p Statistical conceptions are inseparable from the atomistic picture of the world. The development of atomistic views of matter involved and more and more brought out the idea of statistical laws.

p Even the atomists of antiquity held concepts in embryo which, in developed form, contributed to the notion of statistical law in classical physics. Democritus made external necessity the most important principle of atomism; the atoms, which moved initially in all directions, collided with each other forming vortexes that generated countless worlds in the infinite void. The chaotic motion of atoms in all directions,’according to him, was the basis of everything that happened in the great world, whose phenomena did not resemble the motion of atoms in the void.

p Epicurus modified Democritus’ atomistic teaching substantially. The famous declinatio atomorum a via recta (’ declination of atoms from the straight line’) introduced by him represents an inner necessity inherent in atoms. As Lucretius correctly said, it violated the ’laws of fate’, Democritus’ fatal necessity. Whereas the ’vortex of atoms’ (or the ’motion of repulsion’) in Democritus’ theory was an act of external, ‘blind’ necessity, Epicurus saw in the ’motion of repulsion’ a synthesis of inner and external necessity, external motion and the motion inherent in the atom.^^29^^ As we shall see later, the question of the synthesis of external and inner necessity is decisive for a correct solution of the relation between dynamic and statistical necessity.

p The idea of random motion of infinitely small particles underlies classical physics’ explanation of phenomena in the macroworld. It comes out in Democritus’ well-known dictum: ’cold exists only according to opinion, heat exists only according to opinion, but in reality there are only atoms and the void’.^^30^^

p Democritus’ necessity is essentially the same, abstract, simple necessity as that with which Laplace’s superintellect deals, or rather, it represents the hypostasis of the latter. L t us consider what that means.

p It is usually said that statistical laws are laws of mass random phenomena. This statement opposes statistical 158 laws to dynamic ones and at the same time, in fact, records that the random is necessary, since regularity does not exist without necessity. When, however, statistical laws are studied, various points of view on chance arise.

p (1) It can be assumed (as mentioned above) that elementary processes are indeterminate (nature decides with respect to elementary phenomena). The determinacy of phenomena that exists in the macroscopic world can be explained, on this assumption, by the law of large numbers. But the law of large numbers itself applies to mass random phenomena and therefore does not explain the determinacy of macroscopic phenomena but only their statistical characteristic. The law of large numbers, which means that in certain conditions the sum total of the effect of a huge number of random factors yields a result that is nearly independent of chance, in fact expresses the organic link between chance and necessity that we shall discuss later in more detail. Moreover, the justification of statistical regularity by the law of large numbers disagrees with the history of its origin. Thus, in Democritus, the originator in natural philosophy of the concept of statistical regularity, atomic collisions were inevitable because atoms could not independently change the very different directions of their motion. Moving atoms would thus collide with the same necessity as that of the intersection of an infinite number of straight lines with different directions in space. In other words, every event in the life of an atom and therefore of everything in the world without exception was predetermined for eternity: ’ everything (occurs) because of necessity’ (Democritus).

p (2) It can be assumed that the elementary phenomenon is determined but, for some reason or other, the factors determining it remain unknown (e. g. the observer does not know whether a molecule is moving a bit to the right or to the left before colliding with another molecule, which would strongly affect the result of collision); on this assumption, such incomplete knowledge also leads to statistical conclusions.

p Mechanical materialism (as mentioned above in another connection) takes this assumption to be true. Representatives of ‘physical’ idealism, who have taken on the job of disproving determinism, also accept it in their own way. The standpoint of mechanical materialism on statistical laws, which means in principle acceptance on the whole of 159 necessity in nature, in practice rejects necessity for each individual phenomenon and leaves it at the mercy of pure chance. That the situation is just so is confirmed specifically by Max Bern’s views on law in physics. Pleading that determinism allegedly implies the existence of an initial state with absolute accuracy, Born rejects it in physics in general, and in classical mechanics in particular.^^31^^ We shall consider his views on this point below.

p (3) It can be assumed that each elementary phenomenon occurs independently of every other one while, at the same time, in_their aggregate they determine macroscopic phenomena. It is this aggregate of elementary phenomena that is the substance of statistical regularity. Natural philosophy’s surmise about this, as we mentioned above, was expressed by Democritus; the assumption found adequate form in the hypothesis of the total randomness of statistical physics according to which the individual elements with which statistics operates are completely independent of each other. This understanding of statistical regularity links the chaotic motion of primary particles with necessity in nature, but what had been a conjecture in Democritus gradually received systematic development on the basis of the data of natural science in the work of Robert Boyle, M. V. Lomonosov, Leon Boltzmann, and Josiah Willard Gibbs.

p Thus, necessity, according to Democritus, existed in nature only in the form of external, abstract necessity: in his view, randomly moving atoms could not spontaneously change their motion, and from that aspect the Democritean chaotic motion of atoms was the expression of external necessity.

p At the same time, in antique philosophy, as noted above, Epicurus expressed in his ’declination of atoms from the straight line’ a conjecture about the inner necessity inherent in atoms; he also synthesised, in his ’motion of repulsion’, the external and inner necessity, the forced motion and the motion inherent in the atom. This feature of his atomistics, which remained beyond the understanding of all nonMarxiani philosophers, was first brought out by the young Marx in his doctoral thesis. Marx then, on the whole, of course, held an idealist point of view and accordingly criticised the atomistics of Democritus; he was deeply interested, however, in a dialectic understanding of motion, and 160 this approach enabled him to determine the difference between the atomic theory of Democritus and that of Epicurus.

p As we see it, the difference established by Marx is very important for elucidating the philosophical sources of modern scientific atomism—a question that has engaged the attention of many researchers. Heisenberg, for example, when considering the philosophical problems of atomic theory in connection with quantum physics, and rejecting invariable atoms, stated in particular that ’the development of recent years . . . has very clearly been—if we draw a general comparison with ancient philosophy—the turn from Democritus to Plato’.^^32^^ In reality, as we have shown here, if a comparison is to₍be made at all with ancient philosophy, the development of quantum physics has made a step forward from the materialist Democritus to the materialist Epicurus. This also finds expression in the problem of statistical regularity.

p Scientific conceptions of statistical regularity, in contrast to the natural-philosophical conjectures of the Greek atomists, have developed since systematic study of nature began, when quantitative methods of understanding matter evolved, and physics (above all mechanics) reached preliminary^completion. If Newton, whose atomistic views played an important role in his theory of matter, had not yet arrived at statistical ideas, his older contemporary Boyle who, as Engels put it, made chemistry a science, explained the properties of matter by the statistical behaviour of atoms; he demonstrated that the relation between the pressure and volume of a gas in a vessel could be understood if one assumed gas pressure to be the result of vast number of atomic collisions with the vessel’s wall. The ideas of the great Russian scientist M. V. Lomonosov are particularly remarkable in this connection. Drawing on ’corpuscular philosophy’j hej gave a first sketch of a physical explanation of thermal phenomena, and built a molecular-kinetic theory. When it is said, for instance, that the concepts ‘temperature’, ‘pressure’, and the ’amount of heat’ are inapplicable to individual atoms or molecules, the origin of this statement can be traced to Lomonosov, according to whom ’the property of elasticity [as regards gas—M. 0.] is not manifested by individual particles devoid of any physical complexity and organised structure but is produced by their aggregate’.^^33^^

p From the time of Maxwell, who introduced probability conceptions into the kinetic theory of gases, and especially of Boltzmann and Gibbs who created statistical mechanics, statistical concepts began to be employed systematically in problems of the structure and properties of matter. In statistical mechanics the motion of individual particles is regarded as subject to the laws of classical mechanics with the addition at the same time of statistical postulates to the latter’s propositions.

p According to Boltzmann and Gibbs, the need to introduce statistical probability concepts into physics could be explained as follows: the mechanical properties of a complex system consisting of a vast number of particles are not fully known because of the crudity of the human sense organs and measuring instruments employed. From this point of view, the concept of gas temperature would not be needed if, for instance, the positions and velocities of gas molecules were known. Boltzmann and Gibbs thus interpreted statistical laws as a result of our ignorance of fully determined but seemingly chaotic, extremely complex motions of a vast number of particles forming a system (whole). In reality, to come back to the example of temperature, the behaviour of a gas cannot be reduced to the cumulative behaviour of the individual molecules composing it; the gas and its behaviour are a new quality, and this fact is reflected in thermodynamic concepts and laws. The dialectical thought that the concepts that apply to an element of a set (whole) are by no means applicable to the set (whole), and vice versa (an idea shared by Lomonosov, as we have seen), has become widely accepted today, and many authors who are subjectively remote from dialectical materialism hold it.

p We must now define several of the concepts discussed above, and make the appropriate generalisations.

p The necessary is that which in given conditions can be and cannot fail to be, which can be only such-and-such and not something else, whose being or a kind of being has its basis in itself.

p The random or accidental (chance), on the contrary, is that which in given conditions may or may not be, which may be such-and-such or something else, whose being or non-being, or being of one kind or another has its basis not in itself but in something else.

p in accordance with these definitions every something, representing a certain whole and at the same time regarded as an element of a certain other whole, has its basis in itself and at the same time in another, i. e. something is neither necessary nor random, but both random and necessary at the same time. An inner necessity thus appears on the scene that is not opposed to chance as something external (the latter being inherent in abstract necessity) but considers it an element of itself.

p From the point of view of everything said above about the necessity and chance, dynamic and statistical laws are internally connected with each other, and represent a single pattern of nature in which neither the dynamic nor the statistical aspect can be reduced to the other. Dynamic and statistical laws—forms of a necessary, regular, causal connection between phenomena of nature—are not only linked by transitions from one to the other but are united in their opposition. A dynamic law expresses a change in time of the state of a material system considered in certain conditions in isolation from other systems; it is realised as a direct necessity. A statistical law applies to a set or aggregate of material systems taken in certain conditions as independent of each other. A statistical law is realised as an internal tendency making its way through a mass of random events and manifesting itself in them as an average of numerous random deviations. When the number of systems constituting a set (statistical ensemble) is sufficiently large the generic properties inherent in all the systems, i. e. the properties essential for a given set (which are expressed by statistical averages, their study leading to statistical laws).come to the fore. When, on the contrary, the number of systems forming the set is smaller, the generic properties appear less definitely and properties typical of the individual systems, i. e. the inessential, random properties of the given set, are revealed more definitely.

The concept of statistical law thus actually has nothing to do with the incompleteness or insufficiency of knowledge when very complex systems are studied or with the assumption of the ’lack of cause’ (pure chance) of elementary phenomena. A statistical law exists in objective reality just like a dynamic law, and it is neither ‘worse’ nor ’ better’ than the latter in terms of its truth, definiteness ( 163 accuracy) and validity. The concepts of statistical and dynamic regularity taken by themselves always simplify the objectively real connection between phenomena; in certain circumstances of research, however, each of them corresponds to the real situation.