Lecture
We have noted that the subject of logic is abstract thinking and that any abstract thought (idea) is insensitive. Due to the insensitivity of the idea, the problem of its fixation in the consciousness arises. This problem is solved with the help of language: the idea is expressed in a word or phrase. Although the words of the language themselves are sensual, it is, as a rule, abstract sensuality in relation to the objects designated by them: the word and the object behind it usually do not have a direct sensual connection. The abstractness of verbal (verbal) sensuality makes the language an indispensable helper of consciousness in abstract thinking — so indispensable that the latter can be called verbal. Being knowledge of abstract thinking, logic cannot but be interested in languages. She views them as sign systems. The steady interest of logic (and not only logic) to languages at the end of the XIX century led to the creation of semiotics - the science of signs. She has three main sections:
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The key concept of semiotics is the concept of a sign. A sign is a material object representing (replacing in the process of cognition and communication) another object. In this definition, one should pay attention to the fact that a sign is always material, but it can represent (designate) anything: both material and non-material. For example, the word “table” means a material thing, and the word “thinking” means an intangible process.
By the nature of the relationship of representation, there are three types of characters:
| Sign type | Attitude of representation | Examples |
| Indicator | Causal (causal) | Smoke (towards the fire), smile (towards the good mood) |
| Form | Attitude of similarity (external similarity) | Photography (in relation to what was photographed) |
| Symbol | Indefinite | The letter of the alphabet, Arabic numeral |
Any sign has a semantic and subject meanings (often for brevity they use the words "meaning" and "meaning", having in mind the two kinds of meanings indicated). Meaning is the thought of a subject fixed in a sign. The objective value is the object itself (represented by) the sign itself.
Take, for example, the word "forest". To indicate the meaning, give a description of the thought contained in the sign. For the word "forest" the meaning can be conveyed by the phrase "many trees". This is an inaccurate indication of the meaning. More precisely, you need to put it this way: "an array of wild trees." As for the objective meaning of the word "forest", this is an arbitrary element of the set designated by this word.
In the textbooks of logic, you can find a statement that there are signs without semantic or objective meaning. For example, Yu.V. Ivlev cites a mathematical number as an example of a sign that does not make sense, and he considers the expression "perpetual motion" as a vivid example of a sign with no substantive meaning. All examples of the absence of a sign of one value or another do not stand serious criticism. Take the mathematical number one. Its meaning is the minimum amount with a natural account. As for the "perpetual motion", "centaur", "mermaids", etc., here the statement about the absence of such signs of objective value is based on a too narrow understanding of the subject: the latter, supporters of this point of view, can only be material.
Every expression of a language belongs to one or another semantic category - to a group of terms that perform the same semantic function, i.e., they represent objects in the same way.
Semantic categories are of two types: descriptive and logical. A descriptive category represents a specific object, i.e., an object that is inseparably connected with other objects, and a logical object represents an abstract object, that is, one that is taken by itself, apart from other objects. For example, the word "forest" is usually a descriptive category, since the corresponding object is not considered, as a rule, out of touch with other objects - sky, earth, animals, etc. But the connecting union "and" is a typical representative of the logical categories, or a logical term, since it denotes an abstract connection, that is, a connection of anything, without being tied to any particular objects. What other logical terms are often found in the language will be indicated in the next lecture, but for now let us leave logical categories aside.
Among the descriptive categories, the main one is the sentence - an expression of complete thought. According to the purpose of the statement, there are three types of sentences: narrative, interrogative, exclamatory. The main of these species is the first.
As part of any sentence there are at least two descriptive categories: name and sign. A name is an expression of a language that calls an object, a sign is a sign of the presence of a property. For example, in the sentence “Earth is round” the word “Earth” is a name, and the word “round” is a sign. These two categories are always present in the sentence, even when it consists of a single word. So, in the sentence “It is getting dark”, besides the stated feature “darkens”, there is an unspoken name “space”.
Names are divided into single and common. A single name means a single name, i.e. the one and only, object, and the general - an arbitrary element of a set. For example, the name "Earth" is single, and the name "planet" is common. However, the same expression of the language in some cases can be considered as a single name, in others - as a common one. It all depends on what is meant. Let's compare two phrases: "Man lives on Earth for tens of thousands of years" and "Man is born and dies." The word “person” in the first case is used as a single name, denoting a unique kind of living beings, and in the second - as a common name that indicates an arbitrary representative of many people.
As for the sign, it should be borne in mind that it is standardly expressed in at least two words, the first of which is the verb-link "to be." In the above sentences, this verb is not expressed, but only implied. In many Western European languages such a construction of sentences is forbidden, and in Russian it is found very often.
Russian verb-bundle "to be" in the present tense has two forms: "is" (singular) and "essence" (third person plural). The second form is outdated, now only the first is usually used - both for the singular and for the plural, but in logic for the greater severity of statements they have retained both forms. For example, the sentence “Earth is round” should be standardly represented as “Earth is round”, and the sentence “This clock is lagging behind” - as “This clock is lagging behind.” Details of the standard expression of judgments are covered in the seventh lecture.
Sometimes, in addition to the names and signs in the composition of sentences, there are signs of properties and relationships, and by the property is meant the difference of the subject from other similar objects, and by the relation - the difference inherent in a pair, triple, etc. dissimilar items. Take, for example, the following sentence: "The lecture on logic goes to the 225th audience." We translate into a standard form: "The lecture on logic is going to the 225th audience." All the words of this sentence can be divided into two categories: the name “lecture according to logic” and the sign “there is a audience going to 225th”. But it is possible to conduct another, more detailed semantic analysis, according to which "lecture" and "audience" are names, "according to logic" and "225th" are signs of properties, and "... is going to ..." is a sign of relationship.
When recording the last character, two dots of this relationship are indicated in three dots, which must be occupied by some heterogeneous objects (in the example, these are lecture and audience). This attitude is called double. But there are relationships with a lot of places. For example, in the sentence "The Eagle is between Tula and Kursk, the" relationship "... is between ... and ..." a triple. However, any multi-seat relationship can be reduced to a combination of doubles. For the last example, let's do it this way: "Tula is on the north side of the Eagle, and Kursk is on the south side."
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Logics
Terms: Logics