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Lecture notes, cheat sheets
Логика. Простые суждения. Понятие и виды (конспект лекций)
Directory / Lecture notes, cheat sheets Table of contents (expand) LECTURE No. 11. Simple judgments. Concept and types 1. The concept and types of simple judgments As you know, all judgments can be divided into simple и complex. Almost all of the judgments given above are simple. Simple Judgments can be identified in contrast to complex. The latter consist of several simple judgments, therefore they are expressed in language by longer and more complex constructions. If we assume a tautology, complex judgments are “more difficult” than simple ones in every sense. Often such judgments accurately and correctly reflect the phenomena of the surrounding reality, objects, their properties and relationships. A feature of complex judgments is that they contain information about several heterogeneous objects at once, this makes them more complete. However, this does not mean that simple judgments are “worse.” Thanks to their simplicity and clarity, they can still be found more often. Since in simple judgments there is no need to reflect several heterogeneous objects at once, there is less opportunity for error. We can also say that the construction of such judgments is “simpler”, because it consists of a sentence containing information about only one object (class of objects). Simple judgments are categorical and assertoric. At the same time, simple assertoric judgments, in turn, can be attributive (reflect the properties of the object) and existential (associated with the idea of whether an object exists in reality). The third kind of simple assertive judgments is judgment about relationships between objects. Categorical judgments are affirmative and negative, as well as general, particular and singular. 2. Categorical judgments Considering judgments from the point of view of traditional logic, it can be noted that they are basically categorical. This means that they either affirm or deny this or that subject, and at the same time the third option is not allowed. In this way, categorical judgments can be affirmative and negative. For example, the propositions “The Moon is a satellite of the Earth” and “Great Britain is an island state” are affirmative. The propositions “No capital is a village” or “Some wines are not French” are negative. This division of categorical judgments is carried out according to the quality of the connective. As we remember, the connective can be distinguished by the words “is” and “is not” or “is” and “is not.” Thus, depending on what type of connective is used in this particular case, we can talk about the presence or absence of certain features in the objects of judgment. Presence is indicated by the copula “is”; absence is expressed by the copula “is not”. From the above it is clear that categorical judgments can be affirmative and negative. However, in order to get a more complete understanding of the relationship between these two types of judgments, it is necessary to become more familiar with each of them. affirmative categorical judgment has the ability to determine the characteristics inherent in a particular subject. This makes such a judgment more convenient when reflecting one or another object, because in this way its properties are distinguished more fully. This means that it is enough for a person who forms an idea about an object on the basis of an affirmative judgment to simply distinguish it from the mass of other homogeneous (and, accordingly, heterogeneous) objects. Negative categorical judgment does not have affirmative properties. In terms of reflecting the properties of the object, these two types are opposite. So, a negative judgment does not say that an object has this or that property, but gives us an idea of what property this object does not have. Thus, a rather blurred picture is often obtained. Knowing only what property an object does not possess, it is very difficult to judge its nature. That is, it is much easier to distinguish an object from others, knowing what properties it has, than vice versa. Of course, a negative judgment can also serve the purpose of reflecting a certain subject, but more often it still serves to clarify. The division into types described above was carried out depending on the quality of the ligament. Another basis for division is quantity. This means that the classification is based on the question of how many objects of a certain class are included in a given concept and reflected in it. A concept may contain an indication that it refers to all objects of the class, part of these objects, or even only one of them. Depending on this basis, simple categorical concepts can be divided into general, private and individual. As you can see, all such judgments have a quantitative expression (they contain an indication of the objects contained in them). Therefore, for convenience, a typology (combined classification) of such judgments was derived. This classification consists of four points. First represented by general statements. As the name implies, such judgments are affirmative and general. Accordingly, the structure of such a judgment is "All S is P". For example, "All humans are mammals." The second type judgments is called private affirmative. It has the structure "Some S are P". For example, "Some athletes are snowboarders." The third type of simple categorical judgments is generally negative. A structure of this type is "No S is a P" and an example is "No dog is a reptile". The last and fourth type of simple categorical judgments is the particular negative type. It is reflected in the form of the formula "Some S are not P". An example would be the proposition "Some lakes are not freshwater". All of these types of judgments have a literal reflection. In the case of the general affirmative and the particular affirmative, these are the letters A and I, respectively. General negative judgments are designated as E, and particular negative ones as O. These letters are taken from the words affirmo ("I affirm") and nego ("I deny"). Considering the structure of judgments, one cannot leave aside such an important issue as the distribution of concepts. As is known, any judgment contains at least subject and predicate, denoted in the diagram by the letters S and P. Both the subject and the predicate are concepts, and, like all concepts, they are characterized by volume and content. If the content consists of features that characterize a concept, then the volume contains information about subordinate concepts. It is by the scope of the concepts S and P that an opinion is formed about their distribution or non-distribution. Thus, the scope of a concept is considered unallocated if it is partially included or partially excluded from the scope of another concept. In contrast to non-distribution, distributed is a term whose scope is completely included in or excluded from the scope of another. The distribution of a term may depend on the type of judgment. There are cases when the subject of the judgment is not distributed, in contrast to the predicate. For example, in the proposition "Some athletes are biathletes", the subject is the term "athletes", the predicate is "biathletes", and the quantifier is "some". The scope of the concept (term), which in this case is a predicate, is narrower than the scope of the subject of judgment. The relationship between these two concepts can be expressed using Euler circles. In this case, the circle representing the predicate will be completely inscribed in the larger circle of the subject. The subject here is not distributed, since only a part of the athletes (biathletes) is thought of in it, and the predicate is distributed, since the term "biathletes" is fully included in the scope of the concept "athletes". The above judgment is privately affirmative. The proposition “Some boxers are world champions” is characterized by the fact that both its subject and predicate are undistributed. Expressing these judgments in the form of Euler circles, we get two intersecting radii, neither of which is completely included in the volume of the other, because only some boxers are world champions, but not all champions are boxers. Judgment "All squares are rectangles" universal. Here the subject is the concept of “squares”, the predicate is “rectangles”. The quantifier word is “all”. The predicate in this case is wider than the subject and completely includes the latter in its scope. So, all squares are rectangles, but not all rectangles are squares. This means that the subject of a given judgment is distributed, while the predicate is not distributed. If you change this judgment, you can get the case of mutual distribution of the subject and predicate. Let's add the word "equilateral" to the judgment and get the following: "All squares are equilateral rectangles." In this case, the volumes of the two concepts are equal, they are completely included in each other. The distribution of concepts is reflected in diagrams where the plus sign (+) expresses the distribution of the concept, and non-distribution - the minus sign (-). Let's move from affirmative to negative concepts. Private negative judgments have the structure "Some S are not P". In the judgment "Some servicemen are not engineers" the subject is the concept "servicemen", the predicate is "engineers", the quantifier word is "some". The subject is undistributed, since in its scope we mean only a part of the military personnel, while the predicate reflects all engineers, none of which is part of the subject's scope. On Euler's circular scheme, this judgment is reflected as two intersecting circles. None of them is completely included in the scope of the other. This example shows that sometimes you can make a mistake. This is due to the external similarity of the circular schemes of particular negative and particular affirmative judgments. In this case, the error may be as follows: based on the fact that the subject and the predicate are characterized by mutual intersection, these terms can be incorrectly defined as undistributed. In simple terms, we note that in this judgment we are not considering the entire set of military personnel (S), but only the part that is not engineers (P). In the predicate, however, we think of all engineers, none of whom is included in the scope of the subject. Since the subject does not contain a single engineer, the entire set of people of this profession is conceived in the predicate. Thus, the predicate, unlike the subject, is distributed. All-negative judgments have the structure "No S is a P". The proposition "No man is a bird" is generally negative. Here both the subject and the predicate are completely distributed. This is due to the fact that the volumes of the concepts "man" and "bird" do not intersect, they are completely excluded from each other. On a circular diagram, the relationship between these concepts looks like two circles standing side by side, but not intersecting with each other. Having considered all these cases, we can conclude that there is a pattern. The distribution of subject and predicate depends on the type of judgment. The subject is distributed in general judgments, but not distributed in particular ones. Regarding the predicate, we can say that it is distributed in affirmative and negative judgments, but if in negative it is always distributed, then in affirmative ones only if it is equal in volume to the subject or if the volume of the subject is wider. The possibility of establishing the distribution of terms is very important, as it is one of the mechanisms for checking the correctness of judgments. This mechanism allows you to check the correctness of the construction of categorical syllogisms. Direct inferences are also checked. 3. General, private, singular judgments General categorical judgments have the structure "All S is (is not) P". They can be selective and exclusive. First on the basis of certain features, one object is distinguished from a group of others and considered separately. Thus, the role of this subject, its connections, relations with other subjects are considered somewhat more thoroughly. The selection of an object from the class of others is carried out with the help of the word "only", which is used in all such judgments. An example would be the following sentences: "It was as if winter had come in all the rooms of the house, and only in the living room it was warm" or "Only Ivanov did not pass the exam on time." Exclusive judgments also separate one object from a group of others. They contain the words "except", "except", etc. For example: "All students passed the session on time, except for Ivanov"; "With the exception of the Moon, celestial bodies are not satellites of the Earth." Rules of the Russian language, mathematics, physics, logic, foreign languages and other sciences containing exceptions from the general should also be considered as excluding concepts. Private judgments can be reflected as "Some S are (are not) P". Scientists are considering a point of view regarding which such judgments can be uncertain and certain. According to researchers, uncertain judgments are those that do not contain a more or less precise indication of the range of subjects, the opinion of which is reflected in these judgments. So, for example, the proposition "Some cars are sports" is considered indefinite, since in it we do not say that all cars should be recognized as sports, but we do not give an indication that only a part of the cars can be considered sports. The word "some", which indicates that a given judgment belongs to particular ones, is considered by researchers who adhere to this point of view to be an insufficient limitation on the number of subjects in relation to which this judgment is derived. In order to change the meaning of this word and obtain certain judgments, it is proposed to clarify them with the word "only". For example, certain there will be a judgment "Only some cars are sports". Drawing the line of reasoning further, it must be said that the formula "Some S are (not are) P" is common to all particular judgments and they can be placed within the framework of this formula. This can be seen in the example of indefinite judgments. Certain propositions, which are also particular, obey the formula "Only some S are (are not) P". In certain private judgments one can meet the quantified words "a lot", "several", "majority", "minority", "many", etc. Singular categorical judgments have the structure "This S is (is not) P". Accordingly, their subject is a single concept, i.e., a concept, the scope of which is exhausted by only one element. Thus, single judgments are: "Moscow is the capital of Russia"; "J. London is not a Russian writer"; "The sun is not a planet." Author: Shadrin D.A. << Back: Judgment (General characteristics of judgments. Linguistic expression of judgments) >> Forward: Complex judgments. Formation of complex judgments (The concept of complex judgments. Expressing statements. Denial of complex judgments)
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