p The concepts of the simple and the complex or compound are usually associated with that of development. In Marxist philosophical literature one finds definitions of development as a transition from the lower to the higher, from the simple to the complex.^^1^^

p Such statements, it seems to us, do not so much define development as express one of its many aspects; development itself still has to be defined. Indeed, if the complex is the developed simple—and the concept of the ‘complex’ should not, it seems, be defined except through ’ development’—then the content of this concept is elucidated through understanding of development as such. Let us assume that development is understood as diminution and increase, as repetition (the metaphysical conception of development); then the complex is just the ’augmented simple’; now let us suppose that development is understood as a unity of opposites (the dialectical concept of development); then the complex differs qualitatively from the_simple and at the same time repeats the simple in some way. All this follows from Lenin’s analysis of the concept of development in his famous fragment On the Question of Dialectics*

p In the history of philosophy the problem of the simple and complex in application to the Universe appears as the problem of the substance of the world from which the concrete diversity of things is formed. Two main tendencies are 198 to be observed in study of this problem in the history of materialism and of science. The first (which in essence presupposes a dialectical understanding of development) regards the world as regularly developing matter that is one in its diversity. The second (in its complete form it is the trend of mechanical materialism) recognises only external combination and dissociation of the constant elements underlying the Universe.

p Before the rise of Marxism the mechanistic conception seemed to be the fuller, and related to the concrete tasks of science. The atomistics of Leucippus and Democritus, Descartes’ physics in the new philosophy, Newton’s Principia, the philosophical theories of the eighteenth century French materialists, Lomonosov’s scientific work and his ’corpuscular philosophy’, the notions about matter and its structure of the coryphaei of classical physics—such are the landmarks in the history of the mechanistic doctrine. At the same time we must not forget that the work of these thinkers devoted to the ’structure of the Universe’ or ’the world order’ contains many elements of dialectics: suffice it to recall Descartes’ cosmological theory, the ideas of an internal connection between matter and motion of the atomists of antiquity and of the French materialists, and Lomonosov’s thesis of the conservation of matter and motion— although it is impossible to separate their philosophical views from their metaphysical understanding of nature as something basically constant and invariable.

p In the history of philosophy the dialectical conception as applied to problems of the Universe is represented by the teaching of Heraclitus, the atomistic ideas of Epicurus and Lucretius, the natural philosophy of Giordano Bruno, and the philosophical views of Alexander Herzen, as regards the materialist trend. The dialectical conception developed spontaneously in natural science, and in the classical period (the seventeenth to nineteenth centuries) it was not fully expressed: the law of action and counteraction in Newton’s mechanics, the differential and integral calculuses devised by Newton and Leibniz, which made it possible to depict the processes of nature mathematically, Kant’s and Laplace’s cosmogonic hypothesis, the law of the conservation and transformation of energy, and classical electromagnetic theory did not shake classical physics’ scheme of spacetiine-matter.

p The theories of idealist philosophers contain many dialectical constructs relating to the philosophy of nature. They often brilliantly guessed the dialectics of modern science. In this connection Aristotle’s analysis of the relationship of matter and form as that of possibility and actuality, or, say, Leibniz’s theory of monads, which considered individual monads as closed yet at the same time connected with the whole world, are of considerable importance for the modern theory of elementary particles. The idealists’ natural- philosophical, dialectical constructs, however, did not directly yield science any new scientific results; having grown out of‘pure’ thought they, like all idealist philosophy in general, were isolated from the concrete concerns of science, and the atomistic ideas of Democritus-Newton-Dalton dominated classical science.

p These ideas and classical physics’ scheme of space- timematter were struck a crucial blow from the positions of science itself by relativistic and quantum physics, which made a further advance in the cognition of nature. The deep transformations and progress of modern science are integrally linked with dialectical materialism, as Lenin had already demonstrated at the time when the new physics was being created, and as has been confirmed by its subsequent development.

p What are the simple and the complex as applied to matter?

p The simple (we do not distinguish it from ‘elementary’) and the complex (or compound) cannot be defined by the difference between genus and species. They are defined, like other opposite philosophical categories, by analysing their reciprocal connection. In one way or another the simple and the complex resemble the individual and the general, the discontinuous and the continuous, the chance and the necessary, the possible and the actual. Lenin’s ideas about the individual and the general or universal are of the greatest importance for the theme of this section. Let us recall them here: ’the individual exists only in the connection that leads to the universal. The universal exists only in the individual and through the individual. Every individual is (in one way or another) a universal. Every universal is (a fragment, or an aspect, or the essence of) an individual. Every universal only approximately embraces all he individual objects. Every individual enters incompletely into the universal, etc., etc.’^^3^^ ’Every individual is 200 Emacs-File-stamp: "/home/ysverdlov/leninist.biz/en/1979/DMP383/20090805/299.tx" connected by thousands of transitions with other kinds of individuals.’^^4^^

p It follows from this statement of Lenin’s, in particular, that knowledge of the laws of nature enables us to discover new phenomena, i.e. the laws make it possible to identify the reciprocal connection between many phenomena; every law is narrow, incomplete, approximate^^8^^; the laws of nature are reciprocally connected. This same statement of Lenin’s leads one to the idea that objects united in a certain whole (and appearing as elements of a system) exist as elements only within the connection that makes them a whole, and the system exists only through its elements. In abstraction, however, the system and the element are separated and opposed to each other.

p We have come close to a definition of the elementary (simple) and the complex (compound), but to make the last step we must define such concepts as a thing or object (which are treated here as equivalent), property, and relation.

p We shall omit the appropriate argumentation and give the following definition: a thing is an aggregate of properties.^^8^^ The essential element of this definition of a thing through its opposite is that a thing is interpreted as constant and invariant with respect to the variation of properties, since one property differs from another. Our definition corresponds approximately to Ashby’s interpretation of a system as ’a list of variables’.^^7^^

p A thing’s diverse relations to other things reveal its properties, i.e. they are relative, although the metaphysical mind frequently ascribes the same absolute meaning to a property as it does to a thing. Discovery of the relativity of one property or another of an object in physics more than once constituted an epoch in its development (the relativity of mechanical motion in classical mechanics; the relativity of the extension and duration of events in the special theory of relativity; the relativity of the particle and wave properties of micro-objects in quantum mechanics). Things themselves are dialectically contradictory; each thing is connected with every other thing, each property passes into every other property; the development of a thing is an endless process of discovering new properties, relations, etc., etc.^^8^^ We shall not go into details here of the dialectics of things properties, and relations.

p Now let us consider the definition of a system and of structure. If objects are linked through relations with one another into a single whole, these objects become the elements of a system that possesses structure. The following examples are well known: atoms can form a molecule, an atomic nucleus and electrons an atom, neutrons and protons an atomic nucleus. In this case the atoms, the atomic nucleus and the electrons, the neutrons and protons, which are connected by certain interactions, are elements of corresponding systems—the molecule, atom, and atomic nucleus, which have a structure. Every system has a structure, which remains unchanged in certain transformations of this system; from that angle structure is an invariant of a system.

p This definition of system and structure accords with the view of these concepts that has become established in the contemporary mathematical literature. ’To define a structure,’ we read in Bourbaki, ’one takes as given one or several relations into which these elements [of a set—M.O.  [201•* ] enter ... then one postulates that the given relation, or relations, satisfy certain conditions (which are explicitly stated and which are the axioms of the structure under consideration)’^^9^^ (my italics—M.O.).

p A system of objects, which has structure, is something complex in relation to the objects that are its elements. Systems of objects, or complex objects, in turn, may be elements of a system of a higher level with respect to the initial systems. The elements of a system, on the other hand, may be objects that have been formed from objects of a deeper level. A hierarchy of various levels of systems or structures thus emerges. In the next sections we shall consider the relations between the levels of structures and whether there is a finite or an infinite number of such levels. As modern science has demonstrated, the world is a hierarchy of material structures.

p In the same way that a thing’s properties are revealed in its relations with other things, so the elements (and their relations) of a system of a certain level are revealed in its relations with systems of other levels. In that sense a 202 material system’s structure is something relative. Here are a few comments on this relativity.

p First of all, there are systems of varying degrees of complexity in nature, in addition to simple ones. The great complexity of these systems depends (1) on their embodying some part of the hierarchy of material systems (a macroscopic body, for example, consists of crystals, which consist of molecules, which consist of atoms, and so on); (2) on the fact that the number of a system’s elements may be very great, and so may be their connections. Macroscopic bodies, for example, with typical dimensions of the order of 10* to 10 ^^2^^ centimetres include molecules and atoms with typical dimensions of the order of 10 ^^8^^ centimetre; the atom includes the atomic nucleus with typical dimensions of 10 ^^12^^ centimetre, while atomic nuclei are formed of protons and neutrons, which are elementary particles with even smaller typical dimensions. One has to remember here that the elements of a system and their various combinations regarded as systems of the same level as the initial one (e.g. at molecular level there are mono-atomic molecules) represent the parts, while the initial system represents the whole. Parts are independent in relation to each other to the extent that they constitute a whole (which is opposed to the parts). This dialectic of the whole and its parts also finds application in study of the problem of the structure of matter.

p When very complex systems are cognised, the principle known as the law of the transition of quantity into quality (and vice versa) operates. As the system becomes more complex, i.e. as the number of elements and the connectedness of the system increase, the properties of the whole differ qualitatively from those of its parts. Generally speaking, an object as a system is exactly a connected unity and not an agglomerate, and this unity is a new quality formed as a result of the combining of a large number of the system’s various interconnected elements. From this angle there is no need, for instance, to employ the laws of atomic physics when designing a locomotive; for that purpose the laws of classical physics dealing with macroscopic phenomena are quite adequate.

p Knowledge of the properties and behaviour of structures of a deeper level provides the key to explain phenomena and laws that belong to a higher level, but not at all in the 203 sense that the laws of chemistry, for example, can be reduced to the laws of quantum mechanics and the Pauli principle. The laws of structures of various levels differ qualitatively from each other; and at the same time they are related through transitions (quantum mechanics, for instance, is related to classical mechanics through the correspondence principle).

p A decisive methodological role is played in analysis of the problem of the simple and the complex in relation to matter by the idea of the infinite diversity of nature, the inexhaustibility of matter in any of its parts, the infinity of matter in depth and breadth. This infinity is composed of many finite objects of various levels of a single matter, and the transitions from one level to another represent transitions of quantity into quality and vice versa. Definition of a system consists in essence (1) in separating the part from the whole, and (2) in unifying the parts into a whole.

p From this position one can say that knowledge of an object is knowledge of it as an element in a certain system and at the same time knowledge of it as a certain system. The first aspect was predominantly developed in classical physics, which led to a tendency to explain the phenomena of nature in terms of elementary phenomena. The second aspect is typical of relativistic theory in which a tendency to explain elementary phenomena from the standpoint of knowledge of the whole finds a certain expression. Quantum physics unites both aspects, and this connection is getting closer and closer as quantum theory develops. When an object representing a very complex system is cognised and the mental transition is made from the elements to the system and from the system to the elements, a need arises to employ statistics and the theory of probability. That is how matters stand in the transition from macroscopic phenomena to molecular and atomic ones, and in the reverse transition from elementary phenomena to macroscopic ones.

The question of the system and structure of matter thus cannot be separated from the philosophical problems of regularity, necessity and chance, possibility and actuality. We shall discuss this more concretely in the sections that follow.