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Because connecting judgments can be wrong.

Because connecting judgments can be wrong.

In this case, the subject is understood as everything that can be the object of thought – things, phenomena, processes, properties and relationships of both real objects (or those that existed) and imaginary, which either do not yet exist, or in in principle cannot exist. Without marking objects with appropriate names, people can not only communicate but also think (on a theoretical level).

Between the name and its denotation there is a relation of naming, that is the name names, names the denotation. Denoting (names) are words, phrases, sentences, and denoted – individual objects or classes of objects. And the same denotation can have different names. Thus, the name "author of the story" Shadows of Forgotten Ancestors "and the name" Ukrainian writer, friend of M. Gorky "indicate one person – M. Kotsyubynsky. What makes it possible to associate in each case a certain name with the appropriate subject (denotation)?

The fact is that in the process of naming involved a mediator, which creates an opportunity to use names and find and distinguish some objects from all others. This mediator is a certain knowledge of the denoted object, which is called the meaning (concept) of the name. The meaning and significance (denotation) are the meaning of the name. Only those names that denote existing or existing objects (Rome "kangaroo" "dinosaur") matter.

Imaginary names only symbolically denote something, because the objects they denote do not exist (there is no "man who first visited Mars" or their existence is impossible at all – "eternal engine" "witch" "absolutely black body").

As for the meaning, all names have it. Since it is the meaning that connects the name with the object, the identification of the meaning is extremely important. Logic in the theory of names is interested in the connection of names with the objects they denote, in particular the ratio of the meaning of the name and the content of the concept, the dependence of the logical meaning of the statement on the meanings of names that are its components, and so on.

When building logical systems, they strive to ensure that the naming relationship corresponds to such principles.

1. The principle of unambiguity: the name should have only one denotation, ie denote one object or class of objects. In natural languages, this principle is often violated due to the ambiguity and uncertainty of words and expressions. Therefore, it is necessary to strive for our words and expressions to relate to the same subjects within at least one context. As for specialized languages, in particular the languages ​​of science, here it is possible and necessary to ensure that each name has a single meaning and one meaning. Otherwise, logical errors await us.

2. The principle of objectivity: connections and relations expressed by a complex name are connections and relations not between constituent names, but between objects denoted by simple names included in this complex name. That is, a complex name expresses the relationship between the meanings of simple names. Any statement speaks of the denotations of those expressions that are its components. Yes, the phrase "Tbilisi is a city" refers to Tbilisi and the city, not their names.

The principle of objectivity seems simple, even obvious, but there are situations in which a violation of this principle is possible. This is manifested, in particular, in the identification of a linguistic expression with a statement about the same linguistic expression.

Consider, for example, the following reasoning:

A car is a vehicle. "Car" is a word. So some words are vehicles.

In the first judgment, the name "car" denotes the corresponding type of vehicle, and in the second – names itself. This can lead to confusion.

3. The principle of interchangeability: if two names have the same substantive meaning (the same denotation), then any of them can be replaced by another, while the statement will not change its true meaning. For example, the name "Amazon" can be replaced by the name "the deepest river in the world." And if in the statement "The Amazon flows in South America" ​​to replace the name "Amazon" with the name "the world’s deepest river" then the new statement "The world’s deepest river flows in South America" ​​will not change its true meaning, that is, it like the first statement, will be true.

The principle of interchangeability is also called the principle of extensionality (from "extension" – volume), because it is the basis for distinguishing between two types of context – extensional and intentional (from "intention" – meaning).

Extensional context is a context in which only the denotations of the linguistic expressions that are included in it are important. The substantive meaning of such a context depends only on the substantive meanings of the component names. In these contexts, the principle of interchangeability is preserved, because the replacement of names with the same denotations does not change the meaning of the truth of the statement in which such a replacement of names is made.

Intentional context is a context in which not only the denotations of the linguistic expressions included in it are important, but also their meaning. The substantive meaning of such a context depends on both the substantive and the semantic meaning of the names that are part of it. Therefore, the principle of interchangeability in such contexts is violated, because the replacement of names with the same denotations leads to a change in the value of the truth of the statement in which the replacement of names.

Intentional are contexts that contain direct speech; the so-called pragmatic contexts, which include terms that express a person’s attitude to objects – "wants", "doubts", "knows", as well as some contexts in which the necessary connections between phenomena are expressed.

Depending on the chosen basis of division, names can be divided into appropriate types: names whose denotations exist or existed ("full" names), and so-called empty names in which there are no denotations; these names, in turn, can be divided into singular and general, specific and abstract, and so on.

An example of "full" names can be "G. Skovoroda" "I. Drach" "ocean" "plant" and an example of empty – "Zeus" "ancient deity" "woman who visited the moon".

It would seem that there are no difficulties in understanding singular and common names. And the definition of these types of names is quite banal (single name – a name whose denotation is one object; common name – a name whose denotation is a class of homogeneous objects). However, B. Russell found a problem here. Thus, in his opinion, the word "man" does not mean a set of people, but an indefinite person. And here is the fate of the truth.

Content and scope of concepts

Each concept has a meaning and scope. The meaning of the concept – a set of essential and general features that are thought in it.

Thus, the concept of "parallelogram" means the following features: quadrilateral (generic feature) and pairwise parallelism of the parties (specific feature).

The scope of the concept – a set, a class of objects, each of which is a carrier of features that make up the content of the concept.

Thus, the individual objects (elements of volume) that are thought of in the concept of "forest" are not trees, as none of them has the characteristics of a forest, but individual forests – Black Forest, Ovruch Forest and so on.

There is a relationship between the content and scope of the concept, which is called the law of inverse (content and scope). According to this law, the more related the meaning of the concept (ie, the more abstract the concept, the fewer features it thinks), the wider (and therefore more indefinite) is its scope. Conversely, the richer the meaning of the concept, the narrower and

The scope of the so-called zero concepts is imaginary. its volume is more definite. By the way, this law operates between concepts that are in genus-species relations. Known logical operations of generalization and limitation of concepts (the essence of which will be disclosed below) are based on this law.


Some types of judgments. Abstract

Complex judgments. Unconditional judgments. Conditional judgments. Logic of statements

Complex judgments

A complex judgment is a judgment that includes two or more subjects, or two or more predicates, or two or more subjects and predicates.

Complex judgments are divided into unconditional and conditional.

Unconditional judgments

Unconditional judgments are divided into connecting, dividing, dividing and plural.

In unifying judgments, in contrast to simple ones, there is a statement or denial of belonging to the subject of two or more features. For example: "Taras Shevchenko is a genius poet and a talented master of painting." Since the unifying judgments can be about one subject or about many (complete or incomplete) objects, they, as well as simple, are divided into single, general and partial.

The cognitive function of connecting judgments is that they contain knowledge about the compatibility or coexistence of different features in the same subject (or multiple subjects). The idea of ​​the compatibility of these features is expressed by the conjunction "and" ("and" "a" "and"). Why ugly? Because connecting judgments can be wrong. For example: "This number is prime and divisible by two."

The predicate of a divisive judgment, as well as the predicate of a conjunction, indicates two or more features. However, unlike the conjunction, the divisional judgment does not state that all these features belong to the subject judgment. It is either about belonging (or not belonging) to the subject of only one (besides it is not known which) of the listed signs, or about belonging (or not belonging) to the corresponding subject of at least one of these signs.

The first of these divisive judgments are called exclusive divisive, and the second – connective-divisive. An example of the former is the proposition "This angle is either acute, or straight, or obtuse." And an example of connecting-dividing can be the judgment "Petrenko plays volleyball or football".

To distinguish the connecting-separating from the exclusive dividing judgments, it is necessary to build the first of them according to the scheme "S is P or P;" ("S is P or P}") and the second is "S is either P or P" ("S is either P or P}").

Dividing judgments are divisive. their specificity is that they give a complete list of varieties of the subject of thought. For example: "Forests are deciduous, coniferous and mixed." A kind of divider is the judgment by which the dichotomous division is carried out. For example: "People are divided into genius and non-genius."

All kinds of complex unconditional judgments that we have considered so far differed from simple judgments in that they had two or more predicates.