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, 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 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 more than one 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 the mathematical sign of identity is still ).

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 a 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: “Every equilateral triangle 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

see also

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

See what “Judgment” is in other dictionaries:

JUDGMENT- a thought expressed by a declarative sentence that is 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 (despite the fact that truth in itself is not a value). Judgment... ... Sponville's Philosophical Dictionary

judgment- Court, review, report, opinion, reasoning, consideration, understanding, view; discretion, prudence, understanding, eye, sagacity, insight. Submit at whose discretion (discretion). At my age I shouldn’t dare to dare my judgment... ... Synonym dictionary

JUDGMENT- JUDGMENT, judgment, cf. 1. units only Action under Ch. judge in 1 meaning, discussion (book obsolete). “They sentenced based on general judgment.” Krylov. Lengthy judgment about the matter. 2. Opinion, conclusion. “I dare not pronounce my judgment.” Griboyedov. "In my... Ushakov's Explanatory Dictionary

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 C are developed. Psychology studies the development ... Great psychological encyclopedia

JUDGMENT- JUDGMENT, narrowed, see judge Dahl's Explanatory Dictionary. IN AND. Dahl. 1863 1866 … Dahl's Explanatory Dictionary

judgment- JUDGMENT (German Urteil; English, French Judgment) a mental act that expresses a person’s attitude to the content of the thought he expresses. In the form of affirmation or negation, S. is necessarily accompanied by one or another modality, associated as ... ... Encyclopedia of Epistemology and Philosophy of Science

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

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

Judgment- expression of elements of sensory experience in a generally meaningful verbal form... Psychological Dictionary

Books

• Judgment of an Orthodox Galician on the reform of Russian church government, projected by Russian liberals of our time, Dobryansky-Sachurov. Judgment of an Orthodox Galician on the reform of Russian church administration, projected by Russian liberals of our time / Op. ... Galician-Russian. activist and patriot Adolf Ivanovich...

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

Excellent definition

Incomplete definition ↓

JUDGMENT

In traditional In formal logic (up to Frege's works on logical semantics), S. was understood (with certain minor reservations and additions) as an affirmative or negative declarative sentence. However, in 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 intuitively implied. and "declarative sentence". The former was usually used as a logical term to designate statements (or negations) of "something about something" made through declarative sentences (in a language). The second served for the linguistic characterization of statements, i.e. remained Primarily a grammatical term. This implicit difference found explicit expression in the distinction (in the general case) between the logical structure of a sentence and the grammatical structure of sentences, which has been carried out since the time of Aristotelian syllogistic. So, in the classic attributive S. sub eqt (that about which something is said or said - the subject of speech) was identified, as a rule, with grammatical. subject, and predikat (what is expressed, or 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. Unlike the grammatical one, the logical form of saying (S. form) always meant that the object (S. subject) has (or does not have) a determinant. sign, i.e. boiled down to an attributive three-term connection: subject – linking verb – attribute. The indicated difference in the use of the terms "C." and the “narrative sentence” subsequently led 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) narrative sentence. Characteristics of a (narrative) sentence from a perspective. its truth value goes back to Aristotle and is, of course, not new. The main thing that distinguishes the new understanding from the traditional one is the abstraction of the content of a (narrative) sentence - S. in the proper sense of the word - from its truth value and from the material (linguistic) form of its expression, the isolation of S. exclusively as a logical element of speech - an abstract object “...the same degree of generality as a class, number or function” (Church?., Introduction to Mathematical Logic, M., 1960, p. 32). Essentially new is also the identification of the truth values ​​of sentences - “truth” and “lies” (which can be put in correspondence with each narrative sentence as its meaning) - as independent abstract objects included in the interpretation of logical calculus. This new t.zr. explained the meaning of equivalent transformations in logic based on the principle of volumetricity (see Volumetricity 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 made it possible to generalize traditions. the concept of structure of a system based on 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 tradition. understanding corresponded to the scheme “S is P”. If in this scheme S and? understood as variables having different domains of meaning, or as variables of different semantic levels, or of different sorts, or, finally, belonging to different alphabets: S as a variable in the domain of “individual names”, and P as a variable in the domain of “concepts” , then when choosing the concept “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 completely definite, albeit arbitrary, unspecified meaning in a 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 replacing the variable S with an individual name (value), “Socrates” turns into a true sentence. It is obvious that 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 a certain subject, playing here the usual role of an argument of a function. Similarly, the expression “...more than...” is a function of two variables, and the expression “is between... and...” is a function of three variables, etc. Thus, modern a look at the structure of S. comes down to the fact that its traditions. the elements "predicate" and "subject" are replaced by exact mathematics, respectively. concepts of a function and its arguments. This new interpretation meets the long-felt need for a generalized description of logical. reasoning, which would cover not only (and even not so much) syllogistic, but also especially non-syllogistic inferences - main. conclusions of science. In turn, the functional form of expression of S. opens up wide opportunities for formalizing the proposals of any scientific. theories. (For an explanation of how the subject-predicate structure of the system is characterized and formalized in modern logic, see article Quantifier and Predicate Calculus.) M. Novoselov. Moscow. V i d y S. Much attention in the history of logic and philosophy was paid to the problem of division into types. One of the most important is the division of systems into simple and complex. The concept of simple symbolism is already found in Aristotle in his book “On Interpretation.” Aristotle here calls simple the S. of existence, i.e. S., in which only the existence of the object S. is affirmed (or denied) (for example, there is a person). Aristotle contrasts a simple symbol with a three-membered symbol, which, in addition to knowledge about the existence (or non-existence) of the object of the symbol, also contains knowledge about the inherent (or non-inherent) nature of the object of the symbol. certainty of being (for example, “man is just”). In the Megarostoic school, a simple s. was called a s., consisting of a subject and a predicate. Complex - were called S., formed from simple ones with the help of various kinds of logic. connectives such as negation, conjunction, disjunction, implication. This understanding of simple and complex symbols is close to the interpretation given in modern times. logic of statements. Basic The classification headings for simple symbols were also already known to Aristotle: the division of symbols by quality (affirmative and negative) and by quantity (general, particular and indefinite) was given by Aristotle in the First Analytics. In textbooks of traditions. The logics of dividing S. by quality into affirmative and negative and by quantity into general and particular (by private here was meant an indefinite private judgment of the type “Some, and maybe all S, are P”) were combined into one heading. This heading was called S.'s division by quality and quantity. This included four types of C: 1) generally affirmative (“all S are P”), 2) generally negative (“no S is P”), 3) particular affirmative (“certain S are P”), 4) particular negative ( "certain 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 quantity include: 1) general s. (s. with a general quantifier), 2) indefinite. private S., called simply particular (S. with the quantifier of existence) and 3) individual S. The division of S. into S. of reality, possibility and necessity, later called the 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. possibilities - S., in which we are talking about what could be different, i.e. which may or may not be the case. For example, “Tomorrow there may be a naval battle.” In modern In logic, statements with modal operators “possible”, “impossible”, “necessary”, etc. are studied in various systems of modal logic. The distinction between 1) distinguishing and including S. and 2) S. properties and S. relations can also, in a certain sense, be derived from Aristotle. In the fourth and tenth chapters of the first book of Topics, Aristotle considered the trace. four types of correlation between what is said about an object and the object itself: 1) definition, 2) proper, 3) gender, 4) accidental. According to Aristotle, a definition should be called such a S., in which the proper one is revealed. the essence of the object C. What is reflected in the definition belongs to the object C; it cannot affect another subject. We should call such a S., in which, as in the definition, we are talking about something that belongs only to the subject of the S. But unlike the definition, what is reflected in its own S., does not mean the essence of the conceivable object. A family should be called such a S., in which inappropriateness is revealed. the essence of the subject, i.e. such an essence that other objects have, besides the object S. Random should be called everything that, without being the essence of the object S., can, just like the genus, affect many other subjects. This teaching of Aristotle, later called by his commentators the doctrine of predicabilia, makes it possible to establish two more important types of s., namely, isolating and including s. It is natural to call those s., in which we are talking about a distinctive feature of the subject of s., independent on whether this attribute is essential (definition) or non-essential (proper). For example, “A square is a rectangle with equal sides” (definition). “Mars is a planet that glows with red light” (proper). It is natural to call those S. inclusive, in which we are talking about the belonging to the object of S. of such features, about which it is known that they belong not only to the object of S., for example: “The whale is an animal” (genus), “This the man is lying down" (random). For the division of S. into S. properties and relations, it is of interest that the reduction of all categories to three, namely, “essence”, “state” and “relation”, which Aristotle carried out in the 14th book of “Metaphysics”. Based on 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. relationships, in which various kinds of relationships 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, Institutio logica, ed. C. Kalbfleisch, Lipsiae, 1896). It was developed in great detail by Karinsky (see “On the course of logic by M.I. Karinsky”, “VF”, 1947, No. 2). In modern times (in X. Wolf, I. Kant and in many school logic textbooks that followed them) there was also the so-called. division of S. in relation to categorical, conditional (or hypothetical) and dividing. By categorical S. we mean here a 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 cl.-l. conditions. A clause was called separative, which contains several predicates, of which only one can relate to the subject, or several subjects, of which only one can relate to the predicate (see M. S. Strogovich, Logic, M. , 1949, pp. 166–67). In modern Logically, the division of S. in relation is not recognized. so-called a categorical judgment is identified here with a simple judgment, and various types of conditional and disjunctive judgments are considered as types of complex judgments (see Conditional Judgment, Disjunctive Judgment). In Kant's classification of S., in addition to the division by quality, quantity, modality and relation, we also find a 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 ideas or concepts are combined in the act of S. Kant calls a posteriori those concepts 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 thought of as strictly universal, that is, 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” (Kant I., Works, vol. 3, M., 1964, p. 107). Such a priori principles are, for example, according to Kant, mathematics. S., axioms of logic, etc. In distinguishing a priori and a posteriori judgments, Kant tried, from the position of apriorism, to solve a problem that runs through the entire history of philosophy, namely the problem of the difference between the empirical (fact-fixing) and the theoretical. knowledge. From view 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 exist, and we can intuitively distinguish them in some cases [for example, in the case of fact-fixing (empirical) and necessary (theoretical) knowledge]. The problem is to specify the exact logic. signs by which Crimea could be distinguished, expressing empirical. knowledge (empirical C), from judgments expressing theoretical. knowledge (theoretical C). This problem cannot be considered finally resolved, 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 Kantian philosophy is played by the division of philosophy into analytical and synthetic. Analytical S. differ from synthetic ones in that through their predicate they do not add anything to the concept of the subject, but only divide it by dividing it into subordinate concepts, which were already thought in it (albeit vaguely), while synthetic. S. “...attach to the concept of the subject a predicate that was not at all thought of in it and could not be extracted from it by any division” (ibid., pp. 111–12). Immanuel Kant's merit on the issue of dividing judgment into analytical and synthetic lies primarily in posing this question: he was the first to distinguish the problem of dividing judgment into analytical and synthetic from the problem of dividing judgments into empirical (a posteriori) and theoretical (a priori). Before Kant (for example, with Leibniz), these problems were usually identified. At the same time, I. Kant could not indicate the logical. signs that make it possible to distinguish between analytical S. from synthetic. In the future, the problem of analytical and synthetic. S. has been discussed several times (see Synthetic and analytical judgments). The divisions of S. into types discussed above were created by Ch. way to serve the needs of tradition. formal logic and, above all, for solving fundamental problems. its section is the theory of inference. Thus, the division of S. by quantity, quality and modality was established by Aristotle for the needs of the theory of syllogistics he created. inference (see Syllogistics). The division of logic into simple and complex and the development of the question of the types of complex logic by the logicians of the Megaro-Stoic school were necessary 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 the like. non-syllogistic inferences. 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 knowledge. and the construction of an all-encompassing classification of S. Attempts to construct such classifications have taken place in the history of philosophy [such, for example, as Wundt’s classification of S. (see W. Wundt, Logik, 4 Aufl., Bd 1, Stuttg., 1920)]. However, it should be noted that, in addition to formal logic. approach to the question of the types of S., when S. are divided into types according to exactly fixed factors. logical bases of division and the division itself is established to serve the needs of the theory of inference, another, epistemological one is also quite legitimate. approach to this issue. For a correctly understood epistemological The approach to the problem of the types of S. is characterized by an 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, looking at it from this perspective. dividing S. by quantity, we draw attention to the fact that single S. play mainly a dual role in the process of cognition. Firstly, individual S. express and consolidate knowledge about the department. subjects. This includes a description of the historical. events, characteristics of the department. personalities, description of the Earth, Sun, etc. Moreover, among this kind of individual S. we note a transition from the so-called. S. belonging, in which only the belonging of a feature to an object is asserted, to inclusive and distinguishing S., as soon as we establish that the asserted characteristic belongs not only to a given object (inclusive judgment) or only to a given object (selective judgment). Secondly, individual S. prepare the afterbirth, the formulation of particular and general S. Having examined all layers of the s.-l. geological section and having recorded in a number of individual statements that each of the studied layers is of marine origin, we can state a general statement: “All layers of a given geological section are of marine origin.” Regarding particular S., we note that in the process of cognition of reality, a transition is made from indeterminacy. private S. to definition. to a particular S. or to a general S. In fact, indefinite. private S. (or simply private S.) is expressed in such cases when, knowing that certain objects of k.-l. of a class of objects have or do not possess a known attribute, we have not yet established either that all other objects of a given class of objects also possess (do not possess) this attribute, or that certain others do not (possess) this attribute. objects of this class of objects. If it is subsequently established that the decree. only some or all objects of a given class possess the attribute, then the particular S. is replaced by the definition. private or general S. Thus, the particular S. “Certain metals are heavier than water” in the process of studying metals is refined into a definition. private S. “Only certain metals are heavier than water.” Particular S. “Certain types of mechanical motion pass through friction into heat” is replaced by general S. “Every mechanical movement passes through friction into heat.” Definition 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 particular objects have or do not possess the approved characteristic. To eliminate this uncertainty, define. particular S. must be replaced by either general or multiple emphasizing S. To move from the definition. private S. to the so-called multiple excreting S. needs to establish qualities. the certainty of each of those certain objects that are discussed in the definition. private C. In this case, for example, define. the particular S. “Only certain students of this class do well in the Russian language” is replaced by the plural emphatic S. “Of all the students in this class, only Shatov, Petrov and Ivanov do well in the Russian language.” The transition to a general distinguishing system occurs when we can identify one or more of the known common features of certain objects of a given kind as a characteristic feature of all these (“certain”) objects. For example, having learned that all those (“certain”) animals that are discussed in S. “Only certain animals have large intestines” constitute the class of mammals, we can express a general distinguishing S: “ All mammals, and only mammals, have large intestines." Transitions of this kind between S. can also be established from the point of view. their modality and in certain 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., Aristotle’s logical doctrine, M., 1900; Smirnova E. D., On the problem of analytical and synthetic, in: Philosophy. question modern formal logic, M., 1962; Gorsky D.P., Logic, 2nd ed., M., 1963. P. Tavanets. Moscow.

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

Types of simple assertoric judgments

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

1 . Judgments of property (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 proposition with a relation, 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 generally has greater significance than a negative one, 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 judgment. 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

Each judgment has quantitative and qualitative 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 student 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 generally 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 Olympic champions.” The symbol for negative judgments is taken from the word NEGO, or I deny.

Distribution of terms in categorical judgments

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 “Perpetual motion is possible” will be false, although in terms of specific content they have nothing in common, no subject , nor a 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 the semantic difference here is less than in the previous case, they also cannot correlate with each other in terms of 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.

According to their logical form, first of all, according to 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 (albeit 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 this case, this is a false judgment. 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. The falsity of one of them implies 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, most reliable method of refutation.

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 the features of such relations between relational judgments according to their truth or falsity is important wherever there are relations of this kind. This is of particular importance in the field of legal relations. Thus, 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 conjunctions (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 every complex proposition is necessarily expressed by a complex sentence, but every complex sentence expresses a complex proposition.

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 call a judgment that includes as components other judgments-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 conjunctively 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 of 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.

Types of judgments and logical relations between them

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

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

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

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

1. By subject volume(in count).

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

This S is (is not) P.

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

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

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

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

"Only some S There is R".

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

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

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

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

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

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

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

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

Property judgments reflect whether or not the object of thought belongs to one or another property or state: for example, “In our time, the acquisition of philosophical knowledge is the most important element of a person’s spiritual culture.”

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Thinking

Topic 5. Judgment (statement) as a form

Along with the concept, judgment is one of the main forms of thinking. This form of thinking is, in essence, an obligatory element of all cognition, especially associated with the processes of reasoning, with the implementation of conclusions and the construction of evidence. In this form, the results of cognition of individual objects, classes of objects, and some situations in general are recorded. A thought of this type contains, on the one hand, a description or at least simply a designation of these objects, classes, situations, and on the other, an affirmation or denial of the presence of one or another characteristic in them.

Example. The proposition “Each planet of the Solar System rotates around its axis” states the existence of a situation in reality: rotation around its axis of each planet of the Solar System. And in the judgment “Not a single planet in the Solar System is stationary” the existence in reality of a situation of rest for each planet in the Solar System is denied.

A judgment is a form of thought containing a description of a certain situation and an affirmation or denial of the existence of this situation in reality.

The most important distinguishing feature of judgment is affirmation or denial of something about something. Nothing is affirmed or denied in the concept. It only highlights the subject of thought itself (for example: “day”, “night”, “sunny day”, “non-sunny day”). In judgment, attention is focused on the very relationship between any objects of thought: “It’s a sunny day” or “It’s not a sunny day,” “The day has passed,” “The night has come.”

Both in the simplest and in quite complex judgments, the presence of certain characteristics in some objects is always affirmed or denied. Therefore, in general terms, the definition of a judgment can be formulated as follows:

A judgment is a thought in which the existence of a connection between objects and attributes is affirmed or denied.

Familiar, in the form of which the judgment is expressed, is declarative sentence. The meaning of this sign should be the thought associated with it. This is what it is judgment. As for the meaning of a sentence, sometimes it is considered to be a situation that occurs or does not occur in reality and which is described by a judgment. However, most often the meaning of a sentence is considered to be the truth or lie.

In modern logic, instead of the term “judgment,” they prefer to use the term “statement.” In traditional logic, the term “judgment” denoted precisely a certain meaning of a narrative sentence, taking into account the fact that it can be common to various sign forms. In other words, the same judgment can be expressed in different forms of declarative sentences.

Example. One can assert that “Every person is capable of thinking” and that “All people have the ability to think,” but in both cases the same thought (the same judgment) is expressed.

The term “utterance” is usually associated with some meaning (judgment) together with its symbolic form. When speaking about judgment, it is not necessary to have in mind any specific sign form. When we talk about a statement, we mean a certain sign form along with its meaning. When we mean only the sign form of the statement itself, abstracting from its meaning, i.e. from the judgment expressed in it, then we use the term “narrative sentence”.

Types of judgments. When distinguishing types of judgments, first of all, they distinguish simple And complex. Simple such a judgment is called, not a single logical part of which is a judgment.

Example. "Mathematics is an abstract science."

Difficult is a judgment that contains as its correct part, i.e. part that does not coincide with the whole, some other judgment.

Example. “If you study well, you will definitely get a diploma.”

Types of simple judgments. The main parts of simple judgments are one or more subjects of the judgment (logical subjects) and a predicate of the judgment (logical predicate). The subject and predicate of a judgment are called the terms of that judgment.

Subject of judgment is a term, possibly expressing a concept and representing an object about which something is affirmed or denied. The subject of judgment is usually denoted by the letter S.

Predicate of judgment- part of a judgment expressing what is affirmed or denied about the objects that the subjects represent. The predicate is denoted by the letter R.

Example. In the proposition “The Sun is a red-hot celestial body,” the subject is “Sun” and the predicate is “a red-hot celestial body.” In the proposition “The Earth revolves around the Sun” there are two subjects – “Earth” and “Sun”, the predicate is the relation “rotates”.

Depending on the content of the predicate of the judgment, i.e. from what exactly is affirmed or denied about certain objects, attributive, existential and relational judgments are distinguished.

Attributive are called judgments in which the presence of some property in an object is affirmed or denied. The logical form of an attributive judgment has the form: S(do not eat R.

Example. "Sun ( S) is a hot celestial body ( R)"; "Great Britain ( S) is a constitutional monarchy ( R)"; "Some swans ( S) white ( R)"; "The Great Schemer ( R) this Ostap Bender ( S)"; "Need ( S) will make God pray ( R)».

Existential are judgments in which the existence of an object is affirmed or denied.

Example. "Snake-Gorynych ( S) does not really exist ( R)"; "Natural anomalies ( S) exist ( R)"; “There are no hopeless situations” (“No hopeless situations ( S) does not exist ( R)»).

Relational- these are judgments in which the relationship between certain objects is affirmed or denied.

Example. "The earth revolves around the sun"; “Peter is Ivan’s brother”; “Moscow is located between St. Petersburg and Yekaterinburg.”

In attributive judgments, as in judgments of existence, there is always only one subject. In attitude judgments there is more than one.

Types of attributive judgments. Based on quality, attributive judgments are divided into affirmative and negative.

Affirmative are judgments that indicate that the predicate belongs to the subject of the judgment. Negative- these are judgments that indicate the absence of a given predicate in the subject.

When determining the type of judgment based on quality, one must pay attention to the quality of the connective “is” (“is not”). The proposition “This is a bad person” is affirmative, since it states that the subject (“person”) belongs to the predicate “bad.” The proposition “He was never a good friend” is negative, since it states that the subject (“he”) does not have the predicate “good friend.” In this judgment, the logical connective “is” (“was”) stands with the negation “not”.

By quantity, attributive judgments are divided into single, particular and general. The quantity of a judgment is its characteristic, which determines the extent to which the subject of the judgment is considered.

IN single judgments the predicate is expressed about a single object, i.e. all terms playing the role of subjects are singular names.

Example. "This man has criminal tendencies."

IN private judgments the predicate speaks about some elements of the subject's scope.

Example. "Some people have criminal tendencies."

IN general judgments the predicate speaks about the entire scope of the subject.

Example. "All people have criminal tendencies."

The meaning of the word “some” in natural language and in logic is somewhat different. In natural language it is used to mean "only some, but not all" and "some, but maybe all." In logic - only in the sense of “some, and maybe all.”