Lecture
In the world around us there are an infinite number of different objects and properties, and in our mind they are reflected in the form of concepts.
A concept is a form of thinking that denotes an object or its property. For example, we call one object a mountain , another - a celestial body , the third - a plant ; one property or attribute we call courage , the other cunning . Any concept is expressed in a word or phrase, for example: home, autumn list, the first president of America . Each concept has content and volume.
The content of the concept is the most important feature (or signs) of the object that is designated (expressed) by this concept.
For example, in order to establish the content of the concept “ person ”, it is necessary to indicate such a trait that is most important for a person who distinguishes him from all other creatures, objects and objects. Such a sign for a person is the presence of reason. Consequently, the content of the concept of " man " includes only one important feature - the presence of reason. And the content of the concept of " man " already includes two important signs: the presence of reason (this sign is repeated, because any man is a man); belonging to a certain sex (to one of the halves of humanity; the word “sex” comes from the word “half”). And if you need to establish the content of the concept of " Russian man ", then you should specify three important features: the presence of reason; belonging to a particular gender; belonging to a particular nationality. Thus, the content of a concept can include as one attribute of an object (or objects), as well as two or many signs, and their number depends on the object, which is denoted by this concept. But why in one case the content of the concept consists of a single attribute, and in the other - of a multitude of signs? This question is easy to answer if you know what the volume of the concept.
The scope of a concept is the number of objects covered by this concept that are included in it. For example, the volume of the concept of " man " is much larger than the volume of the concept of " man ", because there are fewer men than people in general. And the volume of the concept “ Russian man ” is much less than the volume of the concept “ man ”, because there are much less Russian men in the world than in general all men. And finally, the scope of the notion “ first president of Russia ” is equal to one, because it includes only one person. Similarly, the scope of the concept of “ city ” is very wide, because this concept covers all cities in the world, and the volume of the concept of “ capital ” is less than the scope of the concept of “ city ”, since this concept covers only capitals that are much smaller than cities. The scope of the concept of "the capital of Russia " is equal to one, because it includes a single city.
Let's return once more to the content and scope of the concept and recall the examples above. What is the concept - " man " or " man " - more in content? Of course, the concept of " man ", because its content includes two signs: the presence of mind and belonging to a particular sex, and the content of the concept of " man " includes only one sign: the presence of mind. And now we will answer the question: what concept - “ man ” or “ man ” - is more by volume? The concept of " man " is more because it covers far more objects than the concept of " man ." Thus, there is an inverse relationship between the scope and content of a concept: the larger the content of a concept, the smaller its volume, and vice versa. For example, the content of the concept “ celestial body ” is narrow, as it includes only one sign - to be outside the Earth, however this concept is very broad in scope, because it covers a huge number of objects: any star, planet, meteorite, comet it is a heavenly body. And the concept of " Sun ", on the contrary, is very narrow in volume, as it includes only one object, but very wide, rich in content, which is made up of many signs: the size of the Sun, its mass, density, chemical composition, temperature, age etc.
All concepts in terms of content and content are divided into several types. In terms of volume, they are single (only one object is included in the concept, for example: the Sun, Moscow, the first president of Russia, writer Leo Tolstoy ), common (there are many objects in the concept, for example, the celestial body, city, president, writer ) and zero (the scope of the concept does not include a single object, for example: Baba Yaga, Koschey Immortal, Father Frost, perpetual motion machine, Martian inhabitant , that is, the concept exists, and the object that it designates does not exist). In terms of scope, concepts are also collective (a concept denotes an object that consists of, is assembled from some limited set of elements, is divided, breaks up into some component parts, for example: Grade 10 "A", a company of soldiers, a musical group, a wolf pack, constellation ) and uncooperative (the concept denotes an object that is not composed, not assembled from some limited set of elements, is not divided, does not break up into some component parts, being something single, whole, for example: man, plant, star , ocean, pencil ).
According to the content, concepts are concrete (a concept means an object, for example: a table, a mountain, a tree, a planet ) and abstract (a concept means not an object, but a sign, a property, for example: courage, stupidity, untidiness, darkness ). The content of the concept is also positive (the concept denotes the presence of something, for example: an animal, school, skyscraper, comet ) and negative (the concept denotes the absence of something, for example: not an animal, not a school, not true, tactlessness ). It is easy to notice that a concept is negative when the word by which it is expressed is used with the particle “not” or with the prefix “without-”, however, if this particle “not-” is part of the word that is not used without it, for example: slob, carelessness, bad weather, negligence, ignorance , the concept expressed in such a word is positive.
The above material can be represented as a table. one.
Any concept can be given a logical characteristic. It means - to disassemble it by volume and content. First, it is necessary to determine whether it is singular, common or zero, then to establish whether it is collective or non-selective, then find out whether it is concrete or abstract and, finally, answer the question whether it is positive or negative. For example, the concept of the “ Sun ” is a single (one object, one celestial body enters its volume), an unsightly (the Sun does not consist of any parts, is not divided into them), a specific one (the Sun is an object, not a sign or property) , positive (this concept indicates the presence, not the absence of an object). In the same way, a “ plant ” is a general, non-collecting, concrete, positive concept, and the “ Orion constellation ” concept is a single, collective, concrete, positive one.
1. What is a concept?
2. What is the content and scope of the concept? How do they compare?
What is the principle of the inverse relationship between the content and volume of the concept? Give examples of concepts illustrating this principle.
3. What are the concepts in terms of volume and content? Give ten examples for the concepts of single, common, zero, collective, unmatched, concrete, abstract, positive, negative.
4. What is the logical characteristic of a concept? How is it made up?
5. Give a logical description of the following concepts: Moon, plant, state capital, musical group, famous artist, centaur, Danish physicist Niels Bohr, ancient philosopher, Antarctica, Atlantis, Russian team, sheet of paper, water molecule, criminal community, crime rate, ignorance, stupidity, an intelligent man, a precious stone, a drunken company, lies, hydrogen, geometry, a company of soldiers, injustice, exploitation, air, philosophers of the Milesian school, the famous work of art, silence .
A concept is defined when it has a clear content and sharp volume. As we already know, the content of a concept is the most important feature of the object it expresses, and volume is the number of objects it covers. Thus, the concept has a clear content in that case, if you can specify the set of essential features of the expressed object, as well as accurately establish the boundary between those objects that this concept covers, and those that do not belong to its volume.
For example, the concept of " master of sports " is defined. It has a clear content, since it is possible to accurately indicate its most important distinctive feature - to officially possess the sports category of the master of sports. Also, this concept has a sharp scope - with respect to any person, you can say for sure whether he is a master of sports or not, that is, falls or does not fall into the scope of this concept; in other words, it is possible to draw a sharp boundary between all the masters of sports and all those who are not, precisely to separate them from others.
A concept is ambiguous when it has obscure content and unsharp volume. If the concept is characterized by obscure content, then this means that it is impossible to accurately indicate the most important distinctive features of the object that it expresses; and the unsharp scope of a concept indicates the impossibility of drawing an exact boundary between those objects that are within the scope of this concept and those that are not part of it. For example, the concept of “ good athlete ” is vague. It has an obscure content, since it is impossible to accurately indicate the essential signs of a good athlete: one cannot unambiguously answer the question of who should be considered a good athlete. Either it is the one who has the rank not lower than the master of sports, or the one who set at least one world record, or a multiple Olympic champion, or a good athlete is someone who considers himself as such.
It is clear that the opinions of different people about who should be considered good athletes will differ: some will say one thing, others will say something else. Also, this concept has an unsharp scope - it is impossible to say with respect to any person whether he is a good athlete or not, that is, falls into the scope of this concept; in other words, it is impossible to draw a sharp boundary between the multitude of good athletes and all those who are not, precisely to separate one from another.
The scope and content of the concept, as already mentioned, are closely related to each other. However, if in quantitative terms the relationship between them is inverse: the greater the volume of the concept, the less its content, and vice versa, in a qualitative sense, this relationship is direct: the clear content of the concept determines its sharp volume, and unclear content necessarily corresponds to the unclear content, and vice versa.
Of course, it is much more convenient and easier to deal with certain concepts than with undefined ones, but the latter occupy a significant place and play an important role in thinking and language.
The main reasons for the emergence and existence of vague concepts are as follows:
1. Many objects, properties and phenomena of the surrounding world are multifaceted and complex. As a rule, they are expressed in thinking with vague notions. For example, the concept of “ love ”, differing in a highly obscure content and, consequently, unsharp volume, is indefinite, because it means a phenomenon so complex that over the entire history of mankind no one has been able to finally and comprehensively answer the question that is love
2. As the ancient Greeks rightly noted, everything in the world is changing forever. The diversity and smoothness of transitions from one state to another is difficult to express accurately and unambiguously, in the form of certain concepts. It is not surprising that these transitions are usually denoted by indefinite concepts. Can we say for sure when a person is young, when young, when mature, when he reaches middle age and, finally, when he becomes old? Of course, the concepts of " young ", " young ", " mature ", " old " and many others like them, are vague.
3. The existence of indefinite concepts is largely due to the fact that people often evaluate the same objects, properties, phenomena and events in different ways. A certain book will seem interesting to one person, to another - boring. The same act can cause admiration in one, in the other - indignation, the third - leave indifferent. Differences in the estimates of reality surrounding us are embodied in the uncertainty of many concepts, for example: an interesting film, fashionable clothes, a capable student, a boring book, a difficult task, unworthy behavior, a pretty girl, a tasty dish .
It should be noted that the three named reasons for the emergence and existence of indefinite concepts are not isolated, but closely related. They always act together, and, most likely, in any vague concept one can see the simultaneous participation of these reasons.
Despite the vagueness of the content and the vagueness of the volume of ambiguous concepts, we usually use them without much difficulty, as a rule, intuitively understanding what we are talking about when they talk about a boring book, an uninteresting film, a clever person, a shameless trick, a comfortable chair, a high salary and etc. Of course, if only certain concepts functioned in thinking and language, then they (thinking and language) would be more accurate. In this case, discrepancies, ambiguity, ambiguity would disappear, and in human communication there would be much less difficulties and barriers in the form of mutual misunderstanding and disagreement. However, greater accuracy of language and thinking would make them poorer and less expressive.
In one of the textbooks on logic, it is proposed to recall the description of Chichikov from Nikolai Vasilyevich Gogol's “Dead Souls”:
“ In the cart there was a gentleman not handsome, but also not of a bad appearance, not too thick, not too thin; it is impossible to say that it is old, but it’s not that it is too young ” [1] . As you can see, the description of the appearance of the hero consists entirely of indefinite concepts. But you could make this description of certain concepts, and then it would look, for example, like this:
“ A 45 year old gentleman sat in a car, 175 cm tall, in shoes of 41 size, head volume - 60 cm, chest - 80 cm ... ”. However, in this case, we would not be a work of art, but something like a police report. As we see, in some areas of thinking and language it is impossible to do without indefinite concepts, for example, in fiction, which without them will cease to be itself. But in everyday communication, vague concepts are often more appropriate than certain ones. Describing someone, most likely, we will say just " tall man ", and not "a man of 187 cm tall ."
In an effort to make thinking and language more accurate, trying to expel vague concepts from them, we risk remaining without thinking and language at all. While grinding the blade of the knife, trying to achieve its maximum sharpness, you can sharpen it until nothing remains of the blade.
So, vague concepts occupy a significant place in our intellectual speech practice. They are its integral component, and getting rid of them is just as senseless as impossible. Uncertain concepts are a source of inaccuracies, disagreements and communicative (associated with communication) interference, not on their own, but depending on the situation in which they are used. As already mentioned, they are even necessary in fiction. Uncertain concepts can lead to various kinds of difficulties if they are used, for example, in official documents. Uncertain concepts that fall into the texts of laws can create a basis for misunderstandings and incorrect decisions. Thus, the notion of “ violation of public order ” is vague and, being present in the text of any legislative act without explanatory comments, may cause a guilty person to be acquitted and an innocent person punished.
1. What are certain concepts?
2. What are vague concepts?
3. What are the main causes of the emergence and existence of indefinite concepts? Is it possible to do without them, eliminating them altogether from thinking and language? If not, then why?
4. Are vague concepts in themselves, regardless of the situation in which they are used, communicative interference? Why, in your opinion, the use of indefinite concepts in everyday communication does not lead us to communication difficulties?
5. In what cases can vague concepts cause various difficulties and play a negative role? Каким образом можно бороться с ними в этих ситуациях?
6. Give ten examples each for specific and indefinite concepts.
7. Determine which of the following concepts are definite and which are indefinite: crucian carp, mammal, big dog, wild cat, prestigious educational institution, Moscow educational institution, planet Neptune, bright star, talented person, rich man, mediocre teacher, candidate of physic - mathematical sciences, bully, famous writer, high mountains, textbook on chemistry, good music, boring lecture, good clothes, modest food, the Russian national football team, a large city, the capital of the state.
Name, utterance, and inference are the three central categories of logic. Let's consider each of them in more detail.
Name is a linguistic expression denoting objects, their properties and relationships.
Names are a necessary means of cognition and communication. Designating objects and their aggregates, names connect the language with the real world.
The names are natural and familiar, like the things with which they are associated. So natural that at one time they seemed to belong to the things themselves, just as color, weight and other properties are inherent in them.
Primitive people viewed their names as something concrete, real, and often sacred. The psychologist L. Levy-Bruhl, who created at the beginning of the XX century. concept of primitive thinking, considered this attitude to names an important factor confirming the mystical and extralogical nature of such thinking. In particular, he pointed out that “the Indian sees his name not as a simple label, but as a separate part of his personality, like his eyes or teeth. He believes that he will suffer as surely from the malicious use of his name as from a wound inflicted on some part of his body. This belief is found in different tribes from the Atlantic to the Pacific. " On the West African coast “there are beliefs in a real and physical connection between a person and his name; you can injure a person using his name ... The real name of the king is secret ... ”.
These naive notions of names as properties of things are surprisingly tenacious. Astronomer V. Vorontsov-Velyaminov recalls that at popular lectures listeners often asked him a question: “We assume that it is possible to measure and find out the dimensions, distance and temperature of celestial bodies; but how, tell me, did you know the names of the heavenly bodies? " The answer to this question is simple. Astronomers learn the names of the celestial bodies they discovered in the same way that parents learn the names of their children - by giving them these names. But the very fact of such a question shows that the illusion of “sticking” names to things requires a special explanation.
All sciences studying the language are engaged in the study of the name as one of the basic concepts of both natural and artificial languages. And above all, logic, for which names are one of the main semantic categories.
In different scientific disciplines, "name" means different and sometimes incompatible things. Logic has spent a lot of effort to clarify what a name is and what principles the operation of naming, or designation, obeys. Perhaps nowhere are names interpreted so comprehensively, deeply and consistently as in logical studies.
For example, the word "Caesar" denotes a separate object - the first Roman emperor Caesar; the word "scientist" denotes a class of people, each of whom is engaged in scientific research; the word "black" can be regarded as designating a class of black objects; the word "further" - as a designation of a certain relationship between objects, and the so-called.
The names differ from each other depending on how many items they mean.
Single names refer to one and only one item. For example, the only name is the word "Sun", meaning the only star in the solar system. The name "natural satellite of the Earth" is also unique, since it designates the Moon, which is the only such satellite of the Earth.
Common names refer to more than one subject. Common names include "man", "woman", "schoolboy", etc. All of these names are associated with sets, or classes, of objects. Moreover, the name does not refer to the set as a whole, but to each object included in it. The word "man" does not mean all people together, but each of the people, ie. any object about which one can say: "This is a person." Unlike “human”, the word “humanity” is not a common name, but a single name: there is only one object that can be called “humanity”. The word "galaxy" is a common name, since there are other galaxies in the universe besides our galaxy. The word "Universe" is a singular name, since the Universe is the only one. Among common names, concepts are of particular importance.
A concept is a common name with a relatively clear and stable content, used in common language or in the language of science. For example, the concepts are “house”, “square”, “molecule”, “oxygen”, “atom”, “love”, “infinite series”, etc. There is no clear boundary between those names that can be called concepts and those that do not belong to concepts. "Atom" has been a fairly well-established concept since Antiquity, while "oxygen" and "molecule" until the 18th century. could hardly be attributed to concepts.
The word "concept" is widely used in both everyday and scientific language. However, there is no consensus in the interpretation of the content of this word. In some cases, “concepts” mean all names, including singular ones. The concepts include not only the "capital" and "European river", but also the "capital of Russia" and "the largest river in Europe." In other cases, concepts are interpreted as general names that reflect objects and phenomena. in their essential features. Sometimes a concept is identified with the content of a common name, with the meaning behind such a name.
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Logics
Terms: Logics