p The atomistics of Leucippus and Democritus was applied and developed in classical physics and chemistry. Not only was the basic idea of invariable fundamental particles of matter moving in empty space taken into the arsenal of natural science in the seventeenth to nineteenth centuries but concepts of the atomistics of antiquity are also met in the theories of classical science that appear naive even from the standpoint of those theories (let alone of modern science). Democritus’ atoms, for instance, were furnished with hooks so as to combine by means of them into sensibly perceptible bodies; the same idea in rather modified form was held by Boltzmann, although Lomonosov had already criticised the theories of his day for their ’wedges, needles, hooks, rings, bubbles, and numerous other figures of particles created in the head with no foundation of any kind’.^^10^^ According to Boltzmann an atom resembled a sphere with a sensitive process (each atom having a definite number of processes); atoms were repelled when they collided with one another, except when the processes overlapped; then a molecule was formed.^^11^^ We shall consider Boltzmann’s atom again below; the ideas of classical chemistry on the eve of its transformation into modern chemistry found visual expression in it.

p In classical science, which (as we know) began the systematic scientific study of nature, the idea of atomism had already been expressed quite fully and with the greatest clarity by Newton. Although the author of the Philosophiae Naturalis Principia Mathematica held strictly to his dictum hypotheses non fingo, he created remarkable hypotheses when the tasks of investigations required it. His idea of atomism, which he set out in detail in his Optica and related works, and also in his short memoir De Natura Acidormu (1692), was just such a hypothesis.^^12^^

p Although Newton’s Principia did not explicitly contain the concept of the atom, it is impossible without it to comprehend correctly the definition of the ’quantity of matter’, which (according to Newton) was measured by its density 205 and volume conjunctly.  [205•*  One can get an idea of Newton’s atomism from the following extract from his famous ’31st optical problem’, which is often cited: ’God in the beginning formed matter in solid, massy, hard, impenetrable, movable particles, of such sizes and figures, and with such other properties, and in such proportions to space, as most conduced to the end for which he formed them; and ... these primitive particles being solids, are incomparably harder than any porous bodies compounded of them; even so very hard as never to wear or break in pieces.’^^13^^

p For Newton, as for the atomists of antiquity, matter was discrete, but unlike them he put forward a conception of a hierarchy of systems of successively diminishing solidity containing indestructible, absolutely hard particles only at the deepest level. In place of the kinetic conceptions of the ancient atomists about direct collisions as the sole cause of a change of atoms’ state of motion (in the new philosophy these notions were shared by Descartes), Newton employed a dynamic scheme: particles moving in a vacuum became a sort of focus of forces acting at a distance.

p Newton thus arrived at a hierarchic scheme of the structure of matter. The foundation of the hierarchy consisted of absolutely hard, invariant particles. Being connected with one another by great forces they formed systems of great strength and very small dimensions. These systems, being linked by interactions of less force, formed new (more complex), less strong systems of larger size, and so on, up to the bodies observed in everyday life, which could be broken up relatively easily.

p As Vavilov convincingly demonstrated, one can say with great certainty that the founder of classical science arrived at an atomic conception that retained its significance fully for the whole period of classical physics.^^14^^ The development of physics after him, down to the twentieth century, added nothing essential to this conception. It has also passed, in a transformed version, and on a new basis, into modern physics. Let us consider the atomic conception of classical physics in greater detail.

p The atomism of classical science rests on Newton’s scheme 206 of space, time, and moving matter. According to him space and time have no internal connection either with each other or with the matter moving in them; the motion of matter itself is understood as the displacement of particles, which is changed by the effect of forces acting between particles and dependent solely on distance. Newton’s theory of matter was the pinnacle of the view on matter developed in classical science. It explained a certain circle of thermal phenomena in accordance with experience and provided a consistently mechanical picture of the structure of matter.

p A kinetic conception developed alongside Newton’s dynamic scheme in classical physics, and in struggle with it, a conception based on Descartes’ ideas of natural philosophy and Huyghens’ related physical ideas (the ether as a continuous medium; the wave theory of light). The contradictions between these two conceptions, which led through their development to the Faraday-Maxwell theory of an electromagnetic field, were resolved by Einstein’s theory of relativity, which arose from the problem of field and was the last theory of classical physics and at the same time the first theory of non-classical physics. It created a new physical doctrine about space, time, and moving matter in which these concepts lost their ‘classical’ isolation.

p Within classical physics itself there were the premises for its transition into deeper, non-classical theories. The idea of forces acting at a distance in empty space thus potentially included the concept of field (in Newton, though, in the form of a mathematical presage). From the point of view of mechanism, indeed, action at a distance without the mediation of a substance filling space is meaningless. The idea of mutual contact between particles, however, preferred by the kinetic conception, did not differ essentially from the idea of action at a distance. There can be no absolute contact between particles; otherwise they would merge together and matter would not be discrete. It was left to assume that particles had forces that did not allow them to merge with one another. Contradictions of this kind were resolved with the development of field theory in physics.

p Although the idea of a hierarchy of structural levels of matter was first legitimated in classical science, the principle of development that goes with such a scheme and 207 cannot be separated from it did not receive consistent application. From the standpoint of classical science the same mechanical laws operated, in the final analysis, at all rungs of the hierarchic ladder, and the job was to explain all non-mechanical phenomena and regularities exactly, or to subordinate them to the laws of mechanics (as fundamental laws). Mendeleev, for example, had no doubt that chemical processes would be explained in terms of Newton’s mechanical laws.^^15^^ Boltzmann and Gibbs explained the need to introduce statistical concepts into physics by the circumstance that the mechanical properties of a complex system consisting of an enormous number of particles were inaccessible to cognition because of the crudity of the human sense organs, measuring instruments, etc. Maxwell’s electromagnetic theory was long misunderstood by physicists because it could not be reduced to mechanics (such reduction had to be abandoned in physics, of course).

p Classical atomistics is thus inseparable from the mechanistic rejection of qualitative transitions in the development of matter. This development is interpreted, in the last analysis, simply as quantitative growth, and the complex as the augmented simple. From this position matter is governed everywhere and always, at all levels, by the same laws of mechanics.

p The natural form of determinism for classical science and its theory about the structure of matter, and the only one, was mechanical determinism (most clearly represented by Laplacian determinism in classical mechanics). Much has been written in Marxist philosophical and physical literature about its being impossible to reduce determinism, i.e. the theory of the objectively real, universal connection, to mechanical determinism, about causality (as conventionally understood) being only a small part of the universal connection, and about statistical and dynamic laws being of equal value in the pattern of nature.^^18^^

p According to classical mechanics, a material object is a dynamic system governed by the laws of mechanics, i.e. a determined system in the sense of Laplacian determinism. The theory of relativity left the foundations of mechanistic determinism undisturbed, but quantum mechanics demonstrated its inconsistency and connected dynamic and statistical laws into a single whole, which made it possible to get a deeper understanding of determined systems. 208 Quanturn physics brought complex objects (especially those of great complexity), before which, as a matter of fact, classical theories had come to a halt, into the sphere of deterministic analysis.

p Classical science, in explaining the development of nature, ultimately stressed constancy in transformations, repetition in natural processes, and renewal of one and the same forms in the phenomena of nature. The facts of the relativity of such constancy and repetition, and the need to explain this relativity, were ignored. Accordingly the idea that universal change was based on constant, eternal primary particles incapable of transformations and moving by one and the same laws, appeared absolutely correct. The indestructibility and constancy of the moving primary particles should, from the standpoint of classical scientific conceptions, determine the constancy of everything happening in nature and the repetition and recurrence of its phenomena.

p Another characteristic idea of classical notions about matter was that of the separation between matter, on the one hand, and motion, space, and time, on the other. Matter was discrete particles whose combination into systems of various complexity, and the dissociation of the latter into their components, determined the diversity in nature. Motion, space, and time, however, are represented in classical science as continuous entities. With this is associated the fact that various absolutes are often encountered in classical physics, e.g. mechanical ether, absolute motion, absolute time, etc.

Finally there is a typical tendency in classical science (expressed in its notions about the structure of matter) to consider that it is possible in principle to calculate and cognise the parameters of material systems of any degree of complexity, i.e. of any material objects, from the properties of primary particles. This classical tendency also operates to some extent in modern physics, when the idea is expressed that it is possible to explain the properties (and behaviour) of any material system in the universe in terms of elementary particles and the laws of their behaviour. The development of the theory of relativity and of quantum field theory, however, has advanced an opposite tendency, namely to explain the properties of particles by those of the systems formed by them. We shall consider the problems that arise in analysis of these tendencies later.