Incommensurable theories. Growth of scientific knowledge

INCOMmensurability of theories(in the philosophy of science) - the thesis according to which it is impossible to determine rational criteria for comparing, comparing different theories related to the same empirical field. The concept of incommensurability is borrowed from Greek mathematics, where it meant the absence of a common measure. Segments of a certain length were considered commensurable if there is a certain common measure of their comparison. Not all segments are commensurate: the diagonal of a square is incommensurable with its side. In the philosophy of science, the concept of incommensurability of theories was introduced at the beginning. 70s T. Kuhn and P. Feyerabend. The authors of the thesis about the incommensurability of theories drew attention to the fact that successive fundamental scientific theories, describing the same range of empirical data, proceed from different ontological assumptions, operate with the same name, but different in meaning, concepts, put at the center of research activity different problems. At the same time, adherents of the old and new paradigms use different criteria for evaluating and selecting theories (these criteria turn out to be paradigmally dependent), which raises the question: is it possible (and if so, how) to compare and choose between theories?

Two formulations of the thesis about the incommensurability of theories that differ in strength and content (respectively, TH1 and TH2) can be distinguished. According to TH1, there is no common basis for comparing them that is preserved during the transition from one theory to another. According to TH2, there are no absolute estimates on the basis of which one could make an unambiguous choice between theories.

TN1 is based on the belief that traditional philosophy of science ideas about comparing successive theories are simplified and do not correspond to real scientific practice. The "traditional" ideas about comparing theories were as follows. Let there be two competing theories T1 and T2. From T1 follows E1, from T2 - E2, where E1 and E2 are consequences of theories T1 and T2. Let it be possible to carry out an experiment confirming E1 and not confirming E2. Based on the result of this experiment, T1 is considered to be correct and T2 is not correct, and the former is preferred.

Proponents of TH1 argue that traditional beliefs are based on two incorrect assumptions. One of them consists in the assumption that the meaning of the terms common to two theories is preserved when passing from one theory to another. The other consists in the assumption that there exists, if not theoretically free, then at least a language of observation that is neutral with respect to the theories being compared.

Rejecting the first assumption, TN1 supporters argue that the meaning of terms does not remain unchanged when fundamental theories change. At the same time, they refer to such examples as changing the meaning of the concepts "mass", "length", "time interval", etc. during the transition from classical mechanics to the special theory of relativity (SRT) or a change in the meaning of such fundamental concepts of classical physics as "coordinate", "momentum", etc., during the transition to quantum. In SRT, the concept of mass acquires a property that the corresponding concept did not have in classical physics: dependence on velocity; the concepts of position and momentum in quantum mechanics are so different from the concepts of the same name in classical mechanics that they can be consistently applied only in an additional way.

Changing the meaning of concepts gives rise to problems of two kinds. One of them belongs to the field of psychology of science. The non-invariance of the meaning of the same (by name) terms makes it difficult to understand between adherents of different paradigms, and therefore the question of communication between them becomes non-trivial. Another problem is epistemological and concerns the comparison of theories, the impossibility of which is precisely stated in TN1. Many researchers have noted, however, that contrary to the opinion of TN1 supporters, the change in the meaning of concepts is not an obstacle to comparing theories. If, following G. Frege, a distinction is made between the meaning (intensionality) and referentiality (extensionality) of a term, the problem becomes solvable. In establishing the relation of contradiction between the consequences of theories, which is required for the choice between theories, the stability of meaning is not necessary. If two theories have overlapping areas of applicability (in the case of two successive theories, this condition is satisfied), then, despite the change in the meaning of common terms, the consequences of these theories can be compared due to the fact that the terms have a common referentiality. Another difficulty is the absence of a language of observation neutral with respect to successive theories, which is really real in connection with the fact that these theories are used in the interpretation of the experimental result, which is intended to play the role of a test in relation to them. In a number of works, however, it was shown that in cognition there is a layer of empirical data, which, being theoretically loaded, nevertheless turns out to be neutral with respect to the compared theories, since other theories different from the compared theories participate in its interpretation. It is capable of playing the role of a language of observation that is neutral with respect to the theories being compared.

Thus, TH1 is too strong to correspond to the real process of cognition. Contrary to the assertions of the supporters of TN1, it is possible to compare theories already on an experimental basis. The incompleteness and ambiguity of such a comparison is partly compensated by the use of various non-empirical considerations, for example. comparative simplicity or various aesthetic considerations.

TH2 is a weaker version of TH1: the existence of only absolute criteria and evaluations is denied. And if TH1 is inadequate to scientific practice, then ΤΗ2 is justified with some reservations: there really are no absolute criteria and evaluations of theories. It makes no sense to raise the question which of the successive theories is "better", if we use this word in the sense of a greater correspondence of the "best" theory to some abstract, ahistorical standard for evaluating theories. The new theory is a more in-depth, accurate and specialized reconstruction of reality, and with this in mind, one can speak of progress in the development of scientific knowledge. But, remaining within the framework of scientific knowledge itself, it is impossible to indicate an unambiguous criterion of progress - for this, it is necessary to enter the area of the relationship between theories and practical activities of people taken in their historical development.

Supporters of the thesis about the incommensurability of theories consider not only TH2, but also TH1 to be fair. Characteristic in this regard is the position of P. Feyerabend. Recognition as a fair TH1 serves as a basis for him to search for non-empirical standards for evaluating theories. P. Feyrabend points to a number of formal and informal criteria for comparing theories. However, he believes that these claims are largely subjective. Asserting on this basis the inevitability of the transformation of the evaluation and selection of theories from a routine procedure into a complex solution based on the struggle of opinions, preferences, etc., Feyerabend concludes that it is impossible to rationally reconstruct the process of changing fundamental scientific theories. In modern literature, this conclusion is subjected to thorough criticism.

Literature:

1. Kuhn T. The structure of scientific revolutions. M., 1975;

2. Porus V.N. Actual problems of the analysis of "scientific revolutions". - In the book: Analytical reviews of foreign literature. M., 1983, p. 7–40;

3. Feyerabend P.K. Explanation, Reduction and Empiricism. – Minnesota Studies in the Philosophy of Science: Scientific Explanation, Space and Time. Minneapolis, 1962, vol. 3, p. 28–97;

4. Putnam H. Mind, Language and Reality. Philosophical Papers, vol. 2. Cambr., 1979.

INCOMmensurability of theories

INCOMMARIABILITY OF THEORIES (in the philosophy of science) - according to which it is impossible to determine rational criteria for comparing, comparing different theories related to the same empirical field. The concept of incommensurability is borrowed from Greek mathematics, where it meant the absence of a common measure. Segments of a certain length were considered commensurate if there is some common comparison between them. Not all segments are commensurate: the diagonal of a square is incommensurable with its side. In the philosophy of science, the incommensurability of theories was introduced at the beginning. 70s T. Kuhn and P. Feyerabend. The authors of the thesis about the incommensurability of theories drew attention to the fact that successive fundamental scientific theories, describing the same range of empirical data, proceed from different ontological assumptions, operate with the same name, but different in meaning, concepts, put different concepts at the center of research activity. Problems. At the same time, adherents of the old and new paradigms use different criteria for evaluating and selecting theories (these criteria turn out to be paradigmally dependent), which raises the question: is it possible (and if so, how) and the choice between theories?

Two formulations of the thesis about the incommensurability of theories that differ in strength and content (respectively, TH1 and TH2) can be distinguished. According to TH1, there is no common one that is preserved during the transition from one theory to the basis for their comparison. According to TH2, there are no absolute estimates on the basis of which one could make an unambiguous choice between theories.

TN1 is based on the fact that traditional philosophy of science ideas about comparing successive theories are simplified and do not correspond to real scientific practice. The “traditional” ideas about comparing theories were as follows. Let there be two competing theories T1 and T2. From T1 follows El, from T2 - E2, where El and E2 are consequences of theories T1 and T2. Let it be possible to implement , confirming El and not confirming E2. Based on the result of this experiment, T1 is considered to be correct and T2 is not correct, and the former is preferred.

Proponents of TH1 argue that traditional beliefs are based on two incorrect assumptions. One of them consists in the assumption that the terms common to two theories are preserved when passing from one theory to another. The other consists in the assumption that there exists, if not theoretically free, then at least neutral with respect to the theories of observation being compared.

Rejecting the first assumption, TN1 supporters argue that terms do not remain unchanged when fundamental theories change. At the same time, they refer to such examples as the meaning of the concepts “mass”, “length”, “time interval”, etc. in the transition from classical mechanics to the special theory of relativity (SRT) or the change in the meaning of such fundamental concepts of classical physics as “ coordinate”, “momentum”, etc., in the transition to quantum. In SRT, the concept of mass acquires such that the corresponding concept in classical physics did not have: from speed; the concepts of momentum in quantum mechanics are so different from the concepts of the same name in classical mechanics that they can be consistently applied only in an additional way.

Changing the meaning of concepts gives rise to problems of two kinds. One of them belongs to the field of psychology of science. The non-invariance of the meaning of the same (by name) terms makes it difficult for mutual understanding between adherents of different paradigms, and therefore communication between them becomes non-trivial. The other is epistemological and concerns the comparison of theories, which is exactly what TH1 asserts. Many researchers have noted, however, that contrary to the opinion of TN1 supporters, the change in the meaning of concepts is not an obstacle to comparing theories. If, following H. Frege, we draw between the meaning (intensionality) and the referentiality (extensionality) of a term, the problem becomes solvable. In establishing the relation of contradiction between the consequences of theories, which is required for the choice between theories, the stability of meaning is not necessary. If two theories have overlapping areas of applicability (in the case of two successive theories, this is true), then, despite the change in the meaning of common terms, the consequences of these theories can be compared due to the fact that the terms have a common referential. Another difficulty is the absence of a language of observation that is neutral with respect to successively changing each other theories - is really real in connection with the fact that these theories are used in the interpretation of the experimental result, which is called upon to play the role of a test in relation to them. In a number of works, however, it was shown that in cognition there is a layer of empirical data, which, being theoretically loaded, nevertheless turns out to be neutral with respect to the compared theories, since other theories different from the compared theories participate in its interpretation. It is capable of playing the role of a language of observation that is neutral with respect to the theories being compared.

Thus, TH1 is too strong to correspond to the real process of cognition. Contrary to the assertions of TN1 supporters, there are comparisons of theories already on experimental grounds. The incompleteness and ambiguity of such a comparison is partly compensated by the use of various non-empirical considerations, for example. comparative simplicity or various aesthetic considerations.

TH2 is a weaker version of TH1: only absolute criteria and ratings are denied. And if TH1 is inadequate to scientific practice, then TH2 is fair with some reservations: there really are no absolute criteria and evaluations of theories. It makes no sense to raise the question which of the successive theories is “better”, if we use this in the sense of a greater correspondence of the “best” theory to some abstract, ahistorical standard for evaluating theories. The new one is a more in-depth, accurate and specialized reconstruction of reality, and with this in mind, we can talk about progress in the development of scientific knowledge. But, remaining within the framework of scientific knowledge itself, it is impossible to indicate an unambiguous progress - this requires access to the area of the relationship between theories and practical activities of people taken in their historical development.

Supporters of the thesis about the incommensurability of theories consider not only TH2, but also TH1 to be fair. Characteristic in this poster is P. Feyerabekd. Recognition as a fair TH1 serves as a basis for him to search for non-empirical standards for evaluating theories. P. Feirabend points to a whole range of formal and informal criteria for comparing theories. However, he believes that these claims are largely subjective. Asserting on this basis the inevitability of the transformation of the evaluation and selection of theories from a general procedure into a complex procedure based on a struggle of opinions, preferences, etc., Feyerabend makes it impossible to rationally reconstruct the process of changing fundamental scientific theories. In modern literature, this is subjected to thorough criticism.

Lit .: Kun T. The structure of scientific revolutions. M., 1975; Porus V.N. Actual problems of the analysis of “scientific revolutions” .- In the book: Anali

tical reviews of foreign literature. M.,! 983, p. 7-40; Feyerabend P. K. Explanation, Reduction and Empiricipm.- Minnesota Studies in the Philosophy of Science: Scientific Explanation, Space and Time. Minneapolis, 1962, vol. 3, p. 28-97; Pumam H. Mind, Language and Reality. Philosophical Papers, vol. 2. Cambr., 1979.

E. A. Mamchur

New Philosophical Encyclopedia: In 4 vols. M.: Thought. Edited by V. S. Stepin. 2001 .

See what "INCOMMARIABILITY OF THEORIES" is in other dictionaries:

INCOMMENSURABILITY- (incommensurability) 1. A relationship between scientific theories in which their judgments and content in general cannot be directly compared. 2. The concept of scientific theories that all observations are theoretically relative... Big explanatory sociological dictionary

- (Greek geometria, from ge Earth and metreo I measure) a branch of mathematics that studies spatial relations and forms, as well as other relations and forms similar to spatial ones in their structure. The origin of the term "G. , what… … Great Soviet Encyclopedia

HUBNER Kurt- (b. 1921) German philosopher, representative of the pluralistic philosophy of science, specialist in the theories of myth and nation. His concept synthesizes a number of intentions coming from phenomenology, hermeneutics, existentialism, but mainly critically ... ... Sociology: Encyclopedia- (Feyerabend) Paul (Paul) Carl (1924-1994) American-Austrian philosopher and methodologist of science. A native of Vienna, he studied history, mathematics and astronomy at the University of Vienna, drama theory in Weimar. He began his scientific career in 1951, working in England ...

- (Feyerabend) Paul (Paul) Carl (1924-1994) American philosopher and methodologist of science. He began his scientific career in 1951, working in England, since 1958 in a number of North American universities and in the university centers of Western Europe. Main works: ... ... The latest philosophical dictionary

American-Austrian philosopher and methodologist of science. A native of Vienna, he studied history, mathematics and astronomy at the University of Vienna, drama theory in Weimar. He began his scientific career in 1951, working in England, since 1958 in a number of North American ... ... History of Philosophy: Encyclopedia

- - was born on May 26, 1799 in Moscow, on Nemetskaya Street in the house of Skvortsov; died January 29, 1837 in St. Petersburg. On his father's side, Pushkin belonged to an old noble family, descended, according to the genealogy, from a native "from ... ... Big biographical encyclopedia

- (born c. 490, Elea, Lower Italy - d. 430 BC) the first ancient Greek. philosopher who wrote prose works. and who used the methods of indirect evidence, for which he was called the "inventor of dialectics", became famous for his paradoxes. ... ... Philosophical Encyclopedia

Science is in a state of constant development. In the course of scientific knowledge, the totality of actual problems changes, new facts are discovered and introduced into consideration, old theories are discarded and more perfect ones are created. In the very philosophy and methodology of science there is a problem of dynamics. If in lane floor. XX century was dominated by problems associated with the logical analysis of the scientific language, the structure of the theory, the procedures of deductive and inductive inference, then from the second. floor. In the 20th century, a turn from logic to history becomes very noticeable. The dynamics of science, the laws and driving factors of its development, the problems of the relationship and commensurability of old and new theories, the relationship between conservatism and radicalism in science, the issues of rational overcoming of scientific disagreements and rational transition from one theoretical position to another - the object of the problem. Cumulative- the development of knowledge occurs through the gradual addition of new provisions to the accumulated amount of knowledge. Proponents of cumulative thinking represent the development of scientific knowledge as a simple gradual multiplication of the number of accumulated facts and an increase in the degree of generality of the laws established on this basis. The concept of Stephen Toulmin brings to the fore another type of organization of scientific thinking, based on understanding. Understanding is set by standards and problematic points. According to Toulmin, the scientist considers understandable those events or phenomena that correspond to the standards adopted by him. That which does not fit into the “matrix of understanding is considered an anomaly, the elimination of which (i.e., the improvement of understanding) acts as a stimulus for the evolution of science. The decisive condition for the survival of certain concepts is the significance of their contribution to improving understanding. Sometimes the cumulative model is explained on the basis of the principle of generalization of facts and generalization of theories; then the evolution of scientific knowledge is interpreted as a movement towards ever greater generalizations, and the change of scientific theories is understood as a change from a less general theory to a more general one. Anti-cumulative - suggests that in the course of the development of knowledge there are no stable (continuous) and preserved components. The transition from one stage of the evolution of science to another is connected only with the revision of fundamental ideas and methods. The history of science is portrayed by representatives of anti-cumulativeism as an ongoing struggle and change of theories, methods, between which there is neither logical nor even meaningful continuity. An example of the model of scientific revolutions is Thomas Kuhn. The main concept of this concept is a paradigm, i.e. the dominant theory that sets the norm, a model of scientific research in any field of science, a certain vision of the world by scientists. The paradigm is based on faith. The structure of the paradigm: 1. Symbolic generalizations such as Newton's second law, Ohm's law, Joule-Lenz's law, etc. 2. Conceptual models, examples of which are general statements of this type: "Heat is the kinetic energy of the parts that make up the body." 3. Value attitudes adopted in the scientific community and manifest themselves in the choice of research areas, in assessing the results obtained and the state of science in general. 4. Samples of solutions to specific problems and problems that, for example, a student inevitably encounters in the learning process. Uniqueism began to come to the fore in the 1970s. In works of this kind, first of all, the need to focus on a single event in the history of science, which occurred in a certain place and at a certain time, is emphasized. The process of individualization of the historical events under study, which began with bringing to the fore as a subject of study the way of thinking of a certain era, which is radically transformed in the course of the global scientific revolution, ends with case studies, which are already a direct antipode of cumulative, linear models of the development of science. In historical works of the former type, the historian strove to study as many facts as possible in order to discover something in common in them and, on this basis, to deduce general patterns of development. Now the historian studies a fact as an event, an event of many features of the development of science, converging at one point in order to distinguish it from others. Research is focused not so much on some ready-made fact, the final result of a scientific discovery, but on the event itself, as complete and unique as possible. An event of small size is taken: as a rule, it is not the culture of some long period of time in history, not the culture of a large region, no, localized events are studied, such as a separate text, a scientific dispute. The ability to characterize events as a kind of funnel into which both previous events and subsequent events are drawn. Anarchism. Paul Feyerabend was destined to complete the development of the logical-analytic direction in the philosophy of science, which was then only emerging within the walls of the University of Vienna. 1. The principle of proliferation. every scientist - generally speaking, every person - can invent his own concept and develop it. 2. The principle of incommensurability. Theories cannot be compared with each other, protects any concept from external criticism from other concepts. So, if someone invented a completely fantastic concept and does not want to part with it, then nothing can be done about it: there are no facts that could be opposed to it. There is not a single methodological rule or norm that would not be violated at one time or another by one or another scientist.

The social status of science (N). F-tion of science.

In quality social yavl N incl. in itself 3 comp. parts: knowledge system; activities for their production; social institution. Some textbooks on philosophy also point to the status of science as a productive force and as a form of social consciousness. N. as a system of knowledge represents a holistic, developing unity of all its constituent elements (scientific facts, concepts, hypotheses, theories, laws, principles, etc.). This system is constantly updated thanks to the activities of scientists. N. as an activity is a specific, organized process of producing reliable knowledge, carried out by people specially trained for research - scientists. In other words, science is a form of spirit activity. people, aimed at the production of knowledge about nature, society and knowledge itself, with the immediate goal of comprehending the truth and discovering objective laws. Science as a system of knowledge is the result of creative, scientific activity. N. as a social institution represents the body of specific organizations, institutions, unions, schools, creative groups, temporary formations that are engaged in forecasting, organizing, implementing, monitoring research, fixing and disseminating (implementing) scientific knowledge. As a social institution, science emerges in the 17th century. in Western Europe. The decisive reasons for the acquisition of the status of a social institution by science were: the emergence of a disciplinary organized science, the growth of the scale and organization of the practical use of scientific knowledge in production; the formation of scientific schools and the emergence of scientific authorities; the need for systematic training of scientific personnel, the emergence of the profession of a scientist, the growth of the authority of science, its transformation into a factor in the progress of society and the formation of scientific activity as a permanent condition for the life of society, turning it into a relatively independent sphere. The transformation of science into a productive force consists in the ever-expanding trend of interdependence in the development of research, implementation and production activities, in the growth of the economic efficiency of the application of scientific knowledge, in the progressive renewal of equipment and technology based on them, in increasing labor productivity and improving product quality. As a form of social consciousness, science is a reflection of reality in the system of knowledge. Science functions: 1) cognitive- consists in the fact that science is engaged in the production and reproduction of knowledge, which allows a person to navigate in the natural and social world; 2) cultural and ideological- not being a worldview itself, science fills the worldview with objective knowledge about nature and society and thereby contributes to the formation of the human personality as a subject of cognition and activity; 3) educational meaningfully fills the educational process, i.e. provides the learning process with specific material, science develops methods and forms of education, forms an education strategy based on the developments of psychology, anthropology, pedagogy, didactics, and other sciences; 4) practical- this function acquired a special role in the course of the scientific and technological revolution of the middle of the 20th century, when there is an intensive "scientificization" of technology and the "technicalization" of science, i.e. science becomes a direct productive force, participating in the creation of production at a modern level, while simultaneously penetrating into other spheres of society - health care, communications, education, everyday life, forming such branches of science as the sociology of management, the scientific organization of labor, etc.

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Odessa National Medical University

Not/ commensurability of systems

Lyashenko D.N.

annotation

The article is devoted to the philosophical and methodological analysis of the problem of incommensurability of systems. The hidden metaphysical premises of the classical understanding of the concept of incommensurability are critically examined. The philosophical role of the principle of extensionality in the emergence of contradictions in the analysis of this concept is revealed. The methodology of the intensional systems approach is applied. The possibility of a systemological solution to the problem of incommensurability is demonstrated by constructing a meta-system of commensurate systems.

Keywords: incommensurability, systemic approach, meta-system, concept, structure, substrate.

philosophical incommensurability extensionality contradiction

Pstop problem. If you want to be correctly understood, then you need to take care of the commensurability of your linguistic means, life worlds with the interlocutor, that is, the intersubjective consistency of worldviews, worldviews, etc. This does not exhaust the problem of commensurability, which in one form or another concerns many scientific and non-scientific fields. In the methodology of the natural sciences, there is a problem of commensurability of conceptual frameworks, paradigms, theories, etc. which echoes the problem of the commensurability of languages, which the translator faces, and the problem of plurality or universality of normative-value systems in the social sciences and humanities.

In philosophical logic, the problem of commensurability (comparability) arises from the level of analysis of relations between concepts. The concepts are comparable or incomparable. If they are comparable (have a common gender), then they may or may not be comparable. Concepts can coincide, be in generic relations, intersect, contradict, be opposite, subordinated. The first three cases relate to comparability, the next three to incompatibility. However, if there is no common gender, then the concepts are said to have no relationship. To compare such concepts, it is required to bring them to a common genus.

Analysis of recent research and publications. In modern philosophy of science, the problem of commensurability was developed by such researchers as: K. Aidukevich, B. Popper, W. Quine, D. Davidson, H. Putnam, S. Kripke, W. Sellars, D. Lewis, T. Kuhn, P. Feyerabend , N. Goodman, W. Maturana, C. Wilber, V.A. Smirnov, M.V. Popovich, V.V. Petrov, V.V. Tselishchev, A.Yu. Tsofnas, Yu.A. Petrov, G.I. Ruzavin, V.S. Stepin and many others. others

Isolation of previously unsolved parts of the general problem. Most of the proposed solutions to the problem of commensurability, to one degree or another, have one specific feature, which is associated with the value-semantic orientation of Western European civilization towards the category of quantity as opposed to quality. Strictly speaking, we are talking about an orientation towards extensionality as opposed to intensionality, which, in turn, lends itself more easily to quantification. That is, we are talking about one way or another accepted principle of extensionality, and rather not in a logical, but in a metaphysical sense. Moreover, even when meaningful reasoning points to the intensional contexts of the issue of commensurability, when trying to formalize it, the course of reasoning invariably becomes predominantly extensional in both the logical and metaphysical senses. As a consequence, the accepted extensional ontological assumptions lead the entire consistently carried out system of reasoning to an extreme degree of reduction (nominalistic, eliminative, etc.) and to a contradiction, when reductionists declare the reduction of intensionality to extensionality, thereby making an intensional statement. In order to avoid contradictions, one can use other logical and methodological means, and, accordingly, another metaphysics, different from the metaphysics of extensionality.

Actually, from a systemic point of view (using the apparatus of systems theory), this problem is undeservedly rarely addressed. Without exhausting all the possible implementations of system models in this matter, we will limit ourselves to such paradigmally different intension-oriented system approaches as U. Maturana's concept of autopoiesis, K. Wilber's integral metatheory, and A. Uemov's parametric system theory.

In the first of these system models, U. Maturana's concept of autopoiesis (see c.), the problem of commensurability is solved with the help of the concept of "corporeality" (bodyhood) of living systems. We are talking about the point of intersection of various ontological spheres that are "created" by living beings in the process of life-cognition and seem incommensurable based on the theoretical assumptions of the observer. The concept of autopoiesis has a well-defined subject area - biological systems. True, some researchers use the methodological apparatus of this concept far beyond biology, simply on the basis that some systems behave like biological systems. In any case, the immediate subject area of this systems theory is limited by clear boundaries of self-creating, cognitive systems that are in the process of structural interfacing with the environment. It is obvious that it is not always possible to speak, for example, about mathematical structures in terms of cognizing, self-created, structurally conjugated with the environment systems and to measure them through "corporality".

The integral metatheory of K. Wilber, including the concept of autopoiesis as one of its fragments, offers a more capacious model, which consists of paradigmatic and meta-paradigmatic aspects. The first describes a variety of theoretical and practical areas of activity, while the second includes principles and structures that streamline the conceptual constructs associated with these areas of activity. In general, the integral metatheory is built on the basis of three methodological principles: nonexclusion (“non-exclusion”), unfoldment (deployment of a preliminary conceptual model), enactment (“enactive” constructivism). Wilber's concept is a good candidate for commensurate "incommensurable", but there is at least one objection.

Both mentioned system models approach the problem of non-commensurability mainly from the content side (despite the incomplete attempts of formal modeling within the considered approaches). The possibility of an intensional, but formalized, systemological consideration of the problem of incommensurability remains open. The properties necessary for this have the general parametric theory of systems (OPTS) A. Uemova, which we will use as a methodological toolkit (the logical language of the OPTS will also be used - the language of ternary description (LTO)).

aim This article is an explication of the problem of non/commensurability from the standpoint of the intensional system-structural approach of the OPTS.

Presentation of the main material. Even K. Aidukevich showed that the picture of the world (in this work, the terms: paradigm, picture of the world, conceptual and linguistic framework, theory, etc., are considered from the semiotic and systemological points of view and therefore do not differ, since they represent certain systems of terms and judgments that interest us only from the structural point of view) is formed as a result of the interaction of a set of sentences and a set of judgments of a language (conceptual apparatus) with experimental data, in accordance with the rules for assigning values (axiomatic, deductive, empirical). The adoption of a certain conceptual apparatus and its application to certain experimental data forms a picture of the world. The early Aidukevich blurs the distinction between fact-fixing and interpretative sentences: experience is functional in relation to the choice of a conceptual apparatus, changing which also changes the factual experimental content. Thus, different pictures of the world are incommensurable, if such are the conceptual apparatuses.

Similar reasoning can be found in R. Carnap, W. Quine, T. Kuhn, H. Putnam and other researchers (see in). All of them are united by the position that any systems of knowledge (pictures of the world, paradigms, language frameworks) are incommensurable if they “generate” different facts. That is, the main criterion of non/commensurability is the extensions of knowledge systems. Speaking in system language: incommensurable systems of knowledge, according to the above methodologies, cannot be compared because of the different substrates (elements) of these systems. It can be objected that these thinkers always assume a theoretical (i.e. conceptual) “loading” of facts, and it is this loading that is the cause of incommensurability. It should be noted here that when it comes to understanding, one should avoid attributing one's understanding of the matter to others (the fact that the behavior of an amoeba can be rationally explained to some extent does not mean that the amoeba has any idea about this explanation). That is, it is one thing what is declared as the cause of incommensurability, and another thing is what we are really dealing with as incommensurable.

If we accept that incommensurability implies such relationships between knowledge systems that take into account the conceptual and structural (we are talking about the so-called system descriptors: concept (meaning, the main function of the system), structure (method of implementing the concept), substrate (system elements)) aspects that cannot be reduced to the substrate aspect, and incompatibility is associated mainly with the extensional level of systems, then it can be argued that these authors, in fact, do not mean the incommensurability of systems, but the usual incompatibility, and the main criterion for incompatibility is the properties of extensions of sign systems . The "litmus test" for such a claim is the notion of a total system of interpretation, which theoretically Aidukevich, Quine et al. refused to accept. They believed that pragmatic criteria, conventions play a key role in the choice of a referential system, i.e., that the issue of admitting one or another ontology is just a matter of convenience. However, in reality, denying the reality of the total system of interpretations, all the above-mentioned thinkers consider as such, at least the world of everyday life, the world of scientific discourse, etc. -- in a structural sense, this is what J. Searle refers to as background (see in). It is doubtful that at least one of these philosophers considers the real possibility that different paradigms (language frameworks, etc.) give rise to different ontologies in the natural-ontological sense of the word. In fact, it is only a matter of semantics. Different paradigms produce different models of knowledge of a certain total system of interpretations (meta-paradigms, if you like), in relation to which the adequacy, correspondence, of a particular model is assessed. In any case, the mentioned total system of interpretations is a certain ultimate ontological horizon, which acts as a common genus for different systems that in one way or another reflect its different aspects (are contradictory or opposite, etc.). Moreover, it is assumed that the basic part of this meta-paradigm is the material world of physical phenomena (or the world of sensory experience). In this case, different paradigms (language frameworks, etc.) only model these same physical phenomena, events, and processes in different ways.

Real incomparability (incommensurability) would imply the existence of truly different ontologies (in the natural-ontological sense). Consistent ontological pluralism, for example, in the form of many-world interpretations of quantum mechanics, or the modal realism of D. Lewis is extremely rare, although even here all these so-called. "Different worlds", differ mainly in the ways of organizing phenomena and processes (in time and space) of the same material world. Thus, the total system of interpretations of modern scientific discourse is naturally connected with materialistic ontological assumptions (obviously, other metaparadigms are possible: idealistic, dualistic, etc.).

The problem of incommensurability lies in the fact that Aidukevich, Carnap, Quine, Kuhn and others insist on the plurality of different systems in relation to the so-called correspondence principle. According to this principle, some systems of knowledge can be deduced from others, since they are only special (asymptotic) cases of these systems (for example, Newtonian mechanics is a special case of relativistic mechanics). In fact, in the case of relativistic and Newtonian mechanics, we are talking about the correspondence only of mathematical semantics, and not physical (see in). That is, different theories (paradigms, language frameworks, etc.) are not always in deductive connection with each other, since they are closed systems with different substrates. If the systems of knowledge were logically connected, then from the negation of the "false" system (the phlogiston hypothesis, for example) one could deduce the "true" one (the oxygen theory). Therefore, the paradigms do not have deductive (structural) relations with each other (they do not flow and do not follow from each other), but are simply extensionally incomparable (within the framework of the meta-paradigm, the total language framework). Thus, structural incommensurability (absence of logical relations), materialistic background and substratum (extensional) incompatibility are the main metaphysical principles adopted by classical methodologists engaged in the analysis of commensurability.

Moreover, only the principle of incompatibility of substrates of different paradigms is explicitly stated, while the first two principles are implicit. Everything would be fine, but only implicit principles are not always realized by researchers, especially the principle of transcendental conditions for the existence of a total system of interpretation (in this case, a materialistic background), the presence of which explodes theoretical systems from the inside, since it is entered from the back door (cf.). After all, it is obvious that the total meta-paradigm can be completely different.

These shortcomings can be avoided by using the methodological reflection of a systematic approach, in the case of OPTS, which gives an explicit opportunity to evade the need for a direct or indirect solution of the basic question of natural ontology. This is achieved with the help of the fundamental principle of structural ontology (indifference to metaphysical choice), adopted in systems theory.

“No matter what the degree of reality of a thing, defining it as a thing, as that to which properties are attributed or relations are established, the question of its objective or subjective reality possible until some time - until the time when it comes time to take practical action, in general leave unanswered. The nature of things, as already noted, is not the subject of structural studies. .

Comparison of systems, one way or another, implies metatheoretical relations within the framework of the metasystem, through which the objects of the system are measured. This presupposes a comparison of systems not only in terms of the substrate, but also an explicit differentiated commensuration in terms of structure and concept. The concept of constructing such a meta-theoretical meta-system can be some particular principle, but for cognitive purposes it is better that this be a provision that allows you to take into account an unlimited (arbitrary) number of points of view on the world, while being defined precisely in this aspect. In LTO, the structure of this concept can be expressed using the following formula: A ^ [( A ) t ]. That is, we are talking about an arbitrary thing A , which has a certain property t (see in).

Here we can recall the principle of "nonexclusion" of the integral metatheory of K. Wilber: "All points of view (systems) are right (correct) in some way." However, problems of a different kind arise here.

At one time, P. Feyerabend put forward a similar epistemological principle “Anything goes!” . However, Feyerabend himself not only did not offer any unified, ordering meta-system, but believed that such a meta-system, if possible, is harmful, since it is something akin to a Procrustean bed, all the more so since it is impossible to systematize proliferating theories precisely because they incommensurable.

Let us consider the problem of the “impossibility” of a meta-system in more detail. Obviously, a meta-system is a system. Therefore, to illustrate the refutation of the proposition about the “impossibility of a meta-system”, one can use the paradox of “the inevitability of a system”, formulated and analyzed by A. Uyomov and A. Tsofnas (see in).

If you set the concept of system 1 - "do not form a system", you can get the implication: 1 ^ ([a(*A)])1 Here a is some relation that corresponds to the concept. As you can see, the consequent of this formula exactly corresponds to the definition of the formal scheme for defining a system with an attributive concept: ([a(*A)])1 In other words, if we do not construct a system that organizes the data of our experience consciously, then this system will still be constructed spontaneously, unconsciously (if we succeed in ordering the data of experience, since any thing can be represented both as a system and as a non-system, according to principles of universality and relativity of system modeling).

It turns out that even such an anarchist principle as “everything will pass”, nevertheless, can be a concept of the system, however, in such a system, all responsibility lies with the structure of the system. Such relations of commensurability can also act. When describing a thing as a system, first of all, descriptors (concept, structure, substrate) are distinguished, that is, when comparing different systems with each other, it must be taken into account that systems that are incommensurable in one descriptor are commensurable in another (the simplest example of such the kind of relations is the semantic and syntactic differentiation of the compared systems (see c. )). Thus, the structure of the meta-system must take into account the explicit possibility of the coexistence of different comparison criteria. These can be relations of iso-concept, isomorphism, iso-substrateness, partial iso-substrateness, structural-substrate non/commensurability, concept-substrate non/commensurability, etc. Comparable systems appear in the substratum of the constructed meta-system.

Further, one can achieve much greater rigor of reasoning (or at least heuristically interesting conclusions) if one uses the LTO apparatus to compare incommensurable systems, for example, when comparing systems through synthesis operations - rheistic, relational, attributive. Let's designate two concepts of commensurate systems through symbols 1 and 1 (a fixed object and an object other than it). In one of the LTO variants, theorems of the so-called attributive synthesis are derived, for example: (Ґ) 1 ^ 1. It is written here that if a certain property is attributed to a thing other than a fixed one, then we get a certain thing. That is, if we make a conceptual comparison of two systems according to the type of attributive synthesis (in this case we are talking about considering one thing through the prism of another), then as a result of the comparison, one concept will be “absorbed” by another, the one through which the comparison is made. If we relate the concepts of our systems according to the type of rheistic synthesis, as two equal things, then we will get strictly indefinite results according to the following theorem: Ґ 1 ^ ba. The symbol in the consequent means "strongly indefinite object". Obviously, when we interpret Aristotle's physics with the help of Newton's physics, or the latter's physics through the prism of relativistic theory, the relations between these paradigmally different theories are built according to the type of attributive synthesis. Then, when we do not make a choice regarding the "best" theory, but correlate them "modulo", as in the case of a rheistic synthesis, then we cannot predict the exact result of this comparison. Considering that in addition to attributive and rheistic synthesis there are also relational synthesis theorems, it seems that all three types of synthesis make it possible to correlate different systems according to all three descriptors, and with different variability of the ratios.

ATconclusions from this study

Thus, within the framework of our brief consideration, the explicit and implicit premises of the classical extensional approach to the problem of non/commensurability were revealed. Some implicit assumptions lead to contradictions. The application of a systematic approach allows us to deal with the problem of non/commensurability on structural and ontological grounds, placing it in the context of a meta-system, where it receives a differentiated explication, in accordance with the theoretical-system categorical apparatus. The prospects of this direction of research include the possibility of further development of the problem of non/commensurability, using system-parametric and/or formalized modeling within the framework of OPTS and LTO.

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