On the question of the existence of abstractions

Kuzmin Vladimir 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. The topic of abstraction is very extensive and great. This article explores only one aspect: to what extent abstractions exist and how different they are from material objects. There is still no clarity on this issue. In particular, G. Rosen points out the difficulties in defining the abstract and in distinguishing abstract and concrete objects. He analyzes two definitions:

1. According to G. Frege, "an object is abstract if and only if it is simultaneously non-mental and non-sensual";

2. "An object is abstract if and only if it is non-spatial and causally inefficient."

And he gives a number of examples (an afterimage in memory, an impure multitude, real–life heroes of works of art, a chess game, etc.) that are difficult to attribute to both concrete and abstract objects in accordance with these definitions^[1]. S. L. Katrechko believes that an abstract object is a possible object, "the characteristics of which, unlike specific objects, are only partially defined"^[2]. According to A. N. Whitehead, abstraction, unlike reality, is devoid of movement as a material body^{[3, p. 218]}. M. M. Novoselov wrote most fully about abstraction and its current state in his book^[4]. V. V. Tselishchev describes in great detail the essence of the abstract ^{[5, pp. 60-63]}. He notes that in philosophy there are several principles of distinguishing the abstract from the concrete. Among them, he identifies the following: firstly, the concrete implies the spatiotemporal nature of the object; secondly, the abstract entity is inseparable in its existence from other entities. For example, the color of an object (as an abstract) is inseparable from the object itself. And finally, thirdly, abstraction is associated with the process of abstraction.

What is meant by abstraction? "... The operation of abstraction, which results in the formation of abstractions, is understood as the procedure of abstraction from certain properties of objects and/or phenomena that are insignificant in a certain respect"^[6]. Abstraction takes place as a sociocultural object for both the "I" and the Other (original "I") and is supported by the orientation of consciousness of the participants in the abstraction process. Abstraction is conditioned by the subjectivity of the cognizing subject itself ("I" or Another). The types of abstraction known in logic take the place of the relative Other and are objective in nature.

Having presented abstraction not as an abstract logical operation or its result, but as a given in the constitution, we investigate the question of the extent of the existence of abstraction. We will see that in this perspective, the boundary between the concrete and the abstract is blurred. Since everything that the subject's attention (including mental) is directed at is an object (in intentionality), then abstraction is an object. We will take into account the modes (ways of being) of abstraction as an object. This will expand our understanding of abstraction. The topic of relativity (relativity) of the abstraction process itself will be touched upon. Abstraction can be achieved according to the selected property intensively or extensionally, depending on the "location" of the cognizing subject. When describing objects, we will proceed from the phenomenological concept of A. Meinong. In order not to complicate the text, we will explore only some types of abstraction.

The article uses the approach adopted in the interval methodology (M. M. Novoselov, F. V. Lazarev, A. I. Kreminsky, etc.). Abstraction is studied in a certain range of applicability – the abstraction interval in which the corresponding restrictions apply. In accordance with this, abstraction, as an object, is set in a certain range of properties and relationships. It "reflects those boundaries within which the category of an object (thing) has a specific meaning, i.e. the fact of the unity of the object and the environment. The interval ... is an indication of those qualitative boundaries of the environment in which the existence of an object turns out to be inseparable from the environment, and the environment acts as a means of manifesting the potential properties of an object"^{[7, p. 7]}. F. V. Lazarev clarifies: "The interval of elementary abstraction is the area of practical and theoretical admissibility of considering a particular subject as "abstract". The interval characterizes the conditions of unambiguous applicability of this abstraction in terms of their universality"^{[7, p. 12]}. It performs the function of the cognitive position of the subject^[8].

An actual property and segment of reality. In the act of attention, an object in the abstraction interval is endowed with only one (intentional) property, whatever it may be (even a very complex one consisting of many simpler "elementary" properties). We will call it relevant (F. V. Lazarev calls it quality ^{[7, p. 8]}). In being, such a property has the structure of a certain "polyhedron", and for the subject, that facet of it is relevant, which is important in the selected interval of abstraction. In perception, it is "turned" to the cognizing subject from the side that matters in the situation or within the framework of the task. At the same time, not only the property of the object itself is updated, but also all its connections, by which it is connected with the properties of other objects in the same abstraction interval. Because of this, the actual property will be an action, circumstance, etc., for example, "to exist relative to ...", "to get away from ...", "why?", etc. Other facets of the actual property are hidden, they are present in "here-being", but they are not actualized in the act of attention, or they are not fully disclosed to the subject, but only in some part of it.

By virtue of the above, we agree to consider the abstraction interval as a systemic whole in the following presentation. According to the degree of coverage in the act of attention, we divide it into three different types, designating them as segments of reality (by the way, V. A. Bazhanov uses another term – "reality section"^[6]). Such segments include: (current) "situation", "co-existence" (being of subject-related situations) and "universe". The subject constitutes an object of interest with an actual property (therefore, in connection with other objects) as given in a situation, in co-existence, or in the universe. And abstraction can be performed in each of these segments of reality. It should be borne in mind that the situation has priority over the co-existence or the universe, at least due to the fact that the consciousness of the subject every second constitutes exactly the situation in which it is present. Co-existence also begins with the initial situation and extends in the act of attention to some next situation until the task or problem is solved. The universe is given in the act of attention at once as a whole. When abstracting, it is necessary to rely on the abstraction interval that coincides in the act of attention with the specified segment. Note that it is performed according to the inherent property of the object. Due to the non-existent property in the situation, abstraction cannot be built due to the definition of the actual property. For example, abstracting the object "red apple" by the property "to be red" gives the object "apple". Meanwhile, abstracting by the non-essential property, for example, "being chocolate" gives the same object "red apple". Abstraction does not arise.

Object modes. The datum of an object is defined as its being in some area ("here and now" or "there and then") relative to the "I" and/or the Other (Others). It is determined by the mode. The mode of an object in a segment of reality, according to its actual property, is the value of its objectifying function, depending on the ratio of the components. The latter include: 1. the presence (or absence) of an object in the act of attention for the "I"; 2. the presence (or absence) of an object in the act of attention for Another (Others); 3. the presence (or absence) of an object in a given segment of reality "here and now"; 4. the presence (or absence) of the object "there and then". The reality of an object, characterized by its mode, conveys all the diversity of its being in the corresponding segment of reality. So, for example, we talk about the existence of an object if its reality has one of the following modes: the existence of an object for the "I" "here and now", being for Another (Others) "here and now" and/or "there and then". The most obvious existence of the object under study will be in the mode: being for the "I" and the Other (Others) "here and now". The existence, possibility or non–existence of an object for the "I" or the Other (Others) are special cases of the given object, which we are talking about here.

In each situation (lasting from 0.08 seconds to several minutes), the object to which the attention of the "I" and/or the Other (Others) is directed has only one mode associated with this situation. In some future situation, the modus of the object may change. L. Wittgenstein reasoned on this topic. If we see in front of us a tree that exists for us at this moment in time, then, turning away from it, we are not sure that it continues to exist. "This tree disappears when we turn our backs on it"^{[9, p. 99]}. If the subject's attention is not directed at the tree, then it has a lesser measure of existence (it becomes possible only at this point in time).

So, the measure of an object's existence in a situation is determined by its mode. The more witnesses ("Me" and/or the Other (Others)) they fix the existence of an object (the more acts of attention directed at it), the greater the measure of the existence of this object (it is more obvious). Accordingly, the fewer such witnesses there are, the smaller the measure of his existence will be. It is less obvious or not at all obvious. For example, the Moon is obvious to everyone, billions of people see it both day and night. And the UFO that many people talk about is obvious only to those who have directly seen this phenomenon. The measure of UFO existence is very small and its existence is characterized in the range from possibility to complete denial. In the first case, we are talking about the strong mode of the object ("Moon"), in the second case – about the weak one ("UFO" object). Thus, the modes of objects in different situations can be compared with each other. It should be noted that E. Husserl distinguished between the actual mode of an object (the one in the act of attention) and the irrelevant mode (with the potentiality of believing). In his opinion, the role of attention itself is to actualize the potential ^{[10, p. 351]}. Above, we talked about the mode of an object in the simplest case – its being in a specific situation. There are exactly the same modes of the object, constituted in co-existence or in the entire universe as a whole. It depends on the chosen segment of reality in the problem being solved.

By analogy, we introduce a comparative measure of abstraction for objects. We say that an object is more abstract than another if the first has a weaker mode than the second. It is obvious that in the process of abstraction, by its inherent property, its mode changes to a weaker one. The stronger the modus of an object, the smaller the measure of its abstraction in the corresponding segment of reality. Conversely, the weaker such a modus, the more abstract the object will be.

Note that the actual property fully characterizes the corresponding object in its segment of reality. But abstraction cannot be performed precisely according to this most relevant property. To get away from it is to deprive the object of its privilege to be in existence. We can abstract on some part of the actual property that allows such an action. Therefore, we are talking about abstracting not by an actual property (this would contradict the definition of the latter), but by one of its components – by an inherent property, by one of the faces of the very "polyhedron" of the actual property, which was discussed above.

The modes of objects only show their existence both for the "I" and for the Other (Others) "here and now" and/or "there and then" and nothing else. By designating the mode of an object, we can say with respect to whom it takes place (by whom it is constituted) and in which area of existence it resides. Meanwhile, this is not enough for unambiguous intending of the object. It is necessary to know how an object with an actual property and mode is constituted in a given segment of reality. The (constitutive) restrictions on the modes of the object are introduced. Firstly, this is the type of object constitution in the segment of reality. There are only four of them: "speculation", "discussion", "observation" and "experiment". The difference between an experiment and an observation lies in some effect on the object. In addition, it can be repeated an unlimited number of times while maintaining the same conditions. (By the way, Yu. F. Vilesov identifies only three ways (types) of object constitution: "contemplation", "observation" and "experiment"^[11]). Secondly, this is the state of the object's relative givenness according to the corresponding property: the object in abstraction is given either intensively or extensionally. Note that the idea of a relational entity is not new. V. F. Lazarev points out the position of the cognizing subject "from the outside" or "from within" the cognizable situation in his article^[12].

We need to accept one immutable truth: any object that we observe or think about is already abstract in one way or another. By the way, F. V. Lazarev points out this in one of his early works: "An object taken in an interval is an "abstract" (specific) object as a mutual quality of two opposite sides – the object and the environment"^{[7, p. 7]}. The concrete object familiar to us is given in the vision, and the measure of abstraction for it will be minimal. It will take place in the constitution of invisible elements or in the distraction from properties that are not immediately perceived (for example, weight, electrical conductivity, etc.).

Abstraction for the "I" – the Other (Others) in the localities of "here and now" and "there and then". Abstraction for the "I" is of an individual subjective nature, and for the Other (Others) it is objective. In the discussion, the traditional process of abstraction eliminates subjectivity and makes its result acceptable to the Other (Others). Meanwhile, abstraction can be performed not only by Others and for Others (Others), the source of the belief itself is important – the subjective "I". The abstraction produced by a separate "I" (especially in hypothesizing, when creating theories), in all segments of reality: in speculation, discussion, observation and experiment, can bear the features of individuality and originality.

The subject in the segment of reality, when constituting an object, stands in one of the positions: either he is given an object in the area "here and now", or he is given "there and then". Moreover, both localities are limited by the corresponding segment of reality. If the terrain "here and now" presupposes both concrete and abstract content, then the terrain "there and then" is only abstract, as indicated by A.V. Rodin^{[13, p. 65]}.

When we think about something or talk with someone, we somehow operate with abstract entities - concepts, representations. It would be reasonable to say that abstractions in a situation (in co-existence or in the universe) are given "here and now", since we work with them in this area. But what about the abstract in the locality of "there and then"? After all, when we talk about something that happened or was given sometime and somewhere, in any case we are talking about it "here and now". It must be understood that when speaking or reasoning (or imagining) "here and now" about something taking place "there and then", we operate with ready-made abstractions fixed in being (in memory, in an image, in books, etc.). And those abstractions that we create ourselves in the current moment, for us, is given "here and now". Therefore, for abstractions, the statement of the area in which it is located indicates only its existence or formation. So, firstly, for the "I", abstractions in the localities "here and now" and "there and then" are generally accepted or created again (becoming in hypothesization, in memory, in representation). Secondly, for the "I" (especially in speculation) and for the Other (Others), abstractions become ("here and now" in discussion, observation or experiment) or they are already generally accepted entities ("here and now" and "there and then", these will be concepts, categories). And, finally, thirdly, only for Another (Other) abstraction there are ready-made, generally accepted (in discussion, in observation, in experiment "here and now" and "there and then") entities, but not becoming in any way. With ready-made abstractions, it remains only to operate in some way, unlike becoming ones. In the latter case, in order for them to become generally accepted, it is still necessary to prove that they take place in being. This is typical for mathematical research. Therefore, in the following presentation, we will not specify in which area the abstraction is located, as well as its mode itself. Obviously, all abstractions are given for the "I" and/or for the Other (Others).

Abstraction and types of object constitution. We have outlined the types of constitution above. These are "speculation", "discussion", "observation" and "experiment". Naturally, abstraction is performed in different ways in each of them. The most obvious manifestation of abstraction takes place in speculation (when making hypotheses, as well as in other types of operating with concepts, mental constructions and structures) and in discussion, in which the role of concepts in communication is obvious. In observation and experiment, abstraction is less noticeable, but it is present. Here, the very concept of abstraction should be somewhat expanded. This will not only be a distraction from some speculative or discussed properties, but also a distraction from observed properties or some experimental data.

Abstraction in speculation. A trivial kind of abstraction, the most common. Obviously, any thought exists only in the form of abstraction. Mental attention focuses on one aspect of what is thought in the representation or imagination.

Abstraction in the discussion. Abstraction in the issues under discussion takes place everywhere. Discussion in itself is the operation of abstract forms – concepts. The latter manifest themselves in communication between the "I" and Others (including in speculation, when the "I" formulates its positions in terms for the Other (Others)). It takes place when describing any historical events, in this case the historian ("I") narrates for Another (Others) about the events using concepts, generally accepted terms. The same applies to categories.

Abstraction in observation. The object seen is completed to the whole in the act of attention. At the same time, we distract ourselves from invisible connections and relationships with other objects, and consider the visible object to be already given as a whole, as existing independently. It takes place, for example, in the vision of a cube: its mental completion takes place to the whole, when only its front faces are visible. This is one of the forms of abstraction in observation. In the very perception of objects in the real world, their abstraction is already taking place^[8]. In the literature, abstraction in vision is usually defined as categorization (M. Heidegger^{[14, pp. 66-67]}, J. Lakoff^{[15, p. 20]}), gestalt perception^{[15, p. 252]} or as acts of thinking in cognitive psychology (U. Maturana^[16]). "... Such a procedure is actually performed in the very act of observation as a kind of "natural ": it is a reduction of existence to the a priori space-time characteristics of its perception. However, this reduction of existence to a phenomenon means the need to consciously "complete" it to its full concept"^[17]. For example, when we see a red object, we already classify one of its characteristics (color) into a category, and this happens already in the vision itself. This procedure applies to any observed object.

All our beliefs about an object are based on visible properties: its shape, color, the material it is made of, etc. In vision, we abstract from obviously invisible properties, for example, from the gravity of an object: we can only assume to what extent the object is heavy or light. In order for this property to become concrete, it is necessary to take the object in hand. In the act of seeing within the framework of natural attitudes, the constitution and abstraction of objects merge into one act. We are distracted from some invisible and non-obvious properties due to our physiological and mental capabilities. If the eye, in addition to perceiving the obvious and natural, would also see, for example, the electrical conductivity of everyday objects, then this property would become obvious in the act of seeing.

Abstraction in an experiment. During the experiment, one effect is isolated (measured), while other (side) effects are not taken into account and ignored. It is based, as M. M. Novoselov points out, on two types of abstraction: isolating (highlighting the range of questions that the experiment answers, as well as setting its initial conditions) and abstraction of indistinguishability due to the accuracy of the instruments (the parameters of the objects under study must be within the accuracy of the measuring instruments used)^{[4, c. 70]}.

As we can see, abstractions take place in one form or another in every type of object constitution, both in speculation and discussion, as well as in observation and experiment.

Relativity in abstraction. The constituted object is given to the subject in the act of attention either intensionally or extensionally, respectively, the subject thinks of his presence either "inside" or "outside" the abstraction interval according to the corresponding property (feature) of the constituted object. The abstraction interval can also be defined through the relational states of a given. Situation and context are two relative states of the givenness of one object, the actual situation. The problem (the task) is the "inside" of being, given intensively. And the concept is an extensional reality of co–existence. Similarly, the world of the subject (in the sense of A. V. Rodina^[18]) and the universe (conceivable as a whole, "from the outside") – two relative states of the universe. The first is given intensively, the second is extensional. In all cases, the relevant property is "to have a cognitive position."

The actual property is defined to the extent that its disclosure is sufficient to adequately define the object (or class of objects). It bases the inscribability of an object into a segment of reality. In practice, this is expressed in its adequate applicability (meaning). In each of the above three types of reality segment, the actual property of the object is given in two interrelated (mutually complementary) parts:

1. its content and

2. the region of being in which it is revealed in the act of attention in terms of inscribability-embeddedness with its "polyhedron" of an actual property for the "I", the Other or Others. With regard to abstraction, we highlight only one feature (inherent property) - one of the facets of the "polyhedron" of the actual property.

In accordance with this, abstraction of an object by its inherent property can be performed either by content within its segment, or by the region of being to which the object with this property belongs. In the first case, it will be an abstraction already known in traditional logic. In the second case, abstraction is performed in the aspect of the participation of the specified property in the existence of the object in the corresponding segment of reality. Thus, the abstraction of the object can be performed from two sides. Firstly, traditionally (a distraction from secondary properties, this is abstraction by content, "internal" abstraction). And, secondly, taking into account the relationship with the whole (segment of reality) how to identify the meaning of an inherent property for the "here-being" of an object (abstraction in the enclosing whole, "external" abstraction). Depending on the "size" of the reality segment, we distinguish three forms of abstraction of an object: 1. "object in itself"-"object in context" (in a situation), 2. "concept"-"concept" (in co-existence) and 3. "object in general" with the quality or originality of its presence in the universe. All three forms have two different ways of manifestation, depending on the actual property – this is "external" and "internal" abstraction.

Abstracting in segments of reality

Abstraction in a situation. The concrete object in the situation will be abstracted. In fact, a specific object is one that is not subject to any actions on our part in the act of attention. On the contrary, any action with it (choosing from a variety of similar ones, moving, even ordinary vision, etc.) already makes it abstract from some properties. Therefore, abstraction is present in the experience at the most minimal level as an action with specific objects. Here lies a stone, this is a specific object. I take it and throw it. A thrown stone is already, to some extent, an abstract object for me. I do not know its exact location in space at any point in time, nor its speed, etc. When I approach the door and try to open it, I do not see its opposite side, but I can only assume what it is on the other side. What is it like abstracting to its minimum extent? Abstraction in a situation is typical for the types of constitution: "observation" and "experiment".

In the aspect of relativity, abstraction in a situation is constructed as follows. "Internal" (intensive) abstraction is performed as highlighting one property and ignoring all others in the act of attention. For example, the subject ("I") is given the object "red rubber ball". Abstracting by the property of "being rubbery" gives the object a "red ball". "External" (extensional) abstraction on the same property is performed as a clarification of the meaning of this property in a given context. This abstraction gives the object a "red ball that can be rubber".

In this segment of reality, an abstraction of constructivization is given, which consists in fixing the developing being in some one fragment, in a situation. At the same time, they are distracted from connections and relationships with other objects in the studied fragment of being ^{[19, p. 26]}. It is used to cut off the studied object from the existing connections and relationships with some other objects in the environment. This abstraction is given extensionally. Here the subject needs to be distracted from external relations, but it implies the existence of other objects outside the specified situation.

Abstraction in co-existence. Co-existence consists of at least two objectively related situations. In the first, the object is given as it is. In the other, there is an abstraction, an object that has some properties in the "polyhedron" of properties mentally removed. But such a case is rare. Most often, in our mental activity, when solving a problem, we are not limited to only two fixed situations. There may be some intermediate situations.

If co-existence consists of situations in each of which, at least potentially (with a weak mode), an object belonging to some class of similar objects is given, then abstraction in this case leads to an abstraction of identification. Instead of considering a class of homogeneous objects, we consider one object with a property already abstracted in it, under which all objects of the class we are interested in fall. Such an object is a complete whole – a concept. At the same time, "we abstract not only from all the properties of objects with the exception of those indicated and from the material carriers of objects themselves, but also from the fundamental impossibility of carrying out such objects (in fact, there are "long legs", "long nails", but there are no lengths as special objects)"^{[19, p. 35]}. Obviously, abstraction of this kind is given intensively. Within the framework of co-existence, the cognizing subject does not turn to external objects, the existence of which is implied. He is mentally "present" in the studied class of similar objects. If an equivalence class is defined, then an abstract object with a common property corresponding to this class is also defined^{[7, p. 19]}.

Note that abstraction manifests itself in co-existence during the transition from observation (or experiment) to discussion, because what is seen and recorded is discussed only with the help of concepts.

In the same segment of reality, an isolating abstraction is given. It "leads to the formation of so-called "abstract objects" ("whiteness", "facade", "elasticity", "hardness", etc."^{[19, p. 25]}). This type of abstraction, as F. V. Lazarev writes ^[12], appears already at the stage of the subject's constitution of the necessary interval of abstraction (it is easy to see that it coincides with a segment of reality). It is produced in co-existence, a set of situations in which the abstracted object is connected with some other objects. Therefore, the isolating abstraction is given extensionally. D. P. Gorsky points out that isolating abstraction "can be considered as a kind of abstraction of identification. However, there is also a new moment in comparison with the abstraction of identification, namely, the process of “objectifying” distractible properties and relationships: they begin to be considered as some “abstract objects" separated from their material carriers. Therefore, this type of abstraction stands out as an independent one"^{[19, p. 25]}. In relation to scientific knowledge, V. S. Stepin gives such an example of isolating abstraction. "... An inertial space-time frame of reference ... is an idealized object." It "can be identified ... with a real physical laboratory with clocks and rulers, but on condition that such a laboratory is endowed with a number of really non-existent features. It is assumed that it can be completely isolated from external influences (a sign of inertia). It is further assumed that the effect of the measured bodies on the laboratory clocks and rulers can be neglected"^{[20, pp. 105-106]}.

The relative reality of abstraction in co-existence manifests itself as follows. Let's use the previous example. The subject sees children playing with a red rubber ball. The "internal" abstraction of the object "red rubber ball" by the property of "being rubber" leads to the concept of "red ball" (in the task at hand, the problem, in this case, the ball game). "External" abstraction by the same property gives the concept of a "red ball", which is inscribed in a kind of systemic whole. This alignment involves the following aspects: the purpose of the red ball, how to use it, the rules of the game, security measures, etc.

With regard to the concept, we explain the following. As an abstraction, it has two relational states of reality in co-existence: actually, a concept that generalizes some internal inherent property for objects of the same type, and a concept indicating a connection with other objects from the same class. Such a class of objects is expressed in one of its typical elements, constituted as an element of the class. The first is obtained in the course of "internal" abstraction (as a characteristic property), the second – in the course of "external" (as an element of the class).

Abstraction in the universe. A concept is the result of abstraction (identification) of a class of objects that have some one characteristic property. A distinction should be made between a concept and a category. The first is given as a result of abstracting a limited number of homogeneous objects according to some common feature (property), for example, the capital of a state (the number of capitals on our planet is limited). The second term is given as a result of abstracting (generalizing) a potentially unlimited object (for example, necessity, being, etc.). Here we will not distinguish between general and single concepts – this is a topic for a separate article.

In the universe, there is an abstraction of infinity and an abstraction of potential feasibility. In the first, an infinite object is abstracted: it is considered as finite. "Such an abstraction gives us the opportunity to consider the infinite as "actual" given, as finite, and apply ... all the laws of formal logic revealed as a result of operating with the finite"^{[19, p. 30]}. It is given intensively according to the property describing the infinity of the studied object. At the same time, the property of "being infinite" is limited within the universe. The second type of abstraction is performed to prevent an infinite number of operations. Here we abstract from the external conditions that generate infinity. It takes place in a universe in which the existence of potentially infinite objects is possible. It is given extensionally by the property that generates an infinite iteration. "This abstraction assumes that by carrying out a finite number of individualizations of the elements of any set, we can always carry out another individualization of the element of the set in question"^{[19, p. 30]}.

Returning to our example, we will reveal the relative reality of abstractions in the universe. The "internal" abstraction of the object "red rubber ball" by the property of "being rubber" gives an object with the quality of "being a red ball" (in the world of the cognizing subject without any aspects of applicability). "External" abstraction by the same property gives an object whose way of being in the universe is its meaning as "redness" in being. This very "red-balledness" creates a certain kind of presence in the universe. So, in our case, an object with the quality of "being a red ball" and an object present as a "red ball" in the region of being outlined by us are two different forms of abstraction in the universe.

Abstraction and idealization are two sides of the same process. In logic, abstracting an object involves tacitly ignoring secondary properties. And idealization, on the contrary, involves attributing some meaning to a certain property (objects such as an "ideal gas", a "material point", etc., are a form of idealization). Meanwhile, such a formulation in the light of what has been said above becomes not entirely true. Abstraction and idealization are two states of reality relative to each other of an object, which is known only that it is determined by the actual property "to highlight-to distract from ...". Accordingly, the intensional reality of this object is abstraction, as a distraction from some inherent properties of the object ("internal" abstraction). And idealization is an extensional reality of the same object. Some feature is taken from the outside, there is a distraction from the properties, connections and relationships that connect the idealized object with the external environment in the studied segment of reality). This will be an "external" abstraction. Thus, we consider abstraction and idealization to be two sides of the same process.

Conclusion. In the light of the modus representation of the given abstract object developed here, the line between material and abstract objects is naturally blurred. All objects exist in one way or another, only some of them have a strong mode (can be identified in direct perception), while other objects have a weaker mode (traditionally, abstract objects belong to them). We have expanded the very concept of abstraction. Abstraction is subject not only to speculative and discussed objects, but also to those observed or obtained in an experiment. There is no separation between existing and abstract objects. There is only one thing: the existence of objects with some modes and limitations on their constitution in a situation, in co-existence or in the universe. Indeed, what difference can there be between the objects "this is an apple" and "apple", which is referred to in the imperative statement "take an apple and come to us"? In the first case, it would seem that we are talking about a specific apple, and in the second, it is not clear from the statement which apple we are talking about (it is defined as a concept, but where it is located is not indicated). And this apple in a situation (or in co-existence) can be as concrete as it is abstract.

In the modus representation, the boundary between concrete and abstract objects is fuzzy, it actually does not exist. It is defined only by a measure of abstraction. Such a boundary is established by the cognizing subject, who, by his process of cognition, interferes with the order of being of the studied objects. Only our own cognition, with its limitations in constitution, endows an object with a measure of abstraction: whether the object is real, concrete or abstract, imaginary. Everywhere there are objects to which our consciousness attributes some measure of abstraction in order to separate "here-being" from "there-being". In addition, it follows from the modus representation that any object has already been given to the cognizing subject in some abstracted form to a large extent (these will be concepts) or to a small extent (specific real objects). Here we are not talking about existence (as a very strict requirement for objects), but about the existence of objects that already tend to be abstract to some extent. If we abandon the term "existence" and use the more general term "being" (of objects), then there will be no dispute between nominalists and realists – all objects exist to some extent.

The object "moving train" in the film is abstract, and the object "train moving next to me" is already a concrete object. The question arises: is my fear of being hit by a moving train determined only by the measure of abstraction of this object? Restrictions related to natural attitudes are imposed on the constituted object (to some extent already abstract). They are conditioned by the knowledge of the subject, his worldview, prejudices, moral principles, self-care, etc. Such boundary conditions manifest themselves in every situation, in every co-existence, or in the universe in general. So, from a modus-phenomenological point of view, there is no difference between abstract and concrete objects. Everything that is thought, discussed, observed, measured – all these are objects with some properties actualized in the corresponding segment of reality. They are given in some mode and with some measure of abstraction, both with a strong mode (concrete objects) and with a weak one (abstract objects to some extent). To the question of whether abstractions exist, let's answer briefly: they are given for the "I" and/or the Other (Others) "here and now" or "there and then" in one way or another, like any other object.