Parts of judgment. Judgment as a form of thinking

To understand the essence of judgment, as well as its role in the cognitive and practical activities of a lawyer great importance has its classification. Judgments are divided into simple and complex.

Simpleis a judgment that expresses the connection between two concepts or is expressed by one concept, when the second is implied, only thought. For example, “Sidorov has a higher legal education,” “Night,” “It’s drizzling.” A judgment consisting of several simple propositions is called complex. For example, “The criminality and punishability of an act is determined by the criminal law in force at the time the act was committed.” This judgment consists of two simple ones: “The criminality of an act is determined by the criminal law in force at the time the act was committed” and “The punishability of the act is determined by the criminal law in force at the time the act was committed.”

Simple judgments are classified on the following grounds.

1. By subject volume (in count):

Single- judgments that include a statement or denial about one subject of the subject of reasoning. Their formula:

This S is (is not) P

Thus, the expression “The Moscow Institute of Humanities and Economics prepares qualified legal advisers” is a single judgment, since the scope of the subject - “The Moscow Institute of Humanities and Economics” - includes a specific higher educational institution.

Private- judgments in which something is affirmed or denied about a part of objects of a certain class. This part can be definite or indefinite. Depending on the given circumstance, private restrictions are divided into definite and indefinite.

A certain private judgment contains knowledge about both parts of the subject of judgment. It has the following logical diagram:

Only some S are (are not) P

For example, “Only some legal concepts are based on philosophical principles.”

The logical scheme of an indefinite proposition is as follows:

Some S are (are not) P

The quantifier “some” gives it uncertainty. For example: “Some problems of jurisprudence are philosophical in nature.”

Are common- judgments in which something is affirmed or denied about each object of a given class. The logical schemes of such judgments have the form:

All S are P or No S is P

For example, "Every country has its own anthem" is a general proposition, since the scope of the subject includes the entire class of objects displayed.

2. By quality of the bundle (by quality) the judgment can be affirmative or negative.

Affirmativea judgment expresses the belonging of an object to some attribute. For example, “A person guilty of committing a crime is held criminally liable.”

Negativea judgment expresses the absence of a certain attribute in an object. For example, “Some illegal acts are not crimes.”

In this case, one should distinguish between a negative judgment (for example, “A war of conquest has no legal basis"") and a negative form of expressing an affirmative judgment (for example, “War of conquest is illegal”). This type of judgment is not always identical.

3. According to the content of the predicate judgment is divided into judgment of property (attributive), judgment of relation (relative) and judgment of existence (existential).

Property judgment (attributive judgment) reflects whether or not the object of thought belongs to one or another property or state. For example, “A prosecutor is a person with a special legal education.”

Judgment of attitude (relative judgment) expresses various connections between objects of thought according to place, time, and cause of dependence. For example, “The welfare of the state depends on the laws” (Aristotle).

Judgment of existence (existential judgment) indicates the fact of the presence or absence of a particular object of thought. Such judgments include, for example, “There is no crime without an indication of it in the law” or “There is no absolute repeatability of phenomena.”

In classical logic there are also categorical judgment in which affirmation or denial is expressed without stating any conditions and without any options. Usually all attributive judgments are classified as categorical.

These are the main types of simple judgments. Any judgment has quantitative and qualitative certainty. Therefore, in logic it is used combined classification of judgments by quantity and quality. As a result, we obtain four types of judgments: general affirmative, general negative, particular affirmative and particular negative. Let's look at them in detail.

General affirmative judgment - general in terms of the volume of the subject and affirmative in terms of the quality of the connective. Its logical structure: “Everything S is P”, and the symbol is the Latin letter “A”. An example is the statement: “All lawyers are lawyers.”

General negative judgment - general in terms of the volume of the subject and negative in terms of the quality of the ligament. Its logical structure is: “No S is a P.” The symbol of generally negative judgments is the letter “E”. For example, “No forged document is evidence.”

Particularly affirmative judgment - quotient in terms of the volume of the subject and affirmative in terms of the quality of the connective. Its logical structure is: "Some S are P." The symbol of private affirmative judgments is the Latin letter “I”. Examples of such judgments are: “Some students are lawyers” or “Some writers are front-line soldiers.”

Partial negative judgment - quotient in terms of the volume of the subject and negative in terms of the quality of the connective. Its logical structure is: “Some S is not P,” and the symbol is the letter “O.” Examples of partial negatives are the following statements: “Some European countries are not members of NATO” or “Some people are not lawyers.”

Single judgments in the combined classification are equated to general judgments, for example, “The Moscow prosecutor’s office is conducting an investigation,” since the entire volume of the subject is meant.

The relationship between the volumes of terms in a judgment is associated with the problem of their distribution.

Distributeda term is considered when it is taken in full. The term is considered unallocated, if it is taken in part of the volume. The study of the distribution of the terms of a judgment is not a formal logical operation, but a confirmation of the correct connection between the subject and the predicate in a judgment, that is, its correspondence to the objective relationship of the objects themselves. Let's look at how terms are distributed in judgments A, E, I and O using specific examples.

In a generally affirmative judgment “All lawyers are lawyers”, the scope of the predicate “lawyers” is wider than the scope of the subject “lawyers”. The volumetric relations of subject and predicate in such judgments can be depicted in the form of the indicated circular diagram. It can be seen from this that the volume S is only part of the volume P, so in addition to S the scope of P may include the scope of other concepts (in the example given, these could be “prosecutors”, “investigators”, etc.), which means S - distributed, and P - not distributed.

In many generally affirmative propositions (in all correct definitions), subject and predicate will be equivalent concepts. For example, " Rent- the amount paid by the tenant for the use of the leased property.” In such judgments, the scopes of the terms coincide, since they are taken in full, that is, distributed.

Consequently, in general affirmative propositions, the subject is distributed, but the predicate is not distributed, or both terms are distributed.

General negative judgment - “No forged document is evidence.” The complete incompatibility of the subject “forged document” and the predicate “evidence,” as is clearly shown in the diagram, is characteristic of all generally negative judgments, that is, their volumes completely exclude each other, they are always distributed.

In a private affirmative judgment “some students are lawyers”, the subject “students” and the predicate “lawyers” are intersecting concepts, their scopes, as shown in the diagram, partially coincide, that is, each term is taken as part of the scope, which means it is not distributed.

However, in some private p In active judgments, the scope of the subject is wider than the scope of the predicate.

For example, “Some students are excellent students.” The scope of the predicate “excellent students” here is included in the scope of the subject “students”, since in addition to excellent students there are good students, C students, etc., therefore the scope of the subject only partially coincides with the volume of the predicate - which means that in this case the subject is not distributed, but the predicate distributed

Consequently, in partial affirmative propositions the subject and the predicate are not distributed, or the predicate is distributed and the subject is not distributed. Volumetric relations of subject and predicate in private negative judgments, for example, “Some European states are not members of NATO,” resemble similar schemes in private affirmative judgments with the only difference that in those cases we're talking about about the coinciding part of the volumes of terms, and in partial negatives - about the non-coinciding part of the volume of the subject with the volume of the predicate.

Consequently, in partial negative judgments the subject is not distributed, but the predicate is distributed in both cases.

Based on the analysis of judgments according to the combined classification, we formulate terms distribution rules:

1. In general affirmative propositions, the subject is distributed, but the predicate is not distributed. Both terms will be distributed if they are equivalent.

2. In general negative judgments, both terms are always distributed, they completely exclude each other, and are incompatible concepts.

3. In particular affirmative propositions, both terms are not distributed if they are expressed by intersecting concepts. If in a particular affirmative judgment the predicate is subordinated to the subject, then the predicate will be distributed.

4. B partial negative in judgments the subject is not distributed, but the predicate is always distributed.

5. B single in judgments, the terms are distributed in the same way as in the corresponding general judgments.

To remember the distribution of terms in judgments, we present the following table, indicating the distribution of a term with a “+” sign, and non-distribution with a “-” sign.

Thus, the subject is always distributed in general judgments and not distributed in particular judgments; but the predicate is distributed in negative judgments and not distributed in affirmative judgments. The exception is some generally affirmative and particular affirmative propositions, in which the predicate can be distributed.

Logic: Textbook for students of law universities and faculties Ivanov Evgeniy Akimovich

1. Simple judgments

1. Simple judgments

The Nature of Simple Judgments. Simple propositions, since they reveal the unconditional connection between objects of thought, are also called categorical. From the point of view of functions, they serve as a reflection of one or another relatively independent connection of the objective world - regardless of what kind of connection it is in its content. From the point of view of structure, simple categorical judgments, being further indivisible into even simpler judgments, include as components only concepts that form subject and predicate.

However, simple judgments are very diverse in their manifestations. They are divided into types according to the following basic logical characteristics: the nature of the copula, the subject, the predicate, as well as the relationship between the subject and the predicate. Particular importance in logic is attached to the division of simple judgments into types according to the nature of the connective (its quality) and the subject (according to its quantity).

Types of judgments by quality and quantity. The quality of judgment is one of its most important logical characteristics. It does not mean the actual content of the judgment, but its most general logical form- affirmative or negative. This reveals the deepest essence of any judgment in general - its ability to reveal the presence or absence of certain connections and relationships between imaginable objects. And this quality is determined by the nature of the connective - “is” or “is not.” Depending on this, simple judgments are divided according to the nature of the connective (or its quality) into affirmative and negative.

IN affirmative judgments reveal the presence of any connection between the subject and the predicate. This is expressed through the affirmative connective “is” or the corresponding words, dashes, and agreement of words. The general formula for an affirmative proposition is “S is P.” For example: “Whales are mammals.”

In negative judgments, on the contrary, the absence of one or another connection between the subject and the predicate is revealed. And this is achieved with the help of the negative connective “not” or words corresponding to it, as well as simply the particle “not”. The general formula is “S is not P.” For example: “Whales are not fish.” It is important to emphasize that the particle “not” in negative judgments certainly comes before the connective or is implied. If it is located after the connective and is part of the predicate (or subject) itself, then such a judgment will still be affirmative. For example: “It is not false freedom that gives life to my poems,” “Not every fruit is sweet.”

In this regard, two main types of affirmative judgments are distinguished: a) judgments with a predicate, which is expressed by a positive concept. Formula "S is P". Example: “Judges are independent”; b) judgments with a predicate representing a negative concept. The formula “S is not-P.” Example: “Judges are independent.” Other examples: “Many laws are in effect,” “Some laws are inactive.”

Negative judgments also have two varieties: a) judgments with a positive predicate. Formula: “S is not P.” Example: “Petrov is not a patriot”; b) judgments with a negative predicate: “Petrov is not an unpatriot.” More examples: “Local self-government bodies are not part of the system of state authorities” and “The Federal Assembly is not a non-state body.”

The division of judgments into affirmative and negative is to a certain extent relative. Any statement contains a hidden negation. Let us remember the aphorism: “Determinatio est negatio.” And vice versa. So, if “This is an elephant,” then “this” is not some other animal - a lion, a giraffe, etc. And if “This is not an elephant,” then “this” is another animal - a lion, giraffe, etc. This is why an affirmative judgment can be expressed in the form of a negative one and vice versa. For example: “Petrov is a patriot” - “Petrov is not an unpatriot.” It’s like in mathematics: a double negative is equal to a statement.

The cognitive significance of affirmative and negative judgments is determined by their features, which are objective in nature. Affirmative judgments (if they are true) provide knowledge about what exactly the object of thought is, what is its qualitative certainty that distinguishes it from other objects. And since everything in nature and society is interconnected, corresponding, and, moreover, diverse, consequences follow from any statement. So, saying that “This is a man,” we at the same time assert that “This is an animal, capable of work, gifted with reason and speech,” etc.

Negative (true) judgments, contrary to the opinion of some logicians, also have a rational meaning, if you do not mean judgments like “A rose is not a camel.” They are important primarily in themselves, since they reflect the objective absence of something from something. No wonder they say: “ Negative result also a result." But they are no less important in their relation to affirmative judgments. Establishing what the object of thought is not is a step towards revealing its real essence. Thus, the judgment: “Whales are not fish” is dialectically related to the judgment: “Whales are mammals” and serves as its prerequisite.

And yet, affirmative judgments are more informationally rich and, therefore, have greater cognitive power. From a negative judgment it does not always clearly follow what the object directly is. And from the affirmative it follows quite definitely not only what it is, but also what it is not.

Knowledge of the characteristics of affirmative and negative judgments has not only theoretical, but also practical significance. Take for example a well-known legal principle presumption of innocence. Which is more correct, stronger, more categorical, and therefore more humane and democratic to formulate it: “The accused is considered innocent” or “The accused is not considered guilty”? The legislation of our country adopted its first formulation - affirmative. During the discussion of the draft new Constitution Russian Federation some authors suggested giving him a different, negative one. In this case, reference was made to the constitutions of some states, in particular Italy, Poland, and Yugoslavia. And yet, in the currently adopted text of the Russian Constitution, the principle of the presumption of innocence is given in an affirmative form: “Everyone accused of committing a crime is considered innocent until his guilt is proven in the manner prescribed by federal law and established by a court verdict that has entered into legal force” (Article 49 ). This was done, of course, correctly, since the affirmative form of judgment is somehow “stronger” than the negative one.

In addition to the initial, fundamental division of simple categorical judgments by quality, there is also their division by quantity.

Quantity judgments are its other most important logical characteristic. By quantity here we do not mean any specific number of objects conceivable in it (for example, the number of days of the week, months or seasons, planets solar system etc.), and the character of the subject, i.e. its logical scope. Depending on this, general, particular and individual judgments are distinguished.

General are called judgments in which something is stated about the entire group of objects, and, moreover, in a divisive sense. In Russian, such judgments are expressed by the words “everyone,” “everyone,” “everyone,” “any” (if the judgments are affirmative) or “none,” “nobody,” “none,” etc. (in negative judgments). In symbolic logic such words are called quantifiers(from Latin quantum - how much). In this case it is general quantifier. Is there a symbol used to represent it? (from English, all - everything). Formula "? xP(x) is interpreted as follows: “for all x, P(x) holds.” In traditional logic, general propositions are expressed by the formula “All S are P” (“No S is P”).

Examples: “All men are mortal”, “No man is immortal.”

Legal examples: “All lawyers are lawyers”; “No one can be held responsible for an act that was not recognized as an offense at the time it was committed.” The quantifier word is often omitted; it can only be substituted mentally. Thus, in the judgment: “He who thinks clearly, speaks clearly” means “everyone”, “anyone”. In Pushkin’s judgment “There is no sharp joke final verdict" means "none". General judgments of the same type are aphorisms: “Comparison is not proof”, “Ignorance is not an argument”, etc.

Legal documents often contain statements like this: “Citizens of the Russian Federation...” (meaning “everyone”) or “Judges are inviolable” (also referring to “everyone”).

General judgments have their own varieties. First of all, they can be excretory or non-excretive.

IN highlighting something is said only about this group. In Russian they are expressed by the words “only”, “only”, “only”, etc. Examples: “Only people are intelligent beings on Earth” (this means that there are no other intelligent beings on Earth); “Only the court administers justice in the Russian Federation”; “Only a person who has committed a socially dangerous act can be found guilty of a crime.”

IN non-releasing what is said about this group can be applied to other groups: “All people are mortal” (this means that not only people are mortal, but also animals and plants). “All lawyers are lawyers” (means that prosecutors, judges, investigators, etc. can be lawyers).

Private judgments are those in which something is expressed about a part of a group of objects. In Russian they are expressed by words such as “some”, “not all”, “most”, “part”, “separate”, etc. In symbolic logic, such words are called “quantifier of existence” and are denoted by the symbol “?” (from English, exist - to exist). Formula? x P(x) reads: “There is an x ​​such that P(x) holds” or “For some x, P(x) holds.” In traditional logic, the following formula for private judgments is accepted: “Some S are (are not) P.”

Examples: “Some wars are just”, “Some wars are unjust” or “Some witnesses are truthful”, “Some witnesses are not truthful”, “Some customs officers are lawyers”, “Some customs officers are not lawyers”. The quantifier word can also be omitted here. Therefore, in order to determine whether there is a particular or general judgment, one must mentally substitute the corresponding word. For example, the Latin proverb: “Errare humanum est” (“To err is human”) does not mean that this applies to every person. Here the concept of “people” is taken in a collective sense. Another Latin proverb: “Quod licet Jovi, non licet bovi” (“What is permitted to Jupiter is not permitted to the bull”) does not mean “everything,” only “something.”

It is not difficult to understand that the quantifier words of private judgments, which are logically identical, actually characterize the scope of the subject differently. Therefore, in practice they are far from interchangeable. Thus, the propositions: “The majority of the population voted for the Constitution” and “The minority of the population voted for the Constitution” are logically both partial, but their specific meaning is fundamentally different. Therefore, their political and legal consequences are directly opposite: “The Constitution is adopted” or “The Constitution is not adopted.”

One of my listeners, Vera Aksenova, subtly grasped a similar difference. She told how the work of the department was once checked entrepreneurial activity Committee for State Property Management of Istra. As a result, it was revealed that “ Some enterprises were registered without submitting the necessary documents” (out of 30 enterprises there were 5 such enterprises). However, the inspection report states that “ Majority enterprises were registered without submitting the necessary documents.” Of course, both judgments are private. But if the first judgment based on facts is true, then the second is false.

Private judgments also have their own varieties. They are divided into definite and indefinite.

IN certain In private judgments, something is said only about a part of a group of objects and cannot be extended to the entire group of objects as a whole. The word “some” here is understood to mean “only a few.” Examples: “Some people are beautiful”; “Some books are not interesting”; “Some lawyers are deputies of the State Duma.”

IN uncertain In private judgments, something is expressed about a part of objects in such a way that it can be attributed to their entire group in general. The word "some" is used here in a different sense: "At least some, and perhaps all." For example, having seen a new logic textbook on the first tables of the student audience, I can already make the judgment: “Some students have a logic textbook.” After interviewing the others, I can make sure that “All students have a logic textbook.” This means that the previous judgment was indefinitely particular.

Of course, in the living practice of thinking it is not always so easy to decide in what sense a particular judgment is expressed. Take for example the proverb: “All that glitters is not gold.” Clearly this is a personal judgment. But which one? Let us first find the subject and predicate of the judgment, and for this we express it in the appropriate grammatical form: “Not everything that glitters is gold,” i.e., “Only some shiny things are gold.” Now it is clear that this is a certain private judgment.

Single judgments are those in which something is expressed about a separate object of thought. In Russian they are expressed by the words “this”, proper names, etc. The formula “This S is (is not) P.” Examples: “This is the Kremlin”; “The Moscow Kremlin is the most beautiful in the world”; "St. Petersburg is not the capital of Russia." Legal examples: “The Criminal Code of the Russian Federation has been revised,” “ Pension Fund Russia is working successfully."

Single judgments, just like general and particular ones, have their own varieties. One of them is judgments about an individual object: “This is the Sun,” “The Sun is the source of life on Earth,” “The Moon is not a planet.” The other consists of judgments about a set of objects, considered as a whole and expressed by collective concepts. For example: “The solar system is not the only planetary system in our Galaxy"; "Ursa Major - constellation." Since in both cases something is said about the subject of thought as a whole, individual judgments in logic are equated to general ones and are not subject to separate logical analysis.

There is also no absolute line between particular and general judgments. For example: “All but two of the students came to the logic seminar.” What kind of judgment is this? On the one hand, there is a quantifier word “all”. This means that this is a general judgment in form. And on the other hand, the words “not counting two.” This means not “all”, but “some”. Therefore, this is essentially a private judgment. Such judgments, which are intermediate in nature, are called in logic exclusive. They are expressed in Russian with the words: “excluding”, “except”, “besides”, etc. In legal practice, such judgments are not uncommon. For example: “As a rule, the law does not have retroactive effect” (i.e. there are exceptions); “Proceedings in all courts are open, except in cases where this is contrary to the interests of protecting state secrets”; “The victim is usually interviewed before the witnesses.”

Finally, the line between particular and individual judgments is relative. Thus, the verbal expression of a private judgment “at least some” means “at least one”. For example, it is enough for someone in scientific or philosophical literature, the media, etc. express any opinion so that one can say: “Some authors put forward such an opinion...” Or if at least one of the constitutions of the countries of the world contains any article, then one can say: “In some constitutions...”

The cognitive value of general, particular and individual judgments is different, but great in its own way. Thus, individual judgments contain knowledge about individual objects and phenomena: historical events, great personalities, facts of modern public life. Legal practice, in essence, everything is based on individual judgments: for example, civil and criminal cases - on individual facts, persons, things. Single judgments also provide knowledge about entire Aggregates, “ensembles” of objects, and therefore can express certain general patterns, acquire enormous ideological significance. For example: “Earth is an ordinary heavenly body"(and not the center of the universe, as was believed before Copernicus); “The solar system is not eternal” (but arose from the original giant nebula, as I. Kant assumed); “The Universe is nonstationary” (as A. Friedman proved on the basis of A. Einstein’s theory of relativity).

Particular judgments contain knowledge about types, forms, species, varieties, etc. one or another group of objects. For example: “Some metals are lighter than water,” “Some mammals live in water,” “Some people are geniuses.” Under certain conditions, private judgments can turn into general ones. For example: “Some metals are electrically conductive” - “All metals are electrically conductive.”

General judgments express general properties(or entire sets of properties) of conceivable objects, general connections and relationships between objects, including objective patterns. Legal laws, decrees, and other regulations take the form of general judgments. Thus, in the form of general judgments expressed constitutional rights and duties of citizens of the Russian Federation, articles Labor Code, Criminal Code, Customs Code, etc.

In the process of cognition and communication, individual, particular and general judgments interact with each other. On the basis of individual judgments, generalizations arise in the form of particular and general judgments. Thus, a painstaking study of the facts of crime in the country allows us to draw general conclusions about its causes, nature, development trends, possible consequences. In turn, the presence of general judgments becomes the basis for subsuming individual cases under a general rule.

Considered separately for methodological purposes, the quality and quantity of judgment are closely related. Therefore, in logic great importance is attached unified classification of judgments according to their quantity and quality. There are four possible types of such judgments: generally affirmative, particular affirmative, generally negative and particular negative.

Generally affirmative judgments are called, by quantity, i.e., by the nature of the subject, general, and by quality, i.e., by the nature of the connective, affirmative. For example: “All lawyers are lawyers.”

Privately affirmative judgments are partial in quantity, affirmative in quality. For example: “Some witnesses give reliable testimony.”

General negative judgments are general in quantity, negative in quality. Example: “No accused is acquitted.”

Finally, partial negatives judgments are partial in quantity, negative in quality. Example: “Some witnesses do not testify correctly.”

To formally record these types of judgments in logic, the vowels of two Latin words “affirmo” (“I affirm”) and “nego” (“I deny”) are used. Specifically, they mean judgments:

A - universally affirmative,

I - privately affirmative,

E - generally negative,

O - partial negatives.

To correctly understand the meaning of judgments and correctly operate with them, you need to know distribution of terms in them - subject and predicate.

Distributed a term is considered to be conceivable in its entirety; unallocated- if it is conceived not in its entirety, but in part.

In general affirmative propositions (A): “All S are P” - the subject is distributed, but the predicate is not distributed. This can be seen in graphic diagram(shading indicates the degree of their distribution).

The only exceptions are cases when the judgment is general. For example: “Only people are intelligent beings on Earth.” Here both subject and predicate are distributed.

In particular affirmative propositions (I): “Some S are P,” the subject and predicate are not distributed.

The only exceptions are cases when the subject is wider in scope than the predicate. For example: “Some mortal beings are men,” “Some lawyers are lawyers.” In them the subject is not distributed, but the predicate is distributed.

In general negative propositions (E): “No S is P,” the subject and predicate are distributed.

Finally, in partial negative propositions (O): “Some S is not P” - the subject is not distributed, the predicate is distributed.

Summarizing what has been said, we can derive the following patterns characterizing the distribution of terms in judgments:

a) the subject is distributed in general and not distributed in private judgments)

b) the predicate is distributed in negative and not distributed in affirmative judgments.

Knowledge of the distribution of terms in judgments is of great importance in the practice of thinking. It is necessary, firstly, for the correct transformation of judgments and, secondly, for checking the correctness of inferences (see below).

Types of judgments by the nature of the predicate. The predicate of a judgment, being a carrier of novelty, can have a very different character. From this point of view, in the whole variety of judgments, three most common groups are distinguished: attributive, relational and existential.

Attributive judgments (from the Latin attributum - property, sign), or judgments about the properties of something, reveal the presence or absence of certain properties (or signs) in the object of thought. For example: “All republics former USSR declared their independence"; “The Commonwealth of Independent States (CIS) is fragile.” Since the concept expressing a predicate has content and volume, an attributive judgment can be considered on two levels: content and volume.

In terms of content, this is a judgment about whether the object of thought possesses or does not possess a set of properties or a separate property. Depending on this, two types of attributive judgments are distinguished. In one of them, the predicate is expressed by a specific concept, that is, the concept of the objects and phenomena themselves in the strict sense of the word. For example: “Mercury is a metal” (that is, it has all the properties of metals).

In another variety, the predicate is abstract concept. For example: “Mercury is electrically conductive” (that is, it has a separate property - electrical conductivity). It is not difficult, however, to notice the relative differences between these varieties. It is enough to compare the following pairs of judgments: “Man is a thinking being” and “It is human nature to think”; “Every crime is a socially dangerous act” and “Every crime has a social danger.”

In volumetric terms, attributive judgments are judgments about whether an object of thought is included or not included in a particular class of objects. They are then called “judgments.” inclusion(or non-inclusion) in the class of subjects.” Depending on the volumetric relationships, there are also two types of them. One is characterized by inclusion (or non-inclusion) subclass to class. For example: “All metals are electrically conductive” (here the subclass of metals is included in the class of electrically conductive substances). In another it is installed belonging(or non-belonging) element to class. “This substance is metal.” In symbolic logic, these and other judgments are expressed by the formulas: S ? P (read: volume S is included in volume P) and S ? P (read: S belongs to P).

True, the line between these two types of judgments of inclusion (non-inclusion) in a class is also relative. For example, “All metals are electrically conductive” means that any item that is a member of the class of metals is also a member of the class of electrically conductive substances.

Relational judgments(from Latin relatio - relationship), or judgments about the relationship of something to something, reveal the presence or absence of a particular relationship in the object of thought to another object (or several objects). Therefore, they are usually expressed by a special formula: x R y, Where X And at- objects of thought, a R(from relatio) - the relationship between them. For example: “The CIS is not equal to the USSR”, “Moscow is larger than St. Petersburg”, “The law is not written for a fool.”

Relational judgments also have their own varieties. One of them is judgments about the relationship between two objects. For example: “Ryazan is smaller than Moscow”, “Knowledge is like money” (the more you have, the more you want to have); “Even the smallest offenses give rise to great crimes.” Or, as Kozma Prutkov noted, “it’s easier to hold the reins than the reins.” In contrast to the “one-place” predicate of attributive judgments, the predicate in them is called “two-place”. Another type of relational judgment is judgments about the relationships between three or more objects. For example: “Ryazan is located between Moscow and Tambov.” The predicate here is “multiple”.

The relativity of the differences between attributive and relational judgments is manifested in their ability to transform into each other. Thus, attributive judgments can be represented as special case relational, since in them the connective “is” (“is not”) reveals the relation of identity (belonging, inclusion, etc.) between objects conceivable in S and P. And a relational judgment, in turn, can be represented as a special case of an attributive one.

Examples. The proposition “All metals are electrically conductive” can be transformed into the proposition “All metals are like electrically conductive bodies.” In turn, the proposition “Ryazan is smaller than Moscow” can be turned into the proposition “Ryazan belongs to cities that are smaller than Moscow.” Or: “Knowledge is something that is like money.” In modern logic there is a tendency to reduce relational judgments to attributive ones.

Existential judgments (from the Latin existentia - existence), or judgments about the existence of something, are those in which the presence or absence of the very subject of thought is revealed. The predicate here is expressed by the words “exists” (“does not exist”), “is” (“no”), “was” (“was not”), “will” (“will not”), etc. For example: “Smoke without there is no fire”, “the CIS exists”, “there is no Soviet Union”. In the legal process, the first question to be resolved is whether the event took place: “There is a crime” (“There is no evidence”).

Undoubtedly, existential judgments have certain specifics. However, it is more appropriate to consider them as a special case of attributive judgments. Thus, the proposition “The CIS exists” means that “The CIS has the property of existing,” or in a comprehensive interpretation: “The CIS belongs to the class of existing interstate associations.” That is why in the subsequent logical analysis existential judgments are not independently considered.

The cognitive significance of the considered types of judgments based on the nature of the predicate is difficult to overestimate. Knowledge about the ever new discovered properties of infinitely diverse objects of thought is clothed in attributive judgments. For example, Pierre and Marie Curie established that polonium, like uranium, has the property of radioactivity, and thereby significantly expanded the horizon of our knowledge. Identifying certain properties of the objects under study or the characteristics of certain individuals is important, for example, in criminology.

Relational judgments reflect the infinite richness of relationships between objects of thought: spatial and temporal, natural and social, and among social ones - production and non-production (political, moral, religious, family, etc.). With their help, the whole gamut of legal relations between people is expressed: the relationship of creditor and debtor, seller and buyer, boss and subordinate, parents and children, participants trial etc. For example: “Ivan borrowed from Peter”, “Petrov entered into an agreement with Sidorov”, “The judge asked a question to the witness.”

Existential judgments are of particular importance. The first thing a person encounters in his practical activity is the existence (or absence) of certain objects and phenomena. And currently we are concerned with questions: is there life on other planets, are there other intelligent beings in the Universe, are there “ big Foot", "biofield", "telepathy", "poltergeist" and much more. In judicial practice, the establishment of the fact of a crime, labor or civil dispute is the beginning of all subsequent proceedings.

Knowledge of the features of attributive, relational and existential judgments is therefore important for every person in general and a lawyer in particular.

Types of judgments by modality. In conclusion, there is another division of simple judgments into types - according to modality (from the Latin modus - image, method). Lawyers are well aware of the legal term “modus vivendi” based on this word. It refers to a certain way of life or way of being. This is a set of conditions under which temporary, but more or less normal, peaceful relations between the parties are possible (if, in the current situation, it is impossible to achieve a permanent or comprehensive agreement between them).

The logical term “modality of judgments”, also derived from the word “modus”, means that in addition to the main specific content, any judgment one way or another carries with it an additional semantic load. This is information about the objective nature (or method) of the connection between the subject and the predicate, revealed in the judgment, about the subjective attitude of a person towards it, the nature and degree of probability of the knowledge contained in the judgment, etc. In the Russian language, the modality of a judgment is expressed through a huge variety of words, such as “possible”, “allowed”, “valuable” and the like, as well as their negations: “impossible”, “not allowed”, etc. They are called “modal operators” in logic. Often they are replaced by context.

The most important and widespread types of modality are alethic, deontic, axiological and epistemic.

Alethic, or true, modality (from the Greek aleteja - truth) expresses the nature of the connection between conceivable objects, and, consequently, between the subject and the predicate of the judgment. Modal words in Russian are “possibly”, “necessary”, “accidentally” and their synonyms.

From the point of view of alethic modality, the following types of judgments are distinguished:

A) assertoric judgments, or judgments about the fact, the reality of something. For example: “Russia is moving to a market economy.” In such judgments, modality is not expressed, but only the very fact of something is stated;

b) problematic judgments, or judgments about the possibility of something. For example: “Russia can move to a market economy”;

V) apodictic judgments, or judgments about the necessity of something. For example: “Russia will, of necessity, move to a market economy.”

Of course, the differences between these varieties are relative. The possible can become necessary, the necessary can become accidental, etc.

In the relationships between modal judgments, certain patterns can be noticed - for example, imbalance (asymmetry). So, what is real is also possible, but not vice versa; what is necessary is real, but not vice versa.

Deontic, or normative, modality (from the Greek deon - necessary, due) refers directly to the activities of people, the norms of their behavior in society, both moral and legal. It is expressed in Russian using words such as “allowed”, “prohibited”, “obligatory” and their analogues.

Depending on the character social norms deontic modality has varieties. Thus, any legal relationship, like a “two-faced Janus,” presupposes, on the one hand, some right, and on the other, a corresponding obligation. Therefore, it is not without reason that they say: “There are no rights without duties, and there are no duties without rights.” Taking into account this principle, the entire set legal norms can be divided into two important groups: empowering, i.e., law-granting (or prohibiting) and binding norms. Hence there are at least two main varieties of deontic modality:

A) judgments about the presence (or absence) of any right. They are formulated using the words “allowed”, “prohibited”, “right”, etc. For example: “Everyone has the right to life”; “Ideological diversity is recognized in the Russian Federation” (legal norms). Or: “Forced labor is prohibited”; “No one can be convicted twice for the same crime”; “No ideology can be established as a state ideology...” (prohibitory norms). The modal word may be absent: “Labor is free.” The dialectic between the presence and absence of rights is reflected in the well-known formula: “Everything that is not prohibited by law is permitted.” True, it presupposes the existence of a rule of law state with a developed system of legislation that would cover all spheres of public life and, therefore, would clearly delineate the “forbidden zone.” Applying only to individual citizens and their associations, it is supplemented by the formula: “Everything that is not permitted by law is prohibited” for officials and government bodies;

b) judgments about the presence (or absence) of any obligation. They are formulated using the words “obligated”, “must”, “necessary”, etc. For example: “State bodies... are obliged to fully assist trade unions in their activities”; “Basic general education is compulsory” (legally binding norms). Without a modal word: “The right of private property is protected by law.”

There must be a so-called “deontic balance” between rights and responsibilities. It means that every right corresponds to a duty, and every duty corresponds to a right. Otherwise legal system may be ineffective.

Epistemic, or cognitive, modality (from the Greek episteme - knowledge) means the nature and degree of probability of knowledge. It is expressed using the words: “know”, “believe” (“consider”, “believe”) and the like. In this regard, we can distinguish at least two main types of judgments of epistemic modality in accordance with two types of knowledge - objective (scientific) and subjective (opinions):

A) judgments based on faith. It does not matter whether she is religious or non-religious. For example: “I believe that God exists”, “I believe that there is afterlife", "Christ is risen" or "I believe in the offensive better life", "I believe that I am a happy person";

b) judgments based on knowledge, regardless of whether they are problematic or reliable. For example: “I know that there is a law universal gravity"; “There appear to be other intelligent beings in the universe”, “Telepathy probably exists”; “There is a certain absence of life on Mars.”

Axiological, or value, modality (from the Greek axios - valuable) expresses a person’s attitude towards values ​​- material and spiritual. It is fixed by such words as “good”, “bad”, “indifferent” (in terms of values), “better”, “worse”, etc. For example: “He who laughs last laughs well”; “It’s good to learn caution from the mistakes of others”; “It’s bad to live without friends,” “Unfortunately, democracy is an imperfect form of government, but it is better than others.”

Of course, what has been said does not exhaust all forms of manifestation of the modality of judgments. They are studied in detail by the so-called “modal logic”: this is a vast, relatively independent and rapidly developing branch of modern logic, which has great theoretical and practical significance, including, as noted above, for lawyers.

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Types of judgments and logical relations between them

To understand the essence of judgments, as well as their role in human practical activity, their scientific classification is of great importance.

All judgments can be divided into two large groups: simple and complex. A simple proposition is a proposition that expresses the connection between two concepts: for example, “Some volcanoes are active.”

A judgment consisting of several simple judgments is called complex: for example, “The transparent forest alone turns black, and the spruce turns green through the frost, and the river shines under the ice.”

Let us consider the types of simple judgments that are classified on the following grounds.

1. By subject volume(in count).

Singular - judgments that include an affirmation or denial about one subject. The formula for such a judgment is:

This S is (is not) P.

Thus, the judgment “The Hermitage in St. Petersburg is the largest museum in Russia” is a single judgment, since the scope of the subject includes a specific cultural institution.

Particular judgments in which something is affirmed or denied about a part of objects of a certain class. This part can be indefinite or definite. Depending on the given circumstances, private judgments are divided into uncertain and definite.

IN uncertain in judgments the logical scheme is: “Some 8 are P.” The word "some" makes them vague. For example: “Some problems in political science are philosophical in nature.”

Definite a private judgment contains knowledge about both parts of the subject of judgment. It has the following logical diagram:

"Only some S There is R".

For example: “Only some problems of linguistics are of a philosophical nature.”

General - judgments in which something is affirmed or denied in each subject of a given class. The logical scheme of such judgments looks like:

"All S There is R" or "None S do not eat R"

For example, a quote from “Eugene Onegin” by A.S. Pushkin: “We all learned a little” is a general judgment, since the volume of the subject includes the entire class of displayed objects.

2. By quality of the bundle judgments can be affirmative or negative.

Affirmative judgments expressing the belonging of a certain attribute to an object: for example, “The scientific organization of labor increases the efficiency of an engineer.”

Negative judgments expressing the absence of some attribute in an object: for example, “Not a single dolphin is a fish.”

In this case, one should distinguish between a negative judgment and a negative form of expressing an affirmative judgment: for example, “A war of conquest has no legal basis” and “A war of conquest is illegal.” This type of judgment is not always identical.

Property judgments reflect whether or not the object of thought belongs to one or another property or state: for example, “In our time, the acquisition of philosophical knowledge is essential element spiritual culture of man."

Relational judgments express various connections between objects of thought in place, time, size, etc.: for example, the judgment “Everest is higher than Mont Blanc” is determined by the relation (through comparison) of one mountain to another; or "L.N. Tolstoy was a contemporary of I.S. Turgenev and A.M. Gorky."

Judgments of existence are designed to resolve the question of the existence of the subject of our thought - any phenomenon of nature, society or spiritual life. For example: “One of the objects of sociology research is public opinion.”

Any judgment has both quantitative and qualitative characteristics. Therefore, in logic it is used combined classification judgments of quantity and quality. As a result, we get four types of judgments; general affirmative, general negative, particular affirmative and particular negative. Let us consider them in more detail.

A generally affirmative judgment is general in volume and affirmative in the quality of the connective. Its structure: "Everything S There is R", and the symbol is the Latin letter " A" . An example is the following judgment: “Any study of foreign languages ​​develops the mind, giving it flexibility and the ability to penetrate into someone else’s worldview” (D.I. Pisarev). Second example: “All perches are fish.” In these judgments, the scope of the predicate is wider than the scope of the subject and is its subordinate concept. The volumetric relations of subject and predicate in such judgments can be depicted in the form of the indicated circular diagram. It can be seen from this that the volume S is only part of the volume R, so except S in volume R the scope of other concepts may be included (in the first example it could be “the study of history”, “the study of philosophy”, etc.).

In many generally affirmative propositions (in all definitions), subject and predicate will be equivalent concepts. For example: “The wealth of language is the wealth of thoughts” (N.M. Karamzin). Or another example: “All squares are equilateral rectangles.” In such judgments the scopes of the terms completely coincide

Thus, in general affirmative propositions, the subject is subordinate to the predicate or both terms are equivalent concepts.

	A general negative judgment is general in terms of the volume of the subject and negative in terms of the quality of the connective. Its structure: "None S do not eat R" . The symbol of generally negative judgments is the letter " E" . An example would be the following proposition: “No tiger is a herbivore.” Complete incompatibility of subject and predicate is characteristic of all generally negative judgments, i.e. their volumes completely exclude each other.
	A partial affirmative judgment is partial in terms of the scope of the subject and affirmative in terms of the quality of the connective. Its structure: "Some S There is R" . The symbol of private affirmative judgments is the letter " I" . An example is the following judgments: “Some students are book lovers”; "Some technicians are philatelists."
	In these judgments, the subject and the predicate are intersecting concepts; their volumes, as shown in the diagram, partially coincide. However, in some private affirmative propositions the scope of the subject is wider than the scope of the predicate: for example, “Some actors are veterans of the Great Patriotic War"; "Some writers are heroes of Russia." The scope of the predicate here is included in the scope of the subject, but the scope of the subject only partially coincides with the scope of the predicate. Thus, in particular affirmative judgments, the subject and the predicate are intersecting concepts or the predicate is subordinate to the subject.

A partial negative judgment is partial in volume and negative in quality of the connective. Its structure: "Some S do not eat R", and the symbol is the letter " ABOUT" . An example of private negative judgments is the following: “Some European countries are not French-speaking”; "Some students are not athletes." The volumetric relations of the subject and the predicate in these judgments resemble similar patterns in partial affirmative judgments with the only difference that in those judgments we are talking about the coinciding part of the volumes of terms, and in partial negative ones - about the non-coinciding part of the volume of the subject with the volume of the predicate. Using circular diagrams, the given examples can be illustrated accordingly as follows:

Consequently, in partial negative judgments we are talking about a part of the volume of the subject that is incompatible with the volume of the predicate.

The analysis of the scope of concepts - terms of judgment is further connected with the clarification of their distribution.

A term is considered distributed when it is taken in full. If a term is taken as part of the volume, it is considered unallocated. The study of the distribution of the terms of a judgment is not a formal logical operation, but a confirmation of the correct connection between the data of the subject and the predicate in the judgment, i.e. its correspondence to the objective relationship of the objects themselves.

Based on the analysis of judgments according to the combined classification, we formulate terms distribution rules:

In general affirmative judgments the subject is distributed, but the predicate is not distributed. Both terms will be distributed if they are equivalent.

In generally negative judgments both terms are always distributed, they completely exclude each other, they are incompatible concepts. For example: “No vegetable is a fruit.”

In private affirmative judgments both terms are undistributed if they are expressed by overlapping concepts: for example, “Some students are inventors.” If in a particular affirmative judgment the predicate is subordinated to the subject, then the predicate will be distributed: for example, “Some aircraft are space rockets.”

In partial negative judgments the subject is not distributed, but the predicate is always distributed. Thus the subject is distributed in general judgments and not distributed in particular judgments; the predicate is distributed in negative judgments and undistributed in affirmative judgments. The exception is general affirmative and particular affirmative propositions, in which the predicate is distributed.

In accordance with the functions of logical connectives, complex judgments are divided into the following types.

Conjunctive judgments (conjunctive) are judgments that include other judgments as components - conjuncts, united by connectives “and”, “a”, “but”, “as”, “so and”, “as well”, etc. For example: “Language and thinking interact in the process of translation” or “Student Ivanov lives in Moscow and studies at Moscow State University.”

Disjunctive judgments (disjunctive) are those judgments that include disjunctive judgments as components, united by the connective “or”.

Distinguish weak disjunction when the conjunction “or” has a connecting-disjunctive meaning, it does not give an exclusive meaning to the components included in a complex judgment. For example: “People offend each other either out of hatred, or out of envy, or out of contempt.” Strong disjunction As a rule, it occurs when a logical conjunction “or” is used, which has an exclusive-dividing meaning. For example, in the expression of M.E. Saltykov-Shchedrin: “Either in the snout, or please give me the hand” - judgments that are incompatible with each other are combined. They characterize a person’s readiness to easily move from rough dealing with a subordinate to kissing the hands of those on whom he is directly dependent.

Conditional propositions (implicative) are those propositions that are formed from two by means of logical conjunctions: “if...then”, “there...where”, “insofar...as”. As an example, we can use the idea expressed by the Tajik poet of the 11th century. Qaboos: “If you want to have friends, then don’t be vindictive.” An argument that begins with the word “if” is called a reason, and a component that begins with the word “then” is called a consequence.

These are the main types of judgments. Mastering the skills of their logical analysis is effective means accurate use of your thoughts as well as suggestions.

Judgment is one of the forms of thinking, without which cognition cannot occur. Judgments express the connection between an object and a characteristic; they confirm or deny the presence of this quality in a given thing. Actually, this is thought, its form, which tells us about the connection of objects, and that is why judgment takes special place in and construction of analytical chains.

Characteristics of judgments

Before we begin to classify judgments in logic, we need to find a clear distinction between a judgment and a concept.

Concept - speaks about the presence of an object. The concept is “day”, “night”, “morning”, etc. And a judgment always describes the presence or absence of a characteristic - “Early morning”, “Cold day”, “Silent night”.

Judgments are always expressed in the form of narrative sentences; moreover, earlier in grammar the essence of sentences was called a judgment. A sentence that expresses a judgment is called a sign, and the meaning of the sentence itself is either truth. That is, in both simple and complex judgments, a clear logic is observed: the sentence denies or confirms the presence of a characteristic of an object.

For example, you can say that “All the planets of the solar system rotate around their axes,” or you can say that “Not a single planet in the solar system is stationary.”

Types of judgments

In logic there are two types of judgments - simple and complex.

Simple judgments, being divided into parts, cannot have a logical meaning; they contain a judgment only in an inseparable totality. For example: “Mathematics is the queen of sciences.” This simple sentence expresses a single proposition. Complex types of judgments in logic denote several different thoughts at once; they consist of combinations of simple, simple + complex, or a set of complex judgments.

For example: If it rains tomorrow, we will not go out of town.

The main characteristic of a complex proposition is that one of its parts has a different meaning and separately from the second part of the sentence.

Complex judgments and their types

In logic, complex judgments are made by combinations of simple propositions. They are connected by logical chains - conjunction, implication and equivalence. Simply put, these are conjunctions “and”, “or”, “but”, “if... then”.

Judgment- This mental act, expressing attitude any person to content(meaning and truth value) expressed by him thoughts. A judgment is expressed by a declarative sentence (simple or complex, in the form of affirmation or negation) and is necessarily accompanied by one or another modality, usually associated with psychological state doubts, faith, knowledge regarding any state of affairs or belief in something. Thus, de facto judgment goes beyond pure logical reflection. Expressing an evaluative act, it is closely related to such concepts as “definition” and “understanding”, and thereby characterizes the ability of the mind to classify concepts (I. Kant). True, in the post-Kantian era (mainly through the efforts of B. Bolzano and G. Frege), a different interpretation of the term “judgment” began to emerge. The main thing that distinguishes this interpretation from the traditional one is the abstraction of the content of a narrative sentence not only from its linguistic form of expression, but also from its possible assessment, and the selection of a judgment as an abstract object “of the same degree of generality as a class, number or function” (Church A. Introduction to mathematical logic. - M., 1960. P. 32). In this case, the judgment is declared to be a kind of operator that determines the truth value of a sentence, and the process of judgment is reduced to recognizing the truth of a certain thought. This understanding allows, on the one hand, to consider a judgment as an invariant in the class of its possible linguistic representations, and on the other hand, it eliminates the psychological connotation inherent in the traditional understanding of the term “judgment.” In fact, it opened the way to the formalization of logical reasoning by rethinking the traditional doctrine of the structure of judgment.

The term "judgment" was widely used in traditional logic (see). In modern logic (see) the term “statement” is usually used, denoting a grammatically correct sentence taken together with the meaning it expresses (see). Today, judgments in their traditional understanding actually remain the subject of special study only in modal logic(see), with them usual classification, which is presented below.

Traditionally it is customary to distinguish simple And complex judgments. A judgment is called simple in which it is impossible to identify the correct part, that is, a part that does not coincide with the whole, which in turn is a judgment. The main types of simple judgments are attributive judgments And judgments about relationships:

1. Attributive are judgments that express the belonging of objects to properties or the absence of any properties in objects. Attributive judgments can be interpreted as judgments about the complete or partial inclusion or non-inclusion of one set of objects in another, or as judgments about whether an object belongs or does not belong to a class of objects. Attributive judgments consist of a subject (logical subject), a predicate (logical predicate) and a connective, and some also contain so-called quantifier (quantitative) words (“some”, “all”, “none” and others). The subject and predicate are called terms judgments. The subject is most often denoted by a Latin letter S(from Latin word"Subjectum"), and the predicate is Ρ (from the Latin word "Praedicatum"). Thus, in the judgment “Some sciences are not humanitarian” the subject ( S) - “sciences”, predicate ( P) - “humanitarian”, the connective is “are not”, and “some” is a quantifier word. Attributive judgments are divided into types “by quality” and “by quantity”. In terms of quality, they can be affirmative (the connective “essence” or “is”) and negative (the connective “not the essence” or “is not”). By quantity, attributive judgments are divided into single, general and particular. Single judgments express whether an object belongs or does not belong to a class of objects. In general, the inclusion or non-inclusion of a class of objects in a class. Partial judgments express the partial inclusion or non-inclusion of a class of objects in a class of objects. They use the word “some” in the sense of “at least some, and maybe all.” Judgments of the form “Everything” S essence P"(general affirmative), "None S not the point P"(generally negative), "Some S essence P"(particular affirmative), "Some S not the point P"(partial negative) are called categorical. Terms in categorical judgments can be distributed (taken in in full) and not distributed (not taken in full). In general judgments, subjects are distributed, and in negative judgments, predicates are distributed. The remaining terms are not distributed.
2. Judgments about relationships are judgments that say that a certain attitude takes place (or does not take place) between elements of pairs, triplets, and so on objects, are called judgments about relationships. They are divided by quality into affirmative and negative. By quantity, judgments about two-place relations are divided into single-single, general-general, particular-particular, singular-general, single-particular, general-unit, particular-single, general-particular, particular-general. The division into types according to the number of judgments about three-place, four-place, and so on relations is similar.

In addition to attributive and judgments about relationships, special types of simple judgments include: existence judgments And identity judgments(or equalities like " a = b»).

These judgments, as well as complex judgments formed from them, are called assertoric. They are [simply] affirmations or negations. Along with affirmations and denials, there are so-called strong And weak affirmations and negations. Strong and weak affirmations and negations are alethic modal propositions. Among them are judgments of necessity (apodictic), possibility and chance.

Among complex judgments, several types are distinguished. Conjunctive propositions are those propositions that assert the existence of two or more situations. In natural language they are formed from other judgments most often through the conjunction “and”. This conjunction is denoted by the symbol ∧, called the (commutative) conjunction sign. A proposition with this conjunction is called (commutative) conjunctive. The definition of the conjunction sign is the table below, showing the dependence of the meaning of a conjunctive judgment on the meanings of its constituent judgments. In it, “I” and “L” are abbreviations for the meanings “true” and “false”.

A	B	(A ∧ B)
AND	AND	AND
AND	L	L
L	AND	L
L	L	L

Judgments that assert the sequential occurrence or existence of two or more situations are called non-commutative-conjunctive. They are formed from two or more judgments using conjunctions indicated by symbols Τ 2 , T 3 and so on depending on the number of judgments from which they are formed. These symbols are called signs of non-commutative conjunction and accordingly read “..., and then …”, “..., then..., and then …” and so on. Indices 2, 3... and so on indicate the location of the union.

Disjunctive judgments are judgments that assert the existence of one of two, three, and so on situations. If the existence of at least one of two situations is asserted, the proposition is called (loosely) disjunctive, or disjunctive. If the existence of exactly one of two or more situations is asserted, the proposition is called strictly disjunctive or strictly disjunctive.

The conjunction “or”, by which a statement of the first type is expressed, is denoted by the symbol ∨ (read “or”), called a sign of weak disjunction (or simply a disjunction sign), and the conjunction “or..., or...”, by means of which a statement of the second type is expressed, - the symbol y (reads “or..., or..."), called the sign of strict disjunction. Below are tabular definitions of loose and strict disjunction signs.

A proposition that states that the presence of one situation determines the presence of another is called conditional. Conditional propositions are most often expressed by sentences with the conjunction “if..., then...”. The conditional conjunction “if..., then”... is indicated by the arrow “→”.

In the languages ​​of modern logic, the conjunction “if..., then...”, denoted by the symbol “⊃,” is widespread. This symbol is called a sign of (material) implication, and a proposition with this conjunction is called implicate. The part of an implicational proposition located between the words “if” and “then” is called the antecedent, and the part located after the word “then” is called the consequent. The sign of the implication is determined by the truth table below.

A	B	(A ⊇ B)
AND	AND	AND
AND	L	L
L	AND	AND
L	L	AND

An equivalence judgment is a judgment that asserts the mutual conditionality of two situations.

The conjunction “if and only if..., then...” is used in another sense. In this case, it is indicated by the symbol "≡", called the material equivalence sign, which is determined by the truth table presented below.

A	B	(A ≡ B)
AND	AND	AND
AND	L	L
L	AND	L
L	L	AND

Judgments with this conjunction are called judgments of material equivalence.

Simple alethic modal propositions are characterized above. Complex judgments formed from other judgments by means of the expressions “necessarily that”, “accidentally that”, “possibly that” are also called alethic modal judgments. Alethic modal propositions are also complex propositions, the individual components of which are alethic modal propositions. Alethic modal concepts (“necessary”, “accidentally”, “possibly”) are divided into logical and factual (physical). In them, a state of affairs may be logically possible or actually possible, logically necessary or actually necessary, logically contingent or actually contingent.