Semantic uncertainty of the general theory of systems and problems of its interpretation and formalization

Gribkov Andrei Armovich ORCID: 0000-0002-9734-105X Doctor of Technical Science Senior Researcher, Scientific and Production Complex "Technological Center" 124498, Russia, Moscow, Zelenograd, Shokin Square, 1, building 7 andarmo@yandex.ru Other publications by this author

Introduction

The desire to formalize the general theory of systems and turn it into a language for describing systems of any nature with unambiguously defined lexical units and rules initiated the creation of a significant number of applied versions of the general theory of systems (OTS). Among the most developed applied general theories of systems characterized by a high level of formalization should be attributed to A.A. Bogdanov's tectology ^[1], M.D. Mesarovich's mathematical general theory of systems ^[2], A.I. Uemov's general theory of systems ^[3], etc. 

Despite the indisputable advantages of such theories, they have not been widely disseminated and applied. The main reason for this is the inability to ensure the integrity of the system representation on the basis of such general theories of systems. As you know, the central idea of the general theory of systems is the isomorphism of forms and processes in the universe, which is an empirical confirmation of the integrity of the world. Therefore, it is the integrity of the formed model of being that is the task of the general theory of systems. On the basis of formalized (including mathematical) general theories of systems, it is impossible to ensure this integrity.

How do formalization and mathematization interfere with the holistic representation of the universe? Why does the natural human language (supplemented in some cases by the formalized language of science) cope with this task better? Confirmation of the possibilities of natural language as the main tool of human thinking is a huge array of discoveries, creative achievements born of intuition, fueled by the unity of the world, which finds its manifestation in isomorphisms, in analogies, and sometimes formalized through tradition.

The human language is not a random set of lexical units and rules, but a dynamic system that has developed and adapted to solving problems of optimal communication between people and reliable reflection of reality. Both of these tasks, considered within the framework of the knowledge system, are solved on the basis of the use of generalized concepts, qualitative descriptions, complexes of essential features for the identification of the object of cognition, etc., i.e. through semantically indefinite lexical units. Note that when we talk about "indefinite" lexical units, we mean their ambiguity, sometimes "vagueness".

Many leading researchers in the field of general systems theory believed that this theory could not be considered as part of philosophy. In particular, A.A. Bogdanov wrote "... I would doubt whether it is advisable to apply the name "philosophy" to organizational science ..." ^{[1, book 1, p. 57]}. For A.A. Bogdanov's general theory of systems (general organizational science or tectology) and a large number of other versions of the general theory of systems, this assessment probably has a right to exist. However, according to the author, this assessment is not a qualification of the essence of general system theories, but a statement of their incompleteness and incompleteness, which results in limited possibilities and, as a consequence, practical application. These incompleteness and incompleteness can be overcome by including an ontological component in the general theory of systems, which substantiates the genesis of the integrity of the universe and thereby provides the philosophical basis of the theory. The author is working on creating such a version of the general theory of systems (empirical-metaphysical general theory of systems ^[4]). As a result, a theory will be formed that is fully philosophical.

Formal philosophy is a direction that has been successfully developing since the beginning of the XX century (the works of D. Hilbert ^[5] and R. Carnap ^[6]) to the present time. At the same time, formal philosophy does not pretend to solve philosophical problems, its purpose is exclusively auxiliary: "... to clarify and clarify theses, accelerate the correction and improvement of philosophical and scientific theories, work more effectively with natural language intuitions, analyze the consequences of accepted hypotheses" ^[7]. Similarly, mathematical (formalized) general theories of systems can be useful in solving individual particular problems, but the whole variety of problems of cognition of the world (many of which are formulated with significant uncertainty, and this is normal for cognition) is not covered by available tools and methods.

In the framework of this study, we will try to answer the question about the possibility of formalization of the general theory of systems, as well as about the objective reasons that prevent formalization. To answer this question, we will consider the phenomenon of semantic indeterminacy of languages, as well as its use to expand the cognitive capabilities of the general theory of systems.

Semantic uncertainty of languages

The system of knowledge about the world is a model of being formed through all the tools of cognition available to mankind, among which one of the most important is the natural human language (a set of languages of different peoples, as well as the language of science common to all peoples). By necessity, the human language has been formalized to a certain extent – for each of the languages, a vocabulary and a set of rules for the formation and use of lexical units have been formed, as well as their semantics have been determined. At the same time, in order for a language to fulfill its function as an instrument of cognition, the lexical units used in it (words, phrases, established phrases, etc.) must have the ability to be used to describe objects of cognition of different nature. In practice, this ability is realized in the simplest way – due to semantic uncertainty ^[8].

The phenomenon of semantic uncertainty can take various forms, among which, in particular, are distinguished ^[9]: pragmatic uncertainty of language expression, according to which a decrease in the accuracy of expressions encourages communicants to more creative thinking and "completing cognitive gaps", as well as referential diffuseness, which consists in pointing through language expressions to a wide class of events or phenomena, the boundaries between which are not clearly defined.

Semantic uncertainty is based on the ambiguity of lexical units. The certainty of their content in practical use is ensured due to the context and nature of the relationship of lexical units ^[10]. The variability of the relationship of lexical units forms by means of language patterns of form or relations that characterize the described object of cognition. In this case, the identification of the object of cognition (or its properties) is carried out by comparing it with the corresponding pattern (template of forms or relationships). Thus, the ambiguity of lexical units ensures the universality of the means of description, and identification by the corresponding pattern (taking into account the context) ensures the consistency of the description.   

The futility of improving the accuracy and logical certainty of the language is well illustrated by the Ithkuil language ^[11], developed by the American linguist John Quijada. In this language, any ambiguity is excluded. The language is characterized by the highest phonetic complexity (45 consonants, 13 vowels in 7 tones).  There are two parts of speech in the language: word-forming and adjuncts (defining). The first ones change according to 9 configurations, 4 accessories, 4 perspectives, 6 extensions, 2 entities, 4 contexts and 2 assignments. The latter are inclined into 22 morphological categories. There are 98 cases in Ithkuil. In addition, suffixes clarifying the meaning can be added to any word (a total of 1800 different suffixes), including 14 valence suffixes, 32 aspect suffixes, 24 emotional color suffixes. The practical use of the Ithkuil language is extremely difficult. A significant part of the statements (if there is some uncertainty, ambiguity in them) is impossible in it, and those that are possible are formulated much more difficult than in ordinary language. Initially, when creating this language, it was assumed that it would allow you to express thoughts faster than ordinary languages, but this hope was not fulfilled.

Can the Ithkuil language and similar logical languages be useful? Absolutely, yes. However, their use is limited to the formalization of existing knowledge, as well as their archiving. For creativity, the usual content of which is the search for answers to finally unformed questions that are clarified in the process of cognition, such languages are completely unsuitable.

Quoting out of context

The experience of scientific activity, involving the preparation of publications containing references and citations of other researchers in this field, shows that quite often references and citations are used out of context, as a result of which their meaning is distorted, interpreted, and sometimes even distorted. To the greatest extent, this tendency of quoting out of context is inherent in philosophical and other poorly formalized sciences. Along with quoting out of context, there is also another related phenomenon – the use (acceptance, statement) of conclusions formulated within another context, without confirming their argumentation (conclusion, proof). In the future, by "quoting out of context" we will mean both of these phenomena.

One of the most obvious examples of "quoting out of context" is the correlation of the laws of development in dialectical materialism and Hegel's philosophy ^{[12, p. 40]}. Dialectical materialism borrows from Hegel's philosophy the laws of dialectics, deduced and reasoned in the logic of objective idealism, and transfers them into a materialistic context incompatible with idealism. At the same time, there is no new proof of the validity of the laws of dialectics, they are accepted "as is", without adjustments, with only some semantic interpretations. The question of why, nevertheless, the laws of dialectics (or, to put it more correctly in terms of materialistic ideas, the laws of development) are relevant deserves attention and will be considered further in this article.

Another example of "quoting out of context" is A. Einstein's formulation of the "Mach principle": "... the cause of inertia is the interaction of a material point with all other masses..." ^[13]. A. Einstein believed that in his formulation he expresses E. Mach's ideas about relative inertia, while the coincidence in Einstein's judgments and Mach on this issue exists only at the level of terminology. Speaking about inertia, each of them meant different physical phenomena by this: Einstein meant inertial mass of a body by inertia, and Max – inertial motion ^[14].

As an example of accepting conclusions without confirming their argumentation, one can cite the discreteness of being claimed by Plato and Aristotle, which is due to its definiteness and completeness. And it is impossible not to agree with this statement (including the materialist). At the same time, it must be remembered that Plato and Aristotle were objective idealists and by being they understood the world of ideas (forms), and not matter at all. The material world (matter), in their opinion, is becoming, i.e. it is on the eternal path to being. The world of things and bodies, in their opinion, is infinite, continuous, and therefore it is not being.

The practice of "quoting out of context" at first glance seems to be an extremely destructive phenomenon that calls into question the reliability of the knowledge obtained. But then why don't they give it up? Because to a greater or lesser extent, no scientific work is free from this practice. Indeed, only in some rare cases, subsequent scientific or philosophical research can fully rely on the previous ones, without correcting the interpretation of concepts and connections between them in them. Moreover, in those rare cases when such an adjustment does not occur, the scientific value of the work usually turns out to be low.

And there is nothing strange in this, since the formation of new knowledge is a creative process, the distinctive feature of which is the impossibility of determining the result before it is obtained. A scientist cannot know for sure what his research will lead to. And even when a scientist completes his research, the continuation of this research by other scientists will again face the lack of reliable knowledge of the expected result. Since every result of cognition is formalized in the form of concepts, the process of knowledge formation must inevitably be accompanied either by the introduction of new concepts, or (in most cases) a change in the interpretation of existing concepts.

The experience of scientific and philosophical knowledge clearly testifies to the right of the practice of "quoting out of context" to exist. According to the author, this is due to the existence of isomorphism of forms and laws in the world, manifested in all objects of cognition, including lexical constructions of various levels of complexity, which are descriptions of the relations of objects and processes in the universe. And at the same time, it is not always important in what context these lexical constructions were formed – there is a kind of equifinality ^{[15, p. 132]} in the formation of forms and connections that fit into limited sets of patterns. 

The equifinality of forms and connections corresponding to lexical constructions is due to the fact that these constructions in most cases represent open models of being. By "open" we mean models that turn out to be applicable outside the field of cognition, based on the data on which the model was created ^[16].

In this case, we do not consider the reliability of the model, only the ability to predict new (not embedded in the model) connections in the universe on its basis is important. The experience of cognition accumulated in the form of a human knowledge system clearly demonstrates that even erroneous theories (ideas, concepts) can serve to expand knowledge, find the right answers to the riddles of nature, which can be verified and clarified in the future ^[16]. Along with private scientific theories that have made a significant contribution to the development of knowledge, but were later rejected (phlogiston, hydrogen, ether, etc.), religion can also be cited as an example, which fundamentally contradicts scientific ideas, but is nevertheless relevant in terms of social and spiritual issues. 

So, the practice of "quoting out of context" and similar phenomena are permissible in cognition. At the same time, it is necessary to understand that such practice is appropriate at the stage of searching for answers, but not their argumentation and proof. The unity of the world, manifested in the form of similarity of forms and laws, equifinality of forms and connections (including in relation to lexical units), gives us an instrument of isomorphism, analogies, and deduction, through which we get "hints" about the structure of the world. These "hints", however, can only indicate the likely direction or area of the search, but do not guarantee correct answers.  

Requirements for the language of general systems theory

Determining the probable directions or areas of search for answers to questions about the structure of the universe based on isomorphism and the patterns of forms and relationships that follow from it is the main task of the general theory of systems ^[4]. Therefore, for the general theory of systems, the semantic uncertainty of language and the practice of quoting out of context are natural and organic phenomena. Naturally, as the general theory of systems develops, the language used in it can evolve, in particular, be supplemented with universal concepts corresponding to the system description. At the same time, its rigid formalization is impossible, since it would entail the complete loss of its functionality by the general theory of systems.   

The impossibility of full formalization of the general theory of systems is not a reason for refusing to formalize its individual components. One of the areas where formalization is necessary and possible is the methodology of applied system analysis. At the same time, it is necessary to understand that in this case formalization is carried out within the framework of the theory of knowledge – at the level of universal and generalized concepts, the genesis and inner content of which is either not disclosed or unknown. As a result, such generalized and formalized concepts have internal semantic uncertainty in the sense that, using them, we only roughly understand what they mean, and rarely have an idea of their ontological genesis (if they have one at all).

As an example of formalization in applied system analysis, we can cite the division of ways to solve problems into four options ^{[17, p. 13-15]}: non-interference (in the expectation that the natural course of events will lead to the resolution of the problem), partial intervention (a solution that reduces dissatisfaction, weakens the severity of the problem, but does not eliminate it completely), the optimal solution (the solution that is the best in these conditions based on the existing limitations and alternatives) and dissolution (a solution that ends with the complete disappearance of the problem and prevents the emergence of new problems). Within the framework of this classification, solutions to problems seem to be formalized, but there are many details within each of the options that need to be clarified in terms of content and implementation mechanisms.

Another area of necessary and possible formalization of the general theory of systems, which should become an integral part of the general theory of systems (at least the author in his empirical-metaphysical general theory of systems strives for this) is the ontological part of the theory – the metaphysics of material being, which determines the primary properties of being and the laws logically following from them ^[18]. For such properties and laws, formalization is possible and necessary, which does not imply ambiguity and semantic uncertainty. These properties and laws are not only used for cognition and description of the world, but are also the basis for the formation of the methodology of cognition within the framework of the general theory of systems.

Semantic uncertainty in the formation of the ontological basis of the general theory of systems is unacceptable for two reasons. Firstly, the area where it realizes its usefulness is the theory of cognition. Ontology serves to comprehend reality as it is, and not our ideas about it or methods of its representation in the knowledge system, and therefore does not need semantic uncertainty. Secondly, one of the tasks of forming the ontological basis of the general theory of systems (the author calls it the metaphysics of material existence) is the consistent determination on the basis of the primary properties of being (i.e. a priori knowledge) of the laws and forms logically following from them, which in the future can be used as patterns for the analysis of nondeterministic complex objects of cognition. The construction of reliable logical chains, the elements of which have semantic uncertainty, is extremely difficult because in the process of their construction, the options will multiply, going beyond the limits of the practical availability of their critical analysis.

The general attitude of the general theory of systems, conditioned by the requirement to preserve its functionality, is to preserve the natural uncertainty inherent in human languages, allowing for ambiguity, changing depending on the context, but providing flexibility and the possibility of describing objects of cognition at the stage of their incomplete certainty.

How can this general attitude be combined with the formalizations of the general theory of systems? This task is completely unsolvable, but it is possible to increase the degree of formalization of the general theory of systems. Formalization will not reduce the epistemological possibilities of the general theory of systems in the case of translation of semantic uncertainty into universality and generality of concepts. At the same time, it is necessary to understand that for a significant part of the concepts used in the practice of cognition (including with the help of the general theory of systems), such a translation is impossible. Therefore, the general theory of systems should preserve the semantic uncertainty of concepts, forms and connections in the arsenal of its tools.

Conclusions

Based on the reflections given in the article , the following main conclusions can be drawn:

1. The experience of creating formalized general theories of systems shows that such theories are not widely used and do not provide coverage of the entire problem of system description of objects of knowledge.

2. The limitation of formalized (mathematized) general theories of systems is due to the fact that in reality the general theory of systems cannot be exclusively an applied theory, but must be supplemented with an ontological component. In this case, the general theory of systems becomes a philosophical theory for which complete formalization is impossible without loss of functionality.

3. A necessary property of language as a tool of communication and cognition is its semantic ambiguity, which provides flexibility of the lexical constructions formed due to the ambiguity of lexical units. The certainty of their content in practical use is ensured due to the context and nature of the relationship of lexical units.

4. The practice of quoting out of context and the use (acceptance, statement) of conclusions formulated within another context without confirmation of their argumentation (conclusion, proof) is a phenomenon whose permissibility is due to the creative nature of the cognitive process in which the result of cognition is unknown in advance. As a result, the content of the concepts through which the results of cognition are formalized change their interpretation as knowledge expands. In addition, the existence of isomorphism of forms and laws in the world, manifested in all objects of cognition, including lexical constructions of various levels of complexity, makes these constructions elements of the knowledge system and allows us to consider them in isolation from the context of their formation.

5. The language of the general theory of systems, which, as we have established, should become part of philosophy, cannot be fully formalized. At the same time, the formalization of individual components of the general theory of systems is possible and even necessary. In particular, according to the author, it is necessary to formalize its ontological component – the metaphysics of material existence, which, along with practical application in cognition, also serves to define the internal logic of the general theory of systems itself.