Ideal objects in philosophy and science: genesis and concept

Rozin Vadim Markovich Doctor of Philosophy Chief Scientific Associate, Institute of Philosophy of the Russian Academy of Sciences  109240, Russia, Moskovskaya oblast', g. Moscow, ul. Goncharnaya, 12 str.1, kab. 310 rozinvm@gmail.com Other publications by this author

Introduction

The concept of "ideal object", of course, is used less often than the concept of "object", but still it is quite common and no less ambiguous. In the Russian philosophy of science, this concept is used and developed by many researchers, for example, V.A. Lektorsky, A.P. Ogurtsov, P.P. Gaidenko, A.L. Nikiforov, etc. ^{[7; 13; 14; 15]}. The polar characteristics of an ideal object are set, on the one hand, by the idea of idealization, on the other hand, by opposition to empirical phenomena. Both of these concepts, although they grasp certain aspects of this concept, nevertheless do not clarify the nature of ideal objects, it remains unclear why ideal objects are created and how they are then used in philosophical or scientific discourse (thinking). Unfortunately, the philosopher and methodologist O.I. Genisaretsky, who left us not so long ago, offered an interesting explanation about the nature of ideal objects at the seminar.  

"Now," he said, "I will talk about the situation where it becomes necessary to talk about the ideal object, where it appears. It is necessary to immediately identify a paradox from which there can be no absolute way out, but there are certain ways of resolving it, accepted in the culture of thinking. This paradox is connected within the cognitive attitude with the problem of the objectivity of knowledge (or its truth). It can be set this way. Due to the fundamental relativity of the idea of an object (since it is connected with something else), it is argued, on the one hand, that our knowledge of an object is always objectively mediated, and, on the other hand, that the object, by definition, must be independent of the subject and of the subject activity...

Next, I will talk about the ideal object, bearing in mind its objectness, the status of the object. The ideal-object orientation originated in the region of Greek philosophy and, apparently, the first ideal object was Thales' "water", which he approved as the primary basis of all things. An obligatory feature that has since been preserved for the object and the term "object" is, apparently, its representability or visibility...The property of observability is also important in the sense that when observing an ideal object, the same state of thinking consciousness is reproduced that takes place in the process of direct visual observation of real things. However, since the ideal object is not a thing, and it is not considered, but only seen (you cannot look at it, look for details!), then here the very visibility is an internal sign for the thinking consciousness, by which it identifies some of its state.  her" ^[11] .         

 These provisions are very close to me, but again I would like to understand why ideal objects are introduced and how they are arranged, for example, why visibility, whether idealization contradicts clarity, what idealization is in general in this case; a number of other questions arise that I would like to get an answer to.

The main part

Ideal objects began to be created during the period of the formation of ancient philosophy and thinking

It is known that Aristotle, criticizing his teacher's teaching about ideas, drew attention to definitions. "Socrates, he writes in Metaphysics, "dealt with the question of moral virtues and for the first time tried to establish general definitions in their field (of the physicists, only Democritus slightly approached this and in some way gave definitions for warm and for cold; and the Pythagoreans ? before him they did it for a few individual things, the concepts of which they cited in connection with numbers, indicating, for example, that there is luck, or justice, or marriage). Meanwhile, Socrates legitimately sought the essence of a thing, since he sought to make logical conclusions, and the beginning for conclusions is the essence of a thing... But only Socrates did not attribute separate existence to the general sides of a thing, and neither did definitions; meanwhile, supporters of the theory of ideas isolated these sides and called such realities ideas" ^{[1, pp. 29, 223]}.

In retrospect, it can be argued that this is the very first discussion of the situation of idealization and the associated construction of ideal objects. For a number of reasons, Stagirite denies the interpretation of ideal objects as ideas (in addition to the above, he shows that the introduction of ideas leads to a doubling of reality, the ambiguity of the existence of things, moreover, there are more ideas than things), offering another interpretation ? ideal objects are the first entities that coincide with things. The first essence, according to Aristotle, is that "it does not affect any subject and is not in any subject" ^[2].

The course "Introduction to the Philosophy of Aristotle" provides such an explanation. "Aristotle uses a special expression both here and in other texts, in Greek it sounds like this: " " ("tode ti"). " " are two words. What is the first entity? This is the . Literally translated as: this is it. That is, to the question "what is the first essence?" (non-predicative), according to Aristotle, the most accurate answer would be pointing a finger: "What is the first essence? "This is it." As soon as we begin to clarify our understanding of what the first essence is, i.e. to saturate our knowledge with some predicates, some accidental characteristics, we immediately leave the field of discussion of the first essence, i.e. we go beyond the knowledge that is recorded exclusively in the expression "this is it". We cannot say anything more meaningful about the first essence" ^[3].

I think we can still. Knowing the context of Aristotle's reflections, it can be assumed that "this is it" for the Stagirite meant an indication of a thing. To make our assumption clear, it makes sense to characterize the situation of the formation of Greek philosophy and thinking from the angle of interest in our problems.

Two important prerequisites can be indicated that preceded this formation: first, the emergence of a new type of person, ("becoming an ancient personality") moving to independent behavior and actions, building a world (and himself in it) different from the generally accepted one (before ancient culture, man believed that all his behavior was determined by the gods, in as a result, independent behavior by communities was not allowed), secondly, the invention of reasoning, i.e. a new way of obtaining knowledge, some based on others.

         For example, Socrates at the trial gets the knowledge that death is rather a blessing by reasoning. First, he exposes two knowledge ? that "sleep is like death" and how "it's good when we get enough sleep" ? then, based on this knowledge, he gets, concluding, another knowledge that "death is rather a blessing."

But it turned out that reasoning in some cases gives, so to speak, normal knowledge that does not contradict observations and common sense, and in others ? "aporia" (contradictions), which often looked like a real catastrophe for the consciousness of the emerging ancient personality. For example, Aristotle in "Physics" discusses one of the aporias of Zeno of Elea, showing that there is no motion, since no distance can be passed to the end. To walk a certain distance, Zeno said, you need to walk half of it. And to walk half the distance, you need to walk a quarter of it. Etc. Since every distance (segment) is divisible to infinity, then in order to go any distance, you need to go through an infinite number of even the smallest segments. But to go through even the smallest segment, it takes a certain amount of time. Since there are an infinite number of segments, an infinite travel time is obtained. But in infinite time, Zeno concludes, the movement will never end and the distance will not be covered.

Two social movements reacted to the paradoxes. The ideologist of the first, Protagoras, arguing that "man is the measure of all things, both existing and non-existing," in fact, recognized the right of the reasoners to receive contradictions and, accordingly, to consider the world contradictory. Parmenides, obviously belonging to one of the first ancient personalities, actually declared the supporters of Protagoras crazy.

People are about two heads, in which the heart helplessly rules.

An idly wandering mind. They are deaf and blind.

A tribe incapable of judgment is rushing about, stunned,

Those who are to be and not to be are the same thing together,

It's not the same thing: they have a backward path to everything ^[19]

From his point of view, the world is consistent and integral (the gods could not create a contradictory world), and the criterion of correctness (normality, "truth") of knowledge is not a reasoning person, but this world (not the empirical one that man observes, but created by the gods; Parmenides calls it "existing", "being" it is assumed that it still needs to be reached with the right thought)

              ...because you won't find

Thoughts without the Existence of the one who speaks in it.

For there is nothing else and there will be nothing else in the world,

Except for the fact that Moira is in chains

Keeps it still and whole. Everything else is just a name,

Everything that mortals put in their faith as the truth ^[19]

The implementation, from our retrospective bell tower, is actually a real program (since the provisions of Parmenides were adopted and implemented by his followers, Socrates, Plato, Aristotle, etc.) and led to the invention of definitions, which Stagirite writes about, polemicizing with the doctrine of ideas. The Pythagoreans, Democritus and Socrates noticed that contradictions in reasoning are obtained if the characteristics (properties) of the objects in question in the premises change. Here, for example, is another Zeno's aporia "Arrow": "A flying arrow is stationary, since at every moment of time it occupies an equal position, that is, it is at rest; since it is at rest at every moment of time, it is at rest at all times, that is, there is no point in time at which the arrow makes movement". Here, in one case, time is understood as consisting of indivisible moments of time (this conclusion, writes Aristotle, "follows from the postulate that time consists of [separate] "now": without this assumption, inference is impossible" ^[3]), and in the other (but in the same reasoning), as continuous ("after all, time does not consist of indivisible "now", as well as no other quantity") ^[3]. These thinkers proposed to define the subjects in question in the discussion and adhere to these definitions.

         But let's compare an ordinary object, which the Greeks called a "thing", and an object defined by a definition. Ordinary time is understood differently, with many meanings: both as moving, and as consisting of separate "now", and as continuous, and as a special space, and as an event, etc., and time, given by definition, we are forced to understand unambiguously, attributing to it strictly defined characteristics (properties). This object, defined by the definition, gets the name of the ideal object in modern times. Where do ideal objects exist? Clearly not in the ordinary world. They exist in correct, consistent thinking.

Realizing this moment, Plato calls them ideas and places them in a special space ? in heaven, among gods and goodness, where there are no contradictions. Being partly influenced by the Pythagoreans, who believe in the possibility of deification (although if you know how the world was arranged by the gods with the help of numbers and drawings), Plato came to an esoteric worldview. He believed that there were two worlds (realities): authentic, consistent, where the souls of people contemplate gods and ideas, and inauthentic, contradictory, where there are things and where souls periodically descend to begin a new cycle of life. At the same time, having descended to earth and incarnated into the material bodies of people, souls forget the true world, but salvation and a correct life represent a recollection of the world of ideas and heaven, which in turn presupposes "dialectics", including, among other things, consistent reasoning.

         Aristotle strongly disagrees with this, because he was not an esoteric and was sure that although the earth and heaven are separated as realities, nevertheless, they are one. Therefore, in particular, patterns from heaven can be transferred to earth and vice versa. For example, in the work "On the Soul", Stagirite discusses why a person moves. Because, he argues, the reason for his movements is thought. But Aristotle attributes the same reason to Reason-God, who moves the planets. "There is something that eternally moves in non-stop motion <...> At the same time, the mind, by virtue of its involvement in the object of thought, thinks itself: it becomes conceivable by coming into contact with its object and thinking it, so that the mind and what it thinks are the same thing. <...> And life is undoubtedly inherent in him: for the activity of the mind is life<...> and his activity, as it is in itself, is the best and eternal life" ^{[1, p. 211]}

By the way, by proposing to build a practical action in accordance with the nature of the phenomenon ("by nature"), Aristotle, on the contrary, transfers the pattern from heaven to earth. His thought can be reconstructed as follows. Reason moves everything, both in heaven and on earth, and since "reason and what it thinks are the same thing," the reason for movement on earth, although hidden to an ordinary person, can still be revealed to a philosopher who knows the causes of phenomena. These reasons set the movements "by nature", which must be taken into account if the master expects the effectiveness of his action. This explanatory scheme, in my opinion, can be seen in the following reasoning of Aristotle: "At the same time, a healthy body is obtained as a result of the following series of thoughts from a doctor: since health consists in this, then it is necessary, if the body is to be healthy, that this is given, for example, uniformity, and if this is needed, then warmth (warming) is required; and so he thinks all the time until he leads to the last link, to the fact that he He can do it himself. The movement that begins from this moment, which is aimed at ensuring that the body is healthy, is then called creation <...> Where the process goes from the beginning and the form (that is, the causes. – V.R.), this is thinking, and where it begins from the last link to which the thought comes, this is creation" ^{[1, p. 122]}.

Here, cognition and thinking are, according to Aristotle, a movement in knowledge, as well as reasoning, which allows you to find the last link (in this case, heat), and practical business, on the contrary, is a movement from the last link, based on knowledge of the nature of the phenomenon obtained in the previous reasoning. According to Aristotle, this will be the correct (effective) creation of a thing. At the same time, Stagirite shows that in order to know what is happening "by nature", it is necessary to go to the essence and causes of the phenomenon. A side effect, but a very important one, is that Aristotelian things have an essence that, if they strive to act effectively, a philosopher must know. At the same time, the essence itself acquires a thing; this new quality of essence Stagnates and designates it as the "first essence".  However, we have got ahead of ourselves, let's return to the formation of ideal objects in ancient philosophy.

Ideal objects allowed not only to think consistently, but also to know the world and phenomena

Note that the conditions of consistent thinking formulated by Parmenides simultaneously pointed to a new way of cognition. It should be consistent and describe a single world.

Would it be there or here: it is indestructible everywhere,

Everywhere it is equal to itself, it is one in the judgment of the limit ^[19]

But much more often a person talked not about the world, but about specific things (objects) and wanted to get true knowledge about them. Plato, following the Pythagoreans, Democritus and Socrates, finds a solution to this problem: the construction of definitions and ideal objects, understood, however, as ideas, he argues, is the knowledge of phenomena. It remained, however, to answer one more question: and how, knowing a certain phenomenon, to come up with the right ideas? "Remembering the ideas that the soul contemplated before birth," Plato should have replied. But in the "Seventh Letter" he does not answer quite like this: thinking dialectically (giving a name, definitions, building images, reasoning, arguing with others), which forms the conditions for recalling an idea ("enlightenment", "shine", Plato writes). "For each of the existing objects, there are three stages by which its cognition must be formed; the fourth stage ? this is knowledge itself, but the fifth should be considered that which is known in itself and is genuine being: so, the first is a name, the second is a definition, the third is an image, the fourth is knowledge…All this must be considered as something unified, since it exists not in sounds and not in bodily forms, but in souls... Only with great difficulty, by mutual verification - by definition, by visible images ? by sensations, and moreover, if it is done in the form of benevolent research, with the help of harmless questions and answers, the mind can shine and an understanding of each subject can be born to the extent that it is accessible to a person" ^{[16, pp. 493-494, 496]}.

To understand why Plato gives such an answer, let's look at how he gets new knowledge about love in The Feast. It turns out that it is precisely by defining love, thinking consistently, arguing with listeners. Reflecting on the way in which new knowledge about love was obtained in the "Feast", Plato writes that "we just did this when talking about Eros: first we determined what it was, and then, for better or worse, we began to reason; therefore, our reasoning came out clear and did not contradict itself" ^{[17, p. 176]}. Yes, but the question remains: how did Plato come up with the correct definitions?   

Let's pay attention to the phrase in the "Seventh Letter": "the first is a name, the second is a definition, the third is an image, the fourth is knowledge." What does Plato mean by "image" here? It is unlikely that I will make a mistake by pointing to the "schemes". The fact is that Plato's definitions are always preceded by schemes. "Before," says Aristophanes, "people were of three sexes, and not two, as now, male and female, for there was still a third sex that combined the signs of both; he himself disappeared, and only the name that became abusive remained of him, androgynes…Terrifying in their strength and power, they harbored great designs and even encroached on the power of the gods…And so Zeus and the other gods began to confer on what to do with them…Finally, Zeus, having come up with something, says:…I will cut each of them in half, and then, firstly, they will become weaker, and secondly, more useful for us…So, each of us is a half of a person divided into two flounder?like parts, and therefore everyone is always looking for the half corresponding to him." And here is the definition that completes this story-narrative: "Thus, love is called the thirst for integrity and the pursuit of it" ^{[18, p. 100]}.

What is this narrative like as an "androgynous scheme", what role does it play in the dialogue exactly as a scheme? On the one hand, it sets the main characteristics of love as an ideal object, on the other hand, it clearly inclines listeners to understand and accept this scheme, therefore, the gods, on the third hand, as I show, this narrative looks to Plato and his followers as a solution to the "problematic situation" that objectively developed during this period ^[20]. The content of this problem was approximately as follows: the emerging ancient personality aspired to independence in all spheres of life, including in love, but could not realize itself in this area, since the generally accepted social model of love did not imply independence, but on the contrary, subordination of the individual to the decisions of the gods of love (Aphrodite and Eros). Plato's scheme looked like a solution to this problem, since the choice of the beloved was now transferred to the personality itself. Next in line are the following questions: how does Plato grope for the characteristics of the scheme itself and whether it was possible to do without it (after all, it seems that there are no schemes in Aristotle's works)?

It can be noted that the individual characteristics of the androgynous scheme were determined by the nature of love (the halves of the androgynous stretch and search for each other) and the problematic situation (it was necessary to create conditions for the possibility of independent choice in love). Nevertheless, the work of Plato himself cannot be discounted. By inventing the androgynous scheme, he solved a problematic situation according to his personality, which concerned many at that time. The androgynous scheme helped Plato organize and connect various meanings that had previously been, figuratively speaking, on different shelves of his consciousness. In this regard, it can be argued that the invention of the scheme is subject not only to the logic of objectivity (the influence of the problem situation and the prevailing ideas about the phenomenon itself), but also to the logic of subjectivity (the peculiarities of understanding and vision of the author of the scheme, his ingenuity, reaction to the statements of others, etc.; recall how Plato wrote: "besides, if this is done in the form of benevolent research, with the help of non-malicious questions and answers").

An analysis of this case and others in which schemes were created allows us to suggest that it is impossible to build ideal objects without bypassing schemes, since their inventors (creators) are people. The individual must first make an objective (in this sense, first "intersubjective") a situation of your own, individual, private. Then offer a solution to it by building a diagram. It is the scheme, as Kant wrote about it, that allows us to organize the heterogeneous meanings of an individual in a new way, taking into account both the problematic situation and our own intentions and values. "The scheme of a triangle," Kant writes, "cannot exist anywhere except in thought, and means the rule of synthesis of imagination in relation to pure figures in space... The scheme of a pure intellectual concept is something that cannot be brought to any image; it is only a pure synthesis expressing a category in accordance with the rule of unity based on concepts in general, and is a transcendental product of the imagination" ^{[12, pp. 223-224]}.

In this case, one can understand Genisaretsky's position that an ideal object has the properties of representability or visibility. He owes these properties precisely to schemes that, according to Kant, cannot be created without imagination. But since the schemes ? These are also semiotic constructions that provide consistent reasoning and cognition, imagination is corrected during the construction of schemes and is limited by thinking (the need to go out to definitions and constructions of ideal objects).

 But what about Aristotle, who dispenses with schemes? Nothing like that, Stagirite creates ideal objects based on diagrams too. But since he believed that Plato's schemes were subjective (in part, this is true, but only in part), after the schemes played their role, Aristotle removed them from his works and arguments. By the way, Aristotelian categories are an excellent example of schemes, and generalized ones, describing a whole class of phenomena under study and presented not as schemes, but types of ideal objects. "And just as the first essences," writes Aristotle, "relate to everything else, so the species relates to the genus: the species is the subject of the genus, because genera affect species, species do not affect genera. Hence, also for this reason, the species is more of an entity than the genus" ^{[2, p. 57]}. Here, the relation of a species to a genus is a generalized scheme. Let's apply it, for example, to an individual (say, Socrates) and a community of individuals (people). The correct attitude is when, reasoning, we transfer properties from people to Socrates (people are mortal and Socrates is mortal, people are bipedal and Socrates, people have blood and Socrates, etc.). The wrong attitude is when characteristics from Socrates are attributed to people (Socrates is bald and people too, Socrates has a grumpy wife Xanthippe and people too).  

Ideal objects allow us to characterize facts (empirical objects) in a different way.

By constructing love as an ideal object, Plato was able to radically rethink the common understanding of love at that time. He belittled this understanding and interpreted it as vulgar, vulgar, in order to raise a new understanding, which, on the contrary, rises. "So, Aphrodite's vulgar Eros is truly vulgar and capable of anything; this is just the kind of love that insignificant people love. And such people love, firstly, women no less than boys; secondly, they love their loved ones more for the sake of their body than for the sake of their soul... That's why they are capable of anything ? good and bad in the same degree. The eros of Aphrodite of heaven goes back to the goddess, who, firstly, is involved only in the masculine principle, but not in the feminine, - no wonder this is love for young men, ? and secondly, is older and alien to criminal audacity. That is why those who are obsessed with such love turn to the male sex, giving preference to what is stronger by nature and endowed with great intelligence... Such is the love of the goddess of heaven: heavenly itself, it is very valuable both for the state and for the individual, since it requires great care from the beloved for moral perfection. All other types of love belong to another Aphrodite ? vulgar" ^{[18, pp. 107, 111]}.

  Aristotle does the same. For example, having come up with the idea of essence as movement by nature, Stagirite introduces a scheme of "movement to its place", which allows us to give a new understanding to empirical cases (facts), namely, the fall of heavy bodies and the rise of light ones. "Under the natural,? writes M.According to the classical Aristotelian concept, it is caused by an innate desire for all things to their place, the point at which the whole essence of the element, of which this body consists, is concentrated, as it were. Movement, generally speaking, can occur in all directions, but natural movement can occur only in one direction, determined, for a solid point located in space, by a line connecting this point to the center of the world or, what is the same thing, to the center of the earth" ^{[10, p. 19]}.

From the point of view of Aristotle, A. Grigoryan and V. Zubov explain, "the four elements (earth, water, air, fire) are located concentrically in the universe, or, what is the same, their "natural places" are located in this way. If the overlying element is forcibly moved to the underlying one, it shows a desire to return to its "natural place", i.e. it acquires "lightness"; water, being in the ground, rushes upwards, just like air moved into the ground or water" ^{[9, p. 94]}.

It is clear that the idea of "striving of bodies to their places", as a condition for their acquisition of essence, is not an empirical observation, but a pure construct (ideal object) designed to explain various observed phenomena and coordinate natural movement with the system of Aristotelian categories. For example, an explanation is based on this view, "why the same bodies descend in the air and float in the water, for example, a tree. Such bodies contain a certain amount of air in their composition" ^{[9, p. 94]}. Or another explanation for why the rate of fall is directly proportional to the weight of the falling body: "if the body tends downwards as a result of the innate desire in its very substance to connect with its proper place, then it is natural that the more of this substance in it, the faster it will tend to this place" ^{[9, p. 24]}.

So, ideal objects not only allow us to think consistently and to know, but also to rethink empirical cases (facts) in a new way, according to the approach and views of thinkers. But there is another important characteristic of ideal objects, which becomes especially prominent when comparing historical changes in philosophy and science.

The construction of ideal objects is conditioned by the historical type of philosophical or scientific thinking   

The strategy of constructing ideal objects in Galileo's famous work "Conversations and Mathematical Proofs concerning two new branches of science related to mechanics and local Motion" differed significantly from Aristotle's. First, he sets ideal objects using mathematics. "But if human understanding is considered intensively, and since intensity means a perfect understanding of certain judgments, then I say that the human intellect really understands some of these judgments perfectly and that in them it acquires the same degree of certainty that Nature itself has. Only mathematical sciences belong to these judgments, namely geometry and arithmetic, in which the divine intellect really knows an infinite number of judgments, since it knows everything" ^{[8, p. 61]}.

Secondly, in this case, nature is known, the objects and processes of which are subject to mathematical relations and eternal laws. Thirdly, Aristotelian methods of induction and construction of ideal objects recede into the background, and methods of mathematical description of natural processes are put forward in the first place, which make it possible to identify in the latter "ideal processes" corresponding to mathematical models (in this case, the process of falling bodies in the void) and factors distorting ideal processes (insignificant pushing force according to Archimedes and the significant one is the resistance of the medium). Through the mouth of the hero of the dialogue, Salva Galilei says: "... the reason for the different rate of fall of bodies of different weights does not lie in their weight itself, but is due to external causes ? mainly the resistance of the medium, so if the latter were eliminated, then all bodies would fall at the same speed" ^{[8, p. 160]}. Here, "bodies falling at the same speed" is an idealized case of falling, "the resistance of the medium" is a factor distorting the idealized fall of the body.

Thirdly, by creating an experiment, Galileo brings a real object (falling bodies in the air) in line with an ideal object, i.e. he is sure that he himself can create objects of nature, which Aristotle or Archimedes would never agree with. As F. wrote a little earlier. Bacon: "As for the content, we make up the History not only of nature free and left to itself (when it spontaneously flows and does its work), what is the history of celestial bodies, meteorites, earth and sea, minerals, plants, animals; but, to a much greater extent, of nature bound and constrained when art and the service of a person takes it out of its usual state, affects it and shapes it... the nature of Things affects more in constraint through art than in one's own freedom" ^{[4, pp. 95, 96]}. (the italics are ours. ? V.R.) In this case, art is a human activity, including technical. 

         It is clear that the mental and categorical space in which Galileo builds ideal objects is different from that of Plato or Aristotle ^[22]. Indeed, by this time, Roger Bacon's concept, formulated back in the 13th century, had become increasingly influential, according to which nature was created by God on the basis of mathematics (but even earlier in Timaeus and other dialogues Plato formulated similar ideas). And Galileo could build a mathematical analysis based on the work of Archimedes, whom he always admired. The belief that man can create "second natures" by imitating the first nature is almost a common place of Renaissance thinkers (if man is a "second God", according to Nikolai Kuzansky, then why can't he create?).

Within the framework of such a mental space, another logic of constructing ideal objects operates while maintaining the other three conditions (ideal objects are created in such a way that it is possible to think consistently, to learn and comprehend facts).  

The four functions of ideal objects discussed here in specific cases can be identified in the case of other cases, including art cases. Here, for example, is a beautiful quatrain by Marina Tsvetaeva:

Like a warm tear –

A drop fell into my eyes.

Up there in the sky,

Someone is crying for me.

In it, the image of rain-crying (the one who cries, and about whom they cry) is an obvious metaphor in which two ideal objects can be distinguished: one is obtained when the artist thinks and builds events in separate realities (in this case, either in the earthly or in the heavenly), the other when he combines movements in these realities (for example, it combines the characteristics of an ordinary person and the guardian spirit grieving for the hero). In the first case, we can talk about artistic analysis, in the second – artistic synthesis ^{[21, p. 63]}.

Conclusion

I have considered only a number of cases that allow us to build a satisfactory modern doctrine of ideal objects. Subsequent analysis can make significant adjustments to the understanding of the nature and features of this concept. Nevertheless, it is already clear that the construction of ideal objects is an important link in philosophical, scientific, and, I suppose, other types of thinking. Moreover, if the task is to trace the development of philosophy or science, then ideas about ideal objects are put forward in the center of research. It is not the problems of theory with their confirmation or refutation, not the formation of a new paradigm, but the analysis of problematic situations, schemes and ideal objects. Perhaps the concept of "research programs" by I. Lakatos is closest to this approach. Here it is worth paying attention to the fact that schemes can be used in different ways. In the field of cognition for the construction of ideal objects, in art for the construction of metaphors and other tropes, in engineering and technology for the construction of technical products, in transport systems (for example, in the subway) for the organization of traffic flows or the orientation of an individual passenger. If we are talking about the study of ideal objects, then, as we tried to show, they perform three main functions: they allow us to think consistently, to carry out cognition, to interpret (understand) facts in a new way, in addition, ideal objects are essentially conditioned by the historical type of philosophical and scientific thinking. Some types of ideal objects in science and philosophy are best characterized, but only some. The next step is the study of other types, as well as in other practices (art, engineering, technology, etc.).