Complex judgments are formed from simple ones by combining them in various ways. Typically, the characteristics of simple and complex judgments do not cause difficulties. However, situations are possible when the boundary between simple and complex judgments should be recognized to a certain extent as conditional. This applies to such constructions in which, not without reason, one can identify either one statement (or negation), or two or three. The assessment of a detailed judgment as simple or complex depends to a certain extent on the position of the researcher. Let’s take the judgment: “This person is a police officer and an athlete.” It can also be considered as simple, if we proceed from the fact that the phrase “internal affairs officer and athlete” expresses one concept. On the other hand, we can assume that the person in question is an employee, but has never been involved in sports. It turns out that the construction we are considering, along with true information, also contains false information. This false information cannot be contained in the concept “athlete”, because the concept does not have a truth value. The bearer of truth value is judgment. But can one judgment be the bearer of two truth values? This is possible only in the case when the judgment consists of two judgments, i.e. is complex. Thus, there is reason to interpret this judgment as complex, consisting of two statements: “This person is a police officer” and “This person is an athlete.”

Types of complex judgments according to the nature of the logical union.

1. Conjunctive(or connecting) propositions. They are formed from initial simple judgments through the logical conjunction of the conjunction “and” (symbolically “”) A  B, i.e. A and B. In Russian, the logical conjunction of conjunction is expressed by many grammatical conjunctions: and, a, but, yes, although, and also, despite the fact that. “I will go to college, even though it will be a lot of work.” Sometimes no alliances are required. Here is a statement from one of the American presidents of the early 20th century: “We are facing a new era in which we will obviously rule the world.”

There are 4 possible ways of combining two initial judgments “A” and “B”, depending on their truth and falsity. A conjunction is true in one case if each of the propositions is true. Here is a table of the conjunction.

2. Disjunctive(divisive) judgments.

a) a weak (non-strict) disjunction is formed by the logical conjunction “or”. It is characterized by the fact that the combined judgments do not exclude each other. Formula: A V B (A or B). The conjunctions “or” and “or” are used here in a dividing and connecting sense. Example: “Pontsov is a lawyer or an athlete.” (He may turn out to be both a lawyer and an athlete at the same time). A weak disjunction is true when at least one of the propositions is true.

The semantic boundary between conjunction and weak disjunction is in a certain respect arbitrary.

b) strong (strict) – logical union “either...or”, . Its components (alternatives) exclude each other: A B. (either A or B). It is expressed essentially by the same grammatical means as the weak one: “or”, “either”, but in a different dividing-exclusive meaning. "We will live or die." “Amnesty can be general or partial.” A strict disjunction is true when one of the propositions is true and the other is false.

AND

3. Implicative(conditional propositions). They combine judgments based on the logical conjunction “if..., then” and “then... when” (symbol “→”), (A → B; if A, then B). “If the weather improves, we will find traces of the criminal.” The judgment that comes after the words “if”, “then” is called the antecedent (preceding) or the basis, and the one that comes after “then”, “when” is called the consequent (subsequent) or consequence. The implication is always true, except for the case when the reason is true and the consequence is false. It must be remembered that the conjunction “if ... then” can also be used in a comparative sense (“If gunpowder itself was invented in China in ancient times, then weapons based on the use of the properties of gunpowder appeared in Europe only in the Middle Ages") and, as is easy to see, can express not an implication at all, but a conjunction.

4. Equivalent(equivalent) judgments. They combine judgments with mutual (direct and inverse) dependence. It is formed by the logical union “if and only if..., then”, “if and only if..., when”, “only if”, “only if” symbol “↔” (A ↔ B), if and only if A , then B). “If and only if a citizen has great services to the Russian Federation, he has the right to receive the high award of the Order of Hero of Russia.” The signs “=” and “≡” are also used. An equivalence is true when both propositions are true or both are false.

Equivalence can also be interpreted as a conjunction of two implications, direct and inverse: (р→q)  (q → р). Equivalence is sometimes called double implication.

Summarizing what has been said about complex judgments, it should be noted that some also distinguish the so-called counterfactual judgment (the conjunction “if..., then”, the symbol “● →”. This is a sign of counterfactual implication. The meaning is this: the situation described by the anti-incident does not take place, but if it existed, then the state of affairs described by the consequent would exist. For example: “If Pontsov were the mayor of Krasnoyarsk, he would not live in a hotel.”

Complex judgments- these are judgments formed from their simple ones through one or another logical connection. The structure of complex judgments differs from the structure of simple judgments. The main structure-forming elements here it is not concepts (terms - subject and predicate), but independent simple judgments, the internal subject-predicate structure of which is no longer taken into account. The connection between the elements of a complex judgment is carried out using logical unions: « And», « or»; « if...then...»; « if and only if... then»; « It's not true that...”, which are close to the corresponding grammatical conjunctions, but do not completely coincide with them. Their main difference is that logical conjunctions are unambiguous, while grammatical conjunctions have many meanings and shades.

These types of connections of simple judgments are expressed by corresponding logical connectives: conjunction("And"), disjunction("or"), strict disjunction(“either, ...or”), implication(“if... then”), equivalent(if and only if...", denial(“it’s not true that...”). Logical connectives are denoted by the symbols: ~ respectively. Each of these logical conjunctions, with the exception of negation, is binary, i.e. connects only two judgments, regardless of whether they are simple or themselves, in turn, complex, having their own unions within themselves.

Complex judgments are considered in logic only from the point of view of their truth values, which depend on the truth values ​​of the simple judgments included in it, as well as on the nature of the connection between these judgments. The nature of the connection is determined by the meaning of logical conjunctions, which consists of answering the question: under what conditions will a complex judgment be true, and under what conditions will it be false? In other words, at what combinations of truth and falsity of simple judgments included in a complex one does a given logical union give a true connection, and at what combinations - a false one? . The meaning of logical conjunctions can be determined using the so-called truth table, in which at the entrance(see Table 1, columns 1,2) are written out all possible combinations of truth values ​​of simple propositions(included in the complex under consideration), and at the exit(Table 1 – columns 3 – 9) – the meaning of a complex judgment formed from given simple ones using corresponding logical union. In this case, the initial simple judgments are denoted by letters: A, B, C, D..., and truth values ​​are symbolized: “ And» - true; " l" - false.

Table 1.

Types of complex judgments

Based on the nature of the logical connection, there are five main types of complex judgments: connecting (conjunctive), dividing (disjunctive), conditional (implicative), equivalent, negated.

Connective or conjunctive a judgment is a complex judgment formed from initial judgments through the logical conjunction “and”, denoted by the symbol “”. For example, the judgment: “Today I will go to a lecture on logic and to the cinema” is a conjunctive judgment consisting of two simple judgments (let’s denote them respectively - A, IN): : “Today I will go to a lecture on logic” ( A), “Today I will go to the cinema” ( IN). Symbolically, this complex proposition can be written as: A B, Where A,IN– elements of conjunction; “ ” is a symbol of a logical union - conjunction. In the Russian language, the conjunctive logical conjunction is expressed by many grammatical conjunctions: and, a, but, yes, although, however, and also... Often such grammatical conjunctions are replaced by a comma, colon, semicolon. For example, in the judgment “Russians harness for a long time, but drive quickly.”

Conjunctive judgment true only if all its constituent elements are true And false if at least one of them is false(see table 1 - column 3).

Knowledge of the features of the truth value of a conjunction is of particular importance in the practice of thinking, because One false judgment is enough to give falsity to an entire, even very complex, conjunctive thought. This fact underlies many Russian proverbs, for example, about what a fly in the ointment does. This feature is important to take into account in legal practice, in discussions - when a complex chain of thoughts is being built, which can fall apart with one false link. On the other hand, it is enough to discover at least one false argument in the opponent’s arguments to refute his entire reasoning as a whole.

Dividing or disjunctive a judgment is a complex judgment formed from initial judgments through the logical conjunction “or”, denoted by the symbol “”. For example, the proposition: “Law can promote or hinder economic development” is a disjunctive proposition consisting of two simple ones: “Law can promote economic development,” “Law can hinder economic development.” Accordingly, designating them through letters A, IN– let’s highlight its logical form: A V.

Since the connective “or” is used in two different meanings – non-exclusive and exclusive, we distinguish weak And strong disjunctions accordingly. The above example is a weak disjunction, because law can simultaneously promote economic development in one respect but hinder it in another. Weak disjunction is true in those cases When true at least one of its constituent judgments (or both together) and false, when both of its constituent propositions are false(Table 1 – column 4).

Strong disjunction(symbol “ ”) differs from weak in that its components are mutually exclusive. For example: “A crime may be intentional or negligent.” In order to emphasize the strictly separative, exclusionary nature of the connection, natural language uses a strengthened double form of separation: “...either...or”, “or...or”, for example: “Either I will find a way, or I I’ll pave it.” Strict disjunction true only when one of its constituent propositions is true and the other is false(Table 1 – column 5).

Among disjunctive judgments one should distinguish also complete And incomplete disjunction when, respectively: listed All characteristics, species of a certain genus, or this enumeration remains open (incomplete), which in natural language is expressed by the words: “etc.,” “etc.”

Disjunctive judgments are widespread in the practice of thinking. It is in them that the logical operation of division is expressed.

Conditional or implicative a judgment is a complex judgment in which judgments are united by the logical union “if..., then” (the “ ” symbol), for example: “If the government breaks the law, it creates disrespect for it,” “If a number is divisible by 2 without a remainder, then it’s even.” A conditional proposition consists of two constituent propositions. The judgment expressed after the word “if” is called basis or antecedent (previous), and the judgment after the word “that” is called consequence or consequent (subsequent). Conditional proposition formula: A B, Where A– base, IN– consequence. At the same time, judgments that play the role of basis and consequence can themselves be either simple or complex judgments.

When forming a conditional proposition, first of all, they mean that it cannot be that what is said in the basis takes place, and what is said in the consequence does not exist. In other words, it cannot happen that the antecedent is true and the consequent is false. This determines what a conditional proposition is true in all cases except one: when the antecedent is present, but the subsequent is not(i.e. – a judgment in form A B- false only in one case, when A- true, and IN– false). This is expressed in Table 1 - Column 6.

In the form of conditional propositions, they express both the objective dependencies of some objects on others, and the rights and responsibilities of people associated with certain conditions.

Equivalent judgment is a complex judgment that combines judgments with mutual conditional dependence. Therefore they are also called double implication. They are formed using the logical conjunction “if and only if..., then,” which is denoted by the symbol “ “. Equivalence formula: A B, Where A, B- judgments from which an equivalent judgment is formed, for example: “A person has the right to an old-age pension if and only if he has reached retirement age.” In natural language, including economic and legal texts, grammatical conjunctions are used to express equivalent judgments: “only if..., then”, “only if..., then”, “that and only in the case when..., then.”

The truth conditions for equivalent judgments are presented in the 7th column of Table 1: equivalent judgment true in two cases - when both constituent propositions are true or when both are false. In other words, the connection (relationship) between the elements of an equivalent judgment can be characterized as necessary: ​​truth A sufficient to recognize the truth IN and vice versa; falsity A serves as an indicator of falsity IN and vice versa.

Denied proposition is a complex judgment formed using the logical conjunction “ It's not true that..." (or simply "not"), which is called the negation sign (the "~" symbol). Unlike the above-mentioned binary conjunctions, it refers to a single judgment. Adding it to any judgment means the formation of a new judgment, which is in a certain dependence on the original : the negated proposition is true if the original one is false, and vice versa. This is expressed in table 1 – columns 8,9. For example, if the initial proposition is: “All witnesses are truthful,” then the negated proposition is: “It is not true that all witnesses are truthful.”

All identified types of complex judgments are used in ordinary reasoning and contexts, including economic and legal ones. To more accurately understand the meaning of these contexts, it is important to master the skills of logical analysis of complex judgments using symbolic language to express their logical structure. Often, to achieve certainty in a statement, it is necessary to identify the main connection in a judgment. For example, the statement “A crime has been committed A And IN or WITH” is not distinguished by certainty, since it is not clear which of the two logical connectives - conjunction or disjunction - is the main one. Therefore, this statement can be interpreted as conjunctive judgment (1): " A And ( IN or WITH)", and maybe how disjunctive judgment (2): “( A And IN) or WITH" But according to logical significance, i.e. in their truth value, they are not equivalent. This can be determined by constructing truth tables for them, and using them to compare the truth values ​​of these judgments.

For this purpose, it is important to know how truth tables are generally constructed for various complex judgments. This is done as follows.

At the table input:

1. Write everything out simple judgments ( A, IN, WITH, D...), included in the complex judgment under consideration. Let their number be n .

2. Determine the number To rows in the table using the formula To = 2n

3. In the input columns of the table, write down all possible combinations of truth values ​​of simple judgments in the following order: in the rightmost column alternate And And l one at a time; in the second column from the right, two values ​​alternate in a row And and two meanings l; in the third column four values ​​alternate in a row And and four meanings l; the fourth column has eight values And in a row and eight values l in a row, etc.

Output table:

4. From left to right, write out the logical forms of all complex judgments included in the judgment in question, in order: at the beginning of a judgment of the 1st degree of complexity (i.e. with one logical sign); then 2nd degree (with two logical conjunctions); further to the 3rd degree (with three logical conjunctions) and so on until the last judgment represents the logical form of the original complex judgment.

5. Columns of truth values ​​for the written out logical forms are formed based on: (1) the meaning of the logical conjunction (see. table 1) and (2) truth values ​​that simple propositions included in this form take (see table entry lines).

We can compare the above propositions (1) and (2). For this purpose, we will now build table 2 for the conjunctive proposition (1), expressing it symbolically as “ A (IN WITH)", And table 3 for the disjunctive proposition (2), writing it symbolically as “( A IN) WITH».

Table 2		Table 3
A	IN	WITH	B C	A (B C)		A	IN	WITH	A B	(A B) C
And	And	And	And	And		And	And	And	And	And
And	And	l	And	And		And	And	l	And	And
And	l	And	And	And		And	l	And	l	And
And	l	l	l	l		And	l	l	l	l
l	And	And	And	l		l	And	And	l	And
l	And	l	And	l		l	And	l	l	l
A	IN	WITH	B C	A (B C)		A	IN	WITH	A B	(A B) C
l	l	And	And	l		l	l	And	l	And
l	l	l	l	l		l	l	l	l	l

From tables 2 and 3 it is clear that the truth values ​​of judgments (1) and (2) are not the same (in two lines - when one is false, the other is true), and therefore they are not equivalent, and represent judgments expressing different connections between their structural elements.

Thus, to carry out a logical analysis of the form of complex judgments, it is necessary to write them down symbolically in the form of a formula and construct corresponding truth tables with their subsequent comparison.

Relationships between judgments

There are logical relationships between judgments. Judgments, like concepts, can be comparable and incomparable, compatible and incompatible. But there are significant differences caused by their different logical structure. If comparable concepts are related to each other in terms of their scope, then between comparable judgments there are diverse relationship first of all according to their truth values. Analysis of these relations involves clarifying the following questions: can the judgments under consideration be true together and false together, whether the truth of one determines the truth of the other and the falsity of one determines the falsity of the other. Such an analysis has important theoretical and practical significance, but its implementation has its own specifics regarding simple and complex judgments, since they differ in their logical structure.

Relationships of judgments according to them truth values are explored in logic between comparable judgments.

Incomparable simple judgments have different subjects and predicates, for example: “The law is harsh” and “The sky is clear.” The truth and falsity of such judgments do not depend on each other. Comparable simple judgments have same subject and predicate(that’s why they are comparable in content), but differ in the quantitative and qualitative characteristics of the logical form. Incomparable complex judgments include simple judgments that are completely or partially different in content. For example, the propositions: “Prosecutors and investigators have a legal education” and “Prosecutors and investigators guard the rule of law.” Comparable complex judgments include identical initial simple judgments, but differ in the type of connection between them (i.e. logical unions). For example: "Theft And fraud is strictly punishable by law", "Theft or fraud is strictly punishable by law", " Wrong that theft and fraud are strictly punishable by law."

Between comparable judgments distinguish two types of relationships: compatibility And incompatibility. Judgments are considered as compatible if they can be true at the same time, and how incompatible if they cannot be true at the same time.

Compatibility there are three types: equivalence, subordination And partial compatibility.

1. Judgments equivalent if they always accept identical truth values. Simple categorical judgments ( A, E, J, O) are in a relation of equivalence if they are different in quantity and quality, and one of them is negated: ~ A is equivalent to O(“It is not true that all lawyers are lawyers” is equivalent to “Some lawyers are not lawyers”); ~O is equivalent to A(“It is not true that some lawyers are not lawyers” is equivalent to “All lawyers are lawyers”); ~J is equivalent to E(“It is not true that some students are professors” is equivalent to “No students are professors”); ~E is equivalent to J(“it is not true that no mushroom is poisonous” is equivalent to “Some mushrooms are poisonous”).

Complex judgments are in a relation of equivalence when, given the same truth values ​​of the original simple judgments, they take on the same values. This can always be established by constructing truth tables for the complex judgments under consideration.

2. Judgment is in relation submission to another ( subordinate), if it is true in all those cases in which the subordination is true. This relationship occurs between simple categorical judgments, in which the quantity is different, but the quality is the same. In this relation there are: universal affirmatives ( A) and private affirmative ( J) judgments; general negative ( E) and partial negatives ( ABOUT) judgments. Here are the following patterns: (1) from the truth of the general ( A or E) follows accordingly the truth of the particular ( J or ABOUT), but not vice versa; (2) from the falsity of the quotient ( J or ABOUT) follows the falsity of the general ( A or E), but not vice versa. For example, if " All students in our group are successful" ( A), then all the more true " Some students in our group are successful" ( J). In turn, if “Some people have the right to break the law” is false ( J), then it is all the more false that “All people have the right to break the law” ( A).

Attitude submission V complex judgments has properties logical consequence, which is characterized by the fact that if the subordinating judgment is true IN subordinate judgment WITH is always true, and it cannot be that the judgment IN true, and the proposition WITH– false. For example: “If a person has a fever ( IN), then he is sick ( WITH)". If a person has a fever ( IN) – true, should of necessity the truth of the judgment ( WITH). But if false IN, judgment WITH can be either true or false.

3. Attitude partial compatibility also occurs between simple and complex judgments. This relationship is characterized by the following pattern: joint falsity is impossible judgments in relation to partial compatibility. In the case of simple judgments, this is the relationship between judgments of the same quantity, but of different quality: between partial affirmatives ( J) and partial negatives ( ABOUT) judgments. The falsity of one of them implies the truth of the other, but not vice versa: the truth of one of them does not necessarily entail the falsity of the other - it can also be true. This pattern should be especially taken into account in the practice of thinking. Yes, when truthfulness (J) – “Some investigators are independent” may be true And ( ABOUT) – “Some investigators are not independent.” But when falsity judgments ( J) – “Some investigators are independent” will need to true a judgment of opposite quality, i.e. ( ABOUT) – “Some investigators are not independent.”

Let's now consider incompatible judgments. There are two types of incompatibility: contradiction And opposite.

Contradiction- this is a relationship between judgments in which truth one necessarily entails the falsity of the other and vice versa. In other words, contradictory propositions cannot together be either true or false. Among simple judgments, this relationship occurs between: general affirmatives ( A) and partial negatives ( ABOUT) judgments; generally negative ( E) and private affirmative ( J) judgments. So, if false the proposition “All investigators are independent”, then “Some investigators are not independent” is true. The relation of contradiction between complex propositions means that their truth values ​​can only exclude each other.

Opposite between judgments is manifested in the fact that these judgments cannot be true together, but can be false together. This relationship is characterized pattern the inverse of that which is characteristic of the partial compatibility relation: if one of the two judgments true, then something else necessary false, but at falsity one of them the other may be as true, so and false. In other words, both judgments may be false.

In the case of simple judgments, this relation takes place between universal affirmatives ( A) and generally negative ( E) judgments. So, if true ( A) – “All lawyers are lawyers”, then false ( E) - “No lawyer is a lawyer.” But if false ( A) – “All witnesses are truthful”, then the truth of the judgment does not follow from it ( E) – “No witness is truthful”, it is also false. But in other cases ( E) may be true. So, if the proposition ( A) – “All citizens have the right to break the law”, then true ( E) – “No citizen has the right to break the law.”

Knowledge of the relationships between judgments according to their true meanings is important in cognitive and practical terms, since it helps to avoid possible mistakes in one’s own reasoning and allows one to competently analyze various contexts and the statements of opponents. There are often situations when judgments are operated as mutually exclusive. For example, when someone makes a judgment of the form "Some S There is R", and the other in the form "Some S don't eat R" A logical analysis of these judgments shows that judgments expressed in this form do not exclude each other, but are partially compatible, and both may turn out to be true. Very often also in a dispute over the truth of a private judgment ( J or ABOUT) deduce the truth of the general ( A or E) accordingly, which violates the correctness of the relationship between them.

In a discussion or dispute, in particular on legal and economic issues, in order to refute a general false judgment, the opposite general judgment is often used. But it’s so easy to get into trouble: it can also turn out to be false. From a logical point of view, for an exact refutation it is enough to give contradictory judgment(see diagram of a logical square below). Mixing opposing and contradictory judgments is a fairly common mistake in thinking practice. Therefore, it is important to be able to carry out a logical analysis of the relationships between judgments.

To carry out a logical analysis of the relationships between simple judgments use a graphical diagram called a “logical square”: its vertices symbolize four types of simple categorical judgments - A, E, J, O; sides and diagonals are the relationships between these judgments.

subordination

subordination

contradiction

To determine the relationship between simple categorical judgments, you need:

1. determine what type of these judgments are: A, E, J, O;

2. find the corresponding angles of a logical square;

3. see what relationship is inscribed between them;

4. by the nature of the relationship, establish a connection between truth values ​​for the analyzed judgments.

For example, we need to determine the relation between the propositions: (1) “Not all metals are hard” and (2) “Some metals are hard.” To do this, we will carry out their logical analysis. First of all, we determine the type of judgments (1) and (2): the second judgment is privately affirmative ( J) , and the first judgment is generally affirmative with negation. We transform it according to the above equivalences (~ A equivalent ABOUT) into an equivalent proposition – ABOUT. Using a logical square, we determine the relationship between J And ABOUT. The relationship between them is partial compatibility, which means that joint falsity is impossible, but joint truth is possible.

To determine the relationships between complex judgments you need:

1. determine by the main logical conjunction view analyzed complex judgments;

2. write down symbolically in the form of formulas their logical forms;

3. construct their joint truth table;

4. compare the truth values ​​of the formulas of these judgments and, based on their nature, determine the type of relationship.

As an example, let us define the relations between the propositions: (1) “He reads neither detective nor historical novels” and (2) “He reads either detective or historical novels.” The first judgment is conjunctive and consists of two negative judgments: “He doesn’t read detective novels” (~ A), "He doesn't read historical novels" (~ IN), the connecting conjunction () is omitted. Symbolic recording of the form of judgment (1): ~ A ~B. The second judgment is strictly disjunctive and consists of two propositions: “He reads detective novels” ( A), "He reads historical novels" ( IN), which are connected by the double disjunctive conjunction “either...or” (). Therefore, the symbolic notation of the logical form of judgment (2): A B. Let us construct a joint truth table for them, where A, B- initial judgments.

Comparing the resulting columns (the two on the far right), which represent the formulas of judgments (1) and (2), we see that these judgments cannot be true at the same time, which means they incompatible judgments. But in the first line we discover their joint falsity, therefore they are in relation opposites.

Complex judgment is a judgment consisting of several simple propositions interconnected by logical unions.

Complex judgments are divided into types depending on the logical conjunction used between them.

Types of complex judgments:

1. 1. Connective proposition (conjunction).
   2. Dividing judgment (disjunction).
   3. Conditional proposition (implication).

Connective proposition or conjunction (from Latin conjunction - union, connection)

The conjunction is used And, as well as other conjunctions in the sense of and ( ah, but, yes etc.).

For example: “Ivanov and Petrov are students of the Faculty of Law.” and: “Ivanov is a student of the Faculty of Law”, “Petrov is a student of the Faculty of Law”.

The conjunction and in logic is denoted by the sign “Λ” or “&”, and simple propositions in its structure by any variables, for example, a and b, where a is the first simple proposition, b is the second simple proposition.

His scheme: “a Λ in”. It reads “A and B”, where “a” and “b” are members of the conjunction.

Separation judgment or disjunction (from Latin disjunction - separation)

The conjunction is used or (either).

Since the conjunction or (or) is used in natural language in two meanings - connective-disjunctive and exclusive-separation, then two types of disjunction should be distinguished:

1. 1. weak (lax) and
   2. strong (strict).

Conjunctive-disjunctive proposition (weak disjunction)- this is a complex judgment in which the simple judgments included in it do not exclude each other.

For example: “A student may make a spelling or punctuation error in a dictation.”

In this example, two simple propositions connected by the conjunction or:

1. “A student may make a spelling mistake in a dictation,”
2. “A student may make a punctuation error in a dictation.”

Since a student can make either only a spelling or only a punctuation error in a dictation, or both, this judgment is a weak disjunction. The terms of such a judgment are not mutually exclusive.

A weak disjunction is denoted by a “v”.

The judgment scheme “a v b” reads “A or B”.

Exclusive-disjunctive judgment (strict disjunction) is a complex proposition in which the simple propositions included in it exclude each other.

For example: “A person is either alive or dead.”

In this example, two simple propositions connected by the conjunction or:

1. "The man is alive"
2. "The man is dead."

A strict disjunction is indicated by a check mark with a dot at the top. The sentence reads: “either A or B.” The terms of a strict disjunction exclude each other and are therefore called alternatives.

Conditional proposition or implication (from the Latin implico - I closely connect).

When conveying a condition in natural language, we start with the word “if”, so the conjunction is used in the implication if... then... .

Indicated by the sign “→”.

Judgment scheme: “a → b”. It reads: “if A, then B.”

For example: “If you cut the wire, the lamp will go out.”

The first judgment (ground) is “The wire was cut”, the second (consequence) is “The lamp went out.”

The judgment “a” is called the basis or antecedent (from the Latin antecedens - previous, previous), the judgment “b” is the consequence or consequent (from the Latin concequens - consequence).

Double implication or equivalence

The conjunction is used if and only if... then … (then and only when …).

For example: “If a student has passed all tests and exams, he can be transferred to the next course.”

Equivalence is indicated by the sign “↔”.

Scheme: “a ↔ b”. It reads: “if, and only if A, then B.”

Difference between implication and equivalence:

• If in an implication the positions of the reason and the consequence are reversed, the judgment will cease to be true and will only become probable. For example: “If the engine stalls, then the car will not move” is a true proposition. On the contrary, the judgment “If the car does not move, it means the engine has stalled” is only probable.
• In equivalence, rearranging the basis and consequence does not lead to a change in the meaning of the judgment. For example: “If the subject and predicate of a general affirmative proposition coincide in volume, then both terms are distributed” is as true as the proposition “If the subject and predicate of a general affirmative proposition are distributed, then their volumes coincide.” Equivalent judgments are equivalent.

It should be noted that if in a conjunction, weak and strict disjunction there can be more than two members of a judgment, then in implication and equivalence there can be only two.

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Judgment as a reflection of truly existing significant connections and relationships between objects. General characteristics of judgment, subject of attributive judgment. Reasons for the meaninglessness of judgments. The concept of "quantifier of existence" in modern logic.

abstract, added 03/11/2012


Characteristics of the logical determination of judgments. Study of logical connections between judgments. The truth value of complex judgments. Features of logical connectives that connect individual judgments. Conditional (hypothetical) syllogism and dilemmas.

abstract, added 08/13/2010


The logical essence of a simple proposition. Consideration of the basics of building a connection between an object and its attribute. Characteristics of attributive relations and judgments of existence. Distribution of subject and predicate. Relations between simple propositions.

abstract, added 11/08/2015


The concept of judgment as a form of thinking that reflects truly existing significant connections and relationships between objects. Classification of judgments according to the elements of its structure: the content of the predicate, the quality of the connective, the scope of the subject and modality.

test, added 02/06/2011

MINISTRY OF EDUCATION AND SCIENCE OF THE RUSSIAN FEDERATION

Federal Agency for Education

St. Petersburg State University of Service and Economics

Law Institute

Discipline: Logic

on the topic: Complex judgments

Saint Petersburg

The concept of a simple proposition

Judgment- a form of thinking through which something is affirmed or denied about an object (situation) and which has the logical meaning of truth or falsity. This definition characterizes a simple judgment.

The presence of an affirmation or denial of the described situation distinguishes a judgment from concepts.

A characteristic feature of a judgment from a logical point of view is that, if it is logically correct, it is always true or false. And this is connected precisely with the presence in the judgment of an affirmation or denial of something. A concept, which, unlike a judgment, contains only a description of objects and situations for the purpose of mentally highlighting them, does not have truth characteristics.

A judgment must also be distinguished from a proposal. Sound shell of judgment – offer. A proposition is always a proposition, but not vice versa. A judgment is expressed in a declarative sentence that asserts, denies, or reports something. Thus, interrogative, imperative and imperative sentences are not judgments. The structures of the sentence and the judgment are not the same. The grammatical structure of the same sentence differs in different languages, while the logical structure of a judgment is always the same among all peoples.

The relationship between judgment and statement should also be noted. Statement is a statement or declarative sentence that can be said to be true or false. In other words, a statement about the falsity or truth of a statement must make sense. A judgment is the content of any statement. Suggestions like "the number n is prime", cannot be considered a statement, since it cannot be said about it whether it is true or false. Depending on what content the variable “n” will have, you can set its logical value. Such expressions are called propositional variables. A statement is denoted by one letter of the Latin alphabet. It is considered as an indecomposable unit. This means that no structural unit is considered as part of it. Such a statement is called atomic (elementary) and corresponds to a simple proposition. From two or more atomic statements, a complex or molecular statement is formed using logical operators (connectives). Unlike a statement, a judgment is a concrete unity of subject and object, connected in meaning.

Examples of judgments and statements:

Simple statement - A; simple judgment - "S is (is not) P."

Complex statement – ​​A→B; complex judgment - “if S1 is P1, then S2 is P2.”

Composition of a simple judgment

In traditional logic, a division of judgment into subject, predicate and connective.

The subject is the part of the judgment in which the subject of thought is expressed.

A predicate is a part of a judgment in which something is affirmed or denied about the subject of thought. For example, in a judgment “Earth is a planet of the solar system” the subject is “Earth”, the predicate is “planet of the solar system”. It is easy to notice that the logical subject and predicate do not coincide with the grammatical ones, that is, with the subject and predicate.

Together the subject and predicate are called in terms of judgment and are denoted by the Latin symbols S and P, respectively.

In addition to terms, a judgment contains a connective. As a rule, the connective is expressed by the words “is”, “essence”, “is”, “to be”. In the example given it is omitted.

Concept of complex judgment

Complex judgment– a judgment formed from simple ones through logical unions of conjunction, disjunction, implication, equivalence.

Logical union- this is a way of combining simple judgments into a complex one, in which the logical value of the latter is established in accordance with the logical values ​​of the simple judgments that comprise it.

The peculiarity of complex judgments is that their logical meaning (truth or falsity) is determined not by the semantic connection of the simple judgments that make up the complex, but by two parameters:

1) the logical meaning of simple judgments included in a complex one;

2) the nature of the logical connective connecting simple propositions;

Modern formal logic abstracts from the meaningful connection between simple judgments and analyzes statements in which this connection may be absent. For example, “If the square of the hypotenuse is equal to the sum of the squares of the legs, then higher plants exist on the Sun.”

The logical meaning of a complex proposition is established using truth tables. Truth tables are constructed as follows: at the input, all possible combinations of logical values ​​of simple judgments that make up a complex judgment are written down. The number of these combinations can be calculated using the formula: 2n, where n is the number of simple judgments that make up a complex one. The output is the value of the complex judgment.

Comparability of judgments

Among other things, judgments are divided into comparable having a common subject or predicate and incomparable that have nothing in common with each other. In turn, comparable ones are divided into compatible, fully or partially expressing the same idea and, incompatible, if the truth of one of them necessarily implies the falsity of the other (when comparing such judgments, the law of non-contradiction is violated). The relationship in truth between judgments comparable through subjects is displayed by a logical square.

The logical square underlies all inferences and is a combination of the symbols A, I, E, O, meaning a certain type of categorical statements.

A – General affirmative: All S's are P's.

I – Private affirmative: At least some S are P.

E – General negative: All (none) S are P.

O – Partial Negatives: At least some Ss are not Ps.

Of these, general affirmatives and general negatives are subordinate, and particular affirmative and particular negatives are subordinate.

Judgments A and E are opposed to each other;

Judgments I and O are opposite;

Judgments located diagonally are contradictory.

In no case can contradictory and opposing propositions be simultaneously true. Opposite propositions may or may not be true at the same time, but at least one of them must be true.

The law of transitivity generalizes the logical square, becoming the basis of all direct inferences and determines that from the truth of subordinate judgments, the truth of judgments subordinate to them and the falsity of opposite subordinate judgments logically follows.

Logical connectives. Conjunctive judgment

Conjunctive judgment- a judgment that is true if and only if all the propositions included in it are true.

It is formed through a logical conjunction of conjunction, expressed by the grammatical conjunctions “and”, “yes”, “but”, “however”. For example, “It shines, but it doesn’t warm.”

Symbolically denoted as follows: A˄B, where A, B are variables denoting simple judgments, ˄ is a symbolic expression of the logical conjunction of conjunction.

The definition of a conjunction corresponds to the truth table:

A	IN	A˄ IN
AND	AND	AND
AND	L	L
L	AND	L
L	L	L

Disjunctive judgments

There are two types of disjunctive propositions: strict (exclusive) disjunction and non-strict (non-exclusive) disjunction.

Strict (exclusive) disjunction- a complex judgment that takes on the logical meaning of truth if and only if only one of the propositions included in it is true or “which is false when both statements are false.” For example, “A given number is either a multiple or not a multiple of five.”

The logical conjunction disjunction is expressed through the grammatical conjunction “either...or.”

A˅B is symbolically written.

The logical value of a strict disjunction corresponds to the truth table:

A	IN	A˅ IN
AND	AND	L
AND	L	AND
L	AND	AND
L	L	L

Non-strict (non-exclusive) disjunction- a complex judgment that takes on the logical meaning of truth if and only if at least one (but there may be more) of the simple judgments included in the complex is true. For example, “Writers can be either poets or prose writers (or both at the same time)”.

A loose disjunction is expressed through the grammatical conjunction “or...or” in a dividing-conjunctive meaning.

Symbolically written A ˅ B. A non-strict disjunction corresponds to a truth table:

A	IN	A˅ IN
AND	AND	AND
AND	L	AND
L	AND	AND
L	L	L

Implicative (conditional) propositions

Implication- a complex judgment that takes the logical value of falsity if and only if the previous judgment ( antecedent) is true, and the following ( consequent) is false.

In natural language, implication is expressed by the conjunction “if..., then” in the sense of “it is likely that A and not B.” For example, “If a number is divisible by 9, then it is divisible by 3.”