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p The difficulties in the way of investigating the logic of the origin of logic itself are made the worse because science has no direct sources providing evidence of the first steps toward the forming of logical thought. The bits of the skeletons of primitive man. and the tools used by him, ancient cave and cliff drawings, etc., enable us to reconstruct their physical appearance, and provide information on their possible way of life, but it is difficult to form an idea of the way the first Homo sapiens thought from study of archaeological remains.

p We are therefore forced, when examining these problems, to rely on the information we can get from studying the thinking of tribes that have been backward in their development and preserved many features of the primitive, communal system.^^1^^ The myths of ancient peoples that have come down to us are of great scientific value in this respect. Although the mythological picture of the world is later historically than animativistic and animistic ideas, it arose from them, so that analysis of myths can throw light on the peculiarities of primitive thought.

p From study of these sources, investigators of the way of thinking of people living in the epoch of the primitive communal system have come to the nearly unanimous conclusion that, in spite of a number of features peculiar to any one group, they all have something in common in their mental perception of their environment and of themselves. This common element is a belief in the impersonal animate character of nature or its separate parts (animatism), arid a 138 belief in spirits presumed to control both people and natural phenomena (animism), i.e. a view of the world

p by which men, animals, plants, and objects of nature possess in addition to a sensory-perceptive side, a special, active principle, independent of their corporeal nature—a soul.^^2^^

p This circumstance is widely utilised in idealist philosophy, and in the theological tracts of ministers of religion, to substantiate man’s allegedly primordial religiosity, and unscientific statements that it is the existence of a ’ religious spirit’ that is the main, basic thing distinguishing rational men from all irrational ‘creatures’. The concept of the religious spirit, moreover, includes various components, even such essentially incompatible forms of social consciousness as religion and science.^^3^^

p Animals, unlike humans, do not, of course, have a world outlook, let alone a religious one. But it does not follow from this that the cause of the singling out of man from the animal kingdom was the rise of a religious form of reflecting reality. On the contrary, the rise and development of religious forms of consciousness were a consequence of the weak development of the productive forces and relations of production in the primitive communal system. The ’impotence of the savage in his battle with nature gives rise to belief in gods, devils, miracles, and the like.’^^4^^

p Even if we were to start from the assumption that primitive man’s childishly naive spiritualising of the objects of the environment, and at the same time of himself, had a religious character, that is not justification of a need to retain religious hangovers in people’s consciousness in the age of rapid development of the scientific and technical revolution. The fact that mankind was forced to pass through the system of slave-owning, for example, in its development, does not give grounds for demanding its retention, even though slavery still persists in certain remote corners of our planet; and it hardly enters the minds of sensible people, at the modern level of knowledge, to demand its restoration (except perhaps fascist spokesmen of imperialism striving by any means to maintain the system of exploitation of man by man surviving in our age).

p Attempts to substantiate a primaeval religiosity of man are scientifically quite groundless. With close, unbiased examination of the fact of primitive man’s original spiritualisation of objects of external nature, it inevitably 139 follows that the notions of man just emerging from the animal kingdom did not and could not have a religious character. If we try to draw a parallel between primitive thought and the later rise of religious and philosophical notions, then the initial spiritualising of objects of the environment displays a similarity not so much with religion as with hylozoism, the initial premisses of which about the universal animation of things were employed by certain spokesmen of materialism to criticise claims about the divine origin of reason.

p In spite of the fact that the spiritualising of objects of the environment contained the germ of a possibility of singling out a spiritual ‘force’ in consciousness in an independent incorporeal substratum, it took a long period of social and historical development to convert it into reality. The typical notion of religion about the dichotomy of soul and body, of spirit and matter arose much later and had its own social and epistemological roots. Primitive man’s initial, original ‘spiritualising’ of objects and forces of nature did not separate ‘spirit’ from matter. That is confirmed by the fact that a distinctly traceable idea of the inseparability of the ‘spiritual’ principle from any of its bearers can be discovered in the animatistic views of primitive tribes that have come down to us (which are undoubtedly a later product of creativity than the ‘first’ ancestors’ views).^^5^^

p There is nothing mystical in the fact that primitive man could differentiate himself from nature around him as a rational creature by ‘transferring’ his activity to a tool as ’his other’. The anthropomorphising of surrounding nature typical of primitive tribes was at the same time a process of man’s recognising himself in the ‘mirror’ of the inner patterns of action of natural forces discovered during labour activity with tools. From the height of modern knowledge one can, of course, be ironical about the fact that primitive man abstracted this ‘vision’ of himself in the childishly naive form of endowing inert objects with a soul. But for the time when man was becoming differentiated from the animal kingdom his recognition of the patterns of his own living activity in the ‘mirror’ of the activity of external natural forces was immeasurably more important than the fact that this ‘mirror’ still gave an extremely distorted image. For it was already an image inaccessible to the direct sense perception of animals.

p A ‘curtailed’, brief repetition of all stages of his path 140 of development is peculiar to man not only as regards the stages of the transformation of the biological embryo from the fertilised maternal egg cell into a human child, but also in the course of his mental development. However paradoxical it may seem to say that primitive man’s naive views were closer to materialism than contemporary religious notions, or refined idealist philosophical systems, the statement can be supported by weighty evidence.

p Surely it is worth noting that, according to the totemic notions common among primitive tribes, exogamous clans trace their pedigree from minerals, plants, birds, and other animals, though it would seem much simpler for them to take the people from whom they were actually born as their ancestors. This circumstance, however, becomes logically quite explicable when the materialist premiss is taken as the starting point, that the first act in man’s differentiation from the animal kingdom was recognition of his properties in the properties of the external world. Once we start from the supposition that primitive man initially used objects of inert nature as a mediator-implement (e.g. a stone or a stick), and only later began to pass to use of plants and animals as mediators, we can conclude that totemic pedigrees tracing origin from, say, stones are more ancient, and therefore belong to more forgotten traces of man’s establishing his ‘kinship’ than those fixed in the memory of generations linking it with plants and animals introduced later into the sphere of labour activity.^^6^^

p However that may be, savages’ naive notions of origin from stones, palms, wild beasts, etc., are closer to the truth in the final analysis than modern religious myths about man’s creation by a supreme, incorporeal divinity after its own image and likeness. Modern science is based on recognition of the origin of living organisms from inanimate nature, and of Homo sapiens from his animal ancestor, a wild anthropoid ape.

p The mechanism of the transference of man’s own activity to external mediator-objects was a necessary, but only ‘intermediate’, stage to understanding the material world as an objective reality existing outside consciousness and independent of him, which is a sine qua non of man’s existence.

p We shall pay special attention to the initial period of the forming of a rational being because, in spite of the thesis generally accepted in Marxian literature about the decisive 141 role of labour in the conversion of the ape into man, the concrete mechanism of the rise of logical thought still needs further investigation. As man’s practical and cognitive activity evolved there was an emancipating of consciousness from the clan heritage of anthropomorphism. When, for example, the capacity of a sharp weapon to pierce the body of a victim more easily than a blunt one received its explanation in a simple mathematical formula that establishes the dependence of the pressure on the force and area of thrust (the pressure is directly proportional to the force and inversely proportional to the area of thrust), there remained no place for naive anthropomorphism of a sharp object. With the discovery of exothermic oxidising reactions,which are the basis in most cases of combustion, it clearly became superfluous to resort to various unscientific concepts like phlogiston in order to explain this process, let alone to mythical notions going back deep into antiquity of a mysterious capacity of wood to generate fire. The subsequent development of knowledge in this field led to formulation of the theory of ramifying chain reactions underlying explanation of the processes of combustion (including spontaneous combustion, explosions, detonation, etc.), the creation of which is linked with the work of the Soviet Nobel prize-winner, N.N. Semyonov.

p It is hardly worth spending time on listing similar wellknown examples. It is much more interesting to turn again to consideration of primitive thought so as to disclose its logical mechanism hidden behind its external metaphorical character and still largely sensory visual form of expression. The difficulty of discovering a strictly logical structure in mythological notions is that it is complicated by mutually exclusive assumptions, dissolved, as it were, in a seemingly disordered conglomeration of events and images, in a host of unexpected turns in the lives of the heroes, and the intervention of fantastic creatures possessing supernatural powers, and so on.

p The contradictory character of mediating representations included in the structure of primitive thought as a special element put its stamp on primitive man’s way of thinking. It was manifested as a contradiction of primitive thought itself, which was a reason for the spread of views about its illogical, or prelogical nature. Such views found expression, in particular, in the work of Lucien Levy-Bruhl, who claimed that primitive thought did not always fit into the 142 framework of formal logic and its demand of consistency. The thesis of the existence of insurmountable barriers between primitive and ‘Western’ thought was eagerly seized on by racists as evidence of the mental inferiority of peoples at early stages of social development. To the credit of LevyBruhl himself (as will be seen from his posthumously published work), he was able to surmount the one-sidedness of his approach to evaluating the logicality of primitive thought, and expressed himself in favour of conceptions of the universality of the structures of thought.^^7^^ The first attempts to discover such structures in primitive thinking, and to single them out in the mythological way of thinking from the seeming chaos of metaphorical narration, were successful, in spite of the many difficulties.

p In this connection the research of the well-known French scholar Claude Levi-Strauss merits attention.^^8^^ From a structuralist analysis of the myths of various peoples, he discovered a logical orderliness in them compatible in many ways with the logic of modern times.

p The logic of mythical thought seems to us as demanding as that on which positive thought rests, and at bottom little different. ... Perhaps we shall discover one day that the same logic is at work in mythical thought and in scientific, and that man has always thought so well.^^9^^

p We would like to draw attention to this conclusion, which has a very important place in Levi-Strauss’s whole conception. The aim of a myth consists in a logical model for overcoming some contradiction. The logical instrument for uniting fundamentally opposed aspects, moreover, consists in the introduction of a mediator that also performs the role of a connector of opposites. The mediator is thus endowed with a dual character of guise, behaviour, etc., that also enables it to mediate. The myth of Oedipus, for example, according to Levi-Strauss contains a logical instrument enabling the contradictions of the initial problem to be bridged: is a man, who is one, born from one or from two? The role of the scalp in Red Indian myths consists in mediating between war and peaceful agriculture (the scalp is the ‘harvest’ gathered during war), and so on. If the contradictoriness cannot be united by the introduction of just one mediator, a whole number of other mediating images is successively introduced. In that case

p the mechanism of mediation consists in the fundamental opposition of life and death being replaced for example, by a less 143 sharp opposition of the plant and animal kingdoms, and this in turn by the narrower opposition of herbivores and carnivores. The latter opposition is removed by the introduction of a zoomorphous creature as a ’cultural hero’ that feeds on carrion (the coyote among the Zuni, the crow among the Indians of the north-west coast).^^10^^

p Levi-Strauss’s conclusions about the logic of mythical thought, one may note, have a similarity to our logical scheme ’If A, then B (through mediator M)’, following from development of reflection of the interaction S-+M-+N in the head of primitive man. But Levi-Strauss, having discovered a certain logical consistency in the structure of various mythical tales, did not attempt to disclose the real historical roots of the rise of logical thinking. Strictly speaking, it was impossible to do so without passing to a position of dialectical materialism. His attitude to dialectics can be judged from the following:

p Psychoanalysts, and certain ethnologists, would like to substitute interpretations drawn from sociology and psychology for cosmological and naturalist interpretations. But then things would become too easy. Should a mythological system give an important place to a certain person, say a malevolent grandmother, they would explain to us that in such a society the grandmothers have a hostile attitude to their grandchildren; mythology would be held to be a reflection of the social structure and of social relations. And if observation contradicts the hypothesis, they will immediately suggest that the proper object of myths is to offer a derivation to real but compressed sentiments. Whatever the real situation, a dialectic that wins at every turn will find the way to hit on the meaning.^^11^^

p Of course, Levi-Strauss was right when he objected to the reduction of each separate myth to direct reflection of the social structure and social relations. But the objection can be addressed to advocates of metaphysical materialism and not of dialectical materialism. Spokesmen of dialectical materialism in fact consider the mythological world outlook as a reflection of social existence, but not a direct, mirror reflection; rather an indirect reflection that is the result of primitive man’s transition to indirect, mediated labour. And he quite unjustifiably hints that dialectics permits any incompatible hypothesis to be arbitrarily substituted for another. Such a reproach can be directed to sophistry but not to materialist dialectics, because the basis of the latter is not a playing with words but the objective patterns of development of the material world that operate of necessity 144 irrespective of verbal exercises. Dialectical materialism is theiefore no less strict and inwardly integral a science than formal logic; on the contrary, being the most adequate reflection of the inner oppositions inherent in the material world, it underlies the rigorousness of formal logical operations in whatever field of the natural sciences they are applied.

p Neither a natural historical nor a dialectical materialist approach to logical schemes is characteristic of adherents of structuralism (one of whose founders Levi-Strauss himself was), but a striving to extrapolate linguistic models a priori onto a broad range of the most varied phenomena. As a result many structuralists arrive at idealistic statements that language and a system of communication (and not socially productive labour) underlie social structures, and that the main thing in the science of man is analysis of unconscious norms, rules, and symbolic groups.^^13^^ The source generating myths, according to Levi-Strauss, is not practical, mediated activity, but an inexplicable intellectual impulse.

p Dialectical materialists, while recognising the role of people’s active thinking, do not limit themselves to stating that. In order to bring out the mechanism of the activity of thought as a property of rational beings, it is necessary to explain the origin of the capacity for logical thought, and its structure itself, in a materialist way. This faculty arises, as we have seen, during the passage from the organism’s direct to mediated interaction with its environment. Once that capacity has arisen, however, it acquires a relative independence and cannot be reduced to a simple mirror reflection of reality, although the laws of logical thought are given by objective necessity. The logical scheme ’If A, then B (through mediator M)’ continues to operate, even when a visible mediator linking the different results of observation is not found in the external world.

p When primitive man came up against results that had vital significance for him, he mentally united them according to an already elaborated logical scheme—by means of a mediator, albeit even an imaginary one. Imagined images of mediators thus began to be substituted, as it were, for objectively existing intermediate links. Since primitive animatistic thinking had still not separated thought (‘soul’) from body, although it distinguished between them, the mental image of the mediator called for its ‘attachment’ to some external object. An at first glance paradoxical phenomenon therefore came about when the rise of a mental image 145 preceded the real object in consciousness and was subsequently identified with it.

p The link between the vitally important, but obviously different results of peaceful agricultural labour, for instance, and war against neighbouring tribes could thus be reflected in the heads of primitive Indians in accordance with the established logical scheme ’If A, then B (through mediator M)\ The whole system of primitive man’s thinking, owing its origin to constant use of actually existing mediators, called for precisely such a logical operation, even when it was not distinctly realised as such. So, for the mentally created image of the mediator to be able to fulfil the role of connecting link, it had to be endowed with certain properties perceived as common to both A and B. In that way development of the image of a scalp as ’the harvest of war’ is explicable. The savage, pointless custom of scalp-hunting thus gets a logical explanation applicable to the level of primitive primordial thought.

p We would stress once more that there was already a logical mechanism hidden behind primitive, primordial thinking, which had something within it that was common for other forms of cognitive activity, including scientific knowledge. This something in common consists in the linking of two different results brought into opposition through the action of a mediating producer according to the logical scheme ’If A, then B (through mediator M)\

p When we consider the historical process of the development of understanding in its most common form from the moment of the genesis of consciousness to our day, we can notice that it contains degrees whose sequence of rise and change is subordinated to the universal laws of materialist dialectics.

p The origin of consciousness is linked with the transition to activity with tools, i.e. with the introduction of a real, and not an imaginary, mediator between subject and object. But because the true nature of the mediator still remained unknown, it was endowed by the strength of imagination with the mysterious properties of a producer. That led to the place of real mediator in the logical mechanism being takeable (and taken) by an imaginary one. The logical scheme ’If A, then B (through mediator M)’ is thus employed to explain incomprehensible events without disrupting its integrity. But this is an illusory integrity because the mental link so established may not coincide with the objective 146 causal links. That mode of thinking is characteristic of prescientific forms of understanding (animistic, mythological, etc.).

p F.I. Georgiev writes:

p The extremely low level of development of consciousness conditioned by the primitive character of labour forced ‘instinctive’ man to substitute unsubstantiated notions not reflecting the real link between phenomena for causal analysis of them. The men’s successful hunt, for example, is held to depend on silence by the women remaining at home. This ’unconnected link’ means that the logical analysis of events was far from always adequate to what actually was.^^13^^

p During the further evolution of practical and cognitive activity there was a return to reality from the figment of the imagination but already in such a form that the objective nature of the causal links was disclosed, and it was demonstrated in practice that the actions of an objectively existing mediator, and not of a fantastic one, led to certain results without the intervention of any supernatural imaginary forces.

p As the place of imaginary mediators was taken by real ones it became clear that if there were no really existing mediator between phenomena A and B, then there was also no relationship between them (like, for example, the absence of an objective relation between a black cat and bad luck for the wayfarer whose path it crossed).^^14^^ This circumstance led to the creation of a new mediating representation that reflected the fact that two phenomena, different from the angle of their connection between themselves, could be in two opposing states: either connected or not connected. The notion of the absence of a connection became, besides, a sort of ’inside out’ mediator; the relation of unconnected phenomena began to be reflected mentally as a connection (relation) between them that consists precisely in the absence of any connection between them.

p Examination of the process of the transition from prescientific to scientific forms of understanding, as a passage from imaginary to real mediators deserves attention, in our view, and could lead to certain generalisations that are not without interest. The age-old attraction of alchemy, for example, which became particularly common in the Middle Ages, cannot be considered simply as deliberate charlatanry, though there were quite a few enterprising rogues among the alchemists. The alchemists’ attempts (often conscientious in the sense that they sincerely believed in the possibility of success) to convert iron scale into noble gold lay in 147 the common channel of the logical scheme ’If A, then B (through mediator M)’. The role of the mediator here was assigned to the ’philosopher’s stone’, sometimes called a medicament.

p Within the context of our logical scheme expressions of the type ’if a person is ill, then (through the intermediary of a drug) ho will become well’ or ’if it is iron, then (through the intermediary of the philosopher’s stone) it will become gold’ appeared quite ‘correct’. From the practical aspect, however, the alchemists’ attempts to convert iron into gold were attempts to attain a desired goal by useless means. The ’philosopher’s stone’ was only an imaginary mediator, and in that sense the alchemist mode of thought was similar to the mythical. It was no accident that the real object to which the imaginary mediating role of the ’philosopher’s stone’ was attached, was endowed with supernatural power, the procedure of ‘summoning’ it was linked with ritual, magical charms and incantations.

p That does not imply that alchemy can be completely reduced to myth. While the mythical mediator was more or less firmly pinned onto some definite imaginary image or external (or cult) object, the imaginary image of the ’ philosopher’s stone’ had rather a symbolical character that in its own way stimulated search for the ‘real’ mediator among a host of different chemical elements, objects, etc.

p Alchemist notions were closely linked with the Christian outlook prevalent in the Middle Ages, which was also permeated with fantastic notions about a mediator. The mythical image of Jesus Christ corresponded, it would seem, to the image of the ’philosopher’s stone’, the mediator, rather than to the alchemist image of gold as the ’noble and incorruptible’ metal. In any case, the image of the god-man had the duality characteristic of the mythical mediator, which enabled opposites to be united mentally, in particular the opposition between the concepts of death and immortality, human and divine nature. Attempts to explain the duality of the image of Jesus (on the one hand god, on the other man) evoked wordy discussions then among philosophers and theologians.

p In the christological disputes that developed in the fifth to seventh centuries A.D., the personality of Jesus was interpreted as embodying a ‘pure’ unity of the divine and human principles that did not, on the one hand, admit of a simple uniting of them, but on the other hand expressed 148 their fullness and indissolubility ’not through a blending of essences but through the unity of a person’. The duality of the nature of divine personages, incidentally, who had the quality of the sensuous and the supersensuous, the natural and the supernatural, is characteristic of many other religions and mythologies, and not just of Christianity. The secret of this duality and, moreover, its logical inevitability, become clear when we examine the image of Jesus (or of other similar divinities) precisely as an imaginary, mythical ‘mediator’.

p The mechanism of mentally uniting different events that are not in fact causally connected by means of an imaginary mediating producer plays its role in supporting superstition right to our own day (recall again a black cat, crossing one’s path). But the logical mechanism of the uniting of different events by means of a mental operation (hypothesis), so long as it does not embrace the fantastic but an objectively existing relation of the events, has an important place in the development of scientific knowledge. The criterion of the truth of a hypothesis, and its conversion thereby into a scientific theory, is the practical reproduction of the assumed connection between the events predicted by it, or practical confirmation of their happening. The alchemists’ surmise of the possibility of transmuting one substance into another has received scientific and practical substantiation in our time. In the USSR, for example, apparatus has been built for producing artificial diamonds from graphite, which was designed and constructed on the basis of knowledge obtained about the structure of chemical elements. It plays the role of a real mediator that makes it possible to transform soft graphite into hard diamond, i.e. the role of the ’ philosopher’s stone’ that mediaeval alchemists sought so unsuccessfully for.

p Conviction of the methodological value of mediating representations and confidence that they can reflect the objective existence of mediators which can actually connect contradictory phenomena of reality into some kind of whole are being more and more confirmed in the development of the natural sciences. According to the contemporary notions of physicists, for example, all the interactions of elementary particles are due to intermediate particles that are exchanged between the main interacting particles. These intermediate particles, transferring the interaction, are located for their whole life between the interacting objects on the way 149 from one to the other. Similar notions underlie the hypothesis of the unity of electromagnetic and weak interactions, whose experimental confirmation would be an important step toward creation of a theory of the possible single nature of all known interactions of elementary particles (strong, weak, electromagnetic, and gravitational). Direct confirmation of a single theory of electrically weak interactions would, in the view of physicists, be the discovery of what are called intermediate vectorial bosons. The fact that the notion of the existence of these hypothetical bosons is not regarded simply as a product of the imagination, to which nothing corresponds in reality, is confirmed by the projected building of huge, expensive experimental installations in which protons will collide with antiprotons of superhigh energies.^^15^^

p So the initial form of logical thought proper was thinking on the principle that ’if A, then B (through mediator MY, which underlay the rules of mental operations in primitive society. This means that logical thought has been dialectical from the start, in the sense that it established a connection between different aspects of reality, united its contradictory phenomena in a whole, and contained a unity of opposites up to and including identity.

p The inner contradictoriness characteristic of the mediating representation (that performed the role of middle link in the logical scheme) was overcome in mythologies by the creation of a mentally visualised image whose duality had a more or less visible character. The middle link emerges in the image of a two-faced Janus who simultaneously faced forward and back.

p The ancient god Janus in fact represents one of the clearest examples of the mythological mode of mentally ’ overcoming’ contradictions reflected in consciousness. His name was mentioned in its time in prayers before all other names, as the god of all beginnings, the god of the Sun who was in charge of the opening and closing of the heavy gates through which the sun came out to the earth in the daytime and went in at night. Later not only was the transition from dark to light linked with the name of Janus but also the passage from peace to war, etc. Janus gradually became the god of the entrances and exits of refuges or shelters, and his image was often placed on all doors and crossings.

p Mythology did not, and could not, disclose the true nature of objectively existing contradictions. It is nevertheless 150 obvious that these contradictions were already reflected in this primitive form of thought of the ancients, who tried to overcome them by the means available to them of mentally visualised mythological images.

p The constructions of formal logic, which are contained in undeveloped form in the scheme ’If A, then B (through mediator M)’, gradually became singled out from the graphic-metaphorical mode of primitive thought. A mediating representation, being essentially the result of all foregoing development of practice and understanding, was an inference, but it was not an inductive conclusion drawn from recurring, directly observable phenomena, although that was also a sine qua non of its formation.

p Many animals, as we have said, can also observe the heating of stones after sunrise countless times, but they are unable to form the causal judgment ’The sun heats objects it shines on’. Primitive man did not reach that judgment because it came into the head of some one of his animal ancestors, warming himself in the sun to contemplate the azure of the clear, sunny sky or the beauty of the sunrise and sunset. Savages were forced to be quite ‘practical’ by virtue of vital necessity. They could hardly be numbered among idealist dreamers. They were most likely able to turn their gaze to the celestial luminary, and ‘include’ it in the sphere of their cognitive activity, only at a comparatively late stage of their differentiation from the animal kingdom, after, in particular, they had mastered the art of maintaining and making fire.

p We can fully apply one of Lenin’s requirements of dialectical logic to primitive man’s forming of notions about the sun, namely that ’a full “definition” of an object must include the whole of human experience’.^^18^^ The judgement ’The sun heats objects it shines on’ included a mediating representation corresponding to the level of primitive practice, of the ‘vivifying’ capacity of the sun to transform darkness into light, cold into warmth, in its periodically repeated movement from sunrise to sunset.

p On the socio-historical plane, the evolution of scientific thinking signified overcoming of primitive man’s naive way of thinking which was expressed in a metaphorical, mythological form. The basis was thus laid for the hugely important work of ridding thought of mythical mediators. There opened up before scientific thought a prospect of revealing the real, and not imaginary, contradiction between motion and self- 151 motion. It is well known that the reflection of the movement of concepts in logic is attended with great difficulties, a fact remarked by the ancient Greeks; Zeno’s aporias still engage the attention of philosophers and logicians occupied with problems of the reflection of the processes of motion in consciousness.

p One can say that the overcoming of these difficulties lay along the path of developing the problems of serious dialectical logic in their connection with the problems of formal logic, while these problems can, in turn, be resolved through the broadest approach to the genesis and evolution of consciousness and knowledge as a natural process conditioned by socio-historical practice. The historically arising capacity to create mediating representations provided the possibility of mentally uniting different phenomena into an interconnected whole according to definite rules given by the initial scheme ’If A, then B (through mediator M)\ rather than arbitrarily by a subject just beginning to think. That mental operation already contained the unity and difference of the content and formal logic aspects, and provided the abstract possibility of singling out constructs of formal logic in a selfdependent field of thinking relatively independent of its content. As we showed earlier, the initial logical scheme can be transformed into the syllogism of formal logic or into the implication ’If M and A, then B’. When the mediating representation is ’taken out of brackets’, there is a transition to the implication ’If A, then B\ widely employed in modern mathematical logic. But when sight is lost thereby of the historical roots of the genesis of logical thought, it begins to appear that some inexplicable, rationally intuitive lucidity, not determined by anything, underlies formalised logic. Since it is impossible with that approach to say whether the connection of the logical symbols reflects real links and the properties of objective objects, it is at best said to be a ‘pseudo-question’ lying outside positive science.

p In actual fact the answer to the question is that mediating representations, arising historically, by linking the reflection of different phenomena in an interconnected whole according to a scheme of formal logic, gave that scheme a certain content from the outset that reflected (adequately or in distorted form) the really existing contradictoriness of the objective world. The mediating representation, having performed that role, was dissolved as it were in the content of the knowledge generated by it, and ‘disappeared’ in the 152 wholeness of the scheme of formal logic. The content aspect of knowledge could now ’be taken out of the brackets’ of formal logic, and become a field in which the rational movement of thought was developed in formal logic. That field determines the character of the way of thought at any stage of social development, and forms the starting point of contemplation of the world, and the guiding principles of interpretation of the world, the ’epistemes’ and ‘paradigms’ that distinguish one vision of the world from another.

p The guiding principles fixed in consciousness with time may become so habitual that they are simply not noticed. Consciousness is liberated from them as a matter of course and they pass into the sphere of the subconscious. Something happens similar to what can be observed in the working of a computer. From the logical aspect (but not of the technological) a necessary condition of a computer’s faultless working is the development of an algorithm from a mathematical apparatus constructed on rigorous observance of the principle of logical consistency. It may thus be quite forgotten that the machine itself will only work in that case when it is plugged into the mains with their opposite poles (‘positive’ and ‘negative’).

p To the extent that a notion uniting different phenomena within the framework of some consistent scheme of formal logic is fully incorporated into the content of thought, formal logical analysis may not, with abstraction from the content aspect of thinking, discover its presence in the logical scheme itself. So the illusion is created that an act of imagination, in particular intuitive prevision, expressed in a sudden ‘dawning’, ‘insight’, ‘guess’, has a cognitive structure extra-logical in principle.

p The solution of any of these difficult scientific problems really does happen unexpectedly sometimes, like an instantaneous dawning. From the numerous cases confirming that we would take Kekule’s discovery of the structure of the benzene ring, which is often cited to explain the ostensibly extra-logical character of scientific discoveries; in fact it proves the opposite. What did Kekule’s solution of the problem consist in? All the elements forming the benzene ring analytically revealed were already known to chemists, but they seemed a disordered multitude to the mental gaze, an odd set of elements. The ‘rules’ of the linear bond between elements then known did not work when applied to the structure of the benzene molecule. What dawned on 153 Kekule, when he was tackling the problem, was the notion of a ring, of the closed character of the bond between the elements forming the molecule. The idea of a ’benzene ring’ was the mediating link that enabled him to pass in thought from a disordered multitude of elements to an ordered one according to the logical scheme ’If A, then B (through mediater MY. Something similar can be observed in Mendeleyev’s discovery of the periodic law. The role of the mediating representation making it possible to unite chemical elements menially in a certain order was played then by the idea of atomic weight.

p Materialist dialectics sees the source of matter’s selfmotion in the unity and struggle of the opposites included in it. The relations of the categories of dialectics that reflect the unity and struggle of opposites are expounded, moreover, with observation of the rules of formal logic, in a logically consistent form, without permitting arbitrary uniting of any incompatible propositions. It is consequently a matter of seeing the hidden contradiction of the objective processes that are reflected in thought, in order to get logical consistency.

p From the dialectical, content-wise angle, formal logic’s identification of the object with itself can be thought of as a unity of the opposition of the object to itself up to and including identity which leads to splitting of its unity. The dialectical category of the self-motion of the object includes an identity of the object with itself such that the object is and is not, at one and the same time, and in one and the same relation, in one and the same state, which leads ultimately, by virtue of inner laws, to a change in its qualitative determinacy and to its transformation into another object.

p The contradictoriness of self-motion reflected in formal logic could be logically overcome, formally, by the introduction of a formal admission of the possibility of relating the self-moving object with itself as with ’its other’, which would appear quantitatively, provisionally speaking, as the identity of equal quantities, but of opposite sign.

p At the dawn of human society the development of labour activity with tools had already led to mental differentiation of the various properties and attributes of objects brought out in practice. In particular a possibility developed of identifying and differentiating external objects by their form (e.g. by their sharpness) in relative independence of their material substratum, and of comparing them 154 quantitatively by their shape. The prospect was thus presented of abstract operation with formal quantities that seemed quite independent of the relation of the form and content of the really existing objects.

p The creation of a mathematical apparatus gave a powerful instrument for human reason’s penetration of the mysteries of nature. But with the development of mathematics a gnosiological version began to be spread that the concept of a material world could be replaced by mathematical symbols. The sharp criticism that Lenin made of these views, revived by ’physical idealists’ at the turn to this century, is well known; these views again made topical the Kantian idea of the inaccessibility of the material world, which was always doomed to remain ’a thing-in-itself, to knowledge, in particular to mathematical knowledge.

p The thesis of the a priori character of the foundations of mathematics was expressed quite clearly in Kant’s philosophical system. When characterising the concept of a triangle as one of the figures underlying geometrical constructs, he wrote:

p No image could ever be adequate to our conception of a triangle in general. For the generalness of the conception it never could attain to, as this includes under itself all triangles, whether right-angled, acute-angled, etc., whilst the image would always be limited to a single part of this sphere. The schema of the triangle can exist nowhere else than in thought, and it indicates a rule of the synthesis of the imagination in regard to pure figures in space.^^17^^

p One can agree with him that the images of all possible triangles really cannot be fitted into a general concept of a triangle. It is also true that it would have been impossible to create a general concept of a triangle without involvement of the subjective faculty of forming mediating representations, i.e. a capacity for productive imagination. But one cannot agree that a mediating representation is a product of the mind that is not linked in any way with an image of external objects, and that the faculty of creating such notions is an a priori one of the subject, appearing from somewhere unknown. (We have shown earlier that the mediating representation has its material determinant, viz., the tool as an objectively existing, and not imaginary mediator between subject and object).

p Another of Kant’s errors follows from that. While correctly noting that attempts to deduce general concepts 155 about an object by adding all its possible images together were logically unsound, he drew the mistaken conclusion at the same time that the source of the formation of general concepts lay hidden in a faculty of imagination that had no rationally explicable starting points, and could be only taken as an eternally given faculty of the human spirit inaccessible to understanding.

p As a theorist of the natural sciences who generalised the factual data obtained by experimenters, Kant was closer to the truth than Kant, the philosopher, in spite of all the depth and refinement of his philosophical system. His hypothesis of the formation of the solar system through the spontaneous evolution of matter was a great advance toward smashing old ideas about the creation of the world by a supernatural being, or about the immutability of a once and for all established order of observed phenomena. In the field of epistemology, however, Kant not only refused to recognise the existence of the material world’s capacity of immanent self-development, but came to a conclusion bordering on solipsism, that order and regularity are introduced into nature by the human mind. The error could have been eliminated through discovery of the natural historical sources of the formation of that very faculty of productive imagination that was later the direct source of the formation of general concepts, i.e. through discovery of objectively determined causal connections leading to the transition from direct sense reflection of reality to its rational reflection.

p The credit for discovering that belongs to the creators of Marxian materialist dialectics, who demonstrated that the reason for man’s differentiation from the animal kingdom, and his transformation into a rational being, was labour, sensory material activity to transform the natural environment by means of tools. It is in labour that we must seek the cause of the historical evolution of rational thought that led, in its development, to the formation of concepts, judgments, and inferences. The source of the connection between the concept of the object of knowledge and the manifold of its mentally visualised images arose at the time of the genesis of logical thought. That is why attempts to discover these sources in the complex, growing structure of the knowledge attained at a certain level of development of society have proved hopeless, i.e. attempts to regard this structure of knowledge as a ‘posited’ one. In order to 156 establish the link of any concept with mentally visualised images, each of which is only a limited representation of the denotation of the concept, it is necessary to start from the features of the formation and development of rational reflection of reality. Such an approach enables us to regard the relation between the concept of an object and the mentally visualised images of it as an interconnected formation.

p We have already said that direct sense images become mentally visualised ones to the extent that an idea is already concealed in each sense image, and an idea is seen in a mentally visualised image only insofar as it is a mediating representation whose objective determinant on the plane of the genesis of consciousness was man’s ancestors’ transition to the use of tools.

p That thesis can be extended, in particular, to solution of the problem posed by Kant about the relation of the generalness of the concept of a triangle with the visual images of separate triangles included in it, and to the attempts associated with that problem to substantiate the principles of geometry, since the concept of a triangle has been recognised from the time of Plato as one of the basic geometrical concepts.

p There are no doubts about the existence of initial mathematical axioms undemonstrable in the deductive construction of a theory by the means of that theory. As for man’s capacity to construct theories deductively, we have already remarked that the creation of new universals, new hypotheses and theoretical conceptions, etc., requires the involvement of a creative imagination which ‘grasps’, through the creation of new mediating representations, such links between phenomena which are inaccessible to rational thought. The thesis of the a priori character of axioms, outside experience, reveals its one-sidedness when we regard it broadly, on the plane of the natural, historical sources of the origin of knowledge in general, and of mathematical knowledge in particular, sources that stem in the last analysis from the formation and development of man’s labour and practical activity.

p Lenin, when criticising Hegel’s views about the figures of Aristotelian syllogisms, wrote:

man’s practice, repeating itself a thousand million times, becomes consolidated in man’s consciousness by figures of logic. Precisely (and only) on account of this thousand-million-fold repetition, these figures have the stability of a prejudice, an axiomatic character.^^18^^

157 It follows from that profoundly deep remark of Lenin’s that the figures of logic owe their origin to human practice; by practice, in Marxist-Leninist theory, is understood primarily labour, i.e. mediated activity with tools, and not the organism’s direct relation with the environment. Limitation of the concept of man’s practical activity to his direct inleraction with the world around him would lead to a subjectivist interpretation of practice as a criterion of truth that itself creates the whole objective world rather than of truth comprehended by man in the process of transforming reality. With that interpretation of practice the figures of logic would be reduced to an expression of the structure of practice itself, rather than to a reflection of the laws and patterns of the external world.

p In that connection we must turn once again to the very important point that underlying man’s practical interaction with the natural environment there is the mediated, indirect interaction ’subject—subjectivised object—object’. It was the passage to that interaction that put operation of external nature’s objective laws at the subject’s service and so led to the genesis of logical thinking. The figures of logic, by their very origin, therefore reflect the patterns of the objective world (in one approximation or another to the truth), and not just the structure of man’s subjective activity. The structure of practice, moreover, can only be properly understood as the structure of material activity based on man’s use of objective laws existing independently of consciousness.

p Furthermore, according to Lenin, billion-times repeated practice leads to consolidation of the figures of logic in consciousness; and it is because of that billion-times repetition, and only because of it, that the figures of logic have the stability of a prejudice and an axiomatic character. From that we can conclude that the thesis about the a priori character of axioms, outside experience, was a prejudice with the force of habit (according to Lenin) because of an uncritical interpretation of recurrence of the results of practice.

p In fact we are already convinced that the formation of concepts of the identity and difference of objects by their shape, for example, in relative independence of their material substratum, had its source in the labour activity of still primitive people. Initially the concept of form, in particular of the pointedness of a tool, could only be of a 158 very general character; a sharp implement was mentally distinguished from a blunt one. The question of what angle a tool should be pointed by (a more or a less acute one) was posed and decided later in the course of practical use of various tools and implements in accordance with the more or less successful results of their use to achieve definite aims.

p We shall not try here to establish the direct genetic kinship of a triangle with the pointedness of a stone tool (though one cannot rule such a kinship out completely). But there is no doubt that before the concept of a triangle arose as a geometrical figure, human society had passed through the stone age. From that time people must have been learning (once more on the basis of practice) to transfer visualised images of spatially three-dimensional objects mentally onto a two-dimensional plane, and to trace out on a plane the more or less straight or bent lines of the contours of the external objects involved in the sphere of their activity (in cave drawings, and so on), finally reaching such a degree of development that the marking out of worked patches of land became an objective, socio-historical fact that required the drawing of boundary lines designating the ownership of sections by one person or another. But, for all that, it is logical to assume that the concept of a triangle as part of a plane bounded by three straight lines was initially only a very general one, inseparable from its mentally visualised image.

p One may note, moreover, that the mental drawing of a triangle lies in the general bed of mental operations according to the scheme ’If A, then B (through mediator M)\ In fact, if we consider the operation of tracing two more or less straight lines (and only two) on a plane, how can they be ‘joined’ to make any whole figure? Such an operation could only be perf ormedby means of a mediator whose representation permeated all primitive thought. The real (and not imaginary) mediator (real in the sense that the operation of finding it could be performed by man’s actions in tracing lines on a plane, expressible in mentally visualised images) could have only been the point of intersection of the two lines. So, like the supposed mediator, this point had a ‘two-faced’, contradictory character; it was at once a point in one line and in the other since the two lines were different. As a result, the geometrical concept of an angle was gradually formed. The formation of the concept of a segment of a line, incidentally, also obeyed this rule. Given two different points in spaac, 159 they could be united by the menial movement of one of them along a path leading to coincidence with the other, while remembering the original position of the moving point, which in practice signified the joining of two points on a plane by the tracing of a line. The shortest path in that would have been a straight line. The line also plays the role of mediator here, uniting the given points. It is not difficult to conclude that the formation of the concept of a triangle obeyed the patterns of the same logical scheme, assuming a more broken-down form without loss of the scheme’s original wholeness. Given the mentally visualised image of an angle as two different segments of lines with a common point of intersection, and two different points at opposite ends of these two lines, then these last points could also be united by tracing mediator-line. Such a construction of a triangle would initially have had a very general character, independent of what concrete triangle (right-angled, acute, etc.) was so constructed.

p Following that road, a mentally visualised image of a geometrical figure can be created, mediated by itself. For that it is necessary to represent a segment of a line limited by points A and B which bends in a circle to full coincidence of the points. In other words, it was necessary to continue tracing the line mentally until it intersected itself at some point; from that one could even attempt to construct a nonEuclidean geometry one of whose axioms would be the postulate that it was impossible to draw through a point on a plane a line continuing in one direction that would not intersect itself. The notion of the point of self-intersecting of a line is already both mediating and contradictory because the beginning and the end of the drawing of the line coincide at it.

p To conclude this chapter we must touch on the fact that a theory, constantly coming up against objectively existing contradictions, quite naturally tries to overcome them not in any way it can, not by introducing mythological mediatorimages (although attempts may also be made to mythologise phenomena even in our day), but by creating uncontradictory, consistent, formal logical constructs. The contradictions discovered in a theory are removed by creating another of a higher degree of abstraction, one that plays the role of a more fundamental theory in relation to the first. The immense fruitfulness of creating that kind of theory is demonstrated by the whole practical development of human 160 cognitive activity. One can say that the creation of each more fundamental theory in a branch of scientific knowledge raises the latter to a new level of its progressive development. But from the epistemological angle there is a danger here that may pass unnoticed, especially when the creation of ever newer general theories becomes ‘fashionable’ in science.

p Attempts to create a successive series of theories of a higher and higher order (‘super-theories’ of sorts, each succeeding the other, that would lead to theoretical generalisation of all theories) are dictated by noble intentions to build a system of logically impeccable theories that would give grounds for saying that a branch of science rested on a foundation of some sort of unique consistent theory. That way, it may escape attention that the elimination of the difficulties in a previous theory (achieved by creating a new one, that alters the content of the old one) leads to the discovery of new difficulties. From the standpoint of dialectical materialism it is quite clear that the sole criterion of the truth of each new theory is ultimately practice, in spite of the certain relativity of this criterion noted by Lenin. The epistemological requirement of caution in evaluating theories is also linked with the fact that the conceptions of defenders of the creation of ever newer ‘super-theories’ in a branch of science may lead opponents of a priori origin of its fundamental concepts to a position of associationism (as a kind of subjective idealist view leading to one-sided, sensationalist, agnostic conclusions on the plane of ‘bad’ infinity) or the opponents of a priorism may find themselves siding, without noticing it, with the defenders of ’super a priorism’, or Bergsonian or Nietzschean intuitionism (which, as we have seen, has happened more than once in the history of philosophy to the orthodox of a thesis of direct perception of truth ’through the eyes of reason’, put forward by rationalists against sensationalists).

p The true value of fundamental theory in any branch of science is revealed, in particular, in the fact that, in eliminating the exposed difficulties of the old theory, it produces new ones in the new content of knowledge; the higher the approximation of the new theories to ’the theory of all theories’, the internal contradiction of the material world latent behind the outward appearance of things will be reproduced in an ever more ‘naked’form. Consistent supporters of dialectical materialism can only welcome this trend, because it 161 signifies nothing else than a natural historical process of the transition of natural scientists to the only true philosophical positions of dialectical materialism. Marxist-Leninist philosophy, which quite justifiably rejects the title of the science of science, long ago laid bare the objective essence of the process of the reflection of this world by human reason.

p Notes to Chapter 6

p  ^^1^^ There is interesting information on this in, for example, Wilbur S. Chaseling’s book about Australian aborigines, among whom he lived for many years. See W.S. Chaseling. Yulengor: Nomads of Arnhem Land (Epworth Press, London, 1957).

p  ^^2^^ Filosofskaya entsiklopediya, Vol. 1 (Moscow, 1960), p. 67.

p  ^^3^^ In his philosophical novel Les animaux denatures ( Editions Albin Michel, Paris, 1952) Vercors faced a parliament with the need to give a precise definition of man, which in the end was given juridical form in the following statute (p. 296):

p ’Art. I—Man is distinguished from the animal by his religious spirit.

p ’Art. II—The principal signs of the religious spirit are, in diminishing order: belief in God, Science, Art, and all their manifestations; fetishism, totems, and taboos, magic sorcery, and all their manifestations; ritual cannibalism and its manifestations.

p ’Art. Ill—Every animate being that displays any one of the signs mentioned in Article II is admitted to the human community and his person is guaranteed throughout the territory of the Commonwealth by the various stipulations made in the last Declaration of the Rights of Man’.

p  ^^4^^ V.I. Lenin. Socialism and Religion. Collected Works, Vol. 10 (Progress Publishers, Moscow, 1978), p. 83.

p  ^^6^^ In his book Volkerpsychologie. Eine Untersuchung der Entwicklungsgesetze von Sprache, Mythus und Sitte, Vol. 2. Mythus und Religion, Part I (Engelmann, Leipzig, 1900- 1909), Wilhelm Wundt, for example, came to the conviction that initially there was a belief in a corporeal spirit inseparable from the body (and not simply in a spirit ‘free’ of the body). Considering that the concepts of animatism and animism traditionally employed in science to characterise the later views of primitive tribes, when 162 the initial notions of Itie inseparability of the ‘spiritual’ element from the material body had already begun to be lost, he suggested that the term ‘archaeoanimatism’ be used to designate these initial notions in contrast to the later ones.

p  ^^6^^ From this interpretation of the origin of primitive notions of totems it is obviously impossible to conclude that there is a direct link between the tolemic name that an exogamous clan bears, and the inclusion of the corresponding plant or animal in its ‘economy’ (e.g. palrns, sharks, eagles, etc.). But once we recognise the normalcy of the origin of totems as a reflection of the objective process of mastering external mediators in primitive man’s consciousness then the later appropriation of a concrete totemic name by a tribe or clan no longer presents difficulty. For since notions of a totem-progenitor were affirmed in primitive consciousness as generally recognised, any primitive community of men becoming isolated in the course of the differentiation of growing society must have appropriated its own totemic name in order to assert its relative independence.

p  ^^7^^ See Michael Cole and Sylvia Scribner. Culture and Thought (a Psychological Introduction), (John Wiley & Sons, New York, 1974), p. 29.

p  ^^8^^ ’As Vico put it, myths were the first edition of "humanity’s mental dictionary" and that reading will last a long time, if not forever. Among the various sophisms of our day, interpreting this gratifying theme in all ways we often have to deal with empty phrases about the inaccessibility of myths, as a special form of consciousness, to logical analysis. From that point of view we can congratulate modern science; after almost a century of sneers about the “savage-philosopher”, Levi-Strauss demonstrated the capacity of savages (les sauvages) for abstract thought’ (M. Lifschitz. Critical Notes on the Modern Theory of Myths. Voprosy filosofii, 1973, 8: 143).

p  ^^9^^ Claude Levi-Strauss. Anthropologie structurale ( Librairie Plon, Paris, 1958), pp. 254-255.

p  ^^10^^ E. M. Meletinsky. Claude Levi-Strauss and the Structural Typology of Myths. Voprosy filosofii, 1970, 7: 170.

p  ^^11^^ Claude Levi-Strauss. Op. cit., p. 229.

p  ^^12^^ See M. Nikolova. The Structuralist Interpretation of Man and His Place in Society. Filosofskie nauki, 1974, 2.

p  ^^13^^ F. I. Georgiev. Soznaniye, ego proiskhozhdenie i sushchnost 163 (Consciousness, its Origin and Essence), Vysshaya shkbla, Moscow, 1967, p. 53.

p The reasons for the wide spread of numerous taboos among primitive tribes on committing certain actions in certain conditions are still a matter of learned discussion. The question should, in our view, be examined as well through the prism of the features of the system of mythological thought. As a matter of fact, at the stage of development of society when the place of the real mediator between the results of at least two events A and B was still taken by an imaginary one, and the notion of the impossibility of a link between A and B in the absence of a mediator M had already taken shape, it could have been concluded that refraining from actions that were ostensibly linked with the appearance of the imaginary mediator M would also make it impossible for event B to happen, the result of which would have been undesirable in certain respects for the members of the primitive community.

p  ^^14^^ We have in mind the absence precisely of an objective connection, because, from the subjective aspect, a superstitious person may, on encountering a ’bad omen’, surfer a reverse in a contemplated affair because of his own psychic state caused by the omen, i.e. his lack of confidence in the success of the matter.

p  ^^15^^ See: Will Intermediate Bosons be Discovered? Review of reports in the Scientific American in Nauka i Zhizn, 1982, 10: 81-85.

p  ^^18^^ V. I. Lenin. Once Again on the Trade Unions, the Current Situation, and the Mistakes of Trotsky and Bukharin. Collected Works, Vol. 32 (Progress Publishers, Moscow, 1973), p. 94.

p  ^^17^^ Immanuel Kant. Critique of Pure Reason. Translated by J.M.D. Meiklejohn (J.M. Dent & Sons, London, 1934), p.119.

p  ^^18^^ V. I. Lenin’s conspectus of Hegel’s The Science of Logic in his Philosophical Notebooks (Collected Works, Vol. 38),

Progress Publishers, Moscow, 1976, p. 216.