register judgment. Judgment. Types of judgments

Simple and complex judgments

Simple Judgments- judgments, the components of which are concepts. A simple proposition can only be decomposed into concepts.

Complex judgments- judgments, the components of which are simple judgments or their combinations. A complex judgment can be considered as a formation from several initial judgments connected within the framework of a given complex judgment by logical unions (ligaments). The logical feature of a complex judgment depends on the union with which simple judgments are connected.

Composition of a simple proposition

A simple (attributive) judgment is a judgment about the belonging of properties (attributes) to objects, as well as judgments about the absence of any properties in objects. In an attributive judgment, the terms of the judgment can be distinguished - subject, predicate, connective, quantifier.

The subject of judgment is a thought about some subject, a concept about the subject of judgment (logical subject).
Judgment predicate - a thought about a known part of the content of the subject, which is considered in the judgment (logical predicate).
Logical link - the idea of the relationship between the subject and the selected part of its content (sometimes only implied).
Quantifier - indicates whether the judgment refers to the entire scope of the concept expressing the subject, or only to its part: “some”, “all”, etc.

The composition of a complex judgment

Complex judgments consist of a number of simple ones ("A person does not strive for what he does not believe in, and any enthusiasm, not supported by real achievements, gradually fades away"), each of which in mathematical logic is denoted by Latin letters (A, B, C, D … a, b, c, d…). Depending on the method of formation, there are conjunctive, disjunctive, implication, equivalent and negative judgments.

Disjunctive judgments are formed with the help of disjunctive (disjunctive) logical connectives (similar to the union "or"). Like simple disjunctive judgments, they are:

Implicit judgments are formed with the help of the implication, (equivalent to the union "if ..., then"). Written as or . In natural language, the union "if ... then" is sometimes synonymous with the union "a" ("The weather has changed and, if it was cloudy yesterday, then today there are not a single cloud") and, in this case, means a conjunction.

Conjunctival judgments are formed with the help of logical connectives of combination or conjunction (equivalent to a comma or unions "and", "a", "but", "yes", "although", "which", "but" and others). Recorded as .

Equivalent judgments indicate the identity of the parts of the judgment to each other (draw an equal sign between them). In addition to definitions explaining a term, they can be represented by judgments connected by the unions “if only”, “necessary”, “enough” (for example: “For a number to be divisible by 3, it is enough that the sum of the digits that make it up is divisible by 3 "). It is written as (different mathematicians have different ways, although the mathematical sign of identity is still ).

Negative Judgments are built with the help of connectives of negation “not”. They are written either as a ~ b, or as a b (with an internal negation such as “a car is not a luxury”), as well as with the help of a line over the entire judgment with an external negation (refutation): “it is not true that ...” (a b).

Classification of simple judgments

By quality

Affirmative- S is P. Example: "People are partial to themselves."
Negative- S is not P. Example: "People are not flattered."

By volume

General- judgments that are valid with respect to the entire scope of the concept (All S are P). Example: "All plants live."
Private- judgments that are valid with respect to part of the scope of the concept (Some S are P). Example: "Some plants are conifers."

Relative to

categorical- judgments in which the predicate is affirmed in relation to the subject without restrictions in time, space or circumstances; unconditional proposition (S is P). Example: "All men are mortal."
Conditional- judgments in which the predicate limits the relation to some condition (If A is B, then C is D). Example: "If it rains, the soil will be wet." For conditional propositions
- Base is the (previous) proposition that contains the condition.
- Consequence is a (subsequent) proposition that contains a consequence.

Relationship between subject and predicate

Logical square describing relationships between categorical propositions

The subject and predicate of a judgment can be distributed(index "+") or not distributed(index "-").

distributed- when in a judgment the subject (S) or predicate (P) is taken in full.
Not allocated- when in a judgment the subject (S) or predicate (P) is not taken in full.

Judgments A (general affirmative judgments) Distributes its subject (S) but does not distribute its verb (P)

The volume of the subject (S) is less than the volume of the predicate (P)

Note: "All fish are vertebrates"

The volumes of the subject and predicate are the same

Note: "All squares are parallelograms with equal sides and equal angles"

Judgments E (general negative judgments) Distributes both subject (S) and verb (P)

In this judgment we deny any coincidence between the subject and the predicate.

Note: "No insect is a vertebrate"

Judgments I (private-affirmative judgments) Neither the subject (S) nor the predicate (P) are distributed

Part of the subject class is included in the predicate class.

Note: "Some books are useful"

Note: "Some animals are Vertebrates"

judgments about (particular-negative judgments) Distributes its predicate (P) but does not distribute its subject (S) In these judgments, we pay attention to what is inconsistent between them (shaded area)

Note: "Some animals are not vertebrates (S)"

Note: "Some snakes do not have venomous teeth (S)"

subject and predicate distribution table

General classification:

general affirmative (A) - both general and affirmative ("All S + are P -")
private affirmative (I) - private and affirmative ("Some S's are the essence of P's") Note: "Some people have black skin"
general negative (E) - common and negative ("No S + is a P + ") Note: "No man is omniscient"
private negative (O) - quotient and negative ("Some S's are not P+") Note: "Some people don't have black skin"

Other

Dividing -

1) S is either A, or B, or C

2) either A, or B, or C is P when there is room for uncertainty in the judgment

Conditional-separative judgments -

If A is B then C is D or E is F

if there is A, then there is a, or b, or c

Identity judgments- the concepts of subject and predicate have the same scope. Example: "Every equilateral triangle is an equiangular triangle."
Judgments of submission- a concept with a lesser scope is subordinate to a concept with a wider scope. Example: "A dog is a pet."
Relationship judgments- precisely space, time, relationships. Example: "The house is on the street."

Existential judgments or judgments of existence are those which attribute only existence.
Analytical judgments- judgments in which we express something about the subject that is already contained in it.
Synthetic judgments are judgments that expand knowledge. They do not reveal the content of the subject, but add something new.

Modality of judgments

Modal concepts, or modalities- concepts expressing the contextual frame of the judgment: the time of judgment, the place of judgment, knowledge about the judgment, the attitude of the speaker to the judgment.

Depending on the modality, the following main types of judgments are distinguished:

Opportunity judgments- "S is probably P" ( possibility). Example: "It is possible that a meteorite will fall to Earth."
assertoric- "S is P" ( reality). Example: "Kyiv stands on the Dnieper."
Apodictic- "S must be P" ( need). Example: "Two straight lines cannot close spaces."

Notes

Literature

G. Chelpanov. "Textbook of logic". 9th edition. Moscow 1998
A. D. Getmanova Logic // Izd. Book house "University". 1998. - 480s.

Wikimedia Foundation. 2010 .

Synonyms:

See what "Judgment" is in other dictionaries:

A thought expressed by a declarative sentence that is either true or false. S. is devoid of the psychological connotation inherent in the statement. Although S. finds its expression only in language, it, unlike a sentence, does not depend on ... ... Philosophical Encyclopedia

Judgment- Judgment ♦ Jugement A thought that has value or claims to have value. That is why every judgment is evaluative, even if the subject of evaluation is truth (though truth in itself is not a value). Judgment… … Philosophical Dictionary of Sponville

Court, review, report, opinion, reasoning, consideration, understanding, view; discretion, prudence, comprehension, eye, clairvoyance, insight. Submit at whose discretion (discretion). At my age, one should not sweep away one's judgment ... ... Synonym dictionary

JUDGMENT, judgments, cf. 1. only units Action under ch. to judge in 1 meaning, discussion (book obsolete). "Sentenced by common judgment." Krylov. Prolonged judgment on the matter. 2. Opinion, conclusion. "I dare not utter my judgment." Griboyedov. "In my... Explanatory Dictionary of Ushakov

judgment- one of the logical forms of thinking (see also concept, inference). S. is a connection between two concepts (subject and predicate). In logic, classifications of S are being developed. Psychology studies the development ... Great Psychological Encyclopedia

JUDGMENT, betrothed, see judge Dahl's Explanatory Dictionary. IN AND. Dal. 1863 1866 ... Dahl's Explanatory Dictionary

judgment- JUDGMENT (German Urteil; English, French Judgment) is a mental act that expresses the attitude of a person to the content of the thought expressed by him. In the form of affirmation or denial, S. must be accompanied by one or another modality, conjugated, as ... ... Encyclopedia of Epistemology and Philosophy of Science

judgment- JUDGMENT, assumption JUDGE, suppose ... Dictionary-thesaurus of synonyms of Russian speech

1) the same as a statement. 2) A mental act that realizes the speaker’s attitude to the content of the expressed thought and is associated with conviction or doubt about its truth or falsity ... Big Encyclopedic Dictionary

The expression of elements of sensory experience in a generally valid verbal form ... Psychological Dictionary

Books

Judgment of an Orthodox Galician on the Reform of Russian Church Administration Projected by Russian Liberals of Our Time, Dobryansky-Sachurov. The judgment of an Orthodox Galician about the reform of Russian church administration, projected by Russian liberals of our time / Op. ... Galician-Russian. figure and patriot Adolf Ivanovich ...

Along with the concept, judgment is one of the main forms of thinking. Judgment - a form of thinking in which something is affirmed or denied about the existence of objects, the connections between an object and its properties, or about the relationship between objects.

Examples of judgments: "Astronauts exist", "Paris is bigger than Marseille", "Some numbers appear even". If what is said in the judgment corresponds to the actual state of things, then the judgment is true. The above judgments are true, since they adequately (correctly) reflect what takes place in reality. Otherwise, the proposition is false ("All plants are edible").

Traditional logic is two-valued because in it a proposition has one of two truth values: it is either true or false. In three-valued logics – varieties of multivalued logics – a proposition can be either true or false or indeterminate. For example, the proposition "There is life on Mars" is currently neither true nor false, but uncertain. Many judgments about future single events are uncertain. Aristotle wrote about this, giving an example of such an indefinite judgment: "Tomorrow a sea battle will be necessary."

The language form of expression of a judgment is a sentence. A judgment is expressed by a declarative sentence, which always contains either an affirmation or a negation. Judgment and proposition differ in their composition. Every simple proposition consists of three elements:

1)the subject of judgment - This is the concept of the subject matter. The subject of judgment is denoted by the letter S (from the Latin word subjectum);

2)judgment predicate – concept of the attribute of the object referred to in the judgment. The predicate is denoted by the letter R (from lat. praedicatum);

3)bundles, expressed in Russian by the words "is", "is", "essence".

The subject and the predicate are called terms of judgment. The structure of some judgments also includes the so-called quantifier words (“some”, “all”, “none”, “sometimes”, etc.). The quantified word indicates whether the judgment refers to the entire scope of the concept expressing the subject, or to a part of it.

TYPES OF SIMPLE JUDGMENTS

1. Property judgments (attributive):

they affirm or deny belonging to the subject of known properties, states, activities.

Scheme this kind of judgment: « S there is R" or « S do not eat R".

Examples : "Honey is sweet", "Chopin is not a playwright."

2. Relationship Judgments:

judgments reflecting the relationship between objects.

Formula , expressing a judgment with a two-place relation, is written as aRb or R(a,b ), where a and b- names of objects (members of the relation), and R – relation name. In an attitude judgment, something can be affirmed or denied not only about two, but also about three, four or more objects, for example: "Moscow is between St. Petersburg and Kyiv." Such judgments are expressed by the formula R(a ,a ,a ,…,a).

Examples: “Every proton is heavier than an electron”, “French writer Victor Hugo was born later than the French writer Stendhal”, “Fathers are older than their children”.

3. Judgments of existence (existential):

they express the very fact of the existence or non-existence of the object of judgment.

Scheme this kind of judgment: « S there is R" or « S do not eat R".

Examples of these judgments: "There are nuclear power plants", "There are no causeless phenomena."

In traditional logic, all three of these types of judgments are simple categorical judgments. According to the quality of the link (“is” or “is not”), categorical judgments are divided into affirmative and negative . Judgments: " Some teachers are talented educators" and " All hedgehogs are prickly"- affirmative. Judgments: " Some books are not secondhand" and " No rabbit is a carnivore' are negative. The link "is" in an affirmative judgment reflects the inherent nature of the object (objects) of certain properties. The link “is not” reflects the fact that a certain property is not inherent in the object (objects).

Some logicians believed that there is no reflection of reality in negative judgments. In fact, the absence of certain features is also a real feature that has objective significance. In a negative true judgment, our thought disunites (separates) that which is divided in the objective world.

In cognition, an affirmative judgment is generally more important than a negative one, because it is more important to reveal what feature an object has than what it does not have, since any object does not have very many properties (for example, a dolphin is not a fish, not an insect, not a plant, not a reptile, etc.).

Judgments are divided into general, private and single.

For example: "All sable – valuable fur animals "and" All sane people want a long, happy and useful life "(P. Bragg) – general judgments ; "Some animals – waterfowl" – private ; Vesuvius – active volcano" – singular .

Structure general judgments: "All S are (not the essence) R". Singular judgments will be treated as general ones, since their subject is a one-element class.

Among the general statements there are highlighting judgments, which include the quantified word "only". Examples of highlighting judgments: "Bragg only drank distilled water"; “A brave man is not afraid of the truth. Only a coward is afraid of her ”(A.K. Doyle).

Among the general statements are exclusive judgments, for example: "All metals at a temperature of 20 ° C, with the exception of mercury, are solid." Exceptional judgments also include those in which exceptions are expressed from certain rules of Russian or other languages, rules of logic, mathematics, and other sciences.

Private judgments have structure: "Some S essence (not essence) R". They are divided into indefinite and definite. For example, "Some berries are poisonous" – indefinite private judgment. We have not established whether all berries have a sign of toxicity, but we have not established that some berries do not have a sign of toxicity. If we have established that "only some S have the attribute R", then it will be a certain private judgment, the structure of which is: “Only some S essence (not essence) R". Examples: "Only some berries are poisonous"; "Only some figures are spherical"; "Only some bodies are lighter than water." Quantifier words are often used in certain private judgments: most, minority, many, not all, many, almost all, a few, etc.

AT single in judgment, the subject is a single concept. Singular judgments have a structure: "This S is (is not) P." Examples of singular judgments: "Lake Victoria is not in the USA"; "Aristotle – educator of Alexander the Great"; "Hermitage – one of the world's largest art and cultural-historical museums.

Thus, a special place in the classification of judgments is occupied by distinguishing, excluding and definitely particular judgments, which are built on the basis of attributive judgments and represent some complicated variants of the latter:

The procedure for reducing natural language sentences to the canonical form of categorical propositions

1. Determine the quantifier, subject and predicate of the statement.

2. Put the quantifier words "all" ("none") or "some" at the beginning of the statement.

3. Put the subject of the statement after the quantified word.

4. Put the logical connective "is" ("essence") or "is not" ("is not the essence") after the subject of the statement.

5. Put the predicate of the statement after the logical connective.

When performing the last operation, keep the following in mind:

Firstly, if the predicate is expressed by a noun that can be represented by a single word or phrase, then in this case the predicate remains unchanged;

Secondly, if the predicate is expressed by an adjective (participle), which can be represented by one word or phrase, then in this case a generic concept for the subject of the statement should be added to the predicate;

Thirdly, if the predicate is expressed by a verb that can be represented by one word or phrase, then in this case a generic concept for the subject of the statement should be added to the predicate, and the verb should be turned into the corresponding participle.

Each judgment has both quantitative and qualitative characteristics. Therefore, in logic, a combined classification of judgments by quantity and quality is used, on the basis of which the following are distinguished four types of judgments :

1. BUT – general assertion.

Structure: "All S essence R".

Example: "All people want happiness."

2. I– private statement.

Structure: "Some S's are R".

Example: "Some lessons stimulate the creative activity of students."

ü Conventions for affirmative judgments are taken from the word affirmo, or affirm; in this case, the first two vowels are taken: BUT – to denote a general affirmative and I – to denote a particular affirmative judgment.

3. E – general negative judgment.

Structure: "None S do not eat R".

Example: "No ocean is freshwater."

4. O– private negative judgment.

Structure: "Some S don't eat R".

Example: "Some athletes are not Olympic champions."

ü The symbol for negative judgments is taken from the word nego , or I deny.

In judgments, the terms S and R may or may not be allocated. The term is considered distributed, if its scope is fully included in the scope of another term or completely excluded from it. The term will undistributed, if its scope is partially included in the scope of another term or partially excluded from it. Let's analyze four types of judgments: A, I, E, O(we consider typical cases).

1. Judgment BUT – general affirmative . Its structure is: All S is P ».

Consider two cases:

Example 1 . In the judgment "All carp – fish" the subject is the concept of "crucian", and the predicate – the concept of fish. General quantifier – "all". The subject is distributed, since we are talking about all crucian carp, i.e. its scope is fully included in the scope of the predicate. The predicate is not distributed, since only a part of the fishes that coincide with crucian carp are conceived in it; we are talking only about that part of the scope of the predicate, which coincides with the scope of the subject.

Example 2 . In the proposition "All squares are equilateral rectangles" the terms are: S- "square", R- "equilateral rectangle" and the quantifier of generality - "all". In this judgment S is distributed and P is distributed, because their volumes are exactly the same. If a S equal in volume R, then R distributed. This happens in definitions and in singling out general judgments.

2. Judgment I – private affirmative . Its structure is: Some S is P ». Let's consider two cases.

Example 1 . In the judgment “Some teenagers are philatelists”, the terms are: S - "teenager", R– “philatelist”, existential quantifier – “some”. The subject is not distributed, since only a part of adolescents is conceived in it, i.e. the scope of the subject is only partially included in the scope of the predicate. The predicate is also not distributed, since it is also only partially included in the scope of the subject (only some philatelists are teenagers). If concepts S and R cross, then R not distributed.

Example 2 . In the judgment "Some writers are playwrights" the terms are: S - "writer", P - "playwright" and the existential quantifier - "some". The subject is not distributed, since only a part of writers is conceived in it, i.e. the scope of the subject is only partially included in the scope of the predicate. The predicate is distributed, because the scope of the predicate is completely included in the scope of the subject. In this way, R distributed if the volume R less than the volume S , what happens in particular highlighting judgments.

3. Judgment E – general negative . Its structure is: none S is not P » . For example : "No lion is a herbivore." In it, the terms are: S - "lion", R- "herbivore" and the quantifier word - "none". Here the scope of the subject is completely excluded from the scope of the predicate, and vice versa. Therefore, S , and R distributed.

4. Judgment O –private negative . Its structure is: Some S is not P ». For example : "Some students are not athletes." It contains the following terms: S - "student", R– "sportsman" and the existential quantifier are "some". The subject is not distributed, since only a part of the students is conceived, and the predicate is distributed, because all athletes are conceived in it, none of which is included in that part of the students that is conceived in the subject

So, S is distributed in general judgments and not distributed in particular; P is always distributed in negative judgments, while in affirmative ones it is distributed when, in terms of volume, P ≤S.

Imagine it in the term distribution table:

Terms / Type of judgment	A	E	I	O
S
P
P highlighting judgments

The subject is distributed in general and not distributed in particular judgments. The predicate is distributed in negative and not distributed in affirmative propositions. In distinguishing propositions, the predicate is distributed.

Designations: +– distribution of the term;

– – undistributed term

· JUDGMENTS WITH RELATIONSHIPS are such judgments in which the relationship between two terms - the subject and the predicate is expressed not with the help of a connective (“is”, “is”, etc.), but with the help of a relation in which something is affirmed or denied in relation to two (multiple) terms. In this type of judgment, the predicate is a relation, and the subject is two (or more) concepts. The locality of the relationship is determined by the number of concepts included in the subject.

· Judgments with relations are divided by quality into affirmative and negative. Judgments with relations are divided by number. The most common are judgments with two-place relations. Two-place relations have a number of properties on the basis of which one can draw conclusions from judgments about relations. These are the properties of symmetry, reflexivity and transitivity.

The relation is called symmetrical(from Latin “proportionality”), if it takes place both between objects x and y , and between objects y and x (if X equal to (similar to, at the same time) y , then and y equal to (similar to, at the same time) X .
The relation is called reflective(from Latin “reflection”), if each member of the relation is in the same relation to itself (if X =at , then X =X and at =at ).
The relation is called transitive(from Latin "transition"), if it takes place between X and z , when it occurs between X and at and between at and z (if X equals at and at equals z , then X equals z ).

Every judgment is expressed in a sentence, but not every sentence expresses a judgment.

Ø Judgments are expressed through declarative sentences, which always contain either an affirmation or a negation. That is why declarative sentences, as the grammatical equivalent of a judgment, are a completely complete thought, which affirms or denies the connection between an object and its attribute, the relationship between objects, the fact of the existence of an object, and which can be either true or false.

Ø Interrogative sentences do not contain judgments in their composition, since nothing is affirmed or denied in them. They are neither true nor false. For example: “When will you start gardening?” or “Is this method of learning a foreign language effective?”. If the sentence is a rhetorical question, – for example: “Who does not want happiness?”, “Which of you did not love?” or “Is there anything more monstrous than an ungrateful person?” (W. Shakespeare), or “Is there a person who looks at the river in a moment of thought and does not remember the constant movement of all things?” (R. Emerson), – then it contains a judgment, since there is an assertion, a certainty that "Everyone wants happiness" or "All people love", etc.

Ø Interrogative-rhetorical sentences contain judgments in their composition, since something is affirmed or denied in them. They can be either true or false.

Incentive Offers do not contain judgments in their composition: (“Take care of your health”; “Do not make fires in the forest”, “Go not to the skating rink, but to school!”). But sentences in which military commands and orders, calls or slogans are formulated express judgments, however, not assertoric, but modal (modal judgments include modal operators expressed in the words: perhaps, necessary, forbidden, proved, etc.). For example: “Take care of the world!”, “Get ready to start!”, “My friend! Let us dedicate our souls to the Fatherland with wonderful impulses ”(A.S. Pushkin). These sentences express judgments, but the judgments are modal, including modal words. As A.I. Uyomov, express judgments and such incentive sentences: “Protect the world!”, “Do not smoke!”, “Fulfill your obligations!”. "Before any meal, eat raw vegetable salad or raw fruit" and "Do not harm yourself by overeating" – these advices (calls) of the famous American scientist Paul Bragg, taken from his book "The Miracle of Fasting", are judgments. It is a judgment and a call: “People of the world! Let's unite our efforts in solving universal, global problems!

Ø One-part impersonal sentences and nominal are judgments only when considered in context and with appropriate clarification.

The criterion for the presence of a judgment in the composition of a sentence is the presence of a moment of affirmation or negation, leading to an assessment of the judgment for truth or falsity.

In natural language, the same proposition can be expressed in different sentences. Therefore, in logic, in order to avoid ambiguity and the multiplicity of different meaningful interpretations of the sentence, the term "statement" is used, meaning by it some formalized expression of thought, which can have only one logical meaning. A judgment considered together with the sentence expressing it is a proposition. The latter is a grammatically correct declarative sentence, taken together with the meaning unambiguously expressed by it; it can be either true or false.

II. Types and logical probability of complex judgments

Compound judgments are formed from simple ones, as well as from other complex judgments with the help of the unions "if ..., then ...", "or", "and", etc., with the help of the negation of "it is not true that", modal the terms "it is possible that", "it is necessary that", "accidentally that", etc. These conjunctions, the negation of "it is not true that", modal terms in everyday language are used in various senses. In scientific languages, they are given a precise meaning, as a result of which different types of judgments are distinguished, formed from other judgments by means of, for example, the same grammatical union.

I.connecting are called judgments in which the existence of two or more situations is affirmed. Most often, these judgments are expressed in the language by sentences containing the union "and".

The union "and" is used in different meanings. For example, the sentences "Petrov studied English and he studied French" and "Petrov studied French and he studied English" express the same proposition, while the sentences "Petrov graduated from the university and entered graduate school" and "Petrov entered to graduate school and graduated from the university" express different opinions.

Thus, there are different types of statements about the presence of two or more situations, i.e. different types of connecting propositions: (indefinitely) conjunctive, sequentially conjunctive, simultaneously conjunctive.

(Indefinitely) conjunctive propositions are formed from two judgments by means of a union, denoted by the symbol & (read "and") and called the sign (indefinite) conjunctions. The definition of the conjunction sign is a table showing the dependence of the truth of a conjunctive judgment on the truth of its constituent judgments.
Consistently conjunctive judgments. These judgments assert the successive occurrence or existence of two or more situations. They are formed from two or more propositions with the help of unions, denoted by the symbols & ® 2 , & ® 3, etc., depending on the number of propositions from which they are formed. These characters are called signs of sequential conjunction and are respectively read "..., and then ..", "..., then..., and then ...", etc. Indices 2,3 etc. indicate the area of the union. The form of the judgment with the sign of the double consecutive conjunction: & ® 2 (A, B) or (BUT&® 2 AT). Example judgments of this form: "The buyer paid the cost of the goods, and then the seller issued the goods." Instead of the expression "and then" the union "and" is most often used: "The buyer paid the cost of the goods, and the seller issued the goods." A form of judgment with a tripartite conjunction. Example: "Petrov mortgaged the apartment, then contributed money to the pyramid, and then became a man of no fixed abode."
Simultaneously conjunctive judgments. These judgments are formed from two judgments by means of the union "and", called the sign simultaneous conjunction. Notation - & = . These judgments assert the simultaneous existence of two situations. Example: "It's raining and the sun is shining."

disjunctive, or not strictly separating, or connecting-separating, judgments. These judgments assert the existence of at least one of two situations. They are formed from two propositions by means of the union "or", denoted by the sign v (read "or"), called the non-strict disjunction sign (or simply the disjunction sign).
Strictly disjunctive, or strictly dividing, judgments. These judgments assert the presence of exactly one of two, three or more situations. They are formed from two, three, etc. judgments through the unions "or ..., or ..." ("either ..., or ..."), "or ..., or ..., or ...", etc. Sometimes the union "or ..., or ..." is replaced by the union "or", and its divisive meaning is determined by the context. The conjunctions by means of which strict disjunctive judgments are formed are denoted by the sign v.

III. Conditional propositions are expressed, as a rule, by sentences with the union "if ..., then ...". They argue that the presence of one situation determines the presence of another. Example: "If the sun is at its zenith, then the shadows from it are the shortest." In a conditional proposition, a reason and a consequence are distinguished. foundation the part of the conditional proposition that is between the word "if" and the word "then" is called. The part of the conditional proposition that comes after the word "that" is called consequence. In the proposition "If it rains, then the roofs of the houses are wet," the basis is the simple proposition "it is raining," and the consequence is "the roofs of the houses are wet."

A more strictly conditional proposition is defined by means of the notion of a sufficient condition. Condition is sufficient for any event, any situation, if, and only if, always, when there is this condition, there is also an event (situation). Thus, the presence of free electrons in a substance is a sufficient condition for the substance to be electrically conductive. conditional is called a judgment in which the situation described by the reason is a sufficient condition for the situation described by the consequence. The conditional union "if ... then ..." is indicated by an arrow (®).

IV. Counterfactual statements. Example: "If Petrov were president, he would not travel around the city by bus." As in conditional propositions, in these propositions a reason and a consequence are distinguished. The union "if ..., then ..." is indicated by the sign É, which is called the sign counterfactual implications. The judgment has such a meaning, the situation described by the reason does not take place, but if it existed, then the consequence would exist.

V. equivalent judgments. Judgments of equivalence assert the mutual conditionality of two situations. These judgments are expressed, as a rule, by means of sentences with the union "if, and only if, ..., then ..." ("then, and only then, ..., when ..."). They also have reasons and consequences. The reason in them expresses a sufficient and necessary condition for the situation described by the consequence ( The condition is called necessary for a given event (situation, action, etc.), if, and only if, in its absence, this event does not occur.) The union "if, and only if, ... then", used in the sense described, is denoted by the symbol º

In the judgment of equivalence, the event described by the consequence is also a sufficient and necessary condition for the event described by the reason.

VI. Judgment with external negation. This is a statement that asserts the absence of a certain situation.

External negation is indicated by the symbol "l" (negation sign). This sign in natural language corresponds to the negation “not” or the expression “it is not true that”, which usually appear at the beginning of a sentence. By placing the expression “it is not true that” before an arbitrary false statement, we obtain a true statement, and from a true statement by substituting the expression “it is not true that” to it, we form a false statement. A judgment with an external negation refers to complex judgments and is formed from a simple one through negation.

The truth values of complex judgments depend on the truth values of the constituent judgments and on the type of their connection. The identically true formula A formula is called which, for any combination of values for the variables included in it, takes the value "true". Identical-false formula- one that (respectively) takes only the value "false". The formula to be executed can be either true or false.

So, conjunction(and b ) is true when both propositions are true. Strict disjunction ( a b ) is true when only one simple proposition is true. Nonstrict disjunction ( a b ) is true when at least one simple proposition is true. implication ( a e b ) true in all cases except one - when a - true, b- false. Equivalence ( a º b ) true when both statements are true or both are false. Negation (ù a) false gives truth, and vice versa.

Ø Any language construction consisting of a certain set of judgments can be translated into a symbolic language. To do this, you need to replace judgments with logical variables, and the connection between them with logical unions. The logical feature of a complex judgment, its form, depends on the union with which the variables are connected.

Ø A complex proposition, the logical form of which takes the value "true" for all sets of values of its constituent variables, is called logically necessary. In other words, complex propositions that take the value "true" in all rows of the resulting column of truth tables are logically necessary (logically true) propositions. The logical form of a logically necessary proposition is expressed by an identically true formula, which, for any truth value of the variables, takes the value "true", that is, its resulting column consists only of "AND". Identical-true formulas are the basis of logically correct statements. Each such formula is considered as a law of logic (logical tautology).

Ø A complex proposition, the logical form of which takes the value "false" for all sets of values of its constituent variables, is called logically impossible. In other words, complex judgments that take the value “false” from all sides of the resulting column of the truth table are logically impossible (logically false) judgments. The logical form of a logically impossible judgment is expressed by an identically false formula, which takes the value "false" for any truth value of the variables, that is, its resulting column consists only of "L". Identical false formulas are called contradictions.

Ø A complex proposition, the logical form of which in the resulting column of the truth table takes on the values both "true" and "false", is called logically random. The logical form of a logically random proposition is expressed by a neutral (actually feasible) formula, the resulting column of which consists of both "I" and "L".

Ø The peculiarity of the first two types of complex judgments is that their truth and falsity do not depend on the truth and falsity of the simple judgments that make them up. Logically random propositions are sometimes true, sometimes false. And it depends on which simple propositions are true and which are false.

III. Negation of judgments

NEGATIVE JUDGMENT - this is an operation consisting in transforming the logical content of the negated judgment, the end result of which is the formulation of a new judgment, which is in relation to the contradiction to the original judgment.

When denying simple attributive judgments:

1) a general judgment changes to a particular one, and vice versa;

2) an affirmative judgment changes to a negative one, and vice versa.

Attributive judgments are negated according to the following equivalences:

ù BUT is tantamount to O ù O is tantamount to BUT

ù E is tantamount to I ù I is tantamount to E

The negation of complex judgments is made according to the following equivalences:

u (A& AT) is tantamount to ù Avù B; according to de Morgan's law

u (AvB) is tantamount to ù A& ù B;

u (AÉ B) is tantamount to BUT& ù B;

u (Aº B) is tantamount to (ù A& AT)v(A& ù B);

u (Av AT) is tantamount to BUTº AT

IV. Relationship between judgments

The relationship between judgments of truth is usually depicted schematically in the form of a "logical square":

LOGICAL SQUARE

RELATIONSHIPS BETWEEN COMPLEX JUDGMENTS

Relations between complex judgments are divided into dependent (comparable) and independent (incomparable). Independent - judgments that do not have common components; they are characterized by all combinations of true values. Dependent - these are judgments that have the same components and can differ in logical connectives, including negation. Dependents, in turn, are divided into compatible (judgments that can be true at the same time) and incompatible (statements that cannot be true at the same time).

Relations

V. Modality of judgments

MODALITY - this is additional information expressed in the judgment about the logical or actual status of the judgment, about its regulatory, evaluative, temporal and other characteristics.

Assertoric judgments, that is, attributive and relational judgments, as well as complex statements formed from them, can be considered as judgments with incomplete information. The main function of an attributive judgment is to reflect the links between an object and its features. An object S can simply be said to have property P. Such an attributive judgment is simply a statement. Along with a simple statement (negation), the so-called strong and weak statements and negations, which are modal judgments, are distinguished.

MAIN TYPES OF MODALITIES:

Ø ALETIC MODALITY- expressed in the judgment through the modal concepts "necessary", "mandatory", "certainly", "accidentally", "possibly", "maybe", "not excluded", "allowed" and other information about the logical or factual determinism of the judgment . In the aletic group, there are ontological (actual ) modality, which associated with the objective determinism of judgments, when their truth or falsity is determined by the situation that takes place in reality, and logical modality , which associated with the logical determinism of the judgment, when the truth or falsity is determined by the form or structure of the judgment.

Ø EPISTEMIC MODALITY- it is expressed in a judgment by means of modal operators “known”, “unknown”, “provable”, “refutable”, “assumed”, etc. information on the grounds for acceptance and the degree of its validity.

Ø DEONTIC MODALITY- an instruction expressed in a judgment in the form of advice, wishes, rules of conduct or an order that encourages a person to take specific actions. The norms of law also belong to the deontic ones (the following operators can be distinguished here: “obliged”, “must”, “should”, “recognized”, “forbidden”, “cannot”, “not allowed”, “has the right”, “may have", "can accept", etc.).

Judgment modality ( R) is represented using the operator M, according to the scheme Mr(e.g. "possibly R"). The truth of a modal judgment depends on the truth of the judgment under the modal operator and on the type of the modal operator.

Modal simple judgments

Simple judgments expressing the nature of the connection between the subject and the predicate using modal operators (modal concepts)

pÉ q);M(pº q ).

Example: From the complex statement "If the temperature is above 100 degrees, then water turns into steam" you can get the modal statement "It is physically necessary that if the temperature is above 100 degrees, then water turns into steam."

VI. The concept of a logical law

Correct thinking must meet the following requirements: to be definite, consistent, consistent and justified. Certain thinking is precise and strict, free from any inconsistency. Consistent thinking is free from internal contradictions that destroy the necessary connections between thoughts. Consistency is associated with the non-admission of mutually exclusive, as equally acceptable, in one way or another, thoughts. Reasonable thinking is not just formulating the truth, but at the same time indicating the grounds on which it should be recognized as truth.

Since the features of certainty, consistency, consistency and validity are necessary properties of any thinking, they have the force of laws over thinking. Where thinking turns out to be correct, it obeys certain logical laws in all its actions and operations.

As already noted, the logical form of thought is the structure of thought, that is, the way its components are connected. So, between the thoughts, the logical forms of which are represented by the expressions “All S are P” and “All P are S” there is a connection: if one of these thoughts is true, then the second one is true, regardless of the specific content of these thoughts. Connections between thoughts, in which the truth of some necessarily determine the truth of others, determine the formal logical laws, or the laws of logic.

§ LAWS OF LOGIC- these are such expressions that are true only by virtue of their logical form, that is, only on the basis of the connection of their components. In other words, the logical law is the logical form itself, which guarantees the truth of the expression for any content.

§ LAW OF LOGIC is an expression that contains only constants and variables and is true in any (non-empty) subject area (for example, any law of propositional logic or predicate logic is an example of a logical law). These are the so-called laws of communication between thoughts. The laws of logic are also called tautologies.

§ LOGICAL TAUTOLOGY is an "always true expression", that is, it remains true no matter what domain of objects it is. Any law of logic is a logical tautology.

§ A special role is played by the so-called laws (principles) defining the necessary general conditions, which our thoughts and logical operations with thoughts must satisfy. In traditional logic, these are considered:

In mathematical logic, the law of identity is expressed by the following formulas:

aº a (in propositional logic) and Aº A (in class logic, in which classes are identified with scopes of concepts).

Identity is equality, the similarity of objects in some respect. For example, all liquids are identical in that they are thermally conductive and elastic. Each object is identical to itself. But in reality identity exists in connection with difference. There are not and cannot be two absolutely identical things (for example, two leaves of a tree, twins, etc.). A thing yesterday and today is both identical and different. For example, a person's appearance changes over time, but we recognize him and consider him the same person. Abstract, absolute identity does not really exist, but within certain limits we can abstract from the existing differences and fix our attention on the identity of objects or their properties alone.

In thinking, the law of identity acts as a normative rule (principle). It means that in the process of reasoning it is impossible to replace one thought with another, one concept with another. It is impossible to pass off identical thoughts as different ones, and different ones as identical ones.

For example, three such concepts will be identical in scope: “scientist, on whose initiative Moscow University was founded”; "a scientist who formulated the principle of conservation of matter and motion"; “a scientist who, since 1745, became the first Russian academician of the St. Petersburg Academy” - they all refer to the same person (M.V. Lomonosov), but give different information about him.

Violation of the law of identity leads to ambiguities, which can be seen, for example, in the following reasoning: “Nozdryov was in some respects a historical person. Not a single meeting where he was could do without history ”(N.V. Gogol). “Strive to pay your debt, and you will achieve a double goal, for in doing so you will fulfill it” (Kozma Prutkov). The play on words in these examples is based on the use of homonyms.

In thinking, the violation of the law of identity manifests itself when a person speaks not on the topic under discussion, arbitrarily replaces one subject of discussion with another, uses terms and concepts in a different sense than is customary, without warning about it.

Identification (or identification) is widely used in investigative practice, for example, when identifying objects, people, identifying handwriting, documents, signatures on a document, identifying fingerprints.

2. Law of non-contradiction: If the subject BUT has a certain property, then in judgments about BUT people should affirm this property, not deny it. If a person, stating something, denies the same thing or asserts something incompatible with the first, there is a logical contradiction. Formal-logical contradictions are the contradictions of confused, incorrect reasoning. Such contradictions make it difficult to understand the world.

Thought is contradictory if we affirm and deny something about the same object at the same time and in the same respect. For example: “Kama is a tributary of the Volga” and “Kama is not a tributary of the Volga”. Or: “Leo Tolstoy is the author of the novel “Resurrection” and “Leo Tolstoy is not the author of the novel “Resurrection”.

There will be no contradiction if we are talking about different subjects or about the same subject, taken at different times or in different respects. There will be no contradiction if we say: “Rain is good for mushrooms in autumn” and “Rain is not good for harvesting in autumn”. The judgments "This bouquet of roses is fresh" and "This bouquet of roses is not fresh" also do not contradict each other, because the objects of thought in these judgments are taken in different relationships or at different times.

The following four types of simple propositions cannot be true at the same time:

∧ā. The law of non-contradiction reads as follows: "Two opposing propositions cannot be true at the same time and in the same respect." Opposite judgments include: 1) opposite (contrarian) judgments BUT and E, which can both be false, so they are not negating each other and cannot be denoted as a and ā; 2) contradictory (contradictor) judgments BUT and O, E and I, as well as singular judgments "This S is P" and "This S is not P", which are negative, since if one of them is true, then the other is necessarily false, therefore they are denoted by a and ā.

The formula of the law of non-contradiction in two-valued classical logic a ∧ ā reflects only part of the meaningful Aristotelian law of non-contradiction, since it applies only to contradictory judgments (a and not-a) and does not apply to the opposite (contrarian judgments). Therefore, the formula a∧ ā is inadequate, does not fully represent the substantive law of non-contradiction. Following tradition, we retain the name “law of non-contradiction” behind the formula a∧ ā, although it is much broader than this formula.

If a formal-logical contradiction is found in the thinking (and speech) of a person, then such thinking is considered incorrect, and the judgment from which the contradiction follows is denied and considered false. Therefore, in the controversy, when refuting the opponent's opinion, the method of "reduction to absurdity" is widely used.

3. Law of the excluded middle: Of the two contradictory propositions, one is true, the other is false, and the third is not given.. Contradictory (contradictory) are such two judgments, in one of which something is affirmed about the subject, and in the other the same is denied about the same subject, therefore they cannot be both true and both false at the same time; one of them is true and the other is necessarily false. Such judgments are called negating each other. If one of the contradictory judgments is denoted by the variable a, then the other should be denoted ā . Thus, of the two statements: "James Fenimore Cooper is the author of a series of novels about Leather Stocking, created over a period of almost 20 years" and "James Fenimore Cooper is not the author of a series of novels about Leather Stocking, created over a period of almost 20 years," the first is true, the second is false, and there can be no third - intermediate - judgment.

The following pairs of propositions are negative:

1) "This S is P" and "This S is not P" (single judgments).

2) "All S are P" and "Some S are not P" (judgments BUT and O).

3) "No S is P" and "Some S are P" (judgments E and I).

With regard to contradictory (contradictor) judgments ( BUT and O, E and I) operates both the law of the excluded middle and the law of non-contradiction - this is one of the similarities of these laws.

The difference in the areas of definition (i.e., application) of these laws is that in relation to contrary (contrarian) judgments BUT and E(for example: "All mushrooms are edible" and "No mushroom is edible"), which cannot both be true, but both can be false, only the law of non-contradiction applies and the law of the excluded middle does not apply. So, the scope of the substantive law of non-contradiction is wider (these are contradictory and contradictory judgments) than the scope of the substantive law of the excluded middle (only contradictory, i.e., judgments of the type a and nope). Indeed, one of the two propositions is true: "All the houses in this village are electrified" or "Some houses in this village are not electrified" and there is no third.

The law of the excluded middle, both in a meaningful and formalized form, covers the same circle of judgments - contradictory, i.e. denying each other. Formula of the law of the excluded middle: BUT v ù A

In thinking, the law of the excluded middle implies a clear choice of one of two mutually exclusive alternatives. For the correct conduct of the discussion, the fulfillment of this requirement is mandatory.

4. Law of sufficient reason:Every true thought must be sufficiently substantiated. We are talking about justifying only true thoughts: false thoughts cannot be justified, and there is no point in trying to “justify” a lie, although often individuals try to do so. There is a good Latin proverb: “To err is common to all people, but only fools tend to insist on their mistakes.”

A simple proposition can only be decomposed into concepts.

Composition of a simple proposition

The subject of judgment is a thought about some subject, a concept about the subject of judgment (logical subject).
Judgment predicate - a thought about a known part of the content of the subject, which is considered in the judgment (logical predicate).
Logical link - the idea of the relationship between the subject and the selected part of its content (sometimes only implied).
Quantifier - indicates whether the judgment refers to the entire scope of the concept expressing the subject, or only to its part: “some”, “all”, etc.

The composition of a complex judgment

Disjunctive judgments are formed with the help of disjunctive (disjunctive) logical connectives (similar to the union "or"). Like simple disjunctive judgments, they are:

non-strict(non-strict disjunction), whose members allow joint coexistence (“either ..., or ...”). Written as $a \lor b$ ;
strict(strict disjunction), whose members exclude each other (either one or the other). Written as $a \dot\lor b$ .

Implicit judgments are formed with the help of the implication, (equivalent to the union "if ..., then"). Written as $a\to b$ or $a b$ . In natural language, the union "if ... then" is sometimes synonymous with the union "a" ("The weather has changed and if yesterday it was cloudy, then today there is not a single cloud") and, in this case, means a conjunction.

Equivalent judgments indicate the identity of the parts of the judgment to each other (draw an equal sign between them). In addition to definitions explaining a term, they can be represented by judgments connected by the unions “if only”, “necessary”, “enough” (for example: “For a number to be divisible by 3, it is enough that the sum of the digits that make it up is divisible by 3 "). Written as $a \equiv b, a \leftrightarrow b, a b$ (for different mathematicians in different ways, although the mathematical sign of identity is still $\equiv$ ).

Classification of simple judgments

By quality

Affirmative- S is P. Example: "People are partial to themselves."
Negative- S is not P. Example: "People are not flattered."

By volume

General- judgments that are valid with respect to the entire scope of the concept (All S are P). Example: "All plants live."
Private- judgments that are valid with respect to part of the scope of the concept (Some S are P). Example: "Some plants are conifers."
Single

Relative to

categorical- judgments in which the predicate is affirmed in relation to the subject without restrictions in time, space or circumstances; unconditional proposition (S is P). Example: "All men are mortal."
Conditional- judgments in which the predicate limits the relation to some condition (If A is B, then C is D). Example: "If it rains, the soil will be wet." For conditional propositions
- Base is the (previous) proposition that contains the condition.
- Consequence is a (subsequent) proposition that contains a consequence.

Relationship between subject and predicate

The subject and predicate of a judgment can be distributed(index "+") or not distributed(index "-").

distributed- when in a judgment the subject (S) or predicate (P) is taken in full.
Not allocated- when in a judgment the subject (S) or predicate (P) is not taken in full.

Judgments A (general affirmative judgments) Distributes its subject (S) but does not distribute its verb (P)

The volume of the subject (S) is less than the volume of the predicate (P)

Note: "All fish are vertebrates"

The volumes of the subject and predicate are the same

Note: "All squares are parallelograms with equal sides and equal angles"

Judgments E (general negative judgments) Distributes both subject (S) and verb (P)

In this judgment we deny any coincidence between the subject and the predicate.

Note: "No insect is a vertebrate"

Judgments I (private-affirmative judgments) Neither the subject (S) nor the predicate (P) are distributed

Part of the subject class is included in the predicate class.

Note: "Some books are useful"

Note: "Some animals are Vertebrates"

judgments about (particular-negative judgments) Distributes its predicate (P), but does not distribute its subject (S) In these judgments, we pay attention to what is inconsistent between them (shaded area)

Note: "Some animals are not vertebrates (S)"

Note: "Some snakes do not have venomous teeth (S)"

subject and predicate distribution table

General classification:

general affirmative (A) - both general and affirmative ("All S + are P -")
private affirmative (I) - private and affirmative ("Some S's are the essence of P's") Note: "Some people have black skin"
general negative (E) - common and negative ("No S + is a P + ") Note: "No man is omniscient"
private negative (O) - quotient and negative ("Some S's are not P+") Note: "Some people don't have black skin"

Other

Dividing -

1) S is either A, or B, or C

2) either A, or B, or C is P when there is room for uncertainty in the judgment

Conditional-separative judgments -

If A is B then C is D or E is F

if there is A, then there is a, or b, or c

Identity judgments- the concepts of subject and predicate have the same scope. Example: "Every equilateral triangle is an equiangular triangle."
Judgments of submission- a concept with a lesser scope is subordinate to a concept with a wider scope. Example: "A dog is a pet."
Relationship judgments- precisely space, time, relationships. Example: "The house is on the street."

Existential judgments or judgments of existence are those which attribute only existence.
Analytic judgments are judgments in which we express something about the subject that is already contained in it.
Synthetic judgments are judgments that expand knowledge. They do not reveal the content of the subject, but add something new.

Modality of judgments

Depending on the modality, the following main types of judgments are distinguished:

Opportunity judgments- "S is probably P" ( possibility). Example: "It is possible that a meteorite will fall to Earth."
assertoric- "S is P" ( reality). Example: "Kyiv stands on the Dnieper."
Apodictic- "S must be P" ( need). Example: "Two straight lines cannot close spaces."

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Notes

Literature

Chelpanov G. Logic textbook. - 9th edition. - M., 1998.
Getmanova A. D. Logics. - Book House "University", 1998. - 480 p.
Egorov S. N. Judgment. - St. Petersburg. , 2011. - 264 p.

An excerpt characterizing Judgment

“Yes, it must be so,” thought Pierre, when, after these words, the rhetorician again left him, leaving him to solitary reflection. “It must be so, but I am still so weak that I love my life, the meaning of which is only now being revealed to me little by little.” But the remaining five virtues, which Pierre remembered fingering, he felt in his soul: courage, and generosity, and kindness, and love for humanity, and especially obedience, which did not even seem to him a virtue, but happiness. (He was so happy now to get rid of his arbitrariness and subordinate his will to that and those who knew the undoubted truth.) Pierre forgot the seventh virtue and could not remember it.
The third time, the rhetor returned sooner and asked Pierre if he was still firm in his intention, and whether he dared to expose himself to everything that was required of him.
“I am ready for anything,” said Pierre.
“I must also inform you,” said the rhetorician, “that our order teaches its teachings not only in words, but by other means that, perhaps, have a stronger effect on the true seeker of wisdom and virtue than verbal explanations only. This temple with its decoration, which you see, should have already explained to your heart, if it is sincere, more than words; you will see, perhaps, in your further acceptance of a similar way of explaining. Our order imitates the ancient societies that revealed their teachings with hieroglyphs. A hieroglyph, - said the rhetorician, - is the name of some thing that is not subject to feelings, which contains qualities similar to the one depicted.
Pierre knew very well what a hieroglyph was, but did not dare to speak. He silently listened to the rhetor, feeling in everything that the trials would immediately begin.
“If you are firm, then I must begin to introduce you,” said the rhetorician, coming closer to Pierre. “As a sign of generosity, I ask you to give me all your precious things.
“But I don’t have anything with me,” said Pierre, who believed that they were demanding that he hand over everything he had.
- What you have: watches, money, rings ...
Pierre hurriedly took out his wallet, watch, and for a long time could not remove the wedding ring from his fat finger. When this was done, the Mason said:
- As a token of obedience, I ask you to undress. - Pierre took off his tailcoat, waistcoat and left boot at the direction of the rhetor. Mason opened the shirt on his left chest, and, bending down, lifted his trouser leg on his left leg above the knee. Pierre hurriedly wanted to take off his right boot and roll up his trousers in order to save a stranger from this labor, but the mason told him that this was not necessary - and gave him a shoe on his left foot. With a childish smile of modesty, doubt and mockery of himself, which appeared on his face against his will, Pierre stood with his hands down and legs apart in front of his brother rhetorician, waiting for his new orders.
“And finally, as a sign of candor, I ask you to reveal to me your main passion,” he said.
- My passion! I had so many of them,” said Pierre.
“That addiction which, more than any other, made you waver in the path of virtue,” said the Mason.
Pierre was silent for a while, looking for.
"Wine? Overeating? Idleness? Laziness? Hotness? Malice? Women?" He went over his vices, mentally weighing them and not knowing which one to give priority to.
“Women,” Pierre said in a low, barely audible voice. The Mason did not move or speak for a long time after this answer. Finally, he moved towards Pierre, took the handkerchief lying on the table and again blindfolded him.
- For the last time I tell you: turn all your attention to yourself, put chains on your feelings and seek bliss not in passions, but in your heart. The source of bliss is not outside, but within us...
Pierre already felt this refreshing source of bliss in himself, now filling his soul with joy and tenderness.

Soon after this, it was no longer the former rhetorician who came to the dark temple for Pierre, but the guarantor Villarsky, whom he recognized by his voice. To new questions about the firmness of his intentions, Pierre answered: “Yes, yes, I agree,” and with a beaming childish smile, with an open, fat chest, unevenly and timidly stepping with one bare and one shod foot, he went forward with Villarsky put to his bare chest with a sword. From the room he was led along the corridors, turning back and forth, and finally led to the doors of the box. Villarsky coughed, they answered him with Masonic knocks of hammers, the door opened before them. Someone's bass voice (Pierre's eyes were all blindfolded) asked him questions about who he was, where, when was he born? etc. Then they again led him somewhere, without untying his eyes, and as he walked, allegories spoke to him about the labors of his journey, about sacred friendship, about the eternal Builder of the world, about the courage with which he must endure labors and dangers . During this journey, Pierre noticed that he was called either seeking, then suffering, then demanding, and at the same time they knocked with hammers and swords in different ways. While he was led to some subject, he noticed that there was confusion and confusion between his leaders. He heard how the surrounding people argued among themselves in a whisper and how one insisted that he be led along some kind of carpet. After that, they took his right hand, put it on something, and with the left they ordered him to put the compass to his left chest, and forced him, repeating the words that the other had read, to read the oath of allegiance to the laws of the order. Then they put out the candles, lit alcohol, as Pierre heard it by smell, and said that he would see a small light. The bandage was removed from him, and Pierre, as in a dream, saw, in the faint light of an alcohol fire, several people who, in the same aprons as the rhetorician, stood against him and held swords aimed at his chest. Between them stood a man in a bloody white shirt. Seeing this, Pierre moved his sword forward with his chest, wanting them to pierce him. But the swords moved away from him and he was immediately bandaged again. “Now you have seen a small light,” a voice told him. Then the candles were lit again, they said that he needed to see the full light, and again they took off the bandage and suddenly more than ten voices said: sic transit gloria mundi. [this is how worldly glory passes.]
Pierre gradually began to come to his senses and look around the room where he was and the people in it. Around a long table, covered with black, sat about twelve people, all in the same robes as those whom he had seen before. Some Pierre knew from Petersburg society. An unfamiliar young man was sitting in the chairman's seat, wearing a special cross around his neck. On the right hand sat the Italian abbot, whom Pierre had seen two years ago at Anna Pavlovna's. There was also a very important dignitary and a Swiss tutor who had previously lived with the Kuragins. Everyone was solemnly silent, listening to the words of the chairman, who held a hammer in his hand. A burning star was embedded in the wall; on one side of the table there was a small carpet with various images, on the other side there was something like an altar with a Gospel and a skull. Around the table were 7 large, in the sort of church, candlesticks. Two of the brothers led Pierre to the altar, put his feet in a rectangular position and ordered him to lie down, saying that he was throwing himself at the gates of the temple.
“He must first get a shovel,” one of the brothers said in a whisper.
- BUT! Please, please,” said another.
Pierre, with bewildered, short-sighted eyes, disobeying, looked around him, and suddenly doubt came over him. "Where I am? What am I doing? Are they laughing at me? Wouldn't I be ashamed to remember this?" But this doubt lasted only for a moment. Pierre looked around at the serious faces of the people around him, remembered everything that he had already passed, and realized that it was impossible to stop halfway. He was horrified by his doubt and, trying to evoke in himself the former feeling of compunction, he threw himself at the gates of the temple. And indeed a feeling of compunction, even stronger than before, came over him. When he had lain for some time, they told him to get up and put on him the same white leather apron that the others had on, gave him a shovel and three pairs of gloves, and then the great master turned to him. He told him to be careful not to stain the whiteness of this apron, representing strength and purity; then he said of an unidentified shovel that he should work with it to cleanse his heart of vices and condescendingly smooth over the heart of his neighbor with it. Then about the first men's gloves he said that he could not know their meaning, but he must keep them, about other men's gloves he said that he should wear them in meetings, and finally about the third women's gloves he said: the essence is defined. Give them to the woman you will honor the most. With this gift, assure the purity of your heart to the one you choose for yourself as a worthy stonemason. And after a pause for a while, he added: “But observe, dear brother, that the gloves of these unclean hands do not adorn.” While the great master uttered these last words, it seemed to Pierre that the chairman was embarrassed. Pierre became even more embarrassed, blushed to tears, as children blush, began to look around uneasily, and there was an awkward silence.
This silence was broken by one of the brothers, who, having brought Pierre to the carpet, began to read to him from the notebook an explanation of all the figures depicted on it: the sun, the moon, the hammer. a plumb line, a shovel, a wild and cubic stone, a pillar, three windows, etc. Then Pierre was assigned his place, showed him the signs of the box, said the input word, and finally allowed to sit down. The great master began to read the charter. The charter was very long, and Pierre, from joy, excitement and shame, was not able to understand what they were reading. He listened only to the last words of the charter, which he remembered.

the same as a statement, in which two concepts are connected - a subject and a predicate (see Proposal). S. expresses the speaker's attitude to the content of the expressed thought through the statement of modality (explicitly or implicitly expressed additional information about the logical or actual status of S., about the regulatory, evaluative, temporal, and other characteristics of it) of what was said and is usually accompanied by psychol. states of doubt, conviction, or faith. S. in this sense, in contrast to the statement, is always modal and has an evaluative character. In the classic logic terms "S." and "statement" are synonymous, and as self. S.'s subject of research is not allocated. V.I.Polishchuk

Great Definition

Incomplete definition ↓

JUDGMENT

In traditional In formal logic (up to Frege's work on logical semantics), S. was understood (with various minor reservations and additions) as an affirmative or negative declarative sentence. However, in the traditional teaching about S., especially in the section on the transformation of the form of judgment, the difference in the use of the terms "S." was also intuitively implied. and "declarative sentence". The former has usually been used as a logical term for assertions (or denials) of "something about something" carried out by means of declarative sentences (in one language or another). The second one served for the linguistic characterization of statements, i.e. remained predominantly a grammatical term. This implicit difference was explicitly expressed in the distinction (in the general case) between the logical structure of S. and the grammatical structure of sentences, which had been carried out since the time of Aristotelian syllogistics. Yes, in the classic attributive S. with the subject (what something is said about, or it is said - the subject of speech) was identified, as a rule, with grammatical. subject, and the predicate (what is said, or is said, about the subject of speech - the subject) was already understood grammatically. predicate and was identified with the nominal part of the predicate, expressed, for example, by an adjective. In contrast to the grammatical, the logical form of saying (the form of S.) has always meant that the subject (subject of S.) has (or does not have) a determinant. sign, i.e. was reduced to an attributive three-term connection: subject - verb-copy - attribute. The indicated difference in the use of the terms "S." and "declarative sentence" led later to a clearer definition of the concepts corresponding to them. Already for B. Bolzano, and then for G. Frege, S. is the content (meaning) of a true (or false) declarative sentence. Characteristics of a (narrative) sentence with t. sp. its truth value goes back to Aristotle and is certainly not new. The main thing that distinguishes the new understanding from the traditional one is the abstraction of the content of the (narrative) sentence - S. in the proper sense of the word - from its truth value and from the material (linguistic) form of its expression, the allocation of S. exclusively as a logical element of speech - an abstract object "...of the same degree of generality as a class, number or function" (Church?., Introduction to Mathematical Logic, Moscow, 1960, p. 32). Essentially new is also the selection of the truth values of sentences - "truth" and "falsehood" (which can be assigned to each declarative sentence as its value) - as independent abstract objects included in the interpretation of logical calculi. This new t. sp. explained the meaning of equivalent transformations in logic based on the principle of volume (see Volume principle, Principle of abstraction): all true sentences are equivalent in the interval of abstraction of identification in meaning (but not in meaning). On the other hand, it allowed to generalize the traditions. the concept of structure S. on the basis of the concept of a logical (or propositional) function, the values of which are sentences, or their truth values. Thus, the sentence "Socrates is a man" in the tradition. understanding corresponded to the scheme "S is P". If in this scheme S and? be understood as variables having different ranges of meanings, or as variables of different semantic levels, or of different sorts, or, finally, belonging to different alphabets: S as a variable on the domain of "individual names", and P as a variable on the domain of "concepts" , then when choosing the concept of "person" as the value of the variable? (or in the general case, assuming the value of the variable? is fixed, i.e., assuming that? has a well-defined, although arbitrary, unspecified value in the given context), the scheme "S is P" is transformed into the expression "S is a person" ( in the general case, in the expression "... there is P", where dots replace the letter S), which, when the variable S is substituted for the individual name (value), "Socrates" turns into a true sentence. Obviously, the expression "... there is a person" (in the general case, the expression "... there is P") is a function of one variable, which takes the values "true" or "false" when the name is put in place of the dots some subject, which plays here the usual role of a function argument. Similarly, the expression "...greater than..." is a function of two variables, and the expression "is between... and..." is a function of three variables, and so on. T. o., modern. view of the structure of S. comes down to the fact that its traditional. the elements "predicate" and "subject" are replaced by exact mats, respectively. concepts of a function and its arguments. This new interpretation responds to the long-felt need for a generalized characterization of the logical. reasoning, which would cover not only (and even not so much) syllogistic, but especially non-syllogistic conclusions - osn. the conclusions of science. In turn, the functional form of S.'s expression opens up wide opportunities for formalizing the proposals of any scientific. theories. (For an explanation of how the subject-predicate structure of S. is characterized and formalized in modern logic, see Quantifier and Predicate Calculus.) M. Novoselov. Moscow. In and dy S. Much attention in the history of logic and philosophy was given to the problem of division into types. One of the most important is the division of S. into simple and complex. The concept of simple S. is already found in Aristotle in his book On Interpretation. Aristotle calls simple here the S. of existence, i.e. S., in which only the existence of the subject S. is affirmed (or denied) (for example, there is a person). Simple S. Aristotle opposes the three-term S., in which, in addition to knowledge of the existence (or non-existence) of the subject of S., there is also knowledge of the inherent (or non-inherent) to the subject of S. to. certainty of being (for example, "man is just"). In the megarostoic school, simple S. was called S., consisting of a subject and a predicate. Complex - called S., formed from simple ones with the help of various kinds of logical. connectives such as negation, conjunction, disjunction, implication. Such an understanding of simple and complex S. is close to their interpretation, which is given in the modern. the logic of statements. Main the headings of the classification of simple S. were also already known to Aristotle: the division of S. by quality (affirmative and negative) and by quantity (general, particular and indefinite) was given by Aristotle in the First Analytics. Traditional textbooks. the logics of dividing S. by quality into affirmative and negative, and by quantity into general and particular (by particular here was meant an indefinite particular judgment of the type "Some, and maybe all S, are P") were combined into one rubric. This rubric was called S.'s division according to quality and quantity. This included four types of C: 1) general affirmative (“all S are P”), 2) general negative (“no S is P”), 3) particular affirmative (“some S are P”), 4) particular negative ( "some S are not P"). The textbooks further examined the relationship between these judgments from the point of view of truth and falsity in the so-called. logical square and the relationship between the volumes of the subject and the predicate of these S. in the so-called. the doctrine of the distribution of terms in judgment. In modern In logic, the types of S. by number include: 1) general S. (S. with a general quantifier), 2) indefinite. private S., to-rye called. simply private (S. with the existential quantifier) and 3) single S. The division of S. into S. of reality, possibility and necessity, later called division by modality, also goes back to Aristotle. By S. of reality, Aristotle meant S., in which we are talking about what actually exists, exists in reality. Under S. Necessity - S., in which we are talking about the fact that it cannot be otherwise. Under S. of possibility - S., in which we are talking about what could be otherwise, i.e. which may or may not be. For example, "Tomorrow there may be a naval battle." In modern utterance logic with modal operators "possible", "impossible", "necessary", etc. are studied in various systems of modal logic. Distinguishing 1) separating and including S. and 2) S. properties and S. relations can also, in a certain sense, be carried out from Aristotle. In the fourth and tenth chapters of the first book of Topics, Aristotle considered the trace. four types of correlation of what is said about an object with the object itself: 1) definition, 2) proper, 3) gender, 4) accidental. According to Aristotle, such a S. should be called a definition, in which the property is revealed. the essence of the object C. That which is expressed in the definition belongs to the object C; it cannot affect another subject. Such a S. should be called a proper S., in which, as well as in the definition, we are talking about something that belongs only to the subject S. But, unlike the definition, what manifests itself in its own S., does not mean the essence of a conceivable object. R about d about m should be called such S., in which incompetence is revealed. the essence of the subject, i.e. such an essence that other objects have, except for the object C. Random should be called everything that, not being the essence of the object C., can, like the genus, affect many other items. This teaching of Aristotle, later called by his commentators the doctrine of precabilia, allows us to establish two more important types of S., namely, distinguishing and including S. on whether this feature is essential (definition) or non-essential (proper). For example, "A square is a rectangle with equal sides" (definition). "Mars is a planet glowing with red light" (proper). It is natural to call inclusive those S., in which we are talking about belonging to the subject of S. of such signs, about which it is known that they belong not only to the subject of S., for example: "The whale is an animal" (genus), "This a person is lying" (random). For the division of S. into S. properties and relations, it is of interest to reduce all categories to three, namely, to "essence", "state" and "relationship", which Aristotle carried out in the 14th book of Metaphysics. On the basis of the categories indicated here, S. can be divided into two types: 1) S. properties, in which they are affirmed as beings. properties (essence) and non-beings. (state), 2) S. relations, in which various kinds of relations between objects are affirmed. Aristotle himself does not yet indicate the division into S. properties and S. relations. This division was apparently first given by Galen (see C. Galenus, Institutiologica, ed. C. Kalbfleisch, Lipsiae, 1896). It has been worked out in great detail by Karinsky (see "On M.I. Karinsky's Logic Course", "VF", 1947, No. 2). In modern times (H. Wolf, I. Kant and in many school textbooks of logic following them) there was also a so-called. S.'s division in relation to categorical, conditional (or hypothetical) and divisive. Under the categorical S. was understood here the general S., in which the connection between the subject and the predicate is established in an unconditional form. S. was called hypothetical (or otherwise conditional), in which the connection between the subject and the predicate becomes dependent on the c.-l. terms. The separating was called S., which contains several predicates, of which only one can refer to the subject, or several subjects, of which only one can refer to the predicate (see M. S. Strogovich, Logic, M. , 1949, pp. 166–67). In modern S.'s division in relation to logic is not recognized. so-called the categorical proposition is identified here with a simple proposition, and various types of conditional and disjunctive propositions are considered as types of complex propositions (see Conditional proposition, Separative proposition). In Kant's classification of S., in addition to the division according to quality, quantity, modality and relation, we also meet the division of S. into 1) a priori and a posteriori, and 2) analytical and synthetic. S. are divided into a posteriori and a priori, depending on the way in which representations or concepts are combined in the act of S.. Kant calls a posteriori those S., in which representations are combined in consciousness in such a way that their connection does not have a generally valid character. On the contrary, "... if any judgment is conceived as strictly universal, i.e. in such a way that the possibility of exception is not allowed, then it is not derived from experience, but is an unconditionally a priori judgment" (I. Kant, Soch., t 3, M., 1964, p. 107). Such a priori S. are, for example, according to Kant, Math. S., axioms of logic, etc. In distinguishing between a priori and a posteriori judgments, Kant tried to solve a problem from the position of a prioriism, which runs through the entire history of philosophy, namely, the problem of the difference between the empirical (fact-fixing) and the theoretical. knowledge. With t. sp. logic, the problem is not to recognize (or not to recognize) the existence of both empirical and theoretical. knowledge. In science, both this and other knowledge exists, and we intuitively can in some cases [for example, in the case of fact-fixing (empirical) and necessary (theoretical) knowledge] distinguish them. The problem is to specify the exact logic. signs, according to which it would be possible to distinguish S., expressing empiric. knowledge (empirical C), from judgments expressing theoretical. knowledge (theoretical C). This problem cannot be considered finally solved, although attempts to solve it are being made (see, for example, Art. V. A. Smirnov, Levels of knowledge and stages of the process of cognition, in the book: Problems of the logic of scientific knowledge, M., 1964). An important role in Kant's philosophy is played by the division of S. into analytical and synthetic. Analytical S. differ from synthetic ones in that they do not add anything to the concept of the subject through their predicate, but only divide it by dividing it into concepts subordinate to it, which have already been conceived in it (albeit vaguely), while synthetic. S. "...they attach to the concept of the subject a predicate that was not conceived in it at all and could not be extracted from it by any division" (ibid., pp. 111–12). The merit of I. Kant on the issue of dividing S. into analytical and synthetic lies primarily in posing this question: he was the first to distinguish the problem of dividing S. into analytical and synthetic from the problem of dividing judgments into empirical (a posteriori) and theoretical (a priori). Before Kant (for example, in Leibniz) these problems were usually identified. At the same time, I. Kant could not indicate the logical. signs to distinguish analytical. S. from synthetic. In the future, the problem of analytical and synthetic S. was discussed repeatedly (see. Synthetic and analytical judgments). The above divisions of S. into species were created by Ch. way to serve the needs of the traditional. formal logic and, above all, for solving problems of the main. its section - the theory of inference. So, the division of S. according to quantity, quality and modality was established by Aristotle for the needs of the theory of syllogistic created by him. conclusion (see Syllogistic). The division of S. into simple and complex ones and the development of the question of the types of complex S. by the logicians of the megarostoic school were required for their study of various types of conditional and disjunctive inferences. The division of S. into S. properties and S. relations arose in connection with the consideration of etc. non-syllogistic reasoning. It is usually believed that the task of formal logic does not include the study of all types and varieties of S that occur in cognition. and the construction of an all-encompassing classification of S. Attempts to construct this kind of classifications have taken place in the history of philosophy [such, for example, Wundt's classification of S. (see W. Wundt, Logik, 4 Aufl., Bd 1, Stuttg., 1920)]. However, it should be noted that, in addition to the formal approach to the question of the types of S., when S. are divided into types according to exactly fixed. logical the foundations of division and the division itself is established to serve the needs of the theory of inference, another, epistemological, is also quite legitimate. approach to this issue. For a correctly understood epistemological approach to the problem of the types of S. characteristic is the interest in the comparative cognitive value of the types of S. known in science and the study of transitions from one type of S. to another in the process of cognition of reality. So, considering from this t. sp. division of S. by quantity, we pay attention to the fact that single S. play basically a dual role in the process of cognition. First, individual S. express and consolidate knowledge about the otd. items. This includes a description of the historical events, characteristics personalities, description of the Earth, the Sun, etc. At the same time, among this kind of single S., we note the transition from the so-called. S. belongings, in which only the belonging of a feature to an object is affirmed, to including and highlighting S., as soon as we establish that the asserted feature belongs not only to this subject (including judgment) or only to this subject (selecting judgment). Secondly, individual S. prepare the afterbirth, the formulation of private and general S. Having studied all the layers of k.-l. geological section and fixing in a number of single S. that each of the studied layers is of marine origin, we can express the general S: "All layers of a given geological section are of marine origin." Concerning the particular S., we note that in the process of cognition of reality, a transition is made from the indeterminate. private S. to the definition. private S. or to general S. Indeed, indefinite. private S. (or simply private S.) is expressed in such cases when, knowing that certain objects of c.-l. class of objects have or do not have a certain feature, we have not yet established either that all other objects of a given class of objects also have (do not have) this feature, or that certain others do not (have) this feature. objects of this class of objects. If it is further established that the Dec. only some or all objects of a given class have a sign, then the particular S. is replaced by a definite. private or general S. So, private S. "Some metals are heavier than water" in the process of studying metals is specified in the definition. private S. "Only certain metals are heavier than water." Particular C. "Some types of mechanical motion pass through friction into heat" is replaced by general C. "Any mechanical movement passes through friction into heat." Def. particular S., solving the problem put forward by private S., namely, the question of whether all or not all objects of a given class of objects have or do not have a certain characteristic, at the same time leaves unresolved the question of which objects have or do not have the approved feature. To eliminate this uncertainty, private S. must be replaced by either a common or multiple allocating S. To move from the definition. private S. to the so-called. multiple allocating S. is required to establish qualities. the certainty of each of those certain objects, which are discussed in the definition. private C. In this case, for example, def. the quotient S. "Only some pupils of this class do well in Russian" is replaced by the plural emphasizing S. "Of all the pupils in this class, only Shatov, Petrov, and Ivanov do well in Russian." The transition to the general distinguishing S. is carried out when one or more of the known common features of certain objects of a given kind can be singled out as a characteristic feature of all these ("some") objects. For example, having learned that all those ("certain") animals referred to in C. "Only certain animals have large intestines" constitute a class of mammals, we can express a general distinguishing C: " All mammals, and only mammals, have large intestines." Transitions of this kind between S. can also be established with t. sp. their modalities and in some other respects (see A. P. Sheptulin, Dialectical materialism, M., 1965, pp. 271–80; Logic, edited by D. P. Gorsky and P. V. Tavanets, M. ., 1956). Lit.: Tavanets P.V., Vopr. theory of judgments., 1955: ?opov P. S., Judgment, M., 1957; Akhmanov A. S., The logical doctrine of Aristotle, M., 1900; Smirnova E. D., On the problem of analytic and synthetic, in: Philos. question modern formal logic, Moscow, 1962; Gorsky D.P., Logic, 2nd ed., M., 1963. P. Tavanets. Moscow.

JUDGMENT

If what is said is evaluated only by the truth value (statements: "A is true" or "A is false"), FROM. called assertoric. If approved (of truth) of what has been said [statement mode: "A - perhaps (true)' or 'it is possible that A (true)"], FROM. called problematic. When is it approved (of truth) of what has been said [statement mode: “But it is necessary (true)" or "it is necessary that A (true)"], FROM. called apodictic. Other assessments of what has been said are, of course, also possible. e.g.“L - excellent” or “L - unsuccessful”, but this kind of S. has not yet found a formal expression in c.-l. logical theories.

In the classic the logic of unity. the method of evaluating what has been said is reduced to the first case considered above, but what has been said and assertoric. said (as Tables 1 and 2 show), With t. sp. this logic,

And true

true lie

false truth

indistinguishable. Therefore, in the classical logic terms "S." and "statement" are synonymous and as independent. objects of S.'s research are not allocated. Subject specialist. studying S. actually become only in modal logic.

Siegwart X., Logic, per. With German, t. 1, St. Petersburg, 1908; What's up? Ch A., Introduction to Mathematics. logic per. With English, t. 1, M., I960, § 04; Face R., Modal , per.[from English], M., 1974.

Philosophical encyclopedic dictionary. - M.: Soviet Encyclopedia. Ch. editors: L. F. Ilyichev, P. N. Fedoseev, S. M. Kovalev, V. G. Panov. 1983 .

JUDGMENT

in logic, a proposition, expressed in the form of a sentence, by which two concepts (and a predicate) are connected; cf. Sentence). In judgment, thought crystallizes. Judgment relates to the subject and, at the same time, to its predicates with the help of the link "is", which is always directed to the absolute state of things being affirmed. For it is characteristic of a true judgment that nothing can be allowed that contradicts this judgment and at the same time has validity. If a given state of affairs exists, then by judgment these conditions are juxtaposed as categorically as the state of affairs itself. The internal, inalienable quality of any judgment is that it contains all possible subjects of knowledge, all possible states of things and necessary conditions. This set of all possible subjects, states of affairs and necessary conditions is governed by one general law - the law of non-contradiction. Kant in the Critique of Pure Reason distinguishes the following types of judgments: 1) by quantity - general, particular and singular; 2) by quality - affirmative, negative, infinite; 3) in relation - categorical, hypothetical, dividing; 4) by modality - problematic, assertoric, apodictic. Analytical, or explanatory, judgments are, according to Kant, judgments, the predicate of which is already contained in advance in the subject (“all bodies are extended”); synthetic, or expanding, judgments - judgments that add to the concept of the subject a predicate that is not yet implied in the knowledge of the subject ("all bodies have weight").

Philosophical Encyclopedic Dictionary. 2010 .

JUDGMENT

The indicated difference in the use of the terms "S." and "declarative sentence" led later to a clearer definition of the concepts corresponding to them. Already for B. Bolzano, and then for G. Frege, S. is the (meaning) of a true (or false) declarative sentence. Characteristics of a (narrative) sentence with t. sp. its truth value goes back to Aristotle and is certainly not new. The main thing that distinguishes understanding from the traditional one is the abstraction of the content of the (narrative) sentence - S. in the proper sense of the word - from its truth value and from the material (linguistic) form of its expression, the allocation of S. exclusively as a logical element of speech - an abstract object " ... of the same degree of generality as , number or " (Church A., Introduction to mathematical logic, M., 1960, p. 32). Essentially new is also the selection of the truth values of sentences - "truth" and "falsehood" (which can be assigned to each declarative sentence as its value) - as independent abstract objects included in the interpretation of logical calculi. This new t. sp. explained equivalent transformations in logic based on the principle of volume (see Volume, Principle of abstraction): all true sentences are equivalent in the interval of abstraction of identification in meaning (but not in meaning). On the other hand, it allowed to generalize the traditions. the concept of structure S. on the basis of the concept of a logical (or propositional) function, the values of which are sentences, or their truth values. Thus, the sentence "Socrates is a man" in the tradition. understanding corresponded to "S is R". If in this scheme S and P are understood as variables having different ranges of values, or as variables of different semantic levels, or of different sorts, or, finally, belonging to different alphabets: – as a variable on the domain of "individual names", and P as variable on the field of "concepts", then when choosing the concept "person" as the value of the variable Ρ (or in the general case, assuming that the variable Ρ is fixed, i.e., assuming that Ρ has a well-defined, albeit arbitrary, unspecified in the given context , meaning) the scheme "S is P" is transformed into the expression "S is a person" (in the general case, into the expression "... is P", where dots replace the letter S), which, when substituting an individual name (value ) "Socrates" turns into a true sentence. Obviously, the expression ". ..there is a person" (in the general case, the expression "...there is P") is a function of one variable, which takes the values " " or "false" when a certain subject is put in place of the dots, playing here the usual the role of the function argument.Similarly, the expression "...greater than..." is a function of two variables, and the expression "is between... and..." is a function of three variables, etc. So. , the modern view of the structure of S. is reduced to the fact that its traditional "predicate" and "subject" are replaced by the exact mathematical concepts of the function and its arguments, respectively. would cover not only (and even not so much) syllogistic, but also in particular - the main conclusions of science.In turn, the functional form of expression S. opens up wide opportunities for formalizing the proposals of any scientific theory.(Explanation of how in modern logic characterizes and formalizes the subject-predicate S. see in Article Quantor and Pr. edicate calculus.)

M. Novoselov. Moscow.

The above divisions of S. into species were created by Ch. way to serve the needs of the traditional. formal logic and, above all, for solving problems of the main. its section - the theory of inference. So, the division of S. according to quantity, quality and modality was established by Aristotle for the needs of the theory of syllogistic created by him. conclusion (see Syllogistic). The division of S. into simple and complex ones and the development of the question of the types of complex S. by the logicians of the megarostoic school were required for their study of various types of conditional and disjunctive inferences. The division of S. into S. properties and S. relations arose in connection with the consideration of etc. non-syllogistic reasoning. It is usually believed that the task of formal logic does not include all the types and varieties of S. found in cognition and the construction of an all-encompassing classification of S. Attempts to construct this kind of classifications took place in the history of philosophy [such, for example, S. by Wundt (see W. Wundt, Logik, 4 Aufl., Bd 1, Stuttg., 1920)].

However, it should be noted that, in addition to the formal approach to the question of the types of S., when S. are divided into types according to exactly fixed. logical the foundations of division and the division itself is established to serve the needs of the theory of inference, another, epistemological, is also quite legitimate. approach to this issue. For a correctly understood epistemological approach to the problem of the types of S. characteristic is the comparative cognitive value of the types of S. known in science and the study of transitions from one type of S. to another in the process of cognition of reality. So, considering from this t. sp. division of S. by quantity, we pay attention to the fact that single S. play basically a dual role in the process of cognition. First, individual S. express and consolidate knowledge about the otd. items. These include historical events, characteristics personalities, description of the Earth, the Sun, etc. At the same time, among this kind of single S., we note the transition from the so-called. S. belongings, in which only the belonging of a feature to an object is affirmed, to including and highlighting S., as soon as we establish that the asserted feature belongs not only to this subject (including judgment) or only to this subject (selecting judgment). Secondly, individual S. prepare the afterbirth, the formulation of private and general S. Having studied all the layers of k.-l. geological section and fixing in a number of single S. that each of the studied layers is of marine origin, we can express the general S: "All layers of a given geological section are of marine origin."

Concerning the particular S., we note that in the process of cognition of reality, a transition is made from the indeterminate. private S. to the definition. private S. or to general S. Indeed, indefinite. private S. (or simply private S.) is expressed in such cases when, knowing that certain objects of c.-l. class of objects have or do not have a certain feature, we have not yet established either that all other objects of a given class of objects also have (do not have) this feature, or that certain others do not (have) this feature. objects of this class of objects. If it is further established that the Dec. only some or all objects of a given class have a sign, then the particular S. is replaced by a definite. private or general S. So, private S. "Some metals are heavier than water" in the process of studying metals is specified in the definition. private S. "Only certain metals are heavier than water." Particular C. "Some types of mechanical motions pass through friction into heat" is replaced by general C. "Any mechanical movement passes through friction into heat." Def. particular S., solving the problem put forward by private S., namely, whether all or not all objects of a given class of objects have or do not have a certain characteristic, at the same time leaves unresolved the question of which objects have or do not have a valid attribute. To eliminate this uncertainty, private S. must be replaced by either a common or multiple allocating S. To move from the definition. private S. to the so-called. multiple allocating S. is required to establish qualities. the certainty of each of those certain objects, which are discussed in the definition. private C. In this case, for example, def. the quotient S. "Only some pupils of this class do well in Russian" is replaced by the plural emphasizing S. "Of all the pupils in this class, only Shatov, Petrov, and Ivanov do well in Russian." The transition to the general distinguishing S. is carried out when one or more of the known common features of certain objects of a given kind can be singled out as a characteristic feature of all these ("some") objects. For example, having learned that all those ("certain") animals referred to in C. "Only certain animals have large intestines" constitute a class of mammals, we can express a general distinguishing C: " All mammals, and only mammals, have large intestines." Transitions of this kind between S. can also be established with the so-called. sp. their modalities and in some other respects (see A. P. Sheptulin, Dialectical, M., 1965, pp. 271–80; Logic, edited by D. P. Gorsky and P. V. Tavanets, M. , 1956).

Lit.: Tavanets P.V., Vopr. theory of judgments., 1955: P. S. Popov, Judgment, M., 1957; Akhmanov A. S., The logical doctrine of Aristotle, M., 1900; Smirnova E. D., On the problem of analytic and synthetic, in: Philos. question modern formal logic, Moscow, 1962; Gorsky D.P., Logic, 2nd ed., M., 1963.

P. Tavanets. Moscow.

Philosophical Encyclopedia. In 5 volumes - M .: Soviet Encyclopedia. Edited by F. V. Konstantinov. 1960-1970 .

JUDGMENT

JUDGEΕΗИΕ - a thought that affirms the presence or absence of any state of affairs. Distinguish between simple and complex sentences. A proposition is called simple if it is impossible to single out the correct part, that is, the part that does not coincide with the whole, which in turn is a proposition. The main types of simple judgments are attributive and relationship judgments. Judgments are called attributive, in which the belonging to objects of properties or the absence of objects of any properties is expressed. Attributive judgments can be interpreted as judgments about the full 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 in some there are also so-called quantifier (quantitative) words (“some”, “all”, “none”, etc.). The subject and the predicate are called terms of judgment.

The subject is often denoted by the Latin letter S (from the word “subjectum”), and the predicate - P (from the word “praedicatum”). In the judgment “Some sciences are not humanities”, the subject () is “sciences”, the predicate () is “humanities”, the connective is “are not”, and “some” is quantifier. Attributive judgments are divided into types "by quality" and "by quantity". By quality, they are affirmative (the link “essence” or “is”) and negative (the link “is not the essence” or “is not”). By quantity, attributive judgments are divided into single, general and particular. In singular judgments, the belonging or non-belonging of an object to a class of objects is expressed. In general - or non-inclusion of a class of objects in a class.

In particular judgments, the partial inclusion or non-inclusion of a class of objects in a class of objects is expressed. In them the word "some" is used in the sense of "at least some, and maybe all."

Judgments of the form “All S are Ps> (general affirmative), “No S is su P” (general negative), “Some S are P” (particular affirmative), “Some S are not P” (particular negative) are called categorical. Terms in categorical judgments can be distributed (taken in full) and not distributed (taken not in full). Subjects are distributed in general judgments, and predicates in negative ones. The remaining terms are not assigned.

Judgments that say that a certain relation takes place (or does not take place) between the elements of pairs, triplets, etc. of objects are called judgments about relations. They are divided by quality into affirmative and negative. According to the number of judgments about two-place relations, they are divided into single-single, general-general, private-private, singular-general, single-private, common-singular, private-single, general-private, private-general. For example, the proposition “Each student of our group knows some academician” is a general-private one. Similarly, the division into types according to the number of judgments about tripartite, quadruple, etc. relationships. Thus, the proposition “Some students of the Faculty of Philosophy know some ancient languages better than any modern foreign language” is private-private-general.

In addition to attributive and relationship judgments, existence judgments (of the type “Aliens exist”) and judgments of identity (equality) (of the “a=fe>” type) are distinguished as special types of simple judgments.

The described judgments, as well as complex judgments formed from them, are called assertoric. They are (simply) affirmations or negations. Along with affirmations and denials, so-called strong and weak affirmations and denials are singled out. For example, strengthening the assertoric judgments “Communication with their own kind is inherent in a person”, “A person does not live forever”, “A person has soft earlobes” are, respectively, the judgments “A person necessarily has the property of communication with his own kind”, “A person cannot live forever ”, “A person accidentally has soft earlobes.” Strong and weak affirmations and negations are alethic modal judgments. Among them are judgments of necessity (apodictic), possibility and chance.

There are several types of complex judgments. Connective propositions are propositions that assert the existence of two or more situations. In natural language, they are formed from other judgments most often through the union “and”. This union is denoted by the symbol l, which is called the sign of the (commutative) conjunction. A judgment with this conjunction is called (commutatively) conjunctive. The definition of the conjunction sign is a table showing the dependence of the value of a conjunctive judgment on the values of its constituent judgments. In it, “and” and “l” are abbreviations for the values “true” and “false”.

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 propositions with the help of unions, denoted by the symbols T-t, 7s, etc., depending on the number of propositions from which they are formed. These symbols are called non-commutative conjunction signs and are respectively read “..., and then...”, *..., then..., and then...”, etc. Indices 2,3, etc. . indicate the locality of the union.

Separating judgments are judgments in which the presence of one of two, three, etc. situations is affirmed. If the existence of at least one of the two situations is asserted, the judgment is called (loosely) disjunctive, or disjunctive. If the existence of exactly one of two or more situations is asserted, the judgment is called strictly disjunctive, or strictly disjunctive. The union “or”, by means of which the statement of the first type is expressed, is denoted by the symbol ν (read “or”), called the sign of non-strict disjunction (or simply the sign of disjunction), and the union “or ..., or ...”, by means of which statement of the second type, - by the symbol y (it is read “either ..., or ...”), called the sign of strict disjunction. Tabular definitions of signs of non-strict and strict disjunction:

A judgment in which it is stated that the presence of one situation determines the presence of is called conditional. Conditional propositions are most often expressed in sentences with the union “if ..., then ...”. The conditional union “if..., then...” is indicated by the arrow “->”.

In the languages of modern logic, the union “if ..., then ...”, denoted by the symbol “e”, is widely used. This is called the sign of the (material) implication, and the judgment with this union is called the implicative. The part of the implicative proposition that is between the words "if" and "then" is called the antecedent, and the part that is after the word "then" is called the consequent. The sign of the implication is determined by the truth table:

An equivalence judgment is a judgment that asserts the mutual conditionality of two situations. The conjunction "if and only if...then..." is used in yet another sense. In this case, it is denoted by the symbol “=”, called the sign of material equivalence, which is determined by the truth table:

Judgments with this union are called judgments of material equivalence.

The simple illogical modal judgments have been characterized above. Compound judgments formed from other judgments by means of the expressions “it is necessary that”, “accidentally that”, it is possible that” are also called alethic modal judgments. Alethic modal judgments are also complex judgments, the individual components of which are alethic modal judgments. Alethic modal concepts (“necessary”, “accidentally”, “possibly”) are divided into logical and actual (physical). A state of affairs may be logically possible or factually possible, logically necessary or actually necessary, logically accidental or actually accidental. What is logically possible is that which does not contradict the laws of logic. In fact, that is possible that does not contradict the laws of nature and social life.