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Philosophical Thought
Reference:

The Problem of the Universal in Epistemology

Morkina Yuliya Sergeevna

ORCID: 0000-0001-9520-154X

PhD in Philosophy

Senior Research Fellow, Institute of Philosophy of the Russian Academy of Sciences

109240, Russia, g. Moscow, ul. Goncharnaya, d. 12, str. 1., kab. 420

morkina21@mail.ru
Other publications by this author
 

 

DOI:

10.25136/2409-8728.2024.5.70092

EDN:

DINAXQ

Received:

10-03-2024


Published:

02-06-2024


Abstract: The subject of the study is the concept of the universal in the epistemological aspect. It is shown that any knowledge is based on an absolute background – "implicit ignorance" – defined as an a priori form of cognition common to all people of all cultures and peoples. By virtue of its generality for all people in all situations the absolute background is undetectable and untransferable into explicit knowledge. At the same time the background knowledge of a particular culture with the historical change of cultures begins to be reflected transferred into explicit knowledge including philosophical. Both individual human beings and entire cultures have implicit (tacit) knowledge. Implicit (tacit) knowledge is part of the structure of everyday life, the life world. However along with implicit knowledge there is also a cognitive background in the structure of everyday life – something that is so close and familiar that it is not apparent. The cognitive background cannot be called knowledge due to its fundamental non-reflexivity and taken-for-granted nature. At different times the cognitive background varies for different cultures. The article suggests that there is also an "absolute background" – something that is so common to all people of all cultures and all peoples that it is not possible to identify, problematize, compare with a different state of affairs. The concepts of everyday life, the life world (E. Husserl), the mesocosmos (G. Vollmer) are considered. The importance of the linguistic turn in philosophy for the awareness of philosophical problems related to everyday life and background knowledge of cultures is emphasized. The concept of "absolute background" has methodological significance for epistemology. It is shown how this concept allows answering questions about whether something is universal.


Keywords:

universal, background knowledge, implicit (tacit) knowledge, everyday life, life world, mesocosmos, culture, anthropic principle, human dimension, a priori forms of cognition

This article is automatically translated. You can find original text of the article here.

The considerations expressed here in connection with the concepts of everyday life, the life world, the mesocosm and the concept of an absolute background derived from these concepts may be relevant for modern epistemology. The logic of the mutual transitions of explicit and implicit knowledge takes place in modern culture, in which constantly developing scientific knowledge plays a huge role, subject to complex dialectical development processes. Everyday knowledge and common sense also have complex dialectics. The exchange of meanings between scientific and everyday knowledge never stops. The article suggests that the universal, which, in spite of everything, remains constant for all cultures and epochs in their transformations of cultural universals, is not transformed due to its unreflectability and for this reason remains fundamentally undetectable.

Researchers are asking the question: does the universal exist? So, are the universals of culture universal? Or certain deep structures of the language. Here we are trying to give a new approach to questions about the universal.

 

1. Implicit knowledge

In this work, the question of implicit knowledge (the concept of M. Polani) is considered, as well as the concept of "implicit ignorance" derived from the concept of "implicit knowledge", to which I assign the name of absolute background here. In order to clarify this concept and demonstrate its importance for epistemology, it is necessary to understand what constitutes knowledge and what is ignorance. In accordance with M. Polani's concept, knowledge can be explicit – such knowledge is always articulated or, at least, articulate – fundamentally expressible in words. Explicit knowledge always lends itself to verbal formulation, therefore it is intersubjective. Implicit knowledge is not articulate in all cases, it can be vague, poorly grasped, and therefore not expressible. Bringing it to a verbal formulation involves identifying and translating it into the category of explicit knowledge.

S.A. Filipenok deals in detail with the issue of implicit knowledge. She writes: "The unique structure of consciousness and the inexhaustible personal experience of a person are not fully expressible and inaccessible to the consciousness not only of others, but even of the subject possessing them. An attempt to realize and articulate the implicit prerequisites of cognitive activity, to direct one's attention to them, deprives them of their former functional significance in the structure of consciousness, changes their status, and accordingly leads to a restructuring of the entire semantic context, creates a new cognitive situation. As a result, the implicit knowledge of the subject in its original form cannot in any way be in the focus of attention without losing the content and meaning that it has precisely as implicit prerequisites of knowledge. While implicit, implicit, non-verbalized knowledge enters the sphere of peripheral consciousness, only the object of focal consciousness can be explicit, which is the carrier of the integral meaning of a certain cognitive situation" [1].

M. Polani describes the structure of individual consciousness, according to which "any cognitive act involves the interaction of two ways of realizing objects: focal awareness, directed at the object of cognition and giving explicit, explicit, articulated knowledge and peripheral [subsidiary awareness], which includes implicit, implicit, unarticulated knowledge of side data [clues], which are not in the proper sense of the word objects of cognition, but act as necessary prerequisites for cognitive activity carried out by the subject" [2, pp. 404-405].

Based on the universal model of implicit cognition proposed by M. Polani (the so-called "from-to structure"), implicit cognition (or implicit inference) can be represented as "movement from side data located on the periphery of consciousness to a focal holistic understanding <...> ... this holistic understanding is a gestalt that cannot be analyzed only as a simple sum its parts and rules" [3, p. 29]. Based on this scheme of implicit cognition, M. Polani showed the role of unarticulated, implicit knowledge in cognitive activity, which expands our understanding of the structure and nature of knowledge.

Yu wrote about background knowledge. Habermas, noting that communication in culture is based on background knowledge – the life world of the participants, the realities of the culture in which the communication participants are immersed. In modern linguistics, the concept of background knowledge is widely used. So, according to one definition, background knowledge is "mutual knowledge of the realities of the speaker and the listener, which is the basis of linguistic communication" [4, p. 498].

But along with the concepts of explicit and implicit knowledge, I introduce the concept of "implicit ignorance", an absolute background. What of our knowledge is implicit and why? If we analyze this question, we come to the conclusion that implicit knowledge for us is the most immediate and undoubted, that is, what is taken for granted for us, which cannot and does not arise in doubt. Implicit for us is the state of things that we cannot compare in our minds with a fundamentally different position, the alternative of which is not imaginable for us, at least in the nearest intuition. Explicit knowledge is born out of doubt, which entails the possibility of comparison. So, we know that objects fall down only because we are able to imagine that this could not be the case.

The concept of red is impossible without the concepts of other colors. If absolutely everything were red for us, there's no way we could know that everything is red. This truth would be an absolute background for us, incomparable with anything, and therefore fundamentally undetectable. This is how we come to the concept of "implicit ignorance". We do not know that something is an absolute background for us - we can only assume that such an absolutely undetectable thing exists because of absolute indisputability. Something is implicit for us because it is absolutely impossible to doubt it, so much so that we cannot know it, we cannot single it out for ourselves as knowledge.

This something is too universal, common to the thinking and perception of all people, so much so that none of the people can single it out as knowledge, having discovered the possibility of a different state of things, and therefore making this particular state of things explicit.  To better clarify the concept of an absolute background, let's consider what can serve as a background that is not absolute, be accepted non-reflexively, be taken for granted, but at the same time fundamentally reflexive. The sphere of human existence in which background knowledge is most manifested is everyday life, the life world, so next we will look at examples of what was background knowledge in everyday life.

 

2. Everyday life, the world of life

Each culture has everyday unreflected knowledge as an unnoticed background, which, however, is recognized by another culture if it observes the first one. The world of life and everyday life became discoveries of the XX century, including in Russian philosophy, in particular, epistemology. Everyday life is "an integral socio–cultural life world that appears in the functioning of society as a "natural", self-evident condition of human activity. Everyday life can be considered as an ontology, as a boundary of human activity. The study of everyday life implies an approach to the human world and his life itself as a value... It is necessary to distinguish between everyday life itself and the theoretical discourse about everyday life. At present, everyday life as a specific area of social reality acts as an object of interdisciplinary research (history, social and cultural anthropology, sociology, cultural studies)" [5].

The concept of everyday life is connected with the concepts of the life world (E. Husserl, A. Schutz), common sense. This is a world of direct perception of things and events, familiar, orderly, expected for a person of a certain social reality. This is the world in which an individual lives and thinks every day, in which meanings and rules are formed, standard patterns of social behavior and outlook on things, social memory and traditions. Everyday life is an immediate social reality in which an ordinary individual lives and thinks.

Everyday life is "immediate and immediate" and therefore rarely reflected – what often becomes background knowledge remains on the periphery of awareness, but what explicit knowledge is based on, from which it comes. Here again, the concept of semantic gestalt becomes heuristic – the integrity of combining explicit and implicit knowledge in our grasp of things and situations.

The concept of the "life world" was introduced by E. Husserl to denote the sum of the immediate evidences that define the forms of orientation and human behavior. "The vital world (Lebenswelt) is one of the central concepts of Husserl's late phenomenology, formulated by him as a result of overcoming the horizon of a strictly phenomenological method by addressing the problems of world connections of consciousness" [6]. This concept emphasizes the connection between scientific and pre-scientific knowledge, the rootedness of scientists themselves, who talk about the Big Bang, the expanding universe, Einstein's theory of relativity, in the Aristotelian world of everyday activities, common sense, and automatic routine actions. In this sense, any scientist as a person turns out to be a carrier of pre-scientific consciousness in the everyday world. Everyday life is also what makes the human world coherent, "cements" various fields of knowledge. This is something that is common to a locksmith, psychologist, nuclear physicist, artist, architect. It is common, despite the difference in worldviews and worldviews associated with their occupations.

According to Husserl, the world of life consists of the sum of "immediate evidence". "This is a pre–philosophical, pre-scientific, primary consciousness in the epistemological sense, which takes place even before the conscious acceptance of the theoretical attitude by the individual." The life world is the sphere of the "well–known, immediately obvious", the "circle of certainty", which are treated with long-established trust and which are accepted in human life beyond all the requirements of scientific justification as unconditionally significant and practically tested [6].

It is important for me to note that the life world "has a priori structural characteristics – invariants – on the basis of which the formation of scientific abstractions, etc., is possible, as well as the possibility of developing a scientific methodology" [6]. It is in this property of the life world that Husserl sees the desired basis for substantiating knowledge. The invariants are: "spacetime", "causality", "materiality", "intersubjectivity", etc. The property of invariants is that they are not constructed, but given, according to Husserl, in any experience; they are based on any concrete historical experience of human life in the world. The concept of the life world is systematically used in the phenomenological sociology of A. Schutz, in which attention is focused on the study of the life world as a natural attitude of consciousness, eliminated by Husserl in the process of transcendental phenomenological reduction [7].

 

3. Mesocosm

Another concept that is heuristic for the analysis of everyday implicit knowledge is the concept of the mesocosm, introduced by the evolutionary epistemologist G. Vollmer in 1975. The Vollmer mesocosm appears as an Aristotelian world to which man is adapted, the human habitat. Vollmer considers the concept of the mesocosm, including in the cognitive aspect. The mesocosm, according to G. Vollmer, is the "cognitive niche of man." This is a world of medium dimensions, average magnitudes and speeds, which our brain perceives through the senses and to which humans are evolutionarily adapted [8, pp. 198-199].

According to Vollmer, it is precisely to the mesocosm that human everyday perception is adapted, adapted in the process of biological evolution; thus, pre-scientific experience and common sense are components of human evolutionary adaptation. Vollmer suggests that the subjective structures of pre-scientific cognition (including perception) are adapted to the world in which they developed, that is, the mesocosm [8, p. 211].  Vollmer says, however, that this is why the structures of human cognition cannot correspond to all real structures and are not suitable for cognition of what goes beyond the mesocosm. G. Vollmer denies the suitability of cognitive structures adapted to the mesocosm during biological evolution for cognition of all processes, including the processes of micro- and macro-worlds.

"The mesocosm is a world of medium dimensions: a world of medium distances, times, weights, temperatures, a world of low speeds, accelerations, forces, as well as a world of moderate complexity. Our cognitive structures were created by this cosmos, adapted to it, selected for it and through it, tested on it and justified their reliability" [9, p. 231]. Vollmer writes that man in his everyday experience still lives in the world of Aristotelian physics [10, p. 200] The subject of the study is the concept of the universal in the epistemological aspect. The subject of the study is the concept of the universal in the epistemological aspect.. For us, the sun still revolves around the Earth, and the stones fall down, because that's how it should be, their natural place is there. But our scientific concepts and theories are increasingly moving away from everyday language and everyday knowledge. The scientific picture of the world has long been far from Aristotelian. It, in turn, affects our everyday perception of the "life world".

Implicit and unreflected everyday background knowledge was at one time implicit, background for philosophy as well. This was before a linguistic turn took place in philosophy, which made clear certain cultural realities related, among other things, to everyday knowledge of different cultures and its reflection in their languages.

 

4. Linguistic turn in philosophy

A linguistic turn in philosophy took place at the beginning of the 20th century. At its origins are G. Frege, B. Russell, D.E. Moore, L. Wittgenstein. Their approach to philosophy is determined by the belief that all knowledge about the world exists only when it is expressed through language. The linguistic turn began with an analytical approach, the analysis of the language of science and the desire to clarify philosophical problems by referring to natural language, its analysis and, to some extent, criticism.

V.A. Vasiliev notes that, having already entered the XX century, philosophical thought faced many contradictions reflecting the "new socioculture" due to the peculiarities of non-classical and post-non-classical science [11]. The researcher notes three stages of the linguistic turn. The first stage is connected with the views of B. Russell and L. Wittgenstein. The second stage is with representatives of the "Vienna Circle". The researcher associates the third stage of the turn in linguistic philosophy with the analysis of everyday language. This trend arose in the 30s of the XX century in Great Britain (G. Ryle, P. Stroson, J. Austin, etc.), in the USA (M. Black, N. Malcolm, etc.).

Turning to the research of the languages of various peoples, the philosophers of language began to discover the worlds of concepts of other languages, the phenomenon of linguistic relativity, a variety of grammatical structures. It was necessary to accept the discovery of the fact that the same world appears to man in the forms of completely different linguistic concepts. The pragmatic interpretation of the linguistic turn was an attempt to reconcile the emerging contradictions.

Thus, E. Sepir formulated the principle of "linguistic relativity" (the Sepir-Whorf hypothesis): according to this principle, language does not express the structure of the world, but rather forms the image of the world of a person using language. It follows from this that native speakers of different languages have completely different ideas about reality. The principle of linguistic relativity was developed within the framework of the pragmatic analysis of language. Thus, according to W. Quine, the picture of the world, fixed in the structure of the language used in a particular community, is accepted solely for pragmatic reasons. The main function of language is to provide communication in the community [12].

The criterion of existence, developed by Quine in the 1930s, states: "to exist is to be the value of a related variable." "Names, according to Quine, are terms that point directly to objects. Descriptions are terms that do not point to any objects, but can make judgments about these objects true or false. There are only those objects that are named, so to exist is to be named. The name, according to Quine, indicates the subject, just as a qualified (related) variable indicates its value" [13]

 

5. Space and time

Such universals of culture as space and time can be considered as what was at one time both explicit and implicit knowledge. According to Kant, space and time are a priori forms of pure sensual contemplation. The contemplation of space and time is connected with concepts synthetically. This is a priori, but at the same time an experience [14, p. 68]. When Kant singled out space and time as pure a priori forms of sensuality, he thought of both space and time in the paradigm of modern Western science – physics. For him, space was three-dimensional, homogeneous and isotropic. Time for a man of the XVIII century is one–dimensional, homogeneous, irreversible. The Westerner had no doubt that time and space were like that. This is how a Westerner of the XVIII century perceived them.

The main properties of space in classical physics (and in modern philosophy) were: extension; uniformity (all points of space are equal, space itself does not change the state of objects); isotropy (equivalence of all possible directions); three-dimensionality (the ability to determine the position of any object using three independent measurements as empirically established and theoretically provable property of space); reversibility of space (that is, the ability to return to the same point in this space as many times as necessary). The main properties of time are: duration; uniformity (equality of all moments of time); one-dimensionality (the property is associated with the ability to fix an event in time using a single value); irreversibility or anisotropy (the inability to return to the past). It was assumed that time flows in one direction — from the past to the present and from it to the future). At the same time, space and time were ontologized, being considered as forms of being – categories in which any being, any events of this being, can be comprehended – both objective and subjective reality.

Kant wrote: "There is no need to limit the way of contemplation in space and time to human sensuality. It is possible that every finite thinking being must necessarily resemble a human being in this respect" [14, p. 68].

That this is not the only possible perception of space and time became clear when there was a linguistic turn in philosophy associated with the study of the languages of "primitive" peoples. With a linguistic turn, philosophers faced the space of the ecumene (mesocosm), as it was before the development of scientific physical concepts – the space is heterogeneous and not isotropic: the upward direction is not equal to the downward direction, sacred and profane places are highlighted, preferred and avoided directions of the path ("path" as opposed to "movement" as a purposeful movement). As well as cyclic time with the change of seasons and days, in which days are not equal to nights, winters to summers, which "stretches" or "flies" depending on what a person is doing. Time is most closely associated with Bergson's dur?e, the extension of consciousness. The space and time of the mesocosm remained the same, and the "life world" of scientists remains the same, but this ceased to be realized for a while. This is how scientific concepts (the scientific picture of the world) affect everyday perception, the "life world". So any modern person who has studied at school already intuitively perceives space and time according to the standards of physics of the XVIII century.

Thus, not only implicit knowledge can become explicit, but explicit scientific knowledge in culture often turns into implicit knowledge of everyday life. At the same time, there is a delay and implicit everyday knowledge becomes scientific knowledge that is already outdated, but is already known not only to specialists, and has been the main scientific paradigm for a certain time. Mass and everyday consciousness "does not keep up" with the paradigm shift of the advanced scientific community. It can be assumed that Einstein's world of everyday consciousness will "settle in" in a century or several, but by that time there will probably be more than one paradigm shift in the scientific community.

This is how explicit scientific knowledge turns into implicit everyday knowledge, while ceasing to be clearly reflected and questioned. This happened with the scientific concepts of space and time, which passed from scientific knowledge of the XVIII century into everyday knowledge and became background knowledge in everyday life of the XX century, in order to become reflected in philosophy again as such. Using the example of the transformation of cultural universals of space and time, one can trace the complex dialectic of the mutual transitions of explicit and implicit knowledge in human culture.

 

6. The principle of human proportionality

The concept of an absolute background can be derived from arguments about the principle of human proportionality, from the understanding that there is something universal, immanent precisely to the human perception of things and phenomena, which for a person is integral to his reality. This is Kant's intuition that there are a priori forms of sensuality. Are they space and time? We can't know that. The concept of an absolute background implies that we cannot know what the absolute background is for us. We cannot step out of our human nature to see how a "different thinking being", a non-human, would perceive the world.

One can ask the question: is the principle of human proportionality implemented insofar as the world is ontologically human-sized, or insofar as it is perceived by human standards? The latter statement is known as the weak anthropic principle. One thing is beyond doubt: due to our human nature, we cannot perceive the world as not human-sized.

But the question of the human dimension of the world is also significant for philosophy, including in the mode in which science grasps it – complex intellectual structures developed by mankind and gone far from the mesocosm or the life world. The movement of human thought is sometimes so paradoxical that the very question of everyday life and the interest in philosophy in it arose from the realization of the difference between its knowledge (at the same time practically "implicit") from knowledge of complex intellectual systems, scientific and philosophical constructions. The man suddenly realized that not all of his world is Einstein's. But in order for this to become the discovery it became, it was first necessary to assume that all reality is described by Einstein's theory.

Our everyday life was "not everyday" (at least for the intellectual consciousness) until its difference from the scientific picture of the world was realized. It was this "reverse movement" of thought that ensured intellectual preoccupation with the problems of the "life world" and "everyday life", the task of reflecting on the unconscious stay to this day in the Aristotelian world. But this stay first had to become "implicit" in order for the problem of "identification" to be so urgent. So what kind of world did we live in then?

Post-non-classical science reflects on norms, goals, ideals, and tries to study man as such and human society, as well as social systems as complex systems. This is a return to the principle of human proportionality on a new level. A person studies himself, other people, society, i.e. the systems in which he is included himself, being both an observer and an integral part of them. What does he see at the same time and what fundamentally cannot he see?

Obviously, even here, in our own structure and the structure of society, there will be something so common to all people that it is impossible to reflect on for the reason that nothing else can be thought of. The absolute background must be present both in a person's perception of a non-human but human-sized world, and in the perception of the human world proper.

So, on the one hand, the world is known by man, and is inaccessible outside the forms of human cognition. On the other hand, there is a multiplicity of ways of categorizing the world, including linguistic ones. Do these methods of categorization have something in common, something that is basic and universal for understanding the world? This general should represent an "absolute background", that is, it should not be grasped and not be distinguished in principle.

 

7. Conclusions

The absolute background is defined in this article as universal direct evidence, common to all people of all cultures and peoples and constituting the a priori foundation of human cognition. The absolute background can also be called "implicit ignorance", this is something that, due to its immediacy and universal nature, is inaccessible to identification, comparison, reflection. This is something that can never be translated into explicit knowledge, although any knowledge is based on this background.

At the same time, it is necessary to realize that what is the background now and could claim to be an absolute background, over time and with a change of culture, can "come to light", be recognized as background knowledge of the previous culture and be amenable to description and study. The ways in which this background supports explicit knowledge of a given culture will also be amenable to study. Thus, the absolute background is absolute, but what could be mistaken for it (background knowledge of culture) is historical and culturally relevant. The concept of an absolute background is useful for epistemology precisely because it allows us to determine what is not such a background for us. This makes it possible to identify the complex dialectic of the mutual transitions of explicit and implicit knowledge. At the same time, the idea of having a permanent universal background of knowledge is methodologically useful.

The concept of an absolute background allows us to answer the question: is something universal? So, are the universals of culture universal or certain deep structures of language? The answer is: no, they are not, if we can isolate and describe them. The very sign of the possibility of isolation and description indicates the non-fundamental nature of what is being isolated and described. Therefore, those who insist on cultural differences at the deepest level are right. Because all we can see are the differences. The truly universal, if it exists, will always be epistemologically invisible to us.

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At the very beginning of the reviewed article, the author suggests that there is a certain "universal" component in knowledge, which is represented in all cultures and in all epochs. The reason for this "universal stability" of the "universal," says the author, is its "unreflectability." What does this mean? – The "universal" cannot be the subject of rational analysis. This concept does not mean anything else in the "universal philosophical language". It is not difficult to understand that we are talking about a "thing in itself" that remains outside the activity of the mind, while at the same time forming the "substance" of any culture, "manifesting" (?) both in everyday and scientific knowledge (why then does the author conclude that this "universal prerequisite" is inaccessible to rational knowledge?). Insisting nevertheless on the "unreflectability" of the "universal", the author also says that it "remains fundamentally undetectable." How, then, did the author manage to "identify" him? The need to parse the first paragraph so "meticulously" is due to the fact that the uncertainty and "confusion" that the reader encounters here is reproduced in the subsequent presentation up to the conclusion. So, if initially it was pointed out to the "universal" as a kind of knowledge, albeit eluding rational knowledge, but still, apparently, fixed in some way, then gradually it is reduced to "implicit ignorance", "absolute background", "universal direct evidence", "common to all people of all cultures and peoples and forming the a priori foundation of human cognition." Maybe we can just talk about what in previous centuries was called "human nature", about its "epistemological dimension"? But, apparently, such a decision is unacceptable for the author, since he repeats at the end of the article that this is "ignorance", "background", a universal prerequisite for knowledge, etc., "inaccessible to identification, comparison, reflection"; "this is something that can never be translated into explicit knowledge, although at the same time, any knowledge is based on this background." Let's agree, however, that all such arguments are "very deep classics." Let us recall Jacobi, who noted that without the "thing in itself" one cannot enter into critical philosophy, and with it one cannot remain in it, and let us recall what insurmountable contradictions the creator of critical philosophy faced when, on the one hand, the "thing in itself" had to "affect" (in the author's terminology – "to fund") sensuality, and on the other hand, causal relationships could not be extended to it ("the thing in itself"). However, this is not all, the uncertainty of the author's statements increases even more when it turns out that "what is the background now and could claim to be an absolute background, over time and with a change of culture, can "come to light", be recognized as background knowledge of the previous culture and be amenable to description and studying. The ways in which this background supports explicit knowledge of this culture will also be amenable to study." That is, cognition is still historical in nature, so why talk about the "unreflectability", "non-manifestation" of this supposedly initial and irresistible immediacy of human cognition? The reviewer must admit that he failed to find answers to these questions either in the article itself or in the sources referred to by the author. It should be recognized that the article can arouse the sincere interest of readers, but at the same time, I would strongly recommend that the author, before publishing the article, establish a minimum "conceptual order" in the text, uncertainty, vagueness, contradictions found in the presentation make it difficult to understand the intent and final meaning of the presented article. The text also needs stylistic correction ("the assumption that it is universal that, no matter what ...", "for all cultures and epochs in their transformations of cultural universals, it does not transform ...", etc.). Despite the comments made, I consider it possible to recommend the article for publication in a scientific journal.