The concept of utterance. Types of statements
Types of statements
Logical statements are usually divided into two types: elementary logical statements and compound logical statements.
Compound logical statement is a statement formed from other statements using logical connectives.
Logical connective is any logical operation on a statement. For example, words and phrases used in ordinary speech “not”, “and”, “or”, “if... then”, “then and only then” are logical connectives.
Elementary logical statements- these are statements that are not related to compounds.
Examples: “Petrov is a doctor”, “Petrov is a chess player” - elementary logical statements. “Petrov is a doctor and a chess player” is a compound logical statement consisting of two elementary statements connected to each other using the connective “and”.
Connection with mathematical logic
Ordinary logic is two-valued, that is, it assigns only two possible meanings to statements: true or false.
Let it be a statement. If it is true, then write , if false, then .
Basic operations on logical statements
Negation logical statement - a logical statement that takes the value “true” if the original statement is false, and vice versa.
Conjunction two logical statements - a logical statement that is true only if they are simultaneously true.
Disjunction two logical statements - a logical statement that is true only if at least one of them is true.
Implication two logical statements A and B - a logical statement that is false only if B is false and A is true.
Equivalence(equivalence of) two logical statements - a logical statement that is true only if they are both true or false.
Quantifier universality() is a logical statement that is true only if for each object x from a given population the statement A(x) is true.
Quantifier logical statement with quantifier existence() is a logical statement that is true only if in a given set there is an object x such that the statement A(x) is true.
see also
- Statement
Notes
Literature
- Karpenko, A. S. Modern research in philosophical logic // Logical Research. Vol. 10. - M.: Nauka, 2003. ISBN 5-02-006257-X - P. 61-93.
- Kripke, S. A. Wittgenstein on rules and individual language / Trans. V. A. Ladova, V. A. Surovtseva. Under general ed. V. A. Surovtseva. - Tomsk: Publishing house Tom. University, 2005. - 152 p. - (Library of Analytical Philosophy). ISBN 5-7511-1906-1
- Kurbatov, V. I. Logics. Systematic course. - Rostov n/d: Phoenix, 2001. - 512 p. ISBN 5-222-01850-4
- Schumann, A. N. Modern logic: theory and practice. - Minsk: Econompress, 2004. - 416 p. ISBN 985-6479-35-5
- Makarova, N.V. Computer Science and ICT. - St. Petersburg: Peter Press, 2007 ISBN 978-5-91180-198-4 - P. 343-345.
- Kondakov N. I. Logical dictionary / Gorsky D. P. - M.: Nauka, 1971. - 656 p.
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Propositional logic , also called propositional logic, is a branch of mathematics and logic that studies the logical forms of complex statements constructed from simple or elementary statements using logical operations.
Propositional logic abstracts from the content of statements and studies their truth value, that is, whether the statement is true or false.
The picture above is an illustration of a phenomenon known as the Liar Paradox. At the same time, in the opinion of the author of the project, such paradoxes are possible only in environments that are not free from political problems, where someone can a priori be labeled a liar. In the natural multi-layered world the subject of “truth” or “false” only individual statements are evaluated . And later in this lesson you will be introduced to the opportunity to evaluate many statements on this subject for yourself (and then look at the correct answers). Including complex statements in which simpler ones are interconnected by signs of logical operations. But first, let’s consider these operations on statements themselves.
Propositional logic is used in computer science and programming in the form of declaring logical variables and assigning them logical values “false” or “true”, on which the course of further execution of the program depends. In small programs where only one boolean variable is involved, the boolean variable is often given a name such as "flag" and the meaning is "flag is up" when the variable's value is "true" and "flag is down." , when the value of this variable is "false". In large programs, in which there are several or even many logical variables, professionals are required to come up with names for logical variables that have a form of statements and a semantic meaning that distinguishes them from other logical variables and is understandable to other professionals who will read the text of this program.
Thus, a logical variable with the name “UserRegistered” (or its English-language analogue) can be declared in the form of a statement, which can be assigned the logical value “true” if the conditions are met that the registration data was sent by the user and this data is recognized as valid by the program. In further calculations, the values of the variables may change depending on the logical value (true or false) of the UserRegistered variable. In other cases, a variable, for example, with the name “More than Three Days Left Before the Day”, can be assigned the value “True” before a certain block of calculations, and during further execution of the program this value can be saved or changed to “false” and the progress of further execution depends on the value of this variable programs.
If a program uses several logical variables, the names of which have the form of statements, and more complex statements are built from them, then it is much easier to develop the program if, before developing it, we write down all the operations from statements in the form of formulas used in statement logic than we do during This lesson is what we will do.
Logical operations on statements
For mathematical statements one can always make a choice between two different alternatives, “true” and “false,” but for statements made in “verbal” language, the concepts of “truth” and “false” are somewhat more vague. However, for example, verbal forms such as “Go home” and “Is it raining?” are not statements. Therefore it is clear that statements are verbal forms in which something is stated . Interrogative or exclamatory sentences, appeals, as well as wishes or demands are not statements. They cannot be evaluated with the values "true" and "false".
Statements, on the contrary, can be considered as quantities that can take on two meanings: “true” and “false”.
For example, the following judgments are given: “a dog is an animal”, “Paris is the capital of Italy”, “3
The first of these statements can be evaluated with the symbol “true”, the second with “false”, the third with “true” and the fourth with “false”. This interpretation of statements is the subject of propositional algebra. We will denote statements in capital letters A, B, ..., and their meanings, that is, true and false, respectively AND And L. In ordinary speech, connections between statements “and”, “or” and others are used.
These connections allow, by connecting different statements with each other, to form new statements - complex statements . For example, the connective "and". Let the statements be given: " π more than 3" and the statement " π less than 4". You can organize a new - complex statement " π more than 3 and π less than 4". Statement "if π irrational then π ² is also irrational" is obtained by connecting two statements with the connective "if - then". Finally, we can obtain from any statement a new one - a complex statement - by denying the original statement.
Considering statements as quantities that take on meanings AND And L, we will define further logical operations on statements , which allow us to obtain new complex statements from these statements.
Let two arbitrary statements be given A And B.
1 . The first logical operation on these statements - conjunction - represents the formation of a new statement, which we will denote A ∧ B and which is true if and only if A And B are true. In ordinary speech, this operation corresponds to the connection of statements with the connective “and”.
Truth table for conjunction:
| A | B | A ∧ B |
| AND | AND | AND |
| AND | L | L |
| L | AND | L |
| L | L | L |
2 . Second logical operation on statements A And B- disjunction expressed as A ∨ B, is defined as follows: it is true if and only if at least one of the original statements is true. In ordinary speech, this operation corresponds to connecting statements with the connective “or”. However, here we have a non-dividing “or”, which is understood in the sense of “either or” when A And B both cannot be true. In defining propositional logic A ∨ B true both if only one of the statements is true, and if both statements are true A And B.
Truth table for disjunction:
| A | B | A ∨ B |
| AND | AND | AND |
| AND | L | AND |
| L | AND | AND |
| L | L | L |
3 . The third logical operation on statements A And B, expressed as A → B; the statement thus obtained is false if and only if A true, but B false. A called by parcel , B - consequence , and the statement A → B - following , also called implication. In ordinary speech, this operation corresponds to the “if-then” connective: “if A, That B". But in the definition of propositional logic, this statement is always true regardless of whether the statement is true or false B. This circumstance can be briefly formulated as follows: “from the false everything follows.” In turn, if A true, but B is false, then the entire statement A → B false. It will be true if and only if A, And B are true. Briefly, this can be formulated as follows: “false cannot follow from the true.”
Truth table to follow (implication):
| A | B | A → B |
| AND | AND | AND |
| AND | L | L |
| L | AND | AND |
| L | L | AND |
4 . The fourth logical operation on statements, more precisely on one statement, is called the negation of a statement A and is denoted by ~ A(you can also find the use of not the symbol ~, but the symbol ¬, as well as an overscore above A). ~ A there is a statement that is false when A true, and true when A false.
Truth table for negation:
| A | ~ A |
| L | AND |
| AND | L |
5 . And finally, the fifth logical operation on statements is called equivalence and is denoted A ↔ B. The resulting statement A ↔ B a statement is true if and only if A And B both are true or both are false.
Truth table for equivalence:
| A | B | A → B | B → A | A ↔ B |
| AND | AND | AND | AND | AND |
| AND | L | L | AND | L |
| L | AND | AND | L | L |
| L | L | AND | AND | AND |
Most programming languages have special symbols to denote the logical meanings of statements; they are written in almost all languages as true and false.
Let's summarize the above. Propositional logic studies connections that are completely determined by the way in which some statements are built from others, called elementary. In this case, elementary statements are considered as wholes and cannot be decomposed into parts.
Let us systematize in the table below the names, notations and meaning of logical operations on statements (we will soon need them again to solve examples).
| Bunch | Designation | Operation name |
| Not | negation | |
| And | conjunction | |
| or | disjunction | |
| if... then... | implication | |
| then and only then | equivalence |
True for logical operations laws of algebra logic, which can be used to simplify Boolean expressions. It should be noted that in propositional logic one abstracts from the semantic content of a statement and limits itself to considering it from the position that it is either true or false.
Example 1.
1) (2 = 2) AND (7 = 7) ;
2) Not(15;
3) ("Pine" = "Oak") OR ("Cherry" = "Maple");
4) Not("Pine" = "Oak") ;
5) (Not(15 20) ;
6) (“Eyes are given to see”) And (“Under the third floor is the second floor”);
7) (6/2 = 3) OR (7*5 = 20) .
1) The meaning of the statement in the first brackets is “true”, the meaning of the expression in the second brackets is also true. Both statements are connected by the logical operation “AND” (see the rules for this operation above), therefore the logical value of this entire statement is “true”.
2) The meaning of the statement in brackets is “false”. Before this statement there is a logical operation of negation, therefore the logical meaning of this entire statement is “true”.
3) The meaning of the statement in the first brackets is “false”, the meaning of the statement in the second brackets is also “false”. Statements are connected by the logical operation "OR" and none of the statements has the value "true". Therefore, the logical meaning of this entire statement is “false.”
4) The meaning of the statement in brackets is “false”. This statement is preceded by the logical operation of negation. Therefore, the logical meaning of this entire statement is “true”.
5) The statement in the inner brackets is negated in the first brackets. This statement in inner brackets has the meaning "false", therefore its negation will have the logical meaning "true". The statement in the second brackets means "false". These two statements are connected by the logical operation “AND”, that is, “true AND false” is obtained. Therefore, the logical meaning of this entire statement is “false.”
6) The meaning of the statement in the first brackets is “true”, the meaning of the statement in the second brackets is also “true”. These two statements are connected by the logical operation “AND”, that is, “true AND truth” is obtained. Therefore, the logical meaning of the entire given statement is “true.”
7) The meaning of the statement in the first brackets is “true”. The meaning of the statement in the second brackets is "false". These two statements are connected by the logical operation “OR”, that is, “true OR false”. Therefore, the logical meaning of the entire given statement is “true.”
Example 2. Write the following complex statements using logical operations:
1) "User is not registered";
2) “Today is Sunday and some employees are at work”;
3) “The user is registered if and only if the data submitted by the user is considered valid.”
1) p- single statement “User is registered”, logical operation: ;
2) p- single statement “Today is Sunday”, q- "Some employees are at work", logical operation: ;
3) p- single statement “User is registered”, q- “The data sent by the user was found valid”, logical operation: .
Solve examples of propositional logic yourself, and then look at the solutions
Example 3. Compute the logical values of the following statements:
1) (“There are 70 seconds in a minute”) OR (“A running clock tells the time”);
2) (28 > 7) AND (300/5 = 60) ;
3) (“TV is an electrical appliance”) AND (“Glass is wood”);
4) Not((300 > 100) OR ("You can quench your thirst with water"));
5) (75 < 81) → (88 = 88) .
Example 4. Write down the following complex statements using logical operations and calculate their logical values:
1) “If the clock shows the time incorrectly, then you may arrive at class at the wrong time”;
2) “In the mirror you can see your reflection and Paris, the capital of the USA”;
Example 5. Determine the Boolean Value of an Expression
(p → q) ↔ (r → s) ,
p = "278 > 5" ,
q= "Apple = Orange",
p = "0 = 9" ,
s= "The hat covers the head".
Propositional logic formulas
The concept of the logical form of a complex statement is clarified using the concept propositional logic formulas .
In examples 1 and 2 we learned to write complex statements using logical operations. Actually, they are called propositional logic formulas.
To denote statements, as in the mentioned example, we will continue to use the letters
p, q, r, ..., p 1 , q 1 , r 1 , ...
These letters will play the role of variables that take the truth values “true” and “false” as values. These variables are also called propositional variables. We will further call them elementary formulas or atoms .
To construct propositional logic formulas, in addition to the letters indicated above, signs of logical operations are used
~, ∧, ∨, →, ↔,
as well as symbols that provide the possibility of unambiguous reading of formulas - left and right brackets.
Concept propositional logic formulas let's define it as follows:
1) elementary formulas (atoms) are formulas of propositional logic;
2) if A And B- propositional logic formulas, then ~ A , (A ∧ B) , (A ∨ B) , (A → B) , (A ↔ B) are also formulas of propositional logic;
3) only those expressions are propositional logic formulas for which this follows from 1) and 2).
The definition of a propositional logic formula contains a listing of the rules for the formation of these formulas. According to the definition, every propositional logic formula is either an atom or is formed from atoms as a result of the consistent application of rule 2).
Example 6. Let p- single statement (atom) “All rational numbers are real”, q- "Some real numbers are rational numbers" r- "some rational numbers are real." Translate the following formulas of propositional logic into the form of verbal statements:
6) 
.
1) “there are no real numbers that are rational”;
2) “if not all rational numbers are real, then there are no rational numbers that are real”;
3) “if all rational numbers are real, then some real numbers are rational numbers and some rational numbers are real”;
4) “all real numbers are rational numbers and some real numbers are rational numbers and some rational numbers are real numbers”;
5) “all rational numbers are real if and only if it is not the case that not all rational numbers are real”;
6) “it is not the case that it is not the case that not all rational numbers are real and there are no real numbers that are rational or there are no rational numbers that are real.”
Example 7. Create a truth table for the propositional logic formula 
, which in the table can be designated f
.
Solution. We begin compiling a truth table by recording values (“true” or “false”) for single statements (atoms) p , q And r. All possible values are written in eight rows of the table. Further, when determining the values of the implication operation and moving to the right in the table, we remember that the value is equal to “false” when “false” follows from “true”.
| p | q | r | f | ||||
| AND | AND | AND | AND | AND | AND | AND | AND |
| AND | AND | L | AND | AND | AND | L | AND |
| AND | L | AND | AND | L | L | L | L |
| AND | L | L | AND | L | L | AND | AND |
| L | AND | AND | L | AND | L | AND | AND |
| L | AND | L | L | AND | L | AND | L |
| L | L | AND | AND | AND | AND | AND | AND |
| L | L | L | AND | AND | AND | L | AND |
Note that no atom has the form ~ A , (A ∧ B) , (A ∨ B) , (A → B) , (A ↔ B) . Complex formulas have this type.
The number of parentheses in propositional logic formulas can be reduced if we accept that
1) in a complex formula we will omit the outer pair of brackets;
2) let’s arrange the signs of logical operations “in order of precedence”:
↔, →, ∨, ∧, ~ .
In this list, the ↔ sign has the largest scope and the ~ sign has the smallest scope. The scope of an operation sign refers to those parts of the formula of propositional logic to which the occurrence of this sign in question is applied (on which it acts). Thus, it is possible to omit in any formula those pairs of parentheses that can be restored, taking into account the “order of precedence”. And when restoring parentheses, first all parentheses related to all occurrences of the sign ~ are placed (we move from left to right), then to all occurrences of the sign ∧, and so on.
Example 8. Restore the parentheses in the propositional logic formula B ↔ ~ C ∨ D ∧ A .
Solution. The brackets are restored step by step as follows:
B ↔ (~ C) ∨ D ∧ A
B ↔ (~ C) ∨ (D ∧ A)
B ↔ ((~ C) ∨ (D ∧ A))
(B ↔ ((~ C) ∨ (D ∧ A)))
Not every propositional logic formula can be written without parentheses. For example, in formulas A → (B → C) and ~( A → B) further exclusion of brackets is not possible.
Tautologies and contradictions
Logical tautologies (or simply tautologies) are formulas of propositional logic such that if letters are arbitrarily replaced by statements (true or false), the result will always be a true statement.
Since the truth or falsity of complex statements depends only on the meanings, and not on the content of the statements, each of which corresponds to a certain letter, then checking whether a given statement is a tautology can be done in the following way. In the expression under study, the values 1 and 0 (respectively “true” and “false”) are substituted for the letters in all possible ways, and the logical values of the expressions are calculated using logical operations. If all these values are equal to 1, then the expression under study is a tautology, and if at least one substitution gives 0, then it is not a tautology.
Thus, a propositional logic formula that takes the value “true” for any distribution of the values of the atoms included in this formula is called identical to the true formula or tautology .
The opposite meaning is a logical contradiction. If all the values of the statements are equal to 0, then the expression is a logical contradiction.
Thus, a propositional logic formula that takes the value “false” for any distribution of the values of the atoms included in this formula is called identically false formula or contradiction .
In addition to tautologies and logical contradictions, there are formulas of propositional logic that are neither tautologies nor contradictions.
Example 9. Construct a truth table for a propositional logic formula and determine whether it is a tautology, a contradiction, or neither.
Solution. Let's create a truth table:
| AND | AND | AND | AND | AND |
| AND | L | L | L | AND |
| L | AND | L | AND | AND |
| L | L | L | L | AND |
In the meanings of the implication we do not find a line in which “true” implies “false”. All values of the original statement are equal to "true". Consequently, this formula of propositional logic is a tautology.
Algebra in the broad sense of the word is the science of general operations, similar to addition and multiplication, that can be performed on a variety of mathematical objects.
You study many mathematical objects (integer and rational numbers, polynomials, vectors, sets) in a school algebra course, where you become familiar with such branches of mathematics as the algebra of numbers, the algebra of polynomials, the algebra of sets, etc. For computer science, an important branch of mathematics called algebra of logic; the objects of the algebra of logic are propositions.
An utterance is a sentence in any language whose content can be unambiguously determined to be true or false.
Example:
For example, regarding the sentences “The great Russian scientist M.V. Lomonosov was born in \(1711\)” and “Two plus six is eight” we can definitely say that they are true. The sentence “Sparrows hibernate in winter” is false. Therefore, these sentences are statements.
In Russian, statements are expressed by declarative sentences.
Pay attention!
But not every declarative sentence is a statement.
Example:
For example, the sentence “This sentence is false” is not a statement because it cannot be said whether it is true or false without causing a contradiction. Indeed, if we accept that the sentence is true, then this contradicts what was said. If we accept that the sentence is false, then it follows that it is true.
Incentive and interrogative sentences are not statements.
For example, sentences such as: “Write down your homework”, “How to get to the library?”, “Who came to us?” are not statements.
Statements can be constructed using signs from various formal languages - mathematics, physics, chemistry, etc.
Examples of statements could be:
“Na is metal” (true statement);
“Newton's second law is expressed by the formula \(F = ma\) (true statement);
“The perimeter of a rectangle with side lengths \(a\) and \(b\) is equal to \(ab\)” (false statement).
Numerical expressions are not statements, but from two numerical expressions you can make a statement by connecting them with equal or inequality signs. For example:
- 3 + 5 = 2 ⋅ 4 (true statement);
- “II + VI > VIII” (false statement).
Equalities and inequalities containing variables are also not statements.
For example, the sentence \("x< 12»\) становится высказыванием только при замене переменной каким-либо конкретным значением: \(«5 < 12»\) - истинное высказывание; \(«12 < 12»\) - ложное высказывание.
The justification for the truth or falsity of statements is decided by the sciences to which they belong. The algebra of logic is abstracted from the semantic content of statements. She is only interested in whether a given statement is true or false. In logical algebra, statements are denoted by letters and called logical variables. Moreover, if the statement is true, then the value of the corresponding logical variable is denoted by one \((A = 1)\), and if false - by zero \((B = 0)\).
\(0\) and \(1\), denoting the values of logical variables, are called logical values.
The basic (undefined) concept of mathematical logic is the concept of a “simple statement”.
A statement is usually understood as any declarative sentence that states something about something, and at the same time we can say whether it is true or false in given conditions of place and time. The logical meanings of statements are “true” and “false”.
Here are examples of statements:
1) Novgorod is located on the Volkhov.
2) Paris is the capital of England.
3) Crucian carp is not a fish.
4) The number 6 is divisible by 2 and 3.
5) If a young man has graduated from high school, he receives a matriculation certificate.
Statements 1), 4), 5) are true, and 2) and 3) are false.
Obviously, the sentence “Long live our athletes!” is not a statement.
A statement that is one statement is usually called simple or elementary. Examples of elementary statements are statements 1) and 2).
Statements that are obtained from elementary ones with the help of grammatical connectives “not”, “and”, “or”, “if ..., then ...”, “then and only then” are usually called complex or compound. Thus, statement 3) is obtained from the simple statement “Crucian carp is a fish” using the negation “not”, statement 4) is formed from elementary statements “The number 6 is divided by 2”, “The number 6 is divided by 3”, connected by the conjunction “and”. Statement 5) is obtained from simple statements “The young man graduated from high school”, “The young man receives a matriculation certificate” using the grammatical connective “if ...,
That …". Similarly, complex statements can be derived from simple statements using the grammatical connectives “or”, “then and only then”.
In the algebra of logic, all statements are considered only from the point of view of their logical meaning, and their everyday content is abstracted. It is believed that every statement is either true or false and no statement can be both true and false.
In what follows we will denote elementary statements by letters of the Latin alphabet: a,b,c,…,x,y,z,…; the true value is indicated by the letter I or the number 1, and the false value is indicated by the letter L or the number 0.
If the statement A true, then we will write a=1, if false, then a=0.
Logical statements are usually divided into two types: elementary logical statements and compound logical statements.
Compound logical statement is a statement formed from other statements using logical connectives.
Logical connective is any logical operation on a statement. For example, words and phrases used in ordinary speech “not”, “and”, “or”, “if... then”, “then and only then” are logical connectives.
Elementary logical statements- these are statements that are not related to compounds.
Examples: “Ivanov is a football player” - elementary logical statements. “Ivanov is a football player and a chess player” is a compound logical statement consisting of two elementary statements connected to each other using the connective “and”.
46. Elements of algebra of logic
Algebra of logic is a section of mathematical logic, the values of all elements (functions and arguments) of which are defined in a two-element set: 0 and 1. Algebra of logic operates with logical statements.
Statement – it is any proposition about which there is a meaningful statement about its truth or falsity. In this case, it is believed that a statement satisfies the law of excluded middle, that is, every statement is either true or false and cannot be both true and false at the same time.
Sayings:
– “It’s snowing now” - this statement can be true or false;
– “Washington is the capital of the United States” is a true statement;
– “The quotient of 10 divided by 2 is 3” – false statement.
In the algebra of logic, all statements are denoted by letters a, b, c it. e. The content of statements is taken into account only when their letter designations are introduced, and in the future any actions provided for by this algebra can be performed on them. Moreover, if some operations allowed in the algebra of logic are performed on the initial elements of the algebra, then the results of the operations will also be elements of this algebra.
The simplest operations in the algebra of logic are the operations logical addition(aka: operation OR(OR), disjunction operation) And logical multiplication(aka: operation AND (AND),conjunction operation). To denote the operation of logical addition, the symbols + or V are used, and the symbols or logical multiplication are used. The rules for performing operations in the algebra of logic are determined by a number of axioms, theorems and corollaries. In particular, the following laws apply to the algebra of logic:
1. Conjunctive:
47. (a + b) + c = a +(b + c),
48. (A b) with= A(b With).
2. Traveling:
49. (a + b) = (b + a),
50. (A b)= (b a).
3. Distribution:
51. a (b + c) = a b + (a With),
52. (a + b) c = a c + b c.
The following relations are valid, in particular:
53. a + a = aa + b = b, If a ≤ b,
54. a a = aa b= A, If a ≤ b,
a + a b = aa b = b, If A≥ b,
a + b = a, If A≥ b.
The smallest element of the algebra of logic is 0, the largest element is 1. Another operation is also introduced in the algebra of logic - denial(operation NOT (NOT), inversion), indicated by a line above the element.
A-priory
A function in the algebra of logic is an expression containing elements of the algebra of logic a, b, c and others related by operations defined in this algebra. Examples of logical functions:
etc. These relationships are used to synthesize logical functions and computational circuits.
Aphorism - what is it? Each of us has heard this word, but not everyone can explain what its meaning is. Every day we come across aphorisms in literature, cinema and in everyday life; we use them in speech without even realizing it. Therefore, it is necessary to understand the meaning of this concept.
What are aphorisms?
Aphorisms are catchphrases, stable phrases said by someone, most often invented by poets or writers. These are the statements that have become popular among the population and are often used as a single lexical whole, without separating individual words. An example of an aphorism is the expression of M. Zhvanetsky: “It is difficult to enter history, but it is easy to get into trouble.”
Origin of the term "aphorism"
The term "aphorism" comes from a Greek word that translates as "definition." Indeed, this is a definition of one or another action, deed, feeling, event, dressed in a literary statement.
An aphorism is an original thought that is characterized by logical completeness. Such expressions are easy to remember, due to their clarity and conciseness, and are repeated many times by people. Often an aphorism consists of 3-5 words, but there are also more detailed statements.
An example of a short aphorism is the popular expression of Francis Bacon: “Knowledge is power.” It explains as accurately as possible the importance and significance of knowledge in the life of mankind.
Where do aphorisms come from?
Often aphorisms penetrate our speech from art: literature, cinema, theater. Most of these expressions have their own author. Many aphorisms were invented by writers, poets, screenwriters, actors, philosophers and thinkers.
Famous world "creators" of aphorisms are the medieval philosopher from Tibet Sakya Pandita, writers Shota Rustaveli, Juan Manuel Francois de La Rochefoucauld, Mikhail Turovsky, Bernard Shaw.
Among these famous people is rightfully the theater and film artist Faina Ranevskaya, whose caustic and sharp statements, laconic judgments, and apt phrases have earned nationwide love and fame. They are constantly quoted even by those who are completely unfamiliar with the work of Faina Georgievna. Examples of aphorisms belonging to this wonderful actress: “If a patient really wants to live, doctors are powerless,” “The companion of fame is loneliness,” “Women are not the weaker sex. The weaker sex are rotten boards.”
It is no coincidence that they say that aphorisms are the wisdom of the people. Many of them happened spontaneously: someone uttered a sharp and apt phrase, another repeated it, and so on along the chain until the expression was transformed into an aphorism. Examples of aphorisms that originated in this way: “When leaving, turn off the light,” “For nothing - behind the barn.”
Examples of aphorisms in literature
What is a literary aphorism? Very often people confuse aphorisms and quotes. Indeed, these two concepts are very similar. And often a quotation can be an aphorism, and an aphorism can be an excerpt from a work, that is, a quotation. It should be remembered that quoting is a verbatim repetition of an excerpt from a literary work or, for example, a movie. That is, a quote is a phrase that is a verbatim excerpt from the text without any changes. An aphorism is a laconic and complete thought, a phrase that most accurately and aptly defines the content of the statement.
Aphorisms are widely used in Russian and foreign classics. Aphorisms themselves are a small form of literary art. Many of them originated in literary works.
For example, the title of A. S. Griboyedov’s novel “Woe from Wit” is itself an aphorism. And the expression “Happy people don’t watch the clock” was first used by the classic in the same novel. The most famous aphorism “We are responsible for those we have tamed” was born in the work of Antoine de Saint-Exupery “The Little Prince”.
Another example of an aphorism is a phrase that is often used in everyday conversation: “Getting married means not going to the bathhouse.” It belongs to the pen of N.V. Gogol.
A.P. Chekhov owns the famous aphorism “Brevity is the sister of talent.” It is precisely such laconic and apt statements that describe the essence of what is happening as accurately as possible, express a complete thought and pass into the category of aphorisms.
Examples of aphorisms from Krylov's fables
The ironic fables of Ivan Andreevich Krylov are rich in aphorisms. Each of his works contains not only deep meaning and morality, but also many apt sayings that we use in everyday life.
Examples of aphorisms from I. A. Krylov’s fables (the most famous):
- And the casket simply opened (the fable “The Casket”). An expression that means that the solution to a problem was much simpler than it seemed at first glance.
- Your snout is covered in fluff (fable "The Fox and the Marmot"). This aphorism means that a person has done a bad thing.
- And Vaska listens and eats (fable "The Cat and the Cook"). This aphorism means that a person listens, but does not perceive information, does not draw conclusions.
- Don't spit in the well (fable "The Lion and the Mouse").
- The jumping Dragonfly sang red summer.
It is impossible to imagine the speech of a modern person without aphorisms. When communicating with friends, colleagues, and family, we very often, without noticing it ourselves, pronounce well-known and stable phrases, and they make our speech brighter, richer and more interesting.
