The relational states of the given object: intensionality and extensionality. Some examples from physics, mathematics and everyday life

Kuzmin Vladimir Gennad'evich PhD in Philosophy Researcher 214000, Russia, Smolensk region, Smolensk, Konenkov str., 2/12, sq. 21 kvg-17@mail.ru Other publications by this author

Introduction. According to N. Hartmann, the reality of an object is defined through its "here-being" and "so-being". The difference between them in a sense is "the difference between 'fact' (Dass) and 'essence' (Was)"^{[4, p. 233]}. In this article, we show that the reality of an object in a situation has not only an ontic, but also an epistemological dimension, depending on its position in relation to the cognizing subject. The main idea of the article is as follows. In a person's cognitive activity, much depends on how he thinks of his presence in relation to the object being studied. For example, a man in the street thinks of himself inside the house, he participates in some event, lives in some city, etc. Similarly, he can think of his presence outside the house, outside a moving train, outside a concert that is taking place somewhere in Moscow, etc. Consider the object "house". It can be viewed from the outside, it will be the exterior of the house. Or you can – from the inside (the interior of the house). And although the same object is meant here, its study in a situation can be carried out by the subject from one of the two specified positions. Both of these positions complement each other in two different situations, which creates the integrity of the cognizable object "home". Similarly, any other object can be studied from two different positions. For example, an astronomer draws a diagram of our Galaxy, mentally being "outside" it, and shows our hypothetical position on it. At other times, he looks at the starry sky and sees the Milky Way, being present "inside" it. These are two givens of the same object – our Galaxy. Some objects are always viewed "from the inside", for example, time or the entire universe as a whole. It is impossible to imagine the presence of an observer outside these objects. There are many objects that are given only "from the outside", for example, a "soccer ball" or a "green apple".

Let's give two definitions. What the subject's attention is directed at at some insignificant moment in time is an object, regardless of whether it is perceived by the senses or by the mental eye (according to Meinong). At the same time, in the act of attention, the cognizing subject actualizes only one property of the object, whatever it may be. We will call this (intentional) property relevant. It characterizes the existence of an object in an appropriate situation. In a language, it can be expressed by a phrase or any part of speech: a noun, an adjective, a verb, an adverb, etc. Moreover, it is set by the verb in the event that the corresponding situation unfolds in time, whereas, for example, the adjective does not imply such unfolding. The actual property includes the whole complex of aspects, due to which the object of interest is highlighted in the act of attention. The idea that object A has an actual property p in a situation is conventionally denoted by A(p).

The relative states of the given object. The givenness of the object A(p) in the constituted situation is expressed through one of its relational states: "intensional" or its "extensional" givenness according to the property R. For example, a house can be seen either from the outside or from the inside, the actual property is "to see". Because of this, the interior and exterior of a house are the relative states of a given one object – "home". The same applies to other objects that are constituted by the subject in some situation according to the relevant property of interest to him. If both states of the relational reality of the same object take place, but in different situations, then we say that they constitute two of its exhaustive sides.

In order not to burden the text with the terms "intensional" and "extensional" in the following presentation, we introduce the following conventions. The idea that in a situation the object A is given intensionally according to the actual property p, we will denote by L: A(p). Similarly, the idea that the object A is given extensionally is denoted by G: A(p). For example, in our example, the object is A ? "house", p ? "to see", then L: A(p) ? "interior of the house", and G: A(p) ? "exterior of the house". Another example. The object is "a flying plane", the actual property is "to see how it flies", then in L: it will be the object "a flying plane with "I" (passenger)", and in G: it will be the object "an airplane observed by someone Else (from the ground)". Let us emphasize that the relative reality of an object does not take place in general in the "whole", but only according to the very property that is relevant to the subject in intention. If this property cannot be identified (even in a general context), then there is no need to talk about any relative reality. Let us note an important point: there are no intermediate states between two relativistic states of the givenness of the same object in the constituted situation.

The linguistic expressions "to be inside" and "to be outside" (for example, a house or a park) are special cases of a relative given (here the actual property "to be" is implied). In accordance with this, the object in the act of attention has two givens: "internal" (in L:) and "external" (in G:). For example, the object is "humanity"; being "inside" the specified object is characteristic of anyone who considers himself to be a human civilization (in L: "humanity"); being "outside" this object means associating himself in an act of attention with an alien or a savage.

It is interesting to trace the "part-whole" relationship in this aspect. Ontologically, the study of an object in a situation as a whole is equivalent to the presence of a subject "outside" this object, i.e. in G: according to the actual property due to which this whole takes place. On the other hand, the study of an object is equivalent in content to the imaginary presence of a subject "inside" this object according to the actual property of "being whole".

The givenness and modes of the object. The object is given to the subject not as a unitary phenomenon, but through the duality of its relational states. These states have different modes (modes of existence). The mode of an object in a situation according to the actual property of p is the value of its objectifying function (predication of existence). The mode is conventionally expressed by four numbers (a, b, c, d), where a denotes the presence (value "1") or absence (value "0") of an object in the act of attention for the "I" (the source of reliance in its subjectivity); b – the number of Others (in communication, in intersubjectivity), for which the object is present (b > 0) or absent (b = 0); c and d– indicate the presence (value "1") or absence (value "0") of the object in the situation, respectively, "here and now" and "there and then". The modes of the same object at different points in time may be different, it depends on the number of subjects-witnesses, on the change in the corresponding situation.

A given, characterized by a mode, conveys all the diversity of an object's existence in a given situation. So, for example, we talk about the existence of an object if its reality in a situation has one of the following modes: (1, 0, 1, 0) – existence for the "I" is "here and now"; (1, 0, 0, 1) – existence for the "I" is "there and then"; (0, b, 1, 0), (0, b, 0, 1) – existence for Others, respectively, "here and now" and "there and then". An object with mode (1, b, 1, 0) or (1, b, 0, 1) in a situation exists simultaneously for "I" and Others, respectively, "here and now" or "there and then". The periphery of being is a collection of these objects with modes of the form (0, 0, 1, 1), (0, 0, 1, 0), (0, 0, 0, 1), (0, 0, 0, 0), – these are all what I. Kant called "things in myself." Such objects cannot be described using the term "exist", but they are given (for some fictional subject, since these objects are in question), although they are unknowable neither by the "I" nor by any Other. Reality includes objects with a given denoted by modes of the form (a, b, c, d), where a and b are 0 at the same time.

The modes of objects can be compared with each other. For the mode four (a, b, c, d), we introduce a measure (quantity) of existence, determined intuitively: object A with mode (a ₁, b ₁, c ₁, d ₁) compared with object B having mode (a ₂, b ₂, c ₂, d ₂), has a higher measure of existence if the mode of the first is higher than the mode of the second: (a ₁, b ₁, c ₁, d ₁) > (a ₂, b ₂, c ₂, d ₂), i.e. at least one of the conditions is fulfilled: a ₁ > a ₂, b ₁ > b ₂, c ₁ > c ₂, d ₁ > d ₂. In this case, we say that object A has a stronger mode than object B in the same situation.

For cognition of an object, its givenness alone (the way of being) is not enough. In order to make a statement about an object, it must be knowable. And cognition is always a limitation of the original existence of an object. In reality, the object is limited by the capabilities of the cognizing subject himself: his level of knowledge, predisposition, methods and means of cognition that he has, etc. The main of these limitations is the form of cognition (the term used here differs from the one generally accepted in epistemology). At each moment of time, the cognitive act is expressed through one of the forms:

1. "speculation" takes place for objects conceivable in subjectivity. An object in speculation is a imagined, imaginary object;

2. "discussion" takes place for objects in communication, in dialogue;

3. "observation" is inherent in objects observed visually or with the help of devices both "I" and Others (By Others);

4. The "experiment" takes place for an unlimited number of Others. It is similar to observation, but unlike the latter, it is characterized by repeatability (reproducibility). An experiment is the strongest limitation of a given.

Modes (1, n, 1, 1), (0, n, 1, 1) (1, n, 1, 0), (0, n, 1, 0), (1, 0, 1, 0), n > 0 with the restrictions "observation" and "the experiment" will be called strong, and all other modes will be called weak. The modes of an object determine its measure of existence in a given situation.

The asymmetry of the states of a relational datum. By virtue of the action of natural attitudes, the object in the constituted situation is already recognized by us in some aspect (according to the actual property). It is already given in some kind of given state: either in L: or in G: and in no other way. The resulting one-sidedness occurs due to the peculiarities of the constitution of objects. For example, the objects "soccer ball", "closed book", "ripe cherry" according to the actual property "to be visible" are given in G:. The objects "humanity", "native language", "own life" according to the actual property of "being in" for the subject in any situation are given in L:. In mathematics, for example, a number of natural numbers are given in L:, the actual property is "recalculate".

In cognition, one or another object is asymmetric in the given of its relational states. In essence, he shows only that part of himself that is cognizable, which is "closer" in epistemological terms, which is natural and open to the subject. There is an "advantage" of one relative state of reality over another. The object is known in accordance with natural attitudes: we live on an "island of reality", which was formed thanks to them. In language, this "island of reality" is limited by categories. And around it is a boundless ocean of being, where the properties of objects and the relationships between them, different from our habits and beliefs, operate. All of them are aspects of the still unknown relative states of givens. Our world is defined by the epistemological differences between the relative realities of the objects provided to us. In order to move from the given in L: to the given in G: (or vice versa) of the same object according to some actual property, the cognizing subject needs to make some kind of transformation of natural attitudes that would facilitate such a transition. For example, the flat?footed heroes of the novel by E. Abbott, who live in two dimensions, perceive their world as given in L:. And in order for them to view it in G:, it is necessary to go out into three-dimensional space. Such a transition can be made when replacing natural installations: it is enough to make the necessary measurements (about this in detail F. Capra in ^{[8, p. 153]}) and draw a conclusion about the three-dimensionality of space.

A description of something can be made on the basis of the asymmetry indicated above. This asymmetry is clearly evident in science. In particular, A. V. Rodin writes about mathematical objects: "In geometry, there is only one kind of thing that can only be viewed from the outside (i.e., that does not have an "inside") ? these are dots. The assumption that all geometric objects in some sense consist of points means that any geometric object can be ... represented externally... (For example, ... a sphere or a torus can be completely defined in an external three-dimensional space...)… Obviously, there is only one kind of thing that can only be viewed from the inside, i.e., things that do not have an exterior, these are worlds. This can be used as a definition of the world"^{[15, p. 515]}. The subject always places himself in the center of the world he is exploring (L: "my world"), the actual property of "being in ...". In this regard, the traditional terms of philosophy are applicable to the worlds: "transcendence" and "immanence". In the first case, we are talking about the cognition of objects that reside outside the world, in the second – on the contrary, those who reside "inside" his world. E. Husserl wrote about immanence and transcendence as a way of giving the world to a specific "I". For him, these were purely methodological concepts^[2].

Both states of the object's relational reality (L: and G:) have different modes in the same situation. For the cognizing subject, only one of these states is actualized, it will have a stronger mode than the second. In particular, the subject may know only one side: L:? or G:?the reality of the object, whereas the second may be unknown to him (i.e. have a weak mode). For example, according to the actual property of "being visible", the universe is given only in L:, i.e. it is a Metagalaxy, the visible part of the Universe. And it must be borne in mind that there must be a given in G:, but such a given is unknown to us. The asymmetry of the states of the relative reality of an object depends on the most relevant property and is due to the difference in their modes.

So, in reality, the object is given either in L: or in G: according to the relevant property of interest. One of these states of reality will have a strong mode, and the second will have only a weak one in the same situation. The subject with his natural attitudes may not realize this alternative. Based on the above, it is obvious that the object is a community of its two relational states of reality with different modes. And in a specific situation, only one of these states matters to the cognizing subject, the other is eliminated, the situation is taken out of brackets, and is not considered. Of course, cognitive intuition and imagination are necessary to adequately determine the relative state of a given object by the property that characterizes it. Theoretically, it is possible to make a list of objects always given either in L: or in G: in any situation. It will look like a kind of dictionary reference.

Identification of the state of the relative reality of an object in a situation. In science, there is an intuitively clear division of objects into data in G: or in L: according to the actual property being studied. In particular, in mathematics, this position is fixed, respectively, in the principles (hypotheses) of extensionality and intensionality. They are formulated as follows. "The hypothesis that all geometric objects consist of points corresponds to the classical extensional approach, in which geometric space is always considered as external… The atomistic hypothesis, according to which everything consists of indivisible parts, i.e. atoms, can also be considered a metaphysical generalization of the geometric hypothesis of extensionality... The hypothesis of the existence of the world (... as things without appearance) can ... be called the hypothesis of intensionality"^{[15, p. 515]}.

How can I determine if an object is given by an actual property in L: or in G:? This can be determined intuitively. There are three points to be guided here.

1. Any relevant property of an object provides for the relative validity of its states in the appropriate situation. But not for every such property, the relative states of reality are intuitively clear.

2. Human consciousness is limited by natural attitudes formed during its long evolution, so it cannot always reveal another relative state of reality if only one of them is obviously given to it.

3. The relative reality of an object according to some relevant property takes place only in a specific situation, and not at all. The actual property must be specific, containing the parameters of the object and the situation in which it is placed. It cannot be said that this property provides for the relativity of the object, if there is no situation in which it takes place. The reality is always concrete.

There is one indirect feature that allows you to distinguish between the states of a relational datum, however, it works for a limited number of relevant properties, one way or another related to the vision of an object. If the movement of the subject's presence during the constitution of the situation does not change the object relative to it, then in this situation it is given in L according to the actual property:. Such an abstract relevant property can be, for example, "to be unchangeable for the Self." For example, the subject can move as much as he likes with his epistemological presence in the objects "infinity", "numerical series", etc., while the studied objects do not change. This suggests that they are given in L:. If the movement (at least mentally) changes the object in the constituted situation, then it is given in G:. For example, the "cube" object, the actual "see" property, moving the subject allows you to see previously invisible faces. The situation has changed, and the object has changed: it has become visible from the other side.

Consequences of the asymmetry of the relational datum. The report system. Relativity can only be defined in relation to something (this relation is the basis of the actual property). It is impossible to say: this is internal, and this is external. In relation to what are they like that? It is tacitly assumed that relativity is set relative to the cognizing subject, with whom a certain reporting system is associated. Such a system of reporting in epistemological terms sets the boundaries of cognition familiar to the subject. We talk about an object, starting from the frame of reference as a support, as from the known and familiar. The frame of reference in different boundary conditions (natural settings) can take the form of a physical frame of reference associated with some kind of body, in mathematics - with the location of zero, with a coordinate system, etc. In philosophy (or ideology in general), most often the frame of reference is a system of views, the truth of which is taken on faith.

The reporting system always manifests itself when there is an asymmetry of the states of an object's datum according to one or another relevant property in a situation. It is the basis for the constitution of an object with its actual property as part of the situation as a whole. In some other situation (the following) this reporting system is maintained "by inertia". A cognizing subject solving a problem has one exceptional property: it retains the property of the object of interest when moving from one situation to another (i.e. from one reporting system to another). And it may become relevant in the new report system. This property is denoted by one word ? invariance. In particular, categories have invariance (in communication).

Many theories and philosophical systems are based on the centrality of the subject, it is invariant in his own experience. But a different state of affairs is also possible when the theories are based on the centrality of the object being studied. The second is used when we consider the subject to be the same object as any other (i.e. in intersubjectivity). In the first case, being is the sum of worlds, in the center of each of which there is its own subject ("I", this is subjective being). In the second case, we are talking about another being (objective), in which the object being studied is at the center of each world. In this case, all these worlds enter into such an (objective) being is each in its own way through the environment of the studied object. In these worlds, the subjects themselves (Others) ? like many of the objects. In such a picture of being there is no place for the centrality of the subject, but there is a place for the centrality of each object individually. It is he who becomes the object of knowledge (objective, scientific). This is the essence of relativity. Taking into account the relative reality, we have two states of relativity of the object. As mentioned above:

1. with respect to the subject ("I", given in L:, the actual property of "being"); takes place where there is a cognizing subject, i.e. in cognition – everywhere. It unfolds only in the field of activity of the subject.

2. regarding the object (in G:), it takes place in science, it is an objective way of cognition, here subjectivity is eliminated. The object is considered as existing with some kind of strong mode in the series of bodies surrounding it. It is impossible to imagine an existing object outside of its connections with surrounding objects.

Presence and observer. If relativity provides for an equivalent measure of existence in a phenomenological bundle of "relative someone (subject)" or "relative to something (object)", then the presence, as a phenomenon, does not imply such equivalence. It is obvious that the subject is the source of presence, thanks to which being reveals itself to him in its concreteness. His very presence determines the integrity of the picture of the world that is revealed to him individually. The material embodiment of presence in being (subjective) is the observer, in being objective is the object being studied. The combination of both presences: the presence of the subject (observer) and the presence of the object in one situation equalizes the measures of their existence and represents the reality of the object, i.e. the object becomes existent with its mode and corresponding limitations in the situation.

The observer, as an object of knowledge, began to be actively studied thanks to the works of N. Luhmann, U. Maturana, F. Varela and many others, and above all in sociology. So, according to N. Luhmann, an "internal observer" is someone who is part of a social system, and an "external observer" is someone who is outside of it (according to N. Luhmann, this is God). Regarding our topic, L: and G:?the states of the given object are identified as the constitution of the situation with it with respect to internal and external observers, respectively. At the same time, it is quite obvious that the last two terms refer to the identification of the cognizing subject itself ("I"). With regard to the Other (or Others), which may also take place in the situation, nothing can be said about the L:? or G:?states of the given object. This can be judged only on the basis of communication between the "I" and the Other (Others). In general, the observer ("I" or the Other) is the source of presence (or belief), being is revealed to him in all its diversity through the objects given to him with their modes.

Cognition is characterized by one-sidedness on the part of the "I": in relation to himself, he considers the world provided to him in any case as an observer present "inside" him. Thus, the presence of an observer in some situation is nothing more than a "preference" of one relative state of the given object to another (the actual property of "existing"). In this case, there are different modes of these states. It follows from the above that, depending on the mode of the object, not only the subject ("I") can be present relative to the object, but also the object relative to the subject. Knowledge from the Other is scientific knowledge. Meanwhile, scientific facts and theories are recognized by each individual "I". L:– and G:–the givens of the same object in the act of attention correspond to the "internal" and "external" presence of the observer in relation to the cognizable object. For the objects "Universe" and "electron", the question of where the observer is present in relation to them was raised by G. M. Idlis^[7] and independently by M. A. Markov^[11]. They put forward the idea that the universe inside the electron is the same as ours. A.V. Rodin distinguishes between an "internal" and an "external observer" as follows. The inner observer can freely mix inside the world he is forming and at the same time this world does not change. The external observer is motionless, he surveys the world "from the outside" statically, he needs only contemplation ^{[15, p. 508]}.

Since the middle of the last century, physicists have begun to think about the important role of an observer in a physical experiment ("no elementary phenomenon can be considered a phenomenon until it has been observed"^[16]). Some difficulties in quantum mechanics were solved by taking into account the role of the observer in the experiment. A physical reporting system is associated with the observer, in which he (the "observer") is stationary ("being nowhere"), and objects move ^{[15, p. 512]}. The necessary elements of such a reporting system are the instruments and instruments used for measurements, even if they are trivial (for example, the human eye). An observer in such a reporting system becomes an "armed" observer. And only in it there is a strong mode of the studied object with the restriction "experiment" (in such a report system, the concept of possibility is not defined, the object either exists by definition, or it does not exist at all). If measuring instruments are not used in the physical report system and observation is not performed, then the object under study at this point in time has a weak mode with the restriction of "speculation" (hypothesizing) or "discussion" (in communication between researchers).

About the method of relational reality. Actually, no method is described here. What is said below is rather a propaedeutics to the future methodology. Upon receiving any conclusions and conclusions, the subject can move from the given in L: to the study of the same object in G:-given by the relevant property of interest and vice versa, and they should not be confused. They are completely different and cannot be reduced to each other. But for the completeness of the picture, such a transition must be made, i.e., to change natural attitudes, significantly expand the worldview, abandon dogmas, habitual views on known things. The most complete essence of an object is revealed to the cognizing subject if he considers it within the scope of the task in both L:? and G:?givens, without giving preference to any of them. Simply put, each such state has a relative "double" that will be relevant (have a strong mode) at another time, in another situation, or relative to another subject. But in the same situation, for an arbitrary object given in L: (or in G:), the opposite state of its givenness in G: (or in L:, respectively) is only possible and no more (has a weak mode). The constitution of the situation leads to a preference for some one relative state of the given object under study. Attention itself introduces such an asymmetry. If even one of the states of reality is not relevant in reality (has a weak mode), then it can take place in possible worlds.

If, by some relevant property, we consider an object to be given in L:, then there must be a given of the same object in G: and vice versa. The coin can fall "heads" or "tails" (obverse or reverse), but in any case it will be the same coin. Considering an object from one side and drawing conclusions about it, it is necessary to take into account that there is another side of it that may be difficult to reproduce in language, but its study can lead to conclusions that complement the first. This was guessed in Ancient China: "As soon as everyone learned that good is good, evil immediately appeared. For presence and absence generate each other..."^{[10, p. 216]}.

In this regard, there is a method (of relativity), which consists in the following. Let's consider an object with some relevant property. The constitution of the situation provides for the givenness of this object either in L: or in G:. And if one of these states of reality is obvious, then the other must be found and constructed. An example is the simulation of the Solar System. Summarizing astronomical data, Ptolemy, N. Copernicus, Tycho Brahe, I. Kepler built their schemes of the Solar system in G:?given (the object "Solar system", the actual property of "observing"), as if some (fictional) observer is outside it. Astronomical observations are given in L:. Thus, based on the L: –datum of the Solar system, astronomers of the past supplemented the picture of the sky using the G: –datum, i.e. mentally imagining themselves as being away from the Solar System. Such a methodological scheme has led to a more complete understanding of the Solar System by this property. Knowledge about an object will be more comprehensive if every judgment about it is supplemented by a judgment about its relative initial state of reality. In modern science (and philosophy), meanwhile, it is tacitly assumed that the object in a situation is given to the subject once as a phenomenon. The method consists in constructing another state of the relative reality of the object under study, if only one of them is given. It is based on three principles.

1. The principle of relational reality. The relativity of an object is recognized for any object by a property that is relevant in the situation.

2. The principle of complementarity. The relational states of an object's datum epistemologically complement each other.

3. The uncertainty principle. The relational states of reality are asymmetric in predicting existence by an actual property, which means that in the same situation they have different modes: strong and weak.

From an epistemological point of view, the method of relational reality allows us to bring together the states of reality of an object and consider them as parts of one whole. And if one of these states is given, then one should look for a relative state of equal importance to it. This idea is emphasized by A. V. Rodin. "Let's say... we want to build a model of some organ, for example, a heart. There are two possibilities: either (1) taking cells as the initial elements, to build an extensional model of the heart (i.e., to understand how a heart can be assembled from cells), or (2) taking an organism as the initial element, to build an intensional model of the heart (showing what function the heart performs in the body). It can be assumed that every thing admits such a double description: extensional in terms of lower-level elements and intensional in terms of higher-level elements"^{[15, 525]}. If there is some value, for example, velocity, pressure, etc., that describes an object in G: (or in L:), then there must be a corresponding value describing the same object, respectively, in L: (or in G:). It is possible that for some objects and their quantities we already know their relative analogues, but we have not yet established by what actual property G:– or L: –they are given. The restriction here may be weaker, and not just an "experiment", as in physics.

The principles of complementarity and uncertainty. All objects by any relevant property are given either in L: or in G:. Ignoring this fact leads not only to the one-sidedness of the resulting picture of ideas, but can lead to all sorts of difficulties and paradoxes. In order to overcome them, in relation to the relative states of the given object under study, it is necessary to be guided by the principle of complementarity. Relativity implies not only confrontation, but also the complementarity of such states. These states of the given object are such that they complement each other in two different modes in the same situation, or both are relevant, but in different situations. This is the principle of complementarity.

At the boundary of the application of natural installations, the actual property is increasingly found not only in one, but also in another relativistic state of the given object. This is manifested, in particular, in wave-particle dualism. The "particle-wave" object is given either in L: ("wave") or in G: ("particle"), depending on which measuring instruments are used (how the quantum mechanical system is constituted), the actual property is "to measure parameters". For example, 1. if a diffraction grating is used, then the particle-wave object is given to the researcher as a wave (has a strong mode); 2. if a target is used, then it is given as a particle (also has a strong mode, but in a different quantum mechanical system, and in both cases the mode has the form (1, n, 1, 0), the restriction "experiment", here n is the number of researchers (Others) taking part in the experiment). The second relative state of this object at the same time will only be possible (have a weak mode, for example, (1, n, 0, 1), the restrictions are the same – "experiment" – respectively, 1. – "particle", 2. – "wave"). Prior to the experiment, the particle-wave object has two "symmetric" relational states of its datum. Both are with a weak mode (restriction "speculation" or "discussion"). The experiment introduces asymmetry into the reality of this object according to the actual property being studied. One of his states becomes relevant with a strong mode, the other is not relevant and with a weak mode. In the experiment, there is a deformation of being in the place of the object's presence (its actualization). The actualized being of an object becomes twofold, relational: in the act of attention, the object receives a stronger mode, while its other relational side remains with a weak mode, as it exists in being.

The principle of complementarity in quantum mechanics is well known. "The experimental data obtained under different conditions ... cannot be combined into a single picture. On the contrary, they should be considered as mutually complementary in the sense that only the totality of all possibilities gives an exhaustive idea of the event"^[9]. L. I. Schiff formulates the principle of complementarity of N. Bohr as follows. "... Atomic phenomena cannot be described with the completeness required by classical dynamics. A number of quantities that complement each other and give a complete classical description are actually mutually exclusive. At the same time, for a comprehensive description of phenomena, it is necessary to use all additional quantities"^{[18, p.19]}. The complementarity principle in quantum mechanics applies to objects with the "experiment" constraint. It works for pairs of canonically conjugate quantities, for example, the coordinates of a particle and its momentum, the direction and magnitude of the moment of the amount of motion, the energy of the particle and the time at which it is measured, etc. Each such pair consists of quantities with different modes that are realized in the same situation. Conjugate quantities are states of reality relative to each other of a single object. What values are measured depends on the instruments and instruments used (with their "specialization") in measuring parameters. Each relativistic state of a given quantum object (photon, electron, etc.) is its state given in one quantum mechanical system (i.e. in a situation). The principle of complementarity imposes its own (epistemological) condition on the experiment being conducted. "If we measure the coordinate of a particle (say, an electron), then we must use one type of device, if the pulse is a different type... It is the observer who decides which device to use (a coordinate measuring device or a pulse measuring device). At the same time, the very concept of the device presupposes a person ... fixing the state of the device before and after the measurement act"^[13]. As M. G. Dolidze writes, the measuring device "is not limited to interaction with different objects, but expresses the unity of the subject and the object in the quantum dimension." In his opinion, quantum mechanical measurements are made by an "internal" observer involved in a "measuring interaction". He notes, however, that "at the classical level, the measurement process is completely controlled by an external subject and excluded from the picture of physical reality"^[6].

Another equally well-known Heisenberg uncertainty principle is associated with the complementarity principle. If the first one only indicates the need to take into account another relative state of the given object under study, then the second one speaks about the difference in their modes in the situation (in a quantum mechanical system). "...The measurement of conjugate quantities requires mutually exclusive experimental conditions. This means that, for example, when measuring the coordinate of a particle, its momentum is not fundamentally measurable, since there is no corresponding experimental device for simultaneous measurement of both quantities. It follows that the behavior of the pulse during coordinate measurement is not available for direct experimental verification. All statements about him have only a purely speculative character"^[9] (i.e., this parameter - impulse - has a weak mode).

According to the uncertainty principle, "it is impossible to simultaneously accurately determine the values of both terms of some pairs of physical quantities describing an atomic system..."^{[18, p. 18]}. We are talking about canonically conjugate quantities. In a quantum mechanical system, they have a different measure of existence, i.e. probability. This is reflected in the uncertainty principle. It follows that the more accurately one of the conjugate quantities is measured (i.e., it has acquired a strong mode), the more difficult it is to measure the other (it will be with a weak mode). Moreover, the weak mode of magnitude speaks only about one thing – the low probability of its determination (the measure of existence). Thus, for all measured objects, there is an asymmetry of their relative states of reality. In the conditions of a physical experiment, this position manifests itself in the following form. If one of the two conjugate quantities is measured, then one will have a strong mode, while the second will have only a weak one. So, for example, the object "quantum particle" according to the actual property of "being in motion" for the researcher is given in two states: in G: (as the momentum of the particle, it will have a strong mode) and in L: (the location of the particle, it will have only a weak mode in the same situation), or vice versa- depending on what the researcher is measuring. In other words, simultaneous measurement of the momentum and location of a particle in one quantum mechanical system is impossible. But it is possible in two different situations (quantum mechanical systems), each of which is a single whole (according to N. Bohr): "a particle is an observer device." They use different measuring instruments. The essence of the uncertainty principle consists in the asymmetry of the relational states of the given object under study. In the microcosm, the uncertainty principle manifests itself more strongly due to the fact that the experiment itself affects the state of the measured object (introduces a large deformation into its actual existence).

Other examples of relativity in physics. Note the asymmetry of the relational states of reality for some physical objects. The constancy of the speed of light relative to all reference frames only indicates that the speed of light, as an object, is given in L: in objectivity (relative to Others, the actual property of "measuring"). At the same time, the velocities of other bodies in space-time are different relative to different observers due to the fact that they are considered in G: by the same relevant property.

"Galileo's principle of relativity consists in the impossibility of establishing the uniform motion of one mechanical system relative to another using any mechanical experiments inside this system..."^{[5, p. 258]}. This means that Galileo's principle, as well as Einstein's principle, is given only in the L:?datum, the actual property of "uniformly moving". Actually, with such an actual property in L: all the laws of motion that are performed in certain physical situations are constituted. We can generalize this result. For an observer, it does not matter whether he himself moves relative to the stationary world he is considering, or whether the observer is stationary, and his world moves relative to him to the extent of the movement of his attention (generalized – phenomenological ? principle of relativity).

Some examples of a relational datum in mathematics. To define mathematical objects, in particular sets, the following two principles are followed. 1. Every set is uniquely determined by its elements (the principle of extensionality). 2. Every element is uniquely determined by the sets to which this element belongs (the principle of intensionality). A. V. Rodin notes that the principle of intensionality is interpreted as "belonging to a set, as having a property"^{[15, p. 521]}. M. A. Anisov formulates these two principles somewhat differently. "Two sets or classes are considered equal if they consist of the same elements"^[1] (the principle of extensionality). Otherwise, "if, within the framework of the corresponding set theory, the existence of such a Q is allowed that the statement "P and Q consist of the same elements" does not imply the statement "P=Q", then such a property or relation will be intensional^[1]. A.V. Rodin notes that the "naive" set theory (Zermelo?Frenkel axiomatics, ZF) is built precisely on the principle of extensionality, which is why such an object as the set of all sets is impossible in it^{[15, p. 518]}. It should be noted that the German mathematician G. Weil, who adhered to the phenomenological point of view, wrote about the dual construction of a set: "a set is understood either as a set of things or as a synonym for some property (attribute, predicate) of things"^{[3, p. 78]}. Thus, in mathematics, the presence of an observer subject becomes intuitively clear: either "inside" or "outside" the studied mathematical object, property or relationship. For example, "imagining a ball or a torus on which flatheads crawl, we take ... the position of an external observer"^{[15, p. 512]}. V. V. Tselishchev notes that Godel's incompleteness theorem is formulated intensively^[17].

The relative reality of a mathematical object will be obvious if the mathematical object itself and the actual property that forms it in speculation or discussion in the task are clearly formulated. It should be noted that the above two principles reveal the relative reality only by the actual property "the way of constructing a mathematical object". More generally, we assume that any mathematical object is given either in L: or in G: according to the relevant property of interest. For example, the solution of a problem lies outside the plane of the problem itself. To solve it, it is necessary to understand it in L:, and then cover it entirely as a whole (in G:), then the observer solving the problem goes beyond its limits, beyond the sphere of its completeness. D. Poya writes: "Remaining within the boundaries of the problem, he can study its individual elements until he succeeds to find among them one that can attract some useful element from the outside, i.e. from the knowledge acquired by him earlier. Or he can go from the outside, rummaging through previously accumulated knowledge until an element is found that will be useful for his task"^{[14, p. 258]}.

In mathematics, cardinal numbers are distinguished, denoting the cardinality of a set, and ordinal numbers (ordinal), designed to recalculate the elements of a set. These are two relative states of a given object: the "number of elements" (the power of the set), the actual property of "being readable" or "recalculating". In order to find out the number of elements in the set, the observer must look at the whole set at once (for him these will be cardinal numbers). Here, the cardinality of the set is given in G:?given by the specified actual property. On the contrary, ordinal numbers appear when the elements of the set are incrementally recalculated, the object "number of elements in the set" in this case is given in L:. The same relativity holds for infinite sets. Accordingly, these two states of reality are closely related to each other (one presupposes the other according to the principle of complementarity). By the way, V. Ya. Perminov wrote about this: "Wherever we assert the existence of potential infinity, we inevitably assert the existence of a generating function belonging to an infinite number of elements that are equivalent to each other in the sense of belonging to this function. But this kind of equivalence defines a class consisting of an infinite number of elements, considered as a single and complete integrity. In methodological terms, therefore, the presence of potential infinity presupposes the idea of actual infinity as a sphere of elements corresponding to the function of infinite generation"^{[12, p. 76]}. Thus, for infinite sets, according to the actual property of "being readable", we have two of their relative states of reality: as a potentially infinite (given in L:), or as an actual infinite set of elements (given in G:). Accordingly, the principles of complementarity and uncertainty outlined above are fulfilled for them.

A sinusoid (the trajectory of the wave-like motion of a material point) is relative to a circle (the trajectory of cyclic motion). Object: "trajectory of periodic motion", the actual property of "moving". A sine wave is a given of periodic motion in L:, and cyclic motion along a circle, on the contrary, in G: (in this case, the observer can observe the process of rotation of a material point around a certain center "from the side").

A function represented as an analytical expression and its expansion into a series in the circle of convergence are the relational states of the givenness of one object – an "analytical function", the actual property of "being an analytical representation". At the same time, L:"analytical function" ? "series expansion in the circle of convergence", G:"analytical function" ? "analytical expression".

Some examples of a relational reality from everyday life. The scheme in them is as follows: the object ("what?" or "who?") it is constituted in a situation ("what is happening to him?", "what is he like?", etc., is an actual property that characterizes the object and the situation with it).

1. Travel by yourself (for "I" the object is given in L: "journey"), or travel, for example, on a map or watching others travel (G: "journey", i.e. "I" am actually "outside" the journey). The "travel" object, the actual "travel" property. Similarly, "move along the route yourself" and "plot your route on the map". The first is given for "I" in L:, the second is in G:, object: "route", actual property: "move".

2. Watch a feature film on the screen, carefully observing everything that is happening, being a bystander-a spectator (this will be the life of Another (Others) in G:). Or to participate in the events yourself, to be the hero of the plot, this film will be given already in L:, the actual property of "participate".

3. The "own life" object, the actual property of "tell". For the "I", his own life is given in L:, in the form of a story. It's another thing to hear someone speculate about their own life (given in G:).

4. Watching someone from the outside, for example, watching a football match or playing in this match yourself. The first object is given in G:, the second in L:, the object "football match", the actual property "play". The difference between a player and a fan is that the player is present "inside" the game (L: "football match")", and the fan is present "outside" (in G:).

5. "Work outside the beauty salon" and "work in the beauty salon." Object: "beauty salon", actual property: "work", the first is given in G:, the second in L:.

6. The object is the "host country". The actual property is "to speak your native language". "I" can speak the language of the host country (as a resident of his country, for example), but may not speak it, as a person who finds himself in a foreign country without knowledge of the language. Accordingly, there are two states of reality here: in L: and in G:.

7. "Understanding what is happening as a historical process" (the subject participates in events, in L:) and "understanding what is happening as fatality" (the subject is indifferent to the events taking place, in G:) – both understandings of what is happening are given in relativity. The object is "understanding what is happening", the actual property is "participate".

8. "Spoken" and "spoken". Object: "thought", actual property: "express it." When the subject ("I") expresses his thought, it is given to him in L:. When he listens to someone, he perceives what someone else has said, i.e. for "I" it is given in G:.

All these, as well as many other examples of the relative reality of objects from everyday life, according to the above, obey the principles of complementarity and uncertainty. The reality of one relational state of an object presupposes the reality of another, although in a different situation. For a more complete understanding of the object, it is necessary to update the corresponding states of reality in two different situations.

Conclusion. In the constituted situation, the object is given in two relational states according to the relevant property of interest. Because of this, the corresponding intentionality can be of two types: either in L: (intensionally) or in G: (extensionally). At the same time, one of these states for the subject will have a strong mode (it is the most obvious), and the second – only a weak one (most often they do not even guess about it). Because of this, there is an asymmetry of the states of the given object, manifested in the process of cognition. An example of what has been said in physics is the particle-wave dualism. Actually, the process of cognition introduces such asymmetry. Everything that the subject pays his attention to (including mental attention), all this becomes one-sided in reality to the extent that the cognizing subject is ready to constitute a situation with an object containing itself. The relativity of the states of reality manifests itself in the corresponding natural settings, within which the actual property takes place. A change in natural attitudes allows, in the process of cognition, to move from one state of the given object to another relative state of the given. All of this, as shown in some examples, has applications in physics, mathematics and in everyday human life.

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