By the nature of signs of content distinguish the following types of concepts:
1. Positive and negative concepts. Positive - these are the concepts, mostly the content of which there are only positive signs. They reflect the availability of any qualities, properties, etc. For example: "The crime is a socially dangerous act provided for by the Criminal Code." Negatives are called such concepts, mostly the content of which is met at least one negative feature. They are characterized by the lack of any qualities, properties, and the like objects. For example, the concept of "autocracy", in the content of which there is a sign "The absence of genuine representative institutions" is negative.
2. Absolute and relative concepts. Absolute concepts - such, in the main content of which there are only signs of properties ("Square - rectangular, equilateral quadrangle"). Relative - concepts, mostly content of which meet at least one sign-attitude ("debtor", "lender", "brother").
According to the number of elements, the concept is divided into empty and non-empty. Empty called concepts whose amount is empty, i.e. Does not contain a single element. These include: concepts having a fantastic (mythological) character ("Centaur", "Mermaid"); The concepts that were put forward as scientific or technical concepts, but during the development of science and technology, their inconsistency was found ("Eternal Engine"); The concepts of idealized objects playing a supporting role in the sciences ("perfect gas", "absolutely black body", "ideal state"); The concepts of actually non-existent, but possible ("aliens", "unearthly civilization"). Non-empty is the concepts whose volume contains at least one element ("city", "cosmic body"). The division of concepts on empty and non-empty to a certain extent relatively, primarily due to the mobility of the boundaries between the existing and non-existent. Non-existent in some conditions can become existing in others, and vice versa.
By the nature of the elements of the scope of concepts are divided into the following types:
1. Corrective and irrelevant concepts. In co-relatives, one object involves the existence of another and without it ("Parents", "Children", "Teacher", "Student", etc.). In irresponsible concepts, an object that exists to a certain degree independently, "separately" from others ("Nature", "Plant", "Animal", "Man", etc.).
2. Collective and intimidating (dividing) concepts. Collective - these are notions, the elements of which themselves make up the set of homogeneous objects (for example, the "crowd", "library"). One of the features of collective concepts is that they cannot be attributed to each subject of this class: one book is not yet a library, one person is not a crowd. Separate concepts are called such, the elements of the volume of which are not sets of homogeneous objects. Most of such concepts (for example, "Tree", "Man", "Student", "Stool", "Logic"). The peculiarity of separation concepts is that they refer not only to the group of subjects in general, but also to each individual subject of this group. For example, "Tree" is the whole set of trees at all, and every concrete tree is separate - birch, pine, oak, etc.
3. Specific and abstract concepts. Specifications are concepts, the elements of the volume of which are subjects and phenomena with the relative independence of the existence ("Chair", "Shadow", "Music", "Crime"). Abstract - these are concepts in which the properties of objects or the relationship between objects do not exist independently, without these items: "Justice" (for example, society), "whiteness" (for example, paper), "caution" (for example, a person).
Knowledge of concepts has a considerable practical value, it is important for understanding the meanings of certain allegations, as well as to ensure the accuracy of expression of meaning, which is a significant moment of the logical culture of thinking.
Concepts can be classified for species on the following grounds:
- 1) according to certain characteristics of the volume;
- 2) the nature of those generalized in the concept of objects;
- 3) the character of the signs included in the content.
- 1. In terms of concepts are divided into empty and non-empty.
Empty (or with zero-volume concepts) Called concepts whose volumes are not included in any subject (phenomena, events). For example, the concepts of "Centaur", "round square" - empty concepts, since in reality we will not find a single item that would have a sign "to be a centaur", "to be a round square." There are actual and logically empty concepts.
Actually empty is the concept denoting really non-existent objects, i.e. If there is still no subject h. With this characteristic Oh). For example: "Eternal Engine", etc.
Logically empty The concept is called the logical content of which contradictory. For example: "socially non-dangerous crime", "intersecting parallel straight lines", i.e., i.e. if a Oh) There is a logical contradiction characteristic of objects x.
In fact, non-empty concepts, in turn, are divided into common and single.
Common Called concepts, the actual volumes of which include two or more homogeneous subjects (phenomena, events). For example: the concept of "city" - general, since the number of cities that exist to land, more than two. General concepts are divided into registering and unregistered.
Registering Call the concepts in which the number of objects imaginable in it can be recorded, registered (in any case, in principle). For example, the "cities of Russia", "Works M. A. Sholokhov".
The general concept refers to an indefinite number of objects is called unregistered. For example, a "chess player", "man", etc. So, in the concept of "chess player" all chess players of the past, present and future are thinking.
Single Called concepts, the actual volumes of which include only one subject (phenomenon, event). For example, the concept of "the largest city in the world" is a single, since the property "to be the largest city in the world" may have a single subject. In the process of cognitive activity, sometimes there are disagreements when trying to resolve the issue, whether this concept is common or one due to the nature of ideaable in the concept of objects, for example, the concepts of "water", "love", "Movement", "matter".
In such cases, it is necessary to use the following rule: the concept is general, if within its volume you can select some types of items. So, in the amount of the concept of "love" stand out: "Youth love", "Middle-aged love", etc.
An even more simply resolving disagreement in solving the specified question, when it is possible to individualize conceivable in the concept of objects. For example, the concept of "heroism" is also general, since we can talk about the heroism of A. Matrosov, Yu. A. Gagarin, and the like.
Among the general concepts, universal concepts occupy a special place.
Universal Called concepts whose volumes coincide with the universal (native) of this concept. For example, in the union (kind) of squares, such a concept will be, for example, the concept of "a square, from which all parties are equal." Here, a species difference is the "equality of all sides" - inherent in all squares as a whole.
Non-communicable Call concepts if their volumes do not exhaust the volumes of the universum (genus) of this concept. For example, "a predator living on land." In the department (kind) predators, this concept will be unsusarious, as the species difference is "living on land" - not all types of predators and does not exhaust the entire volume of the native concept of "predator".
2. By the nature of generalized objects, the concepts are divided into collective and intimacy.
Collective The concept is called if each element itself is a set of homogeneous objects. For example, "Student Group", "Forest", "Football Team". The content of collective concept cannot be attributed to each individual element included in its volume, it refers to the entire set of elements. For example, the essential signs of the student group (a group of students, studying jointly) unpacks for each individual member of the student group. Collective concepts can be general and single. For example, the concept of "forest" is general, and the concept of "Bryansk Forest" is a single one.
Dividing It is called the concept, the elements of which are many homogeneous objects. For example, "Man", "Chair", "Crime", etc.
In the process of reasoning, general concepts can be used in a collective and dividing sense.
If the statement applies to all class objects taken in their unity, and not applicable to each class of class separately, then such use of concepts is called collective.
If the statement relates to each class of class and applied to all objects of the class, taken in their unity, then such use is called the dividing.
Example.
"All people are mortal."
Expressing the thought "All people are mortal," we use the concept of "people" in the dividing sense, since this statement relates to each person. In the statement "The average life expectancy in Russia is 70 years old" - in a collective sense, since it is not applicable to each resident of Russia separately, since the individual life expectancy may be more than 70 years, and in some cases it may coincide with this statement.
A) Types of concepts by volume.
When highlighting the concepts of concepts, you need to take into account the various features. The most important grounds for dividing concepts are: (1) the type of their volume, (2) the type of elements included in their volumes, (3) the type of signs on the basis of which is a generalization.
By the nature of volume concepts are divided by empty and non-empty.
– Empty The concept is considered, in the amount of which there is not a single element (for example, "a person who is now president of the USSR")
– Non-empty The concept is considered in the amount of which there is at least one element (for example, the "number that is even").
Non-empty concepts, in turn, are divided into single and are common.
– Single the concept is considered in the amount of which there is exactly one element (for example, the "number that is simple and even").
– Common the concept is considered, the volume of which consists of more than one element (for example, "a person who is a student of any university").
General concepts are also divided into universal and non-communicable.
– Universal the concept is considered, the volume of which coincides with the union (for example, "a square, from which all parties are equal).
– Non-digestible the concept is considered, the volume of which is less than the universum (for example, the "quadrangle, whom all parties are equal")
C) Types of concepts by type of volume elements.
By type of elements, the concept of concepts are divided into
but) concrete and abstract
– Specific the concept, the elements of the volume of which are objects or sets of objects (for example, "a person who knows how to play a violin")
– Abstract the concept, the elements of the volume of which are properties or relationships (for example, "the state of an affect caused by an emergency").
b) collective and disappointing
– Collective the concept is considered, the elements of the volume of which are sets (for example, the "flock of deer grazing on the edge of the forest").
– Disobey the concept, the elements of the volume of which are individual items, properties or relationships (for example, "fear experienced before visiting the dentist").
Exercise 3.. Determine the appearance of the following concepts by the type of elements included in their volume.
a) device designed to receive television programs (TV)
b) many books stored together and affordable for public use (Public Library)
c) a set of sustainable, socially significant properties of a person who are manifested in his behavior (personality)
d) Love that flashed suddenly at the first meeting (love at first sight)
(C) Types of concepts in content.
According to the type of signs, the concept is divided into
but) positive and negative
– Positive the concept in which the objects are generalized on the basis of the feature they have (for example, the book taken in the library) is considered.
– Negative the concept in which the objects are generalized on the basis of the feature that they do not have (for example, "man, not knowing Japanese ").
b) relative and refable
– Relative the concept in which objects are summarized on the basis of their relationship to other subjects are considered. For example, the concept of his wife is relative - "a woman in marriage with some kind of man," because his sign allocates women not by their own qualities, but through attitude To some men, that is, as one of the sides of the married couple.
– Refless the concept in which the objects are generalized on the basis of their own properties are considered. For example, the concepts of the ballerina - the "ballet woman", about beauty - "a woman who has excellent appearance", etc. Here women stand out on the basis of their own characteristics.
Note that you can always pick up another to relative concept correlate that is, to implement conversion . For the above concept of his wife, the concept of husband: "A man in marriage with some kind of woman." For the concept of a parent, the concept of child will be the concept of child, for the concept of the cause - the concept of the investigation, etc.
Exercise 4.. Determine the appearance of the following concepts by type of signs, on the basis of which is a generalization. To the relative concepts, choose correlate.
a) a number that does not have divisors besides himself and units (simple)
b) feudal, which is in personal dependence on some other feudal (vassal)
c) a girl who is a daughter husband of some woman, but is not her own daughter (stepdaughter)
d) a philosopher who was a teacher Alexander Macedonian (Aristotle)
Implement full logical analysis concept It means to determine its universe (genus), the volume and content, as well as to establish, to what kinds it relates on all the above-mentioned fission grounds.
Logic is not interested in the numbers themselves. For example, we will not distinguish the concepts whose volume contains 5 elements and 7 elements. Natural numbers are infinitely a lot, and in our goals it is not to distinguish between the infinitely many types of concepts. Therefore, we will consider such numbers between which a clearly prominent quality boundary runs. The first border between zero and numbers, large zero. In accordance with this, the concepts by the number of volume elements are divided into emptyand non-empty.
Empty The concept is called, the volume of which is an empty set, i.e. does not contain one element.
Example. Eternal Engine, round square, mermaid, Pegasus- All these are different examples of empty concepts. Pay attention to the concepts " eternal Engine"And" round square" There are no objects in the scope of both concepts, but they do not exist differently. Round squareit is impossible to think even (if you do not believe - PRAY!), and eternal Engineit is possible to think, but it prohibits the first beginning of thermodynamics, it does not exist in nature.
Non-emptythe concept of which contains, at least one element.
In a set of non-empty concepts, one more high-quality boundary can be carried out between the concepts whose volume contains exactly one element, and the concepts whose volume contains more than one element. In accordance with this, we will distinguish concepts singleand are common.
Single called the concept in the volume of the engine exactly one element.
Common called the concept of which is more one element.
Example . « Moon», « first President of Russia», « first cosmonaut»- Single concepts. " Earth satellite», « the president», « cosmonaut"- General concepts.
In terms of the number of components, we have the following classification of concepts:
III. Types of concepts allocated by the nature of the volume elements.
but) Collective and dividing.
Almost this is the most important distinguishing of the types of concepts, noteworthy, methods of action with concepts are directly related to the allocation of these species. These types of concepts apply only to commonconcepts. Single (and, of course, empty) concepts cannot be separated or collective.
The elements of the concept may be two types: 1) they may be single objects, 2) they themselves can be sets of objects. In connection with such a division, two types of concepts are distinguished:
Collective The concept is called the elements of the volume of which themselves constitute a set of homogeneous objects.
Example . Collective concepts include: " crowd"Since the elements of the volume of the concept of" crowd "are separate crowdswhich, in turn, consist of homogeneous subjects - people; " library"- Since the elements of the volume of etobot are separate librarieswhich, in turn, consist of homogeneous items - books; parliament, collective, constellation, fleetetc.
Dividing called concept, volume elements which are not sets of homogeneous biscuits.
Example . Most concepts are divided. Human, student, chair, the crime- separation concepts.
The main feature of the method of handling separation and collective concepts is that they should be treated with them. equally. The meaning of our distinction is to always be aware of about actually is elementthe volume of collective concepts, and what is dividing concepts. In the concept " library»An element of the scope of concept is not a book, but libraries. If they say that the library flooded, this does not mean that each book died in water. An element of the scope of the concept " public class»Are not separate people - bourgeois, peasants or workers, but large groups of people. And therefore, if you are told that something in the interests of such a class, it does not mean that it is in the interests of each worker, bourgeois, peasant. From the fact that the regiment is broken, it does not follow that every soldier or officer killed. You also need to make aware what to consider part of volumesuch pheetics. For example, part of the scope of the concept " university"- this is something or another many universities, not the other faculties of this university. Here it should be remembered about the previously distinguished relationship of the genus and species and relationship of part and the whole.
However, the tricks with the phenomenon "Collectivity" do not end. The fact is that many concepts can be used both in the divided and in a collective sense. "Citizens of our state support the idea of \u200b\u200bprivate property" does not mean that the state-owned citizen of the state supports this idea. According to the author of such a statement, citizens of our state generallysupport this idea. Here, the concept of "citizens of our state" is used in a collective sense. "Citizens of our state are obliged to comply with the law" - in this statement we are talking about eachcitizen, i.e. The concept of "citizens" is used here in the dividing sense.
b) Abstract and concrete.
This division of concepts on kinds is most important philosophical. We have already considered the Slochea "Abstraction" and found that it comes from the Latin word that has the meaning to "distract". What and from what we distract in the act of abstraction? The answer to this question suggests our ontology. There are objects in which there are properties and between which there are relations. In the act of abstraction, we distract, separate the property from the subject or the relationship from the items that they are inherent. Consideration of properties and relationships themselves, regardless of those subjects that they belong or which they associate is a characteristic feature of abstract thinking. Any thinking that claims the community of his conclusions is abstract. If we express some faithful judgments regarding the properties or relationships by themselves, regardless of the objects that they belong or which they associate, then we express faithful judgments for all these objects. Therefore, scientific thinking is always abstract.
Such an understanding of abstraction helps us understand what is meant by abrupt and concrete concepts.
Abstract Called concepts, elements of volume which are properties or relationships.
In other words, in these concepts are allocated and generalized not subjects, but their propertiesor relations.
Example . « Justice», « white», « crime», « caution», « invisibility», « paternity" etc. - All this is abstract concepts.
Specific It is called the concept, the elements of the volume of which are subjects.
Example . « Chair», « table», « the crime», « shadow», « music"- All these are specific psnomy.
In the abstract concepts of properties and relationships do not turn into objects. They are considered as objects(See chapter 3, § 1), which gives us the opportunity to make sets of them and consider them as elements of sets that constitute the volumes of concepts. We remember that, describing our logical ontology, we divided the properties and relationships, on the one hand, and the items on the other. This separation helps us clearly think two different types of concepts: abstract and concrete.
Sometimes, based on specific pheetics, form abstract concepts associated with them. For example, based on the concept " human»You can form a concept" humanity", The element of which will be a complex property" being human" Based on such an operation, the famous ancient Greek philosmf Plato constructed such concepts as " souble», « sanness"He calls ideas and who, in his opinion, serve as prototypes of the sensory world. According to Platon, sensual things are given to our feelings, and such concepts like " souble», « sanness" etc. - Only the vision of our mind 1.
Receiving thinking, with which abstract concepts are attached to an independent, independent existence, calledhypostasis.
Therefore, we can say that Plato hypostasted abstract concepts: "good", "truth", "good", "beauty", etc. He did it correctly or not, is no longer the case of logic, this question is considering philosophers.
Most of the abstract concepts, such as the concepts of "justice", "truth", "equality", "brotherhood", etc., are isolated concepts; Since there is only one property of human actions "to be fair", one property of judgment is "true", one relationship between people "be equal" or "be brother". The concept of "justice" is always a single concept, regardless of whether fair deeds are made or not, and there are many of them, since this property still exists and with only one thing.
Some abstract concepts are still common. Consider the concept of "color." Elements of the volume of this concept are such properties: yellow, blue, red, etc., i.e. Some simple properties of objects. Consequently, the concept may be abstract, but at the same time and general, since it contains a more MD element in its volume.
Examples of abstract concepts that we viewed above show that among abstract concepts there are such concepts as "justice", "Truth", "Beauty", "Good", "Equality", etc. Such concepts in philosophy, psychology, Sociology are called valuables. This leads us to the idea that the theory of abstract concepts can be used to determine the concept of "value".
To give a definition of value, we will try to figure out the main signs of this concept: 1) the values \u200b\u200bare accepted / rejected consciously, 2) the values \u200b\u200bare talking about the properties or relationships of objects, 3) the values \u200b\u200bare declared objects with the property specified in value positively significant, and not possess negatively significant ( In another interpretation also indifferent). From here it turns out to determine the value:
Value -this is an abstract concept separating the object of the objects to which it is used, in two classes - positively significant and negatively significant objects.
Example. " True"This is an abstract concept in which the property of judgments" is generalized and allocated. be true" As the value of truth gives judgments with this property ("True judgment") positivemeaning and not possessing this property ("false judgments") - negativevalue.
Example. " beauty"- an abstract concept, in the amount of which contains the property" be beautiful" Accordingly, the value of "beauty" gives objects with this property, a positive value, and not possessing it - a negative enhancing 1.
In these examples, it can be seen how the theory of concept is used to give a clear and distinct interpretation of one of the most important concepts of humanitarian knowledge.
Most likely, few people think about what they think and reason with the help of concepts. Concepts are similar to air: we do not notice them, but we cannot reflect without them. Each child naturally learns to think with their help at seven or eight years, moving from operating with specific objects to operating with ideas. However, this does not mean that everyone knows how to use them right, and without this ability, the path to logical reasoning is closed. That is why in this lesson, we will tell that there are concepts that are the types of concepts, as different concepts relate to each other and how to contact them.
What is the concept?
What is the concept? It seems to be intuitive. Perhaps many will say: the concept is the same as the word or term. However, such a definition is incorrect. Concepts are expressed by words and terms, but not identical to them. Recall, in the past lesson, we said that all the words of our tongue are signs with two characteristics: meaning and meaning. Usually we use the language intuitively, without thinking about the meaning and sense. We simply call some objects with apples, other pears, third oranges. Often we choose this or that word, guided by the context, that is, the boundaries of its use are blurred. Meanwhile, there are no discrepancies when such an intuitive use of words is unacceptable or leads to unpleasant consequences. Imagine, for example, that you all your family are going to vacation abroad. You will serve together documents for a visa, and for this you need your spouse (or your spouse) to take a salary certificate at work. You tell him: "Do not forget to take the necessary paper." In the evening he brings you a pack of wonderful paper A4. In this situation, each of you understood the word "paper" in its own way, and this was the cause of mutual misunderstanding. In many areas (legislation, legal proceedings, jobs and technical instructions, science, etc.) such ambiguity should be excluded. Fighting with her just and are called upon.
From the point of view of logic, to understand the word means to be able to specify which items it is designated, that is, to be able to install relative to any subject, can it be called this word or not. How to achieve this? Through the formation of concept.
Concept - This is a logical thought operation, which on certain features allocates objects from the set and combines them into one class.
Thus, three components are involved in the formation of the concept: a word or phrase (sign), a set of objects that they are denoted (value), and some idea or a distinctive feature that connects this word with objects falling under it (meaning). It is this distinctive feature that speaks the heart of the concept, because he binds the word and objects. As an example, you can cite the concept of a square. "Square" is a term, a distinctive feature - "The right quadrilateer, in which all the corners and parties are equal," objects are a plurality of geometric shapes with this feature. What makes the concept of a square? Of the whole set of geometric shapes it highlights some group of figures, because they have a set of some special features.
It is important not to confuse the concept and the word it is indicated. Sometimes different concepts can be associated with one word, depending on what is taken as a distinguishing feature. For example, with the word "man", the following concepts can be associated: "Social being", "the creature, which has a mind", "the creature capable of creating guns", "the creature with a self-rugge speech", etc. However, it should be borne in mind that for brevity, people most often speak simply about the concept of a square or the concept of a person, without specifying exactly what a distinctive feature is based on the basis of the allocation of this concept. This often leads to disagreements and so-called contractions about words. Therefore, before entering into a dispute, it is useful to clarify what kind of concept your interlocutor invests in this or that word.
Types of concepts
Each concept has two characteristics: content and volume. Content concept - This is the combination of distinctive features, on the basis of which items stand out from the union and are summarized in one group. The volume of concept - This is a combination of all items that have distinctive features. It is important to note that the scope of concept is always set about a certain union of consideration, that is, many objects that, in principle, can have those or other distinctive features. Supervision consideration may be people, living beings, numbers, chemical compounds, household appliances, science, food, etc. So the concept of "elephants" is set on the universible creature, the concept of "physics" - on the department of sciences, the concept of "reading numbers" - on the department of numbers, the concept of "cheese" - on the union of food.
Depending on the volume Concepts are divided into empty and non-empty. In the volume of empty concepts, no element is contained. In the volume of non-empty concepts there is at least one element. If the element is only one, then we are talking about a single concept (the author of the "war and the world"), if there are many of them about general concepts ("French kings"). If the scope of concept coincides with the consideration universal, then they are talking about universal concepts ("Numbers", "People")
Let's talk more about empty concepts. We do not always notice that, but empty concepts are used by people quite often. This may occur unconsciously, but sometimes with their help they are trying to mislead. With one example of a blank concept, we already faced the last lesson: "The current king of France." In all the universible people there is not a single person who would have a distinctive sign "to be the current king of France." It should be noted that in this case the concept turned out to be empty due to the historical coating of circumstances. Go a story differently, this concept could be non-empty. Another example of an empty concept is the "Eternal Engine". Here the emptiness is due not to historical reasons, but the laws of nature. As for scientific concepts, relatively many of them are unknown, they are empty or not. A good illustration of this is the concept of "Boson Higgs", the non-empty of which was confirmed only recently with the opening of a new particle that satisfies the distinctive features of this concept. The concept can be empty and by virtue of the laws of logic. These are the so-called self-consistent concepts, for example, "Round Square".
Depending on the types of generalized items Concepts are divided into collective and intolerable, abstract and concrete. The collective concepts include the concepts of sets of objects or people. Such concepts usually contain the following terms: "Set", "Class", "Aggregate", "Group", "Steen", etc. Examples of collective concepts: "work collective", "Rock Group", "Constellation". Infirable concepts relate to single subjects: "Computer", "Tree", "Star".
Concepts are considered concepts, the elements of the volume of which are individuals or the totality of individuals. It is important to note that under individuals are not understood here, but individual objects, and even if these objects are abstract entities. Therefore, an example of a particular concept may be "Solar System", "Natural Numbers". Abstract concepts include concepts, the elements of the volume of which are properties, subject-functional characteristics, relationships, for example: "Beauty", "hardness".
According to the type of content Concepts are divided into positive and negative, relative and irrelevant. Negative concepts contain a sign of logical denial, positive concepts, respectively, do not contain it. All examples of the concepts that we led were positive. An example of a negative concept: "odd numbers". Relative concepts as a distinguishing feature of objects that fall under it are so-called relational properties, that is, the properties formed from some relationship. An example of a relative concept will be a person as a "creature capable of producing tools." Among relative concepts, you can select a couple of interrelated concepts involving each other: "Teacher" and "Student", "Seller" and "Buyer". Relevance of the concepts of items, the distinctive feature of which is not a relational property, for example, "citrus fruits".
All this rather complex typology of concepts is needed so that we can easily produce on the concepts of operation and determine in what relationship they are in each other.
Relationship between concepts
Concepts are not isolated from each other, on the contrary, they are in a variety of connections with other concepts. The ability to identify these ties is very important, as it allows you to reveal when our interlocutor or the author of the text is mistaken in the use of concepts or even consciously manipulates them. Examples of such manipulation can serve as the use of concepts whose volumes are not equal, as interchangeable, inconspicuous transition to the concept with a smaller volume to facilitate the proof of its position, etc.
Before finding out, in which there are two concepts, you need to determine whether they are comparable at all or not. Roughly speaking, the concept of "dog" and the concept of "natural numbers" can not be in any respect, because they refer to different consideration universities: in the first case of animals, and the second - numbers. Although if, for example, our supervision of consideration is things that people are interested in, these two concepts are becoming comparable, as people are interested in both those and others. Thus, before comparing the concepts, you need to make sure that they, figuratively expressing, have one denominator - refer to one union.
The logic is divided between concepts for fundamental and derivatives. The fundamental relationship is primarily, with the help of their various combinations, you can ask all other relationships. In total, there are three fundamental relationships: compatibility, inclusion and exhaustion.
Concepts compatibleIf the intersection of their volumes is non-empty. Accordingly, if the intersection of their volumes is empty, then the concepts are incompatible.
The concept of A. turns on In the concept B if each element of volume and is also an element of volume V.
Concepts are in relation to exhaustionif and only if each subject from the consideration department is an element of the volume or the first or the second concept.
As a result of the combination of these fundamental relations, you can set fifteen derivative relations between concepts. We will tell only about those of them that operate with non-empty and non-dopeful concepts. There are six of them.
This relation in which the volumes of two concepts completely coincide.
With equidalization of the concept A and B live in one circle. An example is a pair of concepts: "triangle with equal parties" and "triangle with equal corners". Both of these concepts denote the same totality of objects.
It occurs when the volume of one concept is fully included in the volume of another concept.
The circle is fully located in a circle A, and at the same time there are more circles and more than in volume, that is, in and include objects that are not included in the V. Illustration of submission - the relationship between the concepts of "citrus fruits" (a) and "oranges" ( AT).
This is a relation in which the volumes of concepts intersect, but do not completely coincide.
An example of intersection - the relationship between the concepts of "women" and "leaders". There are people who possess the first and second characteristics.
This is such an attitude, when two concepts intersect and at the same time exhaust the entire consideration department.
I specifically depicted concepts a and in different colors so that it was clear that the circle in the center is not a separate concept, but the result of their intersection. The ratio of optional exists, for example, between the concepts "temperature above 0 ° C" and "temperature below 30 ° C". The volumes of these concepts intersect, and at the same time the amount of their addition is equal to the volume of the union of consideration.
This is a relation in which the volumes of concepts do not intersect and exhaust the entire university.
If, for example, the consideration university is people, then and may be the concept of "working", and in the "unemployed". Each person can be either working or unemployed, but not together and not the third.
It occurs when the volumes of concepts do not intersect, but at the same time they do not exhaust the entire consideration department.
I will immediately say that I do not know what those who called this ratio of cointh were guided. In my opinion, it's rather about independence from each other. Apparently, it is meant that both concepts are on submission to some third concept - in this case, the entire consideration universule. Suppose that the consideration department is animals. Then the concept A is "Lizards", the concept of "cats". And lizards, and cats are animals. The volumes of these concepts do not intersect. In this case, the volume of the universal concept of "animals" contains many not falling under the elements.
The law of the reverse relationship between the content and volume of the concept
At the very beginning, we said that the concept possesses two characteristics: content and volume. Accordingly, when we determine the relationship between concepts, not only their volumetric characteristics are important, but also meaningful. In particular, the logic found out that there is a so-called law of the reverse relationship between the volume and content of concepts. The essence of this law is as follows: if the first concept is in terms of volume than the second concept, then the first concept is richer second in content. By and large, this law acts when we are faced with the attitude of subordination between the concepts. Suppose the first concept is "Flowers", the second concept is "chamomile." The concept of "chamomile" is in terms of volume than the concept of "flowers", that is, it includes fewer elements. But it is richer in content. This means that from the concept of "chamomile" we can extract more information than from the concept of "flowers". If a certain object falls under the concept of "chamomile", then we automatically know that it will also be subject to the concept of "flowers", but the conclusion in the opposite direction cannot be done. If a certain object is an element of the concept of "flowers", it does not mean at all that it will also be an element of the concept of "chamomile". It may well be peony, rose, lavender, etc.
Operations on the concepts
The main goal of operations on concepts is the formation of a new concept, with its own volume and content, from other or more concepts. The main operations committed on the concepts are called Boolean operations. They received such a name in honor of the English mathematics and logic of J. Bul, who developed a kind of logical mathematics. True, the operations performed on the concepts are similar to those of the operations that we learned to perform with numbers in elementary school. These include: intersection, association, subtraction, symmetric difference, addition.
Concepts are an operation, during which two or more concepts are taken and as if they are superimposed on each other. As a result, in the place of intersection of their volumes, a new concept is formed, the elements of which will be those objects that simultaneously have the distinguishing signs of all intersected concepts. To imagine it clearly, look at the drawings:
The result of the intersection is the shaded area. For example, if we take the concept of "police" and the concept of "corrupt officials" and will make over the operation of the intersection, then only those people who are both police and corrupt officials will be in the shaded region. So we formed a new concept of "corruption policemen". As can be seen, the intersection operation is based on the attitude of the intersection. This means that if two concepts are in relation to the intersection, we can easily form with their help a new concept.
An association Concepts are similar to addition: we take a few concepts, connect their volumes and thus form a new concept, the elements of which will be those objects that have at least one of the distinguishing features of the combined concepts.
To illustrate, we can take the concepts of "smokers" and "People consisting of alcohol" and through the union to form the concept of "people who smoke or drink alcohol." In this case, not only those people who are simultaneously smoking, and drink, but all those who have at least one of these bad habits will be subject to the concept. Therefore, we shaved both circles.
Subtraction Concepts Again, very similar to mathematical subtraction. When subtracting, two or more concepts are taken and the volume of the remaining are taken out of the volume of one. Thus, a new concept is formed, the elements of the volume of which will be the objects that have a distinctive feature of the first concept, but do not possess the distinctive signs of those concepts that are deducted from it.
Suppose that the concept A is "people suffering from diabetes", the concept of "people suffering from overweight." If we deduct the concept of the concept A, then we get a new concept of "people suffering from diabetes, but not having overweight." It is shown to the shaded area.
This is an operation, in a sense of the inverse intersection. It is necessary to accurately take two or more concepts, impose them on each other, but the new concept formed as a result of this imposition will contain only those elements that have no more than one distinguishing feature of the original concepts.
The shaded area shows this new concept. Objects falling under this concept must have a sign of a or in, but not together. Let a be the concept of "doctor", in the "man". Then we get the following concept: "To be a doctor, but not to be a man, or be a man, but not to be a doctor."
This is an operation, during which the concept is taken, and then its volume seems to be deducted from the entire consideration department. This is how a new concept is created, the elements of which will be only those objects that do not have a distinctive feature of the concepts initially taken.
The new concept A 'is an addition to the concept of A. If the union of our consideration is animals, the concept A is "mammals", then A' - "animals that are not mammals." The operation of the supplement does not need to be confused with an additional relationship.
In addition to Boolean operations, one more series of operations can be carried out on the concepts: restriction, generalization, division.
This is an operation, which is a narrowing concept. Limit the concept A means to go to the concept of in, such that its volume will be strictly incorporated into the volume of concept A. and this transition from A to B is a transition from the generic concept to the species.
As can be seen from the picture, as a result of the restriction of the circle, representing the volume of concept, becomes less. We limit the concept A to the concept of B, and then - the concept of B to the concept of C. It can be assumed that the concept A is "fish". We can limit it to the concept of "sharks". The volume of concepts is wider, since the fish are different, they include many species - not only sharks. In this case, the volume of concepts in fully incorporated in the volume of concept A, because all sharks are fish. The concept of "shark" can be limited to the concept of C - "White Sharks". Again, the concept of "white sharks" is fully included in the concept of "shark", but less than its volume. The limit limit of the concept is a single concept. In our drawing, it would imagine a point in the center, which cannot be narrowed.
The operation of limiting concepts is often accompanied by errors. Most often they are related to the fact that the restriction of concepts are confused with membership of objects, that is, the concept is limited not on the basis of genera signs, but on the basis of those parts that the elements of their volume are separated. For example, take the concept of "cars". By Rodovid signs, we can limit it to the concepts of "cars with a manual gearbox" or "electric vehicles". And this is the right limitation. However, the car consists of a variety of components: headlights, wheels, steering wheel, wipers, engine, etc. Therefore, you can meet this option: the concept of A - "Cars" is limited to the concept of in - "Wheels". Although the wheels are part of the car, such a restriction is incorrect. There is a slight way to avoid this error. With the right limitation of the concept A to the concept of B, there should be a true statement "Everything in A": "All sharks are fish," "all electric cars are cars." If we apply this formula to cars and wheels, it turns out: "All wheels are cars." The statement is incorrect, it means that the restriction operation was incorrectly.
This is an operation, inverse restriction. This time we do not approve, but expand the concept. To summarize the concept of B means to go to the concept A, so that the volume of the concept in will be strictly included in the volume of the concept A. Here is a transition from the species concept to the generic.
The concept of C, represented by the smallest circle, we summarize until the concept of B, which, in turn, can still be generalized to the concept A, and with fully incorporated in B, and in fully included in A. Let C are the concept of "gold", then We can summarize it to the concept of the "metals", and the concept of the concept A is the "chemical elements". The limit of generalization is a universal concept, that is, the concept, whose volume coincides with the consideration department. In our example, the concept of "chemical elements" can be considered as universal.
The generalization operation of concepts may be subject to the same mistake as the restriction: often people generalize the concepts on the basis of non-generic signs, but composite parts. In particular, the concept of "wings" summarizes the concept of "birds", which is incorrect. The inspection method is the same: to see if it will be the approval "All in is A". Obviously, the statement "All wings is birds" incorrect.
Division - This is an operation that takes the concept that some characteristic is distinguished and based on the variation of this characteristic, the initial concept is divided into several parts, resulting in a set of new concepts. The initial concept is called divisible concept. Those concepts that are formed after division - members of division. The characteristic, on the basis of which division is carried out by the basis of division.
The whole circle is the volume of the concept of divisible concept A. B, C, Di E-member of division, that is, the concepts formed as a result of dividing the concept of A. for illustration Suppose that the concept A is "months". The base of division is belonging to the time of year. Then the newly formative concepts in, C, D and E are the "Winter months", the "Spring Months", "Summer Months" and "Autumn Months". Obviously, as a result of division, a different number of concepts can be obtained: it all depends on the division concept and the founding of division.
For division to be correct, the following conditions must be followed:
- The division should be made only one base. If you use our example with the concept of the month, then I can not divide it into the following scenes: "Winter months", "Spring months", "Summer months", "Autumn months" and "My favorite months." In such a division, two characteristics are used: belonging to the time of year and my attitude to a specific month. This is called the confused division. Also, if you use more than one base of divisions, you can make a so-called leap in division, which is that some division members are species A, and others - its subspecies. For example, the original concept is "Wine", the base of division is color. As a result of the right division, we must get three new concepts: "White Wine", "Pink Wine" and "Red Wine". But if a jump was made in the division, then you can come to such a result: "White wine", "Pink Wine", "Cabernet", "Shiraz", "Merlot", "Pinot Noir". In this case, two bases were combined: color and variety, and in the members of the division simultaneously got types of species (white, rose) and subspecies (Cabernet, Shiraz, etc.).
- Members of division in, s, etc. Must be species in relation to the generic concept A. This is the same condition with which we encountered during restriction and generalization. It is impossible to divide the concept of "car" on the concepts of "wheels", "Engine", "steering wheel", etc. Again, you need to ask a question, whether the statement "all is a" is true, "all with is a" and so for all division members. If you are still interested in wheels and the engine, then it is necessary to replace the divisible concept on the "part of the car", then the division will be correct.
- The volumes of division members do not intersect, that is, none of the elements can simultaneously get into B and C or V and E, etc.
- Members of division cannot be empty concepts. Suppose that the initial concept A is "now the ruling kings." Base of division - belonging to countries. So, among the members of the division, there can be no concepts "now the ruling French kings" or "now ruling German kings", as these are empty concepts.
- If all members of the division B, C, D, E are over the combination operation, then we must obtain the volume of division concept A.
There are two types of division: dichotomous division and division by modifying the foundation. The word "dichotomic" is literally translated from Greek as "Division in Overs." With its implementation, the initial concept is divided by only two new concepts. Any base of division is selected, that is, a sign, and depending on the presence or absence of this feature, all elements of volume are separated into two parts. Let a divisible concept be the concept of "people", the basis of division - the presence of higher education. In this case, our initial concept will be divided into two: "People having a higher education" and "people who do not have higher education." Another example: take the concept of "dog", the foundation of division - the pivot. As a result of dichotomous division, we get the concepts: "Purgeons of dogs", "Mongrel dogs".
The second type of division is a division by modification of the foundation. As a result, we can get more than two new concepts. Here, as a base, some objective functional characteristic of the elements of the original concept is selected. In our example, with months, this characteristic was belonging to the time of year. If our divisible concept is "people", then it is possible to take the color of the eyes as the base of the division, the color of the hair, nationality, etc. If a divisible concept is "poem", the basis of division may be their genigous affiliation. To illustrate, we will take the concept of "playing cards", and we will make the basis of division:
The division operation underlies the preparation of classifications and typologies. Classification is carried out by consistent division of concepts on its types, species - on subspecies, etc. The classification is primarily important in scientific knowledge. It can act as the result of studying a subject area (general classification of plants and animals Karl Linnei) and the engine of research (periodic table of chemical elements of Mendeleev). In addition, the classification is very important in training: people are much easier perceived information if it is decomposed on the shelves. Often, even without noticing, we use classifications and in everyday life: the ranking of employees in the office, the organization of clothing in the closet, the distribution of goods by departments in the store is just a few examples.
Correctly performed classification is similar to a turned tree (in my opinion, rather, a twisted chiston). The top of the classification is the original divisible concept - called the root. Lines divergent from her are like branches. They lead to members of the division, which in turn also diverge the branches to new concepts. Each concept in the classification is called a taxon. Taxakhs are grouped by tiers. On the first tier is the root of classification A. On the second tier - taxa in 1 -B n, formed using the first division operation. On the third tier - taxa C 1 -C N, formed as a result of the second division operation, etc. Each tier can contain any number of taxa.
When building classifications, both types of division are used: and dichotomous, and by modifying the foundation. At the same time, they may adjourn even in one classification. The fact is that within the classification, each individual division operation can be carried out on its own base. We give an example. We take as the root of classification the concept of "writers", the foundation of division - whether the writer is Russian or not. Accordingly, we produce a dichotomous division, as a result of which we receive two new concepts at the second level: "Russian writers" and "foreign writers". Then we can divide the concept of "Russian writers" to modify the foundation. As a base, we will take the characteristic: "In which a writer lived in?" We get new concepts: "Russian writers of the XIBER", "Russian Writers of the XIIIV" and so right up to the "Russian Writers of the XXIV). As for the concept of "foreign writers", it can also be divided into the modification of the foundation, but as a basis to take the nationality of writers. Thus, we get: "Spanish writers", "French writers", "German writers", etc.
Sign [...] marked missed members of division. Further, each taxon can be divided into some kind of sign. The main thing in each individual division is to follow the rules listed above.
It should be noted that the compilation of classifications is not such a simple task as it may seem at first glance. It is not rare the situation when it is difficult or impossible to determine what kind of taxon you need to attract one or another item. In our example with writers, in particular, there may be cases when the writer was born and began to create in the same century, and he died in another as Chekhov. Where do you need to attract - in the Writers of the XIXVEK or XXVEK? Sometimes there are objects that are in principle they do not fit anywhere. Then it creates a separate taxon for them or put them in the so-called "sump". It can be marked with the words "all so on", and the objects in it are not connected with nothing else, except that they cannot be determined anywhere.
Exercises
Chinese encyclopedia
Borges in one of his works leads an excerpt from the mysterious Chinese encyclopedia. This "divine repository of beneficial knowledge" says that "the animals are divided into: a) the emperor, b) smelled, c) tamed, d) of dairy pigs, e) sirens, e) fabulous, g) stray dogs, h) included in True classification, and) increasing, as in madness, k) innumerable, l) drawn by a very thin brush from camel wool, m) and others, P) just crashing a jug, o) from afar of apparent flies "(Borges H.L. analytical Language of John Wilkins // Op. in 3 tons. T. Riga: Polaris, 1997, p. 85).
Try to present this classification of animals in the form of a tree. Do you think that it is done correctly? If so, then prove that none of the rules of division in it is not violated. If not, explain exactly which rules are broken. How could this classification be fixed?
Meat is not meant
Cat. Sorry, please, for indiscrimination. I have now wanted to ask you for a long time ...
Cat. How can you eat spines?
A donkey. What?
Cat. In the grass come across, truth, edible stalks. And spines ... dry such!
A donkey. Nothing. I love sharp.
Cat. And meat?
A donkey. What is meat?
Cat. Did you try to eat?
A donkey. Meat is not food. Meat - this is kidding. It is put in the cart, fool. (E. Schwartz, "Dragon")
Determine the relationship between the concepts of "food", "sharp items", "acute food", "barbs", "meat" and "kidding". Picture this relationship with graphic schemes. Remember that concepts can be comparable only if they belong to a single consideration department.
Talking husband with wife
Husband: Cute, you are not right.
Wife: ah, I'm not right. So I lngu. I lie, it means I'm a bad person, that is, the unhurried. Do you want to say that I am an animal? Mom, he called me a cattle!
Determine whether the transition between the concepts of "a man who is wrong", "Liar", "Bad Man", "Neru", "Animal", "Cattle" was correctly performed. Justify your position. What operations on the concepts were used with the transition? What kind of relations are these concepts? Picture them using graphic schemes.
Check your knowledge
If you want to test your knowledge on the subject of this lesson, you can pass a small test consisting of several questions. In each question, only 1 option can be correct. After choosing one of the options, the system automatically moves to the next question. The points you receive affect the correctness of your answers and spent time spent. Please note that questions every time are different, and the options are mixed.