Lecture
The basis of division is a separate feature or combination of features, variations of which allow us to distinguish between the types of objects conceivable in a shared concept.
The most frequent mistake in division is, of course, a change in the base on one of the division steps.
A person begins to divide, say, cereals into rye, wheat, oats, and barley, and then suddenly calls corn and sunflower, since they also play an important role in the nutrition of people and animals. Or someone divides fiction into novels, novels and short stories, and then attaches poems to them, referring to the latter works imbued with a special lyricism.
In one old Ukrainian comedy, a character was bred who, having been at the fair, then set forth his impressions of what he saw: “My God, my God, what is there not at that fair! Wheels, glass, tar, tobacco, a belt, a bow, merchants of all kinds ... so that if there were at least thirty rubles in your pocket, then you wouldn’t have bought the whole fair. ”
In some mental illnesses, actions on the classification of objects are given with difficulty and, which is characteristic, first of all, the requirement of unity of foundation is violated. Some patients suffering from speech impairment - aphasia, are not able to classify uniformly balls of wool of different colors lying on the table in front of them. In one corner, aphasic places the lightest skeins, in the other - red, somewhere else small skeins, and in another place - either the largest, or with a purple tint, or rolled into a ball. By, barely intended, these groups fall apart. The chosen principle of division seems to the patient too broad and therefore unstable. The patient endlessly collects and separates, heaps up various similarities, destroys the most obvious of them, breaks identities, combines various criteria, fusses, starts everything anew, worries and, finally, does not come to anything definite.
Every classification has a specific purpose, and the choice of the basis of the classification is dictated by this very purpose. In one case, it is advisable to divide people by level of education, in the other by age, and in the third, by shoe size, etc. Since there can be a lot of diverse and diverse goals, the same group of objects can be classified for a variety of reasons. The objectives of divisions, and therefore their bases, are determined by certain practical or theoretical considerations to which the rules of division have nothing to do. The essence of these rules is reduced to the requirement that the base, once it was chosen, subsequently did not change within the limits of the division.
Suppose that we need to classify the following six names into groups according to any generalizing features: 1) Gerd, 2) Boris, 3) Alexey, 4) Catherine, 5) Bella, 6) Dodon. How many groups can you allocate? Pa this question can not be answered unequivocally, since there is no limit to the grounds on which the listed names can be divided. They can be divided into male and female (groups 1,4, 5 and 2,3, 6); for the names that are the heroes of famous fairy tales, and other names (1, 6 and 2, 3, 4, 5); names beginning with a vowel or consonant (3, 4 and 1, 2, 5, 6); in names that are quite rare among us and widespread (1, 5, 6 and 2, 3, 4); for names containing two letters “e” and not having this feature (3, 4 and 1, 2, 5, 6), etc.
By what signs can such things as brick, shoe polish, mirror and pencil be divided into groups? If desired, the reader can find at least a dozen different bases for dividing these things.
Sometimes they say that you need to strive to classify objects according to important, essential features, to avoid divisions according to random, secondary properties. However, this wish, no matter how reasonable it initially seemed, is hardly realistic and doable. The important from one point of view may turn out to be less important and even in general insignificant from another a division that meets one goal may hinder the achievement of another goal.
When hiring people it is important to consider their level of education, but when selling shoes to them it is more important to know how they are divided into groups according to its size.
At one time, numerous attempts to classify bacteria along the lines of a comprehensive hierarchy did not lead to noticeable success. However, the border turned out to be very useful; it is customary to draw between bacteria staining and not staining with a specific dye - gentian violet. The division of bacteria into gram-positive and gram-negative does not say anything significant about them, but it is important for those who observe them under a microscope.
In the old days there were such posters and postscript to them: “Virtuoso-pianist V. X. Davingof. Plays head, elbow and seat; 1st place - 50 kopecks, you can sit; 2nd place - 30, you can stand; 3rd place - 10 kopecks, you can do anything. Those who bought the first 50 tickets, with the exception of the gallery, will receive a free portrait of the actress - the wife of Mr. Director ... ”.
It seemed natural and important for organizers of ideas who composed these posters and knew the public at that time to divide the piano game into the head, elbow, “sitting” and other body parts, divide seats into sedentary, standing and unknown ones, divide the audience into those eager to have a free portrait director's wives and all the rest. The basis of these divisions lay, of course, among other things, and purely advertising considerations. “As the mouth is rosy without a smile, without a grammatical mistake, I don’t like Russian,” Pushkin confessed. Mistakes in the division can also like something and somehow attract, while the logically flawless classifications can give the impression of dryness and calculus.
In his book “The Hedgehog and the Fox”, devoted to the historical views of L. Tolstoy, I. Berlin, analyzing the novel “War and Peace”, showed the originality of Tolstoy's approach to history. The ancient Greek poet Archilochus somehow divided people into foxes, pursuing different goals depending on the circumstances, and hedgehogs, who aspire to only one big task. Following him, Berlin identified Tolstoy as a fox who thinks she is a hedgehog.
"The foxes who believe that they are hedgehogs," wrote DS Likhachev, "were all the chroniclers of Ancient Russia: they followed a strictly ecclesiastical ideology and were pragmatists in the concrete interpretation of specific events."
These observations are interesting for us in two ways. Archilochus divides people into foxes and hedgehogs. Berlin complicates this division and divides people, not to mention, however, this explicitly, into four categories: foxes, who think they are foxes; hedgehogs, convinced that they are hedgehogs; foxes thinking they are hedgehogs; hedgehogs who consider themselves foxes. This is a common way to complicate the basis of division, leading to the differentiation of the division itself. Sometimes such a consistent complication leads to the fact that almost nothing remains of the clarity of the original division. Complication of the base is always associated with the risk that the resulting classification will be poorly applicable to real things.
And the second moment. Those who strictly adhere to the same foundation during the classification process can be called, after Archilochus, hedgehogs. And those who modify this basis depending on the circumstances arising along the way, should then be attributed to the foxes. Logical theory requires that everyone always be an adamant hedgehog. Practical circumstances sometimes force us to resort to tricks and become, at least temporarily, a fox. This is connected with the fact that many real divisions, which are, in general, necessary and useful, depart from the ideal outlined by theory.
It is possible to go further and, in the spirit of Berlin, to single out more foxes who consider themselves hedgehogs, and hedgehogs who are convinced that they are foxes. The first ones modify the basis of the classification depending on the circumstances, but do not notice this with its flexibility. The latter, being ready to compromise and retreat in case of need from the chosen base, are nevertheless strictly and unswervingly classified.
Speaking about the bases of divisions, it is necessary to mention a special type of divisions - the dichotomy (literally: division in half). Dichotomic division relies on an extreme case of variation of the trait, which is the basis of the division: on the one hand, there are objects that have this trait, on the other - those that do not have it.
In the case of ordinary division, people can be divided, for example, into men and women, into children and adults, and so on. When a dichotomy occurs, a lot of people are divided into men and “non-male”, children and “not children”, etc.
Dichotomic division has certain advantages, but, in general, it is too rigid and rigorous. It cuts off one half of the divisible class, leaving it, in essence, without any specific characteristic. This is convenient if we want to focus on one of the halves and do not show much interest in the other. Then you can call all those people who are not men, just “non-men,” and at the same time end the conversation about them. Not always, however, such a distraction from one of the parts is advisable. Hence the limited use of dichotomies.
The usual divisions of historical novels are a good example of "divisions in two." The world of today's historical romanistics is very wide in its “spectrum” of problems, chronological times and places of action, stylistic and compositional forms, and ways of conducting a story.
You can try to carry out an all-embracing classification of historical novels on the same basis, but it will inevitably prove difficult, not particularly clear, and, most importantly, practically useless. The fluidity of the “matter” of the novel on the themes of history dictates a particular manner of division: without striving for a single classification, to give a series of dichotomous divisions that are not related to each other. “There are novels, biographies and novels, essays; novels documentary and novels legends, "philosophy of history"; novels concentrating the nodal moments of the life of a hero or a people, and novels unfolding in lengthy cyclical chronicle narratives, in which there is both intensity of internal movement and depth, and not “spreading of thought” at all. This characteristic of the “field” of a historical novel, taken from a literary work, is precisely the time for a series of dichotomies.
Classifications based on the dichotomous division were especially popular in the past, in the Middle Ages. This was explained, on the one hand, by the limitedness and superficiality of the knowledge available at that time, and on the other, by the irrepressible desire to cover the entire world with classifications, including its “extraterrestrial” part, which was assumed to exist but not accessible to a weak human mind.
Here is how, for example, the philosopher of that time classifies Gregory the Great “all that is”: “For all that is, or exists, but does not live; either exists and lives, but has no sensations; either exists, lives, and feels, but does not understand and does not reason; either exists, lives, feels, understands and argues. Stones exist, but do not live. Plants exist, live, but do not feel ... Animals exist, live and feel, but do not understand. Angels exist, live and feel and, with intelligence, reason. So, a person, having with stones what he exists in common, with trees - that which lives, with animals - that which he feels, with angels - that which argues, is correctly indicated by the name of the Universe ... ” Here everything is divided first into the existing and the non-existent, then the existing - into the living and the non-living, the living - into the sensible and the non-sentient, and finally the sentient - into the reasoning and the non-judgmental. This classification is intended to show, according to the intention of its author, that a person has something in common with all kinds of things existing in the world, and therefore he is justly called the “miniature universe”.
To create such classifications, there is, of course, no need for a specific study of any objects. And the conclusion is global: man is a reflection of the entire Universe and the pinnacle of all earthly. However, the scientific value of such classifications is negligible.
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Logics
Terms: Logics