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SUFFICIENCY OF SEVEN SIMULTANEOUS INTERACTION WAYS OF TWO OPPOSITES FOR THE EMERGENCE OF AN INFINITE SET OF IRREDUCIBLE DEVELOPMENT POSSIBILITIES
Abstract
The actuality of contradiction category as an issue of dialectical logic is due to the fact that contradiction is the proper cause of development but, being a form of inventive (creative) task, it rarely becomes the object and purpose of invention. The purpose of this article is to invent a new idea of contradiction. The leading approach to achieve this goal is dialectical logic and the algorithm for solving inventive tasks. The article establishes a conceptual isomorphism, with an accuracy up to a number of parameters, of a dialectical problem of inherent simultaneous methods of interaction of two opposites and a minimax problem solved by mathematicians, in which, beginning with seven parameters, an infinite set of irreducible types of discrete structures emerges, arising within a continuous environment and stable in relation to small changes. The proposed idea of a new categorical structure of dialectical contradiction differs from its traditional understanding and the concept of multipolarity, which reduces the interaction of opposites to unity and struggle, because it reveals seven inherent simultaneous methods of interaction of two opposites, necessary and sufficient for the emergence of an infinite set of irreducible development possibilities. The article contains a description of this alternative idea pedagogical implementation in the form of a self-referent structure of a creative seminar on the system of the continuous development of creative thinking with the active use of inventive tasks solving theory. The materials of the article may prove to be useful not only for further theoretical development of dialectical contradiction category, but also for improving the creative methodology of TRIZ pedagogy.
Keywords
dialectical contradiction, stable non-equilibrium of self-denial, seven-parameter interaction of two opposites, reflective determinateness of contradiction, infinite set of irreducible development possibilities, algorithm for solving inventive tasks, creative seminar,
AUTHOR
Alexander Grigoriev
PhD, Associate Professor, Philosophy and Social Sciences Chair, Institute of Social Engineering, Siberian State University of Science and Technologies named after academician M.F.Reshetnev, Krasnoyarsk, Russia 31, Krasnoyarsky Rabochy Av., Krasnoyarsk, 660037, Russia E-mail: [email protected]
1. Introduction
The purpose of this work is to substantiate a new idea of dialectical contradiction, and its task is to establish conceptual links between theories that were previously thought to be essentially unconnected with each other. The work refers to the field of "Philosophy", "Dialectics" section.
At what minimum number of simultaneous different ways (degrees of freedom, parameters) of interaction of two opposite sides does an infinite set of irreducible development opportunities (tendencies) emerge?
The expression "degrees of interaction freedom" is used here in a sense analogous to the one in which the phrase "degrees of quantum strings movement freedom" is used in modern physics (Klyagin, 2011). The phrase "degree of interaction freedom" is used as the semantic equivalent to the term "parameter" in order to establish in one respect the possibility of obtaining the physical meaning of a dialectical contradiction, and in another, the conceptual connection of dialectics with the theory of differentiable reflections features in order to bring substantiation of the necessity and sufficiency of seven simultaneous ways of opposites interaction for the emergence of an infinite set of irreducible to each other development possibilities up to the stage of accurate proof.
1.1. Topicality of the problem
We discuss such a transformation of traditional categorical structure of dialectical contradiction, which would, without unnecessary complicating this structure, led to an increase of its effectiveness as its own form of creative thinking and would make it possible to fine-tune it every time to a new subject area, and discovering new knowledge, and not to the past experience and ready-made knowledge.
In order to gain the right to propose a new idea of contradiction, it is necessary, within the framework of dialectical tradition, to identify a task that cannot be solved by means of this tradition.
1.2. Substantiation of the insolvability of contradiction antinomian formulation problem within the framework of traditional dialectics
Starting with what minimal systemic interaction of opposites, does the contradiction become the cause, which cannot but generate new itself and everything else? Dialectical contradiction, in its essence, is such a stable and unbalanced open interaction of inseparably related opposites, which cannot but lead to the emergence of its ever newer forms. The more acute is the conflict between opposites, the more intensive and organized becomes their next arrangement (resolution of the contradiction). But is there enough only unity and mutual negation between opposites in order for their interaction to lead to the emergence of a new one and serve as the driving force of development?
1.2.1. Zenon's aporia "Arrow"
The dialectical interpretation of aporia by Zenon of Elay "Arrow" (Zenon, 1991) should seemingly lead to the conclusion that the flying arrow is different from the resting one by contradiction in its location: it partially loses determinateness of its position which it would have at rest, so the flying arrow is and is not in the same place at the same time. This contradiction is seemingly solved by the fact that the arrow moves in a certain time to another nearest place, in which the contradiction is reproduced, but in the same unchanged form.
Impossibility of resolving this form of contradiction, within the two-parameter interaction of opposites, is something obvious, but perhaps this insolvability of this form of contradiction arose from the unsuccessfully selected object of analysis - simple mechanical movement, which is only quantitative determinateness of the independent forms of substance motion and is not capable of qualitative changes in itself.
To clarify this, let us turn to subject fields beyond mechanics, but, first, we will show a way beyond the two-parameter interaction of opposites and the possibility of obtaining the physical meaning of opposites interaction with the "number of freedom degrees" more than two on the material of the quantum strings physical theory and the modern concept of the universe origin. As it is shown in the works of Sh. Yau, the "singularity" (from which disintegration the universe came into existence) occurred as a result of the mutual projection (that is, the interaction) of two, opposing in the phase processes going on in them, three-dimensional spheres of being (Yau, 2013; Klyagin, 2011).
It is precisely because the singular origin of the universe arose as a result of the seven-parameter interaction of the two opposite to each other spheres of being that everything new in it arises from the same "septenary" interaction of two opposites in three-dimensional space.
1.2.2. Antinomy of Marx's surplus value
In order to find out whether the antinomian formulation of the unity and struggle of opposites can be a reliable theoretical criterion in the search for a concrete fact that is the real solution of the contradiction indicated by the antinomy, let us turn to the paradigmatic example, which is generally referred to by the principal opponents of dialectics in general, and by the supporters of traditional dialectics in particular.
In his task about discovering the source of surplus (new) value, Marx noted that surplus value (capital) had to appear in circulation and, at the same time, not in circulation (Marx, 1960). To resolve this antinomy (a sharp contradiction), it is necessary to discover in reality such a commodity, the very consumption of which is production at the same time. Such a commodity, in which the process of production and consumption mutual transformation takes place, seems to be a labor force.
However, the ability to work is not an innate ability of a human body, but only consequence of knowledge. Now knowledge claims to be such a product, the consumption of which is productive, but knowledge cannot be the cause of its emergence and is not innate information (instinct) for the person. It is clear that the antinomian formulation of contradiction, both of affirmation and negation in the same respect, cannot be an exact theoretical criterion in search of precisely that fact, which is a resolution of the contradiction (a new combination of opposites that have come into acute conflict). It is also clear that something new is created by a man as a result of creative activity that does not fit into the two-parameter scheme of traditional dialectics. For a creative act and its understanding, it is necessary to have seven of its own characteristics, revealed by G.S. Batishchev as final conclusions from an analysis of creativity dialectics (Batishchev, 1997).
1.2.3. Paradox of conditioned reflex behavior inheritance
Let us show how the antinomian formulation of contradiction conceals not always realizable forms of creative thinking, which are always real, in one instructive example from evolutionary theory.
At a certain evolutionary stage of development, there is a need for such behavior, which would be reconstructed not only in accordance with the innate species information, but also with the use of information coming from a change in the very individual situation of the living being. There appears an evolutionary need to acquire the life conditioned reflex experience and pass it on to the next generation.
If we do not take into account all the necessary parameters of the evolution driving force, then the conditioned reflex acquires the characteristic of a hopeless antinomy: conditioned reflex behavior must be inherited and programmed in the genotype, but at the same time it should not be programmed (and it should be conditioned reflex dynamic reflection of volatile circumstances). Conditioned-reflex life experience should be passed on to the next generation within the genetic program and at the same time beyond it. Such an antinomian formulation looks like self destructive absurdity, because this evolutionary situation is described abstractly from the systemic nature of the evolution itself.
Life is a self-referral, self-organizing, stable, non-equilibrium open structure, therefore adaptation is a volatile interaction of living beings aggregate number and the surrounding inorganic environment, penetrating and encompassing both of these opposite, complementary sides. The disequilibrium is stable due to the hereditary program of individual development, but the realization of the latter in the process of adaptation of living beings to the environment leads to changes not presumed by this program. Unprogrammed (random) variability of the hereditary program is a condition of the possibility of adapting to unpredictability of environmental changes. The method of random hereditary variability is the extended self-reproduction of living beings, which comes into conflict with the limited number of necessary for this substances, which leads to the need for natural selection. The action of natural selection is removed by circulation of substances, otherwise evolutionarily perspective carriers of mutations that differ in their weakened adaptability to the current situation would be impossible. The impossibility of an accurate assessment of the mutated living beings evolutionary perspective within the mechanisms of biosphere self-regulation is an indicator of the insolvability of each living individuality in relation to the entire biosphere system as a whole. But it is this impossibility of complete solvability and predetermination of each individuality in the biosphere system that leads to the development of the driving cause of development (the evolution of the laws of evolution) and, ultimately, to the informational overcoming of the inherent predetermination of a living body behavior.
The instinct of imitation makes it possible to pass conditioned reflex behavior on to the next generation, but does not contain a criterion for assessing benefits or harms of the imitated behavior, which can lead to the complete extinction of a rather highly organized life form. This explanation is the most plausible model of dinosaurs' extinction, as evidenced by the facts of paleontology (Shimansky, Soloviev & Danilchenko et al., 1978; Karamyan, 1970).
The evolutionary development of motor and affective behaviors inhibition instinct made it possible to overcome the pandemia of imitative forms of behavior which had led preceding mammals highly organized form of life to complete extinction.
The inhibition instinct, which suppresses any deviations from the herd behavior stereotype, was the reason for the evolutionary depression of primary mammals, which lasted for about million years, but was surmounted by the emergence of an innate ability to replace by means of signals one type of behavior with another, actively imposing the latter on all surrounding relatives (Porshnev 1974). On the one hand, the instinctive suggestion made it possible to carry out such extremely indirect but effective way of interacting with the environment as objective (tool) manipulation, but on the other hand, it also allowed active imposition on associate beings the most pernicious form of behavior, leading to the accelerated extinction of all beings implementing instinctive form of tool activity.
The solution to this extremely acute contradiction of natural evolution was the complete blockage of that part of the genetic program which predetermined behavior and activity (Roginsky, 1977).
Thus, the analysis of the evolutionary theory material makes it possible to answer reasonably the question of nature structure, which allows not only the possibility, but also the necessity for the emergence of a free, rational and social being in it, but for this it was necessary to take into account all the essential parameters of the stable unbalanced interaction of all living creatures and inorganic environment: adaptation, heredity, accidental hereditary variability, extended self-reproduction, natural selection, circulation of substances and the biospheric impossibility of predetermining every living individuality.
1.2.4. Self-referent dispute about the law of unity and struggle of opposites
An illustrative and self-referent example of the fact that a contradiction, understood as the unity and struggle of opposites, does not lead, in its discussion and following its logic, to development, but to the state of self-compensated balance of the opposites of a closed and self-destructing system, is the extremely sharp dispute of the 60s-70s about the category of dialectical contradiction in the collection of articles "Dialectical contradiction" (1979). Even philosophical encyclopedia of the Soviet period published two articles referred to "Contradiction dialectical" expressing directly opposite main points of view (Batishchev & Vyakkerev & Narsky, 1967). The participants of this dispute, in which unity and struggle were its exhaustive degrees of freedom, remained on the opposite sides of the same position, which did not change as a result. G.S. Batishchev overcame later the traditional understanding of contradiction, simply leaving the circle of disputants and turning to the problems of communication culture (Batishchev, 1995).
But what prevents unity and struggle of opposites to be a closed whirl of one and the same unchanging contradiction in itself? From the point of view of J.-M. Benoist (Benoist, 1972), who argued with L. Althusser (Althusser, 2006) at the same time for the same reason, it can only be the recognition of the fact that contradiction can be multipolar one consisting of an indefinitely large number of opposing sides that are in unity and struggle with each other. However, J.-M. Benoist, when referring to the physics of elementary
particles (the number of opposite quark charges is four), did not take into account the fact that there are no irreversible events in the microcosm (there is no basic condition for the applicability of the development principle in it, since development is primarily an irreversible qualitative change). In addition, polarity describes not the proper process of the developing and non-equilibrium interaction of opposites, but the state of self-compensated equilibrium between them. Complicating a closed equilibrium macro system with an increase in the number of its opposing interacting sides leads to its chaos and self-destruction due to an increase in the probability of accidental failure in its functioning.
Even in its most developed version, the concept of multipolarity has a significant drawback. It lacks the criterion of necessary and sufficient number of poles - it all comes down to endless increase in their number and combinatorial construction of multipolar systems (Lensky & Kochnev, 1986).
A productive way out of the self-referent dispute about dialectical contradiction is such a conversation about it, the relations between the participants of which are not reduced to unity and struggle. G.S. Batishchev distinguished seven "universals" in the concept of communication culture (Batishchev, 1995), allowing its technological realization in creative communication, creative thinking and learning through the use of seven elementary rhetorical techniques to rethink the usual meaning of the words according to classification by M.L. Gasparov (Gasparov, 2000). However, seven-parameters nature of creative communication, generating new meanings, can be found on the material of seven classical ancient Indian darshans (views), performing the role of simultaneous irreducible to each other functions necessary for potentially infinite production of new meanings in the ancient traditional ritual of philosophical discussion (Silberman, 1998).
2. Methodological basis
In philosophy, the requirements for justifying a new idea are more stringent than in other scientific fields, since they imply not only some new thought as a general principle of explanation, but an expressive and accurate picture of the meaning, on which the meaning looks like it really is, clarifying itself and everything else that cannot be done without rethinking and analytical specification of the established traditional terminology of dialectical logic, which was introduced in the second chapter of the second book "Science of Logic" by G. V. F. Hegel as reflexive definitions of essence (Hegel, 1971) and applied by M.B. Turovsky in his presentation of reflective determinateness system of the generating interaction of opposites (Turovsky, 1997).
The terminological apparatus for transformation with the purpose of presenting a new categorical structure of contradiction: "denialism", complementarity, "withdrawal", "supposition", "assumption", "extraneousness", system insolvability of individuation. All terms, with the exception of "complementarity" and "system insolvability of individuation", are taken from Hegel's "Science of Logic" and mainly refer to the context of his essence doctrine, except for the term "extraneousness" referring to the doctrine of being (Hegel, 1970). The term "complementarity" is given in the version of its universalization that exists in the modern theory of quantum strings, in which not only mass, energy, space and time are interchangeable, but also extremely large and extremely small scales. The phrase "system insolvability of individuation" partly connotes insolvability in mathematical logic, in which not all statements that can be expressed in the formally strict language of a certain logical system of the first kind can at the same time be proved (or refuted) by formalized means of this system.
Without changing the stable denotation of terms that have developed in the dialectical tradition, we will change this most unstable part of their denotation as a
meaning, concretizing it in the context of the dialectics basic problem, which is formulated and solved by G.S. Altshuller's short algorithm for solving the inventive tasks (Altshuller, 2017).
2.1. The main objectives of the study
1. Under what condition cannot something new fail to emerge?
2. Under what condition does an infinite set of irreducible development possibilities emerge?
3. What should be done to ensure inev'tability of creating something new?
4. How can one discover the very logic of discovery?
5. How can one discover new knowledge in the process of studying something old?
6. How can one invent a new way of inventing and teach it the others?
7. How can we motivate every educator and student to find such a task that only he can set and solve for the first time?
2.2. Algorithm for solving inventive tasks as a method of invention and substantiation of a dialectical contradiction new idea
Since two simultaneous necessary opposite sides are given in a dialectical contradiction, the question arises which side to choose to start formulating a contradiction. The question about the rational basis of this choice is solved in a technical contradiction: two opposites are equally important with respect to natural systems, but they are far from being equivalent concerning human actions (and artificial systems). One of the two opposites will be the main production function, and the other will be the necessary auxiliary one. In our case of inventing a dialectical contradiction new idea, we will need technical contradiction not for choosing between two stably objective opposite sides, but for determining the essential sequence of describing simultaneous and inalienable ways of interaction between them with the definition of such a primary function of contradiction as creation (emergence) of something new. It is necessary to distinguish between opposites and such ways of interaction between them as unity and mutual denial. Opposite's interaction parameters are of greater importance than the opposite sides themselves, and denial has priority over unity in terms of the main function of contradiction - to be the cause of development.
How can one create a universal conceptual system for the continuous invention of it and everything else again?
1. Conceptual system for creating, discovering, inventing something new and continuous development of creative thinking
2. includes two opposing sides, as well as unity and mutual denial.
3. The first undesirable effect is in the fact that the traditional understanding of contradiction as the unity and mutual denial of two opposites, does not reflect the actual cause of the emergence of something new (see 1.2.1, 1.2.2).
4. The most obvious means of eliminating the first undesirable effect is to increase the number of interacting opposites (as in the concept of multipolarity) in hope that this quantitative change of contradiction will result in the emergence of such a quality as its ability to generate something new.
5. The second undesirable effect, the main drawback of the traditional conceptual system of dialectical contradiction: such two ways (parameters) of opposites' interaction, as their unity and mutual denial, cannot ensure the emergence of something new.
6. An obvious means of eliminating the second undesirable effect is to increase the number of opposites' interaction freedom degrees (without increasing the number of opposites) to provide an infinite variety of development possibilities.
7. Reappearance of the intensified second undesirable effect: an increase in the number of simultaneous ways of opposites' interaction leads to a loss of the criterion of their necessary and sufficient variety.
8. The first technical contradiction.
If we increase the number and variety of parameters (simultaneous ways) of interaction of two opposites, then this will make the concept of contradiction unbalanced, dynamic and more creative, but lead to loss of opposites' interaction determinateness and will result in the loss of the minimum necessary set of parameters criterion. Two parameters of the traditional dialectical interaction of opposites - unity and mutual denial, are the simplest, minimal variety of simultaneous ways of interaction, but they are clearly not enough to ensure development.
9. The second technical contradiction
If we increase the number of opposites in contradiction, then this will make the description of objective conflicts of real systems more accurate and detailed - multi-polar, but this description does not refer to the process of something new emergence, but to an isolated condition of self-compensated balance between opposites. Whereas the main methodological function of dialectical contradiction category is the discovery of something new, simulating, in an essential sense, the process of this something new emergence in reality. And what is the point of increasing the number of interacting opposing sides if we reduce the interaction between them to unity and struggle?
10. The main technical contradiction
The traditional and extremely simple conceptual system of dialectical contradiction is not an adequate reflection of the genuine cause of something new emergence and development, but its complication does not lead to this problem situation solution, but turns into regression and self-destruction.
11. Intensified technical contradiction
The traditional concept of dialectical contradiction is to be changed, but it is extremely simple any change means its complication. It is necessary to increase the degree of systemic nature and its internal diversity so as to simplify it and to increase its effectiveness at the same time.
12. The model of the problem
It is necessary to remove the unity of opposites as the dominant beginning of contradiction, leaving only their negative, stable, non-equilibrium interaction.
13. It is necessary to create an infinite set of irreducible development possibilities, provided that the structure of the contradiction is then simple and finite (open non-equilibrium discrete structure).
14. The choice of the technical contradiction resolution of dialectical contradiction category
Improves - 35: adaptation, universality
Worsens - 13: stability of the object composition
Mode No. 14: principle of spheroidality - to transit from rectilinear to rotational motion.
15. Consideration of recommendations
The transition from rectilinear to rotational motion means, in this context, a transition from a straightforward understanding of the interaction between opposites as attraction (unity) and repulsion (mutual denial) to the logic of self-referent open non-equilibrium systems capable of self-organization and self-development. The principle of self-referencing as another "me" was used, apart from Hegel, in the presentation of the
reflective determinants of opposites' interaction by M.B. Turovsky (Turovsky, 1997). But how many simultaneously given parameters of the interaction of the two opposites are necessary to cause the emergence of something new and to become the driving force of potentially infinite development?
16. ideas
"What minimum number of simultaneous ways of two opposite sides' interaction is necessary to generate infinite set of irreducible development possibilities?" - this question coincides in its meaning with the mathematical minimax question: "At what minimum number of parameters in the problem of finding extremums there is an infinite set of irreducible to each other singularities? "
As V.I. Arnold noted, "starting from 7 parameters, the number of irreducible singularities types becomes infinite", whereas for "3, 4, 5 and 6 parameters the number of different singularities is 5, 8, 12 and 17, respectively" (Arnold, 2016). The proof of this fact is available in the works of V.I. Arnold, A.N. Varchenko, S.M. Huseyn-Zade (Arnold & Varchenko & Huseyn-Zade, 2009), L.N. Bryzgalova (Bryzgalova, 1977), V.I. Matov (Matov, 1982). The term "singularity" in this context means a discrete structure that arises within a continuous structure and is resistant to small changes.
Confirmation of this fact of providing an infinite number of singularities on the basis of seven-parametric interaction of two opposites, as well as a joint theoretical-empirical evidence of its physical feasibility and practical realizability, is available in rhetoric (Gasparov, 2000), dialectics of creativity (Batishchev, 1997), the concept of communication culture (Batishchev, 1995), evolutionary theory (in the works of this article author on the philosophical and methodological issues of the evolutionary theory published since 1983), psychology (Zinchenko, 2010), history of ancient Indian philosophy (Zilberman, 1998).
If the system of two opposites' interaction had not 7, but at least 6 initial parameters, then a number of possible special ways of development, that could not be reduced to each other, would not exceed 17, but their number is much more, as can be seen when we look at the "tree" of increasingly divergent ways of living beings species evolution, cultural and historical types of development (each with its own criteria for progress), multitude of literary styles, philosophical schools, scientific directions and a table of the use of technical contradictions resolution methods (principles).
At the same time, there is an equally accurate but less time consuming way of determining the real possibility of an infinite number of different distinct types of sustainable development: if the system can simultaneously contain 7 different parameters, then it has an infinite number of different irreducible possibilities for sustainable development.
We can stop considering the "hypothetical scheme" of the heterarchic seven-link personal development, structure of consciousness and creative act, designed by an outstanding psychologist and philosopher V.P. Zinchenko, to be only a metaphorical hypothesis and recognize it as a discovered new idea of creativity psychology and infinite number of its essentially different possibilities (Zinchenko, 2010).
In connection with this justification, the meaning of highlighting seven main blocks and emphasizing the variable nature of the 8th one in the structure of creative training according to innovative pedagogical system of continuous creative thinking formation by M.M. Zinovkina (Zinovkina, 2008) becomes clear. The first seven blocks lead to an infinite number of possible irreducible to each other special resumes and the relevance of the unique individual characteristics of each student and teacher. Besides, those distinctive features of creative tasks that have been investigated by developers of open-type learning tasks become understandable.
The authors of creative tasks collections (Zinovkina, Gareyev & Gorev & Utemov, 2013) turned to the fact established in psychology that psychological discomfort appears with simultaneous perception of 7-10 different objects. But from the perception of seven contradiction parameters simultaneously (the form of the creative task), the psychological barrier is just beginning, which one does not need to overcome, since the basic condition of an infinite number of different possibilities for solving inventive task and development has been achieved. The beginning of psychological discomfort, as dissatisfaction with oneself, is a necessary subjective condition for the very possibility of creativity - creative thinking and new ideas arise only at the limit of all possibilities (but not beyond these limits).
An idea is an entity that shows itself exactly as it really is. The idea of a creative act, according to A.F. Losev, is that it cannot help but create itself, cannot help but discover itself directly, cannot help but describe itself, cannot help but justify itself and, ultimately, this is something unique that is given the power to reject itself (Losev, 1982). Let us proceed with its depiction on the basis of dialectical logic.
17. Final idea - a new idea of dialectical contradiction, which differs from traditional category of dialectical contradiction (Batishchev & Vyakkerev & Nara, 1967) and modern concept of multipolarity (Lensky & Kochnev, 1986) by the fact that, without increasing the number of interacting opposites, it identifies seven simultaneous inalienable ways of two opposites' interaction, necessary and sufficient for the emergence of an infinite number of irreducible possibilities for the emergence of something new and for development.
Since the interaction of opposites is the cause of development and emergence of something new only when all seven of its reflective definitenesses (self-referral ways of this interaction) are given simultaneously, then the principle of transition from one determinateness to another can be only the principle of reflective directness into oneself as another self (which corresponds to the nonlinearity of open self-organizing non-equilibrium systems). Separate reflective definiteness is a completely non-equilibrium possibility brought to extremes.
Self-denialism is the first self-reinforcing stable non-equilibrium of random variability. It is different from traditional dialectical self-denial because if the latter is an integral result of a particular type development, when its possibility has been exhausted, denialism acts as a stable non-equilibrium fluctuations in any arbitrarily small spatial-temporal neighborhood of occurrence. In order to express non-equilibrium overcoming itself indefiniteness of the contradiction beginning, it is necessary to add suffix to traditional term "denial" (that implements the original idea of Hegel more adequately than his "specific identity").
B.M. Turovsky was right when he noted the important fact that to start presentation of dialectical contradiction category not with non-equilibrium indefiniteness, but with the system would mean to construct one more closed preformed structure and to follow the dogmatic way and not dialectical one. Adequate formula of denialism is not antinomy as a clash between two equal and opposite statements (on the one hand - on the other hand), or even self-referral negative statement, but self-referral question, overcoming its own indefiniteness. The spontaneous disintegration of denialism, left to itself, is its only action, apart from its own non-stop auto-fluctuations.
Denialism is directed into itself as complementarity between indefinitely many random, alternative and equally probable differences. Complementarity is the ability to be defined each time by something essentially external to itself. Denialism and complementarity cannot form polar equilibrium according to the "positive-negative" scheme, because they are non-equilibrium chances themselves, directed into themselves
as their other selves. So, doubled reflective definitions (like "denial of denial") are impossible, and not at all due to the change of the self-ordering process hierarchical type.
Complementarity is not self-applicable and provides actively the possibility for everything else to define it. The two stable opposing sides are parts of the generating relationship not by themselves, but only by their complementarity to each other.
Complementarity, being always its own shortcoming, needs to be supplemented by other, alien to it and to denialism, reflective definiteness. The complementarity between external even to themselves indefinite varieties is a random transition from the external prerequisites of the arising order to the reproduction of them as the variable results of the emerging system. The direction of complementarity to itself is defined as withdrawal (but not as a result of "denial of denial").
Withdrawal does not deprive independence of its external prerequisites, but on the contrary, it helps their individual prerequisites to overcome those limitations which, after self-disintegration of denialism, imposes on them the external character of their pre-system interaction, which aligns the essential diversity in its indifferent unity.
In the withdrawal of its external prerequisites' limitation, each random individuality acquires independence, reaching the possibility of a complete break with others so that unique randomnesses each time suppose their organic connection with each other and predetermine the form of their unification.
The breakdown of supposing is a condition for its spontaneous restoration, and its restoration again gives the possibility of every unique randomness to reach complete independence and a break with everything else. In this cyclical crisis, active supposing by the individual separate parts of their own organic system of connections is already presupposed itself in this system. An organic system, reflected into itself, seems to be hopeless spinning around the crisis cycle of its own emergence prerequisites supposed and reproduced by it, and this would indeed be true if supposition itself did not turn out to be an essential extraneousness to each other and to entire whole of unique individualities. Hegel used the term "extraneousness" in philosophy of nature to denote only something insignificantly external and spatially existing, but in this context, extraneousness means insurmountable and incompletely reproduced inorganic moment of the organic system itself, through which it becomes open and capable of changing.
The universality of the systemic whole turns out to be the self-directness of each concrete-single uniqueness that actively removes itself from its all-pervasive interaction with the systemic whole.
System-wide order, due to its own disequilibrium, reduces itself to the position of the minor side of each unique event. Each individuality contains in inimitable form all the definitions of the systemic whole, but goes beyond the essential limits of any resulted whole by its indefinite variability.
The essential irreducibility of individualities to each other and to the whole systemic whole forms insolvability and impossibility of complete predetermination of events by system-wide laws, which leads to the need for the development of the very cause of development, which has just been described in the form of a seven-fold hypercomplex system of reflective determinatenesses of two opposites' generating dialectical interaction: self-denialism, withdrawal, supposing, supposition, extraneousness and, finally, individual systemic insolvability that gives the dialectical interaction structure its openness to its own variability and at the same time the capacity for renewed self-organization.
So, a dialectical contradiction is non-equilibrium self-denialism of the opposites that are complementary to each other, taken in an organic system, that supposes in itself its own inorganic moment opened by supposition of individualities, extraneous to each other and to the whole, that are unsolvable relative to any equilibrium closed system.
3. Results and implementation
Based on the new idea of dialectical contradiction, four pedagogical inventions were made in the fields "General Philosophy Issues" and "General Pedagogy", marked by the diplomas of the winner and laureate of All-Russian Contests of Pedagogical Inventions and Innovative Educational Technologies "Modern School" (2015-2018). This idea of dialectical contradiction was defended by the author at the Moscow State University Academic Council on February 9, 1990. The author's works on this issue have been published since 1983. They are implemented in the fields: dialectical logic of scientific discovery, evolutionary theory, inventive tasks solution theory, rhetoric and theory of literary style, TRIZ-pedagogy.
3.1. The self-referent discovery of the way discoveries themselves are made begins with the formulation of 1) a heuristic question that is exacerbated to the extent of 2) a contradiction pointing to its own 3) solution showing, at the limits of its capabilities, 4) a problem that can be posed, but cannot be solved within these limits.
The subject of philosophy. 1) What cannot become of itself without man's effort in this world? 2) The contradiction between freedom and reality: everything, that is real, is not free, but everything free is not real, whereas philosophy needs such laws that exist in reality and are released in their action from insurmountable restrictions. 3) Labor is a real solution to the contradiction between freedom (universality) and reality. 4) Mystery of personality.
The phenomenon of a human being. 1) How can an imperfect and at the same time a free being exist? 2) A free and perfect being would not have internal conflict with himself, but a human is both imperfect and free. 3) The key to explaining the structure of the human body is the study of nature evolution as self-development of its contradiction: natural systems become more complex on the basis of their own random variability, but the more complex the system, the greater is the probability of its self-destruction due to random variability. Sooner or later the result of nature progressive evolution comes into conflict with its own basis, so that this conflict can be resolved only by the "blockade" of that part of the genetic program that organizes pragmatic behavior. In this case, such living beings will have to create their own behavioral programs and in the unlimited complicating (development) of this artificial program they will not depend on random variability. 4) We explained the structure of the human body, but not a human himself. A human differs from his own body because he is inexplicable.
Ancient philosophy: the mind in the image and likeness of the human body 1) How are the parts and the living whole possible? 2) If the right to life of any natural part is less than the rights of the whole, then such a part perishes (and all the rest of the whole also perishes with it), and if the rights of some part exceed the rights of the rest of the whole, then such part supplants the diversity of other parts, leading the whole and itself to death. 3) The whole and each of its natural parts are possible only as equal to each other. 4) In view of the equality of the whole and each of its natural parts, each part tends to separate from the whole, until the body disintegrates into further indivisible components: living bodies live for the same reason they die. The same fate of "atomization" awaits civilization, which builds itself following the example of the body only.
Medieval philosophy: mind by conscience. 1) How to be according to conscience? 2) The world created by the perfect Master would look exactly like the one which was not created (both would not be able to "break"). 3) The idea of Revelation: people learn about the Author of the world existence to the same extent that they learn, that they are not surrounded just by other human bodies, but by individuals - to that extent they are frank with each other. 4) The unsolvable problem of medieval civilization was the unique character of chance and human individuality.
Philosophy of the Renaissance as an image of universal art. 1) How can each person's own dignity be possible? 2) Human dignity is impossible without freedom, but it is impossible only in freedom, since one is free just like any other, and this overall interchangeability of people excludes the dignity of each person. 3) To be real means to be infinitely unique. 4) An infinite ability to create something new - genius is possible only on the basis of one's own individual uniqueness of the person, but individual uniqueness and talent based on it can not be conveyed as a certain experience of creativity to the next generations.
Modern times philosophy as an experimental-mathematical science of the 17th century. 1) How is it possible to discover new knowledge continuously? 2) Only the repetition of the same can be continuous, and something new arises in an accidental, inimitable way through the interruption of continuously acting regularity, but if something new arises in an unrepeatably random manner, then, once it arises, it disappears forever for all that follows. It is necessary to create a way of interconversion of continuity and emergence of something new. 3) An experiment is practical experience with controlled conditions isolated from the outside world, which is conducted to obtain unpredictable, new facts. On the basis of complete controllability of such experiment conditions, one can repeat once-accidentally obtained new result many times. 4) The experimenter can cognize everything, but not himself.
Science as a continuous production of new knowledge is impossible without the mass attraction of people with equal rights. But how can equality be possible?
The Enlightenment Age philosophy as the universal pedagogy of the 18th century. 1) Is a human worthy by nature of any rights, and if he is worthy, what are they? 2) A human is kind by nature, but acts against his own nature. 3) A human, unlike a beast, does not have innate knowledge of his nature, so he acts against it. Only by enlightening people about their own good nature one can nonviolently correct their morals in accordance with their own nature. 4) Blind faith in the unlimited opportunities of science and enlightenment is not scientific and unreasonable.
German classical philosophy as a study of the very ability to scientific research: Kant, Fichte, Schelling, Hegel.
Kant 1) How are infinite and at the same time true generalizations possible? 2) Beyond science, all infinite generalizations are false, and all true generalizations are limited. 3) Science studies not so much the results of human experience as prerequisites that make human experience itself possible, therefore all objects that might contradict scientific generalizations go beyond the limits of human capabilities to have any experience concerning them. 4) Things exist independently of us insofar as we do not know anything about them. Objective things exist by themselves, but it is impossible to have knowledge and idea about them.
Fichte 1) How is it possible to have the subjective image of something that is independent of consciousness? 2) An image of the object should reflect such property of the object as the property to be independent of consciousness, and also, like the object itself, it should not depend on consciousness, but the image itself is the result of subjective activity. 3) Subjective images of things are the results of unconscious creativity that do not depend on consciousness, therefore subjective images can model the basic property of objective reality. 4) Creativity itself is not clear: unconscious creativity cannot cognize itself, because it is unconscious, and consciousness cannot cognize creativity because consciousness is not capable of creativity.
Schelling 1) How is something eternally and continuously new possible? 2) On the one hand, something new can only arise chaotically and through violation of the existing order, and on the other hand, this something new needs order, so that having arisen once, to exist forever. This makes us think that 3) the unity and struggle of equal opposites is the
working reason for its own continuous self-renewal. 4) In the traditional formal two-valued logic, it is forbidden to express a contradiction in the form of concepts. Schelling refused to reform logic, therefore he considered contradiction and development fundamentally incomprehensible to science.
Hegel 1) Why is something new simply cannot not help but arise continuously? 2) According to the plan, the contradiction is the reason for the development of itself and everything else, therefore the problem of contradiction and its solution must be stated in the form of contradiction itself. On the one hand, we have to recognize the contradiction as unsolvable - it is incapable of disappearing eternal reason for the emergence of everything new, and on the other, just the same hand, we have to include uncontradictoriness in the contradiction itself (because it is unity and struggle of opposites), presenting it as disappearing in itself. 3) The mode of contradiction existence is not a state of equilibrium, but a process of continuous generation of ever new forms of its resolution, when the contradiction is resolved (disappears), but arises again at a higher level and in a more acute form. 4) That unequally distributed social practice, which Hegel considered to be the criterion of truth, needed its correction, because it spoiled the human essence.
Philosophy of Marx's creative practice 1) How can we build a social order that does not divide people into lower and upper classes? 2) On the one hand, the essence of a human is the whole complex of all social relations, and on the other hand, a human differs substantially from a social animal by the fact that he separates and distinguishes himself from the system of all social relations: he is not this social system. 3) In creative practice, people create themselves and their consciousness in the same way as they simultaneously create their external material circumstances. 4) It is impossible to plan the production of such a fair form of communication as conscience and talent.
Modern philosophy of equitably ordered communication as text philosophy 1) How is possible an order without domination and subordination? 2) Order and equality exclude each other and, at the same time, are impossible without each other. 3) An indicative example of this contradiction resolution is the Russian language, which includes both subordination of all communicative and semantic elements and all means of overcoming this subordination without losing its own harmony. 4) The drawback of this example is its limitedness to only one area: we speak and write only from time to time, and we live almost continuously in a society that is arranged as an irony over our own language.
Social Philosophy: 1) In response to what question does the society itself meet the questioner as an unexpectedly new and, at the same time, clearly accurate discovery? -In response to the question: "How can an imperfect and, at the same time, a free being exist?" 2) The contradiction between social security and economic efficiency is formulated in the form of two technical contradictions. 3) It is solved according to the algorithm of inventor with the transformation of TRIZ pedagogical system. 4) The theoretically unsolvable problem (but practically solved inventive task) of society is the problem of its unity.
3.2. Correspondence of seven elementary rhetorical parameters (tropes of usual words meaning rethinking) of creative thinking to the degrees of its categorical forms development freedom
With regard to the sequence of elementary rhetorical rethinking techniques according to classification by M.L. Gasparov (Gasparov, 2000), we must take here the advantage of self-referent description, when statements are good examples of what they report about. Irony is the first in the tropes sequence on rhetorical axis line of creative thinking: the shift of meaning to itself as the opposite to itself - self-irony, disintegrating into a number of its own adjacent to each other, complementary to each other and maximally differing particulars of metonymy - the shift of meaning due to adjacency (that
will unite any of the most remote opposites, since it is always possible to select such a vast class that all of them will be adjacent in it). Metonymy corresponds not only to pair antinomy (thesis-antithesis), but to the multipolar "polynomial folding" of D.B. Zilberman (Zilberman, 1998). This indefinite situation of multiplying neighboring "poles of equal forces" is solved by the interpretation of neighborhood adjacency as partial intersection, growing to the scale of the whole - metaphor, which, in its turn, intersects with synecdoche as the shift of meaning of the whole on its own part, but only in order to be assisted in the performance of a function beyond its power by a whole system of interrelated words of periphrasis, replacing the meaning of word that is released from the statement for a well-deserved rest. Finally, periphrasis, with its increasingly complex and detailed expression of released word meaning, exaggerating to huge hyperbole, takes risks to collapse and destroy it in a situation, where the more detailed and more thorough explanation is the less listeners and readers understand things they understood before this explanation. There comes the legitimate turn of meaning condensation through its narrowing - emphasis.
As you can see, all the other tropes can be reflected on each trope of rethinking, but this methodological case just represents the thinking world of rhetoric, fully reflected in its every detail, capable of working independently as a "technical system" of producing an undetermined yet possibility of meaning emergence. And now imagine, that a dialectical dimension is added to this yet one-dimensional and only potentially thinking world in the form of consecutive formulae of creative thinking (question-contradiction-solution-insolvability), resulting in the following table, which makes it possible for both the researcher and the student to design the semantic topology of their individual way of cognition.
TABLE 1. - CORRESPONDENCE OF SEVEN RHETORICAL PARAMETERS OF CREATIVE THINKING TO THE DEGREES OF ITS CATEGORICAL FORMS DEVELOPMENT FREEDOM
Category Heuristic question Dialectical contradiction Contradiction solution Insolvability
Parameter
Irony How is the question possible? Denialism Self-denialism paradox solution in multiciphered logic How to solve self-denialism paradox in the framework of two-valued logic?
Metonymy What question neighbors with all others? Complementarity Universalization of overall complementarity principle. Impossibility to determine measure in the framework of complementarity poles multiplication
Metaphor What question is its own answer at the same time? Withdrawal The system produces conditions for the unlimited activity of each of its individual prerequisites. The problem of order without subordination and without crisis at the same time.
Synecdoche What does this very «what?» mean? Supposing Interaction of the prerequisites leads to the emergence of a self-reproducing system. The unique randomness of any regularity emergence circumstances.
Periphrasis The question of what words replace the question mark itself Supposition The prerequisites of the system are produced by it as its results in the cycle. The cycle cannot be completely closed.
Hyperbole What is less than Nothing itself? Extraneousness The unique character of individuality. Irreplaceable incompleteness of any individuality
Emphasis How is questioner possible? Insolvability of individuality Development of the law of development. Anti-emphasis as the meaning of silence.
3.3. Pedagogical realization of alternative idea of contradiction in the form of the creative seminar block structure on the topic "Dialectical contradiction" (based on the system of continuous creative thinking formation by M.M. Zinovkina)
Block 1. Motivation
The principle of denialism, as opposed to denial implies a more organic form of its introduction into the educational process than formal, precise and shocking self-referral negative statements like the following: [This sentence, taken in square brackets, is impossible]. Meanwhile, you can find the relevant facts for such statements. M.K. Mamardashvili revealed philosophy as a fact, showing its own impossibility, and overcoming all the conditions of its own impossibility at the same time (Mamardashvili, 2000).
The meaning of denialism opens with the question of how the question and the questioner himself can be possible. From the philosophical question of how emergence of something new is possible, and the question of why something new cannot help but emerge, we should go further to inventive problem: what must be done to ensure that it would be impossible to stop creating something new.
Block 2. The first content part
It is advisable to reveal complementarity, which makes up the content of the second block, through examples which show how the sense emerges in the mutual reflection of two opposite sides to each other (K.Godel turned negative self-referral proposition into constructive principle of proof thanks to mutual transformation of propositional calculus logic and arithmetic computations). Complementarity is revealed more fully in the fact of the universe singular beginning origin as a result of the interaction of two spheres of being opposite in phase of physical processes, taking place in them.
Block 3. Psychological relaxation
Relaxation block corresponds to such a parameter of opposites' interaction as withdrawal by emerging system of few prerequisites limitedness of its emergence, which was characteristic to the stage of pre-systemic isolation. This is most easily verified in familiar meanings of words rethinking game, using the ancient system of elementary methods of rethinking (from irony to periphrasis).
Block 4. Puzzles
Supposing interconnection by unique isolated elements of the system is modeled by obvious self-referencing judgments of L. Henkin, asserting their own provability and representing their own proof or instructions for proving themselves (Hofstadter, 2001; Podnieks, 1992). [This sentence, stating that it is possible, is proved by its direct reading].
For all its ineradicable self-affirmation, supposing is one of the parameters of non-equilibrium opposites' interaction and has the fourth degree of the original self-denialism modification. [This sentence, stating that it is impossible and self-denying at the same time, is proved by its direct reading].
Block 5. Intellectual warming-up
This block corresponds to supposition, but if we used this term in its objective meaning in the construction of reflective definitions of opposites' interaction, then in this
case supposition means creation of a number of alternative hypotheses at the initial stage of discovery and cognition due to the existence of science as a system generating new knowledge. We exercise in creating alternative hypotheses about how and why it is possible to create many new alternative hypotheses about the same thing. In spite of all self-referencing, this will not become a self-isolated circle, since we speak about an open, non-equilibrium self-organizing structure.
Block 6. The second content part
Corresponds to extraneousness as a parameter of opposites' interaction. Its physical meaning is revealed: two opposite spheres of existence, the interaction of which led to the emergence of the universe, are beyond its borders, neighboring with it and influencing it - they change the direction of their impact on the world's three-dimensional surface of the universe, as a result of which "folds" appear on it in the form of virtual, short-lived particles, quantum strings (Klyagin, 2011). Extraneousness is expressed in the form of non-obvious judgments of Henkin, which contain only an indication of the possibility of their own proof, realized only through the use of the super system (in relation to the judgment itself as a system). [This sentence, stating that an infinite number of irreducible to each other types of singularities arises starting with only seven parameters in the task of finding extrema of functions, is provable by methods of differentiable reflections singularities theory].
Block 7. Computer intellectual support of thinking
This unit organically contributes to revealing of the productive meaning of each individuality insolvability with respect to any equilibrium closed system. It is carried out by the programs "Algorithm of the inventor" (AlgMIP) and "Determinator of the search for basic methods" (TabDtmr). The search is conducted until finding such technical contradiction (from the inventive task) for which the "Search Determinator" program issues "No method" and from which the individual creative search for the solution begins.
Block 8. Summary
Invite the students to check themselves the idea of seven-parameter contradiction as a result of attempts to create the maximum number of all possible irreducible to each other summaries of the seminar, assuming different numbers of its blocks:
At the end of the seminar, the task is given to find, by the "Algorithm of Creativity", a variant of solving the problem of dialectical contradiction using compulsory and additional sources of information on dialectics.
Thus, the reflection of self-referral non-equilibrium open structure of the creative seminar, consisting of seven main blocks, leads to the realization of the infinity of the number of irreducible possibilities for personal development. The irreducibility of individualities to each other only makes them essential for each other: an individually unsolvable problem of one is a completely solvable task for another (and vice versa).
4. Conclusion
The novelty of the proposed solution to the problem of dialectical contradiction is a consequence of its new posing: so far no one has set a goal to re-invent this very form of inventive task and creative thinking. Category of dialectical contradiction was used only in the final and unchanged form taken from traditional dialectics, as a form of inventive (creative) tasks posing. The main "tool" of creativity did not become the object and purpose of creativity. In addition, the formal report about own form of creative thinking diverged substantially from its actual form, acting unconsciously, accidentally and rarely.
And if excessive attention was given to the opposite parts, no attention at all was given to the simultaneous ways (parameters, degrees of freedom) of interaction between them.
Rationale of two opposites' seven-parameter interaction is brought to the stage of exact proof through establishing semantic isomorphism of philosophical problem, underlying cause of potentially infinite development and mathematical minimax problem for a given number of initial parameters. And if it is still possible to ignore both theoretical and empirical evidences from different areas of the humanities and the natural sciences, relating them to unimportant specifics of random empirical particulars conditional description, one cannot dispute the mathematical proof as well as isomorphism of philosophical and mathematical problems any longer, one cannot be able to notice it.
The new idea of dialectical contradiction proposed and substantiated in this paper is the third, along with the traditional category of contradiction and its understanding in the concept of multipolarity.
Further promising works in this direction are related to its moderate (partial) formalization and the use of "multidimensional logic" idea by N.A. Vasiliev (Vasiliev, 1989).
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