoretical problems associated directly with the revolutionary movement arose, Lenin was able to turn to philosophical problems. Important circumstances prompted him to this, which he associated directly with the work of the Party. At the beginning of the 20th century, there was an increase in philosophical and natural science circles of the influence of positivism (empiriocriticism) - of idealistic philosophy stemming originally from Berkley and which contradicted the existence of an objective world as the source of knowledge and did not acknowledge the objectivity of the laws of nature. The effect of positivism increased, because in physics at this time there occurred a turbulent undetermining of ideas due to new discoveries and the development of new theories. It was established that the atom, which had been assumed to be the starting material basis of the outside world, after all was not ~'the last brick of universal knowledge." The radioactive source of energy was discovered; it was found to be inexhaustible and that it refuted the law of conservation of energy. The representation of the absoluteness of space and time was destroyed. The entire system of absolute representations and concepts built up in physics was shaken. Metaphysical materialism, on which physics rested, could not be handled with this breakdown of ideas. Some physicists - including for example Poincar~ - began talking about a general breakdown of physical laws, about the "physics crisis, ~ the ~'disappearance of matter.'1 This confusion of mind was used by positivism, having suggested a philosophy allegedly concurrent with the results of the most recent natural science. It is true that in nature there is nothing absolute, positivism asserted, but this is because outside of us there is nothing objective and our knowledge is related only to sensations and science is a system of ordering of sensations. Positivism came into fashion. Certain writers from a number of the Party intelligentsia were absorbed by it; they attempted further to unite positivism with Marxism, i.e., with the revolutionary doctrine concerning the laws of development and transformation of Society. This "infection ~ was not only a Russian occurrence, it ailed the ruling social-democratic circles in the West and the social-democratic press also supported it. Lenin had the insight to discern in this attempt to unite Marxism and positivistic philosophy, an undetermining of the theoretical foundations of Marxism and, in fact, recent history has shown that withdrawal from the basis of dialectic-materialistic philosophy was not accidental - it was the beginning of the Translated

from

Inzhenerno-Fizicheskii

Zhurnal,

Vol. 18, No. 4, pp. 585-609,

April, 1970.

© I973 Consultants Bureau, a division of Plenum Publishing Corporation, 227 West 17th Street, New YorE, N. Y. 10011. All rights reserved. This article cannot be reproduced for any purpose whatsoever without permission of the publisher. A copy of this article is available from the publisher for $15.00.

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d e p a r t u r e of the s o c i a l - d e m o c r a t i c l e a d e r s f r o m M a r x i s m and by their change, the lot of the working c l a s s was improved. In " M a t e r i a l i s m and E m p i r i o c r i t i c i s m " Lenin r e c a l l e d the e s s e n c e of positivistic philosophy and showed its h i s t o r i c a l r o o t s , its r e l a t i o n to double-dyed idealism, its incompatibility with the scientific r e v o l u t i o n a r y t h e o r i e s of the development and t r a n s f o r m a t i o n of Society and the g r o u n d l e s s n e s s of its p r e t e n c e s to e m e r g e as a philosophy of m o d e r n natural science. Having shown the unscientific nature of p o s i t i v i s m and having grounded h i m s e l f on the works of M a r x and Engels, Lenin developed a theory of r e p r e s e n t a t i o n of the outside world in the c o n s c i o u s n e s s of m a n kind. He analyzed the p r o c e s s e s taking place in physics and showed that a v i g o r o u s revolution was taking place, which was natural for the advancing c o u r s e of knowledge and the breakdown of ideas, and the inc r e a s e d noise in c e r t a i n c i r c l e s concerning the "physics c r i s i s " is of a gnosiological nature. Gnosiological hesitations give r i s e t h e m s e l v e s to the development of science with the special f e a t u r e s of m o d e r n physics. Lenin noted two r e a s o n s f o r physical i d e a l i s m - m a t h e m a t i z a t i o n of physics, beyond which s o m e s c i e n t i s t s c e a s e to r e g a r d m a t e r i a l p r o c e s s e s , and r e l a t i v i s m which in the c a s e of ignorance of dialectic logic leads to negation of objectivityl T h e r e f o r e , in o r d e r to avoid slipping down into i d e a l i s m , Lenin called upon n a t u r a l i s t s to s e i z e hold of m a t e r i a l i s t i c dialectics. As is well known, Hegel developed dialectic logic; but for Hegel it "stopped at the head," as he r e g a r d e d the b a s i s of everything r e a l in s o m e kind of absolute spirit but not in nature and he expounded it in an e x t r e m e l y m y s t i c a l f o r m . Just as in the t i m e of Marx, Lenin posed h i m s e l f the p r o b l e m of "writing Logic with a capital l e t t e r , " i.e., to expound and develop a m a t e r i a l i s t i c dialectic in a special acceptable book. Just like Marx, Lenin did not succeed in writing Logic, as a consequence of the fact that before him stood urgent t h e o r e t i c a l and p r a c t i c a l p r o b l e m s of the r e v o l u tionary movement. But he left to our generation the "Phiolosophical T e t r a d s " in which he e x p r e s s e d many profound ideas by logic. M o r e o v e r , he skilfully used dialectic m a t e r i a l i s t i c logic in his n u m e r o u s writings on the theory and p r a c t i c e of t r a n s f o r m i n g Society and p a r t i c u l a r l y in p a p e r s on M a r x i s m ; a study of these is e s s e n t i a l for the p u r p o s e of m a s t e r i n g the philosophical ideas applied in them. Thus, in o r d e r to m a s t e r the philosophical opinions of Lenin and his contribution to the development of m a t e r i a l i s t i c d i a l e c t i c s , it is n e c e s s a r y to study f r o m this angle the views of all his l i t e r a r y heritage. 2. The idealogical struggle at the beginning of the 20th century posed the question: how do p e r t u r b a tions in the natural s c i e n c e s and, in p a r t i c u l a r , in physics affect the solution of the fundamental p r o b l e m of philosophy concerning the s o u r c e of knowledge, the p r e c e d e n c e of nature and the r e p e a t a b i l i t y of thinking, and how does it affect the conclusion about the understanding of the world and the paths and c r i t e r i a of knowledge? The opponents of m a t e r i a l i s m set the solution of these p r o b l e m s in d i r e c t dependence on the r e s u l t s of physics, which they i n t e r p r e t e d as a denial of the conclusions of m a t e r i a l i s t i c philosophy. Lenin showed that such i n t e r p r e t a t i o n of the r e s u l t s of physics is unscientific: they not only do not refute m a t e r i a l i s t i c philosophy but they cannot refute its fundamental t h e o r e m s . The p r o b l e m as posed is itself i n c o r r e c t : the justification f o r the conclusions of m a t e r i a l i s t i c philosophy does not r e s t on the i n t e r p r e t a t i o n of r e sults, even in the case of such an i m p o r t a n t science as physics. It r e s t s on a much b r o a d e r b a s i s - on the entire activity of mankind. The fact that the feelings and ideas of m a n have an objective intension is shown by the r e s u l t s of p r a c t i c a l suitably directed activity. Mankind has p r e s e r v e d his s p e c i e s and has achieved all the new s t a g e s of individualism only b e c a u s e at e v e r y previous stage, even p r i o r to the genesis of m o d e r n science, he has c o r r e c t l y learned to understand the outside world in a n u m b e r of g e n e r a t i o n s , each t i m e within the l i m i t s of a defined c i r c l e linked with him. This fact is of e n o r m o u s gnosiological i m portance and it is i m p o s s i b l e to refute it with any sophisticated i n t e r p r e t a t i o n s of s o m e or other unique r e sult in physics. The r e s u l t s of physics a r e concerned only with knowledge of the c o n c r e t e s t r u c t u r e of the m a t e r i a l world, with the specific f o r m of i n t e r r e l a t i o n s in it and not with philosophical p r o b l e m s about the s o u r c e and c r i t e r i o n of the knowledge. On the other hand, even philosophy does not dictate the physics of any a p r i o r i r e p r e s e n t a t i o n s about the s t r u c t u r e and f o r m of the i n t e r r e l a t i o n s of objects studied and, m o r e o v e r , of the g e n e r a l conclusion that all nature is one and is in a state of motion, or m o r e p r e c i s e l y in a s t a t e of development (because only this can explain the fundamental philosophical fact that thinking does not stand above nature but is a p r o p e r t y of highly-organized organic s y s t e m s developing in nature). Lenin stipulates d i r e c t l y that "in discussing the p r o b l e m concerning the link between one school of the m o s t m o d e r n physics and the r e a c t i v a t i o n of philosophical i d e a l i s m , we a r e f a r f r o m thoughts r e g a r d i n g special studies of physics. We a r e i n t e r e s t e d exclusively in the gnosiological conclusions f r o m c e r t a i n defined t h e o r e m s and u n i v e r s a l l y known d i s c o v e r i e s . "* In r e a l i t y , consideration of all p r o b l e m s is t r a n s f e r r e d to the gnosiological plane. It is said: *V. I. Lenin, Poln. Sobr. Soch, Vol. 18, p. 266. 392

"matter is vanishing," t h e r e f o r e m a t e r i a l i s m is coming to an end. But what, in fact, vanished as a r e sult of the development of physics and what was this "matter"? The defined, historically bounded r e p resentation of the s t r u c t u r e of molecules and a t o m s vanished - and this, naturally, also is the movement of science ahead. And the m a t e r i a l ? Material is a philosophical category for denoting the s o u r c e of objective m o m e n t s in our c o n s c i o u s n e s s and existing outside of it. But this truth is not refuted - it is conf i r m e d by the entire h i s t o r y of mankind and will be verified by any new step in our knowledge, however cardinal it may be. Lenin s u c c e s s i v e l y draws this line when d i s c u s s i n g all other problems - space and time, causality, etc. He does not consider the question of the specific physical r e p r e s e n t a t i o n s of these c a t e g o r i e s - this is the competence of physics - but he considers the question of their objectivity which is the competence of philosophy. Thus, Lenin sharply divides the subject of philosophy and the subject of physics. Having shown that the fundamental philosophies of a problem a r e not solved in physics, he r e v e a l s by the unscientific position of c e r t a i n scientists following f r o m the r e s u l t s of physics at the dawn of the 20th century, the inadm i s s i b l e philosophical conclusions. Even in our time, c e r t a i n eminent scientists as much as stated unacceptably that philosophical problems a r e allegedly solved in physics. Thus, E. Wigner w r i t e s that he cannot suggest any scientific philosophy until the entire chain of m i c r o p h y s i c a l m e a s u r e m e n t s relating the object of the m e a s u r e m e n t with understanding is traced; he repudiates m a t e r i a l i s t i c philosophy b e cause in his opinion it has been supported by a s y s t e m of laws of c l a s s i c a l physics and not by the d i s c l o s u r e of the entire m i c r o p h y s i c a l chain, including also the p r o c e s s in the brain.* However, the r e f i n e m e n t by Lenin of the competence of the natural sciences and philosophy s o m e times is used for the conclusion that physics and philosophy must be demarcated. Philosophers, in talking to us, may demand f r o m naturalists only recognition of the objective world but in other r e s p e c t s they should not i n t e r f e r e in the development of natural science because their i n t e r f e r e n c e would always be incompetent and would impede the development of science. A tendency toward " d e m a r c a t i o n " cannot be a s s u m e d to be c o r r e c t . It can be understood only as a reaction to a fact f r o m the r e c e n t past, when individual scientists and schools in the name of philosophy, which a r e dominant in our society, advocated one trend to the detriment of another. Such was the case, for example, in relation to the theory of relativity, genetics, and c y b e r n e t i c s . However, although individual philosophers also occupied an unattractive position in this problem, there was no m a t e r i a l i s t i c philosophy in it. The natural philosophical dictate over natural science for the new period was rejected even by Engels, although he also pointed out that in its time natural philosophy played a positive role. But in the struggle against definitive theories in natural science it was frequently not the philosophers who led, but the n a t u r a l ists themselves; against genetics, the agrobiologist Lysenko came out - a g a i n s t the fundamental t h e o r e m s of quantum mechanics, the " t r a n s f o r m e r of natural s c i e n c e " (according to Lenin's definition), the g r e a t physicist Einstein c a m e out, he himself having given a stimulus to the development of quantum concepts and the statistical r e p r e s e n t a t i o n of quantum p r o c e s s e s . It can be seen a l r e a d y f r o m this example that the problem to be freed f r o m the struggle against the "new" is not solved completely by the r e m o v a l of "incompetent philosophers" f r o m interfering in the aff a i r s of the physicist. History shows that the struggle against the "new" also is led by n a t u r a l i s t s t h e m selves, when they do not understand by what paths a knowledge of the "new" is accomplished. The problem of the c o r r e c t relation to the new trends in science is solved not by d e m a r c a t i o n but, on the c o n t r a r y , by the close i n t e r a c t i o n of philosophy and natural science. And here, Lenin gives us a splendid l e s s o n for the c o r r e c t understanding of the relationship between the two s c i e n c e s - philosophy and natural science. He is not entirely s e l f - r e m o v e d f r o m an investigation of by what means thinking a r r i v e s at a knowledge of the truth in any of the sciences, because philosophy teaches this, the theory of knowledge. With the opening of these paths, dialectic m a t e r i a l i s t i c philosophy - in p a r t i c u l a r the works of Lenin - r e n d e r e d considerable a s s i s t a n c e to the physicists. In fact, when it seemed to many physicists that their science suddenly came before the "ruins of the laws," it was the voice of Lenin that sounded encouragement: a revolution is taking place in natural science; it is demolishing the antiquated r e p r e s e n t a t i o n s about nature and the paths for understanding it; this is the natural p r o c e s s of development. And, further, Lenin pointed out: this p r o c e s s is pregnant with the dangers of the departure of * However, in contradiction to what has been said, Wigner in the same paper supported one philosophy, positivistic philosophy, having e x p r e s s e d views on the concept of reality as well as on the synonym of u s e fulness of this concept in information, and on the world - as well as on the s t r u c t u r e of our sensations, perceptions and recollections.

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thinking f r o m nature, f r o m the objective world, if the dialectics a r e not known; the naturalist must study dialectic logic and the a r t of working with understanding. This is why Lenin spoke not about d e m a r c a t i o n but about the union of p h i l o s o p h e r - m a t e r i a l i s t s with the naturalists accepting m a t e r i a l i s m . 3. The history of the development of m o d e r n physics shows that the movement of thinking toward the truth is a complex p r o c e s s , requiring special investigations of the development especially of science. Even prominent foreign naturalists, whose contribution to science we value highly, do not always present this p r o c e s s clearly. At f i r s t sight, this statement appears to be paradoxical, but the next account shows that this is not so. Actually, we know in the 20th century two physical theories which a r e basic for the entire future development of physics - the theory of relativity and quantum mechanics. Both theories have changed in a radical way our Views on the s t r u c t u r e of the m a t e r i a l world, the p r o p e r t i e s of solids, space and time and the absoluteness of concepts on which c l a s s i c a l physics operated. It will be c o r r e c t to say that both t h e o r i e s have produced a radical c a t a c l y s m in the thinking of physicists. They have caused them to muse over how s i m i l a r c a t a c l y s m s a r e being effected, how a scientist who in experiments relies only on c l a s s i c a l concepts which a r e certainly inadequate in the m i c r o w o r l d , even so a r r i v e s at his knowledge by whatever means knowledge of the "new" is revealed. What a r e the a n s w e r s to these problems and where a r e they found? Let us consider the views of two eminent physicists - Einstein and Born - who have made a significant contribution to the development of these theories. Both Einstein and Born valued highly the i m p o r t a n c e of the theory of knowledge, without which science "becomes primitive and confused" (Einstein). But they both proposed that the existing philosophical s y s t e m s a r e t h e m s e l v e s c e r t a i n s c h e m e s into which the actual p r o c e s s of knowledge cannot be fitted. Such s c h e m e s , in their opinion, can be constructed only a b s t r a c t l y , but the naturalist is forced to take account also of experimental r e s u l t s which explode these schemes. T h e r e f o r e , he cannot confine himself to a single philosophical system: he c o n s t r u c t s his s y s t e m by c h o o s ing f r o m one philosophy one useful idea or method, and f r o m another philosophy another idea or method, etc.; in view of this, his opinion by necessity a p p e a r s like an eclectic mixture. Born says directly that when physicists encountered difficulties in understanding events on the atomic scale, when having exp.lained the inapplicability of the methods of c l a s s i c a l physics and the inadequacy of its ideas, not a single existing gnosiologist could help him. It was n e c e s s a r y to work out new gnosiological principles by his own efforts and these w e r e generated in the f o r m of B o r n ' s principle of additivity, H e i n s e n b e r g ' s principle of observability, and a number of others. As concerns Marxist philosophy, physicists would be unable to follow it because its foundations were laid down by Marx 100 y e a r s ago, long in advance of the point when p r o b lems appeared in physics which led to the development of the t h e o r y of r e l a t i v i t y and quantum mechanics. Heisenberg wrote: " F r o m the point of view of common sense it cannot be expected that the thinkers, having created dialectic m a t e r i a l i s m m o r e than 100 y e a r s ago, could f o r s e e the development of the quantum theory. Their r e p r e s e n t a t i o n s of m a t t e r and reality cannot be adapted to the r e s u l t s of our p r e s e n t - d a y refined experimental technology." The problem concerning by what means knowledge of the new is revealed is considered by physicists also in the logical plane. De Broglie, in the r e p o r t "Along the Path of P h y s i c s " (1955), e x p r e s s e s his views "on methods of reasoning and d i s c o v e r y in physics." He says that our understanding r e s u l t s by two different routes - d e duction and induction. Deduction gives the rules of transition f r o m p r e m i s e s to conclusions. It follows s t r i c t l y logical rules but it does not lead to knowledge of the new, as in the conclusions f r o m deduction there is nothing that should not be contained in the p r e m i s e s . According to De B r o g l i e , only the method of induction leads to the new. But how? Here, there is no logical n e c e s s i t y in the reasonings: it is guess, intuition, creativity, and fantasy (imagination) that function; and r i s k - but " r i s k is a n e c e s s a r y condition for any exploit." Thus guess, creativity, and r i s k a r e exposed to logic. Einstein repeatedly expressed himself in the s e n s e that ideas and theory a r e the e s s e n c e of the p r o d uct of the free (from logic) c r e a t i v i t y of thought and that "there is no path f r o m experiment to the construction of a theory." Even in the decline of life, in a letter to Solovin (1952) he outlined the gnosiological cycle as he understood it. Knowledge c o m m e n c e s with perceptions E ("direct sensitive experiment") and f r o m these perceptions c o n v e r s i o n to axioms A is effected; f r o m the latter conclusions S a r e logically drawn (theory, obviously, is also included here; this can be seen f r o m others of E i n s t e i n ' s papers) and the conclusions a r e compared with the perceptions E (verification of experiment). In this gnosiological

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cycle Einstein sees two logical gaps - "there is no logical path leading from E to A" he comments on his scheme; between them "there is only an intuitive (psychological) link." The other logical gap he sees in the transition from S to E. Logical gaps in a gnosiological cycle become obscure, as the conclusions obtained:may coincide with experiment. Long before the letter quoted, even in 1936 Einstein was pondering over this problem but could not find an answer; he wrote then: "The very fact that the combination of our sensitive perceptions by means of thought: (...) can be ordered, in my opinion is astonishing, but we can never have it. We can say that 'the perpetual puzzle of the world is its cognizability.' " The stated views of eminent scientists force us to consider the following questions: I) whether philosophy, whose principles were developed more than I00 years ago, can exert an infh:cnce on modern science; did it solve problems which are of considerable importance to modern science, a~; a former stage; 2) do logical gaps actually exist in the gnosiological cycle and does knowledge of the new truth proceed regardless of free invention, change, risk, and intuition; how i s Marxist philosophy the process of reflection of nature [n understanding the entire gnosiological c y c l e ? 4. One of the problems of philosophy consists in that it should r e v e a l the most c o m m o n relationships of the objective world, the logic of i n t e r r e l a t i o n s in it and it should t r a c e the " m e c h a n i s m " of their r e flection in the a w a r e n e s s of man. These c o m m o n relationships a r e revealed when investigating specific m a t e r i a l objects, so that one and the s a m e logical relation can be important for objects of a different :nature. A parallel can be drawn here which will a s s i s t in explaining the meaning of what has been said and which is s i m i l a r to physics. It is well known that the Hamilton equations were derived for investigating mechanical phenomena and that they were reduced to a high degree of generality. This was done long in advance of the a p p e a r a n c e of quantum problems, m o r e than 100 y e a r s ago. Nevertheless, in the generalized f o r m of the Hamiltonian equations g e n e r a l relations between variables were also included, which a r e also i m p o r t a n t for quantum mechanics, but the variables here a r e of another and m o r e complex nature. If this does not give r i s e to astonishment, then no astonishment should be caused by the fact that the logic of c e r tain interactions which also a r e acting in quantum topics, may also be revealed when investigating other nonquantum topics. Let us take the problem of the relation between the parts and whole of a system. Classical physics considered a s y s t e m as a m e c h a n i c a l c o n g l o m e r a t e of component parts. T h e r e f o r e , the problem of studying a s y s t e m r e d u c e s to a study of the p r o p e r t i e s of the component parts. This approach, whilst it was c h a r a c t e r i s t i c for all sciences, was a definite system of thinking. When vulgar economists (D[iring) attempted to explain the laws of capitalistic society, they reverted to an investigation of the nature of man and in it they searched for the rudiments of properties which were characteristic of a developing society. Thus, the "theory" of the "original cell of society" appeared: Robinson was the exploiter and Pyatnits exploited the fact that the working relations lie in the nature of the individual. Marx refuted this method, by showing through a specific analysis of the economic relationships of capitalism that the laws which are characteristic of it originate in the system whatever the conditions; and these specific laws which originate in the system and which characterize it cannot be reduced to laws of the component parts. Under the action of internal relations new associations originate in the system, i.e., development of the system takes place - this is the most general conclusion at which the founders of scientific materialism had already arrived in the past century and even then there was sufficient material for this conclusion. The physicist remained at the Robinson position for a further long time, and only the development of quantum mechanics persistently suggested the idea that specific laws are characteristic for a system and are not a characteristic of the component parts. The system emerges as a certain entirety in which a particle loses its lines of individuality to a known degree and which therefore must be defined by another nonclassical concept of state. In fact, new relations originate in it. The presence of system laws in quantum physics is specified by the introduction of the wave function as the new characteristic of state, by the establishment of Pauli's principle, the appearance in the system of quasiparticles, etc. It is very good that ideas concerning the specific relations in systems, even if with some delay, also finally penetrate into physics. It should not be otherwise: they dictate the dialectic nature of objective reality and demonstrate the universal nature of a series of logical relations.* * However, what has been said does not imply that the gnosiological meaning of these physical discoveries has been explained. Certain physicists think, for example, that the regularity of biological systems reduces entirely to the movement in them of elementary particles (see discussion on the report by Weisskopf, published in Ukrainsk. Fiz. Nauk, 95, No. 2, 1968) and they even assume that this reduction is a unique weapon against vitalism.

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F u r t h e r , let us take the problem concerning the nature of natural relations. Physicists, right up to the e m e r g e n c e of quantum mechanics, have assumed that in nature there exists a unique fatally developing link between one event and another ("Laplace determinism"). But although in the kinetic theory of gases, even in the 19th century, statistical methods had been developed (Clausius, Maxwell, Boltzmann, et al.) they w e r e considered only as an additional roundabout method applicable by virtue of the fact that it is in practice impossible to establish dynamic relations and the initial conditions for an enormous number of molecules; it was a s s u m e d , however, that in principle the problem can be solved by the methods of investigation of single-valued dynamic relations. Marx studied the economics of capitalistic society in which an enormous multiplicity of " e l e m e n t a r y events" was also present - exchange of commodities: he analyzed this process. Exchange is conditioned by social distribution of labor; on the a v e r a g e it is effected as exchange-equivalent, for which identical amounts of socially essential labor a r e compared to the commodities being exchanged. In events of individual exchange, there a r e always deviations f r o m equality. But so long as they a r e caused by individual r e a s o n s , such as g r e a t e r skill of the commodity m a n u f a c t u r e r or accumulation at a given m a r k e t and in a given time relative to the demand and supply, these deviations do not affect the exchange p r o c e s s as a whole - they a r e accidental for it. But deviations f r o m equivalent exchange may become (at least over a m o r e or less long time) normal, if an individual commodity m a n u f a c t u r e r reduces the production costs of his commodity in c o m p a r i s o n with the a v e r a g e needs of society, owing to the introduction of a technical i m provement. In this case, he r e a p s an additional benefit which will also stimulate further i m p r o v e m e n t in his technology. Thus, in the complete economic o r g a n i s m a definite tendency is created which illustrates the fact of a t r a n s f o r m a t i o n of fortuitousness into a definite law. Our problem is not to t r a c e other tendencies a r i s i n g in this society as a result of this (overflow of capital f r o m one branch of production into another, reduction of the profit norm, etc.); this is all substantiated in the economic world of Marx. It is important to show here that Marx revealed in the economic s y s t e m of a capitalistic society the role and i m p o r t a n c e of chance, the condition for c o n v e r s i o n to a tendency and to a law. Marxist philosophy, t h e r e f o r e , r e c o g n i z e s the objective meaning of the category of chance and r e j e c t s Laplace d e t e r m i n i s m , even in the past century long in advance of the development of quantum mechanics. The utter s a r c a s m of E n g e l s ' comments is well known in the a d d r e s s of the d e t e r m i n i s t s of Laplacian meaning, reducing d e t e r m i n i s m to fatalism. But in contrast f r o m c e r t a i n m o d e r n physicists, Marxist philosophy did not oppose the fortuitousness of a r e g u l a r relation and did not draw false conclusions about the disappearance of a causal relation in its philosophical significance only on the basis that a unique relation between c e r t a i n physical categories (impulse and coordinate) was lost, and reflected in the m a t h e m a t i c a l f o r m a l i s m of c l a s s i c a l physics. Marxist philosophy showed that the boundaries between chance and necessity a r e related and that they both a r e only m o m e n t s of an objective link in a complete process. Or, we may consider such a problem as the s u c c e s s i o n of a c c o m p l i s h m e n t s produced by different generations of people. In s u m m a r i z i n g H e g e l ' s "Science of Logic," Lenin wrote excerpts in which the idea is expressed that knowledge of mankind is developing and, beginning with simple definitions, it is becoming e v e r y w h e r e r i c h e r and m o r e specific and nothing is being lost in its dialectic forward movement; "it i m plies that everything is acquired and is enriched and consolidated within itself." Lenin thus commented on this situation: "This excerpt r a t h e r aptly sums up in its way what is dialectics."* Thus, the idea concerning a s u c c e s s i o n of a c c o m p l i s h m e n t s , their development and enrichment was formulated m o r e than 150 y e a r s ago in the philosophy of Hegel. Subsequently it penetrated also into other sciences. Later, dialectic m a t e r i a l i s m defined it in the doctrine concerning the movement of knowledge toward absolute truth through true comparatives. L a t e r still, under the p r e s s u r e of the n e c e s s i t y for finding some kind of ground for the solution of specific physical problems in the quantum field, in e s s e n c e the same gnosiological idea was formulated by Bohr in the f o r m of the physical principles of conformity. However, physicists were far f r o m understanding - and not everyone - at once the gnosiological significance of the ideal of a s u c c e s s i o n of a c c o m p l i s h m e n t s and the m o v e m e n t of knowledge to the truly absolute through the truly relative. At the time when Lenin wrote "Materialism and E m p i r i o e r i t i c i s m , " welcoming the revolution in natural science, many quite eminent physicists a s s u m e d that physics was a p proaching a c r i s i s and that before us were the "ruins of the laws," etc. Only much later did they r e a l i z e that this was not so, that with all the abruptness of transition to new ideas the s u c c e s s i o n of knowledge still existed. *V. I. Lenin, Poln. Sobr. Soch., Vol. 29, p. 212.

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In connection with the problem being discussed, one cannot but r e m e m b e r Lenin's famous statement that "the e l e c t r o n is also inexhaustible, just like the atom. "* This was said soon after the d i s c o v e r y of the electron and during the time when physicists were a s s u m i n g that they had reached (at last!) the "last b r i c k s of the u n i v e r s e , " the final p r o p e r t i e s of which can be described completely. Such an understanding was reflected also in the s o - c a l l e d " e l e m e n t a r y p a r t i c l e s . " Many have realized now how naive these concepts were. But Lenin was not a physicist and his prediction cannot be considered as physical. He himself implies the inexhaustibility of the e l e c t r o n only as an example, illustrating the infinity of knowledge of nature deep down in view of the singularity of its i n t e r r e l a t i o n s and development. Because of this Lenin r a i s e d the profound question concerning the relativity of this category as the essentialness: The " e s s e n t i a l n e s s " of an object or the "substance" likewise a r e relative; they e x p r e s s only the depth of human knowledge of the objects and if this depth did not go f u r t h e r than the atom y e s t e r d a y , f u r t h e r than the e l e c t r o n today, then dialectic m a t e r i a l i s m insists on a t e m p o r a r y , relative, approximate nature of all these boundary m a r k s of knowledge of nature p r o g r e s s i n g by the science of mankind.* Knowledge is a perpetual infinite a p p r o x i mation of thinking toward an object, in which essentialness e m e r g e s not as a metaphysical, absolute and final substance but as a boundary m a r k of knowledge of nature. "The concept of man," w r i t e s Lenin having r e t u r n e d to this problem in his "Philosophical T e t r a d s , " ~is deepened infinitely f r o m an event to an e s sentialness of the second o r d e r , etc., ad infinitum, tn the c h a r a c t e r i s t i c sense, dialectics is the study of a contradiction in the e s s e n t i a l n e s s itself of the subjects: only the events a r e transient, moving and fluctuating and they differ only in conditional limits but the essentialness of the object is the s a m e . " # The t r a n s i t i o n f r o m c l a s s i c a l physics to the physics of the atomic scale, and f r o m the latter to the physics of e l e m e n t a r y particles (of which in Lenin's time there was no inkling) is the r i c h e s t illustration of this statement of Marxist philosophy. In its entire depth, this idea even today has not reached the cons c i o u s n e s s of all scientists; this is attested by e x p r e s s i o n s concerning the fact that physics is nearing the exhaustion of its subject m a t t e r (see, for example, the r e p o r t by Weisskopf mentioned above and the discussion on it). The examples considered show that Marxist philosophy reveals the general laws of the objective world - its objective logic, hidden f r o m the nonspecialists - and the laws of r e p r e s e n t a t i o n of this world in the knowledge of man, investigating the r e s u l t s of development of individual s c i e n c e s and frequently, long before these problems a r e r a i s e d completely and indeed in obvious and pointed f o r m before the naturalists. F u r t h e r m o r e , this is achieved in the light of consideration of the whole h i s t o r y of knowledge and t h e r e f o r e with a g r e a t e r justification and competence. It is p r e c i s e l y this, that permitted Marxist philosophy to a s s e s s c o r r e c t l y the r e p l a c e m e n t of c l a s s i c a l r e p r e s e n t a t i o n s in physics on the edge of the 20th century as a revolution in natural science and not as a c r i s i s of physics, to explain the inevitability of the breakdown of ideas (this has now b e c o m e c l e a r to all), to warn physicists of the e r r o r s a s s o c i a t e d with the special features of the new stage of development of science - with the a b s t r a c t n e s s and relativity of its r e p r e s e n t a t i o n s . 5. The theory of reflection of the objective world and of nature in the consciousness of man, developed by Lenin, is of considerable i m p o r t a n c e for natural science. Lenin shows in " M a t e r i a l i s m and E m p i r i o c r i t i c i s m " that the objective nature of the elements of understanding is demonstrated by the r e s u l t s of all human activity, including the development of science and technology based on it. These elements of u n d e r standing - sensation, perception, conception, theory and science as a whole - Lenin called reflections or i m a g e s of the outside world. The concept of "image ~ is conceived in the logical sense, i.e., in the sense that the movement of an element of understanding even if it concerns sensation, follows the s a m e logic whatever the m o v e m e n t of the object being reflected, so that there is no incompatibility between them. In " M a t e r i a l i s m and E m p i r i o c r i t i c i s m , " Lenin paid the most attention to revealing the objectivity of sensations, r e p r e s e n t a t i o n s and perceptions and this is natural: even at this stage of understanding, p o s i t i v i s m was stumbling and declared again in the face of Berldey that a feeling can only be like a feeling, and not like any other thing outside the subject. On the one hand it would be n e c e s s a r y to show the unscientific c h a r a c t e r of the subjectivistic interpretation of sensations and perceptions. Such i m a g e s as conception and t h e o r y a r e discussed by Lenin in Chapter 5, which is devoted to the revolution in natural science, and in even m o r e detail in the "Philosophical T e t r a d s . " *V. I. Lenin, Poln. Sobr. Soch., Vol. 18, p. 277. J'V. I. Lenin, Poln. Sobr. Soch., Vol. 29, p. 227.

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T h e o r y is a m o r e profound image; according to Lenin's e x p r e s s i o n it reflects the ~life ~ of an object, its development f r o m origin to t r a n s f o r m a t i o n into an object of another type. The difference is at once explained in the approach to the a s s e s s m e n t of the role of theory by positivists and m a t e r i a l i s t s . P o s i tivists, who consider t h e o r y only subjectively as a s y s t e m of ordering of sensitive perceptions, a s s u m e that this ordering can be accomplished in many ways. In this spirit Mach gave his opinion, his pupil Kleinpeter and, in our time, P r o f e s s o r G. Reichenbach of the University of California, and others. But if theory is a thing of objective reality and not an a r b i t r a r y ordering of an amount of perception, then it is natural that the essentialness of a given o r d e r can reproduce only a single image. It is obvious that the image is unique in the logical sense, because the reflecting theory can be expressed in a different f o r m ; but in such a case, theories which a r e different in f o r m will be logically equivalent to one another and between them there should be unambiguous t r a n s f o r m a t i o n relations, as o c c u r s for example between the m a t r i x and wave f o r m s of quantum mechanics. Lenin concerns himself with the question of the uniqueness of the i m a g e - t h e o r y in a debate with Bogdanov, in which he advances the fact that he had overlooked the idealistic substance of Kleinpeter's conception. And in d e m o n s t r a t i o n of its ideality, Lenin cites a quotation f r o m Kleinpeter's work: 'r~Vhy is it possible to give many theories about one and the same domain of facts . . . this fact is so well known to the physicist, how incompatible with p r e m i s e is any absolute theory of knowledge. And this fact is linked with the volitional nature of our thinking; in it is also expressed the incoherence of our volition with outside c i r c u m s t a n c e s . ~* Here, for the sake of this positivistic idea about the independence of thought on the outside world, Kleinpeter turns his hand to the conception about the multiplicity of theories by means of wMch the set of data f r o m events can be nordered." It is well known that Einstein a s s u m e d that if the perceptions of man to some kind of degree a r e c o m pulsory for him, then concepts and theories should be free inventions of his thinking. T h e r e a r e also other physicists who a s s u m e that theories a r e ~children of free fantasy, n Such concepts, however, give r i s e to objections f r o m the side of the physicists t h e m s e l v e s . In 1955, the s e m i c e n t e n a r y f r o m the time of publication of the fundamental works of Einstein was observed in the Berlin Physical Society (this was during the months before his death). A close friend of Einstein, Max Born, in his a d d r e s s e x p r e s s e d d i s a g r e e m e n t with E i n s t e i n ' s opinions on theory; he said: "The value of theory is the higher and our confidence in it is the g r e a t e r , the less the f r e e d o m of choice in it and the g r e a t e r its logical compulsion." The idea of logical compulsion and uniqueness of theory coincides with the m a t e r i a l i s t i c understanding of theory as the image of objective reality. But let us r e t u r n to problem of theory, as Lenin put it. In the fifth chapter, Lenin speaks about concepts as images (again in the same logical sense). But concepts a r e m o r e mobile than theory. Lenin pointed out that in o r d e r to r e p r e s e n t objective reality, concepts should be flexible and mobile to achieve identity of contrast. This mobility, flexibility of concepts, mutual t r a n s f o r m a t i o n s of concepts one into another, in s h o r t their dialectic nature, was emphasized by Lenin with special f o r c e in the NPhilosophical T e t r a d s . " At the same time he warned that this flexibility is not a r b i t r a r y and not subjective. "Flexibility, applied subjectively = eclectic and s o p h i s t r y , " he wrote. But the question is, what is the guarantee that concepts a r e flexible just to the extent that they adequately but completely e x p r e s s the outside world in all its dialectic relations and, m o r e o v e r , that flexibility is used not subjectively but objectively? Lenin at once gives an answer to this question: "Flexibility, used objectively, i.e., reflecting the c o m p r e h e n s i v e n e s s of a m a t e r i a l p r o c e s s and its uniqueness, is dialectic and is the true reflection of the external development of the world. ~# Here, Lenin points to the condition for which flexibility of concepts p r e s e r v e s its objectivity. This condition consists in that flexible concepts must reflect ~the c o m p r e h e n siveness of a m a t e r i a l p r o c e s s and its uniqueness," i.e., concepts must be considered not in their distinctness but in their mutual relation and in their completeness. Here, Lenin does not call theory by name, but it is not difficult to see that completeness of concepts and the reflection of the c o m p r e h e n s i v e n e s s of a m a t e r i a l p r o c e s s in its uniqueness is indeed theory.

*See, V. I. Lenin, Poln. Sobr. Soch., Vol. 18, pp. 232-233. ~V. I. Lenin, Poln. Sobr. Soch., Vol. 29, p. 99.

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And, in fact, the g u a r a n t e e that concepts a r e used flexibly but not a r b i t r a r i l y , and p r e c i s e l y to the extent that they a r e not detached f r o m the objective world, is their v e r i f i c a t i o n through theory. T h e o r y in this a s p e c t plays a s p e c i a l role. It t a k e s its s t a r t i n g m a t e r i a l f r o m the objective world of events, which it r e f l e c t s in the f o r m of c e r t a i n inflexible r e l a t i o n s - postulates - and it then leads on to p r a c t i c e and to c e r t a i n new inflexible r e l a t i o n s , which a r e v e r i f i e d by c o m p a r i s o n with the r e s u l t of controlled e x p e r i ments. This capability of v e r i f i c a t i o n is the distinctive f e a t u r e of theory, which also advances it as a m e a s u r e of the adequacy of r e f l e c t i o n of the outside world. As r e g a r d s the concepts used in theory, then within the l i m i t s of t h e o r y (defined by its m a t h e m a t i c a l f o r m a l i s m ) they a r e mobile and flexible and, m o r e o v e r , their intension is d e t e r m i n e d by that function by which they p e r f o r m in theory as an entirety. Thus, union of the r e q u i r e m e n t s of dialectic logic and m a t e r i a l i s m takes place through theory as a specific i m a g e of the outside world, the adequacy of which is easily verified. But, e m e r g i n g a s an e n t i r e t y of concepts theory still p e r f o r m s one i m p o r t a n t function. It is well lmown that the c r i t i c a l m o m e n t in the development of any science is the p r o b l e m of knowledge of a new and r e l a t e d t r a n s f e r to a new s y s t e m of concepts. The difficulty of knowing the new, c o n s i s t s in that the r e s e a r c h e r has at his disposal ideas which, in the new c i r c l e of events, a r e n e c e s s a r i l y inadequate for him. Bohr, H e i n s e n b e r g , Born, and others pointed out this situation r e p e a t e d l y in the construction of quantum m e c h a n i c s , and the p h y s i c i s t will always encounter the s a m e p r o b l e m in new fields. But whence can ideas be taken, which a r e adequate in the new field of facts, if the physicist e x p e r i menting by m e a n s of c l a s s i c a l i n s t r u m e n t s has in his a r s e n a l only c l a s s i c a l concepts? And b e s i d e s , it is t h e o r y that p e r f o r m s an i m p o r t a n t function in knowledge, which c o n s i s t s in the r e g u l a t i o n of the t r a n s f e r to the new s y s t e m of concepts, which r e f l e c t adequately the new c i r c l e of objective phenomena. This function is r e v e a l e d in a n a l y s i s of the p r o c e s s of its e s t a b l i s h m e n t and of its genetic r e l a t i o n with e x p e r i m e n t s . This s i m p l e p r o b l e m , it would a p p e a r , in f a c t has not produced an unambiguous a n s w e r by the physicists. We r e m e m b e r the opinions of eminent r e p r e s e n t a t i v e s of c l a s s i c a l physics at the end of the 19th century, having studied the p r o b l e m s of e l e c t r o d y n a m i c s . It had been a s s u m e d that the e l e c t r o m a g n e t i c oscillation d i s c o v e r e d by Maxwell and H e r t z was a p r o c e s s taking place in a global h i g h l y - p e n e t r a t i n g m e d i u m - t h e ether. The technical application of e l e c t r o d y n a m i c s r e q u i r e d p h y s i c i s t s to solve the p r o b l e m of whether moving bodies e n t r a i n this medium? What kind of a n s w e r do e x p e r i m e n t s give? The phenomena of the annual a b e r r a t i o n of s t a r s can be i n t e r p r e t e d as a d e m o n s t r a t i o n of the i m m o b i l i t y of the ether. E x p e r i m e n t s to d e t e r m i n e the velocity of light in moving t r a n s p a r e n t media led to the well-known F r e s n e l f o r m u l a and gave an unexpected and even nonunderstandable answer: the ether is ~partially ent r a i n e d . " It is t r u e that L o r e n t z a t t e m p t e d to explain F r e s n e l ' s s t r a n g e f o r m u l a on the b a s i s of the e l e c t r o n t h e o r y and the c o n s e r v a t i o n of the hypothesis of s t a t i o n a r i t y of the ether. All p h y s i c i s t s w e r e hoping to find an "experimentum cruxis" - "a decisive experiment" -which would solve the problem "finally": is the ether stationary or not? Hopes were laid on Michelson's experiment, in which the property of two coherent beams was used, traversing different optical paths but meeting at the point of origin to interfere with one another. In this experiment, one of the beams travelled along the direction of motion of the earth and the other travelled across it. If the ether is stationary, the beams should return to the point of origin with a phase difference and an interference pattern should be observed. But it was not found to be so! This was inexplicable, this contradicted the phenomenon of star aberration. But here Lorentz introduced a new hypothesis: the ether is stationary but there is no phase shift and no interference is observed because all bodies in the direction of motion are contracted always in the ratio 1 :~/1 - v 2 / c 2 (independently of the nature of the body). Thus, by the introduction of the new hypothesis the previous hypothesis concerning the stationarity of the ether was conserved. In this example an attempt is cited by physicists to construct a theory by treating eaeh newly discovered phenomenon in the light of existing ideas, and if it is contradictory then a special hypothesis is formulated for the eause of the deviation of the effect from that expected. Lenin saw other ways of constructing a theory. He rapidly assessed the understanding of the relation between experiments and theory found by him in Hegel's ~Science of Logic." Hegel criticizes the method of understanding by whieh contradiction of the new experiment "disposes of the fact that he understands and instigates the experiment, not in its speeific entirety but as an example and, moreover, from the side

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f a v o r a b l e for hypotheses and theories. In this subordination of a specific e x p e r i m e n t prefaced with definitions of the b a s i s of theory, it is obscured and a p p e a r s only f r o m the side confirmed by theory. "* Consequently, Hegel c o n t r a s t e d two methods: one of these consists in the s y s t e m a t i c i n t e r p r e t a t i o n of new e x p e r i m e n t s in the light of existing hypotheses and ideas (additional hypotheses a r e r e q u i r e d to explain "anomalies") and the other c o n s i d e r s e v e r y e x p e r i m e n t in its entirety. L e n i n ' s c o m m e n t s on this s t a t e m e n t of Hegel, which he calls " c l e v e r , " a r e v e r y instructive. He w r i t e s : "It is r e m a r k a b l y a c c u r a t e and deep (relative to political e c o n o m i c a l b o u r g e o i s i e c o m p a r e d to s u b j e c t i v i s m and u n l l a t e r a l i s m . "* He not only highly r a t e s H e g e l ' s s t a t e m e n t but he also e m p h a s i z e s that it is directed against s u b j e c t i v i s m and u n i l a t e r a l i s m and s t r a i g h t away he d i r e c t s h i m s e l f toward an a t t e m p t to develop a s c i e n c e s i m i l a r to it. It is not difficult to see that political e c o n o m i c a l b o u r g e o i s i e he called an e x a m p l e of development by the f i r s t of these methods. It cannot be questioned that in Logic he should a l s o have quoted an example of the development of a theory in a c c o r d a n c e with the second method, in which s u b j e c t i v e n e s s and u n l l a t e r a l i s m w e r e f i r s t o v e r c o m e - the political e c o n o m i c s of Marx. An economical e x p e r i m e n t was investigated and i n t e r p r e t e d "in its specific e n t i r e t y , " objectively and c o m prehensively. In m a n y of his works$ Lenin r e m a r k e d that an objective study of r e a l i t y r e q u i r e s an a p p r o a c h to it p r e c i s e l y like the a p p r o a c h to entirety and only such an a p p r o a c h will r e v e a l the objective r e l a t i o n s of r e a l i t y and will eliminate any subjectivity in the i n t e r p r e t a t i o n . This e s t a b l i s h m e n t of the logical union of theory with e x p e r i m e n t and with e x p e r i e n c e is v e r y i m portant for the theory of knowledge. It shows what is the logical path f r o m e x p e r i m e n t to theory (despite what Einstein said) and it c o n s i s t s in the d i s c o v e r y and f o r m u l a t i o n of the conditions of logical compatibility of c o n t r a d i c t o r y (from the point of view of existing ideas) e x p e r i m e n t a l r e s u l t s . The factual h i s t o r y of physics c o n f i r m s exactly the effectiveness of this path. Actually, as is well known, the knot of i n c o n s i s t e n c i e s accumulated in e l e c t r o d y n a m i c s toward the beginning of the 20th century was cut by the young Einstein. He proceeded along a new path and n e v e r a t t e m p t e d to explain each of the well-known e x p e r i m e n t s by m e a n s of hypotheses concerning the m e c h a n i s m of the e l e c t r o m a g n e t i c p r o c e s s , supplemented by hypotheses explaining the c a u s e s of the "anomalous" c a s e s , nor did he look for a new e x p e r i m e n t u m cruxis. He set h i m s e l f another p r o b l e m - to explain under what conditions the equations of e l e c t r o d y n a m i c s r e m a i n c o v a r i a n t for all inertial s y s t e m s . The r e q u i r e m e n t for c o v a r i a n c y , the c o r r e c t n e s s of which was d e m o n s t r a t e d at l e a s t for quantities of the f i r s t o r d e r , was designated by Einstein the principle of r e l a t i v i t y of physical laws in inertial s y s t e m s . To this proposition he added the t h e o r y of the invariability of the velocity of light in these s a m e s y s t e m s (in e s s e n c e , the law of s u m m a t i o n of v e l o c i ties with the velocity of light). Such w e r e the s t a r t i n g postulates of Einstein. The r e s u l t of formulating the conditions for their logical compatibility was a f o r m u l a for the t r a n s f o r m a t i o n of coordinates into t i m e s . The b a s i c h i s t o r i c a l p r o b l e m standing before the physicist - to find the conditions of c o v a r i a n c y of Maxwell's equations - w a s solved by the c o m m o n t r a n s f o r m a t i o n of coordinates, t i m e s and field strengths. The s y s t e m of t r a n s f o r m a t i o n s and all the set of consequences and ideas origir~tting f r o m it, is the special theory of relativity. The t h e o r y c r e a t e d by this method brought fruitful r e s u l t s . It not only substantiated the logical set of all the e x p e r i m e n t s , which p r e v i o u s l y s e e m e d to be incompatible (phenomenon of a b e r r a t i o n , F r e s n e l ' s f o r m u l a , the negative r e s u l t s of M i c h e l s o n ' s e x p e r i m e n t , etc.), but also led to the d i s c o v e r y of p h e nomena which w e r e unknown b e f o r e this theory (for example, D o p p l e r ' s l a t e r a l effect). It r e v e a l e d a s e r i e s of new and unexpected r e l a t i o n s - for example, the proportionality of m a s s and e n e r g y of a body, the d e pendence of the linear dimensions of a body and the duration of p r o c e s s e s in t h e m on the r e l a t i v e velocity of the body. The i n t e r r e l a t i o n s established by the theory of r e l a t i v i t y lay as the b a s i s of calculations in m o d e r n nuclear physics. In the light of the new ideas, the physicist m u s t now consider all phenomena taking place at r e l a t i v i s t i c velocities which a r e c o m p a r a b l e with the velocity of light and he m u s t take t h e m into account in all physical theories. F r o m the logical a s p e c t , the m o s t i m p o r t a n t r e s u l t of the new method of constructing a theory was the c o n v e r s i o n to a new s y s t e m of concepts. In the theory of relativity, the r e l a t i v e nature of these concepts was r e v e a l e d as length, duration, m a s s , and others, the concept of unit f o u r - d i m e n s i o n a l continuum for " s p a c e - t i m e , " the idea of absolute simultaneity no longer a r o s e and the idea of the ether a s s o m e absolute m e d i u m - the c a r r i e r of e l e c t r o m a g n e t i c p r o c e s s e s - passed as u s e l e s s . To s u m up - a new s y s t e m of concepts originated. *V. I. Lenin, Poln. Sobr. Soch., Vol. 29, p. 192. -~See, for example, the P a p e r "Once again about the T r a d e Unions," V. I. Lenin, Poln. Sobr. Soch., Vol. 42.

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The new method of constructing a physical theory proved to be fruitful. Its meaning, however, was not explained by the physicists. F i r s t and f o r e m o s t , it was not explained even by Einstein. Factually, it has b e c o m e the d e c i s i v e revolution in the method of construction of a physical theory, in e s s e n c e having followed the r o a d of the s a m e d i s c u s s i o n of e x p e r i e n c e in its entirety, about which Hegel w r o t e and which Lenin also r a t e d v e r y highly. But in d i s c u s s i n g the theory of knowledge, he maintained that t h e r e is no logical path f r o m e x p e r i m e n t to t h e o r y and that in the gnosiological chain t h e r e a r e logical b r e a k s . Why did he a r r i v e at this contradiction? B e c a u s e the new stage of development of physics r e q u i r e d new methods; a new method m a t u r e d objectively but it was b u r s t open by a talented r e s e a r c h e r . But subjectively Eins t e i n had only a v e r y n a r r o w understanding of logic and he saw it only f o r m a l l y - the standard r u l e s of inf e r e n c e . This, however, was c h a r a c t e r i s t i c not only of Einstein. 6. M a r x i s t philosophy deepened the understanding of logic in a n u m b e r of a s p e c t s . F i r s t of all, M a r x in the c e l e b r a t e d nTheses of F e i r b a c h ~ included the p r a c t i c a l activity of m a n in the s y s t e m of logical c a t e g o r i e s ; this is i m p o r t a n t in principle for knowledge. In criticizing "inductivists," Engels showed that the wealth of all f o r m s of i n f e r e n c e cannot be squeezed into the f r a m e w o r k of deduction and induction and, m o r e o v e r , opposed to one another; such a t t e m p t s t r a n s f o r m these f o r m s winto the p u r e s t a b s u r d i t y . " They both understood logic not only as a s y s t e m of r u l e s of thought but also as an e x p r e s s i o n of the g e n e r a l objective laws of nature. Engels wrote: "Over all our t h e o r e t i c a l thinking, t h e r e p r e v a i l s with absolute f o r c e the fact that our subjective thinking and the objective world a r e computed by one and the s a m e laws and t h e r e f o r e they cannot contradict one another in their r e s u l t s , but they m u s t a g r e e between t h e m s e l v e s . This fact is an involuntary and unconditional p r e m i s e for our t h e o r e t i c a l thinking. "* N e v e r t h e l e s s , the objective nature of logic is e m p h a s i z e d . Both M a r x and Engels showed that an adequate nature can only be dialectic thinking. In p r e p a r i n g the data for the c r e a t i o n of Logic with a capital letter, Lenin also connected logic with the internal intension of the laws of development t h e m s e l v e s of the world and its knowledge. He wrote: "Logic is the study not of the external f o r m s of thought but of the laws of development of all m a t e r i a l , natural and s p i r i t u a l objects, i.e., of the development of the entire specific content of the world and its knowledge, i.e., the s u m total of deduction of the h i s t o r y of the w o r l d ' s knowledge. " t Such an u n d e r s t a n d ing of logic actually r e v e a l s the wealth of f o r m s of the conclusions about which Engels wrote. $ It brought Lenin to the f o r m u l a t i o n of a proposition about the unity of logic, dialectics and the theory of knowledge. In "Das Kapital," logic, d i a l e c t i c s , and the theory of knowledge [three words a r e not n e c e s s a r y : they a r e one and the same] of m a t e r i a l i s m a r e applied to one science, having taken everything valuable f r o m Hegel and moved its value f o r w a r d . * * T h e s e condensed f o r m u l a t i o n s give a deep understanding of the e s s e n c e of logic. Logic is a doctrine not only about the e x t e r n a l f o r m s of thinking but a l s o about the laws of development of the objective world; it does not e x p r e s s any n o r m a t i v e r u l e s of thought, but the v e r y laws of development of the specific intension of the world and its knowledge, i.e., included in its total is the h i s t o r y of knowledge. As this total shows that nature itself is developing in c o n t r a d i c t o r y f o r m s and that adequate knowledge of the world is not p o s s i b l e through f r o z e n f o r m s of thinking, then logic coincides with dialectics. Subjective logic e m e r g e s as the s c i e n c e of complex dialectic laws of the m o v e m e n t of thought toward the truth. The entire theory of knowledge, t r e a t e d by M a r x i s t philosophy, is a doctrine about the s o u r c e of knowledge, about the f o r m s of r e f l e c t i o n of the objective world in c o n s c i o u s n e s s (of sensation, ideas, theory, etc.), about the c r i t e r i a of knowledge (practical purposeful activity), about the p r o c e s s of deepening knowledge by c o n v e r s i o n to the e s s e n t i a l n e s s of a d e e p e r o r d e r with c o n s e r v a t i o n of the f o r m e r knowledge in a " s k i m m e d " f o r m , about the development of ideas, etc. - a l l this is the e x p r e s s i o n of complex dialectic laws of the m o v e m e n t of thinking toward the truth and, consequently, it is logic. T h e t h e o r e m about the unity of logic, d i a l e c t i c s , and the theory of knowledge is a d e e p e r f o r m u l a t i o n of the M a r x i s t theory of knowledge, and we can only r e g r e t that Lenin h i m s e l f was unable to w r i t e Logic with a capital letter and to w o r k out this p r o b l e m in detail. In the light of understanding of the unity of logic, dialectics and the theory of knowledge it is b e coming c l e a r that intelligent knowledge of the new is possible only through logic, but logic which coincides *K. M a r x and F. Engels, Sochineniya (2nd Ed.), Vol. 20, p. 581. SV. I. Lenin, Poln. Sobr. Soch., Vol. 29, p. 84. $ E n g e l ' s Manuscript, under the title "The Dialectics of Nature," f i r s t published in 1925 a f t e r the death of Lenin. **V. I. Lenin, Poln. Sobr. Soch., Vol. 29, p. 301.

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with dialectics. If, in the light of this unity, a real dialectic p r o c e s s of knowledge, a gnosiological cycle is analyzed then it can be seen that the enigmas of knowledge formulated by Einstein a r e reduced. This cycle begins with the determination of the starting elements of knowledge. Then, what Einstein calls a "set of f i r s t - h a n d data f r o m a sensitive experiment" is still v e r y indefinite. But the point is not only that information about the objective s o u r c e of the sensitive experiment is absent here. In the pure f o r m "the f i r s t - h a n d sensitive experiment in question" (even understood objectively) is encountered only with animals and with man at a lower stage of development. A thinking man is found to be at some kind of nonelementary loop of a gradual s p i r a l - s h a p e d movement of knowledge; he is concerned with p e r ceptions illuminated by the light of thought. Not only the elements of logic a r e reflected in them, which a r e a c c e s s i b l e also to an animal (identity, difference, comparison), but also a s y s t e m of ideas and practice attained at a given level as c r i t e r i a of the truth, i.e., the sum total of the f o r m e r cognitive p r o c e s s is included to some extent.* According to this, the starting elements on which the gnosiological cycle of thinking man functions, can be defined m o r e advantageously as "the initial experimentally established r e l a tions." The fact that the starting relations reflect in t h e m s e l v e s the operation of thinking, dialectically includes in itself both positive and negative moments. In fact, if the gnosiological cycle began e v e r y time with "pure" sensations, e v e r y person must have accomplished anew the entire path of accumulation of knowledge. There would be no noticeable p r o g r e s s of knowledge f r o m generation to generation. On the other hand, however, this same c i r c u m s t a n c e leads to a danger; it consists in that c o m m o n sense can be i n t r o duced into the starting relations in excess of that due to observation, and the history of physics gives many examples of this. Control of thinking is essential. Usually, a multiplicity of experimental relations is established in a new sphere of knowledge (probing experiments). F o r the further movement of knowledge it is n e c e s s a r y to make a choice of "a s y s t e m of postulates." Indeed, thought creatively chooses a s y s t e m of starting postulates, but it chooses not r e g a r d less of logic but on the basis of logic in the s a m e way as an inventor who has created a new machine uses creative fantasy, not r e g a r d l e s s of the physical laws but on the basis of them, and that is why it is hopeless to c r e a t e perpetuum mobile. When choosing a s y s t e m of postulates, thought must take into account the r e q u i r e m e n t of the dialectic theory of knowledge, i.e., logic. These r e q u i r e m e n t s a r e not a r b i t r a r y . They a r i s e f r o m the n e c e s s i t y of ensuring adequacy of the future t h e o r y - i m a g e of objective reality. Without pretending completeness here, we shall name the principal ones. The f i r s t r e q u i r e m e n t is that the postulates themselves must be adequate by nature, i.e., they must be relationships whose truth can be established experimentally at the existing level of knowledge. The second r e q u i r e m e n t is that of the logical full value of each of the postulates. It consists in that of all the adequate postulates, those which a r e able to introduce a special contribution to future theory a r e chosen (those which p o s s e s s an inherent "logical intension"). It is Clear that in a set of postulates there should be two postulates with identical logical intension. Finally, the third r e q u i r e m e n t - the choice of postulates must be complete, i.e., all (or all existing) postulates with a specific logical intension must be included in the choice. Without these r e q u i r e m e n t s on the starting postulates, t h e o r y would not accomplish its problem - t o the reflection of the e s s e n c e of new diverse events. It is clear that the choice of a s y s t e m of postulates corresponding to the r e q u i r e m e n t s of adequacy, the full value of the postulates and the completeness of their choice, is found wholly within the sphere of the theory of knowledge or of dialectic logic. For dialectic logic it is important that the c o r r e c t n e s s of the choice of postulates, as well as any component in the p r o c e s s of knowledge, is controlled by the subsequent verification of the adequacy of the theory created. This test can be made to either accept or r e j e c t the choice of postulates made, or even to c o r r e c t it in relation to any of the r e q u i r e m e n t s . Thus, in the p r o c e s s of knowledge there is a r e v e r s e r e l a t i o n which is absent in the interpretations of f o r m a l logic. This r e v e r s e relation is a f o r m of logical bond, i.e., a sphere of logic, but the logic of dialectics. It should be recalled that in dialectic * This fact is admitted in e s s e n c e also by physicists. De Broglie writes: "Data of our feelings can s e r v e for the construction of a scientific theory only when they will be interpreted in the a p p r o p r i a t e manner, and in this interpretation c e r t a i n ideas of our mind, i.e., theoretical ideas, will n e c e s s a r i l y i n t e r f e r e . " Born also expressed s i m i l a r ideas. t It is convenient to call them "probing e x p e r i m e n t s , " b e a r i n g in mind that they a r e like a probe feeling the unknown and deeper nature - i n contrast f r o m c o n t r o l l e d e x p e r i m e n t s which verify the adequacy of the theory created. 402

logic the category of practice emerging as a criterion of truth is included in the gnosiological cycle; practice is a logical category and Lenin emphasized this with great force in his theoretical works, following Marx. The source of the starting postulates is the practical activity of man and his interaction with nature; it is constantly enriched and expanded on the basis of knowledge already acquired. This constantly expanding practical activity of man is one of the sources of new knowledge, although at this stage it is not yet revealed to the end, until a new theory-image of objective reality has been created on its basis. The next stage of the process of k_nowledge is the construction of a theory on the basis of the set of postulates. Dialectic logic requires a joint consideration of the starting postulates; of two possible routes, Lenin counted this as the first and the history of the development of physics also confirmed the correctness of this route at the most critical moment, independently of whether or not the gnosiological significance of this route was achieved by the physicists. Joint consideration of the starting postulates -this is the same as we formulated in the words: the establishment of theory is a process of searching for and formulating the conditions of logical compatibility of the starting postulates (experimental relations). The process of constructing a theory from a set of postulates is not a simple deduction, in the findings of which there is nothing that was not in the premises. First of all, the theoretician is concerned here with a set of postulates and, moreover, postulates which in the light of existing theory are contradictory to one another. The problem is posed therefore, of finding and formulating the condition for their logical compatibility, i.e., formulating a new theory. Consequently, the construction of a theory is a complex logical process and dialectic by nature. Theory, in relation to postulative relations and to the concepts in which they are formulated, plays the same role as played by any complete system relative to its components. This is precisely because, from the set of postulates to the theory, a cognizable logical process is involved; theory is not an identical set of postulates. It is natural, therefore, that this logical process leads to a knowledge of the new, which is revealed in various aspects. In the first place, new interrelationships are revealed of categories which did not lie on the surface in the set of starting postulates itself (for example, the relation between mass and energy in the theory of relativity, the relation of the indeterminacy of noncommuting quantities in quantum mechanics, etc.). Secondly, the generalized meaning of the categories is revealed. The categories used in probing experiments are related of necessity to an existing system of concepts; in resultative theory they receive a new intension, or the function is changed by which they achieve complete compatibility. This change of concepts as a result of transition to a new theory is of considerable importance; it is the key to the understanding of unusual relations in a new field and with a starting point for the further development of knowledge, which will always proceed from what is already achieved to the last stage of knowledge. It is inevitable that later the problem will arise concerning substance of the various orders about which Lenin wrote.

the relation of theories reflecting the

The initial probing experiments and the postulates selected from them are formulated in the concepts of existing theory. This path is inevitable. But only by rational thinking, which "grasps the difference and inconsistence, but not transition from one to the other ~ (Lenin), this inevitability is portrayed as an obstacle to the movement of knowledge to a substance of higher order. Actually, this movement is achieved through the entire gnosiological cycle. Probing experiments considered in the light of this new substance emerge as limiting cases in which the categories - mobile, relative, transient in their contrast in the new substance - acquire a rigidly fixed precision and become accessible to measurement by classical methods. However, the substance of the higher order is associated with the former substance, not by way of individual concepts but through their dialectic unity, i.e., through theory: generalized theory with limiting values of the characteristic parameter assumes the form of the previous theory, which is a form of substance of a less high order. In physics, this connection with theory is shaped in the form of the correspondence principle. In Marxist philosophy this character of the movement of knowledge through truth which are relative to truth of the absolute, i.e., to an even more precise image of the objective world, without leading however to absolute knowledge and to cessation of its movement. Lenin wrote in his "Philosophical Tetrads~: "The coincidence of an idea with an object is a process: the idea (= man) should not represent the truth in the shape of a dead spot in the form of a simple picture (image), pale (dull), without trend, without motion, like a genius, like a number, like an abstract idea .... Knowledge is a perpetual infinite approximation of thought to an object. The reflection of nature in the thinking of man must be understood not

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as "dead," not as " a b s t r a c t , " not without m o v e m e n t , not without contrast, but in a perpetual p r o c e s s of m o v e m e n t and of the genesis of their c o n t r a s t s and r e s o l u t i o n s . " * Finally, in the t r a n s i t i o n to the image of a substance of deeper o r d e r , not just a single c o n c e p t i s changed but the entire set. Individual concepts pass away. T r a n s i t i o n to a new s y s t e m of concepts is a c complished. This m o v e m e n t of knowledge deepens the link between man and the objective world, expounds the possibility of his active influence on nature and t h e r e b y a c c e l e r a t e s f u r t h e r m o v e m e n t of knowledge which we a l s o o b s e r v e in the history of all the s c i e n c e s . The genesis of a new s y s t e m of ideas e x e r t s a r e v e r s e effect on the e n t i r e perception of man. The new generation does not begin knowledge f r o m the s a m e origin, r e p e a t i n g the f i g u r e s of logic at the s a m e qualitative level. N e v e r t h e l e s s , in r e v e a l i n g the " m e c h a n i s m " of t r a n s i t i o n to new concepts by the e x a m p l e of the genesis of m o d e r n t h e o r i e s , dialectic logic gives the key to an understanding of the development o f t h e p r o c e s s of knowledge in the past, and its t r a n s i t i o n f r o m the lowest to the highest f o r m s of thought. Again, M a r x w r o t e that the a n a t o m y of m a n is the key to the a n a t o m y of the monkey. Such is the c o m m o n complete p r o c e s s of knowledge, the gnosiological cycle, which has no logical gaps and in which e v e r y component is linked with the others by a mutual logical chain. Let us c o m p a r e two cycles. The gnosiological cycle of Einstein with its logical gaps inevitably led to a r e s u l t which he h i m s e l f acknowledged as astonishing: the conclusions of the r a n d o m l y devised theory unexpectedly can coincide with sensual p e r c e p t i o n s (with experiment). In the gnosiological cycle of M a r x i s t philosophy none of the unexpected a r i s e s ; h e r e t h e r e is a logical connection in the whole cycle, a dialectic connection which includes a l s o the r e v e r s e connection; t h e r e is no place in it for gaps or f o r i n c o m p r e h e n s i b l e unexpectedness. The fact that in e v e r y e l e m e n t of knowledge, beginning with sensation, t h e r e is an objective intension provides its i n t e g r a l v e r i f i c a t i o n in p r e cisely this gnosiological cycle: the whole s o p h i s t r y of the positivists b e c o m e s c l e a r in its light, defining r h e t o r i c a l p r o b l e m s such as: but what can a sensation r e s e m b l e if not a sensation? Or, w h e r e in a single act of perception (measurement) does the boundary lie between the subjective and the objective? In the light of this gnosiological oycle, which, a f t e r explaining the " m e c h a n i s m " of the e s t a b l i s h m e n t of theory, acquired total c o m p l e t e n e s s , all the p r o b l e m s of knowledge can and should be considered - even the s y s t e m of concepts used and the significance of objective r e a l i t y in whatever a b s t r a c t f o r m s of thinking it has been reflected, and m a n y others. All this c o n f i r m s the fact that logic (subjective), having been elevated to a higher dialectic level, e m e r g e s like a science, learning the p r o c e s s of m o v e m e n t of thought toward truth. The wealth of L e n i n ' s understanding of the p r o c e s s of knowledge is inexhaustible, e x p r e s s e d in the formula: logic, dialectics, and theory of knowledge - these a r e one and the s a m e . 7. Ways have been shown above for establishing the theory of relativity. In the h i s t o r y of the a p p e a r a n c e and in the future destiny of this theory, the r e a l i z a t i o n of the entire gnosiological cycle of M a r x i s t philosophy is traced quite c l e a r l y - probing e x p e r i m e n t s and the selection f r o m them of the s t a r t i n g postulates - f o r m u l a t i o n of the theory as a s e a r c h for the conditions of their logical compatibility - and the c r i t e r i a of p r a c t i c e , confirming the theory. And all this has led to a change of the s y s t e m of concepts, to an explanation of the i n t e r r e l a t i o n between the new and previous theories, i.e., to an explanation of the o v e r a l l p r o g r e s s i v e development of knowledge. If we analyze the p r o c e s s for establishing another fundamental theory of m o d e r n physics - quantum m e c h a n i c s - we can see that in it, a gnosiological cycle of M a r x i s t philosophy was a l s o r e a l i z e d in the final count. If otherwise, p h y s i c i s t s would not have a r r i v e d at such positive r e s u l t s . But the path to this theory was not straight: t h e r e w e r e deviations and r e g r e s s i o n s to the right path in it; there w e r e also a t t e m p t s to work to "new gnosiological p r i n c i p l e s , " although it should be r e m e m b e r e d that no new gnosiology had been created. In related, still did in o r d e r

his a t o m i c model, Bohr used quantum concepts s u c c e s s f u l l y for the s t r u c t u r e of the a t o m and he although superficially, the quantum s t a t e s of the a t o m with its d i s c r e t e s p e c t r a . However, this not provide the theory of events on the a t o m i c scale. P h y s i c i s t s knew what was e s s e n t i a l to t h e m to produce a physical theory: it was n e c e s s a r y that s t a t i o n a r y energy s t a t e s of the a t o m followed

*V. I. Lenin, Poln. Sobr. Soch., Vol. 29, pp. 176-177.

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as solutions of the general equations describing atomic phenomena, that these equations should s i m u l taneously determine also the intensity of the radiations and it was n e c e s s a r y that the theory d e s c r i b e also complex atomic s y s t e m s . However, the path for constructing this theory was not clear; an attempt was made to find the theory by means of the Bohr planetary model of the atom - it had the advantage of v i s u a l i zability. Around the nucleus a r e rotating c l a s s i c a l p a r t i c l e - e l e c t r o n s along an orbit of finite radius in a c cordance with the laws of c l a s s i c a l mechanics. Quantum conditions were introduced in the f o r m of r e q u i r e m e n t s , so that the constants of integration of this motion were nonderivative; it was attempted to identify the frequency of the quantum with the frequency of rotation of the electron along its orbit, which was found to be possible only in the limit for large quantum numbers. The latter led to the idea that in the region of l a r g e numbers, the quantum problem m e r g e d into the c l a s s i c a l problem. This bounded t r a n s i tion was formulated in view of the c o r r e s p o n d e n c e principle by means of which an attempt was made to probe the a p p r o a c h to the solution of m o r e general cases. Of course, the d i s c o v e r y of this principle was a step in the right direction but in itself it still did not give the path to a theory; on the c o n t r a r y , the whole of its deep significance was explained only after the theory was created and it became clear that it e x p r e s s e s not only coincidence of the problem in the limiting case, but f i r s t and f o r e m o s t the union of two theories which r e f l e c t the e s s e n c e of different p r o c e d u r e s . Despite partial s u c c e s s , after 10 y e a r s of searching it b e c a m e c l e a r that the " s e m i c l a s s i c a l method" does not r e v e a l the m e c h a n i s m of quantum events. The picture on the whole had not been clarified. The m e r i t of Heisenberg consists in that he renounced himself f r o m the " s e m i c l a s s i c a l method," f r o m electron orbits, and he attempted to formulate quantum conditions on the basis of the laws of c l a s sical mechanics. T h e r e w e r e no e l e c t r o n orbits and in principle they could not be observed; any attempt at observing them led to d e s t r u c t i o n of the atom. This gave Heisenberg cause to justify his new approach by the existence of a special gnesiological principle - the principle of observability. The introduction of this principle led to c o n t r o v e r s i e s of idealogical procedure. The positivists used it as the natural science "basis" of a thesis, to exist, to mean to be perceptible. Meanwhile, m a t e r i a l i s t i c philosophy considers a b s t r a c t concepts, providing they a r e inseparable elements of an adequate theory, not less but even m o r e r e a l than the c a t e g o r i e s , "directly observable." Lenin wrote: "Value is a c a t e g o r y which deprives a substance of sensitivity,* but it is m o r e real than the law of demand and supply. "# It is inadmissible to demand that if all c a t e g o r i e s p o s s e s s e d a "substance of sensitivity" they should be observable. In the m a t e r i a l i s t i c t h e o r y of knowledge there is no necessity to r e s o r t to such extravagent methods as the announcement of a new gnosiological principle. In it, each step is based logically and naturally. In fact, having posed the problem of constructing a theory for a new range of phenomena and having selected the starting set of postulates, the r e s e a r c h e r naturally should r e q u i r e that the postulates t h e m s e l v e s be adequate by nature. This is an essential but trivial requirement. It does not always coincide with the r e q u i r e m e n t for "observability": as, for example, the postulate concerning the relativity of physical phenomena in inertial s y s t e m s (in the special c a s e s of c o v a r i a n c e of Maxwell's equations) is not an identical "observability." R e p r e s e n t a t i o n s of the c l a s s i c a l t r a j e c t o r i e s of electrons in the atom, moving according to the laws of c l a s s i c a l m e c h a n i c s , should be excluded f r o m the p r e m i s e s of theory but not on account of the special principle of observability, but because there was no proof (and we know now, that this could not be) that these r e p r e s e n t a t i o n s a r e adequate by nature. The r e q u i r e m e n t for adequacy is m o r e strict. If it is not adequate by nature, then obviously it will not be observable. However, independently of the methods of demonstration, the practical steps of Heisenberg in a specific situation w e r e completely rational: they brought him naturally right to the choice of c e r t a i n s t a r t ing, experimentally justified postulates, on the basis of which it was only possible to c o n s t r u c t a new theory (jointly with Born and Jordan) by finding the conditions for their logical compatibility. The entire collection of experimentally verified facts known at that time (1925), led to the conclusion that the atom is a complex integral system. This is shown by the fact that the spectra of the atom a r e subject to a defined systematization; each s p e c t r a l s e r i e s consists of an infinite s e r i e s of s p e c t r a l lines gradually approaching and m e r g i n g at the edge of the s e r i e s . This is also indicated by the fact, established by Einstein, that although in the language of quantum r e p r e s e n t a t i o n s a single act of e m i s s i o n of a quantum r e p r e s e n t s a probable p r o c e s s in which the magnitude and direction of the individual quantum is random, * T r a n s l a t i o n f r o m German: "Entbehrt des Stoffes der Sinnlichkeit." #V. I. Lenin, Poln. Sobr. Soch., Vol. 29, p. 154.

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the entire aggregate of radiations f r o m the atom (for the equilibrium case) is subject to a definite law - P l a n c k ' s distribution of energy density throughout the spectrum. As the purely mechanical c h a r a c t e r i s t i c s (motion of the electrons along an orbit) for the atom decay, it should be n e c e s s a r y to look for some other defined state of the atom or, as Heisenberg formulated, some other kinematics. It was prompted by the fact that in o r d e r to change the atom, it is essentially a change of its energy levels, associated with the e m i s s i o n of defined frequencies. But as atoms a r e c o m plex s y s t e m s which give a stable e m i s s i o n spectrum, t h e n t h e i r kinematics naturally a r e determined not by any unique transition, but by the aggregate of all possible transitions, for which a certain "matrix ~ of transitions can be depicted with components Enm. Such m a t r i c e s should r e p r e s e n t all physical ~quantitles" - "coordinates," "momenta, ~ their derivatives and squares, "energy," which a r e encountered in Hamilton's canonical equations.* It should be n e c e s s a r y to take account of one f u r t h e r fact - t h e wave properties of atomic p r o c e s s e s . The investigations undertaken in 1921-1925 on the d i s p e r s i o n of light showed that e v e r y t r a n s i t i o n of the atom is a s s o c i a t e d with a finite oscillation amplitude. Consequently, the atom can be considered as some kind of oscillator with amplitude qnm = e2~iunmt" This determined the f o r m of the starting m a t r i x of the coordinate f r o m which it should not be difficult to convert to all other matrixes. The use of m a t r i x e s in Hamilton's equations leads immediately to an encouraging result: the energy m a t r i x (for the case of a harmonic oscillator) is found to be diagonal, but its elements a r e t i m e - i n d e pendent, i.e., the use of a m a t r i x calculation d i s c r i m i n a t e s a number of energy states of the atom which corresponds to the r e s u l t s of experiments and to B o h r ' s atomic model, and is found to coincide with the law of conservation of energy. The value itself of the energy levels is found f r o m the quantum condition, according to which the ncommutation relation" - which is c h a r a c t e r i s t i c for the m a t r i x - should be p r o portional to h, or m o r e p r e c i s e l y it is equal to h/2~i. Calculation shows that for elements of the e n e r g y matrix, a value of Wnm = En = hu(n + 1/2) is obtained, which coincides with the r e s u l t s of experiments. Of c o u r s e , the theory developed should also take account of the internal d e g r e e s of f r e e d o m of the e l e m e n t a r y particles (spin, magnetic moment) and the singularities of their bonds in complex s y s t e m s (Pauli's principle). But we a r e not writing the h i s t o r y of quantum mechanics. F o r our purposes it is i m portant to show, even if only in general form, that the s t r u c t u r e of quantum mechanics has been a c c o m plished in complete a c c o r d a n c e with the m a t e r i a l i s t i c theory of knowledge and that the theory was revealed as the formulation of the logical compatibility of a defined set of experimentally verified relations. The difficulties consisted in determining this set and in finding the conditions for their logical compatibility, and not in the absence of any new gnosiological principles. 8. The principle of c o m p l e m e n t a r i t y is frequently introduced as another and perhaps even m o r e fundamental gnosiological principle which supposedly has played a basic role in the creation of quantum mechanics. Born writes about it as ' t h e highest achievement of the p r e s e n t day f o r m of the philosophy of science." However, this principle has not played a leading role in the establishment of quantum m e c h anics. In the well-known review ~Discussions with E i n s t e i n . . . " Bohr himself tells of the r e a s o n for the appearance of the idea of c o m p l e m e n t a r i t y in the fall of 1927. At this time, the f o r m a l i s m of quantum mechanics had already been created by the efforts of Heisenberg, Born, and Jordan (matrix form), S c h r 5 dinger (wave form), and also Dirac; the theory had been found and proved. Bohr wrote: "Quantitative scope of the g r e a t empirical m a t e r i a l did not leave any large doubt in the satisfaction and usefulness of the equipment of quantum mechanics; however, the a b s t r a c t nature of this equipment created a widespread feeling of dissatisfaction." Whence, f r o m 1927 a c c o r d i n g to B o h r ' s statement, the second phase of development began with the purpose of overcoming the feeling of dissatisfaction which had a r i s e n because of the abs t r a c t n e s s of the mathematical equipment. The principle of c o m p l e m e n t a r i t y thus appeared to be the r e sult of a tendency toward visualizability and toward a clear interpretation of the already created theory. Having striven to achieve this visualizability, Bohr assigned different formulations to the idea of complementarity. One of these, the e a r l i e s t and most frequently encountered, states that in nature there exist two mutually c o m p l e m e n t a r y types of i n s t r u m e n t s ; the use of one of them for the a c c u r a t e m e a s u r e ment of a single c o r r e l a t e d (conjugate) quantity gives l e s s e r a c c u r a c y than the other. The tendency toward g r e a t visualizability led him also to another formulation in which the noncommutativity of quantum values was because in any interaction, exchange with the action can be achieved only with a whole number of * The fact of using these equations - but with m a t r i x e s in place of the usual quantities - shows the unity of c l a s s i c a l and quantum physics and at the s a m e time of their specific properties.

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quanta and t h e r e f o r e within the limits of the quantum the p r o c e s s b e c o m e s uncontrollable. This f o r m u l a tion has an agnostic tint; it was subjected to c r i t i c i s m (in p a r t i c u l a r byV. A. Fokke) and in one of the r e c e n t p a p e r s s p e c i a l l y r e p r o d u c e d in the journal "Advances in Physical S c i e n c e s , " Bohr m a k e s the r e s e r vation: " . . . we, obviously a r e concerned h e r e not with limited m e a s u r e m e n t a c c u r a c i e s but with limited applicability of s p a c e - t i m e concepts and the dynamic laws of c o n s e r v a t i o n . . . " (Uspekhi Fizicheskikh Nauk, 67, No. 1, 1959). S u p p o r t e r s , just like opponents, of the principle of c o m p l e m e n t a r i t y r e m a r k e d on the v a g u e n e s s of the f o r m u l a t i o n of this principle. Einstein r e m a r k e d that despite all his efforts, he had not succeeded in understanding the meaning of this principle. Born even a s s u m e d that the i n c o r r e c t u s e s of the concept of c o m p l e m e n t a r i t y frequently encountered in the l i t e r a t u r e to a c e r t a i n extent a r e not exactly explained by B o h r ' s p r e c i s e f o r m u l a t i o n s . It is i m p o r t a n t h e r e for us to note the following. F i r s t of all the idea of c o m p l e m e n t a r i t y a p p e a r e d , a c c o r d i n g to Bohr h i m s e l f , a f t e r quantum m e c h a n i c s was created and its adequacy proved. Secondly, its f o r m u l a t i o n was changed and refined by its author over a period of m a n y decades. Such an idea could not be a new gnosiological principle, which supposedly could be derived only by m o d e r n physics, by the c o r r e c t route in the c o u n t e r b a l a n c e of the m a t e r i a l i s t i c theory of knowledge. The rationale that is in this principle consists not in that it formulates new paths of knowledge, not in that it makes obvious the mathematical formalism of quantum mechanics, but in that Bohr in this form emerged against attempts to reduce the physical presentations either to a wave pattern or to a discrete pattern; such attempts were encountered at this time by other physicists also. It is obvious that the inadmissibility of these tests of knowledge ensues directly from the correct use of the gnosiological cycle of materialistic philosophy. The latter requires flexibility of ideas, unity of contrary definition, which are dictated by an objective nature and Lenin persistently emphasized this special characteristic of nature and knowledge of it. But the fact that this is the inevitable result of the use of a gnosiological cycle and that this is the basic argument in favor of the use of a new system of concepts, was not acknowledged either by supporters of quantum ideas or by their opponents. Therefore, the statement against reduction of objective reality to any one of the patterns had a positive meaning even if this was achieved in the form of complementarity, although it was not found to be convincing for all physicists. 9. The application of the gnosiological cycle to materialistic philosophy leads to the establishment of a new system of concepts. If the whole cycle is achieved correctly in each of its links, the new system of concepts r e f l e c t s the objective r e a l i t y and is imposed upon c o n s c i o u s n e s s with compelling f o r c e , howe v e r " s t r a n g e " (Lenin) it m a y be.

In physics, m a n y d i s c u s s i o n s have taken place which have been a s s o c i a t e d with lack of understanding of the p r o c e s s of knowledge itself (of the gnosiological cycle) and the c o m m i t m e n t s of its conclusions. Many p s e u d o p r o b l e m s a r i s e which lead to u s e l e s s debates and s o m e t i m e s to i n c o r r e c t ideological conclusions which the opponents of m a t e r i a l i s m use. Up to the p r e s e n t t i m e s , demands have i n c r e a s e d to show through what c r a c k in the lattice the e l e c t r o n p a s s e s ; a t t e m p t s have been m a d e to r e g e n e r a t e a cont r a c t i o n hypothesis (Janossy) or by m e a n s of "hidden p a r a m e t e r s ~ to get rid of the s t a t i s t i c a l r e l a t i o n s h i p s in quantum mechanics. Einstein even made repeated attempts to construct, although mentally, an experimental device by means of which it would be possible to verify the most important conclusion of quantum mechanics - the uncertainty relation. Each time, Bohr showed the fallacy of the next device and Einstein constructed yet another mental experiment, even more subtle. Over the period of many years the disputing sides failed to convince one another. Neither took account of the fundamental argument: the assumption of the feasibility of such a mental experiment, which would verify the uncertainty relation, is incompatible with many real experiments which had been reliably substantiated (including all spectral analyses, Planck's distribution, energy levels of the atom, diffraction of electrons, etc.). To the extent that the entire system of quantum mechanics is constructed correctly in relation to the gnosiological cycle (validated probing experiments - theory, as well as the formulation of conditions for their logical compatibility - controlled experiments, practice), acceptance of the uncertainty relation is inevitable. And, in fact, the correctness of the structure of quantum mechanics was not disputed by Einstein. All these and similar pseudoproblems are associated with the well-known conservation of rational thinking: a correctly used process of knowledge leads to a new system of concepts, but reason still tries to use the old categories in the new field of events, which no longer reflect the new relations.

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The p r o c e s s of development of a new s y s t e m of concepts and p r o c e d u r e s for their use, naturally is a philosophical p r o b l e m although the many d i s c u s s i o n s a r i s i n g do not a p p e a r to fall outside the scope of physics. But lack of understanding of the whole p r o c e s s of knowledge s o m e t i m e s leads also to d i r e c t philosophical conclusions. Let us cite an example. In events on the atomic scale, t h e r e has been a v e r y c l e a r dependence of the r e s u l t of o b s e r v a t i o n on the conditions of observation. This has been i n t e r p r e t e d as if a new t h e o r e m had a p p e a r e d in the a t o m i c field: it is possible, in an effect, to distinguish the boundary between that which is being o b s e r v e d and the conditions of observation; it follows f r o m this that the physicist is concerned not with objective r e a l i t y but with an effect in an i n s t r u m e n t , which a l s o is a unique "physical r e a l i t y " and about which the e x p e r i m e n t e r can talk. This ~physical r e a l i t y ~ was opposed to objective r e a l i t y ; the l a t t e r concept was c o n s i d e r e d to be obsolete and its use was considered to be a r e t u r n to c l a s s i c a l physics. Meanwhile, the f o r m u l a t i o n of this p r o b l e m is unacceptable. Of course, a unique happening is the r e s u l t of i n t e r a c t i o n of two p a r t n e r s and in the special c a s e it r e p r e s e n t s an i n s e p a r a b l e c o m p l e t e n e s s of objective and subjective m o m e n t s . But m a n a r r i v e s at the concept of an object not b e c a u s e he has s u c ceeded in drawing the boundary between the objective and the subjective in any unique events. Lenin a s s e r t e d that in our feelings t h e r e is an objective i n s e r t i o n which is not e n t i r e l y r e f e r e n c e to the p r e s e n c e of such a boundary but to the c r i t e r i o n of objectivity. Man a r r i v e s at the concept of the objective as a r e sult of achieving the e n t i r e p r o c e s s of knowledge (gnosiologieal cycle). He o b s e r v e s the r e s u l t s not of a single unique event but of a set of events; this leads him to s e a r c h for the conditions of their logical c o m patibility and he c r e a t e s a theory and then p r o v e s it in practice. If it is substantiated, it e m e r g e s as the i m a g e of an objective r e a l i t y and t h e r e is no question of the p r e s e n c e in it of any boundary in a unique event, and the conditions of i n t e r a c t i o n (observation) exist in it only in a ~stripped" f o r m , implicitly. We can see that m a t e r i a l i s t i c gnosiology is an adequate theory of knowledge of a r e a l world, applicable for knowledge of any regions of nature w h a t s o e v e r - both the m a c r o - and m i c r o w o r l d . Lenin made a significant contribution to this theory. By e m p h a s i z i n g the i m p o r t a n c e of logic f i r s t of all as an e x p r e s s i o n of the m o s t g e n e r a l laws of i n t e r r e l a t i o n s in nature, heJshowed logic subjective as a r e f l e c t i o n in the knowledge of m a n of logic objective, as a complex r e g u l a r p r o c e s s of the m o v e m e n t of thought toward the truth. This m o v e m e n t does not lead to the n o r m a t i v e r u l e s of thinking; it e n c o m p a s s e s logic, dialectics and the t h e o r y of knowledge in a single gnosiological cycle. In this cycle, each link is joined with another; in p a r t i c u l a r , t h e o r y e m e r g e s as the f o r m u l a t i o n of the conditions of the logical compatibility of e x p e r i m e n t s , and this g e n e r a l i z a t i o n of e x p e r i m e n t s i n t h e i r singularity leads to new knowledge, to a new s y s t e m of concepts and dialectics developing on the b a s i s of the previous ones. Science is moving ahead only to the extent that s c i e n t i s t s r e a l i z e finally the g e n e r a l i z e d gnosiologieal cycle of m a t e r i a l i s t i c philosophy, independently of the fact that they do or do not acknowledge this. With many, and frequently leading, s c i e n t i s t s this r e a l i z a t i o n goes by complex z i g - z a g paths, with a sequence and with a t t e m p t s to f o r m u l a t e c h a r a c t e r i s t i c gnosiological principles. Soviet s c i e n t i s t s m u s t show that science gains much f r o m the conscious application of L e n i n ' s theory of knowledge with all its r e p r e s e n tatives. Lenin attached e n o r m o u s i m p o r t a n c e to the conscious application of m a t e r i a l i s t i c gnosiology. It was p r e c i s e l y for the sake of t h e s e a i m s that he r e c o m m e n d e d the a c h i e v e m e n t of union between p h i l o s o p h e r m a t e r i a l i s t s and n a t u r a l i s t s using m a t e r i a l i s m .

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