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Lecture notes, cheat sheets
Logics. Education of concepts, their content and scope (lecture notes)
Directory / Lecture notes, cheat sheets Table of contents (expand) LECTURE No. 6. Formation of concepts, their content and scope 1. Logical methods of concept formation For a person engaged in scientific research, it is constantly necessary to receive new information. To do this, a scientist reads a lot of literature on a chosen subject, conducts observations, and makes experiments. However, all this activity would be useless if it did not lead to the formation of new concepts. In other words, the information received in such a case would remain only information, not clothed in a form suitable for consolidation and transmission. That is why it is necessary to know about the methods of concept formation. Such techniques are: abstraction, analysis, synthesis, comparison and generalization. Abstraction - this is a technique for the formation of concepts, in which it is necessary to abstract from a number of non-essential features of an object, discard them and leave only the essential ones. Comparison plays a significant role in the process of abstraction. Analysis - this is a mental fragmentation of an object, process or phenomenon into its constituent parts in order to establish the interaction of these parts and the relationships between them, as well as to identify the processes occurring inside the object under study. Analysis is necessary to obtain a reflection of an already existing concept. Synthesis - this is a mental assembly of the constituent parts of an object, phenomenon or process together. Synthesis is the reverse process of analysis and is usually used when the latter has already been carried out. Often, mental synthesis is preceded, if we are talking about an object, by the practical assembly of this object with strict observance of the sequence of setting the components. Synthesis is used to create new concepts on the basis of already existing ones subjected to synthesis, or to identify inaccuracies in a concept, as well as to make changes to these concepts. Comparison - this is a mental establishment of the similarity or difference of objects according to essential or non-essential features. Generalization - the mental association of a group of objects into a new row or the addition of one object to an existing one based on the characteristics inherent in these objects. Comparison and generalization make it possible to achieve greater accuracy in judgments, to separate one from the other, or, conversely, to combine several objects into one group (class). As an optional feature, they contribute to better assimilation of information by the human brain. All logical methods of concept formation are of great importance. They are interconnected, it is impossible to imagine one without the other. Often used together or precede one another. 2. Content and scope of concepts Any concept has content and scope. The content of the concept is a set of essential features characterizing its object, implied in this concept. The scope of the concept constitutes a set or set of objects that is conceived in a concept. Sufficient content for the formation of the concept of "isosceles right triangle" will be an indication of the presence in the composition of the geometric figure of two angles equal to 45 °. The scope of such a concept will be the entire set of possible isosceles triangles. Any concept can be fully characterized by defining its content (in other words, meaning) and establishing objects with which this concept has certain connections. Regardless of human consciousness, there are various objects in the world around us. These items are characterized by many. The set may be finite or infinite. If the number of items in a set is calculable, then the set is said to be finite. If such objects are incalculable, the set is called infinite. It is necessary to mention the relations of inclusion, belonging and identity. An inclusion relation is a relation of species and genus. Set A is a part or subset of set B if each element of A is an element of B. It is reflected in the form of a formula A with B (set A is included in set B). With regard to membership, the class a belongs to the class A and is written as a with A. The identity relation implies that the sets A and B are the same. This is fixed as A = B. The content of a concept is called its intensionality, and its relation to any objects is extensionality. Intensity of concepts. Most often, in the process of interpreting the term “content of a concept,” it is defined as a concept as such. In this case, it is implied that the content of a concept is a system of attributes through which the objects contained in the concept are generalized and distinguished from the mass of others. Sometimes content is understood as the meaning of a concept or all the essential features of an object contained in the concept taken together. In some studies, the content of a concept is identified with the entire complex of information that is known about a given subject. It can be seen from the above that the content of the concept is some information containing information about the objects, phenomena, processes included in this concept. This information is necessary for the formation of the concept, the definition of its form and rational consideration. Such information can be any information about an object that allows you to distinguish it from the mass of homogeneous (and heterogeneous) objects and clearly define its characteristics. In other words, this is information about the essential and other features of the subject. In the process of communication, from the point of view of the efficiency of information transfer, of particular interest is such an element of the content of the concept as connotation. It is more or less typical for the languages of different countries and to a very large extent - for the Russian language. These are all kinds of variations of pronunciation, intonation, stress on individual words, ethical, aesthetic, ethnic, professional, diminutive and other shades and colors of concepts used in speech. Such variations can lead to a change in the meaning of a concept without changing its verbal form, and a change in verbal form most often leads to a change in meaning. For example, the words "book" - "little book"; "grandmother" - "grandmother" - "grandmother" quite illustrate the connotation. It is necessary to say about the so-called magnitude of the content of concepts. It is inextricably linked with their volume. In this case, the ability of some concepts to be wider than others, and thus, as it were, "overlap" them, is implied. For example, the concept of "science" is much larger in content than the concept of "logic" and overlaps the latter. When characterizing the first concept, you can use, or you can not use the second, but replace it with another, or even get by with other means. However, when characterizing the concept of "logic", we will inevitably have to use the concept of "science". The concept of "science" in this case is subordinate, and "logic" is subordinate. Take for example two other concepts - "helicopter" and "aircraft". These concepts in relation to each other are not subordinate and subordinate. It is almost impossible to define one of them using the other. The only sign that connects these two concepts is that their objects are devices for making flights. The subordinating concept for both the first and the second will be "aircraft". Thus, only subordinate and subordinating concepts are subject to comparison in terms of the content of the volume. Extensionality of concepts. Any concept reflects an object and contains features that characterize and separate it from other objects. This object is always associated with other objects that are not included in the content of this concept, but have characteristics that partially repeat the characteristics of the object reflected in the concept. These items form a special group. Such a group can be defined as a set of objects characterized by the presence of common features, fixed by at least one concept. However, the mere reflection of the subject by one or another concept is not enough. An object that really exists and an object as an object of thought are not identical. This is connected with the representation of an abstract (imaginary, conceivable) and real (having a real embodiment) object. Abstract subject - this is a mental construction that can accurately reflect the signs, properties of an object, but may also contain an error or inaccuracy. In this context, one can define the scope of a concept as a set of abstract objects related to it. Thus, a real object is an object of the material world, which has characteristic features inherent only to it. An abstract object has no material embodiment and is characterized only by information about its belonging to a concept. There are two approaches to the question of belonging to the concept, according to which the scope of the concept can be the scope of diversity or quantitative. The first approach implies that the scope of a concept includes several other concepts. Accordingly, this last concept is common to all incoming. For example, the concept of "aircraft" includes "aircraft", "helicopter", "airship" and others, so it is general. This approach shows the presence of a sufficient number of elements included in the volume of the subject, respectively, such a volume is called the volume of diversity. Not only the objects themselves are related to the concept, but also the categories inherent in these objects. The scope of the same concept is the totality of objects associated with it. The concept, and accordingly, characterizing its content and volume, are mental formations. Therefore, the scope of a concept cannot consist of real objects, just as the thought of water cannot consist of water itself. It consists of mental reflections of these objects and their properties. The main condition is that such reflections, thoughts about objects, must fall under the signs implied in the concept. What makes a concept and the objects included in its scope real is the idea of the reality of these objects. Thus, the quantitative volume of a concept can be called a volume composed of mental reflections of real-life objects that correspond to a given concept. You should always remember the correct handling of any logical categories. Thus, a mistake related to the scope of concepts is possible. It is unacceptable to identify parts of the subject and parts of the scope of the concept of this subject. Otherwise, a part of a physical object (car wheel, aircraft wing, weapon striker) is identified with independent objects, mental reflections of which are included in the scope of the corresponding concept. It is also necessary to mention empty volumes. In some cases there may be so-called empty volumes. There are two options for the appearance of an empty volume: let us remember that the concept does not include the object itself, but only its mental reflection. Therefore, if an object reflected in a concept contradicts objective physical laws, the scope of such a concept is considered empty. This happens either with concepts containing fantastic objects, or with concepts about objects whose existence is impossible (for example, a perpetual motion machine). In another case, self-contradictory (false) concepts are implied. They have content when the volumes are empty. Different cases of the existence of volumes are studied by formal logic. She considers thinking from the point of view of its extensionality. Or, in other words, in an extensional context. Within the framework of formal logic, thinking is represented as a process of carrying out various operations with the volumes of concepts without considering the content of these concepts. The Purpose of Formal Logic - to determine the truth or falsity of concepts, relying only on their volumes. If there is a formal logic that studies only the scope of concepts, it would be reasonable to assume the existence of a logic of content that would study the content side of concepts and judgments. The object of consideration of the logic of content there must be an intensional part of thinking, the interaction of the content of various concepts and the degree of correctness of reflection in the concepts and judgments of the objective world. Logic studies concepts and judgments about objects in the real world. Concepts are only mental reflections of real-life objects. However, the concept implies the existence of its object. This is where the concept of modality comes into play. Modality is a way of existence of a certain object or process (ontological modality). There is also the notion of logical modality. This is a way of understanding, obtaining a conclusion about an object, phenomenon or process. Logical existence can be called absolute, since this concept defines existence in itself, existence as it is, without being tied to any particular object. Existence can be of the following types: 1) sensual. This is the existence of objects, processes and phenomena, perceived by man. Sense existence can be objective and subjective. The first implies the real existence of the object reflected in the perception of man. Such an object exists independently of the perceiver. The second (subjective) existence reflects not real objects, processes and phenomena, but only imaginary ones. It can be a person's fantasy, his thought about something, a dream, an image; 2) hidden existence. It is interesting that his objects are hidden from human perception for certain reasons. It can be objective and subjective. Objective. The reason for the impossibility of perceiving real-life objects is the inability of the human senses to perceive microscopic objects, various kinds of waves, electromagnetic fields and other similar phenomena. Subjective. This should include the existence of unconscious psychological characteristics that are part of and constitute the subconscious. These are various aspirations, instincts, drives, complexes, etc. The scope of a concept can exist either in a sensible or in a hidden form of existence, regardless of whether it is objective or not. However, such dependence occurs when a mistake is made. Being defined not in its kind of existence, the volume becomes empty. At the same time, we must not forget that the types of existence sometimes do not have clear boundaries. Depending on the circumstances, one of these types can flow into another - a hidden existence can become sensual, an objective - subjective. Therefore, often the scope of the concept may not be empty. It is necessary to consider the scope of the concept separately in each case. The relationship of categories within a concept is subject to logical laws and has its own specifics. Thus, the peculiarities of the effect of the content and scope of a concept on each other are reflected in the law of the inverse relationship between the content and scope of concepts. This law is based on the logical nature of concepts. Taking two concepts, we can notice that one of them is wider than the other in scope, while the other is included in the scope of the first. However, a concept that is included in the scope of another (having, accordingly, a smaller volume) in its content reflects more features and is more saturated with them. It is this phenomenon that forms the basis of the feedback law, which goes like this: the wider the scope of a concept, the narrower its content; the richer the content, the smaller the volume. The essence of this law is that the less information about an object is reflected in the content of the concept, the wider the class of objects and the more uncertain the composition. For example, the concept “airplane” is poor in content, but at the same time it includes aircraft of various types, brands and designs. Expanding the content, we add one more characterizing word and get the concept of “passenger aircraft”. Now the scope of the concept has narrowed significantly, but still contains a significant number of objects. The concept of “Boeing passenger aircraft” has almost the broadest possible content, but the class of objects included in the scope is now clearly defined and few in number. In this way, it is possible to narrow the scope of a concept by expanding its content down to one subject. Author: Shadrin D.A. << Back: Concept as a form of thinking (General characteristics of concepts. Types of concepts) >> Forward: Relationships between concepts (General characteristics of the relationships between concepts. Compatible concepts. Incompatible concepts)
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