3.3 Categorical statements

When considering ways to form complex sentences from simple ones, the internal structure of simple sentences was not taken into account. They were taken as indecomposable particles with only one property: to be true or false. It is no coincidence that simple statements are sometimes referred to as “atomic”: from them, as from elementary bricks, with the help of logical connectives “and”, “or”, etc. various complex ("molecular") statements are built.

Now it is necessary to dwell on the question of the internal structure, or internal structure, of the very simple statements: from which specific parts they are composed and how these parts are interconnected.

Immediately it must be emphasized that simple statements can be decomposed into their component parts in different ways.

The result of decomposition depends on the purpose for which it is carried out, i.e. from the concept of logical inference (logical consequence), in which such statements are analyzed.

Further, only one type of simple utterances is considered - categorical utterances, traditionally also referred to as categorical judgments.

Of particular interest to categorical statements is explained, first of all, by the fact that the study of their logical connections began the development of logic as spiders. In addition, statements of this type are widely used in our arguments. The theory of logical relations of categorical statements is usually referred to as syllogistic.

A categorical statement is a statement that affirms or denies the presence of any sign in all or some of the objects of the class in question.

For example, in the statement “All dinosaurs are extinct,” the attribute “to be extinct” is attributed to dinosaurs. In the judgment “Some dinosaurs flew,” the ability to fly is attributed to individual dinosaur species. In the statement “All comets are non-asteroids,” the presence of the sign “to be an asteroid” in each of the comets is denied. In the judgment “Some animals are not herbivores,” the herbivores of some animals are denied.

If we ignore the quantitative characteristics contained in the categorical statement and expressed by the words "all" and "some", we get two options for such statements: affirmative and negative. Their structure:

S is P, S is not P

where the letter S represents the name of the subject referred to in the statement, and the letter P represents the name of the attribute, inherent or not inherent in the subject.

The name of the subject referred to in the categorical statement is called the subject, and the name of its attribute is called the predicate. The subject and the predicate are called the terms of the categorical utterance and are connected with each other by bundles “is” or “not is” (“is” or “is not”, etc.). For example, in the statement “the Sun is a star” the terms are the names “Sun” and “star” (the first one is the subject of the utterance, the second is its predicate), and the word “is” is a bunch.

Simple statements like “S is (not) P” are called attribute: they are attributed (attributed) to some property of an object.

Attributive statements are opposed to statements about relationships in which relations are established between two or more items: “Three is less than five”, “Kiev is greater than Odessa”, “Spring is better than fall”, “Paris is between Moscow and New York”, etc. . Statements about relationships play a significant role in science, especially in mathematics. They do not boil down to categorical statements, since relations between several objects (such as "equal", "loves", "warmer", "is between", etc.) are not reduced to the properties of individual objects. One of the significant shortcomings of traditional logic was that it considered the judgments about relationships to be reduced to judgments about properties.

In a categorical statement, the connection between the subject and the attribute is not simply established, but a certain quantitative characteristic of the subject of the statement is given. In statements like "All 5 is (not) P" the word "all" means "each of the items of the corresponding class." In statements like "Some S is (ns is) P" the word "some" is used in a non-exclusive sense and means "some, or maybe everything." In an exceptional sense, the word “some” means “only some” or “some, but not all”. The difference between the two meanings of this word can be demonstrated by the example of the statement "Some stars are stars." In a non-exclusive sense, it means "Some, and possibly all stars are stars," and is obviously true. In the exclusive sense, this statement means “Only some stars are stars” and is clearly false.

In categorical statements affirms or denies that any signs belong to the objects in question and indicate whether it is all these objects or some of them. thus, four kinds of categorical statements are possible:

All S is P - general statement. Some S is P - a privately affirming statement.

All S is not P - a generally negative statement. Some S is not P - a private negative sentence.

Categorical statements can be viewed as the results of the substitution of some names in the following expressions with "spaces" (dots): "Everything ... is ...", "Some ... is ...", "Everything ... is not there is ... "and" Some ... do not eat ... ". Each of these expressions is a logical constant (logical operation), which makes it possible to obtain a statement from two names. For example, substituting the names “flying” and “birds” instead of dots, we obtain, respectively, the following statements: “All birds are flying”, “Some birds are flying”, “All birds are not flying” and “Some birds are not flying” . The first and third statements are false, and the second and fourth are true.