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PRINCIPLE OF COMPLEMENTARITY: FROM PHYSICS TO THE GENERAL PARAMETRIC SYSTEMS THEORY
Abstract
The article represents an investigation of complementarity idea as a physical principle introduced by N. Bohr for the description of quantum mechanics objects, and also this idea application in the General Parametric Systems Theory which was developed by A.I. Ujemov and his school. This idea is represented as a principle of dual system descriptions complementarity by the example of deductive and inductive conclusions' system models. The attributive and relational structures investigation is represented in their interrelationship and complementarity to each other. The transformation of the complementarity physical principle into general scientific and philosophical one is also shown in this work.
Keywords
principle of complementarity, General Parametric Systems Theory, system model, attributive and relational system definitions, deduction, induction
AUTHOR
Yuliia Popova
Post-graduate student Natural faculties philosophy department Odessa National I.I. Mechnikov University, , Odessa Juliette-night@yandex.ru
The development of modern society is determined by processes of globalization and scientific knowledge integration. Such processes have a close connection with an appearance of "scientific crossroads" which combine principles and conceptions of different theories. The system method and general systems theory occupy a highly important place in scientific knowledge, and these two theories had a great influence on a development of classical physics, sociology, macroeconomics, medicine, ecology etc. Mechatronics, bionics, bioengineering appeared as a result of sciences' system integration. One of the general systems theory variants is the General Parametric Systems Theory (GPST), which was developed by Ukrainian philosopher and logician A. I. Ujemov and his school.
The General Parametric Systems Theory contains many conceptions which are widely used in other sciences. There are conceptions of system and its descriptors - a concept, a structure and a substratum; then, two basic triads of categories on the basis of which the GPST formalism is formulated - the Language of Ternary Description: objects - properties - relations and the definite - the indefinite - the random, and many others. Besides, the GPST is based on some principles, such as a principle of system description universality, a principle of relativity, a principle of duality, a principle of objects, properties and relations distinguishing functionality [21, 102-123]. These principles are used exceptionally in the systems theory, so they can be called "special principles", but there are some general methodological principles which came to the GPST from other sciences, namely, the principle of complementarity introduced by Danish physicist Niels Bohr for description of quantum mechanics objects' behaviour in 1927.
The principle of complementarity can be defined as "a methodological thesis according to which a phenomenon integrity simulation requires use of mutually exclusive "complementarity" conceptual classes [9, 163]. Such physical phenomena investigation method essence consisted in a fact that mutually exclusive concepts seen as complementary pairs were used for quantum phenomena contradictory aspects analysis, in other words, an electron should have been described as a wave with a definite wave function and as a particle with a definite mass and radius at the same time.
Ukrainian logician L. Terentjeva notes that the complementarity principle background go to ancient times of Greek philosopher Aristotle who used a category of "correlated" more than two thousand years ago for his logics construction. Even at that time, in Aristotle's "Categories", we meet the conception of "reciprocity", or "interrelation", which N. Bohr later used for the complementarity principle characterization in physics: "All correlated sides are reciprocal to each other... That is why, if you point out properly, reciprocity is possible. Thus, a wing is a wing of a winged creature, and a winged one is winged with a wing" [1, 6b 27, 7a 3-6]. L. Terentjeva considers Aristotle's interrelationship, reciprocal principle to be even more than Bohr's complementarity principle because Aristotle investigates being of any objects presented as interrelated, while Bohr paid attention to the quantum phenomena investigation: "In gnoseological orientation of Bohr's complementarity principle are its species qualities discovered with respect to genus qualities of Aristotle's interrelationship principle" [15, 239].
There is also an idea that Bohr's complementarity principle has got many common features with an indeterminacy principle introduced by physicist V. Heisenberg: "Thereby, the quantum postulate effect extends over processes of observable microworld objects -in this sense the principle is connected with a physical meaning of "Heisenberg's relation of uncertainties" [13, 691]. Following A. Einstein, V. Heisenberg noted the dual nature of matter and radiation behaviour as waves in some cases and as particles in others, and N. Bohr pointed that "a certain formal analogy can be found between the theory of relativity postulate and complementarity principle" [5, 206]. Every picture suitable for micro-objects' behaviour description, wave or corpuscular picture, "has certain limits established by the nature. Limits to which the corpuscular picture is used can be received from the wave picture" [6, 15]. When a scientist investigates a micro-object he cannot unambiguously define its spatio-temporal coordinates, even if impulse and energy values are defined, and vice versa, that is why for the whole description of such objects' behaviour scientists should use two complementary descriptions of its kinematic (spatiotemporal) and dynamic (energy-impulse) characteristics. This complementarity method of description is sometimes called "a non-classical use of classical conceptions" [13, 692].
Interestingly, you almost cannot find a word "principle" in Bohr's works; he rather preferred such words as "conception", "idea" and "method". Heisenberg's idea, for its turn, is known as "relation of uncertainties" but it also had its further development as a
heuristic and methodological principle. Besides, it is known that Bohr hesitated over a choice of "complementarity" and "reciprocity" conceptions. A. Pozner writes that "the last conception underlines the idea of mutuality, symmetry, equivalence of opposite definitions, while "complementarity" conception emphasizes an idea of their incompatibility, mutual excludability, subsidiarity" [12, 20]. Now we are going to show how these conceptions were used later in the General Parametric Systems Theory.
One of the constitutive, fundamental conceptions of this theory is the conception of "system". There are many system definitions examined by A.I. Ujemov [20, 103-117], but there are two system definitions dual to each other which are used in the GPST.
The first definition says that "a system is a multitude of objects on which the definite relation with fixed properties is realized" [20, 117]. We can represent this definition with a help of the Language of Ternary Description, the GPST formal language:
(iA)Sist =df ([a(*iA)])t (1)
There is a definiendum (an object we define) in the left part of this formula and a definiens (things which help us to define an object (the right part). (iA) is a system, a multitude of objects in the left part, and the same multitude is in the right part, and this multitude is random. There is a relation realized on these objects, and this multitude of objects with some relations has a definite property. So we can read this formula in such a way: "Any object is a system by definition if in this object some relation with a definite property is realized" [19, 37].
System model represented by this definition is defined beginning from a concept. The concept is a specific system property which is the main meaning of a system. Then we go to a system structure (backbone relations, fixed in a system model) and a substratum (system elements). A concept, a structure and a substratum are called "system descriptors". A. Tsofnas calls this definition of a system "an attributive one" [21, 53] because some relations of this system satisfy a property -a concept, and this concept is attributive, which means that it is represented by a property, unlike in the dual system model which we are going to describe now.
The dual system model represents the second definition of a system and describes a system as a "multitude of objects which have properties defined beforehand with fixed relations between them" [19, 37]:
(lA)Sist =df t ([(iA*) a]) (2)
This definition can be called "relational". Here we get a relational concept which represents a relation, and the structure is a property, so it is an attributive structure. We can reformulate this second definition as we did in the first case: "Any object is a system by definition if in this object some properties, positioned in relation fixed beforehand, are realized" [19, 42]. These two definitions are analogous by structure and stay the same if we replace the conception "properties" by "relations" and vice versa.
Such use of dual system models is a striking example of a special, physical complementarity principle transformation into a general, philosophical one - "the principle of dual system descriptions complementarity". It shows that we can get a complete presentation of an object as a system only if we describe it using two system models - a model with an attributive concept and relational structure and a model with a relational concept and attributive structure.
The principle of dual system descriptions complementarity can be used in logic when we examine objects of logical analysis as system models. Let us illustrate this idea by the example of deductive and inductive conclusions' investigation. It is known that deduction and induction are characterized by a contrary direction of a thought movement: scientists
usually define deduction as a cognition process which leads our thought from the general knowledge to the particular or single, and induction as a conclusion from a knowledge of less generality degree to the knowledge of more generality degree, conclusion of general statements from particular or single premises [7, 36; 3, 240; 10, 124].
Aristotle, an ancient philosopher, examined these types of conclusions and wrote that "by its nature the conclusion through the third term (the syllogism - J.P.) is earlier and more famous, but for us the conclusion through induction is more obvious [2, 68b 3537]. Scientists agree in opinion that deductive thought movement gives trustworthy conclusions but they do not have novelty, while inductive conclusion guarantees novelty but not reliability of the knowledge we get in conclusion. But there is one more important difference between these types of conclusions: difference in their structures.
For the illustration of this difference we can represent deductive and inductive conclusions as two system models - attributive and relational (in terms of A. Tsofnas [21, 53]) accordingly. In this context deductive conclusion can be examined as a system model with an attributive concept and relational structure (see formula 1 ). Attributive concept here is a fixed property which means "not to exceed the limits of objects represented in premises". Relational structure here is a relation between terms which satisfies the property mentioned before. This relational structure is strict, it does not allow changes and exists according to the rules by which we get a syllogism of a first, second, third or forth figure.
Then we can examine an inductive conclusion as a system model with a relational concept and attributive structure (see formula 2). Relational concept here is not a property but a relation of exceeding the limits of objects represented in premises. Attributive structure is represented as a property of multitude of variable values. Such structure allows changes inside it, it does not have strict rules and allows, for example, changing positions of inductive conclusion premises.
When examined in such way, deductive and inductive conclusions show the same duality and complementarity to each other as two system description models. In scientific thought these types of conclusions are really interrelated, according to Aristotle's words, and supplement each other: an inductive conclusion generates hypotheses, while deductive one helps to estimate knowledge we get in a conclusion as true or false. Thus, induction and deduction turn out to be correlated, complementary to each other as system models, and this statement confirms an idea of Bohr's complementarity principle as a general scientific and philosophic one.
Another aspect of deduction and induction investigation is that we can examine these types of conclusions as two dual and complementary system models. We can represent deductive conclusion as a system model with an attributive concept and relational structure (formula 1). Attributive concept of deductive conclusion system model is a backbone property "not to exceed the limits of objects represented in premises". Relational structure here is "a precise, strictly fixed way of elements connection which is defined by according logical scheme or formula". A substratum of this system is "elements of a syllogism" (major, shorter and middle terms).
Now let us look at a dual system model of the same deductive conclusion, coming from the second system definition as a multitude of objects which have properties defined beforehand with fixed relations between them (formula 2). Here we define the system from its structure. Attributive structure of the syllogistic system model here is a backbone property which can be understood as "an impossibility of exceeding the limits of objects represented in premises". Relational concept of this system model is shown here as a backbone relation fixed between the substratum elements, that is, as "a logical connection between premises and conclusion". Substratum of this system model is "a definite number of premises and a conclusion".
Now we will examine a complementary inductive system model. In a system model with an attributive concept and relational structure (formula 1) we define a concept as a backbone property "to exceed the limits of objects represented in premises". Relational structure here is understood as "a way of connection of indefinite number of premises and a conclusion" (a kind of generalization). Substratum of incomplete induction system model is inductive conclusion elements - "an indefinite number of premises and conclusion".
In the dual inductive system model we start system descriptors definition from an attributive structure. Here it is seen as a totality of backbone properties according to which "exceeding the limits of objects represented in premises" is supposed. Relational concept here is a backbone relation of "generalization and connection set between premises and a conclusion". The substratum of a system is elements of incomplete inductive conclusion - "an indefinite number of premises and a conclusion".
When we investigate deductive and inductive conclusions as two separate system models we get a complete system idea of these two types of logical conclusions, while the first variant of investigation helps us to examine deductive and inductive differences in their structure. Researchers' opinions about appropriateness and logical validity of first or second variants differ. Professor L. Terentjeva supports the idea that we can represent a deductive conclusion as a system model with an attributive concept and relational structure and an inductive conclusion as a system model with a relational concept and attributive structure. According to L. Terentjeva's thought, in this way it is possible to show that "induction and deduction, being interrelated, have a property of conclusive knowledge reliability but "defined inversely" [17, 41], besides, such interrelation is internal for these types of conclusions. In the same way, describing differences between attributive and relational structures, L. Terentjeva examines many logical problems such as dual and complementary ideas of a syllogism as a connection of premises and a conclusion [14], system characteristics of a notion and a proposition and their connection in Aristotle's syllogistics [18], and offers a logical square system interpretation with its division into two types - attributive and relational squares [16] - and all that becomes possible due to structure types examination.
A. Ujemov insists on a thought that we can get complete system representation of an object only if we use both system models dual to each other. The scientist believes that the choice of attributive or relational concept and thereafter of relational or attributive structure depends on purposes and tasks of investigation. Each variant can be more or less appropriate, convenient or demonstrative depending on investigation tasks peculiarities but "they cannot be mixed, and we can get a complete system representation only provided that we use both system models which appear to be complementary to each other" [19, 43].
Thus, this research shows that the special scientific, physical principle of complementarity introduced by N. Bohr in physics really became a philosophical one. V. Osipov writes that "complementarity is a through idea in XX century physics which define the modern era thinking style" [11, 136]. In fact, in "scientific crossroads" epoch, the epoch of globalization and integration of scientific knowledge, the complementarity idea takes a general-scientific turn and helps in solving problems of different sciences: in sociology, psychology, economics and, as it was shown in the article, in classical logics and the General Parametric Systems Theory. M. Dolidze underlines significance of the complementarity principle, its philosophic and dialectic character and writes that the importance of this principle application "is an evidence of incompleteness, uncertainty of objective world and its understanding formation and development" [8, 46]. L. Bazhenov adds one more, philosophic level of complementarity principle understanding to its physical interpretation as a quantum mechanics conception: "This is a general philosophic level of complementarity conception because just here the deep ideological commonness of oppositions complementarity and unity can be detected" [4, 9].
Thus, dual and complementarity system representation of an object is not just two different points of view. It is a dual view on a problem from both sides simultaneously, from two different positions - positions of attributive and relational structures, opposite and interrelated. In this investigation we showed how a physical principle of complementarity can be used in the General Parametric Systems Theory. We performed this task by representing deductive and inductive conclusions as dual and complementary in the aspect of their structure differences and then as two separate system models which are dual and complementary to each other. We are sure that both aspects have a right to exist and can be used according to the investigation goal: the first variant helps to examine differences in structures of logical conclusions, while the second one allows to represent these conclusions as system models and get a complete system idea about them. Besides, both these variants turn out to be complementary not only separately but being interrelated too. This conclusion is one more explication of complementarity principle in the GPST, and moreover, it gives a new system-parametric view on a statement and solution outlook for a well-known logical problem - the problem of deductive and inductive conclusions correlation and their conclusive knowledge characterized by reliability (deduction) and novelty (induction).
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