What is not a judgment in logic? Judgment

Affirming or denying something about the existence of objects, about the connections between them and their properties, as well as about the relationships between objects.

Examples of judgments: “The Volga flows into the Caspian Sea”, “A.S. Pushkin wrote the poem “ Bronze Horseman", "The Ussuri tiger is listed in the Red Book", etc.

Structure of judgment

A proposition includes the following elements: subject, predicate, connective and quantifier.

The subject (lat. subjektum - “underlying”) is what is said in this judgment, its subject (“S”).
Predicate (Latin praedicatum - “said”) is a reflection of the attribute of an object, what is said about the subject of the judgment (“P”).
A connective is a relationship between a subject (“S”) and a predicate (“P”). Determines the presence/absence of the subject of any property expressed in the predicate. It can be either implied or indicated by the “dash” sign or the words “is” (“is not”), “is”, “is”, “essence”, etc.
A quantifier (quantifier word) determines the scope of the concept to which the subject of the judgment belongs. Stands before the subject, but may also be absent from the judgment. Denoted by words such as “all”, “many”, “some”, “none”, “no one”, etc.

True and false propositions

A judgment is true in the case when the presence of signs, properties and relationships of objects affirmed/denied in the judgment corresponds to reality. For example: “All swallows are birds”, “9 is more than 2”, etc.

If the statement contained in the judgment is not true, we are dealing with a false proposition: “The sun revolves around the Earth,” “A kilogram of iron is heavier than a kilogram of cotton wool,” etc. Correct judgments form the basis of correct conclusions.

However, in addition to two-valued logic, in which a proposition can be either true or false, there is also multidimensional logic. According to its conditions, the judgment may also be indefinite. This is especially true for future individual judgments: “Tomorrow will happen / will not happen naval battle"(Aristotle, "On Interpretation"). If we assume that this is a true proposition, then a naval battle cannot but happen tomorrow. Therefore, it is necessary for it to happen. Or vice versa: asserting that this judgment in currently is false, we thereby make necessary the impossibility of tomorrow

Judgments by type of statement

As you know, according to the type of statement, three types are distinguished: incentive and interrogative. For example, the sentence “I remember wonderful moment" refers to the narrative type. It is useful to propose that such a judgment will also be narrative. It contains certain information and reports a certain event.

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

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

Quality of judgment

From the point of view of quality, judgments can be either affirmative (S is P) or negative (S is not P). In the case of an affirmative proposition, with the help of a predicate the subject is given a certain property(s). For example: “Leonardo da Vinci is an Italian painter, architect, sculptor, scientist, naturalist, as well as inventor and writer, the largest representative of Renaissance art.”

In a negative judgment, on the contrary, the property is taken away from the subject: “James Vickery's theory of the 25th frame has no experimental confirmation.”

Quantitative characteristics

Judgments in logic can have general character(applicable to all subjects of this class), private (for some of them) and singular (when we are talking about an object that exists in a single copy). For example, one could argue that a proposition such as “All cats are gray at night” would refer to general appearance, since it affects all felines (subject of judgment). The statement “Some snakes are not poisonous” is an example of a private judgment. In turn, the judgment “Wonderful is the Dnieper in calm weather” is isolated, since we are talking about one specific river that exists in a single form.

Simple and complex judgments

Depending on the structure, the judgment can be of the simple or complex type. The structure of a simple judgment includes two related concepts (S-P): “A book is a source of knowledge.” There are also judgments with one concept - when the second is only implied: “It was getting dark” (P).

A complex form is formed by combining several simple propositions.

Classification of simple judgments

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

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

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

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

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

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

Complex judgments and types of logical connectives

As already noted, complex judgments consist of several simple ones. The following techniques serve as logical connections between them:

Simple and complex judgments

Simple judgments- judgments, the components of which are concepts. A simple judgment 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 (links). The logical feature of a complex judgment depends on the conjunction with which simple judgments are connected.

Composition of a simple judgment

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

The subject of judgment is a thought about some object, a concept about the subject of judgment (logical subject).
The predicate of a judgment is a thought about a certain part of the content of an object that is considered in a judgment (logical predicate).
A logical connective is a thought about the relationship between an object and a 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.

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 that is not supported real achievements, gradually fades away"), each of which in mathematical logic denoted by with Latin letters(A, B, C, D... a, b, c, d...). Depending on the method of education, they distinguish conjunctive, disjunctive, implicational, equivalent and negative judgments.

Disjunctive judgments are formed using dividing (disjunctive) logical connectives (similar to the conjunction “or”). Like simple disjunctive judgments, they are:

Implicational judgments are formed using implication (equivalent to the conjunction “if ... then”). Written as or . IN natural language the conjunction “if ... then” is sometimes synonymous with the conjunction “a” (“The weather has changed and, if yesterday it was cloudy, then today there are not a single cloud”) and, in this case, means a conjunction.

Conjunctive judgments are formed using logical connectives of combination or conjunction (equivalent to a comma or conjunctions “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 (they draw an equal sign between them). In addition to definitions that explain a term, they can be represented by judgments connected by the conjunctions “if only,” “necessary,” “sufficient” (for example: “For a number to be divisible by 3, it is sufficient that the sum of the digits that make it up is divisible by 3 "). It is written as (different mathematicians have different ways, although mathematical sign identities after all).

Negative judgments are constructed using connectives of negation “not”. They are written either as a ~ b, or as a b (for internal negation like “a car is not a luxury”), as well as using a bar over the entire judgment for 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 don’t give in to flattery.”

By volume

Are common- judgments that are valid regarding the entire scope of the concept (All S are P). Example: “All plants live.”
Private- judgments that are true regarding part of the scope of the concept (Some S are P). Example: “Some plants are conifers.”

In relation to

Categorical- judgments in which the predicate is stated 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 a (previous) proposition that contains a condition.
- Consequence is a (subsequent) judgment that contains a consequence.

In relation between subject and predicate

Logical square describing the relationships between categorical judgments

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

Judgments A (generally affirmative judgments) Distributes its subject (S) but does not distribute its predicate (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 coincide

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

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

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

Note: “No insect is a vertebrate.”

Judgments I (particular affirmative propositions) Neither subjects (S) nor predicates (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 (partial 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 poisonous teeth (S)”

subject and predicate distribution table

General classification:

universally affirmative (A) - both general and affirmative ("All S+ are P-")
private affirmative (I) - quotient and affirmative ("Some S are P-") Note: “Some people have black skin.”
general negative (E) - general and negative (“No S+ is a P+”) Note: “No man is omniscient”
partial negative (O) - quotient and negative (“Some S are not P+”) Note: “Some people are not black.”

Other

Separating -

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 disjunctive 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 Note: “If anyone wants to receive higher education, then he must study either at a university, or at an institute, or at an academy"

Identity propositions- the concepts of subject and predicate have the same scope. Example: "Everyone equilateral triangle there is an equiangular triangle."
Judgments of subordination- a concept with a less wide scope is subordinate to a concept with a wider scope. Example: “A dog is a pet.”
Attitude judgments- namely space, time, relationships. Example: “The house is on the street.”

Existential judgments or existence judgments are those judgments that attribute only existence.
Analytical judgments- judgments in which we express something regarding 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 judgment: time of judgment, place of judgment, knowledge of judgment, attitude of the speaker to judgment.

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

Judgments of possibility- "S is probably P" ( opportunity). Example: “A meteorite may fall to Earth.”
Assertoric- “S is P” ( reality). Example: “Kyiv stands on the Dnieper.”
Apodictic- “S must necessarily be P” ( necessity). Example: “Two straight lines cannot close a space.”

Notes

Literature

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

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Synonyms
Krasnozavodsk

Solnechnogorsk district, Moscow region

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, valuable... IN previous chapter we have defined logic as the discipline that studies the relation of implication between propositions, that is, the relation between premises and conclusions, with the help of which the truth or falsity of one set determines the truth or falsity of another. Thus, both premises and conclusions are propositions, and, based on the problems facing logic, a proposition can be defined as anything that can be true or false. This definition
It will be clearer if we also say what the judgment is not. 1. A proposition is not the same as the sentence in which it is stated. At three different offers – “I think, therefore I exist”, “Je pense, done je suis”, “Cogito ergo sum” - the same judgment is stated. A sentence is a group of words, and words, like all other symbols, are themselves physical objects , different from what they point to or symbolize. When written, sentences occupy certain surfaces, and when spoken, they are sound waves passing from one organism to another. However, a judgment, the verbal expression of which is a sentence, is different from visible marks or sound waves
2. At the same time, along with the need to distinguish a judgment from the symbols in which it is expressed, it should be noted that not a single judgment can be expressed or transmitted without symbols. Therefore, the structure of a judgment must be expressed and communicated through an appropriate structure of symbols. This is required so that the judgment cannot be conveyed using any combination of symbols. “John the rat is blue Jones,” “walk sat down and eat very much” are not symbols expressing judgments. These symbols are simply nonsense, unless, of course, we are dealing with some kind of code. Only certain arrangements of symbols can express a proposition. And that is why the study of notation systems is of invaluable importance for the correct analysis of the structure of judgments. And that is why the grammar of a language, despite the dissimilarity between grammatical and logical analysis, is often able to clarify differences that are logical in nature.
3. Judgment, as we said, is that in relation to which questions about truth and falsity are understood. Consequently, when Hamlet exclaims: “O my thought, from now on you must be bloody, or dust is your price!” or when he asks: “Why do you produce sinners?”, he does not assert any judgment, and if he does, it is only implicitly. The point is that wishes, questions or commands themselves cannot be true or false. It should be noted that the intelligibility of wishes, questions and commands is based on the assumptions that certain states of affairs prevail. And such assumptions contain judgments. For example, consider the question: “Why do you produce sinners?” It, among many other propositions, undoubtedly assumes that the person addressed exists, is capable of giving birth to children, and that these children will necessarily be sinners. Similarly, in the exclamation “Oh my thought, from now on you must be bloody, or dust is your price!” it is assumed that the speaker is capable of having thoughts, that these thoughts can be deadly, that they can have some value, etc. Moreover, a command or wish can be represented in a declarative form, which, as a rule, expresses a certain judgment. An example of this are the following reformulations: “I want you to come,” “I will be pleased if you come,” “you will regret it if you don’t come.” Declarations are judgments to the extent that what they say may be true or false.
4. Judgments are often confused with the mental acts necessary to have a judgment. This confusion stems from understanding the term “judgment” as a substantivized verb. This leads to vagueness, because in some cases this term denotes the mental act of making a certain judgment, and in others - the judgment itself, as the content of such an act. However, just as we distinguished between a judgment (as an objective meaning) and the sentence in which it is expressed, we must distinguish between a judgment and the mental act associated with making a judgment.
5. Judgments should also not be identified with any specific object, thing or event. They are in best case scenario only individual abstract relationships between things. When we affirm or deny the proposition “The Moon is closer to the Earth than the Sun,” then neither the Moon, nor the Earth, nor the Sun, nor the distance between them, is a proposition. A proposition is a relation which is asserted to exist between these bodies. Such relations as the objects of our thought are elements or aspects of real, specific situations. These aspects are in an inextricable spatiotemporal connection with all other constituent elements of the corresponding situations, but they distinctive feature lies in their meaning. That is why sensory experience cannot turn into knowledge without reflective analysis of what we perceive. And knowledge is knowledge of judgments, and one can possess it only by distinguishing the relationships present between the abstract properties of the corresponding situation.
6. We have defined a proposition as something capable of being true or false. However, this does not mean that we are obliged to know its truth value. “Cancer can be cured” is a proposition, but we do not know whether it is true or not.

This, however, leads to the well-known difficulty that we are sometimes unable to determine whether a certain sentence expresses a proposition. Consider, for example, the expression “a yard is three feet.” Are we asking a question about truth or falsity when we formulate it? It must be admitted that this proposal has the form of a sentence expressing a certain judgment. However, if we analyze its content, we will find that it expresses a resolution rather than something capable of being true or false. We decide to use a unit of three feet. However, the resolution as such cannot be attributed to truth or falsity. Resolutions, often taking the form of definitions, are expressed in ways similar to the way judgments are expressed, but they must be distinguished from judgments.

The question whether the word "yard" is used as defined is, of course, a matter of fact, and the answer to it may be true or false. However, in these judgments we are talking about linguistic use, and not about the objects denoted by the words that make up the judgments.

7. Another difficulty arises from the fact that we often believe that the same propositions can sometimes be true and sometimes false. However, our definition of a proposition excludes this possibility and assumes that if a proposition is true, then it must always be true. How often simple people use similar remarks: “What you say may be true, but not always.” This position refers to statements such as “religion teaches you to love your neighbors,” “it is hard to resist temptation,” “the sword does not cut off a guilty head.” We can overcome this difficulty by recognizing that if given propositions claim that something is a universal rule, then the presence of an exception will only prove them false. The proposition “sometimes religion teaches you to hate your neighbors” does not assert the absurd idea that the general proposition “religion always teaches you to hate your neighbors” is sometimes true.

May be, next example will allow you to better understand this idea. It seems that the proposition "the present governor of Connecticut is Dr. Cross" is true for certain years, but, of course, not for all time. Similar analysis, however, is inadequate since the phrase "current governor" certainly implies specific date. Thus, by explicitly including the desired date in our expression, we obtain expressions for different propositions, some of which will be true and some of which will be false. Generally speaking, the statements we make in everyday speech rarely contain all the necessary conditions to determine their truth or falsity. We are aware of some of these conditions, but we are not aware of others. An incomplete expression is neither true nor false. And when we say that a certain proposition is sometimes true and sometimes false, we only mean that the statement we are using can be completed different ways, sometimes expressing true and sometimes false judgments.

Judgments can be simple or complex; the latter consist of several simple ones. The proposition “Some animals store supplies for the winter” is simple, but the proposition “Autumn has come, the days have become shorter, and migratory birds have gone to warmer climes"- complex, consisting of three simple judgments.

Types of simple assertoric judgments

These are judgments that have one subject and one predicate. There are three types of simple propositions:

1 . Property judgments (attributive).

They affirm or deny that an object belongs to known properties, states, and types of activity. Examples: “Honey is sweet,” “Chopin is not a playwright.” Schemes of this type of judgment: “S is P” or “S is not P.”

2. Judgments with relationships.

They talk about relationships between objects. For example: “Every proton is heavier than an electron”, “The French writer Victor Hugo was born later than the French writer Stendhal”, “Fathers are older than their children”, etc.

A formula expressing a judgment with a two-place relation is written as aRb or R(a, b), where a and b are the names of objects, and K is the name of the relation. In a judgment with an attitude, something can be affirmed or denied not only about two, but also about three, four or more objects, for example: “Moscow is located between St. Petersburg and Kiev.” Such judgments are expressed by the formula R(a„ a 2, a 3, ..., a„).

3. Judgments of existence (existential).

They affirm or deny the existence of objects (material or ideal) in reality. 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. Based on the quality of the connective (“is” or “is not”), categorical judgments are divided into affirmative and negative. The propositions “Some teachers are talented educators” and “All hedgehogs are prickly” are affirmative. The propositions “Some books are not second-hand books” and “No rabbit is a predatory animal” are negative. The connective “is” in an affirmative judgment reflects the inherent nature of the object (objects) of certain properties. The connective “is not” reflects the fact that an object (objects) does not have a certain property.

Some logicians believed that negative judgments do not reflect reality. In fact, the absence of certain characteristics also constitutes a valid characteristic that has objective significance. In a negative true judgment, our thought separates (separates) what is separated in the objective world.

In cognition, an affirmative judgment has, in the general case, higher value than negative, because it is more important to reveal what attribute 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. ).

Depending on whether the subject is talking about the entire class of objects, a part of this class, or one object, judgments are divided into general, particular and individual. For example: “All sables are valuable fur-bearing animals” and “All sane people want a long, happy and useful life” (P. Bragg) are general judgments; “Some animals are waterfowl” - private; “Vesuvius is an active volcano” - single.

The structure of a general judgment: “All S are (are not) P.” Single judgments will be treated as general, since their subject is a single-element class.

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

Among general propositions there are exclusionary propositions, for example: “All metals at a temperature of 20°C, with the exception of mercury, are solid.” Exclusive judgments also include those that express exceptions to certain rules of Russian or other languages, rules of logic, mathematics, and other sciences.

Particular propositions have the structure: “Some S are (are not) P.” They are divided into indefinite and definite. For example, “Some berries are poisonous” is an indefinite private proposition. We have not established whether all berries have the sign of toxicity, but we have not established that some berries do not have the sign of toxicity. If we have established that “only some S have the attribute P,” then this will be a certain private judgment, the structure of which is: “Only some S are (are not) P.” Examples: “Only some berries are poisonous”; "Only some figures are spherical"; “Only some bodies are lighter than water.”

In certain private judgments they often use quantifier words: majority, minority, quite a few, not all, many, almost all, several, etc.

In a single judgment, the subject is a single concept. Single propositions have the structure: “This S is (is not) P.” Examples of single propositions: “Lake Victoria is not located in the USA”; "Aristotle - educator of Alexander the Great"; "The Hermitage is one of the world's largest art, cultural and historical museums."

Combined classification of simple categorical judgments by quantity and quality

Every judgment has a quantitative and quality characteristics. Therefore, logic uses a combined classification of judgments by quantity and quality, on the basis of which the following four types of judgments are distinguished:

1. A is a generally affirmative proposition. Its structure: “All “S are P.” For example: “All people want happiness.”

2. I - private affirmative proposition. Its structure is: “Some S are P.” For example, “Some lessons stimulate students' creativity.” The symbols for affirmative propositions are taken from the word AFFIRMO, or I affirm; in this case, the first two vowels are taken: A - to denote a general affirmative and I - to denote a particular affirmative judgment.

E is a generally negative judgment. Its structure: “No S is a P.” Example: “No ocean is freshwater.”

O is a partial negative proposition. Its structure is: “Some S are not P.” For example, “Some athletes are not champions». Olympic Games Symbol

for negative judgments taken from the word NEGO, or I deny.

Since a simple categorical judgment consists of the terms S and P, which, being concepts, can be considered from the side of volume, any relationship between S and P in simple judgments can be depicted using Euler’s circular diagrams, reflecting the relationships between concepts. In judgments, the terms S and P can be either distributed or undistributed. A term is considered distributed if its scope is completely included in or completely excluded from the scope of another term. A term will be unallocated if its scope is partially included in or partially excluded from the scope of another term. Let's analyze four types of judgments: A, I, E, O (we are considering typical cases).

Judgment A is generally affirmative. Its structure: “All S are P.” Let's consider two cases.

1. In the judgment “All crucian carp are fish,” the subject is the concept of “crucian carp,” and the predicate is the concept of “fish.” The general quantifier is “all”. The subject is distributed, since we are talking about all crucian carp, i.e. its scope is completely included in the scope of the predicate. The predicate is not distributed, since only part of the fish that coincide with crucian carp is thought of in it; we are talking only about that part of the volume of the predicate that coincides with the volume of the subject.

2. In the proposition “All squares are equilateral rectangles” the terms are: S - “square”, P - “equilateral rectangle” and the general quantifier - “all”. In this judgment, S is distributed and P is distributed, because their volumes completely coincide.

If S is equal in volume to P, then P is distributed. This happens in definitions and in distinguishing general judgments.

Judgment I is privately affirmative. Its structure: “Some S are P.” Let's consider two cases.

1. In the judgment “Some teenagers are philatelists” the terms are:

S - “teenager”, P - “philatelist”, quantifier of existence - “some”. The subject is not distributed, since only a part of teenagers is thought of 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).

2. In the proposition “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 the writers are thought of 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. Thus, P is distributed if the volume of P is less than the volume of S, which happens in partial allocating judgments.

Judgment E is generally negative. Its structure: “No S is a P.” For example: “No lion is a herbivore.” The terms in it are: S - “lion”, P - “herbivore” and the quantifier word - “none”. Here the scope of the subject is completely excluded from the scope of the predicate, and vice versa.

Judgment O is a partial negative. Its structure: “Some S are not P.” For example: “Some students are not athletes.” It contains the following terms: S - “student”, P - “athlete” and the quantifier of existence - “some”. The subject is not distributed, since only a part of the students is thought of, but the predicate is distributed, because all the athletes are thought of in it, none of whom is included in that part of the students that is thought of in the subject.

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

Relations between simple propositions

The relationships between simple judgments are determined, on the one hand, by their specific content, and on the other, by their logical form: the nature of the subject, predicate, logical connective. Since, according to the nature of the predicate, simple judgments are divided primarily into attributive and relational judgments, we will consider each of these types separately.

Relations between attributive judgments. In terms of their content, attributive judgments can be found in the two most important relations of comparability and incomparability.

Incomparable judgments. They have different subjects or predicates or both. Such are, for example, the judgments “Space is vast” and “The law is harsh.” In such cases, the truth or falsity of one of the judgments does not directly depend on the truth or falsity of the other. It is directly determined by the attitude towards reality, compliance or non-compliance with it. True, in conditions of universal connection and interaction of objects and phenomena of reality, judgments about them cannot be absolutely independent of each other. Only their relative independence and independence from the point of view of truth or falsity is obvious. So if the proposition “Energy is conserved” is true (and does not disappear and does not arise from nothing, as the law of conservation and transformation of energy says), then the proposition “Energy is conserved” will be false. Perpetual motion machine possible,” although in terms of specific content they have nothing in common, neither subject nor predicate, and, therefore, are incomparable.

So in a sentence the subject or predicate can be the same. For example: “The law is harsh” and “The law has come into force” or “The law has come into force” and “The decree has come into force.” And although semantic difference here less than in the previous case, they also cannot correlate with each other in truth or falsity. Therefore, they are not analyzed further.

Comparable judgments. They, on the contrary, have the same terms - both subject and predicate, but can differ in quantity and quality. These are judgments, as they say, of “the same matter,” and, therefore, comparable in truth and falsity.

In its own way logical form First of all, based on quantity and quality, comparable judgments are divided into compatible and incompatible.

Compatible propositions contain the same thought in whole or in part. The following logical relations arise between them: equivalence, subordination, partial compatibility.

Equivalence (equivalence) is the relationship between judgments in which the subject and predicate are expressed by the same or equivalent concepts (although in different words), and both quantity and quality are the same. Such, for example, are the generally affirmative propositions “All lawyers are lawyers” and “All defense attorneys in court have a special legal education.” The situation may be similar with general negative, particular affirmative and particular negative judgments. The relations between such judgments in terms of their truth or falsity are characterized by one-to-one correspondence: they are either simultaneously true or simultaneously false. Therefore, if one is true, then the other is true, and if one is false, then the other is false.

Subsequent relationships between simple attributive judgments - A, E, I, O - are depicted graphically for clarity in the form of a logical square.

Its peaks symbolize simple categorical judgments - A, E, I, O; sides and diagonals of the relationship between judgments. Opposite (contrary) (Fig. 3.2.1).

Rice. 3.2.1. Logical square

Subordination- this is the relationship between such judgments for which the quantity is different, but the quality is the same. In this relation there are generally affirmative (A) and particular affirmative (I), generally negative (E) and particular negative (O) propositions. When subordinating, the following laws apply:

a) the truth of the subordinate (A or E) implies the truth of the subordinate (I or O, respectively), but not vice versa;

b) from the falsity of the subordinate (I or O) follows the falsity of the subordinating one (A or E, respectively), but not vice versa.

Examples. If it is true A that “All lawyers are lawyers,” then it is even more true that “At least some lawyers are lawyers.” But if it is true that “Some witnesses are truthful,” then it does not follow that A is true: “All witnesses are truthful.” IN in this case this is a false proposition. In other cases A may be true. For example: if it is true that “Some lawyers are lawyers,” then A is true that “All lawyers are lawyers.” In turn, if it is false I that “Some citizens have the right to break laws,” then it is even more false A that “All citizens have the right to break laws.” But if A is false, “All witnesses are truthful,” then it does not follow that I is false: “Some witnesses are truthful.” In this case it is a true proposition. In other cases, I may be false. For example: if A is false, “All citizens have the right to break laws,” then I, “Some citizens have the right to break laws,” is also false. It will be true E that “No citizen has the right to break the laws.”

Partial compatibility (subcontrary)- this is the relationship between judgments of the same quantity, but of different quality: between partial affirmative (I) and partial negative (O) judgments. It is characterized by the following pattern: both judgments can be true at the same time, but cannot be false at the same time. From the falsity of one of them follows the truth of the other, but not vice versa. For example, if I is true that “Some witnesses are truthful,” it may also be true O that “Some witnesses are not truthful.” But it may also be false. For example, if it is true that “Some lawyers are lawyers,” this does not mean that O: “Some lawyers are not lawyers” is true. It is false. However, if it is false I that “Some citizens have the right to break laws,” then it cannot be false O that “At least some citizens do not have the right to break laws.” It will certainly be true.

Incompatible judgments. They have the following logical relationships: opposites and contradictions.

Contrast is the relationship between generally affirmative (A) and generally negative (E) judgments. Both such propositions cannot be simultaneously true, but they can be false at the same time. The truth of one necessarily implies the falsity of the other, but not vice versa. Here, therefore, there is a pattern opposite to that which characterized relations of partial compatibility. Thus, if A is true, “All lawyers are lawyers,” then E is false, “No lawyer is a lawyer.” And if E is true that “No citizen has the right to break laws,” then A is false that “All citizens have the right to break laws.” But if A is false, that “All witnesses are truthful,” then it does not follow that E is true, that “No witness is truthful.” In this case it is also false. It is true here I that "Some witnesses are truthful." It is false that "Some witnesses are not truthful." In other cases E may be true. Thus, if A is false, “All citizens have the right to break laws,” then E is true, “No citizen has the right to break laws.”

Contradiction (contradiction)- the relationship between such judgments as general affirmative (A) and particular negative (O), general negative (E) and particular affirmative (I). They have the following laws: they cannot be true at the same time and they cannot be false at the same time. The truth of one necessarily implies the falsity of the other and vice versa. These are the “most incompatible” of all judgments; between them, figuratively speaking, there is a “cat and dog” relationship, since they cannot get along with each other.

Examples. If A is true that “All lawyers are lawyers,” then O that “Some lawyers are not lawyers” is false. If A is false, “All witnesses are truthful,” then O is true, “Some witnesses are not truthful.”

Knowledge of the relationships between simple attributive judgments in terms of their truth and falsity is important in cognitive and practical terms. It helps, first of all, to avoid possible logical errors in your own reasoning. Thus, the truth of a general judgment (A or E) cannot be deduced from the truth of a particular judgment (I or O). For example, from the fact that “Some judges are incorruptible,” it does not follow that “All judges are incorruptible.” In logic, such a mistake is called a hasty generalization and is often made.

In a discussion or dispute, in particular on legal issues, in order to refute a general false judgment, it is not at all necessary to resort to the opposite general judgment, since it is easy to get into trouble: it may also turn out to be false. Let us recall an example: if A is false, “All witnesses are truthful,” then this does not mean that E is true: “Not a single witness is truthful.” It is also false, although in other cases E may turn out to be true. Logically, it is enough to give the contradictory proposition O: “Some witnesses are not truthful.” If A is false, then O is always true. This is the safest and most invulnerable, the most reliable way refutations.

Relationshipbetween judgments with relationships. Relational judgments (or judgments about the relationships between objects of thought), as already noted, have something in common with attributive judgments: tripartite structure (xRy), the presence of quantity and quality. Therefore, they can also be in relations of subordination, partial compatibility, opposition, contradiction, or logical independence. Thus, if I is true that “Some metals are lighter than water,” this does not mean that A is true: “All metals are lighter than water,” but it means that E is false, “No metal is lighter than water,” and that O , “Some metals are not lighter than water” (in this case it is true).

At the same time, relational judgments differ from attributive ones in that they reveal not the properties of objects, but the relationships between objects and, therefore, they do not have a monomial (one-place) predicate, but a polynomial one (n-place of two or more). Therefore, depending on the nature of the relationship R between objects X And at Within the judgment, its own special relationships are established.

The relationship between x and y can be primarily symmetrical or asymmetrical.

Symmetrical(from the Greek symmetria - proportionality) - these are relations between x and y for which it does not matter which of these members is the previous and which is the subsequent. In other words, they can be swapped, but truth or falsity will not change. These are relations of equality, similarity, similarity, simultaneity, etc., revealed in judgments. For example: “Ivan is Peter’s brother.” Therefore, "Peter is Ivan's brother." Such two relational propositions can be simultaneously true or simultaneously false. If one of them is true, then the other is true, and vice versa, if one of them is false, then the other is false.

Asymmetrical are those relationships between x and y in which the order of their arrangement is important. Therefore, it is impossible to change their places without changing the meaning of the judgment, therefore, its truth or falsity. For example: “Ivan is Stepan’s father.” But this does not mean that “Stepan is Ivan’s father.” If one of these propositions is true, then the other is false. The true word here will be “Stepan son of Ivan.” The following relationships also turn out to be asymmetrical: “Ivan loves Marya.” It does not at all follow from this that “Marya loves Ivan,” but she may or may not love him. If one of these judgments is true, then the other is uncertain.

It is also important to consider the relative nature of the differences between symmetry and asymmetry. What is symmetrical in one respect can be asymmetrical in another and vice versa. For example: if “Ivan is Peter’s brother,” then “Peter is Ivan’s brother.” But if “Ivan is Elena’s brother,” then this means that “Elena is Ivan’s sister.”

The relationship between x and y can be transitive or intransitive.

Transitive, or transitional relationships (from Latin transitive - transition). If, for example, x is equivalent to y, and y is equivalent to z, then x is equivalent to z. These can also be relationships of magnitude (more - less), spatial (further - closer), temporal (earlier - later), etc. For example: “Ivan is Peter’s brother”, “Peter is Elena’s brother”, which means “Ivan is the brother Elena". Such propositions can be either simultaneously true or simultaneously false.

Intransitive(intransitive) relations have an inverse relationship compared to the previous one. So, if “Ivan is Stepan’s father,” and “Stepan is Nikolai’s father,” then this does not mean at all that “Ivan is Nikolai’s father.” He is his grandfather, therefore, such judgments cannot be true at the same time. If one is true, then the other is false.

There are also relations of reflexivity and non-reflexivity.

Reflexive relationships (from Latin reflexio - turning back, reflection) are characterized by the fact that each member of the relationship is in the same relationship to itself. If two events happen at the same time, then they are simultaneous. Both propositions can be either true or false.

Non-reflective the relations are such that if 2 is less than 3, this does not mean that 2 is less than 2 and 3 is less than 3. The truth of one implies the falsity of the other.

Knowledge of features similar relationships between relational judgments according to their truth or falsity are important wherever there are relations of this kind. This is of particular importance in the field of legal relations. So, in judicial practice the simultaneity or multi-temporality of events, kinship relationships, acquaintances between people, etc. are taken into account. For example, if Ivanov knows Petrov, and Petrov knows Sidorov, this does not mean that Ivanov knows Sidorov. Here the relations are intransitive with all the ensuing consequences in terms of truth and falsity between the relational judgments that reveal them.

Complex judgments

Complex judgments also differ from simple ones in their functions and structure. Their functions are more complex, since they reveal not one, but simultaneously several - two or more - connections between objects of thought. Their structure is also characterized by greater complexity, acquiring a new quality. The main structure-forming elements here are no longer concepts-terms (subject and predicate), but independent judgments (and their internal subject-predicate structure is no longer taken into account). And the connection between them is carried out not with the help of the connective “is” (“is not”), but in a qualitatively different form - through logical unions (they are also called logical connectives). These are conjunctions such as “and”, “or”, “or”, “if... then”, etc. They are close in meaning to the corresponding grammatical conjunctions, but, as will be shown below, they do not completely coincide with them. Their main difference is that they are unambiguous, while grammatical conjunctions can have many meanings and shades.

Each of the logical unions is binary, i.e. connects only two judgments with each other, regardless of whether they are simple or themselves, in turn, complex, having their own unions within themselves.

If in simple judgments the variables were the subject and the predicate (S and P), and the constants were the logical connectives “is” and “is not”, then in complex judgments the variables are already separate, further indivisible judgments (let’s call them “A” and “B” "), and constants are logical conjunctions: “and”, “or”, etc.

In Russian, complex judgments have very diverse forms of expression. They can be expressed primarily in complex sentences. For example: “No guilty person should escape responsibility, and no innocent person should suffer.” They can also be expressed in complex sentences. This is, for example, the statement of Cicero: “After all, even if familiarization with the law were a huge difficulty, then even then the consciousness of its great benefits should encourage people to overcome this difficulty.”

Finally, they can also take the special form of simple common sentences. This is not difficult to achieve, for example, as a result of a kind of “collapse” of complex sentences. Thus, the complex sentence “Aristotle was a great logician, and Hegel was also a great logician” can be turned into a simple common one: “Aristotle and Hegel were great logicians.” Thanks to this “collapse”, greater conciseness of speech is achieved, hence its economy and dynamism.

Thus, not everything complex judgment is certainly expressed in a complex sentence, but any difficult sentence expresses a complex judgment.

Difficult called a judgment that includes as components other judgments connected by logical connectives - conjunction, disjunction orimplication. In accordance with the functions of logical connectives, the main types of complex judgments are: 1) connecting, 2) dividing, 3) conditional and 4) equivalent judgments.

Connective (conjunctive) judgment called a judgment that includes as components other propositions-conjuncts, united by the connective “and”. For example: “Theft and fraud are intentional crimes.” If one of the component judgments - “Theft is an intentional crime” - is denoted by the symbol p, another judgment - “Fraud is an intentional crime” - by the symbol q, and the connection between them is a sign, then in general the connecting judgment can be symbolically expressed as plq.

In natural language, conjunctive propositions can be expressed in one of three ways.

The connective ligament is expressed in a complex subject, consisting of conjunctive related concepts, according to the scheme: S 1, And S2, there is R. For example, “Confiscation of property and deprivation of rank are additional types criminal punishment."

The connective connective is expressed in a complex predicate, consisting of conjunctively related features, according to the scheme: Sthere is P 1 and P 2 . For example, “A crime is a socially dangerous and illegal act.”

The connective ligament is represented by a combination of the first two methods according to the scheme: S 1 And S 2 There isP 1 and P 2 . For example, “Nozdryov was also on friendly terms with the police chief and the prosecutor and treated him in a friendly manner” (N.V. Gogol, “Dead Souls”).

Conjunctive ligament grammatically expressed not only by the conjunction “and”, but also by the words “a”, “but”, “also”, “as”, “so and”, “although”, “however”, “despite”, “at the same time” " and etc.