Describe the concept, judgment, inference as forms of thinking.

Previous lessons talked about how to work correctly with concepts and definitions. Although operations on them are very important and are found everywhere, in themselves they do not constitute reasoning. In this lesson we will get closer to the topic of how to reason correctly. We will consider reasoning using the example of syllogistics. Syllogistics is the most ancient logical system. It was invented by the ancient Greek philosopher Aristotle in the 4th century BC. Until now, it remains one of the most understandable, closest to natural language and easy to learn logical systems. One of its main advantages is its ability to be used in everyday situations without much effort.

Judgments and statements

What is reasoning? One could say: conclusion, inference, reflection, proof, etc. All this is true, but perhaps the most obvious answer would be: reasoning is a sequence of judgments that ideally should be interconnected according to the rules of logic. Therefore, learning correct reasoning must begin with what judgments are and how to use them correctly.

A judgment is a thought about affirming or denying the existence of some situation in the world.

In natural language, judgments are conveyed using declarative sentences, or statements. Examples of judgments expressed in statements: “Autumn has come,” “Katya does not know English,” “I like to read,” “The grass is green and the sky is blue.” The same judgment can be expressed using different statements, in particular: “The sky is blue” and “The sky is blue” are different statements, but they express the same judgment, since they convey the same thought. Likewise, the statements “No one left home” and “Everyone stayed at home” are different, but they convey the same proposition.

Since statements through judgments fix some state of affairs in the world, in contrast to concepts and definitions, we can evaluate them from the point of view of their truth and falsity. So the statement “Bill Gates founded Microsoft” is true, but the statement “Oranges are purple” is false.

If we recall Frege's triangle, then the statement will be at the vertex denoting the sign, the judgment will be its meaning, and truth and falsehood will be the meaning.

There are many types of judgments and, accordingly, statements. Different logical systems focus on different aspects of them. Syllogistics works with so-called categorical attributive statements. Categorical statements are contrasted with hypothetical ones. Hypothetical statements speak about the possibility of the presence or absence of some situation in the world: “Perhaps it will rain.” Categorical statements categorically assert that some situation exists or does not exist: “It started to rain.” The term “attributive” means that these statements indicate the presence or absence of a certain property in an object or class of objects. Examples of categorical attributive statements: “My car is blue,” “The park near our house is large,” “Nobody likes fish oil,” “Some people think they are the smartest.” Although at first glance it may seem that due to the concentration on categorical attributive statements, the use of syllogistics is limited, this is not so. A huge layer of reasoning does not go beyond the scope of such statements, and therefore knowledge of syllogistics is enough to learn to think logically and not allow oneself to be misled.

Judgments by type of statement

As you know, there are three types of sentences based on the type of statement: narrative, motivating and interrogative. For example, the sentence “I remember a wonderful moment” belongs to the narrative type. It is useful to propose that such a judgment will also be narrative. It contains certain information and reports a certain event.

In turn, an interrogative sentence contains a question that implies an answer: “What does the coming day have in store for me?” At the same time, it neither states nor denies anything. Accordingly, the assertion that such a judgment is interrogative is erroneous. An interrogative sentence, in principle, does not contain a judgment, since the question cannot be differentiated according to the principle of truth/falsity.

The incentive type of sentences is formed in the case when there is a certain incentive to action, a request or a prohibition: “Arise, prophet, and see and hear.” As for judgments, according to some researchers, they are not contained in sentences of this type. Others believe that we are talking about a type of modal judgment.

Composition and types of categorical attributive statements

Categorical attributive statements consist of terms, predicative connectives and quantifiers.

Terms are divided into subject and predicate.

Subject is a term denoting an object or group of objects about which something is affirmed or denied. Typically the subject is represented using the letter S.
A predicate is a term that actually denotes what is affirmed or denied about the subject, some property, sign, the presence or absence of which is attributed to the subject. The predicate is represented by the letter P.

Predicative connectives , as you may remember from the first lesson, are connectives “is” and “is not.” In natural language, they can be expressed using different words and constructions: “is”, “is”, “essence”, “this”, “proceed”, the dash sign, verbs, or omitted altogether.

Quantifiers are words indicating the quantitative characteristics of a subject. There are two types of quantifiers: the general quantifier (“all”, “everyone”, “any”, “none”, “nobody”) and the existence quantifier (“some”, “not all”, “any”, “many”). "). Just like predicative connectives, quantifiers can be omitted in natural speech. We can say, “Men are equal before the law,” meaning that “All men are equal before the law”; or “Children love sweets” - implying that “Many children like sweets.” It is often best to clarify with your interlocutor which quantifier he has in mind, since this will affect the truth conditions of his statements.

Let's look at the following statement: “Cats purr when they feel good.” “Cats” is the subject, “creatures that purr when they feel good” is the predicate. There is also an invisible connective “is”, which connects the subject with the predicate, and an invisible quantifier of the generality “all”. So, if we write this statement in accordance with its logical form, we get: “All cats are creatures that purr when they are pleased.” Thanks to this example, it becomes clear that before determining whether a statement is true or false, it is necessary to identify its logical form and transform the original statement so that all four elements (quantifier, subject, connective, predicate) are in place.

Depending on the properties of logical and non-logical terms that are part of categorical attributive statements, they can be divided into several types.

Depending on the nature of the subject, categorical attributive statements are divided into single and multiple. If the subject is a name, then we are talking about a single statement (“Socrates was a philosopher”). Single utterances do not have a quantifier before the subject. If the subject is a term denoting many objects, then the statement is called plural. Multiple statements, in turn, are divided into particular and general depending on the quantifier that precedes it. If the existential quantifier is used, then the statement will be particular (“Some girls are beautiful”), if the general quantifier is used, then the statement will be general (“All people strive for happiness”).
Depending on the predicative connective, statements are divided into affirmative and negative. If the presence of some property in a subject is affirmed, then the statement is affirmative (“Petya is a true friend”), if it is denied, then it is negative (“Not a single student came to the first class!”).

If we combine these types with each other, it turns out that there are a total of six types of categorical attributive statements:

Singular affirmative: s is P. Alexander Pushkin is a Russian writer.
Singular negatives: s is not P. Cervantes was not an artist.
General affirmative: All S are P. All apartments in this house have high ceilings.
General negatives: Not a single S is a P. Not a single student from our group passed the exam with an A.
Particularly affirmative: Some Ss are Ps. Some cars in our fleet are in urgent need of repairs.
Partial Negatives: Some Ss are not Ps. Some song lyrics don't make sense.

Section two. Judgment

The Nature of Simple Judgments

.
Simple judgments, 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 their constituent parts only the concepts that form the subject and the 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 a 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 conceivable 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 the 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 unpatriotic.” 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: “A negative result is 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 the well-known legal principle of the 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 of the Russian Federation, some authors proposed giving it 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 of the solar system, etc.), but the nature 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 the Latin quantum - how many).
In this case it is a general quantifier
. To denote it, the symbol ∀ is used (from English, all - everything). The 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 “A sharp joke is not a final verdict”, “none” is meant. Common judgments of the same type are aphorisms: “Comparison is not proof”, “Ignorance is not an argument”, etc.

Legal documents often contain similar statements: “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 “Ǝ” ( from English, exist - to exist). The formula Ǝ x P(x) reads like this: “There is 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 once the work of the business department of the State Property Management Committee of the city of Istra was checked. The result 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 “ Most of
the 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 the 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 being 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,” “The Russian Pension Fund is operating 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 exclusionary

. 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 social life. Legal practice, in essence, is all 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 and acquire enormous ideological significance. For example: “The Earth is an ordinary celestial 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 laws. Legal laws, decrees, and other regulations take the form of general judgments. Thus, the constitutional rights and obligations of citizens of the Russian Federation, articles of the Labor Code, Criminal Code, Customs Code, etc. are expressed in the form of general judgments.

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, and 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 to the combined 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, the 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.

In order to correctly understand the meaning of judgments and correctly operate with them, it is necessary to know the distribution of terms

they contain subject and predicate.

Distributed

a term is considered to be conceivable in its entirety;
undistributed
- 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 the graphical 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 of the 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” (i.e. 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 volume 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 “ 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 the inclusion (or non-inclusion) of a subclass in the class
.
For example: “All metals are electrically conductive” (here the subclass of metals is included in the class of electrically conductive substances). The other establishes
an element
belongs
(or does not belong) . “This substance is metal.” In symbolic logic, these and other judgments are expressed by the formulas: S ⊂ P (read: the volume of S is included in the volume of 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 Lat. relatio - relationship), or judgments about the relationship of something to something, reveal the presence or absence of a particular relationship to another object (or several objects) in the object of thought.
Therefore, they are usually expressed by a special formula: x R y
, where
x
and
y
are objects of thought, and
R
(from relatio) is 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 consists of 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 judgment about the relationship 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 a special case of relational ones, 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 in the 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, do “Bigfoot”, “biofield”, “telepathy”, “poltergeists” and much more exist. In judicial practice, establishing 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”;

c) 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 nature of 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 this principle into account, the entire set of legal norms can be divided into two important groups: authorizing, i.e., law-granting (or prohibiting) and obligatory 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 each right corresponds to a duty, and each duty corresponds to a right. Otherwise, the 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 an afterlife”, “Christ is risen” or “I believe that a better life is coming”, “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 of universal gravitation”; “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.

Truth conditions for categorical attributive statements in traditional syllogistic

We should start with the fact that traditional syllogistics imposes two restrictions on the terms used, namely: they must be non-empty and non-universal, that is, if no object from the universe of consideration falls under the term or, conversely, all objects of the universe fall under the term, then they are not may be subject to consideration. Let's look at the pictures:

The first figure depicts a situation where term A is empty, so the entire square (the universe of consideration) remains white. The second figure shows the case when the volume of the term A coincides with the volume of the universe of consideration, therefore the entire square is shaded. The last figure represents the term A, which is non-empty and at the same time non-universal. The shaded area corresponds to volume A. Traditional syllogistic works only with terms that correspond to the third figure. This condition is set in order to exclude from consideration statements that cannot be assessed as true or false. Take the statement: “All of Ivan’s children are bald.” Everything seems to be in order with the statement, but imagine that Ivan has no children. We cannot simply say in this case that the statement is false. If we call it false, then we mean that not all of Ivan’s children are bald, which is not the case. At the same time, we cannot say that it is true. The way out of this predicament is precisely to point out the emptiness of the term “children of Ivan.” Since Ivan has no children, this term is empty, and we cannot construct a correct statement with it.

The non-emptiness and non-universality of the term will be determined not only by the context, but also by the chosen universe of consideration. If our square represents a universe of living beings or materially existing objects, then, of course, terms such as “mermaid”, “hobbit”, “dragon”, etc. will turn out to be empty, and we will not be able to consider them. However, if the universe of consideration is mythological or fairy-tale creatures, then all these terms cease to be empty. The same is true for versatility. The term "people" can be considered as universal, which excludes it from the realm of traditional syllogistic. However, if we want to say “Socrates is a man,” then it is quite possible to take living beings as the universe of consideration. In the universe of living beings, the term “people” will no longer be universal.

In addition, we must remember that the subject and the predicate must be specified on the same universe of consideration.

Now let's see under what conditions different types of categorical attributive statements will be true. To do this, we advise you to look again at the lesson on the relationships between concepts. By and large, subject and predicate are terms that represent certain concepts. Accordingly, if you combine these concepts in one sentence using predicative connectives and quantifiers, then to find out whether these sentences are true or false, just look at the diagrams illustrating the relationship between these two concepts. So, let's transgress.

Singular affirmative statements of the form “s is P” are true only if the terms s and P are in the following relation:

In other words, singular statements are true if the point representing the name s is inside the circle representing the scope of the term P. For example, take the statement “Leo Tolstoy preached vegetarianism.” “Leo Tolstoy” is the subject, the name s. “A person who preaches vegetarianism” is a predicate, a term P. This statement is true, since the point s will be included in the scope of the term P. If we take the statement “Nikolai Gogol is a great Russian composer,” then the point s representing the name (“ Nikolai Gogol"), will not be included in the scope of the term P (“great Russian composers”). Therefore this statement is false.

Singular negative statements of the form “s is not P” are true if the terms s and P are in the following relation:

As can be seen from the figure, the situation here is exactly the opposite of the conditions for the truth of single-affirmative statements. If the point representing the name s is outside the scope of the term P, then the statement is true. Otherwise, it is false. An example of a true singular negative statement: “Alexander Pushkin has never been to France.” A false single negative statement would be: “Ivan Bunin did not receive the Nobel Prize in Literature.”

General affirmative statements of the form “All S are P” are true if the terms S and P are in one of the following relations:

The first figure depicts the relationship of equal volume, the second - inverse subordination. If the scopes of two terms coincide (S and P share one circle) or the scope of the term S is completely included in the scope of the term P (the circle S is completely included in P), then the general affirmative statement is true. If the terms S and P are in any other relation, then general affirmative statements cannot be true. As an illustration of true statements, one can cite: “All conifers have cones,” “All whales are mammals.” An example of false statements: “All politicians are liars”, “All girls dream of marrying a millionaire.” In these examples, the subject and predicate terms are not in any of the above relationships.

General negative statements of the form "No S is P" are true only if the terms S and P are in the following relations:

The first figure shows a relationship of contradiction, and the second - subordination. As you can see, S and P do not have common elements, their volumes do not intersect. For example, the following statements will be true: “Not a single peacock is a songbird”, “Not a single person under eighteen years of age is an adult in Russia.” An example of a false statement: “Not a single humanist understands mathematics.” The statement is false, since the terms “humanitarian” and “people who understand mathematics” are neither in a relationship of contradiction nor in a relationship of subordination.

Partial affirmative statements of the form “Some S are P” are true if the terms S and P are in the following relations:

The drawings consistently represent the relationships: intersection, complementarity, subordination, equal volume and reverse subordination. With the first three pictures, everything should be quite clear: it is clear that the scopes of the terms S and P intersect, so in the area of intersection there are elements that simultaneously possess both the feature S and the feature P. Examples of true statements of these types: “Some actors sing well,” “Some cars with a price below a million cost more than six hundred thousand,” “Some mushrooms are edible.”

As for the relations of equivolume and inverse subordination, the question may arise why they also represent truth conditions for particular affirmative statements, if the pictures denoting them clearly show that not only some S are P, but all S are P. True, natural language leads us to the idea that if some S are P, then there are also other S that are not P: some mushrooms are edible, and some are inedible. For logicians, this conclusion is incorrect. From the statement “Some S are P” one cannot conclude that some S are not P. But from the statement “All S are P” one can conclude that some S are P, because if something is true regarding all elements of the scope of the term , then it will be true for some individual elements. Therefore, in syllogistics the word “some” is used in the sense of “at least some”, but not in the sense of “only some”. Thus, from the statement “All ferns reproduce by spores” one can safely deduce the statement “Some ferns reproduce by spores”, and from the statement “All fifth-grade students are pioneers” - the statement “Some fifth-grade students are pioneers.”

Partial affirmative statements will be false only if the terms S and P are in a relation of contradiction or subordination: “Some tractors are airplanes,” “Some false statements are true.”

Partial negative statements like “Some S are not P” are true if the terms S and P are in the following relations:

These are relationships: intersections, complementarities, inclusions, contradictions and subordination. Obviously, the first three relations coincide with what was also true for private affirmative statements. All of them precisely represent cases when some S are P, and at the same time, some S are not P. Examples of such true statements: “Some healthy people do not drink alcohol,” “Some of our workers in the category under forty have not yet reached the age of and twenty-five,” “Some trees are not evergreen.”

For the same reasons that the relations of equivocality and inverse subordination represented truth conditions for partial affirmative statements, the relations of contradiction and subordination will be true for partial negative statements. From a statement of the form “Some S are not P” the statement “Some S are P” cannot be logically deduced. However, from the statement “All S are not P” we can move on to the statement “Some S are not P”, since based on the information that we have about all the elements of the scope of the terms S and P, we can draw a conclusion about their individual representatives. Therefore, the following statements will be true: “Some magazines are not books,” “Some fools are not smart,” etc.

Partial negative statements will be false only if the terms S and P are in a relationship of equal volume and inverse subordination. Examples of false statements: “Some fish cannot breathe underwater,” “Some apples are not fruits.”

So, we have found out under what conditions statements of one form or another will be true and false. At the same time, it became clear that the truth and falsity of statements from a logical point of view does not always coincide with our intuitive ideas. Sometimes statements that are identical at first glance are evaluated completely differently, since behind them are hidden different logical forms and, consequently, different relationships between the terms included in them. These truth conditions are important to remember. They will come in handy when in the next lesson we learn how to put statements into chains of reasoning and try to find forms of inference that will always be correct.

Classification of simple judgments

Simple judgments in logic can be of the following types: attributive, judgments with relations, existential, modal.

Attributive (judgment-properties) are aimed at affirming/denying the presence of certain properties (attributes) and types of activity in an object. These judgments have a categorical form and are not questioned: “The nervous system of mammals consists of the brain, spinal cord and outgoing nerve tracts.”

In relational judgments, certain relationships between objects are considered. They can have a spatio-temporal context, cause-and-effect, etc. For example: “An old friend is better than two new ones,” “Hydrogen is 22 times lighter than carbon dioxide.”

An existential judgment is a statement of the existence/non-existence of an object (both material and ideal): “There is no prophet in his own country,” “The moon is a satellite of the Earth.”

A modal proposition is a form of statement that contains a certain modal operator (necessary, good/bad; proven, known/unknown, prohibited, believe, etc.). For example:

“In Russia it is necessary to carry out educational reform” (alethic modality – possibility, necessity of something).
“Everyone has the right to personal integrity” (deontic modality - moral norms of social behavior).
“A careless attitude towards state property leads to its loss” (axiological modality – attitude towards material and spiritual values).
“We believe in your innocence” (epistemic modality - the degree of reliability of knowledge).

Exercises

Read the following categorical attributive statements. Determine what type they are. Use diagrams to show whether they are true or false.

Everything that is real is reasonable, everything that is reasonable is real.
Salt is poison.
The poison is salt.
All musicians have good hearing.
Some musicians have good hearing.
All people with good hearing are musicians.
Some people who have good hearing are musicians.
Some vampires were late for work.
Werewolves are a type of werewolf.
All round squares have no corners.
Nobody likes when their teeth hurt.
No parrot drinks whiskey.
Some people don't like their jobs.
Ivan Ivanovich quarreled with Ivan Nikiforovich.
Tarkovsky's films are considered classics of Russian cinema.
Dostoevsky never played cards.
Some bushes are not gloggy at all.
Every employee dreams of a promotion.
Some dogs can read.
All happy families are alike, each unhappy family is unhappy in its own way.
Some sharks are fish.
Some people haven't gone to Mars.

Judgment

Judgment as a form of thinking involves confirmation or denial of some fact, event, property, feature, connection. It manifests itself in phrases, but we must remember that not every phrase is a judgment. Thus, an interjection or a one-syllable sentence does not belong to this form of thinking (examples: “Oh!”, “How is that possible?”).

Sentences tend to be narrative in nature: “The Earth revolves around the Sun.”

A proposition can be true or false, which is determined by logic. The first involves the presence of one subject with characteristics or the comparison of two subjects.

When a simple judgment is separated, the words cease to carry a semantic load. Example: “A mouse is smaller than a cat.” If this sentence is divided into two, the meaning is lost.

Complex judgments are various combinations that consist of a complex and a simple, two complex or two simple judgments. Examples: “If it hails, the plants may be damaged.” Here, “plants may be harmed” appears as a simple proposition.

Judgment as a form of thinking of a complex nature is impossible without grammatical connectives (“but”, “or”, “and”, “if so, then...”, “when..., then...”, etc.).

It is necessary to distinguish between judgment and other logical forms of thinking: a concept is expressed in a word, and a conclusion is expressed in a conclusion.

This form of thinking can also be:

affirmative (“Botany is the science of plants”, “The tiger is a predator”);
negative (“This sentence is constructed incorrectly”, “In Russian cities there are no bears walking on the streets”).

There is another classification. A general judgment presupposes a statement (negation) that refers to phenomena, subjects, united by a common concept (“All healthy cats have four paws”). Particular implies a part of objects, subjects, phenomena that are united by a concept (“Some poets are graphomaniacs”). An individual property is expressed in a single judgment (“F.M. Dostoevsky is the author of “Crime and Punishment””).

In essence, a judgment reveals the content of a concept (or several) - therefore, in order to make a statement, it is necessary to know the content of all the concepts used.

Inference

Inferences as a form of thinking are formed using several judgments. Thus, existing information makes it possible to obtain new knowledge.

This form of thinking belongs to the highest, as it combines concepts and judgments.

An inference may be correct or incorrect . When they talk about this property, they mean the theoretical possibility of verification, since the correctness of the conclusion is a subjective phenomenon that can be verified over a long period of time through experiments and logical reasoning.

There is a close connection between judgment and inference, since without the first the second is impossible. Conclusions are:

deductive, which are the result of the process of mental reasoning from the general to the specific;
inductive - generalization occurs from the particular to the general;
built on an analogy that uses the properties of phenomena and objects that have similar characteristics.

Concept, judgment and inference interacting with each other form a picture of human consciousness, perception and are the basis for the development of intelligence.

Judgment

Judgment is a statement; a mental act that expresses the speaker’s attitude to the content of the thought being expressed.

When making a judgment, we create those supports that we consider to correspond to reality and therefore allow us to move towards the truth.

Judgment is a reflection of connections between objects and phenomena of reality or between properties and characteristics. For example, the proposition “Metals expand when heated” expresses the relationship between changes in temperature and the volume of metals. By thus establishing various connections and relationships between concepts, judgments are statements of something about something . They affirm or deny any relationships between objects, events, and phenomena of reality. For example, when we say: “The Earth revolves around the Sun,” we thereby affirm the existence of a certain objective connection in space between two celestial bodies.

General, particular and individual judgments

Judgments can be general, particular and individual. In general judgments, something is affirmed (or denied) regarding all objects of a given group, a given class, for example, “All fish breathe with gills.” In private judgments, Affirmation or Denial no longer applies to all, but only to some subjects, for example: “Some students are excellent students”; in single judgments - to only one, for example: “This student did not learn the lesson well.”

Direct and indirect judgments

Judgments are formed in two main ways:

Directly, when they express what is perceived.
Indirectly - through inferences or reasoning.

In the first case, we see, for example, a brown table and make the simplest judgment: “This table is brown.” In the second case, with the help of reasoning, one deduces from some judgments and obtains other (or other) judgments. For example, D.I. Mendeleev, on the basis of the periodic law he discovered, purely theoretically, only with the help of inferences, deduced and predicted some properties of chemical elements still unknown in his time.